Highly sensitive refractive index sensor based on photonic crystal ring resonators nested in a Mach–Zehnder interferometer

Today, with the rapid development of photonics, optical sensors are being considered as efficient tools for detecting environmental variations and have been regarded as one of the most important fields in photonic research. In this study, we have proposed a two-dimensional photonic crystal refractive index sensor using a combination of Mach–Zehnder interferometers and two ring resonators. Our goal is to increase the sensitivity and figure of merit of the sensor, so that the output transmission spectrum can be considerably shifted by changing the refractive index of the simulated analytes. The proposed photonic crystal sensor consists of a hexagonal array of silicon rods on a SiO2 substrate. The finite difference time domain method is used for the numerical simulation of the structure. In this regard, to validate the simulation results, two different commercial software have been used. The quality-factor and the sensitivity of the proposed structure are 1535 and 1658 nm/RIU, respectively, where RIU stands for the refractive index unit. In general, the structure has advantages such as low fabrication cost, high sensitivity to changes in refractive index and a high Q-factor.


Introduction
Today rapid growth of photonic nanotechnology sciences has led to development of devices such as sensors, modulators, optical fibres, switches, etc. Refractive index (RI) sensors are used in a wide variety of physical detectors to measure the concentration of liquids and gases (Wo et al. 2012;Sun et al. 2015). Mach-Zehnder's interferometer (MZI) (Zhao et al. 2017;Du et al. 2019) and micro-loop amplifiers (MRR) (Rahmatiyar et al. 2020;Sumetsky et al. 2007;Wang et al. 2020) are not only widely used in optical circuits, but have also recently been used as optical biosensors. So far, various optical sensors have 574 Page 2 of 14 been proposed to detect refractive index changes designed from different structures, such as Mach-Zehnder interferometers (Du et al. 2019;Lu et al. 2009;Sun et al. 2016;Pawar and Kale 2016;Wu et al. 2015;Zhao et al. 2017), Ring Resonators (Arunkumar et al. 2017;Jannesari et al. 2016;Radhouene et al. 2017;Hsiao and Lee 2009), Fabry-Perot interferometers (FPI) (Wei et al. 2008). A Mach-Zehnder interferometer can be simulated using FDTD while it consists of an optical y-splitter and a y-combiner waveguide. In Tasaki et al. (2020) the bending radius of Y waveguides at 385 μm and the average free spectral range (FSRs) of 18 nm are optimized for the MZI model. Also, a MZI can be used as an optical switch. A low-consumption MZI have been presented as a photonic crystal switch using a phase change material (PCM) (Kumar, et al. 2020). Also, MRRs can be used in the nonlinear mode as an all-optical switch or sensor to shift the resonant wavelength by changing the refractive index (Rakshita Rakshit et al. 2013).
In this study, we demonstrated the combination of MRR with MZI as a highly sensitive RI sensor. For the presented topology, the transmission spectrum experiences a considerable wavelength shift as a result of analyte's RI change. In fact, we used two MRRs nested in an MZI and showed that a small change in refractive index could cause a large change in the resonance wavelength of the structure.

Structure design
In this structure, an optical splitter and a combiner connected to two straight waveguides are used to design a photonic crystal MZI. The structure is designed using a hexagonal array of silicon rods in an air background. The optical response of the structure is obtained using the Lumerical's FDTD Solver. Two photonic crystal rings resonators (PhCRR) are located between straights waveguide arms. Typically, each ring resonator is formed by removing rods in the original photonic crystal (PhC) lattice. The structure is shown in Fig. 1. The lattice constant and the diameter of the rods are considered to be Λ = 1 μm and r = 200 nm, respectively. To determine the refractive index of the analyte, the structure can be placed in the analyte. The refractive index of silicon (Li 1980) and water (Hale and Querry 1973; Thormählen et al. 1985) as analytes are approximately 3.436 and 1.33 at the wavelength range of 2900 to 3100 nm, respectively.
In fact, each of the PhCRR arms acts separately in both through and drop ports (Sreenivasulu et al. 2018;Robinson and Nakkeeran 2013). Figure 2 shows a PhCRR designed in the PhC lattice. Using the splitter, half of the source wave is divided in each of the straight waveguide arms. Each arm plays the role of through and drop relative to each other (Fig. 2). In the photonic crystal ring resonator nested in Mach-Zehnder interferometer (RR-MZI), light is evenly distributed on both splitter arms and then coupled to the PhCRRs from each side up and down. Actually, at the resonant wavelength, both PCRRs act as one meta-ring resonator.

Simulation and optimization
The photonic band structure in the normalized frequency range of 0.28 to 0.37 [a/λ] for the transverse magnetic state (TM) is shown in Fig. 3. In fact, wavelengths between 2700 and 3500 nm can pass through the structure's waveguides.  At the input wavelength of 2971 nm, when the whole structure is immersed in water as an analyte, both RRs are paired. Consequently, light passes through MZI arms and it is later collected in the combinator and transmitted to the output port of MZI. At this wavelength, the maximum amount of light reaches the output port, where the normalized transmission is equal to 0.82. By a 13 nm shift in the input wavelength, the structure will not allow light to pass through, resulting in the MZI output being minimized (Fig. 4a). This results a quality factor (Q-factor) (Siraji and Zhao 2015;Saha and Sen 2018;Kolli et al. 2021; Rebhi and Najjar 2020; Olyaee and Mohebzadeh-Bahabady 2014) approximately equal to 1500. Equation (1) shows the relationship used for calculation of the Q-factor of the photonic crystal ring resonators.
where FWHM is the full width at half maximum (measured using the transmission spectrum). For validation, the results obtained using two different commercial software (Rsoft photonics CAD suite and Lumerical) have been superimposed in Fig. 4b. As seen in Fig. 4b, a very good agreement is observed between the results obtained in each case which confirms the validity of the results.
To optimize the structure, four rods (a and b) have been added at the MZI input and output (Fig. 5). The optimum radii of rods a and b were obtained by sweeping as 185 and 100 nm, respectively. The normalized transmission of the optimized structure increased from 0.82 to 0.93 (Fig. 6). Also, the Q-factor increase from 1518 to 1535.
The sensitivity ( The resonance wavelength and Q-factor for different analyte refractive indices are plotted in Fig. 8a, b, respectively. Also, the sensitivity and FOM of the sensor are shown in Fig. 8c, d, respectively. Actually, with increasing the refractive index of the analyte, the Q-factor increases and the sensitivity and FOM decreases. The FWHM bandwidth for the refractive indexes of the various analytes is about 1.95 nm, and the average FOM of sensor is about 840 RIU −1 .

Discussion and comparisons
In this section, the performance of different RI sensors is compared with the proposed structure. The electric field for the optimized structure (shown in the Fig. 5) shows that at the input wavelength of 2959 nm, both PCRRs are coupled together and light passes through the straight waveguides and it is transmitted to the MZI output port. Instead, at 2946 nm, no signal is directed to MZI output. The electric field intensities though the structure are shown in Fig. 9a, b. Some of the best refractive index sensors are listed in Table 1, where the resolution of the sensors is determined by the following equation: As seen in Fig. 10, two nested ring resonators are used in a Mach-Zehnder to create a large ring resonance at the sensor detection wavelength. As a result, the structure has a higher sensitivity and quality factor than the other works mentioned in the Table 1. Based on the knowledge of the authors, coupling both arms or a Mach-Zehnder to central resonators has not been proposed before. In this case the two small PhC resonators are combined to form a large-scale super resonator, which incorporates Mach-Zehnder arms as part of the resonator loop.
To investigate the effect of changes in device length, the number of rods between the two ring resonators and Mach-Zander arms is changed (Fig. 11) and the normalized output spectrum for each case is shown in Figs. 12 and 13, respectively. To have the maximum bandwidth around the main wavelength of the sensor, a centrality index is defined as follows: (4) R = Δn analyte × Δ min Δ (peak) (RIU) Fig. 9 The electric field intensity for the optimized structure, a at the wavelength of 2959 nm, b at the wavelength of 2946 nm Table 1 Performance where here c is the main wavelength of the sensor and λmax and λmin, show the maximum and minimum peaks around the main wavelength, respectively, so that in the Dλ range, the sensor is considered as a single mode device (Fig. 14).
The results of the study on the effect of device length on the sensitivity index and centrality of the transmission spectrum for changes in the number of rods between the two ring resonators and changes in the number of rods of the MZI arms are given in Tables 2 and 3 respectively. As mentioned in these tables, the optimal state is for the distance between the two ring resonators with 6 rods (a 6Λ distance) and the number of rods in the MZI arms is 27. For this case, it has a sensitivity of 1658 (nm/RIU) and a centrality index of 98.77%. It is also clear from the results that the RI sensitivity is weakly dependent on the length of the device. Also, by changing the lattice constant, the main wavelength of the device can be easily adjusted in the range of 1550 or 1310 nm. For this purpose, the lattice constant for the wavelengths of 1550 and 1310 nm should be considered to be 522 and 440 nm, respectively, and the transmission spectrum for each are shown in Fig. 15a, b.

Conclusions
We have proposed a sensitive refractive index sensor based on photonic crystal ring resonators nested in a Mach-Zehnder interferometer. The sensor structure is simulated using FDTD method and has a good quasi-linear sensitivity to changes in the refractive index of the analyte. In the RI range of 1.33 to 1.37 the average values of Q-factor and    Ethical approval We the undersigned declare that the manuscript entitled "Highly Sensitive Refractive Index Sensor based on Photonic Crystal Ring Resonators Nested in a Mach-Zehnder Interferometer" is original, has not been fully or partly published before, and is not currently being considered for publication elsewhere. Also, results are presented clearly, honestly, and without fabrication, falsification, or inappropriate data manipulation. We confirm that the manuscript has been read and approved by all named authors and that there are no other persons who satisfied the criteria for authorship but are not listed. We further confirm that the order of authors listed in the manuscript has been approved by all of us.