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Admittance loci design method for multilayer surface plasmon resonance devices
Sensors and Actuators B 117 (2006) 219–229
Admittance loci design method for multilayer surface plasmon resonance devices Chii-Wann Lin a,b,c,∗ , Kuo-Ping Chen a , Min-Chi Su a , Tze-Chien Hsiao d , Sue-Sheng Lee e , Shiming Lin f , Xue-jing Shi g , Chih-Kung Lee e a
Institute of Biomedical Engineering, College of Engineering and College of Medicine, National Taiwan University, No. 1, Sec. 1, Ren-Ai Road, Taipei 100, Taiwan, ROC b Department of Electrical Engineering, College of Electrical Engineering and Computer Science, National Taiwan University, No. 1, Sec. 4, Roosevelt Road, Taipei 106, Taiwan, ROC c Center for Nano Science and Technology, National Taiwan University, No. 1, Sec. 4, Roosevelt Road, Taipei 106, Taiwan, ROC d Department of Biomedical Engineering, I-Shou University, Taiwan, ROC e Institute of Applied Mechanics, College of Engineering, National Taiwan University, No. 1, Sec. 4, Roosevelt Road, Taipei 106, Taiwan, ROC f Center for Optoelectronic Biomedicine, College of Medicine, No. 1, Sec. 1, Ren-Ai Road, Taipei 100, Taiwan, ROC g Center for Measurement Standards, Industrial Technology Research Institute, 321 Kuang Fu Rd., Sec. 2, Hsinchu, Taiwan, ROC Received 1 April 2005; received in revised form 17 November 2005; accepted 17 November 2005 Available online 27 December 2005
Abstract Dielectric mirror types of multilayer structures have been applied to enhance the performance of surface plasmon resonance (SPR) devices. It demands a more robust design method than traditional Fresnel’s equations. An admittance locus is a kind of optical thin film design method which has been extensively used for high performance optical coatings. We have applied this method for the design of multilayer SPR devices, including symmetric (glass|Au(40 nm)–[TiO2 (20 nm)–SiO2 (20 nm)]4 –Au(30 nm)) and asymmetric (glass|Ag(50 nm)–[TiO2 (20 nm)–SiO2 (20 nm)]4 –Au(20 nm)) structure. It provides a much necessary guidance for the choices of suitable optical materials, thickness, and number of layers for the intended SPR performance. With a 633 nm light source and a BK7 coupling prism under water, one can shift the resonant angle toward the critical angle and have smaller half maximum band widths (HMBW) at (64◦ , 2◦ ) and (61.52◦ , 0.25◦ ) for symmetric and asymmetric designs, respectively. © 2005 Elsevier B.V. All rights reserved. Keywords: Admittance loci; Surface plasmon resonance; Dielectric mirror; Biosensor
1. Introduction In the past decade, the phenomena of surface plasmon resonance (SPR) have been extensively used to investigate optical constants and thickness of thin films [1], surface properties [2], and molecular interactions on the solid–liquid interface [3–7]. The concept of surface plasmons originates from the quanta representing of collective oscillation of high density free electrons in a metal, which are localized on an interface between a metallic and a dielectric surface. Its charge density fluctua∗
Corresponding author at: Medical Micro Sensor and System Laboratory, Institute of Biomedical Engineering, College of Engineering and College of Medicine, National Taiwan University, No. 1, Sec. 4, Roosevelt Road, Taipei 107, Taiwan, ROC. Tel.: +886 2 33665272; fax: +886 2 33665268. E-mail address: [email protected] (C.-W. Lin). 0925-4005/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.snb.2005.11.030
tions on the surface and field distribution along the interface can be well described by the formulation of Maxwell’s theory [8–10]. For the practical applications of SPR sensing device, we have to apply Fresnel equations to calculate the total reflectance from a multilayered structure. Such a multilayered structure can have very interesting and exciting optical properties which strongly depend on the used materials, layer thickness, and architecture. Other than the traditional Kretschmann (attenuated total reflectance (ATR)) and Otto (frustrated total reflectance (FTR)) configurations, several novel devices based on multilayered structure of mixed hybrid configuration have been reported in literatures, which include long-range surface plasmon resonance (LRSPR) [8–10] and coupled plasmon waveguide resonance (CPWR) [11]. Recently, we have also reported a design based on a dielectric mirror type of alternating dielectric multilayer structure [12,13]. In this paper, we will discuss
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a general design method, admittance loci, which can be used for all these designs in details. It provides a systemic approach to the design of SPR devices, especial for the fine-tuning of resonant angle or wavelength with knowledge of optical properties of dielectric materials in the applications of biosensors or biochips. The admittance loci method provides a specific aim for the SPR design, which is near zero reflectance with a specified resonant angle under a chosen wavelength. Combined with of the optical parameter database, especially for biomolecules, it can be a unique and powerful tool for multilayer optical biosensors/biochips. Even though, this method was first introduced in 1992 by Macleod [14] and recently in his book [15], it has not been fully explored in the SPR device design yet. It might be due to most of the SPR sensors use relatively few layers of structure as in the traditional Kretschmann, Otto, LRSPR, or CPWR devices. However, it becomes an important issue in our new device, which requires stacking of thin films to fine tune the resonant properties. It is thus our purpose in this paper to further elucidate this method for the design of SPR devices. We will use two traditional SPR designs, e.g., Kretschmann and Otto types, and two novel multilayer designs, e.g., symmetric and asymmetric dielectric mirror types as examples. 2. Materials and methods 2.1. Surface plasmon resonance Surface plasmon oscillation is the collective longitudinal fluctuation of free electrons on a metallic/dielectric boundary. Such an oscillation has a frequency of ω, which is a function of its wave vector κx . For a free electron gas, its plasma fre quency can be calculated by ωp = 4πne2 /m, where n is the bulk electron density and m is the mass of oscillating electrons. These charge fluctuations, which can be localized in the z direction, are accompanied by a mixed transversal and longitudinal electromagnetic field. The field can be described by E = E0± exp[+i(kx x ± kz z − ωt)], where kx = 2π/λp = ω/c (ε1 ε2 /ε1 + ε2 )1/2 , kz is proportional to the 1/kx , λp is the wavelength of the plasma oscillation, and ε is the dielectric constant of materials. The field amplitude of the SPs decreases exponentially as exp(−|kzi ||z|) at the interface in both metal and dielectric layers. 2.2. Optical admittance 2.2.1. Single interface system The refractive index of a light beam propagating on a medium is defined as N = c/v, where constant c is the velocity of light in vacuum, and v is the light speed in the material. This can also be expressed as n − ik to take into account of the energy loss caused by the material, where the real number n is the refractive index, and the imaginary part k is the extinction coefficient. Fig. 1(a) shows an interface of two materials with complex refractive indices N0 and N1 , respectively where the light beams obliquely from N0 to N1 .
Fig. 1. Schematic diagram and notation used for theoretical analysis at the interface of (a) two different materials, which have complex refractive indices, N0 and N1 ; and (b) multi-layer with thin film thickness d with refractive index N1 on a substrate with refractive index N2 . The light beam is obliquely incident from N0 to N1 , the E field direction is out of the paper, and the H field is continuous at the boundary.
The total E field and H field can be expressed as
+ − + E0I + E0r = E1T
+ − + H0I − H0r = H1T
.
(1)
Note that the direction of the E field along E// and H// is continuous at the boundary, where a positive value (+) is designated as the incident direction, and a minus value (−) is designated as the opposite direction. Furthermore, let I represent the incident direction; r, the reflected position; and T, the transmitted direction. The optical admittance is defined as the ratio of magnitudes of the magnetic and electric fields of the wave, which has a phase factor of the form exp[i(ωt − κz)] for a harmonic wave propagating along the positive direction of z axis. The optical admittance, y, is expressed as y=
H . E
(2)
Combining Eqs. (1) and (2), the amplitude of the reflection coefficient ρ becomes ρ=
− E0r y0 − y1 + = y +y , E0I 0 1
(3)
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The optical admittance y = N × Y0 , where Y0 is the free space admittance. Y0 = 1/377 simems. The reflectance is N0 − N1 2 R = (ρρ∗ ) = . (4) N0 + N 1 As shown in Fig. 1(a), when a light beam strikes obliquely at an angle θ 0 , the refractive angel θ can be calculated by using Snell’s law as N0 sin θ0 = N1 sin θ.
(5)
At different polarization states, the optical admittance of an obliquely incident light beam changes to p-wave (TM) : s-wave (TE) :
N H = , E cos θ cos θ H cos θ = N cos θ. ηs = E ηp =
(6) (7)
2.2.2. Multilayer system For a multilayer system, we first consider the reflectance of a thin film (N1 ) on a substrate (N2 ). The relationship of E and H at the boundaries of a and b, as shown in Fig. 1(b), is + + iδ1 − − −iδ1 Ea1 = Eb1 Ea1 e = Eb1 e and (8) + + iδ1 − − −iδ1 . Ha1 = Hb1 e Ha1 = Hb1 e
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layer case. The characteristic matrix can likewise be used to obtain an equivalent admittance and reflectance: ⎡ i sin δj ⎤ a cos δj B 1 Ea ⎣ ⎦ ηj ⇒ = . (14) C ηsub Ha j=1 iηj sin δj cos δj The reflectance can then be written as η0 − Ye 2 R= . η0 + Y e
(15)
2.2.3. Total internal reflectance We will now discuss the special case of total internal reflectance (TIR). TIR happens as the incident angle is larger than critical angle when light incident from dense medium to rare medium. As shown in the Fig. 2, when θ 0 > θ c ⇒ sin θ 1 > 1, θ 1 is a comples number, and making: 1/2
η1s = n1 cos θ1 = n1 (1 − sin2 θ1 ) 1/2 n0 sin θ0 2 1/2 = n1 1 − = (n21 − n20 sin2 θ0 ) . n1 (16)
The (+) sign means it is along the positive z-direction, the (−) sign designates the opposite direction, and δ1 is the phase factor due to thin film layer one. The phase factor is a function of the refractive index, thickness, incident angle and wavelength. This is defined as 2πN1 d cos θ1 δ1 = . (9) λ Therefore, Eq. (8) can be rewritten either as ⎧ ⎨ E = E+ + E− = E cos δ + iHb sin δ a 1 1 b a1 a1 η1 . (10) ⎩ + − Ha = Ha1 + Ha1 = iη1 Eb sin δ1 + Hb cos δ1 And in a matrix form, ⎤ ⎡ i sin δ1 cos δ1 Eb Ea ⎦ ⎣ η1 = . Ha Hb iη1 sin δ1 cos δ1
(11)
The above 2 × 2 matrix is known as the characteristic matrix (M1 ) of the thin film. We can define the equivalent admittance (Ye ) as Ye =
Ha , Ea
and let Ye = C/B, then Eq. (12) becomes ⎤ ⎡ i sin δ1 cos δ1 1 B η1 ⎦ . =⎣ η2 C iη1 sin δ1 cos δ1
(12)
(13)
With this equivalent admittance, determining the reflectance of a multiple layer device on a substrate is similar to the single
Fig. 2. Reflectance at the prism (n0 = 1.5)–air (n1 = 1) interface due to s- and p-polarization of incident light.
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The result of the TIR admittance is a pure imaginary number, negative for s-polarization and positive for p-polarization. By the correction of oblique incident, the admittance of p and s polarization can be written as follows: ⎧ 1/2 ⎪ i(n2 sin2 θ0 − n2 ) ⎪ ⎪ = −iS ⎨ ηs = − 0 cos θ0 . (17) ⎪ n2 ⎪ ⎪ ⎩ ηp = = +iP ηs For p-wave, the admittance locus will start at the real axis and approach to ∞, as the incident angle becoming larger. Beyond the critical angle, the admittance will go to the positive imaginary axis and approaching zero with reflectance being 100%. And swave goes in the other way from the real axis to the negative imaginary axis passing by zero [15]. 2.3. Admittance loci design method Other than the reflectance, we can design a multilayer device by using the equivalent admittance approach. As shown in Fig. 3, as the incident light emits from the surrounding medium onto a multi-layer system, it can be treated as an equivalent admittance of ye , as defined in Eq. (12). It can be used to visualize the optical behavior of thin films, as we move a virtual reference plane from the substrate admittance (ysub ) to the front surface of the multi-layer. The equivalent admittance, ye , beyond the reference plane will change due to the thin film thickness change. These changes can be traced from the plot of ye on the complex plane and the trace is called admittance diagram or admittance loci. This method has been successfully applied for thin-film designs of high-reflection (HR) and anti-reflection (AR) coatings in the past. We will discuss the SPR sensor design in details in the following sections.
Fig. 3. Equivalent admittance of multi-layer over-coatings, where η0 , ηsub , and ηe are the admittance of the surrounding medium, substrate, and equivalent admittance, respectively, and treated as if moving a virtual reference plane (Ref) from the substrate admittance (ysub ) to the front surface of the multi-layer.
2.3.1. Single layer of dielectric material We will first begin with a simple case and its behavior on a complex plane, a single layer of dielectric thin film (y) and the equivalent admittance (ye ) with fixed wavelength and incident angle. One layer structure is y0 |y|ysub , and δ means the phase thickness. The equivalent admittance is: ye = α + iβ =
C ysub cos δ + iy sin δ = . B cos δ + i(ysub /y) sin δ
(18)
Making real and imaginary parts on both sides of Eq. (18) equal, we can get: ⎧ ysub ⎪ β sin δ = ysub cos δ ⎨ α cos δ − y , (19) y ⎪ ⎩ β cos δ + sub α sin δ = y sin δ y ⎡ ysub ⎤ α − ysub − β y ⎢ ⎥ cos δ = 0. (20) ⎣ ⎦ ysub sin δ β α −y y For non-trivial solution of cos δ and sin δ, we can have the solutions as follows: ysub α − y − β sub y = 0, ysub β α − y y ys ys ⇒ (α − ys ) α − y + β2 = 0 (21) y y α−
1 2
ysub +
y2 ysub
2 + β2 =
2 1 y2 ysub − . 4 ysub
(22)
As indicated in this equation, for a dielectric layer of admittance, it is a circle starting from (ysub , 0) with clockwise spiral due to the changes of film thickness and cross the real axis again at (y2 /ysub , 0) for every quarter-wavelength thickness. The starting point can be anywhere on the circular locus. It will simply result in a different circle that will be centered on the real axis and cut it in two points α and β such that αβ = y2 . One can then plot for isoreflectance contours, isophase contours, or electricfield contours for different purposes of visualization. One type of representation is the plot of equal reflective intensity contours, isoreflectance contours on the admittance diagram to know the performance of the final design. The centers of isoreflectance contours are given by [y0 (1 + R)/(1 − R), 0] and their radii by 2y0 R0.5 /(1 − R). Fig. 4 shows an example locus of a TiO2 thin film (n = 2.27) with thickness from 0 to 80 nm on top of a glass substrate (n = 1.5) in air. 2.3.2. Single layer of metal For the special case of SPR, we will examine the admittance loci about ideal metal with absorbance (y = −ik) or high performance metal (high k/n value for y = n − ik), as in a Kretschmann type SPR device where the prism is coated with a single highperformance metal layer. We are treating the glass prism as the incident medium and the surrounding air as the substrate.
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in the ideal metal and from (−n, k) to (n, −k) in the high performance metal. The diagram will be rotated slightly about the origin so that the points where all circles intersect are (n, −k) and (−n, k) [15]. 3. Results and discussions 3.1. Simulation program for thin film design
Fig. 4. Examples of dielectric admittance loci design. The clockwise trace of the admittance locus of a 80 nm layer of TiO2 on top of a glass substrate will start from the substrate (ysub , 0) and follow the equation passing through (y2 /ysub , 0) then end at its designed thickness.
Thus, the starting admittance for the film is on the imaginary axis, negative part for s-polarization and the positive part for p-polarization. It will show a near zero reflectance at a particular angle of incident and metal thickness. The condition is very sensitive to the angle of incidence. This very narrow drop in reflectance to a very low value is a surface plasmon wave on the metal film. The phase thickness will become a pure imaginary number under such circumstance and is shown as follows: δ=
2π (−ik)d = −iγ, λ
cos δ = cos hγ sin δ = −i sin hγ
.
The characteristic matrix of the film will become, ⎤ ⎡ i B 1 cos hγ sin hγ ⎦ =⎣ . k C ysub −ik sin hγ cos hγ
(23)
(24)
(25)
Because ye = C/B = α + iβ, the relation of real and imaginary parts of admittance loci is ⎧ β ⎪ ⎨ (α − ysub ) cos hγ = ysub sin hγ k . (26) ⎪ ⎩ β cos hγ = − k + α ysub sin hγ k For non-trivial solution of γ, we can get the locus of α and β, α2 − 2
2 − k2 ysub α + β2 = k 2 . 2ysub
(27)
2 − k 2 /2y , 0) It is also a circle locus with a center on (ysub sub 2 2 and a radius of ysub + k /2ysub . It goes from (0, k) to (0, −k)
We have implemented the above mentioned algorithm in a graphic user interface (GUI) environment (MATLAB version 6.5, Mathworks Inc., USA). The source code of SPR admittance loci design program is attached as a supplement. There are control and text inputs to set-up the layer structure and change the values of used parameters in the program. The results are shown in both admittance loci (Im(Ye ) versus Re(Ye )) and reflectance graphs (R% versus incident angle). For the use of this design method to modulate the SPR angle, we would first plot the original R − θ graph and then identify a new resonant angle and the incident angle that we want to start with. At the selected incident angle, we can now calculate the effective admittance and plot its position on the complex plane of admittance by selecting different visualization methods. The graph will show the trace of Ye according to the designed layer structure until the reflectance is within 5% or less of the isorelectance contour. We can plot the R − θ graph with specified parameters to view the final performance of possible designs. 3.2. Design of two traditional SPR devices We will discuss the design of SPR devices by using above mentioned method. SPR phenomena normally happen when the incident angle is larger than a critical angle, i.e., under TIR condition. In general, if we put a dielectric thin film, the admittance will move along the imaginary axis in a positive direction, and return to the starting point every half-wave thickness. The only way to make the admittance leave the imaginary axis is by a metallic layer. From previous equations, for the p-wave beyond the critical angle, if we add a thin metal film, the admittance will leave the imaginary axis, and have the chance to approach to the real axis. This is the most often used configuration of SPR, Kretschmann type device as shown in the Fig. 5(a) with a 633 nm p-polarized light, a BK7 prism, and a 50 nm Au film under water. It results in a typical resonant peak around 74◦ with final admittance at (1.45932, −0.02247) and 0.04% reflectance. The other often cited SPR configuration is Otto type, which is shown in the Fig. 5(b), which involves excitation of surface waves through an evanescent wave in a FTR layer. The admittance locus for p-polarization of a layer used beyond the critical angle is a circle that is described in an anticlockwise direction. For the correct angle of incident and dielectric layer thickness, the reflectance can be made zero. In this example, we used a 633 nm p-polarized light, a BK7 prism, a 18 nm air gap, and a 65 nm Au film under water. It results in a resonant angle of 74.5◦ with final admittance of (1.48818, −0.00667) and 0.009% reflectance.
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Fig. 5. Admittance loci and SPR (R − θ) spectra of two traditional SPR devices of (a) Kretschmann type (50 nm Au); (b) Otto type (18 nm air and 65 nm Au) are shown as examples. The incident light is 633 nm through a BK7 prism and under water.
3.3. Dielectric mirror type multilayer structure SPR phenomenon is a unique combination of total internal reflection from a high refractive index prism to a high performance metal thin film. Its performance can be further enhanced by using dielectric layers as in the many cases of high performance optical coatings. The important design issues include how to create the zero of reflectance at any desired angle of incidence beyond a critical angle and the width of the resonant. In the following sections, we will discuss two of the cases with symmetric and asymmetric structure for tunable SPR device design. Table 1 lists all the used materials along with its optical constant for reference. 3.3.1. Symmetric structure We recently reported a symmetric multilayer SPR device by using a dielectric mirror of alternating high/low refractive index materials to modulate the SPR resonant conditions Table 1 Optical constants of the materials used in the design cases (at 633 nm) Material
n
k
H2 O Au TiO2 SiO2 Ag Glass
1.33168 0.0666 2.27886 1.45705 0.16172 1.51508
0 4.047 0.00015 0 3.21182 0
[13]. In this case, we proposed to shift the SPR angle from 74 to 64◦ with a 633 nm light source on a BK7 coupling prism under water, which is equivalent to usage of a SF2 prism. With a single layer of 50 nm gold film, its resonant angle is close to 74◦ , where Ye = 1.4593 − i × 0.0225 is close to Yo and its reflectance is near zero. However, at 64◦ , the starting point Ye = 0.0686 − i × 1.5465, is close to the imaginary axis and its reflectance is higher than 80% without proper device design. By using the symmetric structure of glass|Au(40 nm)–[TiO2 (20 nm)–SiO2 (20 nm)]4 –Au(30 nm) shown in Fig. 6(a), its admittance loci will leave the imaginary axis and get close to Yo as shown in the Fig. 6(b). The final value is 1.3664 + i × 0.4685 and within the 5% iso-reflectance region (2.83%). The resultant R − θ spectrum (solid line) is shown as in the Fig. 6(c) compared to the traditional design of single layer of Au film (dashed line). Our laboratory tests confirmed that, under water, there was a 10◦ shift in resonant peak position towards the critical angle (from 74◦ in a conventional single-layer Au film), and a 3.25 times decrease in FWHM (the half-peak width). This device also resulted in a wider dynamic range of an up to a 1.50 refractive index unit (RIU), compared to 1.38 RIU in a conventional single-layer Au film. The calculated intensity sensitivity was about twice the improvement over the conventional single-layer Au film [13]. 3.3.2. Asymmetric multilayer structure It has been well known that silver has better SPR performance than gold. However, its does tarnish when exposed to
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Fig. 6. (a) The symmetric structure of the SPR device with glass|Au(40 nm)–[TiO2 (20 nm)–SiO2 (20 nm)]4 –Au(30 nm); (b) its admittance loci; and (c) SPR spectrum (solid line) with a resonant angle at 64◦ and a HMBW of 2◦ compared to a traditional one (dashed line).
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the sensing environment due to surface contaminations of silver sulphide or silver chloride. It is thus often required an overcoating dielectric layer to protect it from corrosion or a high performance multilayer coating to enhance its optical performance. It is thus reasonable to replace the inner metal layer of Au with Ag to have further enhancement of SPR performance with asymmetric structure as shown in the Fig. 7(a). The admittance locus of the dielectric layer between the air exit medium and the silver layer starts on the imaginary axis and
must remain on the axis if there is no absorption in the layer. Provided the angle in the dielectric layer is not beyond critical, the locus simply climbs to the top of the imaginary axis and disappears to re-enter the diagram at the very foot of the imaginary axis to climb upward and repeat the pattern, if the layer is thick enough. We recently introduced a novel design of an asymmetric multilayer SPR device to modulate the SPR resonant conditions [14]. In this case, we also used a 633 nm wavelength light source on a BK7 coupling prism under water.
Fig. 7. (a) The asymmetric structure of the SPR device with glass|Ag(50 nm)–[TiO2 (20 nm)–SiO2 (20 nm)]4 –Au(20 nm); (b) its admittance loci; and (c) SPR spectrum (solid line) with a resonant angle at 61.52◦ and a HMBW of 0.25◦ compared to the traditional design of a single layer of Au film (dashed line).
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Table 2 Performance comparisons of different SPR devices: (a) 50 nm Au film; (b) symmetric structure design; (c) asymmetric structure design (all with 633 nm through a BK7 prism and under water)
Single layer Au Symmetric multilayer Asymmetric multilayer a b c
SPR angle
HMBW
Dynamic range (RIU)a
Resolution (RIU)b
Intensity slopec
73.9 62.54 61.52◦
6.5 2 0.25◦
1.331–1.38 1.331–1.50 1.33–1.48
8.33 × 10−5 1.25 × 10−5 8.13 × 10−6
58.65 127.5 215.19
RIU is the refractive index unit. Angular measurement of 10−3 angular resolution. Intensity change (0–255)/1 degree shift.
The only difference in the structure design is the replacement of the bottom Au layer with a Ag layer to study its enhancement effect on SPR. With a single layer of 55 nm silver film, its resonant angle is close to 68◦ , where Ye = 1.4595 − i × 0.0226 is close to Yo and its reflectance is near zero. However, at 61.52◦ , the starting point (0.00000, 71.43949) is closed to the imaginary axis and its reflectance is about 100% without proper device design. By using the asymmetric structure, glass|Ag(50 nm)–[TiO2 (20 nm)–SiO2 (20 nm)]4 –Au(20 nm), its admittance loci will leave the imaginary axis and get close to Yo as shown in the Fig. 7(b). The final value is (1.33905, −0.57627) and within the 5% iso-reflectance region (4.28%). The resultant R − θ curve is shown in Fig. 7(c) with a resonant angle at 61.52◦ and a half maximum band widths (HMBW) of 0.25◦ .
3.4. Performance comparisons Table 2 shows the SPR performance of each presented design device as discussed in the previous sections. It is clear that with the admittance loci method we will be able to design the resonant angle by choosing proper dielectric materials and structure. It is especially prominent by using the dielectric mirror type of high/low refractive index structure to fine tune the resonant position and HMBW. With the similar structure used in the design case of symmetric and asymmetric devices, the later one shows a further enhancement of HMBW and resonant angle, which is approaching the critical angle. Such a unique behavior could be partly attributed to the above mentioned characteristics of the silver layer and its effect on the SPR behavior. The other interesting aspect could be observed by plotting out the parallel and
Fig. 8. The normal (a, c) and parallel (b, d) components of the electric field across a symmetric multilayer device vs. an asymmetric one, respectively. There are differences in the penetration depths as indicated in (a) and (c), and the parallel electric field across the last layer of Au film as indicated in (b) and (d).
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normal components of the electrical field across the structure as shown in the Fig. 8. There are differences in the penetration depths as indicated in the Fig. 8(a) and (c). The parallel electric field across the last layer of Au film has a different pattern in the symmetric and asymmetric design as indicated in the Fig. 8(b) and (d). Such a field pattern has been identified in the long range SPR to account for the field extension effect of the intermediate dielectric layer as “antisymmetric” (short range) and “symmetric” (long range) [8]. However, a single layer of a dielectric material as thick as several hundred nanometers is normally used in most of the literatures instead of our proposed designs. 4. Summary and conclusions The principal feature of our SPR design is the use of alternating dielectric layers to enhance the quality of the SPR signal and to modulate its resonant position. The thickness, number of layers, and other design parameters of the material used are optimized by using optical admittance loci analysis. The admittance locus is a kind of optical thin film design method which has been extensively used for high performance optical coatings. It provides a much necessary guidance for the choices of suitable optical materials, thickness, and number of layers for the intended performance. We have applied this method for the design of both symmetric and asymmetric multilayer dielectric mirror SPR devices and are able to fine tune the SPR resonant conditions with different metallic thin films of Au and Ag. With a 633 nm light source and a BK7 coupling prism under water, one can shift the resonant angle toward critical angle and have smaller half maximum band widths at (64◦ , 2◦ ) and (61.52◦ , 0.25◦ ) for symmetric and asymmetric designs, respectively. Bio-plasmonics, which use biomolecules as a part of the plasmon oscillating devices, can be designed for specific resonant conditions by using above mentioned admittance loci method. As in the design and development of biochips or biosensors as medical devices, it would be reasonable to find out the effective dielectric constants and thickness of biomolecules, e.g., DNAs or proteins, under specific operating conditions. Acknowledgments This project is supported in part by the National Science and Technology Program in Pharmaceuticals and Biotechnology, National Science Council, Taiwan, NSC (93-2323-B002-011, NSC93-2323-B002-017) and Council of Agriculture. We would like to thank Prof. Henry Co for valuable comments on this manuscript. References [1] H. Raether, Excitation of Plasmons and Interband Transitions by Electrons, Springer-Verlag, Berlin, 1980. [2] H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings, Springer-Verlag, Berlin, 1988 (Chapter 2). [3] A. Otto, Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection, Z. Phys. 216 (1968) 398.
[4] E. Kretschmann, Die Bestimmung optischer Konstanten von Metallen durch Anregung von Oberfldchenplasmaschwingungen, Z. Phys. 241 (1971) 313. [5] Z. Salamon, H.A. Macleod, G. Tollin, Surface plasmon resonance spectroscopy as a tool for investigating the biochemical and biophysical properties of membrane protein system. I. Theoretical principles, Biochim. Biophys. Acta 1331 (1997) 117–129. [6] Z. Salamon, H.A. Macleod, G. Tollin, Surface plasmon resonance spectroscopy as a tool for investigating the biochemical and biophysical properties of membrane protein system. II. Applications to biological systems, Biochim. Biophys. Acta 1331 (1997) 131–152. [7] J. Homola, S.S. Yee, G. Gauglitz, Surface plasmon resonance sensor: review, Sens. Actuators B 54 (1994) 3–15. [8] F.Y. Kou, T. Tamir, Range extension of surface plasmons by dielectric layers, Opt. Lett. 12 (1987) 367–369. [9] D. Sarid, Long-range surface-plasma waves on very thin metal film, Phys. Rev. Lett. 47 (1981) 1927–1930. [10] G.G. Nenninger, P. Tobiska, J. Homola, S.S. Yee, Long-range surface plasmons for high-resolution surface plasmon resonance sensors, Sens. Actuators B 74 (2001) 145–151. [11] Z. Salamon, H.A. Macleod, G. Tollin, Coupled plasmon-waveguide resonators: a new spectroscopic tool for probing proteolipid film structure and properties, Biophys. J. 73 (1997) 2791–2797. [12] C.-W. Lin, K.-P. Chen, C.-N. Hsiao, C.-K. Lee, S.-M. Lin, Design and fabrication of an alternative dielectric multilayer device for surface plasmon resonance sensor, Sens. Actuators B: Chem 113 (2006) 169– 176. [13] M.-C. Su, C.-N. Hsiao, C.-W. Lin, The design and application of asymmetric multilayer to SPR bio-sensor device, Proc. Chin. Biomed. Eng. Soc. Ann. Symp. 93 (2004) 670–673. [14] H.A. Macleod, Unconventional coatings, in: D.T. Moore (Ed.), Tutorials in Optics, Optical Society of America, Washington, DC, 1992, pp. 121–135. [15] H.A. Macleod, Thin-Film Optical Filters, third ed., Institute of Physics Publishing, Bristol, Philadelphia, 2001.
Biographies Chii-Wann Lin received his PhD degree from Department of Biomedical Engineering, Case Western Reserve University in 1993. He then joined the Center for Biomedical Engineering, College of Medicine, National Taiwan University in September 1993 as research assistant professor. He is now an associate professor at the Institute of Biomedical Engineering and also holds a joint appointment at the Department of Electrical Engineering, National Taiwan University. He is a member of IEEE EMBS, IFMBE and Chinese BMES. His research interests include biomedical micro-sensors, optical biochips, surface plasmon resonance, and nano-medicine. Kuo-Ping Chen received his BS degree in electrical and control engineering from National Chiao Tung University, Taiwan in 2002. He obtained his MS degree in biomedical engineering from National Taiwan University in 2004. He is currently serving his military duty. His research interests include surface plasmon resonance, bio-sensor systems, electronics and signal processing. Min-Chi Su received his BS degree in Electrical and Control Engineering from National Chiao Tung University, Taiwan in 2003. He obtained his MS degree in Biomedical Engineering from National Taiwan University in 2005. He is currently serving his military duty. His research interests include surface plasmon resonance, bio-sensor systems, electronics and signal processing. Tzu-Chien Ryan Hsiao received the MS and PhD degrees from the Institute of Physics at the National Sun Yat-Sen University and Institute of Biomedical Engineering at National Yang-Ming University, Taiwan, in 1996 and 2003, respectively. In 2003, he has been employed as an assistant professor of Institute Biomedical Engineering at I-Shou University, and now he is also a deputy director of biomedical research and development division of Hsinchu Biomedical Science Park. His research interests include neural networks, virtual instrument and multivariate spectral analysis.
C.-W. Lin et al. / Sensors and Actuators B 117 (2006) 219–229 Sue-Sheng Lee received her PhD degree from Institute of Applied Mechanics, National Taiwan University in July 2004. She then became a postdoctoral researcher in NTU Nano-BioMEMS group from August 2004 to August 2005, where she was in charge of the project “Special Type Multifunctional Optoelectronic Biochip System”. She is now a postdoctoral researcher in “Laboratoire de Photonique Quantique et Mol´eculaire” of l’Institut d’Alembert in Ecole Normale Sup´erieure de Cachan, in France. Her research interests include systems design and integration of biochip instrument and optical metrology. Shiming Lin received his PhD from the Institute of Biotechnology, University of Cambridge, United Kingdom in 1995. He is currently an associate professor at the Center for Optoelectronic Biomedicine, National Taiwan University. His research interests include nano-biotechnology and optoelectronic biotechnology, with a special focus on the molecular biomechanics of protein
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helix, viral surfaces and biomolecular interaction forces, as well as on the manufacture of optoelectronic bio-sensors and biochips. Xue-jing Shi received his BS in Civil Engineering from National Taiwan University, Taiwan, in 1998 and MS degree in Institute of Applied Mechanics from National Taiwan University, Taiwan, in July 2002. He became the researcher in Flow Laboratory, Center for Measurement Standards, and Industrial Technical Research Institute from August 2002. Chih-Kung Lee received his PhD degree from Cornell University in 1987. He worked at IBM’s Almaden Research Center in San Jose, California for seven years before returning to Taiwan. He is currently director general of Engineering and Applied Sciences at the National Science Council, Taiwan. He is concurrently a professor at the Institute of Applied Mechanics, National Taiwan University, and holds a joint appointment at the Institute of Engineering Sciences and Ocean Engineering, National Taiwan University.
Admittance loci design method for multilayer surface plasmon resonance devices Chii-Wann Lin a,b,c,∗ , Kuo-Ping Chen a , Min-Chi Su a , Tze-Chien Hsiao d , Sue-Sheng Lee e , Shiming Lin f , Xue-jing Shi g , Chih-Kung Lee e a
Institute of Biomedical Engineering, College of Engineering and College of Medicine, National Taiwan University, No. 1, Sec. 1, Ren-Ai Road, Taipei 100, Taiwan, ROC b Department of Electrical Engineering, College of Electrical Engineering and Computer Science, National Taiwan University, No. 1, Sec. 4, Roosevelt Road, Taipei 106, Taiwan, ROC c Center for Nano Science and Technology, National Taiwan University, No. 1, Sec. 4, Roosevelt Road, Taipei 106, Taiwan, ROC d Department of Biomedical Engineering, I-Shou University, Taiwan, ROC e Institute of Applied Mechanics, College of Engineering, National Taiwan University, No. 1, Sec. 4, Roosevelt Road, Taipei 106, Taiwan, ROC f Center for Optoelectronic Biomedicine, College of Medicine, No. 1, Sec. 1, Ren-Ai Road, Taipei 100, Taiwan, ROC g Center for Measurement Standards, Industrial Technology Research Institute, 321 Kuang Fu Rd., Sec. 2, Hsinchu, Taiwan, ROC Received 1 April 2005; received in revised form 17 November 2005; accepted 17 November 2005 Available online 27 December 2005
Abstract Dielectric mirror types of multilayer structures have been applied to enhance the performance of surface plasmon resonance (SPR) devices. It demands a more robust design method than traditional Fresnel’s equations. An admittance locus is a kind of optical thin film design method which has been extensively used for high performance optical coatings. We have applied this method for the design of multilayer SPR devices, including symmetric (glass|Au(40 nm)–[TiO2 (20 nm)–SiO2 (20 nm)]4 –Au(30 nm)) and asymmetric (glass|Ag(50 nm)–[TiO2 (20 nm)–SiO2 (20 nm)]4 –Au(20 nm)) structure. It provides a much necessary guidance for the choices of suitable optical materials, thickness, and number of layers for the intended SPR performance. With a 633 nm light source and a BK7 coupling prism under water, one can shift the resonant angle toward the critical angle and have smaller half maximum band widths (HMBW) at (64◦ , 2◦ ) and (61.52◦ , 0.25◦ ) for symmetric and asymmetric designs, respectively. © 2005 Elsevier B.V. All rights reserved. Keywords: Admittance loci; Surface plasmon resonance; Dielectric mirror; Biosensor
1. Introduction In the past decade, the phenomena of surface plasmon resonance (SPR) have been extensively used to investigate optical constants and thickness of thin films [1], surface properties [2], and molecular interactions on the solid–liquid interface [3–7]. The concept of surface plasmons originates from the quanta representing of collective oscillation of high density free electrons in a metal, which are localized on an interface between a metallic and a dielectric surface. Its charge density fluctua∗
Corresponding author at: Medical Micro Sensor and System Laboratory, Institute of Biomedical Engineering, College of Engineering and College of Medicine, National Taiwan University, No. 1, Sec. 4, Roosevelt Road, Taipei 107, Taiwan, ROC. Tel.: +886 2 33665272; fax: +886 2 33665268. E-mail address: [email protected] (C.-W. Lin). 0925-4005/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.snb.2005.11.030
tions on the surface and field distribution along the interface can be well described by the formulation of Maxwell’s theory [8–10]. For the practical applications of SPR sensing device, we have to apply Fresnel equations to calculate the total reflectance from a multilayered structure. Such a multilayered structure can have very interesting and exciting optical properties which strongly depend on the used materials, layer thickness, and architecture. Other than the traditional Kretschmann (attenuated total reflectance (ATR)) and Otto (frustrated total reflectance (FTR)) configurations, several novel devices based on multilayered structure of mixed hybrid configuration have been reported in literatures, which include long-range surface plasmon resonance (LRSPR) [8–10] and coupled plasmon waveguide resonance (CPWR) [11]. Recently, we have also reported a design based on a dielectric mirror type of alternating dielectric multilayer structure [12,13]. In this paper, we will discuss
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a general design method, admittance loci, which can be used for all these designs in details. It provides a systemic approach to the design of SPR devices, especial for the fine-tuning of resonant angle or wavelength with knowledge of optical properties of dielectric materials in the applications of biosensors or biochips. The admittance loci method provides a specific aim for the SPR design, which is near zero reflectance with a specified resonant angle under a chosen wavelength. Combined with of the optical parameter database, especially for biomolecules, it can be a unique and powerful tool for multilayer optical biosensors/biochips. Even though, this method was first introduced in 1992 by Macleod [14] and recently in his book [15], it has not been fully explored in the SPR device design yet. It might be due to most of the SPR sensors use relatively few layers of structure as in the traditional Kretschmann, Otto, LRSPR, or CPWR devices. However, it becomes an important issue in our new device, which requires stacking of thin films to fine tune the resonant properties. It is thus our purpose in this paper to further elucidate this method for the design of SPR devices. We will use two traditional SPR designs, e.g., Kretschmann and Otto types, and two novel multilayer designs, e.g., symmetric and asymmetric dielectric mirror types as examples. 2. Materials and methods 2.1. Surface plasmon resonance Surface plasmon oscillation is the collective longitudinal fluctuation of free electrons on a metallic/dielectric boundary. Such an oscillation has a frequency of ω, which is a function of its wave vector κx . For a free electron gas, its plasma fre quency can be calculated by ωp = 4πne2 /m, where n is the bulk electron density and m is the mass of oscillating electrons. These charge fluctuations, which can be localized in the z direction, are accompanied by a mixed transversal and longitudinal electromagnetic field. The field can be described by E = E0± exp[+i(kx x ± kz z − ωt)], where kx = 2π/λp = ω/c (ε1 ε2 /ε1 + ε2 )1/2 , kz is proportional to the 1/kx , λp is the wavelength of the plasma oscillation, and ε is the dielectric constant of materials. The field amplitude of the SPs decreases exponentially as exp(−|kzi ||z|) at the interface in both metal and dielectric layers. 2.2. Optical admittance 2.2.1. Single interface system The refractive index of a light beam propagating on a medium is defined as N = c/v, where constant c is the velocity of light in vacuum, and v is the light speed in the material. This can also be expressed as n − ik to take into account of the energy loss caused by the material, where the real number n is the refractive index, and the imaginary part k is the extinction coefficient. Fig. 1(a) shows an interface of two materials with complex refractive indices N0 and N1 , respectively where the light beams obliquely from N0 to N1 .
Fig. 1. Schematic diagram and notation used for theoretical analysis at the interface of (a) two different materials, which have complex refractive indices, N0 and N1 ; and (b) multi-layer with thin film thickness d with refractive index N1 on a substrate with refractive index N2 . The light beam is obliquely incident from N0 to N1 , the E field direction is out of the paper, and the H field is continuous at the boundary.
The total E field and H field can be expressed as
+ − + E0I + E0r = E1T
+ − + H0I − H0r = H1T
.
(1)
Note that the direction of the E field along E// and H// is continuous at the boundary, where a positive value (+) is designated as the incident direction, and a minus value (−) is designated as the opposite direction. Furthermore, let I represent the incident direction; r, the reflected position; and T, the transmitted direction. The optical admittance is defined as the ratio of magnitudes of the magnetic and electric fields of the wave, which has a phase factor of the form exp[i(ωt − κz)] for a harmonic wave propagating along the positive direction of z axis. The optical admittance, y, is expressed as y=
H . E
(2)
Combining Eqs. (1) and (2), the amplitude of the reflection coefficient ρ becomes ρ=
− E0r y0 − y1 + = y +y , E0I 0 1
(3)
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The optical admittance y = N × Y0 , where Y0 is the free space admittance. Y0 = 1/377 simems. The reflectance is N0 − N1 2 R = (ρρ∗ ) = . (4) N0 + N 1 As shown in Fig. 1(a), when a light beam strikes obliquely at an angle θ 0 , the refractive angel θ can be calculated by using Snell’s law as N0 sin θ0 = N1 sin θ.
(5)
At different polarization states, the optical admittance of an obliquely incident light beam changes to p-wave (TM) : s-wave (TE) :
N H = , E cos θ cos θ H cos θ = N cos θ. ηs = E ηp =
(6) (7)
2.2.2. Multilayer system For a multilayer system, we first consider the reflectance of a thin film (N1 ) on a substrate (N2 ). The relationship of E and H at the boundaries of a and b, as shown in Fig. 1(b), is + + iδ1 − − −iδ1 Ea1 = Eb1 Ea1 e = Eb1 e and (8) + + iδ1 − − −iδ1 . Ha1 = Hb1 e Ha1 = Hb1 e
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layer case. The characteristic matrix can likewise be used to obtain an equivalent admittance and reflectance: ⎡ i sin δj ⎤ a cos δj B 1 Ea ⎣ ⎦ ηj ⇒ = . (14) C ηsub Ha j=1 iηj sin δj cos δj The reflectance can then be written as η0 − Ye 2 R= . η0 + Y e
(15)
2.2.3. Total internal reflectance We will now discuss the special case of total internal reflectance (TIR). TIR happens as the incident angle is larger than critical angle when light incident from dense medium to rare medium. As shown in the Fig. 2, when θ 0 > θ c ⇒ sin θ 1 > 1, θ 1 is a comples number, and making: 1/2
η1s = n1 cos θ1 = n1 (1 − sin2 θ1 ) 1/2 n0 sin θ0 2 1/2 = n1 1 − = (n21 − n20 sin2 θ0 ) . n1 (16)
The (+) sign means it is along the positive z-direction, the (−) sign designates the opposite direction, and δ1 is the phase factor due to thin film layer one. The phase factor is a function of the refractive index, thickness, incident angle and wavelength. This is defined as 2πN1 d cos θ1 δ1 = . (9) λ Therefore, Eq. (8) can be rewritten either as ⎧ ⎨ E = E+ + E− = E cos δ + iHb sin δ a 1 1 b a1 a1 η1 . (10) ⎩ + − Ha = Ha1 + Ha1 = iη1 Eb sin δ1 + Hb cos δ1 And in a matrix form, ⎤ ⎡ i sin δ1 cos δ1 Eb Ea ⎦ ⎣ η1 = . Ha Hb iη1 sin δ1 cos δ1
(11)
The above 2 × 2 matrix is known as the characteristic matrix (M1 ) of the thin film. We can define the equivalent admittance (Ye ) as Ye =
Ha , Ea
and let Ye = C/B, then Eq. (12) becomes ⎤ ⎡ i sin δ1 cos δ1 1 B η1 ⎦ . =⎣ η2 C iη1 sin δ1 cos δ1
(12)
(13)
With this equivalent admittance, determining the reflectance of a multiple layer device on a substrate is similar to the single
Fig. 2. Reflectance at the prism (n0 = 1.5)–air (n1 = 1) interface due to s- and p-polarization of incident light.
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The result of the TIR admittance is a pure imaginary number, negative for s-polarization and positive for p-polarization. By the correction of oblique incident, the admittance of p and s polarization can be written as follows: ⎧ 1/2 ⎪ i(n2 sin2 θ0 − n2 ) ⎪ ⎪ = −iS ⎨ ηs = − 0 cos θ0 . (17) ⎪ n2 ⎪ ⎪ ⎩ ηp = = +iP ηs For p-wave, the admittance locus will start at the real axis and approach to ∞, as the incident angle becoming larger. Beyond the critical angle, the admittance will go to the positive imaginary axis and approaching zero with reflectance being 100%. And swave goes in the other way from the real axis to the negative imaginary axis passing by zero [15]. 2.3. Admittance loci design method Other than the reflectance, we can design a multilayer device by using the equivalent admittance approach. As shown in Fig. 3, as the incident light emits from the surrounding medium onto a multi-layer system, it can be treated as an equivalent admittance of ye , as defined in Eq. (12). It can be used to visualize the optical behavior of thin films, as we move a virtual reference plane from the substrate admittance (ysub ) to the front surface of the multi-layer. The equivalent admittance, ye , beyond the reference plane will change due to the thin film thickness change. These changes can be traced from the plot of ye on the complex plane and the trace is called admittance diagram or admittance loci. This method has been successfully applied for thin-film designs of high-reflection (HR) and anti-reflection (AR) coatings in the past. We will discuss the SPR sensor design in details in the following sections.
Fig. 3. Equivalent admittance of multi-layer over-coatings, where η0 , ηsub , and ηe are the admittance of the surrounding medium, substrate, and equivalent admittance, respectively, and treated as if moving a virtual reference plane (Ref) from the substrate admittance (ysub ) to the front surface of the multi-layer.
2.3.1. Single layer of dielectric material We will first begin with a simple case and its behavior on a complex plane, a single layer of dielectric thin film (y) and the equivalent admittance (ye ) with fixed wavelength and incident angle. One layer structure is y0 |y|ysub , and δ means the phase thickness. The equivalent admittance is: ye = α + iβ =
C ysub cos δ + iy sin δ = . B cos δ + i(ysub /y) sin δ
(18)
Making real and imaginary parts on both sides of Eq. (18) equal, we can get: ⎧ ysub ⎪ β sin δ = ysub cos δ ⎨ α cos δ − y , (19) y ⎪ ⎩ β cos δ + sub α sin δ = y sin δ y ⎡ ysub ⎤ α − ysub − β y ⎢ ⎥ cos δ = 0. (20) ⎣ ⎦ ysub sin δ β α −y y For non-trivial solution of cos δ and sin δ, we can have the solutions as follows: ysub α − y − β sub y = 0, ysub β α − y y ys ys ⇒ (α − ys ) α − y + β2 = 0 (21) y y α−
1 2
ysub +
y2 ysub
2 + β2 =
2 1 y2 ysub − . 4 ysub
(22)
As indicated in this equation, for a dielectric layer of admittance, it is a circle starting from (ysub , 0) with clockwise spiral due to the changes of film thickness and cross the real axis again at (y2 /ysub , 0) for every quarter-wavelength thickness. The starting point can be anywhere on the circular locus. It will simply result in a different circle that will be centered on the real axis and cut it in two points α and β such that αβ = y2 . One can then plot for isoreflectance contours, isophase contours, or electricfield contours for different purposes of visualization. One type of representation is the plot of equal reflective intensity contours, isoreflectance contours on the admittance diagram to know the performance of the final design. The centers of isoreflectance contours are given by [y0 (1 + R)/(1 − R), 0] and their radii by 2y0 R0.5 /(1 − R). Fig. 4 shows an example locus of a TiO2 thin film (n = 2.27) with thickness from 0 to 80 nm on top of a glass substrate (n = 1.5) in air. 2.3.2. Single layer of metal For the special case of SPR, we will examine the admittance loci about ideal metal with absorbance (y = −ik) or high performance metal (high k/n value for y = n − ik), as in a Kretschmann type SPR device where the prism is coated with a single highperformance metal layer. We are treating the glass prism as the incident medium and the surrounding air as the substrate.
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in the ideal metal and from (−n, k) to (n, −k) in the high performance metal. The diagram will be rotated slightly about the origin so that the points where all circles intersect are (n, −k) and (−n, k) [15]. 3. Results and discussions 3.1. Simulation program for thin film design
Fig. 4. Examples of dielectric admittance loci design. The clockwise trace of the admittance locus of a 80 nm layer of TiO2 on top of a glass substrate will start from the substrate (ysub , 0) and follow the equation passing through (y2 /ysub , 0) then end at its designed thickness.
Thus, the starting admittance for the film is on the imaginary axis, negative part for s-polarization and the positive part for p-polarization. It will show a near zero reflectance at a particular angle of incident and metal thickness. The condition is very sensitive to the angle of incidence. This very narrow drop in reflectance to a very low value is a surface plasmon wave on the metal film. The phase thickness will become a pure imaginary number under such circumstance and is shown as follows: δ=
2π (−ik)d = −iγ, λ
cos δ = cos hγ sin δ = −i sin hγ
.
The characteristic matrix of the film will become, ⎤ ⎡ i B 1 cos hγ sin hγ ⎦ =⎣ . k C ysub −ik sin hγ cos hγ
(23)
(24)
(25)
Because ye = C/B = α + iβ, the relation of real and imaginary parts of admittance loci is ⎧ β ⎪ ⎨ (α − ysub ) cos hγ = ysub sin hγ k . (26) ⎪ ⎩ β cos hγ = − k + α ysub sin hγ k For non-trivial solution of γ, we can get the locus of α and β, α2 − 2
2 − k2 ysub α + β2 = k 2 . 2ysub
(27)
2 − k 2 /2y , 0) It is also a circle locus with a center on (ysub sub 2 2 and a radius of ysub + k /2ysub . It goes from (0, k) to (0, −k)
We have implemented the above mentioned algorithm in a graphic user interface (GUI) environment (MATLAB version 6.5, Mathworks Inc., USA). The source code of SPR admittance loci design program is attached as a supplement. There are control and text inputs to set-up the layer structure and change the values of used parameters in the program. The results are shown in both admittance loci (Im(Ye ) versus Re(Ye )) and reflectance graphs (R% versus incident angle). For the use of this design method to modulate the SPR angle, we would first plot the original R − θ graph and then identify a new resonant angle and the incident angle that we want to start with. At the selected incident angle, we can now calculate the effective admittance and plot its position on the complex plane of admittance by selecting different visualization methods. The graph will show the trace of Ye according to the designed layer structure until the reflectance is within 5% or less of the isorelectance contour. We can plot the R − θ graph with specified parameters to view the final performance of possible designs. 3.2. Design of two traditional SPR devices We will discuss the design of SPR devices by using above mentioned method. SPR phenomena normally happen when the incident angle is larger than a critical angle, i.e., under TIR condition. In general, if we put a dielectric thin film, the admittance will move along the imaginary axis in a positive direction, and return to the starting point every half-wave thickness. The only way to make the admittance leave the imaginary axis is by a metallic layer. From previous equations, for the p-wave beyond the critical angle, if we add a thin metal film, the admittance will leave the imaginary axis, and have the chance to approach to the real axis. This is the most often used configuration of SPR, Kretschmann type device as shown in the Fig. 5(a) with a 633 nm p-polarized light, a BK7 prism, and a 50 nm Au film under water. It results in a typical resonant peak around 74◦ with final admittance at (1.45932, −0.02247) and 0.04% reflectance. The other often cited SPR configuration is Otto type, which is shown in the Fig. 5(b), which involves excitation of surface waves through an evanescent wave in a FTR layer. The admittance locus for p-polarization of a layer used beyond the critical angle is a circle that is described in an anticlockwise direction. For the correct angle of incident and dielectric layer thickness, the reflectance can be made zero. In this example, we used a 633 nm p-polarized light, a BK7 prism, a 18 nm air gap, and a 65 nm Au film under water. It results in a resonant angle of 74.5◦ with final admittance of (1.48818, −0.00667) and 0.009% reflectance.
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Fig. 5. Admittance loci and SPR (R − θ) spectra of two traditional SPR devices of (a) Kretschmann type (50 nm Au); (b) Otto type (18 nm air and 65 nm Au) are shown as examples. The incident light is 633 nm through a BK7 prism and under water.
3.3. Dielectric mirror type multilayer structure SPR phenomenon is a unique combination of total internal reflection from a high refractive index prism to a high performance metal thin film. Its performance can be further enhanced by using dielectric layers as in the many cases of high performance optical coatings. The important design issues include how to create the zero of reflectance at any desired angle of incidence beyond a critical angle and the width of the resonant. In the following sections, we will discuss two of the cases with symmetric and asymmetric structure for tunable SPR device design. Table 1 lists all the used materials along with its optical constant for reference. 3.3.1. Symmetric structure We recently reported a symmetric multilayer SPR device by using a dielectric mirror of alternating high/low refractive index materials to modulate the SPR resonant conditions Table 1 Optical constants of the materials used in the design cases (at 633 nm) Material
n
k
H2 O Au TiO2 SiO2 Ag Glass
1.33168 0.0666 2.27886 1.45705 0.16172 1.51508
0 4.047 0.00015 0 3.21182 0
[13]. In this case, we proposed to shift the SPR angle from 74 to 64◦ with a 633 nm light source on a BK7 coupling prism under water, which is equivalent to usage of a SF2 prism. With a single layer of 50 nm gold film, its resonant angle is close to 74◦ , where Ye = 1.4593 − i × 0.0225 is close to Yo and its reflectance is near zero. However, at 64◦ , the starting point Ye = 0.0686 − i × 1.5465, is close to the imaginary axis and its reflectance is higher than 80% without proper device design. By using the symmetric structure of glass|Au(40 nm)–[TiO2 (20 nm)–SiO2 (20 nm)]4 –Au(30 nm) shown in Fig. 6(a), its admittance loci will leave the imaginary axis and get close to Yo as shown in the Fig. 6(b). The final value is 1.3664 + i × 0.4685 and within the 5% iso-reflectance region (2.83%). The resultant R − θ spectrum (solid line) is shown as in the Fig. 6(c) compared to the traditional design of single layer of Au film (dashed line). Our laboratory tests confirmed that, under water, there was a 10◦ shift in resonant peak position towards the critical angle (from 74◦ in a conventional single-layer Au film), and a 3.25 times decrease in FWHM (the half-peak width). This device also resulted in a wider dynamic range of an up to a 1.50 refractive index unit (RIU), compared to 1.38 RIU in a conventional single-layer Au film. The calculated intensity sensitivity was about twice the improvement over the conventional single-layer Au film [13]. 3.3.2. Asymmetric multilayer structure It has been well known that silver has better SPR performance than gold. However, its does tarnish when exposed to
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Fig. 6. (a) The symmetric structure of the SPR device with glass|Au(40 nm)–[TiO2 (20 nm)–SiO2 (20 nm)]4 –Au(30 nm); (b) its admittance loci; and (c) SPR spectrum (solid line) with a resonant angle at 64◦ and a HMBW of 2◦ compared to a traditional one (dashed line).
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the sensing environment due to surface contaminations of silver sulphide or silver chloride. It is thus often required an overcoating dielectric layer to protect it from corrosion or a high performance multilayer coating to enhance its optical performance. It is thus reasonable to replace the inner metal layer of Au with Ag to have further enhancement of SPR performance with asymmetric structure as shown in the Fig. 7(a). The admittance locus of the dielectric layer between the air exit medium and the silver layer starts on the imaginary axis and
must remain on the axis if there is no absorption in the layer. Provided the angle in the dielectric layer is not beyond critical, the locus simply climbs to the top of the imaginary axis and disappears to re-enter the diagram at the very foot of the imaginary axis to climb upward and repeat the pattern, if the layer is thick enough. We recently introduced a novel design of an asymmetric multilayer SPR device to modulate the SPR resonant conditions [14]. In this case, we also used a 633 nm wavelength light source on a BK7 coupling prism under water.
Fig. 7. (a) The asymmetric structure of the SPR device with glass|Ag(50 nm)–[TiO2 (20 nm)–SiO2 (20 nm)]4 –Au(20 nm); (b) its admittance loci; and (c) SPR spectrum (solid line) with a resonant angle at 61.52◦ and a HMBW of 0.25◦ compared to the traditional design of a single layer of Au film (dashed line).
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Table 2 Performance comparisons of different SPR devices: (a) 50 nm Au film; (b) symmetric structure design; (c) asymmetric structure design (all with 633 nm through a BK7 prism and under water)
Single layer Au Symmetric multilayer Asymmetric multilayer a b c
SPR angle
HMBW
Dynamic range (RIU)a
Resolution (RIU)b
Intensity slopec
73.9 62.54 61.52◦
6.5 2 0.25◦
1.331–1.38 1.331–1.50 1.33–1.48
8.33 × 10−5 1.25 × 10−5 8.13 × 10−6
58.65 127.5 215.19
RIU is the refractive index unit. Angular measurement of 10−3 angular resolution. Intensity change (0–255)/1 degree shift.
The only difference in the structure design is the replacement of the bottom Au layer with a Ag layer to study its enhancement effect on SPR. With a single layer of 55 nm silver film, its resonant angle is close to 68◦ , where Ye = 1.4595 − i × 0.0226 is close to Yo and its reflectance is near zero. However, at 61.52◦ , the starting point (0.00000, 71.43949) is closed to the imaginary axis and its reflectance is about 100% without proper device design. By using the asymmetric structure, glass|Ag(50 nm)–[TiO2 (20 nm)–SiO2 (20 nm)]4 –Au(20 nm), its admittance loci will leave the imaginary axis and get close to Yo as shown in the Fig. 7(b). The final value is (1.33905, −0.57627) and within the 5% iso-reflectance region (4.28%). The resultant R − θ curve is shown in Fig. 7(c) with a resonant angle at 61.52◦ and a half maximum band widths (HMBW) of 0.25◦ .
3.4. Performance comparisons Table 2 shows the SPR performance of each presented design device as discussed in the previous sections. It is clear that with the admittance loci method we will be able to design the resonant angle by choosing proper dielectric materials and structure. It is especially prominent by using the dielectric mirror type of high/low refractive index structure to fine tune the resonant position and HMBW. With the similar structure used in the design case of symmetric and asymmetric devices, the later one shows a further enhancement of HMBW and resonant angle, which is approaching the critical angle. Such a unique behavior could be partly attributed to the above mentioned characteristics of the silver layer and its effect on the SPR behavior. The other interesting aspect could be observed by plotting out the parallel and
Fig. 8. The normal (a, c) and parallel (b, d) components of the electric field across a symmetric multilayer device vs. an asymmetric one, respectively. There are differences in the penetration depths as indicated in (a) and (c), and the parallel electric field across the last layer of Au film as indicated in (b) and (d).
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normal components of the electrical field across the structure as shown in the Fig. 8. There are differences in the penetration depths as indicated in the Fig. 8(a) and (c). The parallel electric field across the last layer of Au film has a different pattern in the symmetric and asymmetric design as indicated in the Fig. 8(b) and (d). Such a field pattern has been identified in the long range SPR to account for the field extension effect of the intermediate dielectric layer as “antisymmetric” (short range) and “symmetric” (long range) [8]. However, a single layer of a dielectric material as thick as several hundred nanometers is normally used in most of the literatures instead of our proposed designs. 4. Summary and conclusions The principal feature of our SPR design is the use of alternating dielectric layers to enhance the quality of the SPR signal and to modulate its resonant position. The thickness, number of layers, and other design parameters of the material used are optimized by using optical admittance loci analysis. The admittance locus is a kind of optical thin film design method which has been extensively used for high performance optical coatings. It provides a much necessary guidance for the choices of suitable optical materials, thickness, and number of layers for the intended performance. We have applied this method for the design of both symmetric and asymmetric multilayer dielectric mirror SPR devices and are able to fine tune the SPR resonant conditions with different metallic thin films of Au and Ag. With a 633 nm light source and a BK7 coupling prism under water, one can shift the resonant angle toward critical angle and have smaller half maximum band widths at (64◦ , 2◦ ) and (61.52◦ , 0.25◦ ) for symmetric and asymmetric designs, respectively. Bio-plasmonics, which use biomolecules as a part of the plasmon oscillating devices, can be designed for specific resonant conditions by using above mentioned admittance loci method. As in the design and development of biochips or biosensors as medical devices, it would be reasonable to find out the effective dielectric constants and thickness of biomolecules, e.g., DNAs or proteins, under specific operating conditions. Acknowledgments This project is supported in part by the National Science and Technology Program in Pharmaceuticals and Biotechnology, National Science Council, Taiwan, NSC (93-2323-B002-011, NSC93-2323-B002-017) and Council of Agriculture. We would like to thank Prof. Henry Co for valuable comments on this manuscript. References [1] H. Raether, Excitation of Plasmons and Interband Transitions by Electrons, Springer-Verlag, Berlin, 1980. [2] H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings, Springer-Verlag, Berlin, 1988 (Chapter 2). [3] A. Otto, Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection, Z. Phys. 216 (1968) 398.
[4] E. Kretschmann, Die Bestimmung optischer Konstanten von Metallen durch Anregung von Oberfldchenplasmaschwingungen, Z. Phys. 241 (1971) 313. [5] Z. Salamon, H.A. Macleod, G. Tollin, Surface plasmon resonance spectroscopy as a tool for investigating the biochemical and biophysical properties of membrane protein system. I. Theoretical principles, Biochim. Biophys. Acta 1331 (1997) 117–129. [6] Z. Salamon, H.A. Macleod, G. Tollin, Surface plasmon resonance spectroscopy as a tool for investigating the biochemical and biophysical properties of membrane protein system. II. Applications to biological systems, Biochim. Biophys. Acta 1331 (1997) 131–152. [7] J. Homola, S.S. Yee, G. Gauglitz, Surface plasmon resonance sensor: review, Sens. Actuators B 54 (1994) 3–15. [8] F.Y. Kou, T. Tamir, Range extension of surface plasmons by dielectric layers, Opt. Lett. 12 (1987) 367–369. [9] D. Sarid, Long-range surface-plasma waves on very thin metal film, Phys. Rev. Lett. 47 (1981) 1927–1930. [10] G.G. Nenninger, P. Tobiska, J. Homola, S.S. Yee, Long-range surface plasmons for high-resolution surface plasmon resonance sensors, Sens. Actuators B 74 (2001) 145–151. [11] Z. Salamon, H.A. Macleod, G. Tollin, Coupled plasmon-waveguide resonators: a new spectroscopic tool for probing proteolipid film structure and properties, Biophys. J. 73 (1997) 2791–2797. [12] C.-W. Lin, K.-P. Chen, C.-N. Hsiao, C.-K. Lee, S.-M. Lin, Design and fabrication of an alternative dielectric multilayer device for surface plasmon resonance sensor, Sens. Actuators B: Chem 113 (2006) 169– 176. [13] M.-C. Su, C.-N. Hsiao, C.-W. Lin, The design and application of asymmetric multilayer to SPR bio-sensor device, Proc. Chin. Biomed. Eng. Soc. Ann. Symp. 93 (2004) 670–673. [14] H.A. Macleod, Unconventional coatings, in: D.T. Moore (Ed.), Tutorials in Optics, Optical Society of America, Washington, DC, 1992, pp. 121–135. [15] H.A. Macleod, Thin-Film Optical Filters, third ed., Institute of Physics Publishing, Bristol, Philadelphia, 2001.
Biographies Chii-Wann Lin received his PhD degree from Department of Biomedical Engineering, Case Western Reserve University in 1993. He then joined the Center for Biomedical Engineering, College of Medicine, National Taiwan University in September 1993 as research assistant professor. He is now an associate professor at the Institute of Biomedical Engineering and also holds a joint appointment at the Department of Electrical Engineering, National Taiwan University. He is a member of IEEE EMBS, IFMBE and Chinese BMES. His research interests include biomedical micro-sensors, optical biochips, surface plasmon resonance, and nano-medicine. Kuo-Ping Chen received his BS degree in electrical and control engineering from National Chiao Tung University, Taiwan in 2002. He obtained his MS degree in biomedical engineering from National Taiwan University in 2004. He is currently serving his military duty. His research interests include surface plasmon resonance, bio-sensor systems, electronics and signal processing. Min-Chi Su received his BS degree in Electrical and Control Engineering from National Chiao Tung University, Taiwan in 2003. He obtained his MS degree in Biomedical Engineering from National Taiwan University in 2005. He is currently serving his military duty. His research interests include surface plasmon resonance, bio-sensor systems, electronics and signal processing. Tzu-Chien Ryan Hsiao received the MS and PhD degrees from the Institute of Physics at the National Sun Yat-Sen University and Institute of Biomedical Engineering at National Yang-Ming University, Taiwan, in 1996 and 2003, respectively. In 2003, he has been employed as an assistant professor of Institute Biomedical Engineering at I-Shou University, and now he is also a deputy director of biomedical research and development division of Hsinchu Biomedical Science Park. His research interests include neural networks, virtual instrument and multivariate spectral analysis.
C.-W. Lin et al. / Sensors and Actuators B 117 (2006) 219–229 Sue-Sheng Lee received her PhD degree from Institute of Applied Mechanics, National Taiwan University in July 2004. She then became a postdoctoral researcher in NTU Nano-BioMEMS group from August 2004 to August 2005, where she was in charge of the project “Special Type Multifunctional Optoelectronic Biochip System”. She is now a postdoctoral researcher in “Laboratoire de Photonique Quantique et Mol´eculaire” of l’Institut d’Alembert in Ecole Normale Sup´erieure de Cachan, in France. Her research interests include systems design and integration of biochip instrument and optical metrology. Shiming Lin received his PhD from the Institute of Biotechnology, University of Cambridge, United Kingdom in 1995. He is currently an associate professor at the Center for Optoelectronic Biomedicine, National Taiwan University. His research interests include nano-biotechnology and optoelectronic biotechnology, with a special focus on the molecular biomechanics of protein
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helix, viral surfaces and biomolecular interaction forces, as well as on the manufacture of optoelectronic bio-sensors and biochips. Xue-jing Shi received his BS in Civil Engineering from National Taiwan University, Taiwan, in 1998 and MS degree in Institute of Applied Mechanics from National Taiwan University, Taiwan, in July 2002. He became the researcher in Flow Laboratory, Center for Measurement Standards, and Industrial Technical Research Institute from August 2002. Chih-Kung Lee received his PhD degree from Cornell University in 1987. He worked at IBM’s Almaden Research Center in San Jose, California for seven years before returning to Taiwan. He is currently director general of Engineering and Applied Sciences at the National Science Council, Taiwan. He is concurrently a professor at the Institute of Applied Mechanics, National Taiwan University, and holds a joint appointment at the Institute of Engineering Sciences and Ocean Engineering, National Taiwan University.