Enhancing the Performance of the Photonic Integrated Sensing System by Applying Frequency Interrogation

Lab-on-a-chip systems are currently one of the most promising areas in the development of ultra-compact sensor systems, used primarily for gas and liquid analysis to determine the concentration of impurities. Integrated photonics is an ideal basis for designing “lab-on-a-chip” systems, advantageous for its compactness, energy efficiency, and low cost in mass production. This paper presents a solution for “lab-on-a-chip” device realization, consisting of a sensor and an interrogator based on a silicon-on-insulator (SOI) integrated photonics platform. The sensor function is performed by an all-pass microring resonator (MRR), installed as a notch filter in the feedback circuit of an optoelectronic oscillator based on an electro-optic phase modulator. This structure realizes the frequency interrogation of the sensor with high accuracy and speed using a conventional single-mode laser source. The system sensitivity for the considered gases is 13,000 GHz/RIU. The results show that the use of frequency interrogation makes it possible to increase the intrinsic LoD by five orders. The proposed solution opens an opportunity for fully integrated implementation of a photonic “laboratory-on-a-chip” unit.


Introduction
Gas detection and measurement of its concentration is currently an urgent task in ensuring the safety of residential and industrial buildings in environmental monitoring, industry, and medical diagnostics. In this case, gases that are most often the target of detection are those which are dangerous to humans either due to their toxicity or explosiveness, for example, carbon monoxide, ammonia, nitrous oxide, nitrous oxide, and sulfur dioxide [1]. The speed of the sensor reaction is important in industry, since hydrogen, for example, becomes explosive at a concentration of 4%, which requires a high rate of detection of gas in the air [2]. At low concentrations of acetone in the air, irritation of the skin and mucous membranes is observed, and an increase in this concentration can lead to the failure of the human central nervous system [3]. A similar set of gases is considered in monitoring the state of human health based on the composition of the exhaled gases [4], where the time of analysis of these gases plays a huge role in monitoring patient illness.
In power engineering, special attention is also paid to hydrogen and its compounds when monitoring the state of oil transformers [5][6][7]. Separately, it is also necessary to highlight the development of environmental monitoring systems [5], including the use of unmanned aerial vehicles [6,7]. In all described application situations, it is necessary to provide low sensor weight, small sensor dimensions, low power consumption, and high sensitivity. When used in explosive environments, it is additionally necessary to exclude the possibility of sparking as much as possible. These criteria are met by sensors based on photonics integrated circuits (PIC). They can be implemented in various structures, such as Mach-Zehnder interferometers [8][9][10], couplers [11,12], microring resonators (MRRs) [2,13,14], and more complex The relatively large overall dimensions of the bulk optical components (both active and passive) that make up an OEO system present a significant challenge, especially for sensor applications where compactness, portability, and light weight are critical criteria for use in measuring environmental variables. Integrated photonic technologies can solve this problem due to their advantages in small size, weight, and power consumption, which makes them attractive compared to bulky fiberoptic components to meet the increasingly demanding requirements of sensors [42]. Figure 1 shows the scheme of the gas sensing system. The all-pass MRR acts as a sensitive element and is housed in the feedback path of an interrogator. The interrogator is represented by an OEO based on a phase Mach-Zehnder modulator (MZM). A shift in the MRR's resonant wavelength associated with the refractive index variation of its environment causes a frequency change in the OEO output signal. In addition to the notch filter described, the feedback path includes a photodetector (PD), a trans-impedance amplifier (TIA), and a microwave amplifier. measure gas compositions. Due to the high sensitivity of the SOI-based ring resonator, a small change in gas composition or other parameters results in a shift in the resonant frequency of the sensing element, which can be detected by monitoring the oscillatory radio frequency peak at the output of the optoelectronic oscillator (OEO). In particular, SOI μresonators have shown that they can effectively respond to changes in gas composition [13,[39][40][41].

Sensing System Principle and Design
The relatively large overall dimensions of the bulk optical components (both active and passive) that make up an OEO system present a significant challenge, especially for sensor applications where compactness, portability, and light weight are critical criteria for use in measuring environmental variables. Integrated photonic technologies can solve this problem due to their advantages in small size, weight, and power consumption, which makes them attractive compared to bulky fiberoptic components to meet the increasingly demanding requirements of sensors [42]. Figure 1 shows the scheme of the gas sensing system. The all-pass MRR acts as a sensitive element and is housed in the feedback path of an interrogator. The interrogator is represented by an OEO based on a phase Mach-Zehnder modulator (MZM). A shift in the MRR's resonant wavelength associated with the refractive index variation of its environment causes a frequency change in the OEO output signal. In addition to the notch filter described, the feedback path includes a photodetector (PD), a trans-impedance amplifier (TIA), and a microwave amplifier. The operating principle of OEO is as follows. The narrowband signal from the CW (continuous wave) laser is fed to the phase MZM and is initially modulated by the noise The operating principle of OEO is as follows. The narrowband signal from the CW (continuous wave) laser is fed to the phase MZM and is initially modulated by the noise generated by the photodetector. The most important factor is that the modulated signal's spectral components are symmetric with the carrier and antiphase. Supplying such a signal to the photodiode leads to mutual suppression of the antiphase components, resulting in zero microwave signal at the OEO output. The bandpass filter suppresses the modulated signal's narrow spectral component, which causes an uncompensated optical signal at the detector input with a wavelength determined by the mismatch between the CW laser carrier frequency and the resonant frequency of the notch filter (MRR). Of fundamental importance is the presence of resonance in the MRR. Let us consider the output signal from MZM, u PM (t), which is modulated by the signal, s Ω (t):

Sensing System Principle and Design
u PM (t) = U 0 cos(ω 0 t + Ms Ω (t)). (1) where ω 0 is the angular frequency of the carrier, U 0 is its amplitude, and M is the modulation index. Let us assume that the signal, s Ω (t), has a unit amplitude and it is represented as a set of harmonic oscillations: s sin ω i t.
Then, the modulated signal is written as: Then, using the known representation: where J k (M) is the k-order Bessel function of the argument M, we get: sin ω i t .
If we neglect the high orders of the Bessel functions (|k| > 1, so we take it into account only J 1 (M)), the signal spectrum at the output of the phase modulator has the shape presented in Figure 2. The red line conventionally shows the stopband of the MRR notch filter with the resonance frequency ω res . laser carrier frequency and the resonant frequency of the notch filter (MRR). O mental importance is the presence of resonance in the MRR. Let us consider the signal from MZM, uPM(t), which is modulated by the signal, sΩ(t): where ω0 is the angular frequency of the carrier, U0 is its amplitude, and M is the m tion index. Let us assume that the signal, sΩ(t), has a unit amplitude and it is repr as a set of harmonic oscillations: Then, the modulated signal is written as: Then, using the known representation: where is the k-order Bessel function of the argument M, we get: If we neglect the high orders of the Bessel functions ( 1 k > , so we take it into only ( ) 1 J M ), the signal spectrum at the output of the phase modulator has th presented in Figure 2. The red line conventionally shows the stopband of the MR filter with the resonance frequency ωres.   The signal sidebands are limited by the frequencies ω 0 + ω 1 , ω 0 + ω n , ω 0 −ω 1 , and ω 0 −ω n . MRR suppresses part of the spectrum of the upper band of the phase-modulated signal. Thus, an unsuppressed symmetric band does not have antiphase components on the photodetector. Consequently, only the carrier and a signal with a frequency of ω 0 −ω res are present at the photodetector, resulting in a narrowband microwave oscillation. Therefore, the spectrum of optical signals that cause microwave generation is also narrow. Thus, the signal bandwidth at the thru-port of the sensor is more limited than the bandpass filter's FWHM (full width at half maximum). This increases the system quality relative to the single resonator, which upgrades the sensitivity and resolution.

MRR-Based Sensor Design and Simulation
The main requirement for the sensor design was a small footprint while maintaining a high quality and sensitivity, as well as a simple structure. The gases of interest in terms of the above analysis are shown in Table 1. Carbon tetrachloride CCl 4 1.001768 [46] As mentioned above, it is more challenging to achieve the boundary coupling conditions for add-drop MRR than for all-pass. Below is a comparison of all-pass and add-drop sensors calculated using the FDTD (finite difference time domain) method using Ansys Lumerical software. MRR radius and gap were chosen to provide ring waveguide transmission and a coupling coefficient close to the critical coupling regime [38]. We calculated the sensors' parameters for the TE-mode at the resonant wavelengths and the numerically optimized waveguide width and height to improve TE-mode transmission and excitation [48] and to accommodate common manufacturing platforms [49]. The RI of Si is equal to 3.4955 [50]. Table 2 shows the dimensions of the add-drop MRR sensor. The MRR resonant wavelength in a vacuum is equal to 1545.75 nm. MRR transmission and coupling coefficients were also calculated using the FDTD method. The gap between the waveguides and the ring was set to 0.16 µm. As mentioned above, these values were found using numerically calculated MRR waveguide transmissions to fulfill the critical coupling criterion [38]. The E-field distributions in the non-resonant state and resonant state are shown in Figure 3a,b, respectively. The resonant properties of the MRR were estimated based on the quality factor (Q-factor), full width at half maximum (FWHM), and sensitivity (S):

Add-Drop MRR
where a = exp(αL/2) is the MRR transmission measured in FDTD; α is the MRR waveguide attenuation coefficient; r is the coupler transmission to the in-through waveguide; λ res is the MRR resonant wavelength (λ res = Ln eff /m, where positive integer m is the resonance number); L is the MRR circumference; n g and n eff are the numerically counted values of the waveguide group and effective refractive indices, respectively; λ CCl 4 and λ air are the resonant wavelengths of the gas with maximum RI (CCl 4 ) and the reference gas (air), respectively; and n CCl 4 and n air are the RI of the CCl 4 gas and the reference gas (air), respectively. We should also note that the sensitivity, S, may also be determined as the slope of the curve in Figure 4, equal to 56 nm/RIU. above, these values were found using numerically calculated MRR waveguide transmissions to fulfill the critical coupling criterion [38]. The E-field distributions in the non-resonant state and resonant state are shown in Figure 3a,b, respectively. The resonant properties of the MRR were estimated based on the quality factor (Q-factor), full width at half maximum (FWHM), and sensitivity (S):    The intrinsic limit of detection (LoD) is usually calculated to estimate the sensor quality. It can also be obtained as follows [51]: The sensor was simulated using the finite element method (FEM) and then imported into the INTERCONNECT modeling environment. INTERCONNECT is a part of the Ansys Lumerical software tool designed for PIC system modeling. To simulate MRR in IN-TERCONNECT we calculated its parameters (transmission, coupling effective RI, and group RI) in Lumerical using the finite-difference time-domain (FDTD) and FEM solvers. As a result of the calculations, the dependencies of the transmission spectrum of the MRR on the wavelength ( Figure 5) were obtained for various gaseous substances that are odorless but dangerous to human health. Figure 6 shows the E-field distribution in the MRR for CCl4 analysis, and Table 3 shows the add-drop sensor's characteristics.   The intrinsic limit of detection (LoD) is usually calculated to estimate the sensor quality. It can also be obtained as follows [51]: The sensor was simulated using the finite element method (FEM) and then imported into the INTERCONNECT modeling environment. INTERCONNECT is a part of the Ansys Lumerical software tool designed for PIC system modeling. To simulate MRR in INTERCONNECT we calculated its parameters (transmission, coupling effective RI, and group RI) in Lumerical using the finite-difference time-domain (FDTD) and FEM solvers. As a result of the calculations, the dependencies of the transmission spectrum of the MRR on the wavelength ( Figure 5) were obtained for various gaseous substances that are odorless but dangerous to human health. Figure 6 shows the E-field distribution in the MRR for CCl 4 analysis, and Table 3 shows the add-drop sensor's characteristics. The intrinsic limit of detection (LoD) is usually calculated to estimate the sensor quality. It can also be obtained as follows [51]: The sensor was simulated using the finite element method (FEM) and then imported into the INTERCONNECT modeling environment. INTERCONNECT is a part of the Ansys Lumerical software tool designed for PIC system modeling. To simulate MRR in IN-TERCONNECT we calculated its parameters (transmission, coupling effective RI, and group RI) in Lumerical using the finite-difference time-domain (FDTD) and FEM solvers. As a result of the calculations, the dependencies of the transmission spectrum of the MRR on the wavelength ( Figure 5) were obtained for various gaseous substances that are odorless but dangerous to human health. Figure 6 shows the E-field distribution in the MRR for CCl4 analysis, and Table 3 shows the add-drop sensor's characteristics.

All-Pass MRR
We performed the same simulations for the all-pass MRR sensor with the same geometric parameters as described in Section 3.1. Figure 7 shows the transmission spectra of this sensor for different gases, Figure 8 shows the E-field distribution in the MRR for CCl4 analysis, and Table 4 lists the all-pass sensor characteristics for different gases.

All-Pass MRR
We performed the same simulations for the all-pass MRR sensor with the same geometric parameters as described in Section 3.1. Figure 7 shows the transmission spectra of this sensor for different gases, Figure 8 shows the E-field distribution in the MRR for CCl 4 analysis, and Table 4 lists the all-pass sensor characteristics for different gases.  One can see that applying the all-pass sensor will improve the system sensitivity from 60 nm/RIU to 100 nm/RIU, which corresponds to the sensitivity of the conventional MRR sensor given in [21], and the intrinsic LoD decreases from 23.34⋅10 −4 RIU to 9⋅10 −4 .  One can see that applying the all-pass sensor will improve the system sensitivity from 60 nm/RIU to 100 nm/RIU, which corresponds to the sensitivity of the conventional MRR sensor given in [21], and the intrinsic LoD decreases from 23.34⋅10 −4 RIU to 9⋅10 −4 .  One can see that applying the all-pass sensor will improve the system sensitivity from 60 nm/RIU to 100 nm/RIU, which corresponds to the sensitivity of the conventional MRR sensor given in [21], and the intrinsic LoD decreases from 23.34·10 −4 RIU to 9·10 −4 . Therefore, the all-pass sensor is preferable for use in a sensing system with frequency interrogation.

Sensing System Simulation and Performance Analysis
A simulation was carried out, following the scheme shown in Figure 1, in the Lumerical Interconnect environment with the following parameters. The CW laser was set to 1549.7 nm with an output power of 2 mW. A typical SOI-based structure [52] was applied to the PD numerical model. The PD dark current was 60 nA; the PD, amplifier, and MZM RF bandwidths were equal to 50 GHz; and the MZM V π = 4 V. To initiate generation, microwave amplifiers with a total gain of 65 dB were used. Figure 9 shows the OEO timing diagram. The trigger transient takes less than 1.5 ns, which can provide a sampling rate of more than 600 MHz. Figure 10 shows the spectrum at the output of the sensor's thru-port and the thru-port transfer function for CO detection. The bandwidth of the optical radiation is much smaller than the FWHM of the sensor, which confirms the hypothesis presented in Section 2 that the quality factor of the sensor system is increased due to frequency interrogation. Figure 11 demonstrates the dependence of the OEO output frequency on the refractive index of the gases. Therefore, the all-pass sensor is preferable for use in a sensing system with frequency interrogation.

Sensing System Simulation and Performance Analysis
A simulation was carried out, following the scheme shown in Figure 1, in the Lumerical Interconnect environment with the following parameters. The CW laser was set to 1549.7 nm with an output power of 2 mW. A typical SOI-based structure [52] was applied to the PD numerical model. The PD dark current was 60 nA; the PD, amplifier, and MZM RF bandwidths were equal to 50 GHz; and the MZM Vπ = 4 V. To initiate generation, microwave amplifiers with a total gain of 65 dB were used. Figure 9 shows the OEO timing diagram. The trigger transient takes less than 1.5 ns, which can provide a sampling rate of more than 600 MHz. Figure 10 shows the spectrum at the output of the sensor's thru-port and the thru-port transfer function for CO detection. The bandwidth of the optical radiation is much smaller than the FWHM of the sensor, which confirms the hypothesis presented in Section 2 that the quality factor of the sensor system is increased due to frequency interrogation. Figure 11 demonstrates the dependence of the OEO output frequency on the refractive index of the gases.   Therefore, the all-pass sensor is preferable for use in a sensing system with frequency interrogation.

Sensing System Simulation and Performance Analysis
A simulation was carried out, following the scheme shown in Figure 1, in the Lumerical Interconnect environment with the following parameters. The CW laser was set to 1549.7 nm with an output power of 2 mW. A typical SOI-based structure [52] was applied to the PD numerical model. The PD dark current was 60 nA; the PD, amplifier, and MZM RF bandwidths were equal to 50 GHz; and the MZM Vπ = 4 V. To initiate generation, microwave amplifiers with a total gain of 65 dB were used. Figure 9 shows the OEO timing diagram. The trigger transient takes less than 1.5 ns, which can provide a sampling rate of more than 600 MHz. Figure 10 shows the spectrum at the output of the sensor's thru-port and the thru-port transfer function for CO detection. The bandwidth of the optical radiation is much smaller than the FWHM of the sensor, which confirms the hypothesis presented in Section 2 that the quality factor of the sensor system is increased due to frequency interrogation. Figure 11 demonstrates the dependence of the OEO output frequency on the refractive index of the gases.  . Transmission spectra at the thru-port for CO detection using an SOI-based MRR. Figure 10. Transmission spectra at the thru-port for CO detection using an SOI-based MRR. Nanomaterials 2023, 13,193 11 of 15 Figure 11. OEO output frequency dependence on gas RI using an SOI-based MRR.
We compared the LoD parameters to verify the hypothesis on the possibility of improving sensor parameters during interrogation by the frequency method. The comparison results are shown in Table 5.
The sensitivity of the sensing system, , was calculated as follows: where fg and fair are the resonant wavelengths of the selected gas and the reference gas (air), respectively, and ng and nair are the RI of the selected gas and the reference gas (air), respectively.

Discussion
The paper describes an approach to improving the performance of a sensing system's by applying frequency interrogation. Although the simulation results confirm the proposed method's effectiveness, it has several limitations. The startup speed of OEO is  Figure 11. OEO output frequency dependence on gas RI using an SOI-based MRR.
We compared the LoD parameters to verify the hypothesis on the possibility of improving sensor parameters during interrogation by the frequency method. The comparison results are shown in Table 5.
The sensitivity of the sensing system, S ss , was calculated as follows: where f g and f air are the resonant wavelengths of the selected gas and the reference gas (air), respectively, and n g and n air are the RI of the selected gas and the reference gas (air), respectively.

Discussion
The paper describes an approach to improving the performance of a sensing system's by applying frequency interrogation. Although the simulation results confirm the proposed method's effectiveness, it has several limitations. The startup speed of OEO is largely determined by the gain of the microwave amplifier in the feedback circuit, which can negatively affect the energy efficiency of the sensor system. Another limitation is the frequency selectivity of the microwave circuit. With a microwave circuit working bandwidth of 50 GHz, the largest difference between the optical carrier wavelengths and the notch filter the system can detect will be approximately 400 pm. On the other hand, such a limitation makes it possible to confidently use resonant structures with an FSR greater than 800 pm as notch filters (this criterion is met, for example, by MRR at SOI).
Another problem of the considered scheme is the need to measure the microwave frequency in a wide range. The output frequency of the OEO can be reduced by bringing the optical source wavelength closer to the resonant wavelength of the sensor. However, this will lower the optical carrier level. These losses can be compensated for by increasing the gain of the microwave amplifier, but this can lead to an increase in system noise, device temperature, and overall power consumption.
The third problem to be solved in the future is the temperature dependence of resonant structures. According to [53], SOI-based resonant structures are temperature-dependent. Therefore, the sensing system should be thermostable. Another solution to this problem is to apply machine-learning algorithms to improve sensing system quality [54].
At the same time, the described sensing system has several advantages. First of all, frequency interrogation allows the use of more sensitive sensors. Secondly, considering Figure 10, applying OEO decreases the sensor's FWHM by about 3 orders of magnitude. Numerically it leads to a rise in the Q-factor and a decrease in LoD, according to Equations (7) and (11). However, it is hard to estimate the system LoD using only Equation (11) because it does not take into account the element's noise. At the same time, if we consider the system LoD as the minimum frequency change that the system can detect, we may try to estimate LoD as follows. The resonant wavelength, λ airres , of MRR for the air medium is equal to 1543.05 nm (see Table 4). If we consider that the minimum microwave frequency shift, ∆ f , that can be measured equals 100 kHz (usually in microwave systems the frequency stability is higher [55]), then we can estimate the equivalent wavelength shift, ∆λ, as follows: Using this value we may find the LoD using the following equation [56]: Therefore, applying the frequency interrogation method has resulted in a decrease in the LoD of 5 orders of magnitude.

Conclusions
The paper presents a simulation of a sensor system based on integrated photonics for gas detection using the SOI platform. We chose the sensor's dimensions to accommodate for common manufacturing platforms. The sensor's sensitivity equals 100 nm/RIU, estimated from the numerical simulation results of the detection of various gases. Sensor scanning was performed using a frequency interrogator on an MZM-based OEO. This design means that most parts of the described system (the sensor, phase MZM, and photodiode) are a single PIC, keeping only the CW source and the microwave amplifier as discrete elements. It also allows the implementation of a more sensitive all-pass MRR sensor. The system sensitivity for the considered gases is 13,000 GHz/RIU. The results show that the use of frequency interrogation makes it possible to increase the LoD by at least two-fold (up to five-fold for some gases).