The phase shifted vertical side wall gratings are designed and numerically simulated on a submicron SOI waveguide to obtain the performance characteristics needed for an integrated refractive index sensor. The gratings are designed to obtain narrow band width, high transmittivity and sharp line shape in the resonant transmission so that the sensor sensitivity can be improved. The proposed sensor is easy to fabricate and will provide a linear response over a wide wavelength range with a compact structure dimension which is suitable for label free biosensing applications. The detection limit of the sensor is investigated through both wavelength shift and intensity measurement method and the performance parameter is compared with other silicon based structures like Mach-Zehnder interferometer, ring resonator and surface corrugated Bragg grating.
©2009 Optical Society of America
Integrated optical sensors has a high potential to be employed as a device in many of the areas such as medicine, microbiology, particle physics, automotive, environmental safety and defense. Their main advantages are immunity to electromagnetic interference, high compactness and robustness and prospects of mass production, and also they have fast responsivity and higher sensitivities when compared to Micro Electro Mechanical System (MEMS)/ and Micro Opto Electro Mechanical System (MOEMS) devices . The wide variety of optical sensing platforms are spread over sensors based on planar waveguide structures  directional couplers , micro resonators [4–6], and surface plasmon waveguide structures . Integrated optical biosensors consist of a waveguide to confine light power and are based on evanescent wave sensing. Recently there is a considerable interest in label-free sensing for which the binding event can be detected without the use of tags, and also where binding reactions can be monitored continuously in real time. Label free optical techniques are all based on measuring the local change in index of refraction induced by the presence of molecules. Silicon on Insulator (SOI) is an attracting platform for fabrication of these structures, due to its low cost and structure compactness assured by the high index contrast. It also enables monolithic integration with other optoelectronic components and facilitates CMOS compatible fabrication process. However, very few works are reported based on fully compatible SOI technological platform. SOI based waveguide structures are designed and fabricated for integrated biosensing as waveguide based high sensitive slot waveguide , as Mach-Zehnder interferometer SPR sensor , micro ring resonator  and surface corrugated Bragg grating structure . A Bragg grating structure with a strong index modulation can exhibit the typical properties of a photonic crystal giving a compact structure with steep slopes for band edges in the spectrum for improved sensor performance . However the Bragg gratings on the top surface need multiple fabrication steps to achieve the grating pattern and a large cross section waveguide would require stringent design conditions for a single mode operation. On the other hand a Bragg gratings on the side wall of a strip waveguide is easy to fabricate in a single lithographic step and the effective refractive index of the grating would be less dependent on the grating etch depth variation. The vertical side wall based nano-Bragg gratings device, incorporated with a micro fluidic channel, is designed and fabricated by Jugessur, et.al. to form a reusable biosensor chip through a reversible active sealing method . A phase shift applied to this grating can give a narrow band resonant transmission and is used for various applications such as tunable transmission filters and modulators [12,13]. For an integrated sensing application the resonant transmission peak in the stop band of the phase shifted gratings would allow an easy interrogation of the sensor output through a wavelength shift or intensity measurement approach.
In this paper the phase shifted vertical side wall gratings are designed and numerically simulated on a submicron SOI waveguide for the first time to achieve the performance characteristics needed for a refractive index sensor suitable for biosensing applications.
2. Grating design
Figure 1 (a) shows the schematic diagram of a phase shifted vertical side wall grating. In the figure W and ΔW represents the width and etch depth of the grating, respectively. Λ is the grating period and Λp is the quarter wave phase shift length. The grating period lengths and are related by Bragg condition as
A quarter wave phase shift is applied by introducing a defect layer of magnitude Λp = λ / (4n 2) into the one section of the gratings. The simulated field intensity distribution and the corresponding spectrum are shown in Fig. 1. (b) and Fig. 1(c), respectively. Figure 1(c) is the normalized reflection /transmission of the phase shifted grating. The spectrum is obtained by taking Discrete Fourier Transform (DFT) of the time domain spectrum obtained at an observation point in the output plane as marked in Fig. 1(b). Since grating has a high reflectivity over a broad bandwidth (~100nm) apparently no light will reach at the output, except the resonant wavelength at a narrow band width. The electric field intensity visible at the initial grating region is the reflected light and the intensity at phase shift plane is the light undergoing resonance at Fabry-Perot cavity.
The simulation is performed using 2D Finite Difference Time Domain (FDTD) method  for Transverse Electrical (TE) wave propagation. Since the waveguide thickness is very small and there is no structural variation in the Y-direction uniformly over X-Z plane, the structure can be anlysed as a 2D device without losing much generality. In order to get an exact Bragg wavelength in the simulation the effective index in 2-D simulation is set to a value that obtained from the 3-D Beam Propagation Method (BPM) mode solver. The waveguide width is ‘W’ throughout the Z-direction and the gratings are introduced by corrugating the waveguide with a dimension ‘ΔW’ towards the axis of the waveguide. Typical simulation window dimension used were 20 µm (propagation direction) by 5 µm (transverse direction). A mesh grid size of Δx = 5nm, Δz = 5nm and time step size of Δt = 1.2 x 10−17s were used in the simulation. The time step is based on Courant condition. The simulation is run for 524,288 (219) time steps to get a fine spectral resolution of less than 0.3 nm. The input source was a Gaussian modulated continuous wave (CW) at a wavelength of 1.55 µm having a broad spectral bandwidth. Assuming a silicon substrate, the refractive indices of the core and cladding were set to be n Si = 3.467 and n Clad = 1, the effective indices and were calculated as 2.2526 and 2.5398. Thus the quarter wave phase shift length is calculated as Λp = λ / (4n 2) = 152.6 nm. From Eq. (1) the grating period lengths and are obtained for a Bragg wavelength of 1.55 µm as = 161.5 nm and = 161.5 nm (grating period, = 323 nm) for a duty cycle (D = lw/Λ) of 50%.
The wide stop band (1500 nm-1600 nm) in the transmission spectrum would allow a high free spectral range, so that the resonant wavelength can be tuned over a wide range of wavelength. The effect of change in phase shift lengh and the effective refractive index on the spectrum is shown in Fig. 2 . The phase shift is varied in steps of 5 nm above and below of quarter wavelength value(Λp). A linear shift in resonant wavelength is observed[Fig. 2(b)]. The variation in resonant wavelength with effective refractive index change [ Fig. 2(c)] shows the possibiliy for wavelength tunability of the structure using methods like thermo-optic or elctro-optic effects.
From these simulated spectral charateistics the designed phase shifted vertical side wall grating is assumed to have a resonant behaviour and the grating is suitable for obtaining a narrow band transmission over a wide range of wavelength.
3. Grating parameter to get a high quality factor (Q) resonant transmission
For a sensor based on wavelength shift measurement, a high Q factor and a high transmittivity is desirable in the resonant transmission. The high Q factor (Q = λ r /(Δλ) 3dB, where λ r is the resonance wavelength and Δλ 3dB is its 3dB band width) is dependent on a number of factors such as grating depth, grating duty cycle and grating length (Lout) on each side of the phase shift. The transmittivity is dependent on the loss inside the cavity, which in turn can be minimised by optimising the grtaing parameters. The following section describes how the transmission bandwidth (or cavity Q) and transmittivity of the resonant transmission peak varies with respect to various grating parameters.
The effect of variation in grating duty cycle and grating depth on the resonant spctrum is shown in Fig. 3(a) and Fig. 3(b),respectively. The band width is narrow when the duty cycle is in between 50 and 70 percentages. With an increase in grating etch depth the band width is found to be decreasing. This behaviour is evident with the quality factor relation of the Fabry-Perot resonators as given below 
A low loss is obserevd inside the structure for a high value in duty cycle and a smaller grating etch depth, with a fixed length of the grating [See Fig. 3(a) and Fig. 3(b)]. The loss in the structure is the part of the power which not being detected outside and is calculated using the relation L = 1-(T + R), where T and R are the tranmsittivity and reflectivity obtained from the resonant peak. The loss in the strcuture is mainly due to the out of plane scattering during reflection and mode mismatch loss at the grating-waveguide interface. A decrease in grating depth wll reduce the scattering loss in the strcuture. An increase in duty cycle or decrease in grating depth will reduce the modemismatch loss. This can be explained using the filling factor of the grating. The filling factor can be defined as the percentage of air gap in a period of the grating and is given as . An increase in duty cycle or decrease in grating depth will reduce the filling factor resulting into a lesser air gap per grating period. This in turn increases the effective index of the grating period and hence reducing the mode mismatch loss.
The variation with respect to grating length Lout shows that a longer grating can give a narrow band band width but at the expense of transmittivity. With a fixed grating duty cycle of 60% and grating depth ΔW = 80 nm grating length Lout (in units of grating period Λ) is varied. The superposed transmission spectrum shown in Fig. 3(c) depicts that band width is decreasing with increase in grating length but with a reduction in transmittivity. The variation in band width and transmittivity is plotted in Fig. 3(d). Beyond the grating length Lout = 30 Λ the band width is observed to be constant but the transmittivity drastically reducing to a very low value. The transmittivity is related to the Q factor through the relation Eq. (2) to Eq. (5) suggests that to obtain a narrow band transmission with a high transmittivity there should be a compromise between the grating length (L) and grating coupling coefficient (K) which is a function of the grating etch depth(ΔW). To get a comapct design, the grating length is made shorter and grating coupling coefficient is increased (by increasing the etch depth) to obtain a narrow band width(or high Q). After this the transmittivity is optimised by adjusting the grating length. For a strip waveguide having a width of 400 nm, a maximum value in grating etch depth of 150 nm can give a compact structure, without having a problem in the fabrication and etching procedure. Thus a grating with a grating depth of ΔW = 150 nm with a duty cycle D = 60% is used for further simulations. The transmission spectrum behavior of the grating with etch depth ΔW = 150 nm, for a grating length between 9Λ and 14Λ is shown in Fig. 4 . A drastic variation in band width and transmittivity is observed between these two grating lengths. The grating length Lout = 14Λ shows a band width of 0.11 nm (Q = 13,265) with a transmittivity of 42.7%. If a high transmittivity is needed in the band pass specrum a grating length Lout = 12Λ can be used with a band width and transmittivity of 0.17 nm(Q = 8584) and 85%, respectively.
4. Coupled cavity configuration to get a sharp line shape
For a refractive index sensor based on intensity measurement approach a sharp line shape with a high selectivity is desirable in the transmission spectrum because they can give a larger change in intensity for a shift in resonance when there is a change in analyte refractive index. Coupled cavity configuration is extensively demonstrated in ring resonator structure to get an asymmetrical line shape in the resonance so that the sensor sensitivity can be improved [18–20]. Here the Lorentzian shape in the resonance spectrum is converted into a Gaussian shape through two phase shifts applied in the gratings so that an effective coupled cavity is formed. Figure.5 (a) shows the schematic diagram of a two phase shifted grating forming a coupled cavity. Figure 5(b) is the superposed normalized transmission spectrum of single phase shifted and two phase shifted grating, respectively. Considerable improvement in spectral shape is obtained with two phase shifts applied to the grating. The selectivity of the spectrum, (defined by S = B-1 / B-10, where B-1 and B-10 are the −1 dB and −10 dB bandwidth) is improved by a factor of 2.542 when two phase shifts are applied to the grating, resulting into a sharp line shape for the resoanat transmission. In the coupled cavity configuration shown in the Fig. 5, the grating lengths are set to Lout = 10Λ and Lin = 20 Λ. The other combination of grating lengths (satisfying the condition 2 Lout = Lin) is also exhibiting the same spectral shape improvement but with different spectral band width and transmittivity. Since the band width is insignificant in an intensity measurement approach, a grating with a high transmittivity is used in sensor detection limit calculation, setting the lengths to Lout = 10Λ and Lin = 20 Λ.
5. Sensing principle and minimum detectable refractive index change
Figure 6 (a) shows the schematic diagram of the proposed integrated biosensor based on phase shifted vertical side wall gratings. The beam of light from a tunable laser can be coupled to the grating through one end and the output light can be coupled out from the other end for spectral analysis. The cladding layer is modified with a Poly-Di-Methyl Siloxane (PDMS) material to form a micro fluidic channel across the grating structure, so that the structure imitates a biosensor in a lab-on-a-chip like device. The micro fluid channel having a channel width of approximately 13 µm is assumed to be crossing the sensor structure. A fluid of refractive index n Clad is assumed to be flowing through the channel. The sensor sensitivity and detection limit is calculated through wavelength shift measurement and intensity measurement approach. For a wavelength shift measurement method, the minimum detectable refractive index of the sensor can be expressed asFig. 6(b). The effective index of waveguide grating is calculated through 3-D Beam Propagation Method (BPM) mode solver tool present in the FDTD design software for different cladding fluid refractive indices.
The effective index variation obtained as in Fig. 6(c) gives the slope of = 0.1389. Considering the fact that the smallest shift that can be measurable is one fifteenth of the of the peak width, here the grating with Lout = 14 Λ will offer the smallest spectral resolution of Δλ min = 7.33 pm. Hence the minimum detectable bulk refractive index change is calculated from Eq. (6) as Δn min = 8.1x 10−5. The same detection limit is also calculated from the sensitivity(S) of the sensor using the equation , where R = Δλ min = 7.33 pm is the sensor resolution and = 90 nm /RIU is the sensor sensitivity calculated from spectral shift measurement with varying cladding index. Δλ is the shift in the resonant transmission peak for a Δn change in cladding fluid refractive index. A detection limit of Δn min = 8.1x10−5 is calculated with above mentioned values.
For an intensity measurement approach the transmitted power is to be measured at particular wavelength for a change in cladding fluid refractive index. Here one of the resonance wavelengths is set as a reference wavelength and the change in power is measured with respect to change in cladding fluid refractive index n Clad. Figure 6(d) shows the normalized transmission with respect to the change in refractive index of the cladding fluid. The grating with two phase shifts is used in the analysis and it has given a sharp line shape in the spectrum improving the sensitivity considerably. Considering the power change as a function of cladding refractive index change the minimum detectable refractive index change can be defined as Fig. 5(b)] as 0.4134 nm. and = 0.0111 nm−1. is the power measurement resolution which is the minimum detectable change in optical power, which depends on many factors especially laser power fluctuation and dark current noise of the photo detector. Considering a power measurement resolution of 1%, the minimum detectable refractive index change is calculated from Eq. (7) as Δn min = 4.59x10−5.
The detection limit is also calculated using the power sensitivity which is defined by .Fig. 6(d) as 184.51giving a power sensitivity of S = 184.51. With a power measurement resolution R = = 1% the detection limit is calculated as = 5.43x10−5.
The detection range for refractive index change would be larger for wavelength shift measurement method as the resonance peak can be shifted over the wide stop band (1335nm to 1589 nm). From the spectral shift measurement observed in our structure, this range suggests a possible detection range of approximately 2.8 RIU change. The intensity measurement approach is limited for measuring refractive index change by the one spectral peak used in the measurement. As the resonance peak has a sharp edge and the intensity comes down very fast with small refractive index change the calculation shows that only a range of less than 0.01 RIU change would be able to measure with one resonance peak. However the intensity measurement approach has advantages over wavelength shift measurement, in terms of comparatively good sensitivity with less stringent requirement for detector resolution and high intensity spectrum obtained outside.
Table1 . shows a comparison of the phase shifted grating sensor parameters with some of the silicon based structures such as Mach-Zhender interferometer, ring resonator and surface corrugated Bragg grating.
The parameter comparison shown in Table.1 shows the significant advantage of proposed phase shifted vertical side wall grating sensor over other silicon based structures in terms of compactness. The Mach-Zehnder based structure has got complexity in structure with a long length and 3dB couplers, so that the structure is less suitable large number integration in micro fluidic or multi analyte detection setups. For a ring resonator based structure the free spectral range is very small and is limited by the ring radius. The dimension of the surface corrugated Bragg grating is larger than our structure by one order of magnitude and the structure needs stringent requirements for a single mode waveguide design and fabrication.
In this paper, design and simulation of the phase shifted vertical side wall gratings on a submicron SOI waveguide is presented to obtain the performance parameters needed for a compact label free biosensor. The gratings are designed for a high Q value, high transmittivity and sharp line shape in the resonant transmission spectrum so that the sensor sensitivity can be improved. The compactness of the grating would allow easy integration of the sensing structure with a large number of micro fluidic channels in lab-on-a-chip like devices to form a sensor array for multi analyte detection. The grating which is having a wider stop band in the transmission would allow a linear response over a wide range of wavelength (1335nm-1589 nm). The sensor performance is analyzed through both wavelength shift measurement and intensity measurement approach and a detection limit of Δn min ~5x10−5 is calculated. The designed grating has good performance parameters when compared to other silicon based structures in terms of compactness, sensitivity and free spectral range.
The authors acknowledge the financial support received through ARC 3/08. The support received through NTU-IME CRP is also greatly acknowledged. One of the authors, P.Prabhathan would also like to acknowledge Nanyang Technological University for the research student support.
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