A compact and ultra high sensitive RI sensor using modal interference in an integrated optic waveguide with metal under-cladding

Sensors and Actuators B 240 (2017) 1302–1307

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A compact and ultra high sensitive RI sensor using modal interference in an integrated optic waveguide with metal under-cladding Ranjeet Dwivedi ∗ , Arun Kumar Department of Physics, Indian Institute of Technology Delhi, New Delhi 110016, India

a r t i c l e

i n f o

Article history: Received 13 May 2016 Received in revised form 13 September 2016 Accepted 17 September 2016 Available online 19 September 2016 Keywords: Refractive index sensors Integrated optical waveguide Multimode interference

a b s t r a c t We propose a compact and ultra high sensitive refractive index (RI) sensor based on modal interference in an integrated optic waveguide with a metal under-cladding (MUC). It has been shown that the MUC significantly increases the fractional modal power in the ambient medium, affecting the higher order modes much more compared to the lower ones. This results in an ultrahigh dependence of the modal interference on the ambient RI change. The RI sensitivity of the proposed sensor structure is found to vary in the range 5.28–71.94 ␮m/RIU, for the RI range 1.33–1.37, which is the highest reported RI sensitivity, achieved in modal interference based sensors till date. © 2016 Elsevier B.V. All rights reserved.

1. Introduction Fibre and integrated optic (IO) sensors have been extensively studied for chemical and biotechnological applications because of their unique features such as high sensitivity, immunity to electromagnetic interference and low cost. In the recent past, various sensing schemes based on Mach-Zehnder interferometers [1], fibre Bragg gratings [2], long period gratings [3], surface plasmon resonance [4–7] and multi-mode interference (MMI) [8] etc. have been proposed and experimentally demonstrated. Amongst these, the MMI based sensors are easier to implement as they do not require precise grating writing, film deposition or a reference arm, making them a cheaper and simple alternative. Further, in the integrated optic configuration, such sensors may provide miniaturized designs and allow the simultaneous fabrication of multiple sensing elements [9]. A few MMI based integrated optic sensors have been reported in the literature using both planar [10] as well as rectangular core [11,12] waveguide geometries. However, these sensors are based on intensity interrogation scheme and their performance may be degraded by the source power fluctuations. In a recent paper, we have reported an IO modal interference based sensor using wavelength interrogation scheme [13] having RI sensitivity 1.37–33.84 ␮m/RIU for the ambient refractive index (ARI) varying between 1.33 and 1.44. The sensitivity of such sensors can further

∗ Corresponding author. E-mail addresses: [email protected] (R. Dwivedi), [email protected] (A. Kumar). http://dx.doi.org/10.1016/j.snb.2016.09.103 0925-4005/© 2016 Elsevier B.V. All rights reserved.

be increased if the fractional modal power (FMP) in the sensing region could be increased in a differential manner so that the higher order modes are affected much more than the lower ones by any RI change in the ambient region. This can be achieved by using a metal under-cladding [14,15], using which in Ref. [16], we have recently reported a very high RI sensitivity of 2.5 ␮m/RIU for ARI ≈ 1.33 in a planar waveguide structure. In this paper, we present a RI sensor based on modal interference in a rectangular core integrated optic waveguide with a metal under-cladding. It is observed that the differential enhancement of FMP in the ambient region due to the MUC results in a highly sensitive modal interference based RI sensor. For the considered structure the sensitivity is found to vary from 5.28 to 71.94 ␮m/RIU as the ARI changes from 1.33 to 1.37, which, to the best of our knowledge, is the highest reported sensitivity achieved in modal interference based sensors so far. 2. Effect of metal under-cladding We first discuss the effect of the metal under-cladding (MUC) on the FMP in the cover (FMPC) region by considering a planar waveguide structure, as shown in Fig. 1, where the substrate and the core regions are considered to be of fused silica and 13.5 mol% GeO2 doped silica, respectively. The cover region RI (ns ) is taken as 1.33 while a thin layer of silver (of thickness 200 nm) is included in between the substrate and the core region of the waveguide. Silver is chosen as under clad metal due to its lower loss compared to the other metals, resulting in the longer propagation length of the guided modes. Guided modes of the above waveguide can easily be

Fractional modal power

R. Dwivedi, A. Kumar / Sensors and Actuators B 240 (2017) 1302–1307

0.6 0.5

0.3 0.2 0.1

(1a)

ni () = 0.007684 − 0.58701

(1b)

where  = ( − 924.44) /422.4 and  is in nm. Fig. 2(a) and (b), respectively, shows the variation of the real part of the mode effective indices and FMPC for the TE0 and TE1 modes as a function of core thickness (tc ) with and without the metal layer. In both the cases, tc is varied in a range such that the corresponding waveguide supports first two TE modes only for wavelength ␭ = 1.55 ␮m. These figures clearly show that due to the metal layer, the effective indices of both the modes decrease and their FMPC increases significantly. Further, the above mentioned changes due to MUC are much larger for the TE1 mode as compared to the TE0 mode. It may be noted that in the case of MUC waveguide, the effective indices of the TE1 mode (in the entire considered range of tc ) and that of TE0 mode (for some values of tc ) become less than RI of the substrate (nsub = 1.44402) making them leaky modes. The leakage loss, however, can be reduced significantly by appropriately choosing the metal layer’s thickness tm . In order to show this, in Fig. 3, we present the variation of FMP in the substrate and

50

100

150

200

Metal thickness (nm)

Fig. 1. Schematic of the considered planar waveguide with metal under-cladding.

nr () = −0.00703883 + 0.0390292 + 0.029002 + 0.042719

substrate cover

0.4

0

obtained by solving the Maxwell’s equations with proper boundary conditions. We obtained the propagation constants of various TE modes of the structure by solving the corresponding eigenvalue equation using Newton-Raphson method. In our calculations, Sellmeier relations [17] are used to take into account the wavelength dependence of the refractive index of fused and doped silica while for silver, the dielectric constant data as reported by Johnson and Christy in Ref. [18] is considered by using a cubic fit for the real part and the linear fit to the imaginary part of the refractive index as reported in Ref. [19]. Accordingly, the real and imaginary parts of the refractive index of silver are taken as:

1303

Fig. 3. Variation of FMP for the TE1 mode in the cover and the substrate regions with the metal layer thickness for tc = 2.5 ␮m and ␭ = 1.55 ␮m.

cover regions for the TE1 mode (having a higher leakage loss as compared to TE0 mode) as a function of tm. This figure shows that, as tm increases, the FMP in the substrate region (FMPS) decreases while FMPC increases and for tm ≥ 90 nm FMPS is negligibly small while FMPC reaches almost to its maximum. This means that, for tm ≥ 90 nm, the leakage loss for the mode is negligibly small. In view of this, in the proposed sensor structure (discussed in the next section) we considered the thickness of metal layer as 100 nm.

3. Proposed structure and analysis The schematic of the proposed sensor structure is shown in Fig. 4, which consists of two identical single mode rectangular core waveguides (RCWs) (Sections I and III) joined at the input and output ends of a multimode ridge waveguide (Section II). The core dimensions (thickness × width) of the single and multimode sections are taken as 1.5 ␮m × 4.5 ␮m and 2.5 ␮m × 8 ␮m, respectively. The single mode waveguides (SMWs) are symmetric RCWs having same cladding (SiO2 ) in all the directions while the multimode waveguide (MMW) is a ridge waveguide with a metal under-cladding in between the SiO2 substrate and 13.5 mol% GeO2 doped SiO2 core. The sensing liquid when placed over the multimode section forms the upper and side claddings. Light is launched from the input SMW and detected at the output of the second SMW.

0

TE

0

TE0

ℜ(n ) eff

TE

1

nsub

without MUC

1.4

TE

1

with MUC

1.35

FMPC (dB)

1.45

TE1

−10

TE0

−20

without MUC TE

1

with MUC

TE

0

−30

2

4 6 tc (μm) (a)

2

4 tc (μm)

6

(b)

Fig. 2. Variation of (a) real part of the effective index and (b) FMP in the cover region for the TE0 and TE1 modes with the core thickness tc in the two mode region. Solid and dashed curves correspond to the waveguide with and without metal layer, respectively.

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R. Dwivedi, A. Kumar / Sensors and Actuators B 240 (2017) 1302–1307

Fig. 4. Schematic of the proposed sensor structure (a) 3-D view and (b) x–z cross-sectional view.

If Pin is the input power, the output power Po can be shown to be given by [4]



Po = Pin |

|am,n |2 eiˇm,n L |

2

(2)

where nsub ,nm ,nc and ns represent the refractive index of the substrate, metal, core and sensing regions, respectively and the perturbation ın2 is the dielectric constant difference between the two structures (i.e. given and the unperturbed), and is given by:



m,n

where |am,n |2 represents the fractional modal power coupled from/to fundamental i.e. (0,0)th mode of Section I/III to/from the (m,n)th mode of Section II, and is given by [4]



am,n =



I/III 0,0

I/III 0,0

∗II dxdy m,n

∗ I/III dxdy 0,0

In the above equation,

I/III 0,0



II m,n

(3) ∗ II dxdy m,n

(x, y) represents the modal field pat-

(4)

where n20 (x, y) = n2 (x) + n2 (y) − n2c represents the unperturbed waveguide structure. Here n2 (x) and n2 (y), describing planar waveguides, are given as:

n2 (x) =

⎧ 2 ns x > tm + tc ⎪ ⎪ ⎪ ⎪ ⎨ n2c tm < x < tm + tc ⎪ n2m 0 < x < tm ⎪ ⎪ ⎪ ⎩ 2

n2 (y) =



n2c − n2s 0

n2s |y| > w

(7)

Since n20 (x, y) is separable in x and y, the modal field patterns of the unperturbed waveguide can be written as

0 m,n (x, y)

= Xm (x)Yn (y)

(8)

where Xm (x) and Yn (y) are the TMm /TEm and TEn /TMn modal field patterns corresponding to the planar waveguides described by n2 (x) and n2 (y) for a predominantly x/y- polarized mode (referred as TMm,n /TEm,n modes hereafter) of the RCW under consideration. If ˇxm and ˇyn are the propagation constants corresponding to the 0 (x, y) modes Xm (x) and Yn (y) then the propagation constant of m,n mode of the unperturbed waveguide structure is given as, ˇ02m,n = ˇx2m + ˇy2n − k02 n2c

(9)

where k0 (= 2/) represents the free space wave number. The propagation constant ˇm,n of the (m,n)th guided mode of the given waveguide is obtained by applying the first order perturbation correction due to ın2 as:



ın2 |



(5)

|

2 0 m,n | dxdy 2 0 m,n | dxdy

(10)

It may be mentioned here that in the first order perturbaII tion theory, the field patterns remain unchanged i.e. m,n (x, y) = 0 m,n (x, y).

n2c |y| < w

(x < tm orx > tm + tc )and(|y| > w);

otherwise

2 ˇm,n = ˇ02m,n + k02

nsub x < 0

and

ın =

0 m,n (x, y)

II tern of the (0,0)th mode of the SMWs while m,n (x, y) and ˇm,n represent, respectively, the modal field pattern of the (m,n)th mode of the MMW and its propagation constant, which are obtained by using the perturbation/Kumar’s method [20,21]. According to this method, the dielectric constant profile n2 (x, y) of the given MMW (Section II in Fig. 4(a)) is considered as a perturbed form of n20 (x, y) as:

n2 (x, y) = n20 (x, y) + ın2

2

Similarly the mode field pattern

can be obtained. Once (6)

I/III 0,0

(x, y) and

II m,n

I/III 0,0

(x, y) of the SMW

(x, y) are known, the val-

ues of |am,n |2 and the transmitted power Po are obtained by using Eqs. (3) and (2), respectively.

R. Dwivedi, A. Kumar / Sensors and Actuators B 240 (2017) 1302–1307

0.5

Transmission

00

0.4

TE10 TE

02

0.2

0.3 0.2 with MUC

1.52 1.54 1.56 1.58 Wavelength (μm)

(a)

0.6

without MUC

TE

00

TE

0.4

ns=1.33

ns=1.331

0.8 Transmission

0.5

1.6

(b)

1

2

s

0.4

0.1 1.5

0 1.5 1.52 1.54 1.56 1.58 1.6 Wavelength (μm)

|am,n|

n =1.331

with MUC TE

|am,n|2

n =1.33 s

0.6

1305

10

0.6 0.4 0.2

0.3

0 1.5

1.5 1.52 1.54 1.56 1.58 1.6 Wavelength (μm)

without MUC

1.52 1.54 1.56 1.58 Wavelength (μm)

(c)

1.6

(d)

Fig. 5. (a), (c) Variation of fractional modal power coupled to the various guided modes of the MMW from the input SMW with wavelength and (b), (d) Transmission spectrum of the proposed sensor for the two ARI values ns = 1.33 and 1.331, with and without metal layer, respectively.

0 −1

∂(Δβ)/∂ns (μm )

Sensitivity ( μm/RIU )

80 60 with MUC without MUC

40 20 0 1.33

1.34

1.35 n

1.36

1.37



−1

1.33

s

(a)

−0.5



with MUC without MUC

1.34

1.35 ns

1.36

1.37

(b)

Fig. 6. Variation of (a) sensitivity and (b) ∂ ˇ /∂ns with ns , with and without metal under-cladding.

4. Results and discussion In our calculations, the SMW is considered to be axially aligned with the MMW in the y-direction and is shifted in the x-direction by a distance t0 (see Fig. 4(b)). Fig. 5(a) shows the variation of |am,n |2 with ␭ for the various TEm,n guided modes of the MMW and Fig. 5(b) gives the transmission spectra of the proposed sensor for two different RI values namely 1.33 and 1.331 for this case. The length L of the MMW is taken to be 2 mm so that one of the peaks in the output spectrum appears around ␭ = 1.55 ␮m. As expected, the transmission spectrum is almost sinusoidal due to the interference of mainly TE00 and TE10 modes. The various peaks/dips in the transmission spectrum correspond to the constructive/destructive

interference between these modes, depending upon their phase difference after propagating through the multimode waveguide. By calculating the wavelength shift in a particular transmission peak/dip due to change in the ns (from 1.33 to 1.331), we calculate the sensitivity of the sensor. The RI sensitivity in this case for the transmission peaks at 1.515, 1.544 and 1.575 ␮m come out to be 4.6, 5.25 and 5.9 ␮m/RIU, respectively. The extremely high RI sensitivity of the proposed sensor can be attributed to the fact that the metal under cladding enhances the modal field in the ambient region significantly, affecting the higher order modes much more than the lower ones. It may be mentioned that the extinction ratio (ER = Tmax \Tmin ; Tmax and Tmin representing the maximum and minimum values of the transmission) of the output spectrum

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R. Dwivedi, A. Kumar / Sensors and Actuators B 240 (2017) 1302–1307

depends on the values of the |am,n |2 , which in turn depend on modal field patterns of the SMW and MMW as well as on t0 . In the present case ER is ∼4.5 dB, which can be increased by increasing t0 so that powers coupled from both the modes to the output SMW are nearly same. However, Tmax and Tmin both decreases with increasing t0 . In the present case t0 = 1.8 ␮m, for which Tmax − Tmin is found to be maximum. In order to have an idea about the improvement in the RI sensitivity due to MUC, we also obtained the RI sensitivity of the structure in the absence of MUC. In this case, the thickness of the core region of the MMW had to be increased to 5.5 ␮m so that both the TE00 and TE10 modes are supported by the MMW. The SMW dimensions are kept to be the same as in the previous case. The SMW is again considered to be axially aligned in the y-direction and in the x-direction, no shift is considered (i.e. t0 = 0) as a high contrast of the transmission is observed for t0 = 0. In this case, the variation of fractional modal power coupled to the various guided modes of the MMW from the SMW and the corresponding transmission spectrum for two different ARI values 1.33 and 1.331 are shown in Fig. 5(c) and (d), respectively. In order to get again three peaks in the wavelength range 1.5–1.6 ␮m like the previous case, L is taken to be 15 mm. The three peaks appear at 1.510, 1.543 and 1.578 ␮m, respectively and the corresponding RI sensitivity comes out to be 1.35, 1.55 and 1.65 ␮m/RIU. A comparison between the two cases shows that the RI sensitivity in the case of MUC is about 3.4–3.6 times larger as compared to the case without MUC. The enhancement in the RI sensitivity due to MUC is found to be much higher at higher values of ns , as discussed latter. Since the transmission spectrum is the result of interference between mainly the two modes (TE00 and TE10 ), the sensitivity at different wavelengths can also be calculated as discussed below: The phase difference between the two interfering modes is given by  = (ˇ0,0 − ˇ1,0 )L, which is a function of ␭ and ns both. As ns changes, the phase difference  between the two modes remains constant for a particular peak/dip. Accordingly, the change in   =

∂ ∂ ns = 0  + ∂ ∂ns

The corresponding RI sensitivity is thus given as, =

∂(ˇ0,0 − ˇ1,0 )/∂ns  =− ns ∂(ˇ0,0 − ˇ1,0 )/∂

(11)

As expected, larger is the rate of change of ˇ(= ˇ0,0 − ˇ1,0 ) due to ns , larger will be the RI sensitivity. Using Eq. (11), we calculated the variation of sensitivity with the ARI at ␭ = 1.55 ␮m, which is shown in Fig. 6(a), for both the cases (with and without MUC). The figure shows that the RI sensitivity is increased significantly due to MUC for all values of ns , which is found to be 5.28–71.94 ␮m/RIU as compared to 1.49–2.68 ␮m/RIU in the absence of MUC. Further, as ns increases, the enhancement in the RI sensitivity also increases rapidly. This is attributed to the fact that, due to the larger FMP of the TE10 mode in the ambient region, its propagation constant increases sharply as ns increases, changing the ˇ much more rapidly in the presence of MUC. This is further clear from Fig. 6(b) where we have plotted

the variation of rate of change of ˇ with respect to ns i.e. ∂ ˇ /∂ns as a function of ns in the two cases,





showing that as ns increases, |∂ ˇ /∂ns | increases rapidly in the case of MUC. We would like to add that the proposed sensor is also much more compact (L = 2 mm) as compared to the case when there is no MUC (L = 15 mm). The RI range 1.33–1.37 in the proposed sensor is chosen, keeping in mind its potential applications for biochemical sensing. Its ultra high sensitivity (5.28 × 106 –71.94 × 106 pm/RIU) in the RI range 1.33–1.37 corresponds to a RI resolution of 1.89 × 10−7 –1.39 × 10−8 RIU, assuming a detection system with 1 pm resolution. Such a com-

pact and ultra high sensitive RI sensor can be fabricated by using the well developed film deposition techniques and photolithography. The response time of the proposed sensor will largely depend upon the type of the target bio-molecule and the bio-marker used in the sensor. For just the refractive index sensing applications, however, the response time should be extremely quick because, unlike bio-molecule sensing, no surface immobilization is required.

5. Conclusion In conclusion, we proposed and studied an ultra high sensitive and compact RI sensor based on modal interference in a ridge waveguide with a metal under-cladding. The considered sensor structure shows that at ␭ = 1.55 ␮m the MUC enhances the RI sensitivity by a factor of 3.5–27 in the RI range of 1.33–1.37 and reduces the size of the sensor by 7–8 times.

Acknowledgement Ranjeet Dwivedi gratefully acknowledges the financial support for this work from the Ministry of Human Resource Development, Govt. of India.

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Biographies Ranjeet Dwivedi has received the M.Tech. (Laser Technology) degree in 2013 from Indian Institute of Technology Kanpur, India. Since August 2013, Mr. Dwivedi is pursuing the Ph.D. degree with the Department of Physics, Indian Institute of Technology Delhi, India. His current research interests are modal interference based guided wave devices, integrated optical devices, and surface plasmon polariton based sensors. Mr. Dwivedi is a member of the Optical Society of America (OSA).

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Arun Kumar has received his M.Sc. and Ph.D. degrees in Physics from the Indian Institute of Technology, Delhi (IITD), India in 1972 and 1976, respectively. Since 1977, he has been on the faculty of the Physics Department at IIT Delhi, where he is a Professor since 1995. He has been a visiting scientist at the Technical University of Hamburg, Harburg, Germany, as a Humboldt Research Fellow in 1980–81, at Optoelectronic Group, Strathclyde University, Glasgow, UK, in 1988, at National Institute of Standards and Technology, Boulder, Co., USA in 1993 and 1994, at University of Nice, Nice, France in 1996 and at University of Jean Monnet, Saint Etienne, France in1999, 2004, 2006 and 2007. He has authored/co-authored more than 100 research papers in international journals. His research interests are in the field of Optical waveguides, Fibre optic sensors and Polarization mode dispersion. He has also coauthored a book, “Polarization of Light with Applications in Optical Fibers”, SPIE Press, 2011. Prof. Kumar is a member of the Optical Society of America.