Optical transducers: Optical molecular sensing and spectroscopy

CHAPTER

Optical transducers: Optical molecular sensing and spectroscopy

5

CHAPTER OUTLINE 5.1 Introduction ....................................................................................................232 5.2 Basic EM Theory .............................................................................................232 5.2.1 Maxwell’s Equations ......................................................................234 5.2.2 Wave Equation ..............................................................................235 5.2.3 Phasor Notation .............................................................................237 5.2.4 Interference ..................................................................................238 5.2.5 Polarization, Incidence, and Reflection of Light ................................239 5.2.6 Evanescent Field ...........................................................................242 5.3 Waveguide-Based Molecular Sensors ...............................................................244 5.3.1 Introduction ..................................................................................259 5.3.2 Principles of Wave Propagation in Waveguides .................................246 5.3.3 Slab Waveguide .............................................................................250 5.3.4 Rectangular Waveguide (Channel Waveguides) .................................253 5.3.5 Circular Waveguide (Optical Fibers) .................................................255 5.3.6 Discussion on Waveguide Sensors ...................................................259 5.4 Surface Plasmon Resonance Sensors ...............................................................259 5.4.1 Introduction ..................................................................................259 5.4.2 Principles of Surface Plasmons .......................................................259 5.4.3 Experimental Configuration ............................................................263 5.4.4 SPR Sensor for Molecular Sensing ..................................................264 5.4.5 Recent Advancement in SPR Sensors ..............................................268 5.4.6 Discussion on SPR Sensors ............................................................270 5.5 Absorption Spectroscopy .................................................................................271 5.5.1 Optical Density Measurement .........................................................271 5.5.2 Beer-Lambert Law .........................................................................271 5.5.3 Sensors Based on Absorption Spectroscopy ......................................273 5.6 Fluorescence Spectroscopy .............................................................................275 5.6.1 Basics of Fluorescence ...................................................................275 5.6.2 Fluorescence Spectroscopy and Imaging ..........................................279 5.7 Light Scattering ..............................................................................................282 5.7.1 Forms of Light Scattering ...............................................................282 5.7.2 Methods Based on Light Scattering Measurements ...........................283 5.8 Near-Field Scanning Optical Microscopy ..........................................................293

Molecular Sensors and Nanodevices. https://doi.org/10.1016/B978-0-12-814862-4.00005-3 # 2019 Elsevier Inc. All rights reserved.

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5.8.1 Aperture-Based NSOM Tip ..............................................................294 5.8.2 Metal Plasmonic Tip ......................................................................295 5.8.3 Functional NSOM Tip .....................................................................296 Problems ...............................................................................................................297 References ............................................................................................................305

5.1 INTRODUCTION Optics is a vital part of science and forms the basis of numerous technologies from imaging and spectroscopy to light-based manipulation and manufacturing in life sciences, chemistry, physics, and engineering. More than 50 Nobel Laureates have contributed to optics research, advancing studies on key technologies including Raman scattering (awarded in 1930), laser (1950), fluorescent proteins (2008), optical fibers (2009), the charge coupled device (CCD) (2009), and the blue light emitting diode (LED) (2014). The advantages of optical transducers include lack of direct contact, high spatial resolution, and relatively easy detection. In optical waveguides, there are several high contrast modes available for light transmission, sensing, and imaging. Disadvantages include the need for the optical transducers to be transparent at the wavelength used for sensing, the use of labels, interferences, and issues arising from fluorophore decay in fluorescence imaging. In this chapter, we shall describe molecular sensors based on optical transduction. Fig. 5.1 summarizes the optical phenomena and related sensing methods we describe in this book. Lights interact with molecules in various ways, which are observed as transmission, scattering, fluorescence, etc. We explain principles of optics used for molecular sensing and describe the instrumentation for optical measurements. The chapter starts with the introduction of the basic electromagnetic theory, followed by discussions on waveguides and sensors based on waveguide structures, and surface plasmon resonance-based (SPR) sensors. Lastly, optical spectroscopy techniques, theories, and practices of optical absorption, scattering, and fluorescence are described.

5.2 BASIC EM THEORY Light is a form of an electromagnetic wave that consists of oscillating electric and magnetic fields. Fig. 5.2 illustrates the wavelength and frequency range of visible and invisible light along with those of other types of electromagnetic waves. The wavelength of visible light ranges from about 400 to 650 nm, which defines several critical dimensions in optical sensing techniques. The electric and magnetic fields of propagating light are perpendicular to each other and to the direction of propagation. Such fields are oscillating harmonically in temporal and spatial domains. Two electromagnetic waves can interfere, which leads an interference term that contains a cosine of the phase difference that can

5.2 Basic EM theory

Scattering • Raman spectroscopy • Static light scattering • Dynamic light scattering • Dark field microscopy

Scattering

Excitation

Absorption Thermal/vibrational excitation

Transmission • Absorption spectroscopy • Bright field microscopy

Surface plasmon resonance excitation at metal/air interface

Absorption Electronic excitation of fluorescence molecule

• Raman scattering • Mie scattering • Rayleigh scattering

Fluorescence • Fluorescence spectroscopy • Fluorescence microscopy

Scattering

FIG. 5.1 Interaction of lights with molecules. Frequency (Hz) 1024

1022

1020

1018

1016

Wavelength (m) 10–16 10–14 10–12 10–10 10–8 γ-rays

X-rays

1014

1012

10–6

UV

10–4 IR

1010 10–2 Microwave

Visible

UV

Violet

400

Blue

450

100

106 102

Radio waves FM

Green

500

108

Yellow Orange Red

550

600

104 104

102 106

100 108

Long radio waves

FM

IR

650

Wavelength (nm)

FIG. 5.2 Light as an electromagnetic wave.

be positive or negative. If an electromagnetic wave hits an interface to another medium, boundary conditions have to be fulfilled for the parallel and normal components. The surface defines a plane of incidence that contains the surface normal and the incoming beam. The electric and magnetic fields can be decomposed into separate polarization components parallel and perpendicular to the plane of

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incidence: p- and s-polarization or transverse-magnetic (TM) and transverse-electric (TE) polarization. The two polarizations behave differently at the interface. Only p or TM polarization can show a Brewster angle or can excite surface plasmons, since it is the only polarization with a field normal to the surface. Boundary conditions produce Snell’s law, Fresnel coefficients for the reflectivity, and the evanescent field. The behavior of light as an electromagnetic wave is governed by Maxwell’s equations. We start from these equations to find the wave equation of propagating light, followed by a description of important principles that constitute the fundamentals of optical sensing.

5.2.1 MAXWELL’S EQUATIONS The following equations are the differential form of Maxwell’s equations: rE¼

∂B ðFaraday’s lawÞ ∂t

rH¼J+

∂D ðAmpere’s lawÞ ∂t

(5.1)

(5.2)

r  D ¼ ρv ðGauss’s lawsÞ

(5.3)

r  B ¼ 0 ðGauss’s lawsÞ

(5.4)

where E is the electric field, H is the magnetic field, D is the electric flux density, B is the magnetic flux density, J is the electric current density (current per unit area), and ρv is the electric charge density (charge per unit volume). Faraday’s law described in Eq. (5.1) states that the change in magnetic flux density produces a voltage, the application of which can be seen in devices such as power transformers. Ampere’s law described in Eq. (5.2) states that the flow of current in a given axis z produces a magnetic field orthogonal to the current, i.e., in an xy plane as demonstrated by the righthand rule. Gauss’s law described in Eq. (5.3) states that the net electric flux through a closed surface is proportional to the electric charge density inside that surface. Gauss’s law describing magnetic flux in Eq. (5.4) states that particles always have a dipole as the divergence of B is equal to zero. As such, magnetic particles, no matter how small, will always have a magnetic dipole. The following equations show the conservative relation between the flux densities and the fields: D ¼ ε0 E + P ¼ εE

(5.5)

B ¼ μ0 H + μ0 M ¼ μH

(5.6)

where P is the electric polarization, M is the magnetization, ε is the permittivity, and μ is the permeability.

5.2 Basic EM theory

The following boundary conditions are applied for source-free media where ρv ¼ 0 and J ¼ 0. Ek is continuous : S  ðE2  E1 Þ ¼ 0

(5.7)

Hk is continuous : S  ðH2  H1 Þ ¼ 0

(5.8)

D? is continuous : S  ðD2  D1 Þ ¼ 0

(5.9)

B? is continuous : S  ðB2  B1 Þ ¼ 0

(5.10)

Here, S is the normal unit vector to the boundary surface, Ak and A? are tangential and normal components, respectively, of a field A at the boundary, A1 and A2 are field A in media 1 and 2, respectively, at the boundary (A ¼ E, H, D, B). These boundary conditions are significant in molecular sensor development as they determine the interface between different materials that exhibit different electrical and magnetic properties such as reflection and refraction at air medium interfaces. The air and metal interfaces discussed in the production of surface plasmon waves are also governed by these boundary conditions.

5.2.2 WAVE EQUATION To derive the wave equation from the Maxwell’s equations, we take the curls of both sides of Faraday’s law.
 ∂B r  ðr  EÞ ¼ r   ∂t

(5.11)

For the left-hand side of Eq. (5.11), we use the vector identity r  r  A ¼ r (r  A)  (r  r)A, which is true for any vector A, and an assumption that the divergence of the electric field is zero, namely r  E ¼ 0. r  r  E ¼ rðr  EÞ  ðr  rÞE ¼ r2 E

(5.12)

For the right-hand side of Eq. (5.11), the curl operation and the differentiation operation can be switched since both operations are continuous and linear.
 ∂B ∂ r  ¼  ðr  B Þ ∂t ∂t

(5.13)

If the light propagates nonconducting media, J is zero. From Eqs. (5.2), (5.5), (5.6), and J ¼ 0, we derive: r  B ¼ με

∂E ∂t

(5.14)

Plugging Eq. (5.14) into Eq. (5.13):



 ∂B ∂ ∂ ∂E ∂2 E r  ¼  ðr  B Þ ¼  με ¼ με 2 ∂t ∂t ∂t ∂t ∂t

(5.15)

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Plugging Eqs. (5.12), (5.15) into Eq. (5.11), we obtain: r2 E  με

∂2 E ¼0 ∂t2

(5.16)

Eq. (5.16) is called the electric field wave equation. Following the same procedure from Ampere’s law: r2 B  με

∂2 B ¼0 ∂t2

(5.17)

Eq. (5.17) is called the magnetic field wave equation. Eq. (5.16) has a solution known as a plane wave: Eðr, tÞ ¼ E0 ejðωt + φk  rÞ

(5.18)

j()

When we use e to express the phase of a wave, we only consider the real part of it. More specifically, we may use another form in sinusoidal expression: Eðr, tÞ ¼ E0 cos ðωt + φ  k  rÞ

(5.19)

where r is a position vector, t is time, E0 is a vector perpendicular to the propagation, and k is a vector with the direction of the propagation. The vector k is called the wave vector, and the magnitude of the wave vector is given as: jk j ¼

2π n λ

(5.20)

where λ and n are the wavelength and the refractive index, respectively. It should be noted that plane waves are just one form of solution to the wave equations, and there are many other possible solutions that describe different forms of light wave propagation. Here, we use a coordinate system where the direction of E0 is chosen as that of x-axis and direction of k is chosen as that of z-axis. In this case:
 2πn Ex ðz, tÞ ¼ E0 exp j ωt + φ  z λ

(5.21)

In Eq. (5.21), we consider the magnitude of vector E0. Both Ex and E0 are scalers. In this book, vectors are shown with a bold character, and scalars are italic. Another important thing to note is that the left-hand side of Eq. (5.21) is a real number. We only consider the real part of the right-hand side. Eq. (5.21) may help us better understand the meaning of each term in Eq. (5.18). Furthermore, plugging Eq. (5.21) into (5.1), we find that B is in the direction of the y-axis.
 2πn pffiffiffiffiffiffiffiffiffiffiffiffi By ¼ ε0  μ0  E0 expj ωt + φ  z λ

(5.22)

We can rewrite Eq. (5.22) in a simplified form:


 2πn By ¼ B0 exp j ωt + φ  z λ

(5.23)

5.2 Basic EM theory

x

B

E k

y

z

FIG. 5.3 Plane wave.

where

pffiffiffiffiffiffiffiffiffiffiffiffi B0 ¼ ε0  μ0  E0

(5.24)

The relationship between E and B in a plane wave is illustrated in Fig. 5.3. We now find the important fact that the electric and magnetic fields of a plane wave are perpendicular to each other and to the direction of propagation. The wave vector can be redefined using the directions of E and B: k¼

2π EB n λ jE  Bj

(5.25)

5.2.3 PHASOR NOTATION When the time variation of a field is sinusoidal, the field is called a time-harmonic field. Plane waves are an example of a time-harmonic field. For a time-harmonic field, we can consider the space term and the time term separately. For the case of the harmonic plane wave in Eq. (5.18), it can be rewritten as: Eðr, tÞ ¼ EðrÞ  ejðωt + φÞ

(5.26)

where E(r) is the space term given as: EðrÞ ¼ E0 ej k  r

(5.27)

The term E(r) in Eq. (5.26) is called the phasor. It is a vector, each component of which has an amplitude and a phase. Eq. (5.26) is identical to Eq. (5.18) but is convenient to calculate higher-order differentiations and integrations than instantaneous expression.

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PLANE WAVE Wave equations are derived from Maxwell’s equations: r2 E  με ∂∂tE2 ¼ 0 2

r2 B  με ∂∂tB2 ¼ 0 A plane wave is one of the solutions to wave equations: E(r, t) ¼ E0e j(ωt+φkr) The direction of the propagation is given by the wave vector k: k ¼ 2πλ  n  jEB EBj When the direction  of x and y-axes  are chosen as those of E and B, respectively: Ex ðz, tÞ ¼ E0 expjωt + φ  2πn λ  z By ðz, tÞ ¼ B0 expj ωt + φ  2πn λ z 2

5.2.4 INTERFERENCE The electric field of a plane electromagnetic traveling wave is given as: E ¼ E0 ej ðω t + φk  rÞ

(5.28)

Let us consider multiple waves that are present at one place at the same time with the same wavelength and frequency. E j ¼ E 0  e j ðω t + α j Þ

(5.29)

where αj ¼ k  rj + ϕj and especially rj represents the directed distance from the reference plane at which the phase is ϕj at t ¼ 0. The summation of two waves will lead to interference. For example, if there are E01 ¼ E01ei(ωt+α1) and E02 ¼ E02ei(ωt+α2), the sum of two waves is: E1 + 2 ¼ E1 + 2 eiðωt + αÞ

(5.30)

where the resulting amplitude is: E1 + 2 ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi E201 + E202 + 2E01 E02 cos ðα2  α1 Þ

(5.31)

In addition, the resulting phase is: tan ðαÞ ¼

E01 sin ðα1 Þ + E02 sin ðα2 Þ E01 cos ðα1 Þ + E02 cos ðα2 Þ

(5.32)

Both equations above are derived from the cosine law, as shown in Fig. 5.4. There are two extreme cases of the interference which depend on the phase difference δ ¼ α1  α2: Destructive interference: δ equals an integer multiple of 2π. Constructive interference: δ equals π plus an integer multiple of 2π.

5.2 Basic EM theory

E1+2

a

E02 sin(a2)

E02

a2

E01 a1

E01 sin(a1)

E01 cos(a1)

E02 cos(a2)

FIG. 5.4 Summation of two vectors.

5.2.5 POLARIZATION, INCIDENCE, AND REFLECTION OF LIGHT For reflection of light, the surface and the incoming beam define the plane of incidence. The incoming beam and the surface normal are in the plane of incidence. The angle of incidence α is defined as the angle between the incoming beam and the surface normal. The reflected beam is also in the plane of incidence. As we shall explain later, the angle of reflection γ equals the angle of incidence α (Fig. 5.5).

TM and TE modes The electric field can be separated into two projections: one is parallel to the plane of incidence and defined as Ep or ETM, and the other is perpendicular to the plane of incidence and defined as Es or ETE. The electric field at the surface can also be separated into two projections: one parallel to the surface plane Ek, and one perpendicular to the surface plane E?. Only the p-component has a field component perpendicular to the surface plane (Fig. 5.6). With the introduction of an interface, a specific coordinate system is created. (Note that this is different from the coordinate system used in Fig. 5.3.) • • • •

The plane of incidence is defined by the incoming beam and the surface normal. The plane of incidence defines the x-z plane. The z-axis is the surface normal. The x-axis is on the surface.

b n1 n0

ki a

FIG. 5.5 Boundary conditions.

g

kt

kr

239

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CHAPTER 5 Optical transducers

y Es|| Ep||

Es, ETE a E p z

x

Ep

Ep, ETM y

x

z

FIG. 5.6 Incident and reflected light.

•

The y-axis is on the surface and perpendicular to the plane of incidence.

The electric field components are separated into components parallel p (or TM) and perpendicular s (or TE) to the plane of incidence: • •

The s (or TE) component is completely in the plane of the surface (i.e., parallel to the y-axis). The p (or TM) component has a component perpendicular to the surface plane (i.e., parallel to the z-axis) and a component parallel to the surface (i.e., parallel to x-axis).

We define wave vectors ki, kt, and kr for each of incident, transmitted, and reflected light, respectively. The magnitudes of the vectors are: ω 2π jki j ¼ n0 ¼ n0 c λ

(5.33)

ω 2π jkt j ¼ n1 ¼ n1 c λ

(5.34)

ω 2π jkr j ¼ n0 ¼ n0 c λ

(5.35)

We need to consider the boundary conditions at the surface between two media. Boundary condition for the fields: E0k ¼ E1k

(5.36)

5.2 Basic EM theory

When there is no surface charge, the boundary condition for the electric flux density becomes: ε0 E0? ¼ ε1 E1?

(5.37)

Boundary conditions for magnetic field and magnetic flux density are: H0k ¼ H1k

(5.38)

B0? ¼ B1?

(5.39)

As consequences of the boundary conditions: e j ð ωi

tki  rÞ

¼ ej ðωr

tkr  rÞ

¼ e j ð ωt

tkt  rÞ

(5.40)

All the angular frequencies must be the same: ωi ¼ ωt ¼ ωr

(5.41)

All the wave vectors must be in one plane: ðki  rÞz¼0 ¼ ðkr  rÞz¼0 ¼ ðkt  rÞz¼0

(5.42)

Total internal reflection and Snell’s law From the first part of Eq. (5.42), we find the law of reflection: sinα ¼ sinγ

(5.43)

α¼γ

(5.44)

or From the other part of Eq. (5.42), we find Snell’s law, which is expressed as: n0 sinα ¼ n1 sin β

(5.45)

where α is the incident angle and β is the transmission angle. The incident angle α is smaller than the transmission angle β if the wave is incident on medium 1 from medium 0, which has a larger refractive index than medium 1 (n0 > n1). In this situation, the transmission angle β increases with α until it reaches at π/2. When β is equal to π/2, the transmission wave propagates along the interface. The additional increase of α will result in no refracted transmission wave, and the incident light is totally reflected. The value of the total internal reflection angle, or critical angle αc, can be found by substituting the transmitted angle β ¼ π/2 in Snell’s law. Now the angle of total reflection is: sinαc ¼

n1 sinβ n0

(5.46)

where αc is called the critical angle.

Fresnel equations Solving the boundary condition of Eqs. (5.36), (5.38), we find Fresnel equations.

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rTE ¼


 E0r n0 cos ðαÞ  n1 cos ðβÞ ¼ E0i TE n0 cos ðαÞ + n1 cos ðβÞ

(5.47)

tTE ¼


 E0t 2n0 cos ðαÞ ¼ E0i TE n0 cos ðαÞ + n1 cos ðβÞ

(5.48)

rTM ¼


 E0t n1 cos ðαÞ  n0 cos ðβÞ ¼ E0i TM n0 cos ðβÞ + n1 cos ðαÞ

(5.49)




E0r tTM ¼ E0i

 ¼ TM

2n0 cos ðαÞ n0 cos ðβÞ + n1 cos ðαÞ

(5.50)

The other conditions (5.37), (5.39) are automatically satisfied.

Brewster’s angle There is an angle αB of incidence at which only the component normal to the incident plane (i.e., parallel to the surface) will be reflected. The component polarized parallel to the incident plane (Ep or ETM) will not be reflected at αB. Such an angle is called Brewster’s angle. The condition for this angle is:   rTM ¼ rp ¼ 0

(5.51)

When unpolarized light is incident at this angle, the light that is reflected from the surface is therefore perfectly polarized. tan αB ¼

n1 n0

(5.52)

5.2.6 EVANESCENT FIELD Consider a case of total internal reflection, with the interface between two different media with refractive indexes of n0 and n1 (n0 > n1). When the incident angle α is larger than the critical angle αc, there will be no refracted waves transmitted through the horizontal interface for the impinging light. However, the mathematical description on such total internal reflection implies the fact that there will be evanescent waves formed at its interface. An evanescent wave is a confined electromagnetic wave exhibiting exponential decay with distance from the interface. The properties of an evanescent wave can be derived from Snell’s law. With the total internal reflection condition (n0 > n1 and α > αc), Snell’s law can be rewritten as: sinβ ¼

n0 sinα > 1 n1

(5.53)

There is no solution for real-valued β satisfying Eq. (5.42), and cos β becomes imaginary under given total internal reflection condition.

5.2 Basic EM theory

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n0 2 2 cos β ¼ 1  sin β ¼ j sin 2 α  1, ð sin β > 1Þ n1 2

(5.54)

Let us assume the unit vector akt, which indicates the direction of propagation of a refracted wave: akt ¼ ax sinβ + az cos β

(5.55)

  k  r ¼ kt ðax sinβ + az cos βÞ  ax x + ay y + az z ¼ kt ðxsin β + zcos βÞ

(5.56)

then k  r becomes:

We can now substitute it into the phasor expression of the electric field: Et ¼ Et0 ejk  r ¼ Et0 ejðkt x sinβ + kt z cos βÞ

(5.57)

The incident angle term can be substituted for the transmission angle term using Eqs. (5.53), (5.54): 

n j kt x n0 sinα



qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

kt z

n0 2

2 sin

2

α1

n1 1 Et ¼ Et0  e e |fflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflffl} traveling wave

(5.58)

exponential decay

Although Eq. (5.54) gives two solutions for cos β, the one that gives the positive sign in the exponent part of Et is neglected in order to hold physical causality, since it results in the electric field becoming infinitely large as z increases. Eq. (5.58) demonstrates the evanescent wave along the interface. The first exponential term shows the wave propagates along the interface, which is x-direction in this case, while the second exponential term indicates the exponential attenuation normal to the interface in medium 1 (Fig. 5.7). Note that on average, no electromagnetic energy can be transmitted to medium 1, since the reflectivity on the interface becomes unity for the total internal reflection condition. rTE ¼


 E0r n0 cos ðαÞ  n1 cos ðβÞ ¼ E0i TE n0 cos ðαÞ + n1 cos ðβÞ

(5.59)

rTM ¼


 E0t n1 cos ðαÞ  n0 cos ðβÞ ¼ E0i TM n0 cos ðβÞ + n1 cos ðαÞ

(5.60)

∗ ¼1 RTE ¼ jrTE j2 ¼ rTE  rTM

(5.61)

∗ ¼1 RTM ¼ jrTM j2 ¼ rTM  rTM

(5.62)

The decay length is the reciprocal of the exponential attenuation term. Using kt ¼ 2πn1/λ: 1 λ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi L ¼ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ 2 2 n0 n0 kt sin 2 α  1 2πn1 sin 2 α  1 n1 2 n1 2

(5.63)

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CHAPTER 5 Optical transducers

(A)

(B) FIG. 5.7 Evanescent field induced by total internal reflection: (A) wave vector with imaginary component; (B) exponential decay in z-direction.

For further reading: • Principles of Optics, M. Born and E. Wolf, Cambridge University Press. • Optics 5th edition, Hecht, Pearson Higher Education. • Fundamentals of Engineering Electromagnetics, David K. Cheng, Pearson Higher Education. • Advanced Engineering Electromagnetics, Constantine A. Balanis, John Wiley & Sons. • Evanescent Waves: From Newtonian Optics to Atomic Optics, Frederique de Fornel, Springer-Verlag.

5.3 WAVEGUIDE-BASED MOLECULAR SENSORS Optical principles and measurement techniques are very well established and are valuable for designing molecular sensors. In particular, essential techniques such as transmitting light over multiscale distances and various medium, establishing secure communications, and fabricating miniaturized optical and optoelectronic devices are all based on an understanding of guided-wave optics.

5.3 Waveguide-based molecular sensors

Described in this section is a class of optical molecular sensors based on light waveguides. The main benefit of waveguides is fairly obvious; they are designed to guide or confine lights. With waveguides, large-scale optical experiments or measurements may be assembled into a compact, usable configuration. Several components such as microfluidic channels, light sources, and detectors may be readily integrated with measurement systems. We shall first describe the fundamentals of waveguide design and theories of guided modes; this will be followed by the introduction of applications in molecular sensing.

5.3.1 INTRODUCTION Structures of waveguides commonly used for sensing applications are summarized in Fig. 5.8. We categorize optical waveguides into the following three types [1]: (1)

Slab waveguide. Slab waveguides are a waveguide with a planar geometry. They are also called planer waveguides. They are often fabricated with a thin transparent film on a substrate with an increased refractive index that can guide light waves by total internal reflection. The top surface is usually used as the sensing site. The advantages of planer structure include easier fabrication and a larger sensing site.

FIG. 5.8 Basic waveguide structures: (A) slab waveguide; (B) rectangular (channel) waveguide; and (C) circular waveguide (optical fiber). Adapted from W. Knoll, Interfaces and thin films as seen by bound electromagnetic waves, Annu. Rev. Phys. Chem. 49 (1998) 569–638.

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CHAPTER 5 Optical transducers

(2)

(3)

Rectangular waveguide. Rectangular waveguides are waveguides with a rectangular cross-section, and are also called strip waveguides, or channel waveguides. One type of waveguide is etched out of a substrate, and other types are buried in an etched groove. They are often used for measurements that utilize interferometry or optical resonation, where the path lengths have to be strictly confined to control interference. Circular waveguide (optical fibers). Circular waveguides, commonly referred to as optical fibers, are the most common form of light waveguide used for optical communication. The advantage of optical fibers for sensing applications is the capability to be used as a probe. Typically, one end of a fiber is used as a sensing site. Fiber tips can be brought into the sensing sites of in situ or in vivo measuring applications.

5.3.2 PRINCIPLES OF WAVE PROPAGATION IN WAVEGUIDES The most fundamental principle behind guided light waves is the total internal reflection, where light is confined in a medium with a higher refractive index. As shown in Fig. 5.9, when the incident angle θ0 is larger than the critical angle θc (see Section 5.2.5 for theoretical discussion), the light propagates inside the medium. Especially when the dimensions of a waveguide is relatively larger compared to the wavelength of light, this basic consideration based on geometrical optics provides sufficient information to describe the optical properties of several designs of waveguides.

Waveguide modes In order to design an efficient waveguide, we need to focus on the characteristics of propagating light as an electromagnetic wave, which is described by Maxwell’s equations, or more specifically, electromagnetic wave equations. Here we use the slab waveguide as a simplified model of a waveguide. It usually consists of a thin film with a high refractive index that works as the wave-guiding layer (Fig. 5.10). For rectangular and circular waveguides, different coordinate systems or boundary conditions may need to be introduced. However, they still share most of the fundamental principles with slab waveguides. (2) q0 > qc

(1) q0 < qc q1

n1 n0

q0

FIG. 5.9 Total internal reflection.

q0

5.3 Waveguide-based molecular sensors

FIG. 5.10 Basic planar waveguide structure.

Depending on the propagation angle, wavelength, polarization, refractive indices, and the waveguide thickness, some waves are well confined in waveguides, them allowed to propagate. An important concept in guided-wave optics is “modes,” which are determined as solutions, or eigensolutions, to the wave equations for a specific wavelength and polarization with the boundary conditions given by the properties of the materials and interfaces. The modes are given as particular standing wave patterns of transverse distribution that are maintained at all the distances along the waveguide axis. In concept, they are very similar to finding a solution of vibrational modes of a mechanical cantilever (see Chapter 6, Section 6.3.5). Transverse modes are found for both TE- and TM-guided waves. The total electromagnetic field can be a combination of multiple modes. A simple case of finding propagation modes is described in Problem 5.9. Fig. 5.11 illustrates modes in a slab waveguide [1a]. The air, film, and substrate have refractive indices of n1, n2, and n3, respectively. Index n2 has to be larger than n1 and n3 for total internal reflection to happen. A guided wave is represented by a zigzag wave, as shown in Fig. 5.11A. The mode number is related to the number of m=0

m=1 Air

n1

Film

n2

m=2

Substrate n3

(A)

m=3

m=4

(B) FIG. 5.11 Waveguide modes: (A) simplified structure of a slab waveguide; (B) mode number is related to the number of waves. Adapted from P. Tien, Integrated optics and new wave phenomena in optical waveguides, Rev. Mod. Phys. 49 (2) (1977) 361.

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waves, as shown in Fig. 5.11B. For m ¼ 0 mode, it has the largest incident angle; as m increases, the incident angle nears the critical angle.

Light coupling The wavenumber of a guided wave along the direction of propagation is called the propagation constant. The propagation constant of a waveguide is typically larger than the wavenumber of light that propagates in vacuum or air. In order to couple light from free space into a waveguide, techniques to match wavenumbers needs to be introduced. Light coupling is essentially a process of matching wave numbers of two different media. There are mainly three ways to couple light to a planar waveguide [1]: gratings, prism, and end-fire coupling, as shown in Fig. 5.12. (a) (b)

Gratings fabricated on the top surface will add a grating vector to the light wave, and can therefore match the wavevectors in the waveguide. Optical power may be coupled into or out of a planar waveguide by use of a prism. A prism with a higher refractive index comparing to air is placed close to the waveguide surface with a thin air gap (500–1000 nm) in between. An optical wave is incident into the prism at an angle larger than the critical angle

Grating

(A) Prism

(B) End-fire

(C) FIG. 5.12 The three methods of light coupling. (A) Grating. (B) Prism. (C) End fire. Adapted from W. Knoll, Interfaces and thin films as seen by bound electromagnetic waves, Annu. Rev. Phys. Chem. 49 (1998) 569–638.

5.3 Waveguide-based molecular sensors

(c)

so that it undergoes total internal reflection within the prism. The transverse field distribution extends outside the prism and decays exponentially in the space separating the prism and the slab. If an appropriate interaction distance is selected, the wave is coupled to a mode of the slab waveguide. The operation can be reversed to make an output coupler, which extracts light from the slab waveguide into free space. Finally, light can be coupled into a waveguide by directly focusing it at one end. Such “end-fire coupling” requires collimation of the beam into the planar surface of the waveguide. For optical fibers, this is the most commonly used method for light coupling. Because of the small dimensions of the waveguide slab, focusing and alignment are usually difficult, and the coupling is not always efficient.

Let us take a closer look at light coupling with a prism. The energy from light in the prism excites the surface of the waveguide at the points 1, 2, 3, 4…, as shown in Fig. 5.13. The coupling becomes effective if the fields intensities at these points are in phase with a zigzag wave in the waveguide. This coupling condition is satisfied when the light path length from 200 to 20 in the prism equals to that from 1 to 2 in the waveguide. With geometrical consideration, the path lengths from 300 to 30 and from 400 to 40 equal to those from 1 to 3 and from 1 to 4, respectively. As a result, the amplitude of the zigzag wave in the coupling region increases roughly as the number of zigzags. Overall coupling efficiency of over 90% can be achieved with a welldesigned prism.

4″ 3″ 2″ 1″ 1′ 1

2′ 2

3′ 3

4′ 4

FIG. 5.13 Light coupling with a prism. The coupling becomes effective if the fields intensities at these points are in phase with a zigzag wave in the waveguide. Adapted from P. Tien, Integrated optics and new wave phenomena in optical waveguides, Rev. Mod. Phys. 49 (2) (1977) 361.

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5.3.3 SLAB WAVEGUIDE In the following three sections, we shall describe designs and fabrications of different types of waveguide structures, namely slab waveguide, rectangular waveguide, and circular waveguide, each of which is followed by introduction of applications in molecular sensing. We shall start with the most basic structure of waveguide: slab waveguide.

Implementation Slab waveguides take advantage of the large sensing site easily obtained on the top surface of the wave-guiding layer. They mostly utilize fluorescence excitation by an evanescent field induced on the surface. When light propagates within a slab waveguide, an evanescent field is generated at the surface (see Section 5.2.6 for theories). The evanescent field decays exponentially in the direction perpendicular to the waveguide surface. This characteristic can be used to probe specifically the surrounding medium by exciting only molecules near the waveguide surface. Fluorescence from the excited molecules is guided back and measured by a detector. Fig. 5.14 shows different configuration for: (1) coupling excitation light into the waveguide; (2) coupling fluorescence back into the waveguide; and (3) detection of the fluorescence signals [1b].

Applications Slab waveguide sensors can be specific to an analyte by functionalization of the waveguide surface. Some slab waveguide sensors have been utilized in bacterial sensing applications [1c, 2]. Other types of slab waveguide sensors have also been designed as immunosensors [3]. This device uses antibody-antigen binding to detect the presence of an antigen on the waveguide surface, which offers a highly specific detection method for many different pathogens. It has applications in a clinical setting for diagnosis of pathologies. Clerc et al. utilized an output grating coupler for direct immunosensing [3]. The sensor uses a He-Ne laser light with a wavelength of 633 nm, which is end fired into a waveguide from the output of the waveguide. The outcoupling angle is measured to find the change in the refractive index induced by the sensing event. The waveguide consists of a 150–180 nm dip-coated SiO2-TiO2 core guiding layer on top of a glass substrate. The core layer has a higher refractive index than the surrounding layers. A grating is embossed on the outer surface of the core. Light coupled out of the waveguide is detected by a position sensitive sensor, which detects the change of the outcoupling angle. The outcoupling angle change can be related to the change in effective index of the film surface [3]. In this sensor, the binding of an antigen to bound antibodies at the surface causes a change in the effective index at the surface. This can be used to detect antigen concentrations of less than one nanomolar. Antibodies are bound to the sensor surface by the intermediate avidin. Avidin is first adsorbed to the surface. Biotinylated IgG antibodies are then immobilized to avidin through avidin-biotin affinity binding. This is a very strong binding and ensures

5.3 Waveguide-based molecular sensors

Fluorophore Excitation Light source Fluorescence Imaging optics Detector

(A) Fluorophore

Detector Fluorescence Excitation Collimator

Light source

(B) Fluorescence

Detector

Light source

Fluorophore

Excitation

(C)

Light source

Excitation Fluorophore

Detector

Grating Fluorescence

(D) FIG. 5.14 Different configurations for slab waveguide molecular sensors. Adapted from E. Gizeli, C. Lowe, Biomolecular Sensors, Taylor and Francis, 2012, p. 161, 165.

strong contact with the surface. Therefore, the sensor can be used to sense very small concentrations of antigens. One disadvantage of this sensor is the drift effect. The refractive index of the surface gradually increases while the sensor is contacted with a solution. This effect can be reduced by certain drift correction methods described by Lukosz [3].

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Outlet

Inlet

SiON Channel 1

Channel 2

Channel 3

SiO2

Filtered CCD array FIG. 5.15 Multianalyte assay integrated on a silicon oxynitride waveguide. Adapted from T. Plowman, J. Durstchi, H. Wang, D. Christensen, J. Herron, W. Reichert, Multiple-analyte fluoroimmunoassay using an integrated optical waveguide sensor, Anal. Chem. 71 (1999) 4344–4352.

Plowman et al. developed a multiple analyte immunoassay using a silicon oxynitride integrated optical waveguide [4]. Fig. 5.15 shows a schematic of the multianalyte assay. Three capture antibodies were adsorbed to the surface in channels separated by areas of blocking protein. A rubber gasket with holes clamped on the waveguide was used to pattern antibody capture layers. They used a sandwich immunoassay format, where tracer antibodies (specific for one channel each) are introduced for fluorescence signals. Fluorescent labels on the tracer antibodies are excited by the evanescent field. Malti analyte assay responses for clinically significant ranges of creatin kinase MB (0.5–100 ng/mL), cardiac troponin I (0.5–100 ng/ mL), and myoglobin (5–500 ng/mL) were compared with responses from single analyte assay, and good agreement (R2 ¼ 0.97–0.99) was observed. An interesting material used as the wave guiding layer is a nanoporous silicon substrate (Fig. 5.16) [5]. It was used to increase the sensing properties of the waveguide as well as to allow for the label-free detection of analytes. The waveguide consists of a low porosity (high index) layer, a high porosity (low index) layer, and an air gap. Utilization of two different porosities enabled the creation of waveguides from the same material. In addition, the effective surface area would be increased and allow for greater interaction with certain molecules. The use of silicon in the waveguide is also advantageous to the already established semiconductor market.

5.3 Waveguide-based molecular sensors

a

Prism Air gap Low porosity High porosity

Silicon substrate 1.6 cm

(A)

(B)

FIG. 5.16 (A) Porous silicon waveguide consists of two layers porous silicon with different porosities. (B) Cross-sectional SEM of the waveguide. Reprinted from G. Rong, A. Najmaie, J.E. Sipe, S.M. Weiss, Nanoscale porous silicon waveguide for label-free DNA sensing, Biosens. Bioelectron. 23 (2008) 1572–1576, with permission from Elsevier.

5.3.4 RECTANGULAR WAVEGUIDE (CHANNEL WAVEGUIDES) The behavior of rectangular waveguides is described in a similar way as that of slab waveguides. Although the confinement becomes two-dimensional and mode shapes are different, the essential ideas are the same as the planer waveguides.

Interferometers One advantage of the rectangular waveguide is that it is possible to define light path length precisely so that it can be easily utilized for application based on optical interference. In a typical experimental configuration, a waveguide is split into two channels. One is used as a reference, and the other contains a sensing site. The effective path of the sensing site is changed by molecular adsorption, and the signal is measured as an interference of the signals from the two waveguides. For interferometric applications, waveguides usually need to be a “single mode” waveguide, which allows only a single mode of light propagation. Cross-sectional dimensions of the single mode fiber are very close to the wavelength of the transmitted light, in order not to allow other modes to exist. Fig. 5.17 shows the typical design of waveguide-based interferometer for biosensing, where such interferometer-based sensors measured injection of a streptavidin solution [6]. Multiple waveguides for interferometry was integrated in the following way: firstly A buffer layer of, 2.5 μm thick SiO2 was formed by thermal oxidation. A 350-nm silicon oxynitride layer with a refractive index of 1.55 was then deposited by PECVD (Plasma Enhanced Chemical Vapor Deposition). A 55-nm rib was formed by standard lithography and RIE (Reactive Ion Etching) to define a single mode waveguide. The width w. of the waveguide is 2.5 μm, which was limited by the photolithographic process [7]. Schmitt et al. utilized a commercial planar Ta2O5 waveguide to construct a Young’s interferometer configuration, where interference between the reference and the sensing signal was measured (Fig. 5.18) [8]. They discussed the sensing capability of the sensor for molecular sensing applications. The interferometer

253

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CHAPTER 5 Optical transducers

FIG. 5.17 Mach-Zehnder interferometer based biosensor. Reprinted from M. Weisser, G. Tovar, S. Mittler-Neher, W. Knoll, F. Brosinger, H. Freimuth, et al., Specific biorecognition reactions observed with an integrated Mach-Zehnder interferometer, Biosens. Bioelectron. 14 (1999) 405–411, with permission from Elsevier.

Sensing chip Sensing path Reference path Double slit

Light source

CCD line sensor

Interferogram

Mirror

FIG. 5.18 Young’s interferometer constructed with planer waveguides. Reprinted from K. Schmitt, B. Schirmer, C. Hoffmann, A. Brandenburg, P. Meyrueis, Interferometric biosensor based on planar optical waveguide sensor chips for label-free detection of surface bound bioreactions, Biosens. Bioelectron. 22 (2007) 2591–2597, with permission from Elsevier.

demonstrated an effective refractive index resolution of 9  109, which corresponds to a surface coverage of  13 fg/mm2.

Silicon ring resonators Another important method for channel waveguides is the use of a silicon ring oscillator. It typically consists of a straight waveguide coupled to a ring-shaped waveguide that functions as an optical resonator. Many researchers study this structure in the hope of using it for optical logic devices that can be integrated onto a silicon chip [9]. Another important application area is molecular sensing [10].

5.3 Waveguide-based molecular sensors

Fig. 5.19 shows a photograph of a ring oscillator along with the schematic of the experimental setup studied by De Vos et al. [10]. When the wavelength of the incident light matches the condition for resonance, a sharp dip in the transmission is observed. The condition for optical resonance is simply given by the following equation: λresonance ¼

L  neff m

(5.64)

where L is the round-trip length of the ring, m is the cavity mode order (¼ 1, 2, …), and neff is the effective index of the ring waveguide. Changes in the refractive index in the sensing site are found by measuring the shift in the resonance spectrum. The idea is very similar to the one applied to SPR sensors described in the next section. It is important to note that silicon is not transparent for visible light and the wavelengths are usually around 1500 nm, which is the wavelength commonly used for fiber optics communication. De Vos et al. theoretically estimate the sensitivity for bulk refractive index changes as 105, which corresponds to theoretical sensitivity of 1 fg molecular mass. They experimentally demonstrated detection of avidin/biotin binding with concentrations down to 10 ng/mL. Another group devised a spiral-shaped cavity resonator and demonstrated streptavidin protein binding with a detection limit of 3 pg/mm2, or a total mass of 5 fg [11]. One obvious advantage of this method is that silicon waveguides are suitable for mass production. The ring oscillator-based technique has been commercialized previously. The Maverick™ MT-ADA™ (multitier antidrug antibody assay) from Genalyte, Inc. is a commercially available multianalyte assay based on silicon ring oscillators. The company claims that multianalyte assay requires very a small sample volume of 2 μL and it takes 15 min to complete the assay.

5.3.5 CIRCULAR WAVEGUIDE (OPTICAL FIBERS) Structure of circular waveguides Optical fibers were first discovered in the mid-19th century, when scientists discovered that light could propagate through materials with higher refractive index, relative to a surrounding lower refractive index Since this time, several technological advancements have propelled this phenomenon to a wide array of applications in many industries including telecommunications, healthcare, automotive, and information management. Just as rectangular waveguides do, these fibers utilize the principle of total internal reflection to propagate light over certain variable distances. Optical fibers possess a cylindrical geometry and therefore have a surrounding material (cladding) of uniform refractive index, as opposed to potentially multiple refractive indices, as seen in planar waveguides [12, 13]. A visual representation of an optical fiber is shown in Fig. 5.20. The core is the component material with the higher index of refraction. In stepindex fibers, this region is uniform. Interestingly enough, this region can be of

255

256

0.010

Pass spectrum

0.005

5mm

m 3m

(A)

Drop spectrum 0.000 1545.20 1545.40 1545.60 1545.80 1546.00

Wavelength (nm)

(B) Light from tunable laser

Light to photodetector Optical fibers

Fluidic channel

SOI biosensor chip

(C)

Temperature control

FIG. 5.19 Molecular sensing based on a silicon ring resonator: (A) photograph of a ring resonator; (B) dip in the transmission at the resonant frequency; and (C) experimental setup. From K. De Vos, I. Bartolozzi, E. Schacht, P. Bienstman, R. Baets, Silicon-on-insulator microring resonator for sensitive and label-free biosensing, Opt. Express 15 (2007) 7610–7615.

CHAPTER 5 Optical transducers

Output (a.u.)

0.015

5.3 Waveguide-based molecular sensors

Core

r Cladding

FIG. 5.20 Circular waveguide.

variable permittivity. Graded-index fibers are optical fibers whereby the core is not homogenous and various indices exist. The index is what ultimately determines the mode of the wave that is guided.

Waveguide modes in a circular waveguide Although a different coordinate system, i.e., cylindrical coordinate system, has to be employed for mathematical analysis, the basic idea behind the waveguide mode is the same as that of the slab waveguide. Single-mode fibers are generally constructed for the purposes of sending energy or information through long distances. This gives rise to a small diameter core, which only allows a single mode to exist. Multimode fibers, however, allow light with a range of modes to propagate through a large aperture. The practical purposes for multimode are generally meant for information transfer over shorter distances.

Applications With the growing expansion of fiber optics to various forms of communication, optical fibers are a natural fit for biomedical applications. Their accessibility to the inside of the body may enable in vivo measurements. The small diameter of the fiber allows it to relay important information on the microscopic level. A hollow fiber sensor is a type of sensor that utilizes optical fiber as a miniature probe microscope. Schulz et al. used competitive reversible binding of molecules and measured changes in molecular concentrations by means of fluorescence intensities (Fig. 5.21) [14]. They immobilized a glucose receptor, concanavalin A (Con A), to the inner wall of a dialysis fiber (diameter ¼ 0.3 mm). ðCon AÞ + ðglucoseÞ>ðCon A  glucoseÞ ðiÞ ðCon AÞ + ðFITC  dextranÞ>ðCon A  FITC  dextranÞ ðiiÞ

When the concentration of glucose increases, reaction (i) will be displaced to the right and (ii) to the left, resulting in releasing of dextran from Con A. The concentration of the released dextran is found by measuring the intensity of fluorescence from FITC (a type of fluorescence dye; see Section 5.6.2) that labels the dextran molecules.

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CHAPTER 5 Optical transducers

3 mm Hollow dialysis fiber Immobilized con A Optical fiber Excitation FITC-labeled dextran Fluorescence

Glucose

FIG. 5.21 Hollow fiber optical glucose sensor. Adapted from J.S. Schultz, S. Mansouri, I.J. Goldstein, Affinity sensor: a new technique for developing implantable sensors for glucose and other metabolites, Diabetes Care 5 (1982) 245–253.

There are many variations in hollow fiber sensors. Fig. 5.22 shows an improved design of a fiber sensor form the Shultz group [15]. In this case, Con A instead of dextran is fluorescently labeled and is bound to dextran matrix immobilized within porous beads. In the absence of glucose, fluorescent-labeled Con A is bound to dextran immobilized inside. The dextran matrix is colored to prevent fluorescence excitation of Con A bound within the beads. After glucose diffuses through the hollow fiber membrane, Con A is displaced and excited by the excitation from the fiber. The fluorescence goes back to the fiber to be measured. The new sensor

Excitation

Excitation

Fluorescence

Glucose

FIG. 5.22 Optical fiber chemical sensors. Adapted from R. Ballerstadt, J.S. Schultz, A fluorescence affinity hollow fiber sensor for continuous transdermal glucose monitoring, Anal. Chem. 72 (2000) 4185–4192.

5.4 Surface plasmon resonance sensors

demonstrated a glucose detection range extending from 0.15 to 100 mM (see Chapter 4, Section 4.2.2 for the discussion on glucose concentration in human blood).

5.3.6 DISCUSSION ON WAVEGUIDE SENSORS Optical fibers have been utilized in a variety of application areas. The number of commercially available products based on optical fibers is astounding. Optical fibers have been integrated into virtually every industry where communicating information is critical to success. In optical fibers, information is transferred in the form of light, and nothing can travel faster than the speed of light. Here we reviewed several types of waveguide-based molecular sensors. Waveguide-based chemical sensors designed for oxygen, carbon dioxide, and ammonia are a few sensors that may be applied to industries such as healthcare, environmental, and manufacturing [16]. The usability of waveguides gives them great potential for in vivo localized sensing in biomedical applications. Glucose sensing is a good example, and similar techniques may be introduced for detection of biomarkers related to tumors or other diseases.

5.4 SURFACE PLASMON RESONANCE SENSORS 5.4.1 INTRODUCTION The focus of recent studies on nanophotonics is to better understand and utilize the properties of surface plasmons [17], which are oscillations coupled at the metal and dielectric interfaces. Utilization of surface plasmons has enabled the use of distinguishable optical phenomena, not only for molecular sensors but also for emerging nanodevices such as nanoantenna [18–20], nano grating coupler [21] and plasmonic near-field scanning optical microscopy (NSOM) [22]. Taking advantage of the highly confined near-field properties, it has been proven that efficient optical devices featuring low physical profile can be realized. In this section, we discuss sensors based on measurement of SPR. We start from general theories followed by the introduction of commercially available products. Finally, we discuss recent advancement in molecular sensing.

5.4.2 PRINCIPLES OF SURFACE PLASMONS Surface electromagnetic waves that propagate in a direction parallel to the metal/ dielectric interface are called surface plasmon polaritons (SPPs). Since they propagate along the interface as a wave, they are sometimes called surface plasmon waves (SPWs). SPR occurs when the frequency of light matches the natural frequency of oscillating surface electrons. These oscillations are very sensitive to changes on the sensing event on the surface, such as adsorption and binding of molecules, since the

259

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CHAPTER 5 Optical transducers

waves propagate exactly on the interface of the metal and the dielectric external medium, e.g., air or water. The terms SPP, SPW, and SPR are often used interchangeably or even confusingly, since the light coupling into surface plasmon is associated with the resonance of surface plasmons. However, when a resonant coupling of light arises in nanometer-sized structures such as metal particles or nanoantennas, it is more accurately called a localized surface plasmon resonance (LSPR), because “waves” or “polaritons” may not apply to cases where surface plasmon does not propagate as a regular wave.

Mathematical description In order to describe the properties of surface plasmons, we use an intuitive approach and treat each material as a homogeneous continuum, described by a frequencydependent dielectric constant. The response of materials to external fields usually depends on the frequency of the applied field. This frequency dependence is based on the fact that a material’s polarization does not respond instantaneously but arises after the field is applied, which is represented by a phase difference. We treat permittivity as a complex function of the angular frequency of the applied field ε(ω). For the generalized refractive index and dielectric constant: εðωÞ ¼ ε0 ðωÞ + iε00 ðωÞ

By using complex numbers for the dielectric constant, we can specify the magnitude and phase. The values of the real part ε0 and imaginary part ε00 are related to the stored energy and the dissipation of energy within the medium, respectively. When surface plasmons exist, the real part of the metal dielectric constant must be negative and its magnitude must be greater than that of the dielectric. This condition is satisfied in the wavelengths range of IR-visible lights for air/metal and water/metal interfaces, where the real part of the dielectric constant of a metal is negative and those of air and water are positive. Now let us look at the case of surface plasmon on thick metal film. Consider a waveguide composed of an infinite metal and an infinite dielectric material with a boundary interface in between two mediums (Fig. 5.23). The permittivity of the metal and that of the dielectric material are: εm ¼ ε0m + jε00m

(5.65)

FIG. 5.23 Surface plasmon polariton, excited at the interface between the spectrally thick metal film and semi-infinitely thick dielectric medium.

5.4 Surface plasmon resonance sensors

εd ¼ ε0d + jε00d

(5.66)

Since the launched SPPs at the interface decay exponentially along the transverse direction (z-direction) to that of wave propagation, most of the electromagnetic energy is confined in proximity to the interface and is very sensitive to changes in dielectric properties of surrounding materials. With such squeezed field distribution, one may tailor surface plasmons by presenting surface corrugations and abnormalities to out-couple the part of the surface optical energy. Surface plasmons, which are the wave in strict transverse magnetic (TM) mode, in the given configuration (see Fig. 5.24) can be found by solving the boundary condition of Maxwell’s equation. The magnetic field of excited SPP with the wavenumber of kspp is given by: h i Hyd ðx, zÞ ¼ H0 exp jkspp x  αd z ðz > 0Þ

(5.67)

h i Hym ðx, zÞ ¼ H0 exp jkspp x + αm z ðz < 0Þ

(5.68)

1=2 αd ¼ εd k0 2 + kspp 2

(5.69)

1=2 αm ¼ εm k0 2 + kspp 2

(5.70)

where

and

It should be noted that there is only a single mode of surface plasmons that can exist on thick metal film by following the transverse resonant mode of operation. Due to the high Q-factor of transverse resonance and the confined field, the energy of surface wave decays quickly through the ohmic losses within the metal as the wave propagates along the interface. For instance, the expected propagation length L ¼ j2 Re [jkspp]j1 of SPP is in general contained about 20–30 μm in the visible

lspp hv

z Hyd Ex ed Ezd ⊗ ⊗ Hym Ex em Ezm

Dielectric ++

––

++

––

++

x Metal

FIG. 5.24 Surface plasmon on metal-dielectric waveguides.

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CHAPTER 5 Optical transducers

range. In this respect, it is essential to fabricate devices within a compact physical dimension to allow for utilizing SPP before the most energy dissipates. Now we try to find a dispersion relation, which is a relationship between ω and k. For waveguides and other complex optical devices, the dispersion relation contains most of the important information about wave propagation in the structure. By solving Eqs. (5.67), (5.68) with Maxwell’s equation, we obtain the dispersive wavenumber of SPP: kspp ¼

ω c

rffiffiffiffiffiffiffiffiffiffiffiffiffiffi εm εd εm + εd

(5.71)

rffiffiffiffiffiffiffiffiffiffiffiffiffiffi εm + εd εm εd

(5.72)

It can be rewritten as: ω ¼ ckspp

This is the dispersion relation for surface waves.

Excitation of surface plasmons by light Here we consider excitation of surface plasmons by light. Similar to our previous discussions on light coupling, we need to match the boundary conditions such that the wave number kph and frequency ω of the incoming photon match to the wavenumber kspp and frequency ω of the surface plasmon. We find matching by using a dispersion curve, which is a plot of ω versus k. Fig. 5.25 shows dispersion curves for surface plasmons, air, and glass. The dispersion curve for air is simply given by ω ¼ ckph. Dispersion curves for air and surface plasmons do not intersect, which indicates that it is not possible to match the light propagating in air and surface plasmons. For this reason, surface plasmons are nonradiative. However, if light propagates in a medium whose index n is larger than 1, the dispersion curve becomes ω ¼ ckph/n and there can be intersection, as ω

w = ckph w = ckph/n

ω = ckspp

εm + εd εmεd

kspp

FIG. 5.25 Dispersion curves for SPR matching.

5.4 Surface plasmon resonance sensors

shown in Fig. 5.25. In practice, this can be achieved by passing the incident light through a medium such as glass, on which a metal film is deposited. Details of coupling between the evanescent wave and the surface plasmon are given in Appendix C.

5.4.3 EXPERIMENTAL CONFIGURATION We shall examine how light radiation is coupled to the SPR. There are two popular ways, as illustrated in Fig. 5.26. •

•

Kretschmann configuration: the metal film is evaporated onto the glass block. The light illuminates the glass block, and an evanescent wave penetrates through the metal film. The plasmons are excited at the outer side of the film. Otto configuration: a thin metal film is positioned close to the prism wall so that an evanescent wave can transfer energy to the plasma waves on the surface to excite the plasmons.

The wavenumber along the direction of propagation can be tuned to match SPR simply by changing the angle of incidence of the p-polarized radiation at the prism/ dielectric interface. A triangular or cylindrical prism is generally used to couple evanescent wave with SPR. Mechanical rotational stages are often employed to achieve measurements of angular responses. Fig. 5.27A shows a simplified diagram of SPR measurement. Fig. 5.27B shows the reflectivity curves for p-polarized and s-polarized (flat dotted line) radiation) with gold and silver films deposited on a sapphire prism (n ¼ 1.766) [22a]. The wavelength was λ ¼ 632.8 nm. Strong absorptions at the resonance angle were observed in angular scans [22b]. The angles of the minimum reflectance correspond to the matching of the laser excitation and SPRs on the gold and silver surface. SPR was not induced by s-polarized light as predicted. The dispersion of SPR is no longer dictated simply by the dielectric/metal boundary because it is perturbed by the presence of the additional coupling prism (see Appendix C).

Prism: ep

Prism: ep Metal: em Dielectric: ed

(A)

Dielectric: ed

Surface plasmon

Surface plasmon

Metal: em

(B)

FIG. 5.26 (A) Kretschmann and (B) Otto configuration for plasmon excitation.

263

CHAPTER 5 Optical transducers

Laser

q Prism Metal Dielectric

(A)

Detector

Silver

Reflectivity

264

Gold s-polarized p-polarized

Surface plasmon

32

(B)

34

36

38

40

Incident angle (degrees)

FIG. 5.27 SPR measurement: (A) coupling with a cylindrical prism; (B) SPR responses with Au and Ag films. Part B: Adapted from J. Sambles, G. Bradbery, F. Yang, Optical excitation of surface plasmons: an introduction, Contemp. Phys. 32 (1991) 173–183.

Fig. 5.28A shows a change in the reflectivity and phase as a result of a change in the refractive index at the interface of a gold film in a Kretschmann geometry. The change in the index is observed as a peak shift in the angular scan, as shown in Fig. 5.28B. Since SPR is confined exactly on the metal-dielectric interface, it constitutes a sensor that is sensitive to index changes specifically on the metal surface, which is the main principle of the SPR-based molecular sensor. Molecular absorption at the metal interface can be measured as a peak shift in the angle scan.

5.4.4 SPR SENSOR FOR MOLECULAR SENSING For molecular sensing, the surface of the dielectric layer is functionalized with recognizing elements such as antibodies or DNAs. Metals commonly used for SPR systems are gold or silver, which are suitable for biomolecule functionalization, as discussed in Chapter 2. Once analyte molecules bind to the surface of the SPR sensor, changes in dielectric constant at the metal interface are utilized as the sensing effect. Fig. 5.29 shows the conceptual sketch of the molecular detection system in an SPR sensor. The change is measured as a shift of the absorption peak in a similar way to that illustrated in Fig. 5.28. Major companies that provide commercially available SPR systems include Biacore AB, Affinity Sensors, Windsor Scientific Limited, BioTul AG, and Nippon Laser and Electronics Lab [23]. Among products from these companies, the Biacore biosensor is most popular and considered to be one of the most accurate, precise and sensitive systems. The measureable concentration range for analytes with high molecular weights is 105 to 109 M for direct assay, and 103 to 1011 M for sandwich assays. For analytes with low molecular weight, the minimum concentration range is 103 to 109 M for inhibition assays. Fig. 5.30 shows the composition the SPR module Spreeta™ Liquid Sensor, developed by Texas Instruments [24]. One characteristic feature of the device is

5.4 Surface plasmon resonance sensors

1.0

Reflectivity

0.8 0.6 0.4

n = 1.32

n = 1.35

0.2

Δqr

0.0

Δjr

100

n = 1.32 48

(A)

50

52

54

0

n = 1.35 56

58

60

62

Phase (degrees)

200

–100

Angle of incidence (degrees)

1.0

nD = 1.32

nD = 1.35

0.6

0.4

Δlr

Reflectivity

0.8

0.2

0.0 600

(B)

Δlr

700

800

900

1000

Wavelength (nm)

FIG. 5.28 Reflectivity plot for different refractive indices: (A) reflectivity and phase curves against the angle of incidence; (B) reflectivity curves against the wavelength. Reprinted by permission from Springer: J. Homola, Present and future of surface plasmon resonance biosensors, Anal. Bioanal. Chem. 377 (2003) 528–539, Copyright 2003.

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Prior to binding

Surface plasmon wave (SPW) Biolayer refractive index, n

Recognition element (antibodies)

SPW propagation constant, b Metal

Analyte binding Analytes Biolayer refractive index, n Æ n + Dn SPW propagation constant, b Æ b + Db Metal

FIG. 5.29 Optical transduction. Adapted from J. Homola, Present and future of surface plasmon resonance biosensors, Anal. Bioanal. Chem. 377 (2003) 528–539.

Mirror Gold plasmon surface

Polarizer LED

Photodiode array

FIG. 5.30 Composition of the Texas Instruments SPR module Spreeta™ Liquid Sensor. Adapted from T. Chinowsky, J. Quinn, D. Bartholomew, R. Kaiser, J. Elkind, Performance of the Spreeta 2000 integrated surface plasmon resonance affinity sensor, Sens. Actuators B Chem. 91 (2003) 266–274.

the use of a photodetector array; this eliminates the need of mechanical rotation in the measurement of angular scans. The angular absorption curve is mapped directly onto the photodetector array, reducing the experimental time and complexity involved in the mechanical rotation. The SPR module of the Biacore system is coupled with a microfluidic chip that supplies the analyte solution at a controlled flow rate. For an example of the Biacore 3000 system, the flow rate can be controlled between 1 and 5000 μL/min. It also allows a precise temperature control better than 3  103°C, which corresponds to a measurement error of approximately 0.3 pg/mm2. The schematic of the microfluidic channel design is shown in Fig. 5.31. Fig. 5.31A shows the design of the microfluidic channel that controls the flow of a sample and a buffer solution.

5.4 Surface plasmon resonance sensors

Buffer Flow cell

Serial flow

Sample in

Sensor chip

Valve

Flow

Waste

Valve

Valve Sensor chip

5 mm

(A)

(B)

(C)

FIG. 5.31 Microfluidic channel used in the Biacore system. Part A and B: Adapted from a Biacore Technology brochure. Part C: Adapted from E. Gizeli, C. Lowe, Biomolecular Sensors, Taylor and Francis, 2012, p. 161, 165.

Fig. 5.31B shows a close-up view. In this example, the flow cells are connected in series. Fig. 5.31C shows a side view illustration of a flow cell, which guides the flow onto the sensor chip. The valve works in a similar way as the NanoFlex valve described in Chapter 3, Section 3.3.3. Fig. 5.32 shows an example measurement results obtained from the Biacore system. Interleukin 2 (IL-2), which is a type of cytokine signaling molecule in the immune system, is injected at s flow rate of 100 μL/min with different concentrations of 233, 78, 26, 8.6, 2.9, and 0 nM in 10 mM sodium phosphate. The system uses the SPR response to monitor the refractive index change as molecules interact at the sensor surface. Solid curves represent the best fit of the binding responses to a simple one-to-one bimolecular reaction model of: ka

A + B Ð AB kd

Association

Response (RU)

8

Dissociation

6 4 2 0 0

20

40

60

Time (s) FIG. 5.32 Global analysis of biosensor data. Adapted from R.L. Rich, D.G. Myszka, Advances in surface plasmon resonance biosensor analysis, Curr. Opin. Biotechnol. 11 (2000) 54–61.

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where A and B represent the target molecule and immobilized receptor, respectively. This reaction can be described by the following differential equation [25]. d ½A  ¼0 dt

(5.73)

d ½B  ¼ ka ½A½B + kd ½AB dt

(5.74)

d ½AB ¼ ka ½A½B  kd ½AB dt

(5.75)

Here, the concentration of the target molecule [A] in the flow is assumed to be constant. The amount of receptor sites [B] changes based on the association and dissociation of the molecules and the receptors. The values of ka and kd can be numerically found by curve fitting [25]. The association (ka) and dissociation (kd) rate constants were (4.66  0.04) x 106 M1 s1 and 0.0420  0.0002 s1, respectively. 1 RU approximately corresponds 106 in refractive index, 104 degrees of an angle change, and 1 pg/mm2 for protein.

5.4.5 RECENT ADVANCEMENT IN SPR SENSORS Several interesting studies have recently been reported to improve SPR sensors. One approach is the integration of microfluidic system, which enables parallel high throughput screening. Luo et al. reported on a polydimethylsiloxane (PDMS) microfluidic device containing an array of micro chambers, each of which contains a gold spot designed for SPR measurements (Fig. 5.33) [26]. The flow cell is coupled with a triangular prism, as shown in Fig. 5.33B. After the surface of the gold spots is coated with biotin BSA (bovine serum albumin), anti-biotin antibodies are injected into the flow cell at different concentrations. Immunoreaction was detected and characterized in about 10 min, with the sensitivity of subnanomolar level. When additional gold nanoparticles were selectively coupled to the immunocomplex to amplify SPR signals, the sensitivity was improved to the 10–100 picomolar level, but the time needed for measurement increased to about 60 min. Another approach is the utilization of nanostructures. LSPR in nanoscale metal patterns has been a topic of interest in the study of SPW. Specifically, the peak extinction wavelength, λmax is known to be very sensitive to nanoparticle size, shape, and local (10–30 nm) external dielectric characteristics (see Chapter 7, Section 7.2.1 for details of metal nanostructure and extinction and scattering measurements). Nanoscale metal patterns can be utilized to a substrate SPR measurement with a locally amplified sensitivity. Haes et al. prepared triangular silver nanoparticles (100 nm wide and 50 nm high) on a glass substrate by nanosphere lithography (NSL), where a self-assembled array of nanospheres serves as a

5.4 Surface plasmon resonance sensors

PDMS

Control layer Flow layer

Glass Vertical reagent reservoirs

Opening for vertical valves

Horizontal reagent reservoirs

Opening for horizontal valves

(A)

Prism

Channel substrate Gold spots

Inlets

(B)

Outlets

Pressure ports

FIG. 5.33 SPR Microfluidic device for immunoassays based on surface plasmon resonance: (A) top view schematic of the array of micro flow channel; (B) prism coupled to the cell. Part A: Reproduced from Y. Luo, F. Yu, R. N. Zare, Microfluidic device for immunoassays based on surface plasmon resonance imaging, Lab Chip 8 (2008) 694–700, with permission of the Royal Society of Chemistry. Part B: Adapted from Y. Luo, F. Yu, R. N. Zare, Microfluidic device for immunoassays based on surface plasmon resonance imaging, Lab Chip 8 (2008) 694–700.

shadow mask during the process of metal deposition with an evaporator [27]. Their experiments are illustrated in Fig. 5.34. Fig. 5.34A shows an AFM image of the Ag. Exposure of biotin-functionalized Ag nanotriangles to 100 nM streptavidin caused a red shift of 27.0 nm in the peak extinction wavelength. The surface chemistry of the Ag nano-biosensor is shown in Fig. 5.34B. Haes et al. demonstrated a strategy to amplify the LSPR by introducing biotinylated Au colloids. They

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CHAPTER 5 Optical transducers

(A)

(B) O C

HS

1

OH

2

CH3

HS

O

H2N

O

O

HN H

H N

NH H

3

s O

(C) Ka,surf Ag Glass

Ag Streptavidin

Glass

FIG. 5.34 Localized surface plasmon resonance spectroscopy of triangular silver nanoparticles: (A) AFM image of the triangular silver nanoparticles; (B) surface chemistry of the Ag nanobiosensor; (C) conceptual sketch of the biosensor. Reprinted with permission from A.J. Haes, R.P. Van Duyne, A nanoscale optical biosensor: sensitivity and selectivity of an approach based on the localized surface plasmon resonance spectroscopy of triangular silver nanoparticles, J. Am. Chem. Soc. 124 (2002) 10596–10604, Copyright 2002, American Chemical Society.

concluded the limit of detection (LOD) for their LSPR nanobiosensor is in the lowpicomolar to the high-femtomolar region. A conceptual sketch of the experiments is shown in Fig. 5.34C. Several interesting studies related to utilization of LSPR have been reviewed in Ref. [28]. Recent techniques include the use of nanohole arrays, where LSPR is directly excited by perpendicularly incident light, which minimizes the alignment requirements for light coupling. The signal induced by detection of live viruses were measured with a simple experimental setup with a CCD [29]. LSPR used in light scattering techniques are described in Section 5.7.2. LSPR found in metal nanoparticles will also be described in Chapter 7 (see discussions on gold and silver nanoparticles).

5.4.6 DISCUSSION ON SPR SENSORS In this section, we first introduced the theoretical background and practical applications of SPR-based molecular sensors. Surface plasmons are electron density waves that travel along the surface. These density waves depend on an electric field that collects electrons from the bulk. Only p(TM)-polarized light can excite surface

5.5 Absorption spectroscopy

plasmons. A dispersion relation, which indicates the condition for matching energy and momentum at the interface, determines when surface plasmons can be excited. We then described how SPR sensors are implemented in the experimental setup. Because the k-vector of the surface plasmon wave is always larger than the k-vector of light in a medium, a prism or grating has to be used in the experiments. SPR is detected by measuring the angle at which the intensity of reflected light becomes minimal. Binding is measured under constant flow. Finally, we introduced a popular commercial system and experimental results of measurements of biomolecules. The technique was able to detect binding kinetics (kon, koff, KA). Binding constants are in good agreement with those found by other methods, but showed a small under-estimation. Mechanical and temperature stability determine the sensitivity, which is about 1 pg/mm2. We also introduced recent advancements in the study of SPR sensing. In conclusion, SPR-based molecular sensors are well studied, and one of the most practically used molecular sensing systems.

5.5 ABSORPTION SPECTROSCOPY 5.5.1 OPTICAL DENSITY MEASUREMENT The optical density or absorbance of a material is a logarithmic intensity ratio of the light falling upon the material, to the light transmitted through the material: AðλÞ ¼ log 10

I0 I1

(5.76)

where I0 and I1 are the intensities of the incident and transmitted lights, respectively. Although sometimes confusing, the transmittance I1/I0 or the percent transmittance 100  I1/I0 [%] is also commonly used. Absorbance is dependent on the wavelength (a filter designed to absorb lights of all visible wavelengths equally is specifically called a neutral density filter or ND filter), and is often measured as a function of the radiation wavelength, which is called the absorption spectrum. The absorption spectrum is a very important quantitative measure to evaluate optical properties of solutions. It provides several types of information such as the concentration of a solute, shapes or sizes of suspended particles, and biological activities. The absorbance of a solution is usually measured by preparing a sample in a cuvette or a microwell plate.

5.5.2 BEER-LAMBERT LAW Let us consider a case where the incident light I0 with the cross-sectional area of S passes through a liquid with the thickness of d. The liquid contains particles with the absorption cross section σ at the volume concentration of n (Fig. 5.35). Absorption of light for a small path increment dx is written as: dI ¼ I 

σnSdx ¼ σnI  dx S

(5.77)

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CHAPTER 5 Optical transducers

dx: path increment

I0

I

S: cross-sectional area d

FIG. 5.35 Beer-Lambert law.

or dI ¼ σnI dx

(5.78)

I ðxÞ ¼ I0  eσ n x

(5.79)

I ¼ eσ n d I0

(5.80)

Integration of Eq. (5.78) gives: For the thickness x ¼ d:

From the definition in Eq. (5.77), the absorbance of this solution becomes: A ¼ log 10

I 1 ¼ log 10 eσnd ¼   σnd I0 ln10

(5.81)

This relationship states that the absorbance is proportional to the concentration and the thickness, which is known as the Beer-Lambert law, and is more commonly expressed with the molar extinction coefficient ε and molar concentration c in the following way: A ¼ log 10

I ¼ εcd I0

(5.82)

Comparing Eqs. (5.81), (5.82) and using n ¼ NA c (NA: Avogadro constant), we can find the relationship between absorption cross-section and the molar extinction coefficient. ε¼

σn σ NA ¼ ln10  c ln10

(5.83)

The term ln10 is needed because base 10 (as in Eqs. 5.76, 5.81) rather than base e (as in Eqs. 5.75, 5.78) is more commonly used in practice. We also have to be careful with the units for conversion. In optical measurements, [cm] and [L] are commonly used for distances and volumes, respectively. An absorption cross-section σ, a molar

5.5 Absorption spectroscopy

extinction coefficient ε, and molar concentration are usually given in [cm2], [Lmol1cm1], and [molL 1], respectively.

5.5.3 SENSORS BASED ON ABSORPTION SPECTROSCOPY Optical oximetry

Molar extinction coefficient (cm–1 M–1)

One interesting application of absorption measurement for biomedical sensing is optical oximetry. This method monitors hemoglobin saturation in a patient. Fig. 5.36 shows absorption spectra of hemoglobin and oxyhemoglobin (hemoglobin that contains bound O2), which are present in arterial blood [29a]. The absorbances depend on the content of oxygen. A simple implementation of finding the ratio between the hemoglobin and oxyhemoglobin contents compares the absorbances at two wavelengths, namely red and infrared. Based on a linear approximation, blood saturation (oxygen content) SaO2 can be correlated with the ratio of absorbances at red and IR, as shown in Fig. 5.37. Measurement of arterial oxygenation is important in clinical management of ill or anesthetized patients. The practical technique used in optical oxymetry is pulse oxymetry [30, 31], where pulsing absorbance change due to the heartbeat is measured at wavelengths of red and IR. The method allows the exclusion of changes from venous blood, tissues of skin, bone, muscle, fat, and other artificial elements such as nail polish [32] by finding the change that occurs as a result of arterial pulsation. A typical form of pulse oxymetry is with a small device that clips a fingertip. Each side of the clip has either an LED or a detector. This is a type of measurement called transmission pulse oxymetry, where a thin part of the body’s section has to be chosen for measurement. An alternative method is reflectance pulse oximetry

104

Infrared 940 nm

Red 660 nm

103

102

500

600

700

800

900

Wavelength (nm)

FIG. 5.36 Absorption spectrum of blood. Adapted from G. Harsanyi, Sensors in Biomedical Applications, CRC Press, Boca Raton, 2000, Chapter 6.2.4, p. 205.

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CHAPTER 5 Optical transducers

100 80 SaO2 (%)

274

60 40 20 0 0.5

1.5

2.5

3.5

IR/R

FIG. 5.37 Blood saturation as a function of IR/R intensity ratio from. Adapted from G. Harsanyi, Sensors in Biomedical Applications, CRC Press, Boca Raton, 2000, Chapter 6.2.4, p. 207.

[33–35] as shown in Fig. 5.38B. It is suitable for application to more general body parts including limbs, forehead, and chest.

Glucose sensing As described in Chapter 4, the majority of glucose sensors are electrochemical sensors based on the measurement of reducing properties of glucose (see Chapter 4, Section 4.2.2). However, noninvasive spectroscopic measurements [36] of transmitted or reflected light may be more advantageous since they can potentially eliminate several problems related to blood drawing. Mid-infrared (MIR: 3–50 μm) transmission spectroscopy has been used for in vitro blood glucose measurement by Shen et al. [37]. The spectral range of 950–1200 cm1 (8.3–10.5 μm in wavelengths) was used to find stretching modes of CdC and CdO in glucose molecules. A 4-vector partial least-squares calibration Body part LED

Body part Detector LED

Detector

(A)

Transmission

(B)

Reflectance

FIG. 5.38 Two types of pulse oximetry: (A) transmission pulse oximetry and (B) reflectance pulse oximetry.

5.6 Fluorescence spectroscopy

model was used for a calibration set consisting of samples from 14 patients. A standard-error-of-prediction of 0.59 mM for an independent test set of 14 samples has been demonstrated. Shen et al. also suggested use of two specific wavenumbers to determine the glucose concentration with a prediction error of 0.95 mM. The difficulty in MIR spectroscopy is significant background absorption by other molecules in blood including water. Near-infrared (NIR: 0.78–3 μm) region, in contrast, is more suitable for in vivo sensing, because 90%–95% of NIR light passes through the epidermis. Burmeister et al. evaluated six measurement sites of human body for transmission NIR spectroscopy. The wavenumber region used for the blood glucose sensing extends from 6500 to 5500 cm1 (1.54–1.82 μm in wavelengths) which corresponds to first overtones of CdH and OdH stretching modes [38]. Burmeister et al. demonstrated a standard error prediction of 3.4 mM with measurements across the tongue [39]. Malin et al. demonstrated the use of NIR diffuse reflectance spectroscopy over the 1050–2450 nm wavelength range for blood glucose monitoring. Validation with an independent test set showed a mean standard error of 1.03 mM [40]. Techniques based on Raman spectroscopy and light scattering will be discussed in Section 5.7. Subcutaneous glucose sensors will be introduced in Chapter 8, Section 8.6.2.

CO2 sensing Many commercially available CO2 sensors are based on infrared absorption spectroscopy. A sensor has a small chamber connected to the environment. The intensity of the infrared light transmitted through the chamber is measured by a detector. Parallel to this, a light through the reference chamber, which is filled with an inert gas, is also measured. The comparison of the two signals provides the absorption characteristics of the atmosphere. Since CO2 absorbs specific wavelengths of infrared, the sensor can measure the concentration of CO2. A common application is ventilation control. Wall-mounted CO2 sensors are often used to control ventilation. Monitoring of CO2 concentration allows buildings to comply with standards for air quality by preventing excessive accumulation of CO2. Biomedical application includes CO2 monitoring during ventilation. In Chapter 8, Section 8.8.3, we show an example of a CO2 sensor used in anesthetic machines.

5.6 FLUORESCENCE SPECTROSCOPY 5.6.1 BASICS OF FLUORESCENCE Fluorescence is the emission of a photon by a substance as a result of an electron transition from an excited state to the ground state. Fluorescence is utilized for several types of applications such as lighting, labeling, optical microscopy, chemical sensing, and analysis of material structures.

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Energy levels Fluorescence is usually studied with polycyclic aromatic molecules. The electronic state of a molecule is defined by the distribution of negative charges and molecular geometry. Each electronic state is further subdivided into vibrational energy levels associated with the periodic motion of atoms in the molecule. A Jablonski diagram is often used to illustrate the energy levels of a molecule. An example of a Jablonski diagram is shown in Fig. 5.39. The states are arranged vertically by energy. In Fig. 5.39, electronic states are illustrated as S(0), S(1), S(2), …. The vibrational mode v are denoted as S(i) ¼ vi. For example, the lowest vibrational energy level of the first excited state is denoted as S(1) ¼ 0. Transitions between energy states are indicated by arrows. A transition associated with fluorescence excitation or fluorescence emission (radiative transition) is indicated by a straight arrow. A nonradiative transition is indicated by a wiggly arrow. Horizontally arranged states are grouped by spin multiplicity. There are cases where the electron undergoes an intersystem crossing into a triplet state T(1), which has the higher spin multiplicity. In this case, the transition from T(1) to the lower energy state is “forbidden,” and only occurs on a slower time scale. Luminescence observed in this process is called phosphorescence. Phosphorescence emission is a very slow process (it could take up to several hours) and is often utilized for special painting purposes such as paints for exit signs and clock dials.

E

S2

5 4 3 2 1 0

S1

5 4 3 2

Vibrational relaxation (10–14 – 10–11 s)

Internal conversion (10–14 – 10–11 s)

Intersystem crossing (10–8 – 10–3 s)

1 0

T1 Excitation (10–15 s)

S0

5 4 3 2 1 0

FIG. 5.39 Jablonski diagram.

Fluorescence (10–9 – 10–7 s)

Fluorescence

5 4 3 2 1 0

Excitation

Phosphorescence (10–3 – 102 s)

5.6 Fluorescence spectroscopy

Important features of fluorescence Several important features are found for absorption and the fluorescence spectrum. The energy of the absorbed photon is always larger than the energy of the emitted photon. As a result, the wavelength of emission is always longer than that of excitation (exceptions are cases of multiphoton excitation). The difference in wavelength between the band maxima of absorption and fluorescence spectra is called the Stokes shift. The Franck-Condon energy diagram in Fig. 5.40 illustrates the vibrational wave functions of energy levels for the internuclear distance. Since absorption and emission are very fast processes, the internuclear distance does not change, and thus the transitions are represented as vertical lines. The Franck-Condon principle states that an electronic transition is more likely to occur when the vibrational wave functions of the two levels overlap more significantly. According to the Franck-Condon principle, the probability of an excited electron transition is related to the degree of similarity between wave functions of the energy states. As a result, some transitions are more probable for both absorption and emission than others. For example, in Fig. 5.40, excitation from S(0) ¼ 0 to S(1) ¼ 2 will be most probably followed by emission from S(1) ¼ 0 to S(0) ¼ 2. This principle leads to the mirror image rule, where fluorophores often have a visible band

E 5 4 3 2

S1

1 0 5 4 3 2 S0 1 0

Nuclear coordinates FIG. 5.40 Franck-Condon energy diagram.

277

0-3

0-3

0-2

0-2

0-1 0-1

Fluorescence

CHAPTER 5 Optical transducers

Absorbance

278

Wavelength

FIG. 5.41 The mirror image rule.

sub-structure in the fluorescence spectrum, which resembles the mirror image of that of the absorption spectrum (see Fig. 5.41).

Fluorescence of quantum dots Quantum dots (QDs), nanometer-scale semiconductor crystals, show unique fluorescence characteristics that do not follow many of features discussed in the previous section. The fluorescence of a QD is based on the three-dimensional quantum confinement of electrons [41]. Details are described in Chapter 7, Section 7.6.

Fluorescence lifetime The average time the electron stays in an excited state before photon emission is referred to as the lifetime. Fluorescence lifetime typically ranges in the order of 109 to 107 [s]. The lifetime τ is equal to the time after which the intensity I drops to 1/e of its initial value I0. Fluorescence intensity I typically follows a simple exponential decay: IðtÞ ¼ I0  exp ðt=τÞ

(5.84)

Eq. (5.84) can be rewritten with the decay rate Γ ¼ 1/τ as: IðtÞ ¼ I0  exp ðΓtÞ

(5.85)

Both radiative and nonradiative transitions are included in the decaying process as: Γtotal ¼ ΓR + ΓNR

(5.86)

where ΓR and ΓNR are the contributions of radiative and nonradiative processes, respectively. The fluorescence quantum yield is a measure that indicates the efficiency of the fluorescence process. Quantum yield Q is defined as: Q¼

ΓR ΓR + ΓNR

(5.87)

Quantum yield Q also means the ratio of the number of photons emitted to the number of photons absorbed.

5.6 Fluorescence spectroscopy

Normal excitation

FRET

Excitation

Excitation

Emission

Donor

(A)

Energy transfer

Donor

Acceptor

(B)

Emission

Acceptor

FRET distance (~10 nm)

FIG. 5.42 Energy transfer between fluorescent molecules.

Fluorescence resonance energy transfer QDs can be used as a light. One of the applications where QDs are used as a excitation source is sensors based on fluorescence resonance energy transfer (FRET) is a nonradiative energy transfer from the excitation source (donor) to the fluorescence molecule (acceptor). FRET occurs when (i) the emission wavelength of the donor matches excitation wavelengths and (ii) the distance between the donor and the acceptor becomes smaller than the FRET distance, which is typically 10 nm. Because FRET is very sensitive to the donor-acceptor distance, it used to detect changes in distances at the nanometer scale. As shown in Fig. 5.42, when the donor-acceptor distance is larger than the FRET distance, emission is observed from the donor. FRET is observed only when the distance becomes closer than the FRET distance; emission from the acceptor is observed. Fluorescence lifetime measurement can be used to observe the process of energy transfer as a change in the fluorescence lifetime. QDs are often used as the donor for fluorescence excitation. Examples are described in Chapter 7, Section 7.6.3.

5.6.2 FLUORESCENCE SPECTROSCOPY AND IMAGING Fluorescence microscopy is a technique where samples stained with fluorescent dyes are observed with a fluorescent microscope. Fig. 5.43 shows the basic composition of a fluorescent microscope. Essential components for fluorescence microscopes are the light source, the excitation filter, the dichroic mirror, and the emission filter. The light source is usually a xenon lamp, a mercury lamp, or a tungsten halogen lamp, which has a wide band of emission. The excitation light that passes through the excitation filter is reflected by the dichroic mirror and illuminates the sample. When a laser or a monochromatic light source is used for excitation, the excitation filter is not necessary. Fluorescence from the sample passes through the dichroic mirror and the emission filter. A set of an excitation filter, a dichroic mirror, and an emission filter is usually packed in a 1 in. sized box and called a filter cube or a filter set. Sets of filters have to be chosen for different types of fluorescent dyes. Fig. 5.43 also shows an example of transmission spectra of a filter cube, which consists of a bandpass excitation filter, a long-pass dichroic mirror, and a band-pass emission filter designed for fluorescein isothiocyanate (FITC).

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Detector Fluorescence

Emission filter Dichroic mirror Excitation filter

Emission filter Filter set for FITC Dichroic mirror

Filter set

Light source 1 Excitation filter

Objective lens

Transmittance

280

Excitation light Specimen

400

450

500

550

600

Wavelengths (nm)

FIG. 5.43 Schematic of a fluorescence microscope and the spectra of a fluorescence filter cube.

FITC is one of the most commonly used fluorescent dyes. Fig. 5.44 shows the excitation and emission spectra of FITC. As discussed in the previous section, the emission spectrum of FITC is similar to the mirror image of the absorption spectrum. The structural formula is also shown in Fig. 5.44. Most fluorescent dyes are polycyclic aromatic hydrocarbons like FITC. The isothiocyanate group (dN]C]S) reacts with amino-terminal and primary amines in proteins. FITC has been used for the labeling of antibodies. Immunofluorescence is the most important technique for molecular sensing and imaging. The specificity of an antibody chemically linked to a fluorophore is used to stain specific biomolecule targets. Multiple fluorescent dyes are functionalized with specific antibodies to measure the concentration or visualize the spatial distribution of target molecules. Immunofluorescence is often used with other nonantibody stains such as DAPI, which binds to adenine- and thymine-rich (AT-rich) regions in DNA. Fig. 5.45 is an example of cell identification based on immunofluorescence [41a]. Photographs shown in fluorescence images are a cancer cell (COLO205: colon cancer cell line) and a leukocyte (white blood cell) using a color CCD camera. The cells are fluorescently stained with DAPI for DNA staining, FITC functionalized with an antibody against cytokeratin (a protein found in epithelial tissue) and AlexaFluor 568 dye functionalized with an antibody against CD45 (a protein found on leukocytes). Cubes designed for DAPI, FITC, and AlexaFluor 568 are switched for taking each photograph. The cancer cells are (a) DAPI positive, (b) CK positive, and (c) CD45 negative, while the leukocytes are (d) DAPI positive, (e) CK negative, and (f ) CD45 positive. Most organic dyes are subject to photochemical destruction called photobleaching. After a certain number of photons are emitted from a dye, the dye loses its

Absorbance

Fluorescence

5.6 Fluorescence spectroscopy

400

450

500

550

600

Wavelengths (nm)

FIG. 5.44 (A) Excitation and emission spectra of fluorescein isothiocyanate (FITC). (Plotted based on data from Jackson Immuno Research.) (B) Structural formula of FITC.

(A)

(B)

(C)

(D)

(E)

(F)

FIG. 5.45 Immunofluorescent imaging of a cancer cell and a white blood cell: (A) DAPI (emission 460 nm, blue), (B) CK (emission 520 nm, green), and (C) CD45 (emission 610 nm, red) fluorescence images of a cancer cell, (D) DAPI, (E) CK, and (F) CD45 images of a white blood cell. Bars ¼ 10 μm. From K. Hoshino, Y.-Y. Huang, N. Lane, M. Huebschman, J.W. Uhr, E.P. Frenkel, et al., Microchip-based immunomagnetic detection of circulating tumor cells, Lab Chip 11 (2011) 3449–3457.

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fluorescence functionality due to photo bleaching. Alexa 488 and DyLight 488 are commercial products that have been tailored for improved photostability with similar absorption and emission spectra as those of FITC. Most of the filter sets designed for FITC can be used for them.

5.7 LIGHT SCATTERING Light scattering is a general category for several different physical phenomena. It can be considered as the deflection of a ray from a straight path due to irregularities such as small particles or defects. Here we first introduce types of light scattering that are important in optical sensing and imaging applications; this is followed by discussions on the principles of optical measurement methods that are essential in molecular sensing and imaging.

5.7.1 FORMS OF LIGHT SCATTERING Light scattering is divided into two types: elastic and inelastic scattering. Rayleigh scattering and Mie scattering are forms of elastic scattering where the energy of the incident light is conserved. Raman scattering is a form of inelastic scattering, where the transfer of energy is involved. Raman scattering will also be discussed in this section.

Rayleigh scattering Rayleigh scattering is a type of scattering by molecules and particulate matter much smaller than the wavelength. The intensity of scattered light has a very strong dependence on the size of the particles and the wavelengths. The wavelength dependence explains the reason why the sky appears blue: a light of shorter wavelength (violet, blue, and green) will scatter more than that of longer wavelengths (yellow and red). This scattering makes the sky look blue during daytime regardless of the directions and the position of the sun. When the sun becomes closer to the horizon, the thickness of the air that the sunlight passes through becomes larger, and lights of shorter wavelengths are scattered away before reaching the surface of the earth. The sky appears yellow-red. Rayleigh scattering is the main cause of signal loss in optical fibers.

Mie scattering Mie scattering is the scattering described as the Mie solution. It is the solution to Maxwell’s equations for the scattering by an isotropic, homogeneous, dielectric sphere. Although the Mie solution applies to a particle with any diameter, it is generally used for particles whose size is similar to the wavelength. The Mie solution allows theoretical calculation of the electric and magnetic fields inside and outside a spherical particle. It is useful to discuss scattering and resonances in particles with different diameters and materials. Examples of applications of Mie solution to find resonances in metal nanoparticles will be described in Section 5.7.1.

5.7 Light scattering

5.7.2 METHODS BASED ON LIGHT SCATTERING MEASUREMENTS Dark field microscopy Dark field microscope is a type of microscope that enables microscopic observation of scattered lights from the sample. It is constructed with a simple design of optics and is very useful to study scattering characteristics of nanomaterials. Fig. 5.46 illustrates a schematic of a dark field microscope. The collimated light from the light source is focused onto the specimen by the condenser lens, which is located on the other side of the objective lens. An annular stop (opaque metal disc) is placed before the condenser lens to block the central part of the light from the source, leaving illumination only from an outer ring. The diameter of the stop is designed so the ring illumination light does not directly go into the objective lens, and only scattered lights are collected and observed. In order for this to happen, the NA of the condenser lens has to be larger than that of the objective. In the dark-field microscopy, the specimen is observed as a bright object because of the scattered light, while the background appears dark. Table 5.1 shows the comparison between bright-field, dark-field, and fluoresce microscopies.

Static light scattering Static light scattering is a method that measures the intensity of the scattered light with different measuring angles [41b]. It is called “static” because time-averaged intensity is measured in contrast to dynamic light scattering, where fluctuations in light intensity are measured. Static light scattering is used to determine the average molecular weight of particles such as polymers or proteins. Scattering is dependent on polarizability of a solution, which is related to the size and the shape of the solute molecules. There are several methods [42, 43] that correlate angular intensity measurements and the characteristics of molecules. Objective lens

Specimen Glass slide (sample stage)

Condenser lens Annular stop Collimated light

FIG. 5.46 Dark-field microscope.

Annular stop

283

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Table 5.1 Comparisons of bright-field, dark-field, and fluorescence microscopies Bright-field

Dark-field

Fluorescence

Key components

Two lenses and a condenser

Two lenses, a condenser, and an annular stop

Two lenses, filters, and a dichroic mirror

Image

Bright background Dark specimen

Dark background Bright specimen

Dark background Fluorescent specimen

Specimen

Absorb illumination light

Scatter illumination light

Absorb lights of shorter wavelengths

Measurement at multiple observation angles allows one to calculate of characteristics related to the molecular weight of the solute. Fig. 5.47 shows a typical experimental setup for static light measurement. A laser beam is focused onto a sample prepared in a cylindrical cell. The scattered light can be observed from different angles.

Dynamic light scattering Dynamic light scattering is based on the measurement of time-domain fluctuation of scattered light intensity [44]. The technique is employed to find diameters of suspended particles. It can be used for particles sized about nanometers to micrometers with concentrations of 104 to 1010 particles/mL. Many instruments allow both dynamic light scattering and static light scattering with the same experimental setup. The principle is that the time scale of particle random motion is dependent on the diameter of particles. More specifically, the diffusion constant D is used to discuss the particle motion. In order to find characteristic time scales from the measured signal, the autocorrelation function of the recorded intensity fluctuation is used. The diffusion constant of spherical particles with the radius r in liquid is given as: D¼

kB T 6π ηr

(5.86)

where kB is Boltzmann constant, T is the absolute temperature, and η is viscosity. The autocorrelation function of light scattering in a monodisperse suspension (i.e., suspension of particles with a uniform diameter) is found to be: gðtÞ ¼ exp

t τq

(5.87)

where τq is the time delay given with the diffusion constant D, viewing angle θ, and the wavelength λ in the following way: τq ¼

1 DK 2


 4π θ K ¼ sin λ 2

(5.88)

5.7 Light scattering

Thermostated cell holder

Sample cell Laser

Laser source Observation angle Scattered light Optics

Photo detector

Computer

Correlator

FIG. 5.47 Static light scattering. Adapted from A.P.F. Turner, I. Karube, G.S. Wilson, Biosensors: Fundamentals and Applications, Oxford University Press, Oxford, 1987.

For a polydispersed solution (i.e., suspension of particles with different diameters), the autocorrelation function is given as integral of exponential functions along time delays for all the particle diameters. Z

gðtÞ ¼ 0

∞

GðτÞexp

t  dτ τ

(5.89)

where G(τ) is the normalized distribution of time delays. Fig. 5.48A shows examples of time delay distributions for particle suspensions with narrower and broad diameter distributions. Fig. 5.48B shows a case with two peaks in the diameter distribution [44a].

Laser Doppler velocimetry Laser Doppler velocimetry (LDV) is a technique to measure the velocity of a flow based on the measurement of light scattering caused by particles in the flow [45, 46]. According to the Doppler effect, the frequency of reflected radiation from a flowing particle is shifted from that of the incident light. The change in the frequency is a function of the velocity of the particle. Fig. 5.49 illustrates the principle of LDV. The two coherent laser beams beam1 and beam2, with the directions given as unit vectors k1 and k2, respectively, intersect each other in the flow. Particles with the velocity are flowing in the intersection and the scattered lights are monitored. The direction from the particle to the observer is given with a unit vector ks. Frequencies of the scattered light from beam1 and beam2 are: f1 ¼

c  VP  k1 f0 c  VP  k1

(5.90)

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Broad F = 28,820 m2/r 2 = 0.143 F tmax= 2.8

Narrow F = 29,293 m2/r 2 = 0.0499 F tmax= 2.7

6´10–5

Bimodal distribution (I) F2/F1 = 2.9; A1/A2 = 9 F1 = 7,857 F2 = 22,590

10´10–4

G (r)

4´10–5 G (r)

286

0.5´10–4 A1

2´10–5

0

A2

0 2´104 r (s–1)

0

4´104

6´104

0

1´104

2´104 r (s–1)

3´104

4´104

FIG. 5.48 Dynamic light scattering. Reprinted from E. Gulari, E. Gulari, Y. Tsunashima, B. Chu, Photon correlation spectroscopy of particle distributions, J. Chem. Phys. 70 (1979) 3965, with permission of AIP Publishing.

Incident beam 1

k1

VP kS

k2

Detector

Incident beam 2

FIG. 5.49 Laser Doppler velocimetry.

and f2 ¼

c  VP  k 2 f0 c  VP  k 2

(5.91)

respectively, where VP is the velocity of the particle. The frequency difference, or Doppler shift, between f1 and f2 can be found by measuring heterodyned scattered signals. The basic idea is that the summation of two slightly different frequencies creates a new frequency as: sin ðθ + ΔθÞ + sin ðθ  ΔθÞ ¼ 2 sinθ cosΔθ

(5.92)

LDV is a very important and useful technique because it is a noncontact, noninvasive method that can be used for a wide variety of flows. For molecular sensing, measurement of blood flow [47–49] is one of the important application areas studied earlier [47]. Other measurements include electrophoretic light-scattering studies of bacterial cells [50], and metal and semiconductor nanoparticles [51, 52].

5.7 Light scattering

Raman spectroscopy Raman scattering In contrast to elastic scattering, where the energy is conserved before and after the process, Raman scattering is a process where the incident light interacts with molecules and some of the energy is lost or increased. Raman spectroscopy is a technique based on measurement of Raman scattering, which provides information about vibrational and rotational modes in molecules. In Raman scattering, an incident photon allows a molecule to transit from one vibrational or rotational state to another. The energy difference between the two states results in a shift in the frequency of emitted photon. When the new energy state is higher than the initial state, the scattering is called Stokes Raman scattering. The frequency of the emitted photon will be shifted to lower. The shift is called a Stokes shift. When the new state is lower than the initial state, it is called anti-Stokes Raman scattering. The shift is called anti-Stokes shift. Spectroscopic techniques are crucial in separating the weak Stokes and antiStokes scattering from the intense Rayleigh scattering of the excitation laser light. Fig. 5.50 shows energy diagrams for types of scattering found in Raman spectroscopy. Although Raman scattering has some similarities to fluorescence excitation, they are different phenomena. In the process of fluorescence excitation, the incident light is completely absorbed by the molecule, which is transferred to an excited state. Fluorescence emission occurs after a certain time characterized as fluorescence lifetime (109 to 107 s). Raman scattering, on the other hand, is a spontaneous effect. The wavelengths of fluorescence emission are defined by the energy levels of the molecule. Fluorescence emission is observed only when it is excited by a photon within a certain wavelength range. Raman scattering can take place at any frequency of excitation. Peaks of scattering maintain a constant separation from the excitation Energy level v0 > v1

v0 = v1

E0 = hv0

v0 < v1

E1 = hv1 E1 = hv1

E0 = hv0

E1 = hv1

Vibrational modes

E0 = hv0

Rayleigh scattering

FIG. 5.50 Stokes scattering and anti-Stokes scattering.

Stokes scattering

Anti-Stokes scattering

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CHAPTER 5 Optical transducers

frequency. Unlike the case with fluorescence spectroscopy, the absolute frequency or wavelength of a scattered light does not have a significant meaning. In Raman spectroscopy, the energy shift from the excitation is discussed as the Raman shift: Δw ¼

1 1  λ0 λ1

(5.93)

where λ0 and λ1 are the wavelengths of excitation and scattering, respectively. The Raman shift is usually measured in wavenumbers [cm1] (kayser). The transferred energy ΔE is found from the following relationship:


1 1 ΔE ¼ hν0  hν1 ¼ hc  λ0 λ1



(5.94)

where h is Planck constant, c is the speed of light, and ν0 and ν1 are the frequencies of excitation and scattering lights, respectively.

Raman spectroscopy Raman spectroscopy is a powerful tool in chemistry and solid-state physics. It is used to find vibrational information specific to chemical bonds and structure of molecules. Knight and White (1989) reported the characterization of diamond films based on Raman spectroscopy [53]. Although diamond films are all composed of carbon atoms, the characteristics of CdC bonds are different in different materials. Each band in the Raman spectrum corresponds to a specific vibrational mode within the molecule. The band at 1580 cm1 found in graphitic carbon (Fig. 5.51A) is known as the G-band. The band corresponds to vibration of sp2 carbon atoms, and is not significant in amorphous carbon (Fig. 5.51B). The band at 1357 cm1 in amorphous carbon is known as the D-band. The D band corresponds to the vibrational mode associated with graphene edges and found in disordered polycrystalline and noncrystalline graphitic carbons. The D-band is often called the disorder band. The D/G intensity ratio is often used as a measure of the quality of carbon materials. Raman spectroscopy also plays critical roles in characterizing newly discovered carbon nanomaterials such as graphene or carbon nanotubes. The important feature of monolayer graphene is the G0 band, also known as 2D-band, at about 2700 cm1. It represents a lattice vibrational process but is not related to defects as the D-band. In graphene, the G’ band is observed even when the D-band is not found. The G0 band is also found in graphite (see Fig. 5.51A) but not as significant as in graphene. Fig. 5.52 is an example of the Raman spectrum of a graphene edge, which clearly shows the D, G, and G0 bands [54]. Carbon nanotubes are formed by graphene sheets rolled at specific angles (chiral angles; see Chapter 7, Section 7.7.1). In Fig. 5.53, we can observe the D, G, and G0 bands as expected. The important mode specifically found in nanotubes is radial breathing mode (RBM) bands, which are observed in 100–300 cm1. The bands correspond to the radial expansion and contraction. The RBM bands are characteristic resonant peaks of single-walled carbon nanotubes (SWCNTs). They are not observed in MWNT, because the multi walls restrict radial mode vibrations. The frequency of RBM bands is correlated to the diameter of nanotubes [54a].

Graphitic carbon

Amorphous carbon 1343

1580

1591

Polycrystalline graphite 2710

1357

Glassy carbon

1576

Highly oriented pyrolytic graphite 2719

1580

Relative intensity

Relative intensity

2680 2924 1555

Diamond-like carbon 1357 1586

Coke

Natural graphite crystal

1360 1584

2724

500 1000 1500 2000 2500 3000

(A)

Wavenumber

Charcoal 500 1000 1500 2000 2500 3000

(B)

Wavenumber

FIG. 5.51 Raman spectra of carbon materials. Adapted from D.S. Knight, W.B. White, Characterization of diamond films by Raman spectroscopy, J. Mater. Res. 4 (1989) 385–393.

FIG. 5.52 Raman spectrum of a graphene edge. Reprinted from L. Malard, M. Pimenta, G. Dresselhaus, M. Dresselhaus, Raman spectroscopy in graphene, Phys. Rep. 473 (2009) 51–87, with permission from Elsevier.

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FIG. 5.53 Raman spectra from: (A) HiPco SWNT bundles and (B) a metallic (top) and a semiconducting (bottom) SWNT. The RBM-band, G-band, and G0 -band are found in the spectra. Reprinted from M.S. Dresselhaus, G. Dresselhaus, R. Saito, A. Jorio, Raman spectroscopy of carbon nanotubes, Phys. Rep. 409 (2005) 47–99, with permission from Elsevier.

Surface-enhanced Raman spectroscopy Surface-enhanced Raman spectroscopy (SERS) utilizes enhanced Raman scattering of molecules adsorbed on surfaces of metals such as silver or gold. One theory that explains the enhancement is based on localized surface plasmons on the metal surface [55]. Experimentally measured enhancement factors can be as much as 1014 to 1015 [56]. Many utilize silver or gold nanoparticles prepared in a solution [57] or immobilized on a substrate [56, 58]. Others utilize metal thin films deposited on substrates [59, 60]. Metal surfaces are often roughened to have a similar enhancement effect to nanoparticles. Local enhancement with a metal tip of scanning probe microscopy (SPM) has been also reported [61]. Metal nanoparticles can be functionalized to detect specific target molecules. Fig. 5.54A shows an example of highly sensitive detection of prostate-specific antigen (PSA), which is commonly used as a prostate cancer marker [59]. Gold nanoparticles with diameters of 30 nm are functionalized with PSA specific antibodies and molecular labels which show intense Raman scattering (Raman scatterer). The gold nanoparticles enhance the signal from the Raman scatterer. The detection scheme was based on sandwich enzyme-linked immune-sorbent assay (ELISA), where antigens are first captured by primary antibodies immobilized on a goldcoated glass substrate, and then labeled by Raman scattering gold nanoparticles functionalized with secondary antibodies. Fig. 5.54B shows Raman spectra for different PSA concentrations and a dose-responses curve. Detection limit of 1 pg/mL in human serum has been achieved (PSA levels of more than 4 ng/mL may be considered suspicious in clinical cancer screening).

5.7 Light scattering

FIG. 5.54 (A) Surface-enhanced Raman spectroscopy configuration. (B) Measured signals. Reprinted with permission from D.S. Grubisha, R.J. Lipert, H.-Y. Park, J. Driskell, M.D. Porter, Femtomolar detection of prostate-specific antigen: an immunoassay based on surface-enhanced Raman scattering and immunogold labels, Anal. Chem. 75 (2003) 5936–5943, Copyright 2003, American Chemical Society.

In Ref. [62], SERS was used for in vivo targeting and detection. Gold nanoparticles (60 nm diameter) are functionalized with the epidermal growth factor receptor (EGFR) and Raman scattering molecules and injected into a mouse bearing a tumor. Raman spectra from the tumor and the lever locations were measured 5 h after injection. Fig. 5.55A and B were measured with targeted and untargeted nanoparticles, respectively. Raman scattering of the gold nanoparticles is clearly observed from the lever site in the targeted measurement. SERS has been utilized for in vivo and in vitro glucose sensing. Duyne et al. used the metal film over nanospheres (FON) by depositing a thin Ag film onto a selfassembled, close-packed 2D array of nanospheres. This process creates periodic arrays of nanoscale metal nanoparticles. The AgFON substrates were then modified with a mixed self-assembled monolayer (SAM) consisting of decanethiol (DT) and mercaptohexanol (MH), and used for the SERS measurements of glucose sensing [55]. The substrate is implanted in a rat, and in vivo measurements were also performed as shown in Fig. 5.56 [63].

291

FIG. 5.55 In vivo Raman spectroscopy for tumor detection. SERS spectra measured at the tumor and liver locations with (A) targeted and (B) nontargeted nanoparticles. (C) Photograph of a laser beam focusing on the tumor site or on the location of the liver. Reprinted by permission of Nature: X. Qian, X.-H. Peng, D.O. Ansari, Q. Yin-Goen, G.Z. Chen, D.M. Shin, et al., In vivo tumor targeting and spectroscopic detection with surface-enhanced Raman nanoparticle tags, Nat. Biotechnol. 26 (2007) 83–90, Copyright 2007.

FIG. 5.56 In vivo Raman spectroscopy for glucose sensing. Reprinted with permission from D.A. Stuart, J.M. Yuen, N. Shah, O. Lyandres, C.R. Yonzon, M.R. Glucksberg, et al., In vivo glucose measurement by surface-enhanced Raman spectroscopy, Anal. Chem. 78 (2006) 7211–7215, Copyright 2006, American Chemical Society.

5.8 Near-field scanning optical microscopy

Noninvasive glucose measurements were also reported by another group [64]. During the test, 461 Raman spectra of human skin from 17 subjects were measured along with glucose reference measurements provided by standard capillary blood analysis. Predicted glucose concentrations versus the reference values showed correlations with the mean absolute errors of 7.8%  1.8% (mean  std) with mean R2 values of 0.83  0.10.

5.8 NEAR-FIELD SCANNING OPTICAL MICROSCOPY The resolution of a conventional microscope is limited by Fraunhofer diffraction of light (see Appendix B). NSOM, also known as scanning near-field optical microscopy (SNOM), is a type of SPM that overcomes the resolution limit of conventional microscopes by utilizing a subwavelength sized light source [65–67]. The light source created at the scanning tip measures maps of subwavelength optical properties as well as nano-scale topographic profiles. The optical resolution of NSOM is directly related to the size of the light source at the tip, while the capability of topographic measurement relies on the same force sensing scheme as used in the atomic force microscopy (AFM). Principles and implementation of force sensing with a silicon-based scanning probe are described in Chapter 6, Section 6.3. A quartz tuning fork based sensing described in Chapter 6, Section 6.4.7 is also commonly used for NSOM. Fig. 5.57A shows a typical implementation of NSOM. As the light source at the probe tip scans the sample surface, the nanoscale optical interaction between the light source and the sample is recorded by a photo detector to form optical images. In many practical applications, the probe tip is fixed in the focal point of the detector optics and the sample stage moves to allow the light source to scan. The photo detector is typically located under the sample with the inverted microscope configuration. Side-viewing microscopes are also commonly used to detect scattered light. Fig. 5.57B summarizes types of NSOM tips. The most common type shown in (1) utilizes a nanometer-sized aperture, which defines the size of the light source. Usually, a metal-coated tapered optical fiber is used in this scheme [66]. Type (2) utilizes plasmonic enhancement that occurs at the metal tip. LSPR [68] (see Section 5.4.5) arises when excited by external illumination. An example of this scheme is the tipenhanced Raman spectroscopy (TERS) introduced in this section. Some type (2) probes are integrated with a nano resonator, i.e., a nanoscale metal pattern [22], which improves the plasmonic enhancement at the tip. Type (3) probes are attached with a small-sized light emitting element at the tip. Such fluorescent materials include organic dyes [69], QDs [70], and nanodiamonds [71]. Probe tips attached with a metal nanoparticle [20, 72] may be categorized as type (2), since they rely on the LSPR on the particle.

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CHAPTER 5 Optical transducers

Probe

Detector 2

Sample stage Scanning Light source

Scattering

Transmission/fluorescence Detector 1

(A) (1) Aperture

(2) Plasonic exication

Excitation

(3) Light source attachment (functional probes)

Metal tip · Organic dye · Quantum dots · Fluorescent NPs · Nanoscale LED Emission

Excitation Aperture

(B)

Emission

Emission

FIG. 5.57 Overview of the near-field scanning nanophotonic microscopy: (A) schematic of a standard NSOM and (B) types of NSOM tips. Aluminum d = 250 nm d = 160 nm

Glass

Evanescent decay

HE11

FIG. 5.58 Mode propagation in a fiber-based aperture tip. Reprinted with permission from B. Hecht, B. Sick, U.P. Wild, V. Deckert, R. Zenobi, O.J. Martin, et al., Scanning near-field optical microscopy with aperture probes: fundamentals and applications, J. Chem. Phys. 112 (2000) 7761, with permission of AIP Publishing.

5.8.1 APERTURE-BASED NSOM TIP Fig. 5.58 illustrates mode propagation in a type (1) tapered metal-coated fiber tip. Tapered structures are made by pulling heated optical fibers or chemical etching [66]. Metal is deposited by thermal evaporation. In an aluminum-coated tapered

5.8 Near-field scanning optical microscopy

waveguide (εm ¼  34.5 + j 8.5 and εd ¼ 2.16) with a propagating wavelength of 488 nm, only the HE11 mode is allowed for inner diameters between 250 and 160 nm. Beyond 160 nm, the HE11 mode goes into cutoff, and the mode field decays exponentially. Lower energy efficiency is one of the drawbacks of the tapered fiber-based system.

5.8.2 METAL PLASMONIC TIP Fig. 5.59 shows an example of a type (2) NSOM probe with a metal tip. In this example, the tip is integrated with a grating resonator that enhances the intensity of surface plasmons at the metal tip [22]. One advantage of this method is that a mechanically very sharp tip compared with an aperture probe is possible. The resolution is approximately the size of the tip apex (20–30 nm). The disadvantage is the strong background illumination, which makes fluorescent measurement difficult. Metal tip based probes are usually used for scattered light based imaging. Fig. 5.60 shows an example of TERS, where a silver coated tip employed in an NSOM setup is used to enhance the Raman signals [61]. Fig. 5.60A shows the experimental setup. Total internal reflection is used to create an evanescent field that locally excites organic dye, Rhodamine 6G molecules (RH-6G) on the surface. Fig. 5.60B shows the amplification of the near-field signal due to the field enhancement of the metallic tip. This amplification effect is not observed with a bare silicon tip, which was not coated with silver.

Side view

Far-field excitation Surface plasmon

1

2

3

4

Top view 5 μm

FIG. 5.59 Metal tip probe with an integrated plasmonic resonator. Reprinted with permission from C. Ropers, C. Neacsu, T. Elsaesser, M. Albrecht, M. Raschke, C. Lienau, Gratingcoupling of surface plasmons onto metallic tips: a nanoconfined light source, Nano Lett. 7 (2007) 2784–2788, Copyright 2007, American Chemical Society.

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FIG. 5.60 Tip-enhanced Raman microscopy: (A) experimental setup; (B) amplified near-field signal obtained with a metallic tip. Reprinted from N. Hayazawa, Y. Inouye, Z. Sekkat, S. Kawata, Metallized tip amplification of near-field Raman scattering, Opt. Commun. 183 (2000) 333–336, with permission from Elsevier.

5.8.3 FUNCTIONAL NSOM TIP A novel approach for type (3) probes that we introduce here is the integration of nano-scale QD-based light emitting diodes [73] (QDLEDs). One of the advantages of using QDLEDs is that the emission wavelengths can be easily tailored by choosing QDs with proper diameters. Fig. 5.61A shows multicolor emission from the QDLEDs integrated at the tip. The emission spectra of the LEDs are shown in Fig. 5.61B. The narrow bandwidth of QDLEDs provides considerable potential as excitation sources for fluorescence imaging. NSOM fluorescence imaging with the QDLED probe is performed to demonstrate a 50 nm-order resolution.

Problems

FIG. 5.61 (A) Electroluminescence (EL) from QDLED probe tip. Scale bars ¼ 50 μm. (B) Electroluminescence spectra of QDLEDs at probe tips. Reprinted from K. Hoshino, A. Gopal, M.S. Glaz, D.A. Vanden Bout and X. Zhang, Nanoscale fluorescence imaging with quantum dot near-field electroluminescence, Appl. Phys. Lett. 101, 2012, 043118, with the permission of AIP Publishing.

PROBLEMS 1. Total internal reflection (1) Find the critical angle for indexes n1 ¼ 1.43, n2 ¼ 1.00.

n1 = 1.43 n2 = 1.00

(2) Find Brewster’s angle for indexes n1 ¼ 1.00, n2 ¼ 1.52.

n1 = 1.00 n2 = 1.52

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CHAPTER 5 Optical transducers

2. Reflection and refraction A laser beam is reflected on an air-liquid interface. The angle between the incident and reflected beams is 140°. The refracted light is transmitted at 45°. The refractive index of air is n1 ¼ 1.0. What is the refractive index of the liquid? 3. Multistack thin film filters Calculate the output angle α for a light beam with an incident angle of α0 after passing through the five layers of the structure below.

4. Evanescent field The evanescent field induced by total internal reflection is expressed by Eq. (5.58). 

n j kt x n0 sinα 1



qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

kt z

n0 2

2 sin

2

α1

n1 Et ¼ Et0  e e |fflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflffl} traveling wave

exponential decay

Let us probe why the energy of the incident wave is not transferred in z direction. When the field is a time-periodic sinusoidal electromagnetic field, we can use the time-averaged Poynting vector defined in the following way: 1 S ¼ ReðE  H∗ Þ 2

The Poyinting vector indicates the energy flux density in a certain direction in average time. (1) (2)

Find H from Faraday’s law, assuming there is no magnetization component and H ¼ μ1 B. 0 Calculate the Poynting vector S and explain the result.

Problems

5. Polarization (1) Consider two vectors: pffiffiffi

1 3 E1 ¼ pffiffiffi  ejðω  t + 60°Þ , E2 ¼ pffiffiffi  ejðω  t30°Þ 3 3

We define a new vector: E3 ¼ E1 + E2

Simplify E3 in the form of:

E3 ¼



Ex E  ejðω  t + αÞ ¼ 0x jðω  t + βÞ Ey E0y  e

(2) (3)

Illustrate a pattern drawn by the real part of E3, namely Repeat (1) and (2) for:

E1 ¼

ReðEx Þ . Re Ey

pffiffiffi

1 3  ejðω  t + 60°Þ , E2 ¼ pffiffiffi  ejðω  t30°Þ 3 3

6. Polarization Let us consider a plane wave propagating along z-axis, as shown in the following equation.

z y

0 x

–1

Filter 1 or 2

E1 ¼



Ex 2ejðω  t + 30°zÞ ¼ Ey 2ejðω  t60°zÞ

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CHAPTER 5 Optical transducers

(1) (2)

(3)

(4)

Describe the pattern drawn by the real part of E1 at z ¼ 0. At z ¼  1, we put filter 1 that function that transmits 100% of x component and 5% of y component. Describe the pattern drawn by the real part of E2 at z ¼ 0. This type of filter is called a polarizer. We remove filter 1 and filter 2, which delay the phase of x component by 90°. The y component is not affected by the plate. Describe the pattern drawn by the real part of E3 at z ¼ 0. This type of filter is called a quarter wave plate. Filter 1 and filter 2 can be expressed by simple 2  2 matrixes as shown below. Find such matrixes. E2 ¼



a1 b1 a b E1 , E3 ¼ 2 2 E1 c1 d1 c2 d2

7. Interferometry The following figure shows the concept of dis interferometry-based distance measurement. A plane light wave E ¼ E0 e j(ωt-kz) propagates in the z direction. The wavenumber k is given as k ¼ 2π/λ, where λ is the wavelength. The half of the propagating light, E1, is reflected by a stationary half mirror at z ¼ z1. The other half, E2, is reflected by a moving mirror z ¼ z2. Show that the field intensity of the reflected light measured at z ¼ 0 can be used to measure the position of the moving mirror. Stationary half mirror

Moving mirror

z1

z2

E1 E2 z=0

z

8. Interference When a thin film of silicon dioxide is grown on a silicon wafer, the wafer shows different colors depending on the thickness of the oxide. Calculate the colors generated by oxide films with thickness 220, 440, and 500 nm. Use the refractive index of thermal oxide n ¼ 1.46.

n = 1.46

Problems

9. Propagation modes Let us consider a waveguide consists of two mirrors and air. A light with a wavelength of λ is propagating with an angle φ to the mirrors. The wave is polarized in the x direction. In a waveguide mode, a standing wave arises in the y direction. For this to happen, the field just before reflection at point A and the field just before reflection at C must be in phase. Find the condition for waveguide modes. y

y B q

d

k

Mirror 2 j

l

Air

j

A

(A)

Mirror 1

C

z

z

(B)

10. Photometric waveguide transducers (1) Describe the basic elements of a planar waveguide. Explain how light can be transmitted in the waveguide. (2) Describe three ways to couple light into a waveguide. (3) The following figure shows a fiber-based glucose sensor design. Describe the glucose-sensing mechanism.

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11. Waveguide-based sensors The following figure shows a Mach Zehnder waveguide molecular sensor. We use an input light wave given as: Ein ¼ E0 ejðωtkxÞ

where k ¼ 2π/λ, and λ is the wavelength in air. A part of the waveguide with a length of 1 μm is surface-functionalized as the measurement arm. The effective refractive index is n1. On the other side is a reference arm with the same dimensions and the effective refractive index of n0. When target analytes bind to the measurement arm, effective refractive index of the sensing part changes by Δn. (1)

(2)

Describe the operation principle of the Mach Zehnder waveguide biosensor. Write down the mathematical expression for the resulting output light wave Eout. How can the device be used for rapid detection of bacteria DNA? How can we use the reference arm in order to measure efficiently the changes induced by molecular adsorption? Measurement arm Index: n1

Ein

Eout

L Reference arm Index: n0

Mach Zehnder waveguide biosensor. 12. Surface plasmon resonance-based sensors The following figure shows a prism coupler-based SPR measurement using Keretschmann configuration. The relative dielectric constants of the cylindrical prism, metal, and dielectric material are 2.28, 25 + j1.44, and 1.76 respectively. The wavelength of the incident beam is 836 nm and the thickness of the metal layer is 200 nm. Find the optimum angle of the given structure (see Appendix C).

Prism: ep Metal: em Dielectric: ed

Surface plasmon

Problems

13. Texas Instruments SPR biosensors The schematic of a popular SPR sensor from Texas Instruments is shown in the following figure. (a) (b)

What does SPR stand for? Circle the sensing element in the figure. Explain the functions of the seven sensor components shown in the figure.

14. Absorbance (1) A laser beam with the initial intensity of I0 passes through a neutral density filter with the optical density of OD (¼ absorbance) ¼ 1. What is the intensity of transmitted light?

I0

I1

O.D. = 1

(2) When we have two filters with the optical density of OD ¼ 1, what is the total optical density? (3) A suspension of colloidal QD QDot525 from Life Technologies has the molar extinction coefficient of 360,000 cm1 M1 at 405 nm. If we prepare a sample with the concentration of 0.1 μM in a cuvette with an inside width of 1 cm, what is the optical density at 405 nm? (4) Calculate the absorption cross-section σ of QDot525. Use Avogadro’s constant 6.02  1023 mol1. 15. Molecular oximetry sensor design You are required to design an optical absorption based sensor to measure the oxygen content in blood. The absorption spectrum of hemoglobin and oxyhemoglobin are given in the following figure.

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(a) (b)

Based on the information given in the figure, describe the operation principle for such measurement. List any relevant mathematical equations. Draw a sensor device design schematic, labeling key components.

16. Fluorescence, Raman scattering (1) Explain the difference between fluorescence emission and Raman scattering. Use the keywords “vibrational modes,” “lifetime,” and “antiStokes shift.” (2) Explain what the mirror image rule is and why it happens. (3) Explain why the mirror image rule is not observed with QDs. 17. Fluorescence and waveguides As shown in the following figure, the top surface of a flat waveguide (n ¼ 1.67) is covered with buffer (n1 ¼ 1.22). The bottom surface of the waveguide is a cladding material. A fluorescent protein is bound to the surface of a waveguide, and its fluorescence is measured by capturing the light from the waveguide. Assuming you have a multimode fiber, estimate the maximum fluorescence (as a percentage of the total fluorescence emitted) that can be coupled back into the waveguide for the setup shown below. Assume that there are no losses once the light is coupled into the waveguide and on its way to the detector.

Detector

Light source

Fluorescence

Excitation

Fluorophore

References

18. Laser Doppler velocimetry A laboratory bought a new LDV, and two coherent laser beams of a wavelength of 650 nm intersect each other at the measuring point. However, the intersection angle 2θ is unknown, since the manual has been lost. A study that used the identical device reports a result that the measured Doppler frequency with a sample which moves 150 mm/s is 20 kHz. Find the value of 2θ.

Extinction coefficient (a.u.)

19. Bright field microscopy and dark field microscopy

Scattering

400

500

Absorption

600

700

Wavelength (nm)

We shall perform microscopic observation of a material whose absorption and scattering properties are given above. (1) (2)

If we use a bright field microscope, what color would be observed? Explain why. If we use a dark field microscope, what color would be observed? Explain why.

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