Preamble

Ultra-high resolution large range on-chip Fano-enhanced thermometer based on spectral analysis Desheng Zeng Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Wuhan 430074, China;

Abstract

Temperature detection is essential for evaluating the working condition of various physical, biological, and chemical systems. Optical temperature sensing tools, particularly resonator-based thermometers, have garnered significant attention due to their exceptional performance in selectivity, sensitivity and anti-electromagnetic interference. Recently developed thermometers based on optical whispering-gallery mode barcodes of the microbubble resonator achieve a large temperature range measurement and direct temperature readout. However, the large temperature variation may potentially result in inaccurate results due to similarities in spectra and inadequate precision caused by nonlinear collective shift. In this work, we have developed a novel and directly readable on-chip silicon-based Fano-enhanced thermometer utilizing a Mach-Zehnder interferometer configuration. The device comprises a fishbone waveguide and a curved strip waveguide coupled with an ultra-high Q racetrack microring resonator. The spectrum patterns of the thermometer are uniquely determined by the temperature and exhibit ultra-high slope ratio Fano resonances of over 2.0 ×10⁴ dB/nm. Simultaneously, we have proposed a spectral analysis method to accurately derive actual temperatures, which enables an ultra-high detection resolution of 6.1×10⁻⁴ ℃ and a large measurement range of 65 ℃ by leveraging a temperature database. These advancements support precise and extensive temperature sensing applications.

Keyword: silicon photonics, temperature detection, microring resonator, spectral

Introduction

Temperature is a crucial physical parameter that has a significant impact on various physical, chemical, and biological systems. Temperature sensing with high resolution and a broad range is of great importance and has wide applications in diverse fields such as industrial manufacturing \cite{1,2}, environmental monitoring \cite{3-5}, and healthcare surveillance \cite{6,7}. Among sensing techniques, optical sensing technology has gained popularity due to its selectivity, multiplexing and anti-electromagnetic interference.

Recent advancements in thermal sensing have utilized various optical structures, including waveguide Mach-Zehnder Interferometer (MZI) \cite{8,9}, photonic fibers \cite{10,11}, and Sagnac interferometers \cite{12,13}. However, achieving accurate temperature sensing with high resolution based on single-pass (waveguide or fiber) optical sensors poses challenges due to the limited optical sensing path.

In a high-quality (Q) factor resonant cavity, light may be cycled millions of times, significantly enhancing the interaction between light and matter and thereby improving the sensitivity \cite{14,15}. Consequently, optical sensors based on micro-cavities have been developed for temperature detection over the years \cite{16-18}. The whispering-gallery mode (WGM) resonator, among other optical resonant cavity sensors, has gained popularity due to its high Q factor. The most commonly and widely used sensing mechanism for WGM resonators is tracking single resonance mode shift, due to its easy implementation for a broad range of applications. In addition to sensors based on a single ring resonator, the Vernier-effect of cascaded microring resonators (MRRs) has also attracted increasing attention for its ability to effectively enhance temperature sensitivity and sensing range. However, conventional resonant cavity temperature sensors face challenges in direct temperature readout and detecting a large temperature range. First, temperature detection typically involves monitoring the relative shift of the tracked resonance mode with respect to its original state and calculating temperature based on the thermo-optic coefficient which varies with the temperature and wavelength \cite{19}. Second, large temperature fluctuations may cause the tracked resonance mode to move beyond the laser's scanning range, thereby limiting sensor detection range. In order to address these constraints, a method for direct temperature readout \cite{20,21} has been proposed by analyzing the collective pattern of the WGM spectrum, which is uniquely determined by the temperature. This approach involves calculating collective shifts of the overall spectra patterns using the cross-correlation function \cite{20} or extracting multimode sensing information through a generalized regression neural network \cite{22} that correlates measured spectra with reference spectra in a database to determine the actual temperature. However, large temperature variations may lead to inaccuracies in the collective shifts calculated by the cross-correlation function due to the interference of similar spectra. The generalized regression neural network necessitates a vast temperature database with an extremely high dense sampling interval of 0.01°C and requires a large amount of memory and computing resources, thereby limiting the temperature measurement range. Additionally, considering the variation of the material refractive index with temperature and wavelength \cite{23,24}, the same temperature fluctuation in different temperature ranges will lead to nonlinear wavelength shifts, making the device less accurate. Furthermore, variations in the material refractive index with temperature and wavelength can cause nonlinear wavelength shifts for the same temperature fluctuation across different temperature ranges, resulting in reduced device accuracy.

To address these limitations, we presented a Fano-enhanced thermometer (FET), featuring unique and distinct spectrum patterns with thermally sensitive Fano resonance peaks \cite{25-27} at different temperatures. Simultaneously, a spectral analysis method is proposed to achieve ultra-high detection resolution and a large measurement range based on the temperature database. The temperature readout process mainly includes two steps: establishing the reference temperature database and classifying the correct and incorrect derived temperatures based on the spectral analysis. With a sufficiently extensive temperature database range, precise calculations can be made for any temperature within the range, potentially enabling ultra-wide range measurements. As a proof of this concept, a temperature database ranging from 15 ℃ to 80 ℃ has been established, and the spectral analysis method is employed to accurately derive temperature with an ultra-high resolution of 6.1×10⁻⁴ ℃. The device shows promise as a temperature measurement technology for sensor applications due to its superiority in detection resolution and measurement range capabilities.

2.1. Overall Design and Spectra Measurement

The FET is constructed using a silicon-based MZI structure as illustrated in Figure 1a [FIGURE:1]. One arm (Arm1) is a bus waveguide of an ultra-high Q racetrack MRR \cite{28-31} and the other arm (Arm2) is a fishbone waveguide (FBW), which is a strip waveguide assisted by sub-wavelength gratings (SWGs) \cite{32,33}. The racetrack MRR consists of two straight waveguides of 550 µm and two arc waveguides with a radius of 90 µm. These components are connected by two Euler-bend waveguides with a bending radius gradually transitioning from 1.2 mm to 90 µm. This design facilitates efficient transmission of the fundamental mode with minimal loss and prevents excitation of higher-order modes. The coupling region structure comprises two concentric arc strip waveguides with different widths and radii. The widths of the arc waveguide and bus waveguide are 3.2 µm and 1.2 µm, respectively. The radii of the arc waveguide and bus waveguide are 90.00 µm and 92.42 µm, respectively. This configuration satisfies the phase matching condition and avoids the excitation of higher-order modes. The central angles (θ) of the two concentric arc strip waveguides are π/8, ensuring that the racetrack MRR is in the under coupling state and achieves a narrower full width at half maximum (FWHM) in resonance wavelength. The FBW in Arm2 is a SWG-assisted strip waveguide with a 0.2 μm-wide strip waveguide and a 1.5 μm-wide grating. The strip waveguide with a width of 1.2 μm at both ends is connected by a tapered waveguide with a length of 20 μm. The actual temperature readout process is depicted in Figure 1b. The raw spectra at uniform temperature intervals are pre-processed into transformed spectra, and then a reference temperature database is established based on the transformed spectra. Subsequently, the collective shifts between the measured spectra at any unknown temperature and the reference spectra in the database are calculated using the cross-correlation function to derive all possible temperatures and corresponding the parameters. A detailed explanation of this process will be provided later.

Figure 1. a) The detailed structure of the FET. The racetrack MRR is composed of two straight waveguides and two circular waveguides. The Euler-bend waveguide connects the straight waveguide and the arc waveguide. The structure of the coupling area is composed of two concentric arc strip waveguides with different widths and radii to ensure that the phase matching condition of the fundamental mode is satisfied, as shown in the red solid frame. The other arm of the MZI is a FBW, shown in the red dashed frame. b) The flow chart of the actual temperature readout.

The SWG has a duty cycle of 0.4 and a period (Λ) of 250 nm, as depicted in Figure 2a [FIGURE:2], which is much less than the Bragg wavelength (λB = 2neffΛ, @1550 nm) and prevents Bragg diffraction. Figure 2b illustrates the different variation curves of the effective refractive index for the FBW and the strip waveguide as the temperature increases from 25 ℃ to 100 ℃, leading to different wavelength shifts of the MZI interference peaks and Fano resonance peaks with the same temperature variations.

The 3D FDTD simulation indicates that the light confinement occurs in both the horizontal (xy-plane) and vertical (yz-plane) directions, which means the FBW behaves as a conventional waveguide with an equivalent effective index. In addition, the effective refractive index change of the FBW differs from that of the strip waveguide forming the racetrack MRR as temperature varies. For the bending part of the racetrack MRR, the fundamental mode gradually moves from the center of the waveguide to the edge with increased curvature, without any mode mutation. When the fundamental mode passes through a straight waveguide, an Euler-bend waveguide and an arc waveguide, illustrated in Figure 2c. This phenomenon indicates that the structure can enable a smooth transition of the mode in the racetrack MRR and effectively avoid the excitation of high-order modes. In the coupling region of the racetrack MRR, only fundamental mode coupling occurs between the bus waveguide and the arc waveguide, as shown in the upper part of Figure 2d. By analyzing the mode components, the TE0 mode is exclusively present in the arc waveguide, with almost no higher-order modes, such as the first-order mode, as illustrated in the lower part of Figure 2d.

Figure 2. a) The 3D FDTD simulation results of the FBW. The light field along the propagation direction, the vertical light field of the grating tooth area and the waveguide area between the grating teeth are extracted, which shows that the light is well constrained. b) The effective refractive indices of the FBW and the multimode strip waveguide at 25 ℃ and 125 ℃, respectively. c) The distribution of the electric field when propagating in the Euler-bend waveguides. The center of TE0 mode moves gradually from the center to the edge of the bend waveguide. d) Simulation of energy transfer of the fundamental mode in the coupling area. The plot below shows that only the fundamental mode is coupled and no higher-order mode is excited in the racetrack MRR waveguide.

The output spectrum of the FET consists of the MZI spectra and the Fano resonance peaks, characterized by an exceptionally narrow FWHM and high sensitivity to refractive index changes. The analytical expression of the output spectrum is derived using the transfer matrix method. Assuming that the input light intensity is 1, the output electric field is as follows: where a1 and a2 represent electric field amplitudes in Arm1 and Arm2, respectively.

The phase shifts in Arm1 and Arm2 are denoted as θ1 and θ2, respectively. Here, α, φ and t represent the roundtrip attenuation coefficient, single-pass phase shift and transmission coefficient of the racetrack MRR, respectively. The expression in the bracket on the right side of Eq. 1 determines the shape of the output spectrum, and the design idea of the device can be explained as follows.

On the one hand, the ultra-high Q racetrack MRR and FBW exhibit distinct refractive index changes in response to temperature variations, resulting in noticeable changes of φ and (θ2 – θ1). Consequently, the wavelength shifts of the MZI interference peaks and the Fano resonance peaks exhibit differential responses to temperature variations, shown in Figure 3a [FIGURE:3], which leads to notable alterations in the Fano resonance parameters, including SR, extinction ratio (ER), and Q-factors, even with minor variations in temperature. On the other hand, it should be noted that the ultra-high Q racetrack MRR demonstrates a distinctive output spectrum characterized by a sudden phase transition within an extremely narrow linewidth near the resonance wavelength. The change of is minimal and can be regarded as a constant, resulting in the generation of Fano resonance peaks with significant difference in slope ratio (SR). Figure 3b shows the SRs of the Fano resonance peaks with different phases of the MZI spectrum.

To illustrate the superiority of FBW, simulated spectra are carried out on two FET spectra with and without FBW (the FBW is replaced by a strip waveguide with the same width), under temperature fluctuations ranging from 30 ℃ to 35 ℃, as shown in Figure 3c. One of the Fano resonance peak is chosen as a benchmark for evaluating the relative shifts of the spectra of the two configurations. The device without FBW exhibits nearly zero relative shift, because the shifts of MZI resonance peak and Fano resonance peak are 390.5 pm and 391.2 pm, respectively. However, the device incorporating FBW displays a noticeable relative shift. The shifts of MZI resonance peak and Fano resonance peak are 443.3 pm and 391.1 pm, respectively.

The difference in wavelength shift between the MZI interference peaks and Fano resonance peaks ensures the distinctive spectrum patterns at different temperatures, thus mitigating the risk of wrong collective shifts arising from similar spectra under significant temperature variations. Hence, the FBW and Fano resonances ensure the unique and distinguishable spectral patterns at different temperatures.

Figure 3. a) The wavelength shifts of the MZI interference peak and the Fano resonance peak. b) The SRs of the Fano resonance peaks with different phases of the MZI spectrum. c) Simulated spectra of the FET with and without FBW when the temperature rises from 30 ℃ and 35 ℃, respectively.

Figure 4a [FIGURE:4] illustrates the measurement apparatuses for output spectra. The output light of the tunable scanning laser (TSL) is modulated as a transverse electric wave and coupled into the FET before being received by a high resolution optical power meter. The micrograph of the FET and the SEM images of the racetrack MRR coupling area and FBW are shown in Figure 4b, 4c and 4d.

Figure 4. a) The temperature measurement setup. b) The micrograph of the designed FET. The SEM images of c) the coupling area of the ultra-high Q racetrack MRR and d) the FBW.

The normalized transmission spectrum of the ultra-high Q racetrack MRR from 1550 nm to 1554 nm is shown in Figure 5a [FIGURE:5]. In the racetrack MRR, only the fundamental mode oscillates, with no high-order modes excitation. Benefiting from the low loss Euler-bend waveguides and straight waveguides, the waveguide losses are all less than 0.24 dB/cm and the Q factor of each resonance peak significantly exceeds the order of one million, as shown in Figure 5b. This leads to narrow resonance linewidths and an abrupt phase transition of the FET spectrum occurring in a small wavelength range, facilitating the generation of Fano resonance with an ultra-high SR. The upper part of Figure 5c shows one of the ultra-high Q resonant peaks of the racetrack MRR with a FWHM of 0.68 pm and a Q of 2.25×10⁶. When the racetrack MRR works in the under coupling state, the spectral phase is converted from (–) to (+) sharply, while the phase of the wave in Arm2 varies slowly, as shown in the lower part of Figure 5c. Then the two light waves from Arm1 and Arm2 interfere with each other, forming an ultra-high SR Fano resonance with an ER of 23.1 dB and SR of 2.3×10⁴ dB/nm, as shown in Figure 5d. The blue balls represent the measurement result of Fano resonance, and the red solid line represents the simulation result, where the attenuation coefficient and transmission coefficient of the racetrack MRR are 0.9959 and 0.9969, respectively, proving that the racetrack MRR works in an under coupling state. The different responses of refractive indices of the FBW and racetrack MRR waveguide to temperature variations are validated by the measured output spectra in Figure 4e. The wavelength shifts of the MZI interference peak and Fano resonance peak are 443.1 pm and 407.9 pm when the temperature increases from 30 ℃ to 35 ℃. In addition, at 30 ℃, the ER and SR of the Fano resonance peak pointed by the arrow are 23.44 dB and –2.13×10⁴ dB/nm, respectively. With a 5 ℃ temperature variation, the ER and SR alter to 22.37 dB and –1.72×10⁴ dB/nm, respectively. The variation of parameters will significantly affect the spectrum pattern and prevent the emergence of similar spectrum patterns.

Figure 5. a) The transmission spectrum of the racetrack MRR and b) Q-factors and waveguide loss of each resonance peak. c) The output spectrum and phase of the two arms of MZI. The upper part is the Lorentz resonance peak of the racetrack MRR in Arm1, and the lower part is the output spectrum of the FBW in Arm2. d) The measured ultra-high SR Fano resonance peak and the simulated spectrum of the FET, shown as blue ball and the red line, respectively. e) The output spectra of the device with FBW at 30 ℃ and 35 ℃.

2.2. Process of Temperature Readout and Establishment of Reference Database

We take the temperature range from 15 ℃ to 80 ℃ (limited by experimental apparatuses) as a proof of concept to elucidate the direct temperature readout process in detail. The output spectra of the FET are measured at equal temperature intervals in the range from 15 ℃ to 80 ℃ to establish a reference temperature database, denoted as T_database. The spectra (from 1550 nm to 1554 nm, with a scanning accuracy of 0.1 pm) within the T_database are shown in the left part of Figure 6 [FIGURE:6]. Benefiting from the different temperature response of the FBW and racetrack MRR, the high density reference temperature sampling interval (ΔT) is not necessary. To reduce the number of collected spectra in T_database while maintaining the accuracy of derived temperatures, we set ΔT to 5 ℃.

Prior to performing the cross-correlation function to compute the collective shift between two output spectra, the spectra should be preprocessed to obtain the transformed spectra. This is because fluctuations in the parameters of the Fano resonance peaks may not be readily discernible in the information-rich MZI interferometric spectrum. Consequently, the raw spectra should be smoothed using a Savitzky-Golay filter and then normalized. Subsequently, the normalized spectra are substituted into the f(Tr) function (Eq. 3) to derive the transformed spectra, labeled as D_database and depicted in the right part of Figure 6. This function effectively captures the attributes of the Fano resonance peaks while also reflecting the variation of the MZI interference spectrum (see S1 of the supplementary information). The function takes the form where Tr and λ represent the transmission spectra and wavelength, respectively, and the sign represents the ± sign of the derivative.

Collective shifts of spectra corresponding to neighboring reference temperatures in the D_database are determined by utilizing the discrete form of the cross-correlation function (RDD'), shown as Eq. 4. Considering that the higher the similarity of the two spectra in D_database, the greater the maximum value of their cross-correlation function, the maximum value of the cross-correlation function is extracted, denoted as m (Eq. 5). The position of m indicates the relative collective shift between the two spectra. Figure 7a [FIGURE:7] shows the computation of RDD', collective shift and m for two spectra corresponding to different reference temperatures, T and T' (T