High Sensitivity And Ultra-High Quality Factor For An All-Optical Temperature Sensor Based On Photonic Crystal Technology

In our work, we propose a novel temperature sensor design based on a two-dimensional (2D) photonic crystal resonant cavity structure designed to detect and monitor temperature under very harsh environmental conditions from 0 °C to 500 ºC. The sensitivity of the proposed structure is 109.8 pm/ºC, an ultra-high quality factor, high transmission eciency and ultra-compact size. The characteristics of the proposed sensor under different temperatures are simulated using the Plane Wave Expansion (PWE) method and Finite Difference Time Domain (FDTD) method to calculate, respectively, the Photonic Band Gap (PBG) and transmission eciency. The results obtained show that the wavelength of the resonant cavity increases linearly with increasing temperature. Our sensor is suitable for applications based on nanotechnology.


Introduction
In recent years, Photonic Crystal (PhC) has attracted a lot of attention because of its more important properties for controlling and manipulating light through crystal [1]. Based on this characteristic, many scientists are nding designs and applications for various optical devices, such as optical decoders [2], logic gates [3,4], sensors [5], etc.
Due to their several advantages such as bandwidth properties and the exibility of miniaturization, PhCbased devices are now playing a very important role in new elds such as optical sensing [6].
Recently, optical sensors have attracted the attention of researchers because of their advantage over electronic sensors, which are limited in transferring large data at a very higher speed, which can be solved by all-optical sensors, optical switches, and the tunable lter [7][8][9][10][11]. Optical sensors have been used effectively in many applications to detect various parameters such as pressure [12], biochemical sensors [13], gas [14], electric eld [15], and temperature [16]. Temperature measurements are very important and are widely used in the risk control application of the petrochemical industry, automotive industry, avionics, industrial safety, biomedicine [17][18][19][20], and in many other applications.
Different optical temperature sensors based on 2D-PhC can be realized by ring resonators [21] and waveguides structure [22]. Although nanosensors based on ring resonators offer high normalized transmission e ciency, high sensitivity, and high-quality factor [23]. PhC waveguide-based nano-sensors have a good standardized transmission e ciency but a very low-quality factor [24].
In the present work, we have proposed a new hexagonal nanosensor based on a resonant cavity to detect the temperature in the range of 0°C to 500°C. The proposed temperature sensor has a wide range of applications in the defense, chemical, civil, metal production, semiconductor industry, and other elds. Temperature monitoring is also important for estimating the structural health of the device. The proposed design is more compact and simpler. Also, it offers a very high-quality factor and high sensitivity.

Bandgap Analysis
In this section, we proposed the initial temperature sensor structure based on 2D PhC, with a hexagonal array of circular silicon pillars whose the refractive index is equal to 3.42 suspended in the air. The numbers of the pillars in the x and z directions are respectively 23 and 17 and the ratio between the radius « R » and the lattice constant « a » is 0.3 (Fig. 1a).
In general, we use the PWE method to obtain the photonic bandgap which depends on three major parameters such as the lattice constant, the permittivity of dielectric materials, and the radius of the pillars. As shown in Fig. 1b The second wavelength range of the PBG is between 1481.48 and 1904.76 nm, which is suitable for the proposed sensor design because it belongs to the third window of optical telecommunications.

Analysis Of Temperature Effects
The detection operation of an all-optical temperature sensor is based on the refractive index variation as a function of the thermo-optical effect. The refractive index will be modi ed according to the temperature, which allows the photonic band gap and the center wavelength of the structure to be changed, and this variation is given as [25]: n 0 is the refractive index of the medium at zero temperature (0°C), α is the thermo-optical coe cient is given by 2.4×10 − 4 /°C for silicon [26] and ∆T is the temperature difference.

Results And Discussion
The designed temperature sensor structure of the 2D hexagonal shape based on the resonant cavity is showed in the gure (2). Our sensor is composed of two quasi-waveguides in the horizontal in-line direction, and a resonant cavity is located between them. The in-line quasi-waveguides are created by removing nine silicon pillars for both sides as input and output. The resonant cavity is created by optimizing rays of some internal pillars such as black rod (R*1.3), blue rods (R*0.5), green rods (R*0.45) placed in the hexagonal array to couple the light signal into quasi-in-line waveguides from the input to the output. The resonance wavelength is observed using the monitor which is placed at the sensor output. The total size of our sensor is 18 µm×12 µm.
This section describes the optical detection results obtained for the proposed sensor structure. The Fig. 3 shows the electric eld distribution of resonant cavity for the wavelength 1682.1 nm at the output of our proposed device in the temperature range of 0°C to 500°C with a 50°C step size. This result is obtained by the use of the FDTD method. The Fig. 4 graphically represents the normalized transmission at the output of the proposed sensor at a zero temperature (0°C) which corresponds to an intensity of 81.5 % at the wavelength 1682.1 nm. On the other hand, the relationship of resonance wavelengths as a function of temperature has been illustrated in Fig. 5 and recapitulated in the Table 1. The necessary functional parameters of our designed temperature sensor are compared with the already mentioned sensors, which are summarized in Table 2. It indicates that the dynamic range, quality factor (Q) = λ0/Δλ , and sensitivity (S) = ∂λ /∂T of the proposed temperature sensor are better than those of the previously existing sensor [25,27,28,29,30,31,32].  Proposed Design for the Temperature Sensor The Linear Relation between Resonant Wavelengths and Temperature