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Both refractive index sensors have a minimum detection limit on the order of 10−6, ... based on the phase- shifted sidewall Bragg gratings in slot waveguides.
Highly sensitive compact refractive index sensor based on phase-shifted sidewall Bragg gratings in slot waveguide Xin Wang* and Christi K. Madsen Department of Electrical and Computer Engineering, Texas A&M University, College Station, Texas 77840, USA *Corresponding author: [email protected] Received 30 September 2013; revised 22 November 2013; accepted 23 November 2013; posted 26 November 2013 (Doc. ID 198495); published 23 December 2013

The geometrical and physical parameters of phase-shifted sidewall Bragg gratings in a silicon slot waveguide are optimized to possess performance characteristics desirable for integrated optical sensors. By tailoring the spectral response of such phase-shifted sidewall gratings, highly sensitive compact refractive index sensors detecting the resonance wavelength shift or the variation of light intensity are designed with the transfer matrix method. Both refractive index sensors have a minimum detection limit on the order of 10−6 , and a linear response and a compact structure dimension as small as 11.7 μm, offering the capabilities for sensor array and lab-on-a-chip integration. The resonance-shift sensor has a much wider detection range of 1.32 refractive index units than the intensity-measurement sensor. The performance parameters are compared with other refractive index sensors, including Mach–Zehnder interferometers, ring resonators, surface gratings, and phase-shifted gratings in silicon nanowire. © 2013 Optical Society of America OCIS codes: (130.3120) Integrated optics devices; (130.6010) Sensors; (050.2770) Gratings; (050.5080) Phase shift; (230.7370) Waveguides. http://dx.doi.org/10.1364/AO.53.000096

1. Introduction

Optical sensors play a critical role in numerous applications, including biomedicine, forensic diagnostics, microbiology, drug screening, environment monitoring, and food quality control. Huge progress has been made in the research and development of integrated optical sensors based on silicon planar waveguides that can be fabricated using standard microelectronics technology, allowing mass production and integration of sensor arrays on a chip for simultaneous detection of multiple analytes [1,2]. Different sensing platforms, such as interferometers [3,4], surface plasmon resonances [5,6], guided-mode resonances [7–9], photonic crystals [10], Bragg gratings [11,12] and microring resonators [13–15] have 1559-128X/14/010096-08$15.00/0 © 2014 Optical Society of America 96

APPLIED OPTICS / Vol. 53, No. 1 / 1 January 2014

been investigated. Although conventional strip or rib waveguides are commonly employed in these integrated optical sensors, the slot waveguide formed by placing two strip waveguides in parallel with a nanometer gap (slot) has drawn more and more interest due to its high confinement of electric fields in low refractive index materials [16–18]. In fact, a great variety of optical devices utilizing slot waveguide structures have been designed and proposed, including directional couplers [19], optical filters [20–22], optical modulators [23], optical switches [24], electrically pumped light-emitting devices, [25] and microring resonators [26]. In particular, optical label-free sensing based on single slot waveguides [27], multiple slot waveguides [28], bent slot waveguides [29], and slot waveguide microring resonators [30–33] have also been reported. In this work, compact refractive index sensors based on the phaseshifted sidewall Bragg gratings in slot waveguides

are designed with the transfer matrix method (TMM) [34]. We show that, for the first time to our knowledge, such refractive index sensors have a high sensitivity, a linear response over a wide detection range, as well as a compact structure dimension offering the capability of integration with other electronics, sources, and detectors on the same platform. In the design, a slot waveguide is formed by placing two silicon strips in parallel, with a nanometer gap. Bragg gratings are patterned at the inner sidewalls of the silicon slot waveguide. Sidewall gratings in slot waveguides exhibit several advantages over surface gratings and sidewall gratings in strip or rib waveguides. First, a grating in a slot waveguide periodically perturbs the refractive index distribution of the guiding core (low-index slot region), where the intensity of electric field is much higher than that in the high-index region, yielding a strong coupling strength. As a result, its spectral response is extremely sensitive to the change of refractive index of the material inside the slot [16,27]. It follows that the resonance spectrum changes almost linearly with the refractive index of the slot medium. Second, a high Q-factor resonance cavity can be built using such sidewall gratings with only a few grating periods, making the device dimension very compact. Third, transmission loss arising from out-of-plane scattering and mode mismatch can be reduced when the slot is filled with an analyte material. This helps to sustain a high Q-factor and, thus, high sensitivity. Additionally, such slot waveguide sidewall gratings can be readily fabricated in a few steps by standard microelectronics technologies. In the calculation, the geometric and physical parameters of sidewall Bragg gratings in slot waveguides are firstly analyzed in terms of mode effective index, mode confinement factor, and grating coupling coefficient. The mode effective index, confinement factor, and electric field distribution are calculated with film mode matching (FMM) tools. Material dispersions are included by applying Sellmeier equations [35]. In this paper, two highly sensitive compact refractive index sensors are designed: one resonanceshift sensor detecting the shift of the resonance peak wavelength and one intensity-measurement sensor that detects the variation of light intensity at a fixed wavelength. The resonance-shift sensor is based on a single phase-shifted sidewall Bragg grating with a high Q-factor. Coupled phase-shifted sidewall Bragg gratings with the spectral response of a sharp Gaussian shape are adopted by the intensitymeasurement sensor. Both refractive index sensors have a minimum detection limit on the order of 10−6, a linear response, and a compact structure dimension as small as 11.7 μm. The resonance-shift sensor has a much wider detection range of 1.32 RIU (refractive index unit) than the intensity-measurement sensor. However, the intensity-measurement sensor has relaxed requirements for detector resolution and spectrum measurement. The performance

parameters of designed sensors are also compared with other integrated refractive index sensors. 2. Sidewall Bragg Gratings in a Slot Waveguide

Before the design, the geometric and physical parameters of both the slot waveguide and sidewall Bragg gratings need to be optimized to possess the performance characteristics desired for optical sensing. Figure 1(a) illustrates the cross sectional view of a vertical silicon slot waveguide on silicon dioxide. For single mode propagation (TE0 ), we designed the slot waveguide formed by two silicon strips with the width W  300 nm and the height H  320 nm. The two silicon strips are placed in parallel with an air gap, S, that has a variable value between 50 and 140 nm. We used FMM tools in Fimmwave (Photon Design Inc., UK) to calculate the effective index, confinement factor, and transverse electric field distribution of guided modes in slot waveguides. Figure 2 plots the mode effective index neff as a function of the refractive index of the material loaded in the slot nslot . The existence of a refractive index of the loaded material tends to change the mode effective index in a linear fashion. The change rate is Δneff ∕Δnslot  0.4055 for the 100 nm slot waveguide. A larger slot width leads to a smaller effective mode index because the portion of high-index material decreases as the slot width increases. In the consideration of strong mode confinement and ease of fabrication, we used S  100 nm in what follows. Figure 1(b) is a top view of a phase-shifted sidewall Bragg grating. The gratings are patterned on both inner sidewall interfaces of a slot waveguide. Here, Λ, d, and Lg indicate grating period, grating depth, and grating length, respectively; t is the width of high-index material in one grating period and the ratio t∕Λ is duty cycle (DC). The grating parameters are optimized in aspects of strong coupling strength, compact dimension, and ease of fabrication. Grating period is determined by the phase-matching condition: Λ  λB ∕2neff , where λB is the Bragg wavelength. The phase-shifted Bragg grating is constructed by introducing a quarter-wave spacer in the middle of the uniform Bragg grating so that a resonance microcavity is formed. This quarterwave spacer will create a cavity resonance near the Bragg wavelength [22]. The length of quarter-wave spacer, Lq , is given by Lq  λB ∕4neff . For the 100 nm slot waveguide loaded with a material with

Fig. 1. Schematics of (a) a silicon slot waveguide on silicon dioxide and (b) a phase-shifted sidewall Bragg grating in a slot waveguide. 1 January 2014 / Vol. 53, No. 1 / APPLIED OPTICS

97

1 n

neff

eff

= 0.4055*n

slot

+ 1.595

Transmission

2.3

2.2 S=80nm S=100nm S=120nm Linear fit

2.1

slot

" 

T i21 T i22 j κδ sinhδLi 

2π where Δβ2β− ; Λ β

−j κδ sinhδLi  coshδLi jΔβ 2δ sinhδLi 

#

s  2 Δβ 2 δ κ − ; 2

2π n jα: λ eff

1450

1550

1650

ϵ c Γ 0 4

;

RR

2

(2)

Unlike a surface grating or a sidewall grating in a strip waveguide, a sidewall grating in a slot 0.44

(1)

n

=1.0

n

=1.3330

slot slot

nslot=1.3772 nslot=1.4500

Γ

Figure 3 plots the superimposed transmission spectrum of a uniform sidewall Bragg grating and a phase-shifted sidewall Bragg grating in slot waveguide. A stopband of ∼385 nm centered near the Bragg wavelength λB  1571.35 nm is observed from the uniform sidewall grating. This broad stopband potentially provides a wide detection range for an optical sensor. In the spectrum of the phase-shifted sidewall grating, a sharp resonance transmission peak of a Lorentzian shape with the −3 dB bandwidth APPLIED OPTICS / Vol. 53, No. 1 / 1 January 2014

1850

x; ydxdy : ∞ Px x; ydxdy

slotRRnx; yE

0.4

98

1750

of ∼3.1 nm is observed near λB. Its high transmission, narrow bandwidth and, thus. high Q-factor are key characteristics desired for an optical sensor detecting the resonance wavelength shift. To sustain high transmission and, thus, high Qfactor, a high-index contrast material system, such as silicon on insulator (SOI), is widely used to achieve strong mode confinement. In Eq. (2), we defined mode confinement factor Γ to measure how much mode intensity is well confined in the slot waveguide. Here, ϵ0 and c is vacuum permeability and vacuum speed of light, respectively. Pz x; y is the Poynting vector and Ex; y is the transverse electric field. Figure 4 plots the mode confinement factor, Γ, as a function of slot width, S, when the slot waveguide is filled with different materials. As the slot width increases, the confinement factor decreases if the loaded material has an index of refraction smaller than that of water (nslot  1.3330). For the 100 nm slot waveguide, the confinement factor has an optimal value of 39  3% for a wide variety of materials including isopropyl alcohol (nslot  1.3772), index gel (nslot  1.45), chlorobenzene (nslot  1.5248), and 1, 2, 4-dichlorobenzene (nslot  1.5717). This feature is much desired for multi-analyte sensing applications. Calculation of Γ:

#

coshδLi −jΔβ 2δ sinhδLi 

Uniform Phase−shifted

0.2

Fig. 3. Transmission spectrum of a phase-shifted sidewall Bragg grating with N  8, Λ  360 nm, DC  0.5, d  30 nm, and α  0.

a refractive index nslot  1.45, the corresponding mode effective index is neff  2.18273 at 1.55 μm. The grating period under the phase-matching condition is ∼355 nm. We selected Λ  360 nm for ease of fabrication. The spectral response of a phase-shifted sidewall Bragg grating can be analyzed with the TMM. Each segment of the device structure is described by a 2 by 2 matrix T i (i  g; q for the grating and quarter-wave spacer, respectively) as represented by Eq. (1), where β  2π∕λneff  jα is the complex propagation constant of the guided mode TE0 and α is the loss coefficient. For a grating segment, the elements of T i are determined by wavelength λ, coupling coefficient κ, grating period Λ, and grating length Li  NΛ, where N is the number of grating periods. For a phase-shifted spacer segment, κ is 0 and Λ is infinity. The total transfer matrix of the whole device is simply the product of all involved matrices. For the single phase-shifted Bragg grating in the slot waveguide shown in Fig. 1(b), the total transfer matrix is T single  T g T q T g . The spectral transmission of the structure is given by 1 − jT 21 j2 ∕jT 11 j2 , Ti 

0.4

Wavelength (nm)

Fig. 2. Mode effective index of a slot waveguide filled with different materials at 1.55 μm. The black line is a linear fit for S  100 nm.

T i11 T i12

0.6

0 1350

1.3 1.35 1.4 1.45 1.5 1.55 1.6 n

"

0.8

nslot=1.5248

0.36

n

=1.5717

slot

0.32 0.28

50 65 80 95 110 125 140 S (nm)

Fig. 4. Mode confinement factor, Γ, at 1.55 μm as a function of slot width, S, for slot waveguides filled with different materials. The silicon strip dimensions are W  300 nm and H  320 nm.

κ

    ZZ 4ωϵh − ϵ0  πt 2π sin cos jEx; yj2 dxdy; π Λ Λ grating (3)

where ω  2c∕λ is the angular frequency and ϵh is the dielectric constant of the high-index material. It follows that κ is maximized at t∕Λ  0.5 (i.e., t  180 nm for Λ  360 nm). As analyzed above, high index-contrast material provides larger coupling coefficients. The effects of grating depth and refractive index of slot material on coupling coefficient are plotted in Fig. 6. The coupling coefficient increases with increasing grating depth. Loading material in the slot will reduce the coupling coefficient as it degrades the index contrast. At d  30 nm, the change in the coupling coefficient per RIU is ∼0.7510 μm−1. However, in the following section it will be shown that loading the slot waveguide aids in reducing transmission loss arising from out-of-plane scattering and mode mismatch. 3. Compact Refractive Index Sensor Design

By tailoring the spectral response of the sidewall Bragg gratings in a slot waveguide, we designed two highly sensitive compact optical refractive 80 n

=1.0

n

=1.3330

slot slot

Ey (V/m)

60

nslot=1.4500 nslot=1.5717

40 20 0 2.4

2.6

2.8

3 x (µm)

3.2

3.4

3.6

Fig. 5. Amplitude profiles of transverse electric field Ey at 1.55 μm for a 100 nm slot waveguide filled with different materials. The silicon strips have the same dimensions as in Fig. 4.

1.6

nslot=1.0

1.6

n

1.4

=1.3330

slot

κ (µm−1)

waveguide introduces periodic perturbations directly to the guiding core, other than the cladding, which leads to a stronger coupling strength. That is because the intensity of the transverse electric field confined in the slot region is much higher than that in the silicon strip, as seen in Fig. 5. Indeed, the ratio between the amplitudes of the electric field confined in the slot region and that in the strip region is directly proportional to the square of the index contrast [16], so high-index material, such as silicon, is commonly used in slot waveguides. Due to its strong coupling strength, the spectral response of a sidewall grating in a slot waveguide is extremely sensitive to the change of refractive index of the material in the slot. To quantitatively evaluate the coupling strength, we calculated the coupling coefficient, κ, by overlap integration between the distributions of the electric field and refractive index over the grating regions, as described by Eq. (3),

nslot=1.4500

1.2

n

d=20nm d=30nm Linear fit d=40nm

1.2

=1.5717

slot

1 0.8

0.8 0.6

0.4

0.4

(a) 0

10

20 30 d (nm)

0.2 40

κ = −0.7510*n

slot

+ 1.9921

(b) 1.3

1.4 n

1.5

1.6

slot

Fig. 6. Effects of (a) grating depth and (b) refractive index of the slot medium on the coupling coefficient at 1.55 μm. The black line is the linear fit at d  30 nm.

index sensors: one resonance-shift sensor and one intensity-measurement sensor. A spectral response with a high transmission and a narrow bandwidth is desired by a resonance-shift sensor as it detects the resonance wavelength shift. The intensitymeasurement sensor measures the intensity of transmitted light at a reference wavelength, so it requires a spectral response with a sharp line shape to improve its accuracy and sensitivity. For a phase-shifted grating, the transmission is highly limited by the loss inside the microcavity resonator formed by two uniform gratings on both sides of the quarter-wave spacer. The Q-factor is determined by two types of loss mechanisms: waveguide loss and coupling loss [12,36]. The coupling loss depends on the product of the grating length and coupling coefficients (i.e., κLg ) and can be optimized by adjusting the grating depth, DC, and grating length [12,22]. On contrast, the waveguide loss is inherent in the fabrication (waveguide and grating sidewall roughness). As a result, the intrinsic Q-factor of a phase-shifted sidewall grating is dominated by waveguide loss that can be attributed to out-of-plane scattering during reflections or mode mismatch at grating-waveguide interfaces. However, when the slot waveguide is filled with a material, the scattering loss will be reduced as a result of reduced index contrast. On the other hand, filling a slot waveguide also increases its mode effective index, which helps with mode transition at the grating-waveguide interface. Therefore, the phase-shifted sidewall grating in a slot waveguide filled with an analyte material can provide a spectral response with a high transmission and high Q-factor. In general, a slot waveguide exhibits a relatively higher loss than a conventional silicon strip or rib waveguide. A typical value of ∼10 dB∕cm for a silicon slot waveguide has been reported [26,37]. Taking account of waveguide loss, we used α  10 dB∕cm in the simulations. A. Resonance-Shift Sensor

The resonance-shift sensor is based on a single phase-shifted sidewall Bragg grating in a slot waveguide. To precisely detect the shift of resonance wavelength, due to a small change in the refractive 1 January 2014 / Vol. 53, No. 1 / APPLIED OPTICS

99

Transmission (dB)

0 −10 N=8 N=10 N=12 N=14 N=16

−20 −30 1567

1569 1571 1573 Wavelength (nm)

1575

Fig. 7. Transmission spectrum in dB of phase-shifted sidewall Bragg gratings in a slot waveguide with different grating lengths. Other grating parameters are: d  30 nm, DC  0.5, Λ  360 nm. The refractive index of the slot material is nslot  1.45. The waveguide loss coefficient is α  10 dB∕cm.

index of slot material, high transmission and large Q-factor is highly desired [12,13,15]. The Q-factor is estimated by Q  λB ∕ΔλFWHM, where λB is the resonance wavelength and ΔλFWHM is the full width half-maximum (FWHM) bandwidth. The resonance peak wavelength is close to the Bragg wavelength, λB , due to the structure’s symmetry. The FWHM bandwidth depends on the product of the coupling coefficient and the grating length [22]. Since sidewall gratings in slot waveguides have strong coupling coefficients, high Q-factor can be readily achieved by adjusting the grating length and grating depth. Figure 7 displays the superimposed transmission spectrum in dB of single phase-shifted sidewall Bragg gratings with different grating lengths, for d  30 nm. The resonance bandwidth drops quickly 1

as the grating length increases. At N  16, the bandwidth is suppressed to ∼20.6 pm, yielding a Q-factor as high as 7.6 × 104 . Using the single phase-shifted sidewall grating with N  16 and d  30 nm, we designed a resonance-shift sensor. Figure 8(a) shows the spectral response of the designed resonance-shift sensor. The refractive index of the slot medium varies from 1.35 to 1.55, with an increment of 0.02. As expected, filling the slot waveguide aids in reducing transmission loss by increasing the mode effective index. The transmission loss is reduced to 0.06 dB, with nslot  1.55 from 0.47 dB with nslot  1.35. As the refractive index of slot material nslot increases, the resonance bandwidth increases from 11.04 pm at nslot  1.35 to 41.76 pm at nslot  1.55, as in Fig. 8(b), leading to decreased Q-factors. The decreasing of Q-factor can also be attributed to waveguide loss. For instance, the Qfactor is 9.3 × 104 at nslot  1.45 without waveguide loss (i.e., α  0). However, the Q-factor of this sensor is maintained in the range between 3.83 × 104 and 1.40 × 105 , sufficiently high for efficient light-matter interaction. In Fig. 8(c), a linear response with the slope of ΔλB ∕Δnslot  291.93 nm∕RIU is observed. Considering the fact that the smallest shift that can be measurable is one fifteenth of the resonance peak bandwidth, this sensor has a spectral resolution at Δλmin  1.3733 pm. According to Eq. (4),

Δnmin 

  1 Δnslot Δλmin ; 2Λ Δneff

nslot=1.35

(a)

nslot=1.37

0.8 Transmission

(4)

nslot=1.39 nslot=1.41 nslot=1.43

0.6

n

=1.45

n

=1.47

n

=1.49

slot slot

0.4

slot

nslot=1.51 nslot=1.53

0.2

nslot=1.55

0 1350 1400 1450 1500 1550 1600 1650 1700 1750 1800 Wavelength (nm)

(b)

1600

−10

(c)

(nm)

B

−20

B

Transmission (dB)

0

= 291.93*nslot+ 1148.3

1580

−30

1560

−40

1540

B

1540

1560 1580 1600 Wavelength (nm)

Linear fit 1.35

1.4

1.45 n

1.5

1.55

slot

Fig. 8. (a) Transmission spectrum of the resonance-shift sensor based on a single phase-shifted sidewall Bragg grating in a slot waveguide with N  16 and d  30 nm; (b) zoom in of the resonance transmission peaks in dB for the wavelength range from 1530 to 1615 nm; (c) resonance peak wavelength, λB , as a function of the refractive index of slot material nslot . 100

APPLIED OPTICS / Vol. 53, No. 1 / 1 January 2014

the minimum detectable refractive index change is Δnmin  4.7 × 10−6 RIU, which is improved by one order compared with the SOI refractive index sensor in [12]. Besides, the designed resonance-shift sensor has a compact device dimension of only 11.7 μm, smaller than that in [12]. The detection range of this refractive index sensor is wide because the resonance wavelength can shift over a broad wavelength band from 1404 to 1789 nm. This range suggests a possible detection range of approximately 1.32 RIU. To further extend the detection range, sensor arrays can be implemented by deploying multiple phase-shifted sidewall gratings with successive values of grating periods (Λ1 ; Λ2 ; …; Λn ) on the same chip. B.

Intensity-Measurement Sensor

The intensity-measurement sensor detects the intensity variation of transmitted light at a fixed wavelength, so the sharpness of the transmission spectrum is critical in improving the sensitivity and accuracy. We used a coupled microcavity configuration to optimize the spectrum sharpness. As illustrated in Fig. 9(a), a coupled phase-shifted sidewall Bragg grating in a slot waveguide is realized by inserting two quarter-wave spacers in a uniform grating. Lgg and Lg indicate the length of inner grating and outer grating, respectively. The outer grating length is given by Lg  NΛ. Following the TMM method, the total transfer matrix of such a

coupled grating structure is given by T coupled  T g T q T gg T q T g . Since Lgg  2Lg , we can estimate that T coupled  T g T q T g T g T q T g   T 2single by splitting the inner grating segment into halves, with each having a length of Lg. Analogous to the fact that the function f x  −x4 has a sharper edge and flatter top than the function f x  −x2 where x is a real number, the coupled phase-shifted sidewall gratings exhibit better spectrum sharpness. Figure 9(b) plots the superimposed transmission spectrum of the coupled phase-shifted Bragg gratings with different values of Lgg. As the length of inner grating Lgg gets close to 2Lg , the two resonance transmission peaks tend to emerge and form a flat-top, narrow and sharp Gaussian shape. Compared with the Lorentzian shape from a single phase-shifted Bragg grating, the flat-top feature is undesirable for an optical sensor that detects the wavelength shift, but the sharpness of the Gaussian shape is favored by an intensity-measurement sensor because it provides a large change in the light intensity if there is a small change in the refractive index of the slot material. To quantitatively evaluate the sharpness, we defined the spectrum selectivity as SS  Δλ−1 dB ∕Δλ−10 dB , where Δλ−1 dB and Δλ−10 dB denote the −1 dB bandwidth and −10 dB bandwidth, respectively. The spectrum selectivity of the coupled phase-shifted sidewall Bragg gratings is 2.42 times larger than that of a single phase-shifted Bragg grating for N  12. Figure 9(c) shows the transmission spectrum of

(a)

1

(a)

n

=1.45

n

=1.45005

slot slot

0

Transmission

Transmission (dB)

0.8

(b)

−10 −20

nslot=1.4501 n

0.6

nslot=1.45025

nslot=1.45045 n

0

2L

g

R

1571.5

R N=8 N=10 N=12 N=14 N=16

−20 −30 1570

1571 1572 Wavelength (nm)

1573

Fig. 9. (a) Schematics of the coupled phase-shifted sidewall Bragg gratings in a slot waveguide, and the transmission spectrum of coupled sidewall Bragg gratings in a slot waveguide for (b) different values of Lgg with N  12 and for (c) different values of N with Lgg  2Lg . All the rest of the parameters are the same as those in Fig. 7.

1571.6 1571.7 Wavelength (nm)

1571.8

(b) Transmission at

Transmission (dB)

−10

=1.4505

slot

Lg

(c)

=1.45035

nslot=1.4504

1530 1545 1560 1575 1590 1605 Wavelength (nm) 0

=1.4503

n

slot

0.2

−40

n

slot

0.4

0.5Lg

−30

=1.45015

slot

nslot=1.4502

T = − 2911.1*nslot + 4222.2

1

0.5 T at

R

Linear fit 0

1.45

1.4502 n

1.4504

1.4506

slot

Fig. 10. (a) Transmission spectrum of the intensitymeasurement sensor based on coupled phase-shifted sidewall Bragg gratings in a slot waveguide with Lgg  2Lg and N  12; (b) transmission at the reference wavelength λR as a function of the refractive index of the slot medium, nslot . 1 January 2014 / Vol. 53, No. 1 / APPLIED OPTICS

101

Table 1.

Performance Parameters of Some Integrated Refractive Index Sensors

Refractive Index Sensors SOI Mach–Zehnder interferometer [3] Hydex ring resonator [13] SOI ring resonator [15] SI3 N4 ring resonator in a slot waveguide [30] SOI ring resonator in a slot waveguide [31] Surface grating in silicon rib waveguide [11] SOI nanowire phase-shift gratings [12] Proposed phase-shift grating in a slot waveguide

Δnmin

Device Dimension

Q-Factor

7 × 10−6 1.8 × 10−5 1 × 10−5 2.3 × 10−4 4.2 × 10−5 10−4 5 × 10−5 4.7 × 10−6

L  30 mm Radius  60 μm Radius  5 μm (Area  100 μm2 ) Radius  70 μm Radius  5 μm (Area  130 μm2 ) L  173 μm L  13 μm L  11.7 μm

— Q  12000 Q  20000 — Q  330 — Q  13265 Q  76000

the coupled phase-shifted gratings with Lgg  2Lg and different grating lengths. Similar to the single phase-shifted grating, the transmission bandwidth of coupled phase-shifted gratings also decreases with the grating length. To design an intensitymeasurement sensor as compact as the resonanceshift sensor, we chose N  12, making the device structure dimension to be 17.64 μm. The intensity-measurement sensor is designed to detect the change of light intensity at the reference wavelength λR  1571.55 nm. Figure 10(a) plots the transmission spectrum of this sensor. The refractive index of the slot medium varies from 1.45 to 1.4505, with an increment of 0.00005. The light intensity changes almost linearly at a rate of ΔP∕Δnslot  2911.1 RIU−1 with the refractive index of the slot medium, nslot . It is noteworthy that the waveguide loss is negligible for this sensor. Given the power measurement resolution ΔPmin that depends on the power fluctuation level of the laser source and the dark current noise of the photodetector, the detection limit can be calculated. For ΔPmin  1%, the detection limit is Δnmin  3.4 × 10−6 RIU. Because the spectral response of coupled phase-shifted Bragg gratings has a sharp Gaussian shape and the intensity varies fast with the change of refractive index of the slot medium, the detection range of the intensity-measurement sensor is limited to 0.009 RIU. However, the intensity-measurement sensor has relaxed requirements for the detector resolution and intensity spectrum, since the measurement is based on a single wavelength. The device performance parameters of some integrated refractive index sensors are compared and summarized in Table 1. The proposed refractive index sensor based on a single phase-shifted sidewall Bragg grating in a slot waveguide provides the largest Q-factor at Q  7.6 × 104 , the highest sensitivity on the order of 10−6, and the smallest device dimension at L  11.7 μm. Although the SOI Mach– Zehnder interferometer in [3] has the minimum detection limit on the same order, it requires a device dimension as large as 30 mm. The detection limit of the proposed resonance-shift sensor can be further improved by using relatively longer gratings to realize a microcavity resonator with a larger Q-factor. The designed intensity-measurement sensor based on coupled phase-shifted sidewall Bragg gratings also has a sensitivity on the order of 10−6 and a device 102

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structure length of L  17.64 μm. Besides, the resonance-shift sensor has a linear response over a wide detection range of 1.32 RIU. The intensitymeasurement sensor has a quasi-linear response over a detection range of only 0.009 RIU. For both designed sensors, extended detection range in RIU and simultaneous detection for multiple fluidic analytes are possible by implementing sensor array with successive values of grating periods. 4. Summary

To summarize, refractive index sensors with a high sensitivity, a linear response and a compact dimension are designed using the TMM. The slot waveguide structure provides several advantages over a strip or rib waveguide by offering high confinement of the electric field in the slot region, strong coupling strength from the sidewall gratings, as well as reduced transmission loss when the slot is filled with a medium. By tailoring the spectral response of phase-shifted sidewall Bragg gratings in a slot waveguide, two refractive index sensors are proposed in the paper. A resonance-shift sensor is designed using a single phase-shift sidewall Bragg grating with a high Q-factor. Coupled phase-shifted sidewall Bragg gratings with a spectral response of a sharp Gaussian shape are adopted by an intensitymeasurement sensor. Both designed refractive index sensors have a compact structure dimension as small as 11.7 μm, making it feasible for sensor array packaging and lab-on-a-chip integration. The detection limit and detection range of two designed sensors are investigated. A minimum detectable change in the refractive index at 4.7 × 10−6 RIU is realized for a resonance-shift sensor and 3.4 × 10−6 RIU for an intensity-measurement sensor. The performance parameters of the two designed sensors are compared with other integrated refractive index sensors, including a Mach–Zehnder interferometer (MZI), ring resonator, surface gratings, and phase-shifted gratings in a silicon nanowire. This work is funded by the National Science Foundation (NSF) under grant EEC-0540832. References 1. X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: a review,” Anal. Chim. Acta 620, 8–26 (2008). 2. K. Zinoviev, L. G. Garrascosa, J. S. Rio, B. Sepulveda, C. Dominguez, and M. Lechuga, “Silicon photonic biosensors

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