1. Introduction
Optical refractive index (RI) sensors that measure the change in RI have been proven useful in successfully developing a biochemical sensor that measures biomolecular interactions [
1,
2,
3,
4]. These optical RI sensors exhibit significant advantages over conventional mechanical and electrochemical sensors. These advantages include no fluorescent labeling, high throughput, and better sensitivity [
5,
6,
7,
8,
9]. Several approaches to quantify the RI change of a target layer, which is induced by the variation in the sensing environment, have been proposed and found to be effective in achieving a high-precision RI sensor. The various optical RI sensors include surface plasmon resonance (SPR) [
10], ring resonator [
11], long-period fiber grating [
12], grating coupler [
13], grated waveguide [
14], and metallic photonic crystal sensors [
15]. The proposed techniques utilize the resonant frequency shift of a transmission spectral profile that occurs when a fraction of the guided mode interacts with the change in the RI of the waveguide surface layer. The silicon-based grating waveguide RI sensor possesses two major advantages over other types of optical RI sensors. These advantages are high-resolution performance in detecting changes in the RI and mass production capability regarding device fabrication. The former advantage is due to the shift of a sharp fringe in the transmission spectrum near the stopband edge of the grating [
14], and the latter is due to a solid and matured processing technology of silicon (Si)-based electrical/optical device fabrication such as the standard complementary metal-oxide-semiconductor (CMOS) process [
16]. Several pieces of research successfully demonstrated the capability of Si-based grating waveguide sensor in biochemical applications [
17,
18,
19]. We recently proposed a compact and inexpensive biochemical sensor prototype using the Si-based grating waveguide to selectively detect and quantify the multivalent binding of proteins from a monovalent binding [
19], which is known to be a critical step for better understanding of fundamental mechanisms in the immune system, cancer, and thrombosis [
20,
21,
22]. The proposed biochemical sensor consists of a typical silicon-on-insulator (SOI) bottom layer, a silicon-based grating waveguide core, and a hydrogel functional layer on top of the grating waveguide. We calculated the dynamic range of the effective RI of the waveguide and demonstrated the feasibility of silicon-based grating waveguide sensors assisted by a functional hydrogel layer in addition to determining a design principle for it. Although our previous work and other studies on the Si-based grating waveguide sensor exhibit feasibility and high performance in detecting the changes in the RI of the target layer, the detailed analysis of the sensor performance considering the grating structure parameters and its design procedures have not been demonstrated yet.
In this paper, we propose a method to achieve maximum transmission extinction by choosing appropriate grating waveguide parameters, which are the duty ratio, grating period, and etching depth. We calculated the transmission characteristics of the grating waveguide sensor using a finite-difference time domain (FDTD) method. Here, we defined the transmission extinction as an important figure-of-merit (FOM) because it reflects both the resonance wavelength shift and full-width at half-maximum (FWHM) performance in the transmission spectrum of the RI sensor. We determined the relationship between the parameters and the sensor performance, and found that among the three parameters, the etching depth has the greatest effect on transmission extinction. We established the design guideline to determine the proper grating parameters based on the parameter vs. performance relationship. By using the procedure and with the optimization of the parameters, we achieved 49.2 dB of transmission extinction, which is an improvement of >26 dB when compared with the value attained without careful parameter selection.
2. Principles
Several sensor platforms such as transverse magnetic (TM) field and SPR sensor platforms have been proposed to increase the amount of transmission spectrum shift occurring due to the bioenvironmental target change [
23,
24]. The ratio of the evanescent field to the guiding field in a TM field sensor is larger than that in a transverse electric (TE)-field type sensor, so that the effect of the change in RI can be significantly enhanced, resulting in a high resolution of the RI sensor [
23]. An SPR sensor utilizes the enhancement in the interaction of the surface wave with the target material/phenomenon, which also provides high-resolution capability [
24]. These RI optical sensors can be widely applied to biochemical sensors owing to their high-resolution performances. The high-resolution performance is attributed to the large transmission spectrum shift due to the change in the resonance wavelength. Another important FOM of the optical RI sensor is the FWHM of the transmission spectrum. Resonator-type RI sensors with a high-quality factor (Q-factor) can provide high-resolution performance in measuring a tiny change in the effective RI of the optical waveguide [
25]. Typically, the performance of the resonator-type optical RI sensor is evaluated either by the resonance wavelength shift,
, or the FWHM,
.
Figure 1 shows a grating waveguide RI sensor and its sensing principle. Light that travels through the grating waveguide core is diffracted by the grating structure. The output transmission spectrum exhibits a resonance for which the wavelength shifts owing to the change in the RI of the top cladding layer. The set of figures on the right side of
Figure 1 depict the effects of
and
on the transmission spectrum. In the top right part of
Figure 1, a large transmission extinction
T is achieved by a large resonance wavelength shift. In the bottom right part of
Figure 1, a large transmission extinction
T is achieved by a small FWHM. In designing high-performance optical RI sensors, both the resonance wavelength shift
and FWHM
should be simultaneously considered to increase the transmission extinction
T. Herein, we propose the complete optimization of the design structure of the silicon-based grating waveguide for high-performance RI optical sensors used in biochemical applications by considering both the effect of the resonance wavelength shift
and FWHM
.
Figure 2 shows the silicon-based grating waveguide sensor platform for biochemical applications, which is similar to that discussed in [
19]. The proposed biochemical sensor consists of a typical SOI bottom layer, a silicon-based grating waveguide core, and a target layer on top of the grating waveguide. The waveguide core with grating structures provides Fabry–Perot resonances of the Bloch modes. The resultant transmission spectral profile exhibits multiple resonance peaks due to optical interference of the guided modes in the grating waveguide. In our analysis, a functional hydrogel layer was used as the target layer, as shown in the inset of
Figure 2, because it can provide a highly sensitive RI change when biochemical interaction occurs in the layer. We performed all calculations based on the shape of the hydrogel-waveguide interface assuming that the deposited hydrogel layer penetrates the waveguide groove structure and fills the groove structure completely, as shown in the inset of
Figure 2. It is known that receptor proteins in the hydrogel layer exhibit multivalent bindings with injected target proteins, which result in significant change in the RI of the hydrogel layer by local deswelling. We used a double-layer model for the functional hydrogel layer to adopt the results in [
26]. In the double-layer model, the RI of a part of the upper portion (=20%) of the layer changes to 1.39 (
= 1.39) and that of the other portion (80%) remains at 1.34 (
= 1.34) when the target bio-interaction such as multivalent binding of proteins occurs [
26]. In our previous work on the grating waveguide sensor performance [
19], we varied the top portion of the hydrogel layer that experiences the RI change (i.e., functional volume ratio) between 15–25%, because it can vary with several changing factors such as temperature, receptor-protein pairs, and hydrogel composition. The optimized waveguide parameters can be determined using the method provided in the manuscript for each case of the different biological environment. The hydrogel layer thickness is set at 150 nm because the thickness exhibits the maximum change in the effective RI of the waveguide core [
19]. We applied this functional hydrogel model as the target layer and analyzed the resonance shift
, FWHM
, and transmission extinction
of the grating waveguide sensor.
The change in the RI of the target layer affects the effective change in the RI of the waveguide core, resulting in a change in the transmission characteristic. The waveguide core consists of Si
3N
4 (
) on top of a SiO
2 bottom cladding layer
with a Si substrate (
) at 1550-nm wavelength [
27,
28]. Initially, the thickness of the waveguide core (
) is set at 275 nm, the grating period (
) is 490 nm, the duty ratio (R =
) is 0.5, and the number of the grating structure elements is 200. The duty ratio is defined as the ratio of the tooth grating width
to the grating period
. The total grating length L is 98
. The FWHM becomes smaller when the grating length L increases because of the increased intra cavity effect, and it is represented by [
17]
where
is the group index of the waveguide core and
is the resonance wavelength. As shown in
Figure 1, a smaller FWHM is preferred for achieving a large transmission extinction
T. Although a smaller FWHM can be achieved by increasing the grating length L as in (1), the grating length may not be varied across a wide range because the waveguide transmission loss increases with L. The grating length may also be related to the size of the other sensor components such as the detector, electronic circuits, and optical coupler/divider for an on-chip integration platform. Consequently, we evaluated the dependence of the transmission extinction
T on the three major grating parameters, which are the duty ratio, grating period
, and etching depth
, under a fixed grating length L of 98
. Based on the performance evaluation and its dependence on the grating parameters, we have provided an optimization method and proposed the design procedure of the silicon-based grating waveguide sensor. We performed a numerical investigation of the grating waveguide using a 2-D FDTD method and a finite-difference method for TE mode using software from Lumerical Solutions, Inc., London, UK. We used a Gaussian pulse with a center wavelength of 1550 nm and a span of 400 nm. The waveguide transmission characteristics are calculated by carrying out fast Fourier transform (FFT) with 80,000 sample points. We incorporated a 2-D FDTD simulation window of 115
in the
x-direction (propagation direction) and 5
in the
y-direction (cross-section direction) using perfectly matched layers under boundary conditions. To obtain accurate transmission in the grating waveguide, a mesh grid size of ∆x = 52.9 nm in the
x-direction, ∆y = 6 nm in the
y-direction, and a time-step size of
s was used in the FDTD simulation.
Figure 3a shows the transmission spectrum of a grating waveguide having a target layer as shown in the inset of
Figure 2 and the corresponding
. The stopband is observed due to a strong feedback and the interference of the guided light in the grating waveguide core. Multiple resonance modes are created by the Fabry–Perot feedback. The +1 resonance mode (
), which is located on the longer wavelength side of the stopband, is used as the detecting mode because FWHM reaches its minimum at the mode when compared with other modes. Although the resonance mode located on the shorter wavelength side of the stopband,
, also exhibits a narrow FWHM similar to that at
, we utilized the
mode as the detecting mode. It is because the resonance wavelength typically shifts toward the direction of the longer wavelength when the RI of the target material such as an aqueous solution or a functional hydrogel layer increases because of some biochemical phenomenon. If the
mode is used as a detecting wavelength, the transmission profile of the next resonance mode
, which is located next to the
mode, may possibly overlap the original target wavelength
. The overlap of these two resonance profiles before and after the sensing process may degrade the overall sensor performance.
Figure 3b shows the transmission spectrum and its shift due to the change in RI of the functional hydrogel layer after multivalent binding of proteins. The dashed curve exhibits the transmission spectrum when the RI of a functional hydrogel layer is 1.34 before multivalent binding (
= 1.34). The solid curve exhibits the transmission spectrum when the RIs of the upper and lower hydrogel layer become 1.39 and 1.34, respectively (
= 1.34). It should be noted that the amount of change in RI is relatively large because the RI of the functional hydrogel layer can be made to change significantly to sense the multivalent binding effectively [
26]. The resonance wavelength shift
is calculated as 0.62 nm and the corresponding transmission extinction
T as 22.82 dB.
4. Discussions
We calculated and analyzed the resonance shift, FWHM, and the resultant transmission extinction, as functions of the three major design parameters of the grating waveguide, which are duty ratio, grating period, and etching depth. We found that among the three parameters, the etching depth has the greatest effect on the transmission extinction performance of the grating waveguide sensor. The results and analysis are summarized in
Table 1 and described as follows.
The maximum transmission extinction is achieved at the duty ratio of approximately 0.5. The transmission extinction performance does not change significantly with the variation in the grating period. Although the grating period does not affect the transmission extinction performance, its control can be utilized to set the resonance wavelength of the grating waveguide. The increase in the etching depth enhances the resonance shift as well decreases the FWHM, resulting in significant improvement in the transmission extinction performance. However, the increase in the etching depth might be limited by the fabrication-related waveguide scattering loss. The determination procedure of the grating structure design for obtaining the maximum transmission extinction can be summarized as follows. Set the duty ratio as 0.5; Set the acceptable etching depth as deep as possible considering fabrication issues and waveguide loss; and Match the exact target wavelength of the specific sensor application with the sensor resonance wavelength by proper grating period control.
Figure 8a shows the transmission spectrum before and after target detection using the design rules and parameters discussed when the same target layer as in
Figure 2 is used. The grating parameters are determined to achieve maximum transmission extinction.
Figure 8a shows the resonance shift of 0.61 nm, FWHM of 0.185 nm, and resultant transmission extinction of 49.2 dB. It exhibits improvement in the transmission extinction of more than 26 dB compared with the result in
Figure 8b, where the careful selection of the grating parameters is not considered.
Figure 8b shows the transmission spectrum to achieve the maximum resonance shift. The measurement of the resonance shift sometimes requires lower-cost equipment and simple configuration than the measurement of the transmission extinction at a specific wavelength [
18]. Our design rule and procedure also provide a large resonance shift of 0.71 nm when compared with the result in
Figure 3b. The sensitivity presenting a resonance shift performance is 165.0 nm/RIU for the sensor with the design parameters as shown in
Figure 8b, where RIU stands for an RI unit. This is a 17.8% improvement compared with the experimental results in [
14].