Enhancement of refractive index sensitivity of Bragg-gratings based optical waveguide sensors using a metal under-cladding

Optics Communications 396 (2017) 83–87

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Enhancement of refractive index sensitivity of Bragg-gratings based optical waveguide sensors using a metal under-cladding

MARK

⁎

Nabarun Sahaa, , Arun Kumara, Arup Mukherjeeb a b

Indian institute of technology Delhi, Department of Physics, New Delhi 110016, India Fiber Optika Technologies, Mumbai, India

A R T I C L E I N F O

A BS T RAC T

Keywords: Ambient refractive index Bragg grating Metal clad leaky ridge waveguide Refractive index sensor

We theoretically analyze, a compact Bragg grating inscribed metal clad leaky ridge waveguide (MCLRW) as a refractive index sensor which can be integrated with other elements on a single chip. The grating is considered to be written in the photosensitive core. Using the quasi-TE mode of the structure, it is shown that a metal layer underneath the core enhances the evanescent field in the ambient region resulting in a significant increase in the ambient refractive index sensitivity. The obtained sensitivity and the figure of merit of the considered sensor structure are found to be almost 13–14 times higher than that of a ridge waveguide without any metal layer. Further, due to the higher modal loss of the quasi-TM mode, no in-line polarizer is required to assemble with the device. Effect of the loss due to metal layer on the peak reflectivity as well as bandwidth of the spectrum is also discussed.

1. Introduction Fiber and integrated optical waveguide sensors have several advantages, due to which several such devices are proposed and developed in the last three decades or so. Fiber Bragg gratings (FBG) and long period fiber gratings (LPFG) based devices are the most popular one amongst them as such devices are wavelength interrogated and hence are free from source intensity fluctuations. Initially, for ambient refractive index (ARI) sensing, LPFGs were preferred over FBGs [1,2], as the former one are much more sensitive due to higher evanescent field in the ambient region. However, narrow bandwidth response of the FBG makes it more suitable for detection of spectrum shift with the change in ARI. To enhance the evanescent field in the ambient region, in the case of FBG, the fiber has been etched or side polished [3–5]. Though it increases the sensitivity, etching of the fiber makes it fragile and greatly impacts the durability and strength of the fiber. In contrast, an integrated optical waveguide is definitely a better choice in terms of these; it is much more flexible in terms of fabrication, can have higher evanescent field within the ambient medium and is also suitable for lab on chip applications. In view of the above, an open top ridge waveguide Bragg grating with GeO2 doped SiO2 core has been proposed [6], with a relatively lower sensitivity of 12 nm/RIU around ARI 1.33. Later a corrugated grating in silicon on insulator (SOI) rib waveguide has been proposed by Passaro et. al. [7] with a sensitivity of 33.6 nm/RIU. However, the grating formation

⁎

through corrugation in photo-insensitive silicon core is a difficult task as compared to grating formation in photo sensitive core with UV writing. To overcome this problem Tripathi et. al. proposed an SOI ridge waveguide with the grating written in the photosensitive upper cladding made of GeO2 doped SiO2 with a sensitivity 239 nm/RIU at ARI 1.33 [8]. In this paper we examine the refractive index (RI) sensing characteristics of Bragg gratings written in a ridge waveguide with a metal layer incorporated in between the substrate and the core. The grating is considered to be written in the photosensitive GeO2 doped SiO2 core. Introduction of the metal layer enhances the evanescent field in the ambient medium as well as its RI sensitivity significantly. We exploit the quasi-TE mode instead of quasi-TM mode as the later one is highly lossy compared to the quasi-TE mode. As a result of the higher attenuation, the quasi TM mode dies out after propagating a small distance and hence no in-line polarizer is required to be used with the device to separate out the two polarized modes at the output as in the case of [8]. Though in the literature metal clad leaky waveguides (MCLW) are used to sense the change in ARI [9,10], however all are planar in nature and operated in the reflection mode. To the best of our knowledge no guided wave optic device using Bragg grating in MCLRW, has been explored till date. This paper is organized as follows: in Section 2 we describe the modal analysis of MCLRW and in Section 3 we discuss the effect of metal layer in enhancing the fractional modal power (FMP) in the

Corresponding author. E-mail address: [email protected] (N. Saha).

http://dx.doi.org/10.1016/j.optcom.2017.03.043 Received 30 January 2017; Received in revised form 17 March 2017; Accepted 19 March 2017 Available online 23 March 2017 0030-4018/ © 2017 Elsevier B.V. All rights reserved.

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δn2 (x,

⎧ ⎧ ( x > a / 2, y < 0) 2 ⎪ (n 2 − nARI ) ⎨ ( x > a / 2, y > b) y) = ⎨ co ⎩ ⎪ ⎩ 0 otherwise

(3)

The solution of the wave equation for the unperturbed profile (Eq. (2)) are of the form,

ψm, n (x, y) = Xm (x ) Yn ( y)

(4)

where, ψm,n(x,y) represents the electric or magnetic field components of the MCLRW modes. Using the method of separation of variables it can be shown that Xm(x) and Yn(y) are the solution of wave equation for the planar waveguide structure, characterized by n′(x) and n″(y) respectively. If βm and βn are the modal propagation constants corresponding to Xm(x) and Yn(y) respectively, the propagation constants of the modes for the unperturbed profile can be shown to be given by, 2 β02m, n = βm2 + βn2 − k 02 nco

(5)

Fig. 1. 3-D view of the considered MCLRW structure with a Bragg grating written in the core.

After considering the effect of the modes become as,

ambient medium. A brief analysis of a Bragg grating in MCLRW for calculating its ARI sensitivity and figure of merit (FOM) is presented in Section 4 and finally the results are summarized in the Section 5.

βm, n =

∬

δn2 (x,

y) =

y) +

y)

is given as,

2 dxdy

∬ ψm, n (x, y) 2 dxdy

3

n (λ ) =

(1)

1+

∑ Ai i =1

(7)

λ2 λ2−λi2

(8)

where λ is the free space wavelength and, Ai and λi are the Sellmeier constants whose values are different for different concentration of GeO2 [13]. At a wavelength of 1.55 µm refractive index of the core and substrate are found to be 1.471458 and 1.444024 respectively. Further, for the dielectric constant (ɛm) of metal layer, the Drude model has been used which is expressed as [14],

where, n 0 (x, y) is the unperturbed refractive index distribution given as, 2 n 02 (x, y) = n′2 (x ) + n″2 ( y) − nco

y) ψm, n (x, y)

δβ 2

with k0 being the free space propagation constant. It is worthy to mention that, the quasi-TE mode is TE like for n″(y) and TM like for n′(x). Accordingly, βn and βm are obtained by solving the TE (for n″(y)) and TM (for n′(x)) eigenvalue equations respectively. The reverse is true for quasi-TM mode. In all our calculations presented in the next sections, wavelength dependent refractive index n(λ) of core and substrate has been calculated using well known Sellmeier formula given as [13],

The considered structure, shown in Fig. 1, consists of 19.3 mol% GeO2 doped SiO2 as core, fused silica as substrate and a metal layer of Gold (Au) in between. The cross-sectional view of the considered MCLRW and its dielectric constant variation along y-direction is shown in Fig. 2. Modal field patterns and the effective indices of various modes supported by the MCLRW are obtained using the perturbation method /Kumar's method [11,12], in which the given structure's (Fig. 2) refractive index distribution is written as,

δn2 (x,

(6)

where, the first order correction

2. Modal analysis

n 02 (x,

final propagation constants of

β02m, n + δβ 2

δβ 2 = k 02

n 2 (x ,

δn2 the

(2)

with n′(x) and n″(y) are varying as, ⎧ n2 y < 0 ⎪ ARI ⎧ n 2 x < a /2 ⎪n 2 0 < y < b co 2 2 n′ ( x ) = ⎨ 2 & n″ ( y) = ⎨ co2 and δn2 is the ⎪ n m b < y < (b + d ) ⎩ nARI x > a /2 ⎪ 2 ⎩ nsub y > (b + d ) difference between the dielectric constant distribution of the given and the unperturbed waveguide, given by

⎡ ⎤ ωp2 ⎥ εm (λ ) = ε∞ ⎢1 − ⎢⎣ ω (ω + iΓ ) ⎥⎦

⎪ ⎪

(9)

where ε∞ is the high frequency value of dielectric constant, ωp is plasma frequency and Γ is the damping frequency, for Au the values of which are 8.6, 4.264 PHz and 0.1274 PHz respectively. At 1.55 µm the dielectric constant comes out to be −95.981+10.956i. 3. Effect of the metal layer As mentioned previously, the RI sensitivity of the device depends on the fractional modal power (FMP) in the ambient medium, which is defined as,

FMPamb =

∬ambientregion ψm, n 2 dxdy ∞

∞

∫−∞ ∫−∞ ψm, n 2 dxdy

(10)

As the modal effective index approaches ambient RI, the field in the ambient region increases, leading to a higher FMP in the ambient medium. We observed that a metal layer adjacent to the core region

Fig. 2. (a) Cross sectional view of the MCLRW and (b) its dielectric constant distribution in the y-direction.

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0.04

with metal layer without metal layer

Modal effective index (neff)

FMP in the ambient medium

0.045

0.035 0.03 0.025 0.02 0.015

fundamental mode (TE0,0) st

1.46

1 higher order mode (TE1,0)

1.455

1.45

1.445 2.5

0.01 1.3

1.31

1.32

1.33 1.34 1.35 1.36 1.37 Ambient Refractive Index (ARI)

1.38

1.39

3

3.5 4 Waveguide Dimension (a in µm)

1.4

4.5

5

Fig. 5. Variation of effective indices of TE0,0 and TE1,0 modes of square RW with ‘a’ for ARI 1.33 at λ=1.55 µm.

Fig. 3. Variation of FMP in the ambient medium with and without metal layer (core dimension is 4×4 µm and λ=1.55 µm).

0.5 FMP in the ambient medium

(Fig. 2) can reduces the modal effective indices of the modes, due to its high negative dielectric constant. As a result, the FMP in the ambient medium increases significantly. To show this enhancement in Fig. 3 we have compared the variation of FMP in the ambient medium with ARI, for the fundamental quasi-TE mode of a square ridge waveguide having core dimension (a×b) 4×4 µm with and without a metal layer. The figure clearly shows that the FMP in the ambient medium increases when the metal layer is introduced in between core and substrate of the ridge waveguide. Further it should be noted that for the MCLRW the metal layer prevents modal power to penetrate in the substrate and hence the mode cut offs will be decided by the RI of the ambient medium instead of the substrate which is the case for a ridge waveguide without any metal layer (referred as RW hereafter). As a result of this increment in the effective index contrast towards the substrate, for the same core dimensions, MCLRW supports larger number of modes as compared to the RW. For example for the aforementioned dimensions and with ambient RI 1.33, the RW supports only the fundamental mode whereas the MCLRW supports eight modes. For Bragg grating based waveguide devices single mode waveguide is preferred to avoid multimode interference. So for Bragg grating written MCLRW, dimensions of the waveguide core would be smaller as compared to RW so that it supports only fundamental mode. In the Figs. 4 and 5 respectively we have shown the effective index variation of a MCLRW and RW with the waveguide dimensions (in both cases waveguides are considered to be square i.e. having dimension (a×a) µm). From these figures it is clear that for MCLRW the single mode (SM) region is from (1.1×1.1) µm to (1.96×1.96) µm while for RW it is between (2.9×2.9) µm to (4.8×4.8) µm and the effectiveindex of the mode is closer to ambient RI 1.33 for MCLRW compared to the RW. The enhancement in FMP in the ambient medium is further increased as the core dimension is reduced for the single mode operation. For example, in Fig. 6 we have compared the FMP in the ambient medium considering the core dimension as 1.5×1.5 µm for MCLRW and 3.8×3.8 µm for RW so that both waveguides are at the middle of their respective single mode regions. The figure shows an 11–14 times enhancement of FMP in the ambient medium for MCLRW.

MCLRW (1.5×1.5 µm) RW (3.8×3.8 µm)

0.4 0.3 0.2 0.1 0 1.3

1.31

1.32

1.33 1.34 1.35 1.36 1.37 Ambient Refractive Index (ARI)

1.38

1.39

1.4

Fig. 6. Variation of FMP in the ambient medium with ARI for MCLRW and RW at the middle of their respective single mode regions (at λ=1.55 µm).

It is important to note that for MCLRW the effective index of the fundamental mode (Fig. 4) is lower than the RI of the substrate. As a result, the mode is leaky in nature, which greatly reduces the FMP in the core, leading to a smaller modal overlap in between forward and backward propagating mode in the grating region, i.e. in the core region. However, this leakage can be reduced by selecting the metal thickness appropriately. In Fig. 7, we have plotted the variation of the FMP in the core and the substrate regions as a function of metal thickness. This figure shows that as the metal thickness increases, FMP in the substrate decreases while that in the core increases: almost saturating after 90 nm. In view of this, the metal layer thickness is chosen to be 100 nm in our calculations. We would like to mention that in our analysis, the quasi-TE mode of the structure has been preferred over quasi-TM mode due to its smaller modal loss. In the case of quasi-TM mode, the predominant electric field component (Ey) is perpendicular to the metal layer (see Fig. 2) due to which it is a hybrid surface plasmon mode in nature, having higher propagation loss i.e. lower propagation length. The propagation length is defined as the length at which the power becomes 1/e, and is given by 1/(2×Img(β)). At core dimension (1.5×1.5) µm, the propagation length is found to be 1.57 mm for the quasi-TE mode but it is only about 130 µm for the quasi TM mode at λ=1.55 µm. In our calculations, we have selected the grating length in between the propagation lengths of the two polarized modes, so that the quasi-TM mode dies out

Fractional modal power (FMP)

Real part of effctive index (neff,r)

1 fundamental mode (TE0,0)

1.41

st

1 higher order mode (TE1,0)

1.4 1.39 1.38 1.37 1.36 1.35 1.34

Core dimension (1.5×1.5 µm)

0.8 FMP in the core 0.6 0.4 0.2 FMP in the substrate

1.33 1

1.2

1.4 1.6 1.8 Waveguide dimension (a in µm)

2

0

2.2

Fig. 4. Variation of real part of effective indices of TE0,0 and TE1,0 modes of square MCLRW with ‘a’ for ARI 1.33 at λ=1.55 µm.

10

20

30

40

50 60 70 80 Meta layer thickness (d) in nm

90

100

110

120

Fig. 7. Variation of fractional modal power in the core and substrate regions as a function of metal layer thickness at λ=1.55 µm).

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after propagating a distance of 130 µm, eliminating any requirement of an in-line polarizer to separate out the quasi TE and TM mode at the output.

Sensitivity (nm/RIU)

4. RI Sensitivity of Bragg gratings in MCLRW We consider a Bragg grating of length L inscribed in the core region of a MCLRW as shown in Fig. 1 and compare its RI sensitivity with that of a Bragg grating written RW without a metal layer. In both cases, the grating-induced refractive index changes are described by,

⎛ 1 2π ⎞ δn (z ) = Δn ⎜1 + cos( z ) ⎟ ⎝ 2 Λ ⎠

π Λ

where, δ = β − (where β= β0,0), α = coefficient, defined as [15],

κ=

nco ωε0 2

−

δ2

π Λ

=

(13)

π

(βr − Λ ) − iβi

= δr − iδi where βr and βi represent the real and imaginary parts of β. At the phase matching condition,δr = 0 , so the resonance wavelength for a Bragg grating written in a MCLRW is determined by

λR = 2neff , r Λ

(14)

where, neff , r is βr/k0. Further, δ = − i δi and using Eq. (12) the peak reflectivity can be shown to be given as,

Rmax = rmax

2

=

−iκ sinh(γL ) βi sinh(γL ) + γ cosh(γL )

2

(15)

βi2

+ κ2. with,γ = In the case of a RW, βi =0 and the above expression reduces to the well-known expression, Rmax = tanh(κL ) 2

3

3.5

4

4.5

5

300 200

(16)

FOM =

Using Eq. (14) the RI sensitivity of the grating can be obtained as,

∂neff , r ∂λR S= = 2Λ ∂nARI ∂nARI

10 2.5

1.5

2

2.5 3 3.5 Waveguide Dimension (a in µm)

4

4.5

5

We would like to point out that the sensitivity of the proposed structure is better than that of other reported Bragg grating based ARI sensors e.g. 239.8 nm/RIU in [8] and 250 nm/RIU in [16] around 1.33. It is also much more compact (device length 0.7 mm) compared to the ones reported in [8,16], where the typical device length is in between 3 to 5 mm. In order to study the effect of the metal layer on peak reflectivity and bandwidth of the reflected spectrum, the waveguide's dimensions are chosen such that both are at the middle of their respective single mode region (considering the dimensions (3.8×3.8) µm and (1.5×1.5) µm for RW and MCLRW respectively, as mentioned earlier). The peak reflectivity in the case of MCLRW, is found to be smaller due to modal loss and also due to a smaller fractional modal power in the core as compared to the case of RW when the grating parameters are same in both cases. For example for the considered dimensions, grating length =0.7 mm and for the GS =6×10−4, the peak reflectivity comes out to be 85% for RW and 60% for MCLRW, obtained using Eq.(16) and Eq. (15) respectively. We next compare the bandwidth of the spectrum in the two cases having same peak reflectivity. In order to have the same value of peak reflectivity in the case of MCLRW, either the grating length or the grating strength has to be increased. We decided to select different values of GS in the two cases, keeping the grating length fixed at 0.7 mm so that it is well below the propagation length of the mode as discussed earlier. As such, we consider the GS to be 4.5×10−4 for RW and 7.5×10−4 for MCLRW such that in both cases the peak reflectivity is 70%. The bandwidth is found to be 1.486 nm for RW and 1.736 nm for MCLRW. In order to compare the overall sensing performance of the proposed sensor, in each case, we have calculated the figure of merit (FOM), which is defined as,

In the case of a MCLRW, β is complex and hence

δ = βr − iβi −

20

MCLRW

Fig. 8. Sensitivity of Bragg grating inscribed MCLRW and RW with ‘a’ (at λ=1.55 µm) in their respective single mode region. In the inset an enlarged view of sensitivity variation of RW is shown.

and κ is the coupling

∬ Δn ψ0,0 (x, y) 2 dxdy

400

RW

(12)

κ2

30

0 1

(11)

−κ sinh(αL ) δ sinh(αL ) − iα cosh(αL )

40

500

100

where, Δn is the grating strength (GS) defined as the amplitude of the grating's refractive index modulation and Λ is the grating period. For a Bragg grating, the amplitude reflection coefficient is defined as [15],

r=

50

600

Sensitivity (nm / RIU ) 3 − dBBandwidth (nm )

(18)

The FOM values for MCLRW and RW comes out to be 165.38 RIU−1 and 14.07 RIU−1 respectively, showing an enhancement of twelve times. Thus despite an increment in bandwidth the proposed device performance is much better as compared to RW. In the calculations presented above, we have used the perturbation method due to its simplicity and lower computational time consumption for the calculations. In order to check how accurately the sensitivity is predicted by it we have also calculated S (Eq. (16)) for a MCLRW using Finite Element Method (FEM) analysis by COMSOL [17] for ARI 1.33 and at wavelength 1.55 µm in the entire single mode region which is shown in Fig. 9. This figure shows that the sensitivity calculated from the perturbation method is quite accurate except near the mode cut-off, where it underestimates the sensitivity. This is expected as near the cut-off, more and more power goes in the corner regions and the accuracy of the perturbation method decreases.

(17)

where nARI is the ambient refractive index. Using Eq. (17) we calculated the sensitivity taking the grating length (L) to be 0.7 mm for both the cases which is well under the propagation length of the mode of the MCLRW. In Fig. 8 we have shown the variation of sensitivity with the dimensions of RW and MCLRW in their respective single mode region at wavelength 1.55 µm and ambient RI 1.33. The RI sensitivity for RW comes out to be in the range of 11–42 nm/RIU whereas for MCLRW in the range of 142–617 nm/RIU showing a significantly large enhancement. The enhancement is more than fourteen times near the mode's cut off and twelve times at the top of the SM region. We have also calculated the RI sensitivity for higher values of ARI and found that the enhancement in the sensitivity due to the metal under cladding is of the same order. For example, at the middle of the single mode region of the waveguides, i.e. at the RW dimension (3.8×3.8) µm and MCLRW dimension (1.5×1.5) µm the sensitivity is found to vary between 16.6– 46 nm/RIU and 237–578 nm/RIU respectively in the ARI range 1.3– 1.4.

5. Conclusion In summary, we have investigated a metal clad leaky ridge 86

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700 Perturbation method COMSOL

Sensitivity (nm/RIU)

600 500 400 300 200 100

1

1.1

1.2

1.3

1.4 1.5 1.6 1.7 Waveguide dimension (µm)

1.8

1.9

2

Fig. 9. Variation of Sensitivity of Bragg grating inscribed MCLRW with the waveguide dimension ‘a’ using perturbation method and FEM analysis through COMSOL at ARI 1.33 and λ=1.55 µm.

waveguide (MCLRW) Bragg grating as a refractive index sensor and show that the RI sensitivity and the FOM are significantly increased due to the metal layer. The proposed structure is found to be better than that of other reported Bragg grating based ARI sensors in terms of sensitivity as well as compactness. Further, due to higher modal loss of quasi-TM mode, no in-line polarizer is required to be used at the output of the device. Acknowledgements Author Nabarun Saha gratefully acknowledges the Council of Scientific and Industrial Research (CSIR), India, for providing Senior Research Fellowship. References [1] V. Bhatia, A.M. Vengsarkar, Optical fiber long-period grating sensors, Opt. Lett. 21 (1996) 692–694. [2] B.H. Lee, Y. Liu, S.B. Lee, S.S. Choi, J.N. Jang, Displacements of the resonant peaks of a long-period fiber grating induced by a change of ambient refractive index, Opt. Lett. 22 (1997) 1769–1771.

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