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Abstract
We proposed a high-performance integrated optical sensor based on a stacked resonant compound grating (SRCG). The transmission spectrum of a SRCG is investigated by the theoretical model that combines the coupled mode theory with the eigenmode information of the grating structures. It is found that the spectral width of the SRCG is controlled by changing its structural parameters such as the strip depth, the period of the grating, and cavity length. The simulation results, which are verified by finite element method (FEM), show that the sensitivity of the sensor is 401.8 nm/RIU with its figure of merit (FOM) as high as 57404. The presented sensor is a promising application for high-performance biosensing.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Integrated optical sensors have been widely utilized in chemical detection [1], biological systems detection [2] and medical applications [3] because of excellent performance such as label-free, simple structure, and easy integration. Various resonant structures have been demonstrated as an integrated optical sensor, such as micro-ring resonators [4], photonic crystals waveguide [5], guided-mode resonance (GMR) gratings [6], et al. Among them, GMR-based gratings have attracted much attention in recent years owing to easy optical coupling, high efficiency, and narrower spectral width. The GMR effect is a valuable physical phenomenon occurring in a near-wavelength waveguide grating. The resonant wavelength is shifted with the change of the refractive index of the analyte, which is covered the surface of a GMR-based grating [7]. Thus, previous studies have demonstrated that GMR-based gratings are promising candidates for use as integrated optical sensors [8,9]. For such optical sensors, the sensitivity S is determined by the overlap between analytes and evanescent waves in GMR-based grating, and a figure of merit (FOM) is defined to comprehensively evaluate the sensing performance. However, there is a tradeoff between S and FOM in GMR gratings.
In recent years, many studies have focused on improving the sensitivity S or FOM of grating-based sensors. For enhancing S, several useful designs have been presented, including the use of different materials like metal layers [10,11], low refractive index (RI) cavity layer [12]. Some approaches have focused on optimizing the structure parameters which are essential for optical sensors such as the angle of incidence, grating period or etching depth [13–15]. In terms of increasing the FOM value, the method concentrates more on designing a new structure, such as single layer grating [16], low RI substrate grating [17], dislocated double-layered metal gratings [18], et al. Several discussions on grating structure parameters also give effective methods to optimize the FOM [19,20]. In our previous work, we used a single compound resonant waveguide grating to improve the FOM in RI sensing. However, the performance of the sensor is limited due to the weak interaction between the leaky-mode resonance in the compound grating and analyte liquid [21].
Recently, a new type of stacked grating structure has been presented, which has been used for optical RI sensing [22–24]. This structure can effectively enhance the interaction between the optical field and analyte. Furthermore, the sensing performances can be improved owing to controlling the spacing between the upper and lower GMR gratings. In this work, we propose an integrated optical sensor based on stacked resonance compound gratings (SRCGs). Here, the transmission spectrum of this device was expressed by a theoretic model by combining temporal coupled-mode theory (TCMT) [25] with the eigenmode information of the single-grating structure. As a result, the simulated results show the S and FOM can achieve 401.8 nm/RIU and 57404, respectively.
2. Structure and principle
Figure 1 shows the schematic structure of the present integrated sensor based on SRCGs, which is consisted of two identical silicon compound gratings with high RI (nSi = 3.5), a spacing cavity for analyte liquid, and silica substrates (nSiO2 = 1.46). The structural parameters are described as follows: the grating period is Λ, the grating filling factor is f, the spacing of two gratings is d, the depth of the grating is dg, the depth and width of the groove are h and w, respectively. The analyte liquid flows through the cavity, which is spaced by the two compound gratings. The resonant peak of the transmission spectrum will shift when the analyte liquid has a difference in the RI [24].
As an optical sensor, the Sensitivity (S) and Figure of Merit (FOM) of the sensor are expressed [26]:
where $\Delta \lambda \textrm{res}$ is resonant wavelength shift and$\Delta nc$is the change of the RI of the analyte liquid. The sensitivity S is defined as the ratio of the spectral shift to the RI change of analyte liquid. The $\Delta \lambda $ is defined as full width at half maximum (FWHM) of the resonance. In this work, we focus on optimizing the two sensing performances (S and FOM) together. Here, the compound waveguide grating is used to improve the Q-factor of the sensor. On the other hand, the spacing cavity is exploited to enhance the interaction between the leaky modes and the analyte liquid.In order to design SRCGs sensor with intuitive understanding, we present a new theoretical model, which is established by combining the temporal coupled-mode theory (TCMT) with the finite element method (FEM). The resonance characteristics of SRCGs can be described by a physical process in an insightful way, as shown in Fig. 2. Here, the two stacked GMR gratings can be treated as two coupled identical resonators with both direct and indirect coupling [27]. The a1 and a2 are the temporal change of the normalized mode amplitudes which means the energy stored in GMR gratings. The ${W_{ + i}}$ and ${W_{ - i}}$ are the amplitudes of the incident and the outgoing waves, respectively. The θ is phase retardation, and the μ is the direct coupling strength.
The transmission spectra of the SRCGs including these two coupling modes can be calculated using [27]:
From Eq. (3) and Eq. (4), the transmission spectrum of the SRCGs is given by:
3. Results and discussions
As an example, the structural parameters of the sensor are presented as follows: Λ = 640 nm, f = 0.6, dg = 500 nm, w = 192 nm (w = f × Λ/2), d = 1500 nm, RI of analyte liquid nc = 1.331. The SRCGs structure is considered to be infinite in the y-direction and periodic in the x-direction. The incident light is assumed as a normal TM-polarized light wave with the magnetic field Hy perpendicular to the x-z plane. We investigated the eigenvalues of the TM eigenmodes of the single GMR with different h using the FEM. It was found that the real and imaginary parts of complex N were changed by the depth h, as listed in Table 1. It is found that the central frequency is increased with the increase of the depth h. Transmission spectra of SRCGs are then obtained using the theoretical model, and identified by FEM simulation, as shown in Fig. 3. We obviously find that the central wavelength and FWHM of transmission spectrum are simultaneously tuned by the change of depth h in the SRCGs.
Fig. 3. Transmission spectra of the SRCGs with a different h. (a) h = 260 nm, (b) h = 280 nm, (c) h = 300 nm, (d) h = 350 nm.
Table 1. Eigenvalues of TM eigenmode of the single grating with a different h
Figure 4 illustrates the effect of the grating depth h and the RI of analyte liquid nc on the spectral position and the FWHM of the sensor respectively. Here, the RI of analyte liquid ranged from 1.331 to 1.337. As shown in Fig. 4, it is found that the spectral position is shifted with the change of the RI. Meanwhile, the FWHM of each sensor is first decreased and then increased with the increase of the grating depth h. The sensing performances of the resonant structure with different h are listed in Table 2. It can be observed that the sensitivity S increased with the increase of h, however, the corresponding FOM will be decreased. One can see that there is a tradeoff between the S and FOM. Consequently, the grating depth is chosen at h = 300 nm.
Fig. 4. Transmission spectra are simulated by changing the index of analyte liquid ranged from 1.331 to 1.337 with fixed different grating depths: (a) h = 260 nm, (b) h = 280 nm, (c) h = 300 nm, (d) h = 350 nm.
Table 2. FWHM, S and FOM of the structure with different h in TM polarization
Figure 5 demonstrates that the optical resonance of the sensor can be tuned by adjusting the grating period Λ for TM-polarized light. The resonant wavelength will change significantly with the varied Λ [17], which is ranged from 600 nm to 720 nm. As shown in Fig. 5(a), resonant peak shifts to the long wavelength direction gradually with the increase of Λ. The FWHM reaches a minimum of 0.007 nm at Λ = 660 nm. Figure 5(b) shows the sensitivity (red) and the corresponding FOM (blue) are described as a function of Λ. One can find that FOM can reach a maximum of 57404 when the grating period is chosen as Λ = 660 nm. When Λ changes from 655 nm to 661 nm, the sensitivity of the sensor is around 400 nm/RIU, and the corresponding FOM is above 13000. Figure 5(c) and (d) show the electric field distributions for Λ = 660 nm and Λ = 720 nm respectively. One can see that electric field energy exists in the waveguide layer and the maximum electric field is 8.79089×107 V/m at the wavelength of when Λ is 660 nm, while the maximum electric field is decreased to 2.16364×107 V/m at Λ = 720 nm. It indicates that the light field can be controlled by the change of the Λ.
Fig. 5. Spectrum and the optical sensing performance of the GMR-grating with different value of Λ. (a) Spectrum of different Λ, (b) S and FOM versus different Λ, (c) Λ = 660 nm and the maximum electric field intensity is 8.79089×107 V/m at resonant wavelength λ = 1474.64 nm, (d) Λ = 720 nm and the maximum electric field intensity is 2.16364×107 V/m at λ = 1546.33 nm.
Figure 6(a) shows the transmission spectra of SRCGs are calculated for different d under normal incident light wave with TM polarization. It can be observed that the resonant peak of the transmission spectrum shows red shifted with the increase of d, and spectrum linewidth shows a trend of decreasing first and then increasing. According to the Eq. (3), the spectrum linewidth will be shifted to zero, when the phase retardation θ is equal to near integer multiple of π. In this case, the spectrum linewidth is 0.007 nm when the spacing d is chosen at 1500 nm. Here, the optical field can be trapped in the Fabry–Pérot-like (FP-like) cavity [23], which is spaced by the two GMR gratings. The sensing performance can be tuned by the change of spacing d, as shown in Fig. 6(b). As a result, the sensitivity of the sensor is obtained at around 400 nm/RIU as d varies from 1495 nm to 1515 nm, and the corresponding FOM can achieve above 13000. Interestingly, it is seen that the FOM is extremely sensitive to the change of d in the structure. Physically, the dominant coupling mechanism of SRCGs is the FP-like resonance when the two GMR gratings are separated far enough. Thus, the spacing of two gratings is chosen as d = 1500 nm in accordance with the both values of FOM and S.
Fig. 6. (a) Transmission spectra of SRCGs with different d, (b) Calculated S and FOM versus different d.
According to all the above analysis, we fixed the structural parameters of the sensor as an example (Λ = 660 nm, f = 0.6, h = 300 nm, w = 192 nm, dg = 500 nm, d = 1500 nm). The sensing performances are investigated for SRCGs working into the desired optical range (1476 nm−1480 nm). Under TM-polarized incident plane wave, the transmission spectra are calculated using the theoretic model for a liquid refractive index in the range 1.331−1.337, as shown in Fig. 7. Finally, the resonance peak shows red-shift with the increase of the RI of the analyte liquid. Furthermore, high sensing performances are reached for analyte liquid detection (S = 401.8 nm/RIU, FWHM = 0.007 nm, and FOM = 57404).
Compared the sensitivity and FOM of the proposed sensor with those of some other sensors reported in the references, as shown in Table 3. It is found that a high-performance sensor is presented based on the SRCGs in this work.
Table 3. Sensitivity and FOM comparisons of several types of RI sensors
4. Conclusions
In conclusion, we investigated an optical RI sensor based on SRCGs using an improved theoretical model. The structural parameters can be optimized by the model. As a result, the sensitivity and corresponding FOM are 401.8 nm/RIU and 57404, respectively. Such a RI sensor based on the SRCGs is expected to realize high performance optical sensing.
Funding
National Natural Science Foundation of China (21976049, 61905060); Natural Science Foundation of Hebei Province (A2020402013, F2019402063); Scientific Research Project of the Department of Education of Hebei Province (ZD2021019); Open Project of the State Key Laboratory of Quantum Optics and Quantum Optics Devices of Shanxi University (KF202006).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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