Optical Parametric Oscillator-Based Molecular Sensor

Abstract

A sensor comprising a resonator including a non-linear material having a non-linear susceptibility configured to convert pump electromagnetic (EM) waves into signal EM waves and idler EM waves, wherein at least one of the pump EM waves, the signal EM waves, and / or the idler EM waves is fed back through the non-linear material to form one or more resonant EM waves. An actuator coupled to the resonator or to a pump path to the resonator controls at least one of the pump power of the pump EM waves, the detuning of the frequency mode of the resonator with respect to one or more frequencies of the resonant EM waves, and the phase matching of the non-linear material. The output of the resonator outputs one or more output EM waves containing information regarding a sample coupled to the resonator.

Description

Technical Field

[0001] [Cross - Reference to Related Applications] This application claims the benefit under 35 U.S.C. § 119(e) of U.S. Provisional Patent Application No. 63 / 342,894, docket number CIT - 8825 - P, entitled "Optical Parametric Based Molecular Sensor", filed on May 17, 2022, by Robert M. Gray, Selina Zhou, Mingchen Liu, Arkadev Roy, and Alireza Marandi, and assigned to the assignee of the present invention, and incorporates by reference the disclosure of that application herein.

[0002] [Description of Research and Development Sponsored by Federal Government Funds] This invention was made with government support under award number FA9550 - 20 - 1 - 0040, awarded by the United States Air Force. The government has certain rights in this invention.

[0003] The present invention relates to a sensor system and a method of manufacturing and using the sensor system.

Background Art

[0004] Mid-infrared (IR) is a major spectral region of interest for molecular sensing where most molecules exhibit strong spectral fingerprints. In contrast to conventional spectroscopy, where laboratory analyzers or low-cost semiconductors and electrochemical gas sensors were dominant, optical gas sensors offer both fast response and high gas specificity, bridging the gap between low-performance, low-cost sensors and high-end laboratory equipment [1]. Innumerable applications such as medical breath analysis [2] and environmental sensing [3] have motivated extensive efforts to develop broadband coherent spectrometers in the mid-infrared region for multi-gas sensing using, for example, dual-comb spectroscopy [4-6]. However, achieving a low-noise coherent broadband spectrometer in the mid-infrared region requires addressing significant challenges related to light sources [7] or spectroscopic techniques [8]. Mid-infrared photodetectors also pose barriers (sensitivity, response time, etc.) to making such systems viable for many applications. What is needed, therefore, is a more sensitive and faster sensing system. The present invention meets this need.

Summary of the Invention

Means for Solving the Problems

[0005] Exemplary embodiments of the subject matter of the present invention include, but are not limited to, the following examples.

[0006] 1. A sensor, a resonator including a nonlinear material having a nonlinear susceptibility configured to convert a pump electromagnetic (EM) wave into a signal EM wave and an idler EM wave, wherein at least one of the pump EM wave, the signal EM wave, and / or the idler EM wave is fed back through the nonlinear material to form one or more resonant EM waves; an actuator coupled to the resonator or to the pump path to the resonator, for controlling or modulating at least one of the pump power of the pump EM wave, the detuning of the frequency mode of the resonator with respect to one or more frequencies of the resonant EM waves, and the phase matching of the nonlinear material; and an output of the resonator that outputs one or more output EM waves containing information about a sample coupled to the resonator. A sensor comprising the above.

[0007] 2. In the sensor of Example 1, a detector coupled to the output of the resonator to detect the output power of one or more output EM waves; and a computer coupled to the detector and configured to determine information about the sample from a change in the output power when the resonant EM wave is coupled to the sample The sensor further comprising.

[0008] 3. In the sensor of Example 2, the computer determines the information by comparing the output power with a calculated output power calculated using a model of the response of the resonator coupled to the sample that interacts with the resonant EM wave, and / or determines the information using a machine learning algorithm trained using training data including an association of the concentration or composition of the sample with the output power as a function of at least one of pump power, detuning, and phase matching, and / or determines the information only by analyzing the change in the output power configured (e.g., programmed and / or including circuitry) to be a sensor.

[0009] 4. The sensor according to any one of Examples 1 to 3, further comprising an optical parametric oscillator (OPO) including a resonator.

[0010] 5. In the sensor of Example 4, the OPO is configured to operate during a phase transition between a degenerate operation and a non-degenerate operation (e.g., controlled by phase matching, dispersion control, dimension setting, and / or an actuator). The sensor.

[0011] 6. In the sensor of Example 4, the OPO is configured to operate near the laser oscillation threshold of the resonant EM wave (e.g., controlled by phase matching, dispersion control, dimension setting, and / or an actuator), the EM includes a simulton, A sensor configured such that the sensitivity of the sensor to changes in the sample is improved by near-threshold dynamics such as solitons or other soliton formation mechanisms.

[0012] 7. In any of the sensors of Examples 4 to 6, the actuator is configured to change the operation of the OPO from below the threshold (laser oscillation of the resonant EM wave) to above the threshold.

[0013] 8. In any of the sensors of Examples 1 to 7, the resonator is configured to operate near the oscillation threshold of the laser oscillation of the resonant EM wave characterized by 0.9 ≤ pump power / threshold pump power ≤ 3 (for example, phase matching, dispersion control, dimension setting, and / or controlled by an actuator), or the actuator is configured to perform detuning or phase matching such that the resonator operates at least during a spectral phase transition between a degenerate operation and a non-degenerate operation and / or such that the resonant EM wave includes solitons.

[0014] 9. In any of the sensors of Examples 1 to 8, the actuator is configured to cause the resonant EM wave of the resonator to follow a predictable spectral tuning and reproduce the function of a wavelength tunable laser spectrometer using the output EM wave.

[0015] 10. In any of the sensors of Examples 1 to 9, the actuator is configured to modulate at least one of pump power, detuning, and phase matching to adjust the dynamic range, sensitivity, or selectivity of the sensor.

[0016] 11. In any of the sensors of Examples 1 to 10, the information includes at least the concentration or composition differential of a sample containing one or more molecules.

[0017] 12. In any of the sensors of Examples 1 to 11, the information includes the physical or chemical properties of a sample containing a solid, liquid, or gas.

[0018] 13. In any of the sensors of Examples 1 to 12, the information is output in real time with the change of the sample and with a time resolution limited by the modulation / actuation speed of the actuator and the information acquisition time (for example, 1 Hz to 1 MHz).

[0019] 14. In any of the sensors of Examples 1 to 13, the actuator includes at least one of an actuator configured to adjust the length of the resonator, a heater and / or a cooler thermally coupled to the resonator to modulate the phase matching and / or the length of the resonator, an electro-optic modulator capable of adjusting the refractive index of the path length in the cavity, an electro-optic mirror or beam splitter for controlling the power of the pump EM wave, and a control circuit coupled to the pump source for adjusting the frequency or power of the pump EM wave output from the pump source.

[0020] 15. In any of the sensors of Examples 1 to 14, the actuator includes a scanner that applies one or more ramp functions that modulate at least one of the pump power, detuning, and phase matching.

[0021] 16. One or more chips or photonic integrated circuits provided with any of the sensors of Examples 1 to 15.

[0022] 17. In any of the sensors of Examples 1 to 16, further comprising means for interacting the resonant EM wave of the resonator with the sample, the means including an evanescent field, a slot waveguide, an optical fiber, a chamber of the resonator, a fluid coupling, a free space coupling, or a sample container positioned to couple the sample to the resonator via a hollow core fiber.

[0023] 18. In any of the sensors of Examples 1 to 17, The resonator includes a cavity containing a nonlinear material between mirrors, and the cavity includes a sample space for positioning the sample within the cavity.

[0024] 19. In any of the sensors of Examples 1 to 18, the resonator is a sensor including an optical fiber loop coupled to a non-linear material.

[0025] 20. An analyzer comprising any of the sensors of Examples 1 to 19, configured to output information regarding a sample, the sample including exhaled breath, atmospheric concentration of pollutants or greenhouse gases, or process gas monitored in an industrial environment.

[0026] 21. In any of the sensors of Examples 1 to 20, the information includes the concentration of a sample in a range that causes saturation of a linear absorption sensor according to Lambert-Beer's law.

[0027] 22. A sensing method, comprising the step of coupling a sample to a resonator including a non-linear material having a non-linear susceptibility configured to convert a pump electromagnetic (EM) wave into a signal EM wave and an idler EM wave, at least one of the pump EM wave, the signal EM wave, and the idler EM wave being fed back through the non-linear material to form one or more resonant EM waves, the step of controlling at least one of the pump power of the pump EM wave, the detuning of the frequency mode of the resonator with respect to one or more frequencies of the resonant EM waves, and the phase matching of the non-linear material, the step of detecting the output power of one or more output EM waves output from the resonator, and the step of calculating information regarding the sample from the change in the output power in response to the sample and the modulation. A method comprising the above steps.

[0028] 23. A computer-implemented system, one or more processors comprising, the processor receiving an output power of one or more output electromagnetic (EM) waves output from a resonator when the resonator is coupled to a sample, the resonator including a nonlinear material having a nonlinear susceptibility configured to convert a pump electromagnetic (EM) wave into a signal EM wave and an idler EM wave, and at least one of the pump EM wave, the signal EM wave, and / or the idler EM wave being fed back through the nonlinear material to form one or more resonant photons, the processor controlling at least one of modulation / actuation of a pump power of the pump EM wave, a detuning of a frequency mode of the resonator with respect to one or more frequencies of the resonant photons, and a phase matching of the nonlinear material when the sample is coupled to the resonator, and the processor being a computer-implemented system that calculates information about the sample from a change in output power in response to the sample and the modulation / actuation.

[0029] Next, reference is made to the drawings, in which like reference numerals throughout represent corresponding parts.

Brief Description of the Drawings

[0030]

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[0031] In the description of the drawings, FIG. 3-1 is as follows. JPEG2025521388000002.jpg75166

Best Mode for Carrying Out the Invention

[0032] In the following description of the preferred embodiments, reference is made to the accompanying drawings which form a part hereof and which illustrate specific embodiments in which the present specification may be practiced. It is to be understood that other embodiments may be utilized and structural changes may be made without departing from the scope of the present invention.

[0033] FIG. 1a shows a sensor system 100 according to one or more embodiments of the present invention. The sensor includes a resonator 102 that includes a non-linear material and an actuator 104 coupled to the resonator. When the resonator is appropriately modulated / operated by the actuator in the presence of a sample coupled to the resonator, one or more output electromagnetic waves from the resonator contain information about the sample.

[0034] Examples of resonators include, but are not limited to, resonators configured for non-linear processes such as three-wave mixing and four-wave mixing, and platforms such as free-space cavities based on mirrors, optical fibers, or waveguides (e.g., thin-film waveguides). The non-linear material has a non-linear susceptibility configured to convert a pump electromagnetic (EM) wave 106 into a signal EM wave 108 and an idler EM wave 110, and the resonator is configured such that at least one of the pump EM wave, the signal EM wave, and / or the idler EM wave is fed back through the non-linear material to form one or more resonant EM waves. Examples of materials having a non-linear susceptibility (e.g., second-order non-linearity) include, but are not limited to, lithium niobate, lithium tantalate, potassium titanyl phosphate (KTP), aluminum nitride, gallium arsenide, indium phosphide, aluminum gallium arsenide, GaP, InGaP, silicon, silicon nitride, or silica. Silicon, silicon nitride, and silica can be used to achieve, for example, third-order non-linearity. The non-linear material can be appropriately phase-matched (e.g., periodically poled), dispersion-controlled, or have a resonator length L tailored to a (e.g., second-order) parametric amplification / conversion process, capable of converting a pump wave into a signal wave and an idler wave, and / or according to the present invention, capable of achieving non-degenerate operation, degenerate operation, near-threshold operation, or other operating modes and regimes. In one or more examples, a high-frequency (e.g., 2ω or second harmonic) pump wave is converted into a low-frequency idler wave and a low-frequency signal wave (e.g., frequency ω). The pump EM wave can be output from various electromagnetic radiation sources such as lasers. In some examples, the pump, idler, and signal can include electromagnetic radiation pulses (e.g., femtosecond or picosecond pulses), and the resonator is appropriately dispersion-controlled to control walk-off / pulse overlap. In various examples, the optical pulses each include electromagnetic radiation pulses having a center wavelength, for example, from 200 nm to 10 microns.

[0035] The actuator is coupled to the resonator or to the pump path to the resonator so as to modulate / control at least one of the pump power of the pump EM wave, the detuning of the frequency mode of the resonator with respect to one or more frequencies of the resonant EM wave, and the phase matching of the nonlinear material. Examples of actuators include, but are not limited to, an actuator for adjusting the length of the resonator (e.g., directly or via a mirror) (e.g., a piezoelectric actuator optionally coupled to a translation stage), a heater or cooler thermally coupled to the resonator to modulate / control the phase matching and / or length of the resonator, an electro-optic modulator capable of adjusting the refractive index of the path length within the cavity, an electro-optic mirror or beam splitter for controlling the power of the pump EM wave, an amplitude modulator or polarization beam splitter for controlling the power of the pump EM wave, and a control circuit coupled to the pump source to adjust the frequency or power of the pump EM wave output from the pump source.

[0036] In the embodiment shown in FIG. 1a, a detector 112 is coupled to the output of the resonator so as to detect the output power of one or more output EM waves output from the resonator. In one or more examples, a computer 114 coupled to the detector can be used to determine information about the sample from the change in output power when the resonant EM wave is coupled to the sample 116.

[0037] FIG. 1a further shows the coupling of the sample and the resonator that can be achieved in various ways. For example, the resonator can include or be coupled to a cavity for interacting the EM wave with the sample. In one example, the cavity is configured for sensing the sample through an evanescent field, a waveguide, a fiber, or a fluid coupling. In another example, the cavity includes a cell (e.g., a gas cell that houses the sample) that forms part of the cavity.

[0038] Still other exemplary embodiments and variations of the present invention include, but are not limited to, the following examples.

Example

[0039] A sensor including an optical parametric oscillator Figure 1b shows a sensor system where the resonator is an optical parametric oscillator (OPO). More specifically, the OPO includes a nonlinear material within a cavity surrounded by mirrors M1 and M2. The sample is coupled to the OPO by positioning both the OPO and the sample within a second cavity surrounded by mirrors OC (output coupler) and IC (input coupler). In this example where the sample contains carbon dioxide gas, the detector includes a near-infrared detector (Thorlabs PDAVJ5), and the OPO includes orientation-patterned gallium phosphide (OP-GaP) within a 4-micron-long resonator defined by cavity mirrors M1 and M2, so that the OPO outputs femtosecond pulses having a wavelength centered at 4 μm

[11] .

[0040] In the data obtained in this example, the sample is contained in a 10-cm path-length glass cell having silicon and calcium fluoride windows. The gas cell within the second cavity is housed in a box and the ambient gas is flushed with nitrogen.

[0041] Figures 1c and 1d respectively show the output power and output spectrum as a function of the second cavity detuning. Since the data shows that the output power and spectrum of the OPO depend on the cavity length with extremely high sensitivity [10, 12], by monitoring the output power as a function of the cavity round-trip detuning using a photodetector, data regarding the spectral characteristics of gas molecules within the gas cell can be extracted with high precision. More specifically, each point on the "detuning peak" is the integral of the OPO power spectrum over all wavelengths of the output spectrum at various cavity round-trip lengths, as shown in Figure 1d. When the target molecule absorption line overlaps with the OPO spectrum, spectral information is reflected in the shape of these peaks due to absorption and dispersion. These characteristics are very sensitive to the magnitude and spectral distribution of absorption and dispersion, and can be utilized as the basis for molecular sensing.

[0042] Figure 1(e) shows the output signals at various CO2 concentrations, indicating that the gas concentration can be measured using the change in the amplitude of the tuning peak as a function of the gas concentration. Conventional spectroscopy methods rely on the direct measurement of absorption peaks at specific wavelengths, whereas the OPO sensor output provides multiple sources of information between and within multiple tuning peaks containing different spectral information without the need to analyze the change in the frequency of the spectrum. For example, Figure 1e shows that the maximum output power of the rightmost peak (corresponding to the cavity soliton) decreases as the CO2 concentration in the cavity increases, while other peaks may have the opposite dependence. By cross-referencing other metrics related to the peaks, the sensitivity and specificity in the presence of multiple gases can be improved.

[0043] Furthermore, as shown in Figure 2, by varying the input pump power (centered at a wavelength of 2 microns in this example) in addition to the cavity length, another dimension is added to the output signal for improved sensitivity. Figure 2a was generated by simulating the output signals of the OPO at two different CO2 concentrations of 4120 ppm and 412 ppm and then finding the difference between them. Each "pixel" corresponds to the power difference of the OPO sensor signal at various pump powers (y-axis) and detuning values (x-axis) for these two different concentrations.

[0044] Simulated sensing of 392 ppm and 412 ppm of CO and 412 ppm of N2O was performed to demonstrate multi-gas sensing. Figure 2b shows that by subtracting the 0 ppm baseline from the OPO output peaks for various gas concentrations, it is demonstrated that different gas species can be identified by distinguishing between close concentration values. Furthermore, due to the nature of second-harmonic generation, the output signal profile is reflected in the input signal attenuation, enabling real-time detection of mid-infrared absorption using a near-infrared detector (Figure 2c).

[0045] This embodiment shows broadband mid-infrared gas sensing in the range of approximately 3.5 μm to approximately 4.8 μm, but this range can be expanded by changing the dispersion and losses in the cavity. When implemented with parametric nanophotonics

[13] , the sensing scheme can enable a small on-chip multi-gas sensor without the need for mid-infrared lasers and detectors. The results presented herein show that OPO sensors can enable multi-band broadband real-time gas sensing in applications such as, but not limited to, breath analysis, environmental sensing, and process gas sensing (in industrial environments).

Example

[0046] Modulation of the OPO operating range a. Sensor architecture and sensing configuration The formation dynamics of the secondary cavity soliton of the OPO, i.e., the temporal soliton, can also be utilized for molecular sensing. 33 The cavity soliton-based sensing mechanism relies on the fact that the OPO operation is extremely sensitive to the gain and loss in the soliton regime.

[0047] Figure 3c shows an example of a sensor configured for sensing a target gas sample inserted into a doubly resonant synchronous pump OPO near degeneracy. The OPO includes an optical resonator with a second-order nonlinearity that provides parametric gain. At degeneracy, the nonlinear interaction is phase-matched so that the generated signal and idler lights are at the second harmonic of the pump. 35 The pump repetition period T rep When it matches the effective signal round-trip time in the resonator, synchronous pumping occurs, but the doubly resonant operation means that the OPO resonates the signal and idler in the resonator while the pump is being extracted. Thus, the degenerate signal resonating in the cavity receives gain from the pump by the parametric process at each round-trip following absorption from the sample.

[0048] A bright-dark soliton pair of a signal at frequency ω and a pump at 2ω38,39 When a round - trip delay is added to the conventional operation, cavity solitons occur in a degenerate OPO by simultaneous excitation in the high - gain low - finesse regime. That is, the cold - cavity time T cav increases with respect to the pump repetition period T rep . Figure 3d shows that for stable cavity soliton formation, a dual balance of energy and timing is required, the gain must be equal to the loss, and the soliton group velocity ΔT that occurs when the signal attenuates the pump due to the non - linear interaction of the χ 33 crystal must compensate for the round - trip delay ΔT (2) to re - establish synchronization with the pump pulse. Since the timing advance depends on the pump depletion, the two conditions are linked, and thus the gain must be large enough to satisfy the timing condition, so the response to changes in gain and loss in solitons near the threshold is characteristically strong. RT

[0049] Figure 4 shows that the cavity - soliton - based sensing mechanism, in marked contrast to other active cavity schemes, utilizes the interaction of the energy and timing of the soliton regime to obtain high sensitivity to the target sample. Without being bound by a specific scientific theory, this significantly high sensitivity can be explained by the distinctively large threshold and high slope efficiency of the soliton, as shown in Figure 4a. For a given pump power, when a slight loss due to the sample is added, the threshold increases, and correspondingly the output power ΔP decreases. The absolute output change is proportional to the local slope efficiency at the sensing point, that is, the higher the slope efficiency, the higher the sensitivity.

[0050] In such an example, the corresponding path - length improvement is given by the following equation.

[0051]

Equation

[0052] where L​eff is the effective path length, L is the cavity round-trip length, P signal is the signal power, α is the sample absorption coefficient, and Δα represents a slight change in absorption due to the addition of the sample. Models using single-mode laser theory or continuous-wave OPO theory show that, as schematically shown in Fig. 4b, the path length improvement asymptotically approaches infinity as the number of threshold crossings N approaches 1 17 .

[0053] This large improvement near the threshold is basically accompanied by a decrease in the signal-to-noise ratio (SNR). However, the combination of the high slope efficiency, high threshold, and low spontaneous emission rate of the simaltone OPO makes this SNR decrease extremely slow. In one example, Fig. 4c shows that the measured simaltone threshold is approximately 2.5 times larger than that of the conventional method, and the slope efficiency is 3.5 times. As a net result, in detector-limited measurements, it is possible to operate at the same output power and approach the simaltone threshold by nearly a factor of 9. By being able to obtain a measurable signal very close to the simaltone threshold in this way, a significantly large improvement can be obtained, so simaltone is an excellent candidate for intracavity sensing.

[0054] b. Characterization a. Measurement procedure for acquisition of measured values The following results were obtained using a degenerate synchronous pump free-space OPO with bow-tie formation 34The pump is the output of a periodically poled lithium niobate-based OPO, and supplies a pulse train at 2.09 μm with a bandwidth of 155 nm, a repetition frequency of 250 MHz, and an average power of up to 1.4 W. The pulses were coupled through a dielectric-coated mirror with high transmittance for the pump and high reflectance for the signal. The input coupler was placed on a stage equipped with a piezoelectric actuator for tuning the cavity length. For type 0 phase matching between the pump at 2.09 μm and the signal at 4.18 μm at room temperature, nonlinearity was provided by a 0.5-mm anti-reflection-coated parallel plate aligned patterned gallium phosphide crystal with a poling period of 92.7 μm. Condensing and collimation were performed with two concave gold mirrors with a radius of curvature of 24 mm on both sides of the crystal. The output coupler was a dielectric-coated mirror that enabled 25% output coupling for the signal at approximately 4.18 microns. The cavity length can be adjusted by a piezoelectric actuator (PZT) on the cavity mirror M1 to enter the simulton regime. The cavity can be locked using a dither-and-lock protocol.

[0055] The output was passed through a long-pass filter and sent to an MCT detector at the monitoring valley root. Spectral measurements were performed using a commercially available Fourier transform infrared spectrometer. The OPO and all measurement instruments were placed in a nitrogen purge box. To perform the sensing measurement, the CO2 concentration was changed by adding N2 to the device. The CO2 concentration was referenced to a commercially available CO2 sensor for calibration of the measured values. Five data points were taken at each concentration and averaged to obtain the final result.

[0056] The procedure was as follows. First, a small part of the 2-μm power was taken out to the detector using a pellicle beam splitter with a splitting ratio of 92:8 placed on the input side of the cavity (Fig. 3e). Subsequently, a calibration curve for mapping the 2-μm power to the detector value was obtained using an optical power meter (Fig. 3f). Using a similar procedure, calibration curves for both the conventional method and the simulton method of mapping the measured voltage of the photodetector to the optical power were created with the 4-μm OPO cavity locked and purged. An example of the simulton calibration curve can be seen in Fig. 3h. The R 2 values are shown for each plot and indicate the goodness of fit.

[0057] For sensing measurements, the PZT was continuously scanned with a ramp function supplied by a function generator. This allows all OPO peaks to be monitored approximately simultaneously and also enables the measurement of outputs that are close to the generally low threshold of locking stability. The output was measured with a 4-μm photodetector and then mapped to optical power using a calibration curve. Five measurements were taken at each CO2 concentration using a data acquisition unit triggered by the ramp function used for the cavity length scan. An example of the raw data measured from the system can be seen in Fig. 3g, which shows examples from three different CO2 concentrations of 406 ppm (green), 384 ppm (orange), and 297 ppm (red). The five different traces overlap in different colors and are approximately the same, but there are some variations due to the locking instability of the pump OPO in this case and the dynamic nature of the measurements in this case. The inset is an enlarged image of the signalton peak. Visual comparison with other peaks reveals that the signalton exhibits a significantly dramatic response to the addition of the gas. As described above, the behavior of the other peaks contains additional useful information regarding the gas being monitored, and sensors designed to utilize data from all OPO peaks are likely to be the subject of future research. The final presented value of the output power at any single concentration value, such as in Fig. 3i as well as Fig. 4a of the text, is the result of averaging the five measured signalton peaks, determining the maximum voltage of this average measurement, and then mapping it to optical power using the calibration curve. Fig. 3i shows this output power as a function of concentration for three different numbers of threshold crossings, N = 2.092 (green triangles), N = 1.959 (orange circles), and N = 1.837 (red squares). These three values are significantly closer to each other than the values shown above, emphasizing that fine-tuning of the pump power can achieve high sensitivity at any concentration of interest.

[0058] References 33Numerical simulations were performed according to the method described. Nonlinear propagation in the crystal was calculated using the split-step Fourier method to solve the coupled wave equations that describe the development of the pump and the signal. Round-trip propagation was provided by a linear filter that includes both dispersion and frequency-dependent loss. Important for the simulation of the sensing behavior is an appropriate model of gas absorption and dispersion during the round trip. For this purpose, a Lorentz oscillator model with parameters obtained from HITRAN 44 was used.

[0059] b. Results Figures 5a and 5b show the experimental spectral data for both the simaltone method (Figure 5a) and the conventional method (Figure 5b) for three different CO2 concentrations in the cavity. Figure 5b shows that in a general multimode laser or a conventional OPO where other non-absorbed modes compensate for the loss of the absorption mode, the change in laser threshold or output power due to the addition of the sample is limited, and cavity soliton enhanced sensing cannot be achieved 17 . However, different from the conventional method, the power of all spectral modes of the simaltone method (Figure 5a) decreases approximately uniformly even when a narrowband sample is added, indicating the possibility of threshold sensing. Furthermore, in marked contrast to a single-mode laser, soliton enhancement provides broadband operation, thus relaxing the requirements for fine-tuning the laser line to a single absorption line, providing an SNR advantage, and sensing in wavelength regions that are usually not easily achievable with lasers, especially in the infrared region.

[0060] Figure 5c schematically shows the formation of soliton pulses in multiple round trips in the resonator for two different values of absorption. The round-trip delay ΔT RTAs a result, the newly formed pulse slowly deviates from the gain window determined by the pump pulse and the walk-off length, and grows into a non-linear acceleration strong enough to compensate for the delay. When the round-trip loss is added to the signal, when interacting with the pump in the non-linear crystal, the amount of acceleration decreases, and correspondingly, the gain of all spectral modes of the steady-state simulton supermode decreases, leading to a spectrally uniform power decrease despite the relatively narrow absorption spectrum shown in the measured spectrum of Figure 5a.

[0061] This dynamic behavior is confirmed in the simulation of Figure 5d. Figure 5d shows a comparison of the steady-state signal pulse position (left) and the effective gain (right) as a function of CO2 concentration for three different numbers of threshold crossings: N = 1.2 (green triangles), N = 1.5 (orange circles), and N = 1.8 (red squares). The gain is calculated as the convolution of the pump pulse shape and the walk-off, with the center of the gain window set to 0 fs. The approximate edges of the gain window can be calculated by halving the sum of the pump pulse length and the walk-off length. As the sample is added to the cavity, the steady-state position of the signal pulse moves towards the edge of the gain window, and sufficient gain for resonance cannot be obtained. This large (and rapid) gain reduction associated with the addition of the sample to the cavity enables high sensitivity to simultons near the threshold.

[0062] Figure 6a is a plot of the simulton output power measured as the CO2 concentration in the cavity changes. The green triangles, orange circles, and red squares correspond to pumping at different numbers of threshold crossings (here N = 1.25, 1.64, and 1.84 respectively). Similar to the input-output power dependence shown above, the output power dependence on CO2 changes most rapidly near the threshold. The solid line shows a linear fit to the data near the threshold. The sensitivity is obtained using the slope, and the best-fit sensitivity is calculated to be 4.1 mW / ppm. Furthermore, this data shows that a large dynamic range of the system is possible by changing the high-sensitivity region by adjusting the pump power.

[0063] These observation results are consistent with the simulation sensing results in Figure 6, which show a large sensitivity near the threshold and an adjustment of the sensitivity region due to the change in the number of times exceeding the threshold. It can be seen that the calculated sensitivity is also consistent among different pump conditions. The simulation sensitivity is slightly lower than the experimentally observed results. This difference is mainly due to the incomplete modeling of the gas response.

[0064] Figure 6c shows the improvement in the equivalent path length of the experimental data. This improvement is obtained by defining Δα eff as the effective absorption coefficient by a pump with the same bandwidth as the thermalton that has undergone 1.2 m of CO2 absorption at the reference concentration. Using this definition,

[0065]

Number

[0066] is calculated for the near points of the experimental measurement. When N = 1.84, the maximum improvement of 2491 is observed near the threshold, and similar improvements are also observed near the threshold in other cases. The solid line shows the improvement corresponding to the linear fit from Figure 6a as expected. The good fitting accuracy near the threshold shows a roughly asymptotic trend of the improvement, and the deviation at low sample concentrations is due to the saturation of the thermalton response observed far above the threshold.

[0067] Figure 6d shows the sensitivity in mW / ppm calculated for the near points of the experimental measurement. Note that due to the change in the number of times exceeding the threshold, a sensitivity close to the measured value of 4.1 mW / ppm can be achieved at all concentrations. The sensitivity achievable using the linear method is also plotted (light blue region). The modeled was a 1.2 m linear cavity excited by a pulse source having the same bandwidth as the thermalton measured by the inventors and an average power of 500 mW, and by changing the path length improvement, the maximum sensitivity at each point, compared to the inventors' cavity with a finesse of 2, is up to 10 6Adopt a path length multiplexing technique to achieve an improvement and a finesse exceeding 1.5 million in response thereto. The inventors believe that this is an improvement limit large enough to represent the finesse value that the linear method can actually achieve. Similar to the theory, inverse scaling is observed in this path length multiplexing technique, highlighting the limitations of the dynamic range of linear technology. In contrast, the nearly constant and orders-of-magnitude higher sensitivity demonstrated by the thermalton sensing mechanism at high sample concentrations shows how the thermalton sensing regime breaks the trade-off between the sensitivity and dynamic range of the linear method. Therefore, many applications that utilize thermalton sensing can obtain benefits while avoiding the requirements of ordinary high-finesse cavities.

[0068] The remarkable sensing performance of the thermalton can be further improved in several ways. In some configurations, the OPO exhibits multiple thermalton resonances as the cavity length increases. These further detuned thermal tons can potentially provide large sensitivity and sensitivity improvement by showing higher slope efficiency. 33 Moreover, the thermalton benefits from operating in the high-gain low-finesse regime. OPO embodiments using thin-film lithium niobate nanophotonics with a gain of up to 100 dB / cm have been demonstrated and can further enhance highly sensitive and highly scalable molecular sensors. 40,41 Furthermore, other non-linear behaviors of the OPO, such as spectral phase transitions, can be used as additional means to achieve high sensitivity in intracavity sensing in the OPO. 42 The OPO operating in the thermalton regime can also be configured for various molecular sensing applications.

Example

[0069] Numerical Methods and Calculation Methods In this section, the method used to calculate the numerical results presented in Example 2, or an example of a method for performing calculations to determine information about the sample from the output power, will be described. The simulation is mainly based on the methodology presented in the reference 2 presented.

[0070] The round-trip propagation of the signal in the cavity is modeled in two parts: the nonlinear interaction of the pump and signal in the crystal and the free-space propagation of the light around the cavity described by the linear transfer function. The nonlinear interaction is essentially single-pass optical parametric amplification (OPA) defined by the coupled-wave equations.

[0071]

Number

[0072] where the time coordinate t is set to co-move with the group velocity of the signal wave, and the pump envelope phase is shifted by π / 2 to ensure a real solution when higher-order dispersion is not considered. The subscripts ω and 2ω denote the signal and pump, respectively. The electric field envelope is E j given by, where j ∈ {ω, 2ω}, and is normalized such that the instantaneous power is given by |E j | 2 The strength of the nonlinear interaction is defined by the nonlinear coupling coefficient

[0073]

Number

[0074] where η0 is the impedance of free space, d eff is the effective nonlinearity, w0 is the Gaussian beam waist in the crystal (assuming the crystal length is small compared to the confocal parameter), n j is the refractive index, and c is the speed of light. The absorption coefficient α j accounts for the material losses in the crystal. Δβ’ gives the group velocity mismatch between the pump and the signal. Finally, the dispersion operator

[0075]

Number

[0076] represents the material dispersion experienced by the pump and signal within the crystal.

[0077] Using the split-step Fourier method, the simulation of the non-linear step in each round trip is performed. For this purpose, the spatial coordinate z corresponding to the propagation distance within the 0.5 mm crystal is divided into 50 separate steps. At a given step, the output of the non-linear interaction is numerically solved using the fourth-order Runge-Kutta method. Subsequently, a linear filter considering the dispersion and loss at that step is applied in the frequency domain. References 3 Using the Sellmeier equation for GaP described in, the dispersion is calculated up to the fourth order.

[0078] After completion of the non-linear step, an additional linear filter is applied in the frequency domain to account for the round-trip propagation of the beam. Specifically, the input to the coupled-wave equation

[0079]

Equation

[0080] for the round trip (n + 1) is the output from the previous OPA related by the equation

[0081]

Equation

[0082] where L is the length of the crystal.

Equation

[0083] Here, F and F

[0084] Here, F and F -1represent Fourier transform and inverse Fourier transform respectively, and Ω is the normalized Fourier frequency coordinate. The absorption coefficient α(Ω) takes into account the frequency-dependent losses in the cavity due to the mirror, output coupling, AR coating on the crystal surface, and gas in the cavity. Similarly, the cumulative round-trip phase measured for a perfectly synchronized signal pulse is considered as Φ(Ω)=ΔT RT (πc / λ 2ω +Ω)+ΔΦ(Ω), where ΔT RT is the cavity detuning, c is the speed of light, and λ 2ω is the pump wavelength. ΔΦ(Ω) includes the dispersion terms from various cavity components and gases.

[0085] An accurate simulation of the sensing behavior is provided by the gas model. In our simulations, the Lorentz resonator model is used to calculate the complex refractive index for the signal in a round trip 4 . Specifically, the refractive index n(ω) is given by

[0086]

Equation

[0087] , where the indices i and j refer to the upper and lower states of the transition of interest respectively, f ij is the oscillator strength, N j is the density of the molecules in state j, q is the electronic charge, ε0 is the vacuum permittivity, m e is the mass of the electron, ω ij is the central frequency of the transition, and γ ij is the linewidth of the transition. For an accurate calculation of the response from our experiments, we considered the most abundant ambient gases including N2, O2, H2O, and of course CO2, and the parameters were obtained from the HITRAN database 5 . All simulations assume room temperature and atmospheric pressure. To mimic the experimental procedure to achieve a change in CO2 concentration by purging with nitrogen, after the calculation of the complex refractive index using Equation S3, absorption and dispersion were n(ω)=n’(ω)+iκ(ω) can be considered separately from the relationship, where the real part n’(ω) of the refractive index contains dispersion information and the imaginary part κ(ω) defines the contribution to loss. Examples of the imaginary and real parts of the complex refractive index of the target CO2 band at atmospheric concentrations can be seen in FIGS. 7a and 7b, respectively. Interestingly, although much of the theoretical analysis of the present inventors in this embodiment focuses on the influence of loss, it has been found that an accurate model of dispersion is further required for an accurate simulation of the sensing behavior.

[0088] In addition to helping to confirm the behavior observed in the experiment, the numerical analysis of the present inventors can help to extend their results to different regimes that can further improve the sensing performance. FIGS. 7c and 7d emphasize the importance of the low-finesse operation for the observed sensing behavior. As described in the text and analytically demonstrated in section b below, the sensitivity benefits from a high slope efficiency and a high threshold. In the Simulton regime, both the slope efficiency and the threshold can be increased by the specifications of the low-finesse cavity. FIG. 7c shows the output power as a function of the input power for output coupling values of 0.1 (green), 0.25 (orange), and 0.4 (red), and the output coupling value of 0.25 approximately matches the experiment of the present inventors. Here, it is observed that the threshold increases from about 350 mW for output coupling 0.1 to about 1200 mW for output coupling 0.4. Furthermore, it can be seen that the slope efficiency more than doubles from 81.3% to 204%. Therefore, as shown in FIG. 7d, a sensitivity improvement of more than four times is observed. The fact that such high slope efficiency and threshold can be achieved in the Simulton regime by low-finesse operation is important for the particularly large sensitivity improvement provided by Simulton.

[0089] Furthermore, our numerical results can help to better understand the nonlinear dynamics involved in the simulton formation that contributes to sensing. As shown in Fig. 5c and Fig. 5d, it is the interplay of energy and timing conditions that enhances the sensing behavior of the simultons. Specifically, as shown in Fig. 5d, the dynamic feature that leads to high sensitivity is that the steady-state signal pulse position moves away from the center of the gain window when losses are added to the cavity. The gain window is determined by the pump pulse and the walk-off length and can be approximately found by convolving the pump pulse (here a sech-type pulse with a duration of 35 fs) with a rectangular pulse of duration corresponding to the walk-off length Δβ′L (here 72 fs). The steady-state signal pulse position is located at the "center of mass" of the signal.

[0090]

number

[0091] In the formula, P i and t i Let i denote the pulse power and time of the i-th Fourier bin. Since the addition of sample tends to distort the temporal characteristics of the pulse, the "centre of mass" metric is useful to provide consistency in the measurements.

[0092] To further highlight the opposing roles of gain and loss, we contrast the steady-state pulse position as a function of pump power (Fig. 7e) with the pulse position as a function of concentration (Fig. 7f). In both cases, 0 fs along the y-axis represents the center of the gain window. Here, we see that adding gain by increasing the pump power pushes the steady-state pulse position towards the center of the gain window, whereas adding loss pushes it away. Thus, we see that the same interplay of energy and timing that results in high slope efficiency in the simulton regime can also enable high sensitivity. The jump observed in Fig. 7e around 775 mW is an artifact resulting from the discrete nature of the simulation. The detuning value ΔT that gives the maximum power is RTTo generally mimic the locking experiment, multiple detuning values are simulated and the one that results in the maximum output power is recorded. As the pump power is increased, this optimal detuning changes, and discrete jumps as observed can occur. However, in an experiment where the detuning can be changed continuously, the behavior is thought to become smoother.

[0093] a. Comparison with Linear Absorption Sensing In analyzing the performance of the inventors' method, it is useful to make a direct comparison with linear absorption sensing (LAS). The analysis here is based on the publication in reference 6. Starting from Lambert - Beer's law for light of intensity I passing through a sample of length L with absorption coefficient α, in the output intensity I out is I out = I in e -αL is given by.

[0094] The most common way to quantify the sensitivity improvement is to consider the improvement in the optical path length. This metric is particularly suitable for cavity - enhanced sensing where the ongoing physical mechanism can be directly understood as an increase in the interaction length between light and the sample. In a linear cavity of length L with mirror transmittance T and reflectivity R (intensity) filled with an absorption sample, the input - output power relationship is given as follows.

[0095]

Equation

[0096] The approximation made here is to expand the whole equation up to the first order of α.

[0097]

Equation

[0098] Note that F is the cavity finesse in the formula, and by using T≒1 - R,

[0099]

Number

[0100] it can be seen that it becomes, where in the formula,

[0101]

Number

[0102] the effective path length defined as. This is just a typical Lambert - Beer's law where the path length L is replaced with L eff Therefore, it can be seen that the linear cavity improves the path length by

[0103]

Number

[0104] times. Comparing (S7) with (S5), the direct improvement ξ of the path length can be obtained.

[0105]

Number

[0106] This formula is particularly useful because it enables the calculation of ξ, that is, L eff from the measured value of intensity. This formula can also be generalized for measurements where a sample of a certain baseline concentration already exists in the system. In particular, when measuring the output intensity before and after adding a small amount of sample Δα, it becomes as follows.

[0107]

Number

[0108] This is equivalent to the above equation (1). In equation (1), under the assumption that the spatial profile of the beam is constant between measurements so that the mode area can be taken out from both the numerator and the denominator, the intensity is replaced with power. Therefore, it is obvious that if the values of Δα, the path length L, and the change in power associated with the sample addition are known, the improvement in the path length can be easily calculated. However, since α = α(ω) is a function of frequency, a little more attention is required for the calculation of this quantity using only the measurement of the intensity change of a broadband signal. To address this, I in = Σ i I in,i Consider the case of performing LAS with a multimode light source that includes several frequency modes i such that i If there is an absorption coefficient α

[0109]

Equation

[0110] α i Assuming that αL is small, the following equation is obtained.

[0111]

Equation

[0112] I in Dividing by L and rearranging the terms leads to the following equation for α eff :

[0113]

Equation

[0114] α eff is α weighted by various mode intensities normalized to the total intensity iIt is given by the sum of the loads of ’. Using this equation, Eq. (S9) can be extended to the case of a broadband light source as long as the spectral shape of the light source is known.

[0115] From these results, a comparison between the experimentally measured thermalton behavior and the linear method can be made. For this purpose, the equivalent path length improvement is calculated that is required for a light source having the same spectrum as the thermalton at the reference absorption α to undergo the same intensity change due to a further addition Δα of the sample to the linear cavity. For this calculation, first, the experimental thermalton spectrum (orange line in Fig. 8a) of the purged cavity with a measured CO2 concentration of 11 ppm is acquired, and a spectrum without CO2 (blue dashed line) is reconstructed using interpolation. Next, using the CO2 absorption spectrum provided by HITRAN, the mode intensity Pi(αi) of a light source having a spectrum equivalent to that of the thermalton after propagating 1.2 m through a sample with a mode absorption coefficient αi is estimated.

[0116] As shown in Fig. 4c of the main text of the present application, the calculated improvement is large, reaching a value of 2491. Using L eff defined by Eq. (S7), it can be seen that this is equivalent to the improvement by a cavity having a finesse of 3921. This is important as it demonstrates that second cavity solitons in a low finesse cavity near the threshold can achieve a similar sensitivity improvement as that achieved by the linear method in a high finesse cavity.

[0117] The measurement of the path length improvement defined by (S9) mainly serves to quantify the relative power rather than the sensitivity. Furthermore, the improvement in the case of the thermalton is due to non - linear dynamics that result in broadband losses rather than an extension of the path length, making it difficult to make a fair comparison. This difficulty is particularly prominent when there is already a large baseline level of the sample in the cavity, and in the linear method, generally, α effAbsorption modes that are not seen in the thermalton spectrum used in the calculation will already be significantly attenuated. Therefore, it is also meaningful to directly compare the sensitivity with the LAS for a pump having the same optical characteristics as the output of the thermalton OPO of the present inventors. Start by analytically calculating the sensitivity of the LAS. The sensitivity is the rate of change of the signal I out with respect to the absorption coefficient and is given as the derivative of (S5).

[0118] [Equation]

[0119] From here, it can be seen that the maximum sensitivity occurs when α = 0 and is given by I in L. Considering the large effective path length that can be achieved with a high-finesse cavity, this sensitivity can be very large. The improved sensitivity S eff of a system having an effective path length L enh and the sensitivity S base of the baseline LAS system having a path length L are compared, and the following equation is obtained for the sensitivity improvement ζ.

[0120] [Equation]

[0121] Here, it is assumed that both systems are excited with the same power. It can be seen that when α = 0, the sensitivity improvement exactly corresponds to the path length improvement ξ calculated above. However, considering the dynamic range, it is clear that this sensitivity improvement rapidly decays with the increase of α when L eff > L. As a result, L (i.e., L eff) As the increase of leads to higher sensitivity near α = 0, the sensitivity becomes significantly lower at larger values of α, resulting in an essential trade-off between sensitivity and dynamic range in the linear case. Therefore, directly considering sensitivity improvement is also important for the study of dynamic range. To perform this comparison, the maximum sensitivity achievable using the linear method for any α is determined. By optimizing (S13) with respect to L, it can be found that the sensitivity is maximized when L = 1 / α. Thus, the optimized sensitivity is obtained. S opt =I in / eα

[0122] This optimized sensitivity, which is inversely proportional to α, defines the sensitivity limit of the LAS shown in Figs. 3b and 6d. In the comparison plot of Fig. 6d, a light source with the same bandwidth and average output of 599 mW as the simalton is assumed. In reality, the asymptotic behavior of the LAS near α = 0 is limited by spatial constraints and the achievable accuracy with available cavity mirrors. For comparison, assume a cavity length of 1.2 m, the same as the size of the inventors' OPO system, and a maximum path length improvement corresponding to a finesse exceeding 1.5 million. Especially at such a large bandwidth, it is extremely difficult to actually achieve such a high finesse, so this is considered a reasonable choice. 6 of the maximum path length improvement.

[0123] Plot the sensitivity and sensitivity improvement (S14) given by equation (S13) against the inventors' measurement data in Figs. 8c and 8d. Fig. 8c is very similar to Fig. 6d of the text, but here the linear region is extracted into two lines of the sensitivity limit S opt and the baseline sensitivity S base calculated for a light source with the same bandwidth and power as the simalton as described above. Subsequently, Fig. 8d shows the corresponding sensitivity improvement obtained from the ratio of the inventors' measured sensitivity to S base and the value of the maximum sensitivity improvement reaches 90. This large sensitivity improvement can significantly improve the achievable resolution compared to the linear baseline.

[0124] b. Absorption Sensing in a Single-Mode Cavity Here, the theory of absorption sensing in a single-mode cavity (SM ICAS) is outlined. Starting from the rate equations of the laser system. Defining the average photon number M, the average inversion distribution ρ, the broadband cavity loss γ, the pump rate R, the natural decay rate A of the laser upper level, and the stimulated emission rate B per photon per excited atom or molecule, the following equation is obtained.

[0125]

Equation

[0126] The last term Bρ in Equation (S16a) is the average spontaneous emission rate. This term is often omitted in the analysis of single cavity absorption sensing. Here, by giving the solutions with and without this term, the practical importance of this term can be examined. Setting both equations to 0 and solving for the steady-state average photon number, the following equation is obtained.

[0127]

Equation

[0128] When spontaneous emission is not considered, or

[0129]

Equation

[0130] when it is, the last term inside the root can be ignored, and the following equation is obtained.

[0131]

Equation

[0132] The intracavity power P int is related to the average photon number M by

[0133] [Number]

[0134] can be obtained as, where in the formula, JPEG2025521388000030.jpg2113 is the reduced Planck constant, c is the speed of light, ω is the laser frequency, and a free - space cavity with a round - trip length L is assumed. Assuming the transmittance of the output coupler is T, the output power P out is P out = TP int can be obtained by calculation. Regarding formula (S18),

[0135] [Number]

[0136] becomes, where in the formula, L is the total loss, and the relationship R th = Aγ / B and JPEG2025521388000032.jpg1439 are used. As the last operation before proceeding, T = 1 - R = 1 - e -α R L ≈ α tot L can be rewritten, where in the formula, R is the reflection of the output coupler. The total loss can similarly be JPEG2025521388000033.jpg15102 can be defined, where in the formula, α tot = α R + α samp + α oth is the total absorption coefficient including the output coupling loss α R , the loss α samp caused by the sample, and the loss α oth caused by other in - cavity elements. By rewriting formula (S19) with respect to these absorption coefficients, the following formula is obtained.

[0137] [Number]

[0138] To obtain the improvement factor according to equation (S9), the quantity

[0139]

Number

[0140] is determined, where Δα samp is a slight change in the loss due to the absorbing substance in the cavity. ΔP out (α samp ) - P out (α samp ) + Δα samp ) is defined, and

[0141]

Number

[0142] is assumed, then

[0143]

Number

[0144] is obtained. Using (S20), this quantity can be

[0145]

Number

[0146] determined as, where this system is reparameterized with respect to the number of times N = R / R th . Finally, the improvement ξ = L eff / L is calculated, and the approximation that Δα samp << α samp is made.

[0147]

Number

[0148] Therefore, if spontaneous emission can be ignored, it can be seen that an improvement approaching asymptotically to infinity can be calculated as the threshold is approached. Figure 9a shows the reference 7 for the realistic laser parameters given in, i.e., A = 1.7×10 8 s -1 , B = 10 -2 s -1 , L = 1m, and α R = 0.01m -1 for, the improvement calculated using the full model of Equation (S17) compared with the analytical solution ignoring spontaneous emission given by Equation (S22). With the frequency ω = 4.5×10 14 rad / s, this corresponds to the central frequency of the OPO output by the inventors. For these parameters, the agreement is excellent, with the main variation occurring very close to N = 1, where the simplified model approaches infinity while the full model approaches the peak. Generally, the lower the spontaneous emission rate, the better the agreement.

[0149] To maximize the improvement, here we want to operate the system as close to N = 1 as possible. However, as N approaches 1, the signal approaches zero, so we face a trade-off in the signal-to-noise ratio (SNR). Intuitively, there are two ways to improve this situation as shown in Figure 9b. Here, the output power P out as a function of the pump rate R is shown with respect to the reference line (line 1, medium orange) and compared with two modified lines (thin orange line 2 and thick orange line 3). The minimum detectable power P out is shown as a gray dashed line, and the gray shaded area below it represents the number of photons that cannot be detected. R det,i for i ∈ {1, 2, 3} represents the minimum pump rate at which the number of signal photons exceeds P out,det . The first step towards improvement would be to change the slope efficiency, i.e., the rate of change of the output power with respect to the change in the pump rate beyond the threshold. As shown by line 2, the higher the slope efficiency, the more it becomes possible to operate near the threshold while maintaining an output power large enough to obtain a sufficiently large SNR. Alternatively, as exemplified by line 3, the threshold can also be increased. For the same slope efficiency and output power, a larger threshold means a smaller N. In other words, Rdet,3 / R th,3 <R det,1 / R th,1 That is. Based on this intuition, looking at Equation (S20), we can see how each parameter can contribute to the improvement adjustment. First, rewrite Equation (S20) with respect to P out,det and rewrite it.

[0150]

Number

[0151] Subsequently, it can be arranged to solve for R det and solve for it.

[0152]

Number

[0153] R th =α tot Since cA / B is known, the number of times N det exceeding the detector limit threshold is given by the following equation.

[0154]

Number

[0155] From this equation, we can see the parameters that can be adjusted to operate near the threshold while keeping the signal at the same level, and thus the SNR of the detector-limited measurement is improved. Here, it is clearly understood that by increasing the ratio A / B, N det can be made closer to 1 while keeping the signal constant. This is consistent with Figure 9c showing the output power for various A as a function of the pump rate. Increasing A should increase the threshold and enable operation near the threshold. However, the rates A and B are inherent in the basic characteristics of the laser system and actual adjustment may be difficult. More notably, the only loss present in Equation (S25) is the loss α RThat is. The larger the output coupling, the greater the extraction efficiency, which increases the threshold and can also be advantageous for slope efficiency. This is shown in Fig. 9d. In contrast, other intracavity loss mechanisms simultaneously cause an increase in the threshold and a decrease in slope efficiency, as shown in Fig. 9e. As a net result, the two effects cancel each other out and do not lead to a net benefit in terms of operation near the threshold.

[0156] As a final comparison point, an expression for the sensitivity can be obtained.

[0157]

Number

[0158] R det Assuming operation at a pump rate given by

[0159]

Number

[0160] where S det is the sensitivity at the point determined by P out,det . Similar to the SNR for operation near the threshold, it can be seen that the ratio A / B can be advantageous for the absolute efficiency, further emphasizing the advantage of using a laser with a low spontaneous emission rate. Furthermore, it can be seen that the sensitivity is related to α -1 tot . This suggests that there is the same limit observed by the linear method in the dynamic range of ICAS using a conventional laser. For a given set of system parameters, the maximum achievable sensitivity is inversely proportional to the sample loss. From this relationship and the finding in equation (S22) that the improvement factor is also inversely proportional to the loss, it is clear that conventional intracavity absorption sensing with a single-mode laser benefits from a high-finesse cavity and is optimal for trace gas detection. These conclusions can be used when analyzing the proportionality of intracavity absorption spectroscopy in a WO OPO in the next section.

[0161] c. ICAS of Continuous-Wave OPO Although the focus of this research is on the synchronously pumped regime, which is a pulsed operation mode, it is also desirable to have a basic analytical framework for understanding the ICAS of OPO. The continuous-wave (CW) theory provides such a framework and enables a direct comparison with the general laser case presented above. Specifically, here we derive the improvement factor of the ICAS of CW OPO. Furthermore, we derive the sensitivity equations and see how these quantities scale with the critical parameters of OPO. Such an analysis using the synchronously pumped theory is the subject of future research, but this CW analysis is considered to be a starting point for understanding these important behaviors in OPO.

[0162] The derivations in this section follow those presented in Ref. 8 First, assuming low loss and low gain, we start from the coupled-wave equations of the three-wave mixing process and derive the equations for the input-output power relationship. The coupled-wave equations for the electric fields of the pump E3, signal E1, and idler E2 are given by the following equations.

[0163]

Equation

[0164] where κi = ω i d / n i c is the nonlinear coupling coefficient, z is the propagation distance, α i = μ0σ i c is the round-trip loss of power, and i ∈ {1, 2, 3}. For energy conservation and phase matching, the following relationships for the frequencies ω i and wave vectors k i of the pump, signal, and idler are required. ω3 = ω2 + Ω1 k3 = k2 + k1 + Δk

[0165] Usually, the wave vector mismatch Δk ≒ 0 due to quasi-phase matching in the crystal is achieved. Next, without pump attenuation

[0166] [Number]

[0167] Under the assumption, a hypothesis of the solution of the coupled-wave equation is established to obtain the gain and bandwidth of a parametric amplifier with length l. Since this approximation is approximately accurate below the threshold, it can be used to accurately estimate the threshold gain of the system.

[0168] The hypothesis by the present inventors is as follows.

[0169] [Number]

[0170] By substituting into the coupled-wave equation, the following equation is obtained.

[0171] [Number]

[0172] κ i Substituting and arranging terms,

[0173] [Number]

[0174] Finally, solving for Γ’,

[0175] [Number]

[0176] Therefore, it can be seen that Γ', which is the eigenmode representing the development of the electric field envelope according to the hypothesis of the present inventors, is composed of two main terms. The first term is the loss term and is given by the previously defined round-trip loss of the signal and the idler. The second term determines the gain, and it can be seen that while one eigenmode grows, the other decays. By setting α1 = α2 = α, the following simplified equation is obtained.

[0177]

Equation

[0178] This gives the following solutions for the signal field and the idler field.

[0179]

Equation

[0180] Here, g represents the gain of the field, Γ represents the maximum achievable gain, and complete phase matching is assumed. Having arrived at such an equation for the development of the field, the threshold gain of the OPO is then derived. By obtaining the equations for the changes in the + and - components of the electric field using equations (S31) and (S34), equation (S35) is expanded to obtain the following equations for the electric fields E1(l) and E2(l) at the output of the crystal:

[0181]

Equation

[0182] In the case of complete phase matching, Δk = 0 can be taken. Subsequently, assuming a small gain, the following equation is obtained from the threshold condition (E i (l) = E i (0)).

[0183]

Equation

[0184] Simplifying this system,

[0185] [Number]

[0186] When Γl is small and α1l + α2l << 8, the following equation can be obtained.

[0187] [Number]

[0188] This is the equation for obtaining the threshold gain of the CW OPO, which essentially reduces to the requirement that the gain is equal to the loss. Next, an approximation of the conversion efficiency of the oscillator is derived. First, the internal efficiency η int =(ΔI1 + ΔI2) / I 30 is derived, where in the equation, ΔI1 + I if -I i0 is the intensity change during one pass of the gain medium. To achieve this, first, assuming that dE2 / dz and dE1 / dz can be ignored (i.e., the accumulation in one round trip is small), the following two equations for the pump wave can be obtained.

[0189] [Number]

[0190] Here,

[0191] [Number]

[0192] where + and - refer to the forward-propagating field and the backward-propagating field, respectively. Integrating both equations and assuming that the signal field and the idler field are independent of z,

[0193] [Number]

[0194] From here, the maximum energy transfer from the pump to the signal and the idler occurs when

[0195]

Number

[0196] , which can be seen to be consistent with the phase matching relation. Next,

[0197]

Number

[0198] is used, and the intensity

[0199]

Number

[0200] is substituted into, and the following relationship between the signal power and the idler power can be derived.

[0201]

Number

[0202] The derivation method is as follows.

[0203]

Number

[0204] Between the first line and the second line,

[0205]

Number

[0206] is used. Furthermore, the conservation of intensity means the following.

[0207]

Number

[0208] By solving this, the input-output power relationship can be obtained. Proceed step by step. First, substitute equations (S41a) and (S41b) to obtain the following equation.

[0209]

Number

[0210] The first two terms on the left side cancel each other out, the next two terms can be combined into one sine term, and the last two terms are the same and can be combined. After this is completed, use equation (S42) to rewrite everything in terms of ε 20 and ε 30 Rewrite it.

[0211]

Number

[0212] Next, divide by the right side, arrange the terms, substitute κ3 and the intensity, and the following equation can be obtained.

[0213]

Number

[0214] To match with equation (S39), which is the previous threshold gain equation, the threshold intensity

[0215]

Number

[0216] is defined. Note that by the same steps below, an equivalent equation can be derived for I 10 Finally, from this, assuming Δk = 0, ΔI2 ≈ a2I 20is realized, and the following equation is obtained.

[0217]

Number

[0218] Here, the quantity NI 30 / I 3,th is defined. Subsequently, when the two equations are combined, the internal intensity becomes as follows.

[0219]

Number

[0220] Thereby, considering both the forward and backward propagating waves, the internal efficiency of the CWOPO at N threshold crossings is defined. However, since the OPO of the present inventors is a ring resonator oscillator, the backward wave does not interact with the gain medium and its contribution can be ignored. As a result of repeating the calculation without this final term in Equation (S42), the coefficient becomes twice as large in the final equation.

[0221]

Number

[0222] Next, the extraction efficiency η ext that characterizes the ratio of the signal and idler intensities generated in the OPO to the OPO output must be determined. As before, this is calculated only for the idler and it is inferred that the signal behaves similarly. Assume that the extraction from the resonator of the idler is the intensity T2. Note that this extraction is implicitly included in the round-trip loss parameter, but here it is defined separately for explicit mention.

[0223] If the total internal intensity in the resonator is I 2,int then the output intensity is I 2,out = T2I 2,int For each round trip, I 2,int increases by the above calculated amount ΔI2,

[0224] [Number]

[0225] It decays by the amount of. From here, it can be seen that the internal intensity is given by the following infinite sum.

[0226] [Number]

[0227] Subsequently, it can be seen that the output power is given by the following equation.

[0228] [Number]

[0229] Therefore, the extraction efficiency is as follows.

[0230] [Number]

[0231] An equivalent equation can be derived for the signal. Finally, the conversion efficiency of the signal η1 = η int,1 η ext,1 and the conversion efficiency of the idle η2 = η int,2 η ext,2 are as follows.

[0232] [Number]

[0233] The total conversion efficiency is the sum of two.

[0234] [Number]

[0235] Next, using this conversion efficiency formula, we want to examine the relationship between the system loss and the output power. Consider also the case of degeneracy where ω1 = ω2 = ω. For clarity of notation, redefine the degenerate signal I 1,out +I 2,out =I ω,out , and the degenerate pump I3 as I 2ω , and use the same subscript for all other quantities. Then, for the signal, the following equation is obtained.

[0236]

Equation

[0237] This equation can characterize the OPO behavior in the case of single-mode ICAS. First, look at the improvement factor. For a slight change in loss Δα ω , the following change in the signal is obtained.

[0238]

Equation

[0239] Subsequently, the improvement ξ = ΔI ω,out / lΔα ω I ω,out is given by the following equation.

[0240]

Equation

[0241] This is a behavior very similar to that predicted by the theory of SM lasers. However, one of the advantages of OPO according to this result is that, as shown in Fig. 10a, the denominator that grows to a large value further from the threshold than the N-1 behavior shown in the case of SM lasers

[0242]

Equation

[0243] is the behavior. Here, it can be seen that the CW OPO (orange) grows more rapidly as it approaches N = 1 compared to the SM ICAS (peach).

[0244] In addition to the improvement, other scaling behaviors of the CW OPO system can also be seen, as in the case of the SM ICAS. First, some simplifications are made. First, return to the aforementioned finding that the output coupling is implicitly included in the loss. In fact, the loss α ω is ω = α samp + α R + α oth consists of three components such that. Here, α samp is the loss from the target sample, α R is the loss from the output coupling such that the reflection is

[0245]

Number

[0246] and α oth considers all other round-trip losses within the OPO cavity. Subsequently,

[0247]

Number

[0248] Furthermore, the parameter γ is

[0249]

Number

[0250] and is given by the following equation.

[0251]

Number

[0252] Next, define the detector-limited output intensity I ω,det . The corresponding input intensity I 2ω,det is as follows.

[0253] [Number]

[0254] Using this and noting that the threshold intensity is

[0255] [Number]

[0256] it can be seen that the number of threshold crossings N ω,det required to achieve the output intensity I det is as follows.

[0257] [Number]

[0258] Here, it can be seen that, unlike the case of the SM laser, the number of threshold crossings in the case of the OPO can be made close to 1 by adjusting the loss. This is the result of the loss contributing directly to the threshold by the offset term rather than by the slope as in the case of the SM laser. Furthermore, it can be seen that adjusting the output coupling can provide the greatest advantage as it acts to increase both the slope efficiency and the threshold simultaneously. Finally, due to the same advantage as the output coupling, the detector-limited sensitivity can also be improved by using an increase in γ. These observations are consistent with the scaling behavior of equation (S55) plotted in FIGS. 10b, 10c, and 10d for changes in the output coupling, loss, and γ parameter, respectively. By adjusting both the output coupling and the γ parameter, the threshold and the slope efficiency can be increased simultaneously, while increasing the round-trip loss can increase the threshold without affecting the slope efficiency.

[0259] In addition to looking at the detector-limited improvement, the sensitivity can be calculated here as follows.

[0260]

Equation

[0261] In this case too, there are significant differences compared to the case of the SM laser. Specifically, the loss term due to the sample does not appear anywhere in the equation. However, in line with what was seen in the equation (S57) for detector-limited improvement, the sensitivity can be improved by increasing both the output coupling and the γ parameter. These results suggest that, unlike in the case of the SM laser, the SW OPO can benefit from operating in the low finesse regime if there is sufficient gain to exceed the threshold. Furthermore, since there is no dependence on sample loss, a high dynamic range can be achieved in the sensing measurements performed with the OPO system. These differences are due to the difference in the gain mechanisms of the two systems represented by their respective rate equations, where the laser gain results from the energy exchange in which atomic transitions bring about the emission of photons, while the parametric gain results from the interaction between the pump electric field and the signal electric field due to the second-order non-linearity. Understanding the breather behavior requires more careful handling than the CW model, but these observations are consistent with the inventors' experimental findings, providing further insights into why the high threshold and slope efficiency of the breather can lead to a large improvement in sensitivity, and why a large dynamic range can be achieved in the inventors' measurements.

[0262] d. Breather theory A breather is a co-propagating bright-dark soliton pair for a signal at frequency ω and a pump at 2ω respectively. The breather solution can be easily obtained in a traveling-wave optical parametric amplifier (OPA) operating at degeneracy by considering the coupled-wave equation leaving only the walk-off term and the non-linear coupling term. In this section, the reference 9Derive the solution of the simaton according to the notation, and use the analytical expression of its dynamic change to give the intuition of the presented sensing mechanism. Start from the coupled wave equation of the field at degeneracy.

[0263]

Number

[0264] Here, κ is the nonlinear coupling coefficient, Δβ’ is the group velocity mismatch, and E ω and E 2ω denote the signal field and the pump field, respectively. The time coordinate is defined to co-move with the group velocity of the signal wave. Assuming wave solutions of the form E ω (z,t)=E ω (t + vz) and E 2ω (z,t)=E 2ω (t + vz), the following equation is obtained.

[0265]

Number

[0266] This system of equations can be solved analytically to obtain the solution of the simaton.

[0267]

Number

[0268] In these equations, the system was reparameterized with respect to the signal pulse interval τ, the timing advance T due to gain saturation, the pump amplitude E 2ω,0 , and the simaton signal amplitude a. By defining the small-signal gain coefficient γ0 = κE 2ω,0 ,

[0269]

Number

[0270] and T = -γ0τz.

[0271] Therefore, it can be seen that the simaltone is composed of a tanh-type dark soliton in the pump and a sech-type bright soliton in the signal, and they co-propagate at a group velocity v = γ0τ times larger than the group velocity of the signal. Here, this solution is to be extended to the dynamic regime where the effects of gain and loss on the system can be understood according to the manifold projection method presented in Ref. 10 We want to extend it to the dynamic regime where the effects of gain and loss on the system can be understood, starting again from the coupled-wave equations and using the characteristic curve method to derive the solution of the pump field. The following equation is obtained.

[0272]

Number

[0273] E 2ω Solving for,

[0274]

Number

[0275] To simplify the integral, we make the change of variable t’ = t + Δβ’(z’ - 1), and the following equation is given.

[0276]

Number

[0277] Next, we invoke the assumption of gain without distortion, which generally

[0278]

Number

[0279] varies slowly with z, and γ av for an OPO cavity with mirror reflectivity r and crystal length l

[0280]

Number

[0281] When the following is satisfied

[0282]

Number

[0283] it is defined as follows. With the current variable change, it becomes as follows.

[0284]

Number

[0285] The main variation of the signal is due to this exponential term. Therefore, noting that it disappears extremely rapidly as negative t' increases, it can be assumed that the lower limit of the integral extends to -∞ in a good approximation.

[0286]

Number

[0287] Next, this pump equation can be substituted into the differential equation (S59a) that describes the evolution of the signal. This gives the following equation.

[0288]

Number

[0289] From here, it is assumed that the electric field envelope takes the above sech-like form with respect to the soliton, but the parameters T, τ, and α can be varied with respect to z.

[0290]

Number

[0291] Substitute this into the equation (S66) of Eω(z,t) and assume a constant pump E2 ω、0 Then the following is obtained.

[0292]

Number

[0293] Define the right side of equation (S68) as g(z,t), and then perform a manifold projection to obtain the equation for the evolution of the signal pulse parameters. To perform the projection, first the inner product must be defined, which is

[0294]

Number

[0295] Let it be. The total derivative of E with respect to z is given by the following equation. sim is given by the following equation.

[0296]

Number

[0297] dE sim / dz = g(z,t), and using the orthogonality of partial derivatives under the defined inner product, for example

[0298]

Number

[0299] where ξ,η ∈ {T,τ,a} and ξ ≠ η, the following equation for the evolution of parameter ξ is obtained.

[0300]

Number

[0301] Applying this to the three target parameters gives the following system of simultaneous equations for their evolution.

[0302]

Number

[0303] Here, a sim is the steady-state simaltone amplitude, and

[0304]

Number

[0305] is given by. By analytically solving this system of simultaneous equations, the steady-state solutions for T, τ, and a can be obtained.

[0306]

Number

[0307] Next, the effects of losses and detuning on the system can be considered. Considering the round-trip delay ΔT RT and the round-trip loss Re -αL where R is the total mirror reflection of the round trip and α takes into account the additional loss in the round-trip propagation including that due to the presence of the sample in the cavity for a resonator of total length L. Assuming the nonlinear crystal has a length l, the development of the round trip is as follows.

[0308]

Number

[0309] A steady state is reached when T(n + 1) = T(n) and a(n + 1) = a(n). From this, two requirements for simaltone formation can be seen. The gain is

[0310]

Number

[0311] It must be equal to the loss as such, and the simulton group progress must compensate for the detuning, that is

[0312]

Number

[0313] it is. Furthermore, since the steady-state center-of-gravity position T is determined according to the speed at which the simulton amplitude a saturates to a steady value, the interdependence of the two conditions can be understood. Therefore, since the growth of the amplitude depends on the interaction between the gain and the loss, the steady-state center-of-gravity position is ultimately determined by the gain and loss of the system. Here, the pump is approximated as continuous, but this interaction becomes very important in the case of a pulsed pump where the pump defines the time-gain window of the signal. In this case, the bright solitons in the signal cannot exceed the threshold unless the amplitude grows at a speed sufficient to satisfy the timing condition before being pulled out of the gain window by the detuning. Above the threshold, the gain increases or decreases according to the steady position within the gain window. As shown in FIGS. 1d and 3c, such dynamics cause a high slope efficiency of the simulton near the threshold and a corresponding high sensitivity of the simulton to the addition of the sample to the cavity.

Example

[0314] Implementation of Spectroscopy with OPO In various examples, the OPO sensor can be configured using either a dual-resonant OPO (DRO) or a single-resonant OPO (SRO), and the detection mechanisms are slightly different. In DRO, both the signal and the idler resonate, while in SRO, only one of the signal and the idler resonates. The threshold of DRO can be made much lower than that of SRO, but there are tolerance limits for the cavity length and pump frequency fluctuations due to the need for the resonances of the signal and the idler to overlap [1]. By resonating only the signal (or the idler), SRO can achieve better output power stability and a wider frequency tunable range.

[0315] First, consider the DRO sensor shown in FIG. 11a below, in which both the signal and the idler resonate within the cavity, and the cavity and mirrors are designed accordingly. The output power is measured by a single photodetector at the output of the SRO, and the output power can be monitored as a function of OPO tuning parameters such as cavity length. As shown in FIG. 11b, each OPO peak has a different spectral profile. When the cavity length of the SRO is scanned continuously, the absorption spectrum within the cavity can be partially reconstructed from the time trace of the output power (FIG. 11c). For example, if the absorption features of a certain target molecule overlap only with modes 0 and 7 in FIG. 11b, it will be reflected only as a decrease in the photodetector power on the peaks associated with modes 0 and 7. By manipulating the overall spectral range and the spectral overlap between different cavity modes, effective spectral reconstruction using only the photodetector signal may be possible.

[0316] Next, consider the SRO shown in FIG. 12a, in which only the signal (orange) resonates within the cavity, and neither the idler (green) nor the pump resonates. The signal power is measured by a single photodetector at the output of the SRO. When the output power is monitored as a function of cavity length at any arbitrary signal frequency, no discrete OPO peaks as in the case of the DRO are seen. Instead, the output signal frequency can be changed by adjusting the phase matching (e.g., by adjusting the temperature of the crystal), effectively turning the SRO into a narrow-linewidth wavelength-tunable light source. As an example, by exciting an SRO at a near-infrared wavelength, the signal can be tuned into the mid-infrared spectral region.

[0317] Alternatively, instead of directly monitoring the mid-infrared signal wavelength at the OPO output, since the absorption features of the signal are also imprinted on the idler, only the non-resonant near-infrared idler can be measured. Measuring the idler allows the signal to resonate at a higher Q and enables mid-infrared sensing using near-infrared light sources and detectors.

[0318] The frequency adjustment of the SRO sensor is shown in Fig. 12b, where the curves represent the signal wavelength and the idler wavelength at a certain pump frequency. The degeneracy point corresponds to the case where the signal wavelength and the idler wavelength are equal. Adjusting the phase matching changes the signal wavelength to overlap with various absorption characteristics of the target molecules in the gas cell. The absorption within the spectral range of the signal wavelength is further enhanced by resonance, enabling intracavity sensing. By reading the output signal power as a function of the phase matching adjustment, effective spectral reconstruction is possible without using a spectrometer.

[0319] In one or more embodiments of the single-resonance oscillator, either the signal or the idler can be resonated, and any of the pump, a small amount of extracted resonant beam, or a non-resonant beam can be measured by a photodetector.

[0320] Process step a. Manufacturing method Fig. 13 is a flowchart showing a method of fabricating a sensor system. The method includes the following steps.

[0321] Block 130 represents the step of facilitating a resonator including a non-linear material having a non-linear susceptibility configured to convert a pump electromagnetic (EM) wave into a signal EM wave and an idler EM wave, where at least one of the pump EM wave, the signal EM wave, and / or the idler photons is fed back through the non-linear material to form one or more resonant EM waves.

[0322] Block 1302 represents the step of coupling an actuator to the resonator or the pump path to the resonator so as to modulate at least one of the pump power of the pump EM wave, the frequency mode tuning of the resonator with respect to one or more frequencies of the resonant EM waves, and the phase matching of the non-linear material. The actuator can include a computer or one or more circuits that output a signal for controlling the actuator.

[0323] Block 1304 represents the step of optionally coupling a detector (e.g., a photodetector) to the output of the detector to detect one or more output EM waves containing information about the sample coupled to the resonator.

[0324] Block 1306 includes the step of optionally coupling a computer to the detector.

[0325] Block 1308 represents the step of optionally coupling means for coupling the sample.

[0326] Block 1310 represents the resulting sensor or sensor system. The sensor can be implemented in many ways including, but not limited to, the following examples (see also FIGS. 1 - 16).

[0327] 1. A sensor 100 comprising: A resonator 102 including non - linear materials 130, 302 having a non - linear susceptibility configured to convert pump electromagnetic (EM) wave 106 into signal EM wave 108 and idler EM wave 110, wherein at least one of the pump EM wave, the signal EM wave, and / or the idler EM wave is fed back through the non - linear material to form one or more resonant EM waves 111; An actuator 104 coupled to the resonator or to the pump path to the resonator, configured to control or modulate at least one of the pump power of the pump EM wave, the detuning of the frequency mode of the resonator with respect to one or more frequencies of the resonant EM waves, and the phase matching of the non - linear material; An output 120 of the resonator configured to output one or more output EM waves 122 containing information about the sample 116 coupled to the resonator; And a sensor.

[0328] 2. In the sensor of Example 1, A detector 112 coupled to the output of the resonator, configured to detect the output power of one or more output EM waves; A computer 114 coupled to the detector, configured to determine information about the sample from the change in output power when the resonant EM wave is coupled to the sample. A sensor further comprising

[0329] 3. In the sensor of Example 2, the computer determines information by comparing the output power with the calculated output power calculated using a model of the response of a resonator coupled to a sample that interacts with the resonant EM wave, and / or determines information using a machine learning algorithm trained with training data including an association of the concentration or composition of the sample with the output power as a function of at least one of pump power, detuning, and phase matching, and / or determines information only by analyzing the change in the output power configured as such, a sensor.

[0330] 4. In the sensor of any one of Examples 1 to 3, a sensor further comprising an optical parametric oscillator (OPO) 118, 302 including a resonator.

[0331] 5. In the sensor of Example 4, the OPO is configured to operate during a phase transition between a degenerate operation and a non-degenerate operation, a sensor.

[0332] 6. In the sensor of Example 4, the OPO 302 is configured to operate near the laser oscillation threshold of the resonant EM wave, EM includes a soliton, a sensor configured such that the sensitivity of the sensor to changes in the sample is improved by near-threshold dynamics such as solitons or other soliton formation mechanisms.

[0333] 7. In the sensor of any one of Examples 4 to 6, the actuator is configured to change the operation of the OPO from below the threshold (of the laser oscillation of the resonant EM wave) to above the threshold, a sensor.

[0334] 8. In the sensor of any one of Example 1, the resonator operates near the oscillation threshold of the laser oscillation of the resonant EM wave characterized by 0.9 ≦ pump power / threshold pump power ≦ 3 (for example, about 1), or The actuator is a sensor that sets detuning or phase matching such that the resonator operates at least during a spectral transition between a degenerate operation and a non-degenerate operation and / or such that the resonant EM wave includes a simulton.

[0335] 9. In the sensor according to any one of Examples 1 to 8, the actuator 104 can reproduce the function of a wavelength tunable laser spectrometer using the output EM wave by causing the resonant EM wave of the resonator to follow a predictable spectral tuning.

[0336] 10. In the sensor according to any one of Examples 1 to 9, the actuator 104 is configured to modulate at least one of pump power, detuning, and phase matching to adjust the dynamic range, sensitivity, or selectivity of the sensor.

[0337] 11. In the sensor according to any one of Examples 1 to 10, the information includes at least the concentration or compositional differentiation of a sample containing one or more molecules, one or more molecular species, or one or more compounds.

[0338] 12. In the sensor according to any one of Examples 1 to 11, the information includes the physical or chemical properties of a sample containing a solid, a liquid, or a gas.

[0339] 13. In the sensor according to any one of Examples 1 to 12, the information is output in real time with changes in the sample and with a time resolution limited by the modulation / actuation speed of the actuator and the acquisition time of the information (e.g., 1 Hz to 1 MHz).

[0340] 14. In any of the sensors of Examples 1 to 13, the actuator includes at least one of an actuator configured to adjust the length of the resonator, a heater and / or a cooler thermally coupled to the resonator to modulate the phase matching and / or the length of the resonator, an electro-optic modulator capable of adjusting the refractive index of the path length in the cavity, an electro-optic mirror or beam splitter for controlling the power of the pump EM wave, and a control circuit coupled to the pump source to adjust the frequency or power of the pump EM wave output from the pump source.

[0341] 15. In any of the sensors of Examples 1 to 14, the actuator includes a scanner that applies one or more ramp functions to modulate at least one of the pump power, detuning, and phase matching.

[0342] 16. One or more chips or photonic integrated circuits comprising any of the sensors of Examples 1 to 15 or an array of resonators of any of Examples 1 to 15.

[0343] 17. In any of the sensors of Examples 1 to 16, the sensor further comprises means for interacting the resonant EM wave of the resonator with the sample, the means including a sample container positioned to couple the sample to the resonator via an evanescent field, a slot waveguide, an optical fiber, a chamber of the resonator, a fluidic coupling, a free space coupling, or a hollow core fiber.

[0344] 18. In any of the sensors of Examples 1 to 17, the resonator includes a cavity containing a nonlinear material between mirrors, and the cavity includes a sample space for positioning the sample within the cavity.

[0345] 19. In any of the sensors of Examples 1 to 18, the resonator includes an optical fiber loop coupled to the nonlinear material.

[0346] An analyzer comprising any one of the sensors of Examples 1 to 19, configured to output information regarding a sample, including the concentration of a sample in the range (e.g., pptv to several percent) that causes saturation of a linear absorption sensor according to Lambert-Beer's law, the concentration of exhaled breath, pollutants or greenhouse gases in the atmosphere, or process gases monitored in an industrial environment.

[0347] 21. In any one of the sensors of Examples 1 to 20, the information includes the concentration of a sample in the range (e.g., pptv to several percent) that causes saturation of a linear absorption sensor according to Lambert-Beer's law.

[0348] 22. In any one of the sensors of Examples 1 to 21, the modulation causes an adjustment of a narrow linewidth spectrum.

[0349] 23. In any one of the sensors of Examples 1 to 22, the nonlinear material has a length L that is phase-matched, dispersion-controlled, and / or tailored to a second-order parametric amplification / conversion process, converts a pump wave into a signal wave and an idler wave, and / or achieves the non-degenerate operation, degenerate operation, near-threshold operation, or other operation modes and regimes described in the examples.

[0350] 24. A sensing method comprising: coupling a sample to a resonator comprising a nonlinear material having a nonlinear susceptibility configured to convert a pump electromagnetic (EM) wave into a signal EM wave and an idler EM wave, wherein at least one of the pump EM wave, the signal EM wave, and the idler EM wave is fed back through the nonlinear material to form one or more resonant EM waves; controlling at least one of the pump power of the pump EM wave, the detuning of the frequency mode of the resonator with respect to one or more frequencies of the resonant EM waves, and the phase matching of the nonlinear material; detecting the output power of one or more output EM waves output from the resonator; calculating information regarding the sample from the change in the output power in response to the sample and the modulation. and

[0351] 25. A computer-implemented system, comprising one or more processors configured to receive the output power of one or more output electromagnetic (EM) waves output from a resonator when the resonator is coupled to a sample, the resonator including a nonlinear material having a nonlinear susceptibility configured to convert a pump electromagnetic (EM) wave into a signal EM wave and an idler EM wave, and at least one of the pump EM wave, the signal EM wave, and / or the idler EM wave being fed back through the nonlinear material to form one or more resonant photons, wherein the processor is configured to control at least one of the pump power of the pump EM wave, the detuning of the frequency mode of the resonator with respect to one or more frequencies of the resonant photons, and the phase matching of the nonlinear material upon coupling of the sample to the resonator, and wherein the processor is configured to calculate information about the sample from a change in the output power in response to the sample and the modulation, a computer-implemented system.

[0352] 24. An optical parametric oscillator (OPO)-based molecular sensor, comprising an optical parametric oscillator characterized by a second-order nonlinearity used for down-converting pump photons into signal photons and idler photons, a molecular sample that can flow freely over an optical cavity or can be accommodated in a gas cell or a microfluidic cell disposed within the cavity, a photodetector used for monitoring the sensor output, and an optical cavity coupled to a mechanism for adjusting a round-trip delay that can be provided via a piezoelectric actuator for mechanical adjustment or an electro-optic modulator for electrical adjustment of the refractive index of an optical path. This adjustment can be effectively achieved even outside the cavity by adjusting the pump frequency. The cavity can be configured as an optical fiber, for example, within free space using a plurality of mirrors in a bow-tie configuration.

[0353] 25. An OPO-based sensor, wherein the OPO is configured to operate using its unique non-linear dynamic behavior including spectral phase transition and temporal soliton formation. The spectral phase transition occurs when the OPO transitions from a degenerate operation where both the signal and the idler resonate at the second harmonic of the pump to a non-degenerate operation. This abrupt transition is very sensitive to changes in the resonator loss and dispersion profile, and is thus particularly useful for monitoring the addition of a sample to the cavity. A soliton is a co-propagating bright-dark soliton pair of the signal and the pump that is known to be formed when the OPO operates in a degenerate regime under appropriate conditions. One of the main features of this regime of the OPO is its high slope efficiency near the threshold, i.e., the soliton responds particularly sensitively to the addition of gain and loss to the cavity, making it particularly useful for sensing near the threshold.

[0354] 26. An OPO configured for broadband molecular sensing, for example for various tasks ranging from basic research to medical diagnosis and industrial process monitoring.

[0355] 27. A mid-infrared molecular sensor system and method that utilize the non-linear dynamics of second cavity solitons in an optical parametric oscillator to simultaneously achieve high sensitivity and a wide dynamic range during sensing of a target sample. In one embodiment, the sample is CO2 in a 4.18 μm OPO, and the simulation shows a path length improvement of 2491 and a sensitivity improvement by orders of magnitude compared to the linear method at high gas concentrations. This sensitivity improvement breaks the basic sensitivity limit according to Lambert-Beer's law.

[0356] 28. A sensor according to one or more of the above examples, wherein the resonator includes an SRO OPO tuned across a spectral range for performing spectroscopy, and the absorption spectrum within the cavity is reconstructed using the output power as a function of the tuning. In one example, the OPO is simply a narrow linewidth wavelength tunable light source.

[0357] 29. A sensor according to any of the sensors of Examples 1 - 28, wherein the sample is within a gas cell.

[0358] 30. In any of the sensors of Examples 1 to 28, the resonator includes an optical parametric oscillator including an optical parametric amplifier having a cavity around it, the sensor.

[0359] 31. In any of the sensors of Examples 1 to 30, it includes a single resonance type OPO including a resonator, can resonate either a signal or an idler, and can measure with a photodetector any of a pump, a small amount of extracted resonance wave, or a non-resonant wave (for example, measure the output power), the sensor.

[0360] b. Sensing method In one example, molecular sensing is achieved by analyzing the interaction between the generated signal photons and idler photons and the sample in the cavity. Due to this interaction, the delay caused by the unique frequency components of each resonance of the OPO is adjusted, so different responses are obtained for each resonance. By continuously scanning the delay and monitoring the power of each resonance with a photodetector, real-time sensor data regarding the target molecular sample can be obtained.

[0361] FIG. 14 is a flowchart showing a sensing method according to one or more embodiments of the present invention.

[0362] Block 1400 is the step of coupling a sample to a resonator including a nonlinear material having a nonlinear susceptibility configured to convert a pump electromagnetic (EM) wave into a signal EM wave and an idler EM wave, and at least one of the pump EM wave, the signal EM wave, and / or the idler EM wave is fed back through the nonlinear material to form one or more resonant EM waves, representing the step.

[0363] Block 1402 represents the step of controlling / modulating / operating at least one of the pump power of the pump EM wave, the tuning of the frequency mode of the resonator with respect to one or more frequencies of the resonant EM waves, and the phase matching of the nonlinear material.

[0364] Block 1404 represents the step of detecting the output power of one or more output EM waves output from the resonator.

[0365] Book 1406 includes the step of calculating / judging information about the sample from the change in the output power in response to the sample. In one or more examples, a computer determines the information by comparing the output power (e.g., amplitude and / or shape) with a calculated output power calculated using a model of the response of a resonator coupled to a sample that interacts with the resonant EM wave. In some examples, the computer determines the information using a machine learning algorithm trained using training data, and the training data includes an association between (1) the concentration or composition of the sample and (2) the output power as a function of at least one of pump power, detuning, and phase matching.

[0366] Advantages and improvements Embodiments of the present invention provide a number of novel and useful features.

[0367] 1. Achieve broadband molecular sensing without performing spectroscopy. Conventional spectrometers are often bulky or expensive and require additional elements such as diffraction gratings, spectroscopic filters, reference beam combs as in the case of dual-comb spectroscopy, or large delays as in the case of Fourier transform spectroscopy, which is particularly important in terms of scalability and affordability. In the OPO-based sensor according to the embodiments described herein, an effective non-linear mapping from the frequency domain to the time domain is effectively performed in the detected signal by each unique frequency component of the OPO resonance. This enables broadband sensing that requires only a detector.

[0368] 2. Utilize signal enhancement due to both the resonator and the gain due to second-order non-linearity. Linear cavity enhancement is the result of an increase in the effective absorption path length due to light passing through the sample in the cavity multiple times, and active cavity enhancement can also benefit from the near-threshold dynamics in the active cavity due to the interaction between gain and loss.

[0369] 3. Operations, phase transitions, and within the simaltone regime. Such dynamics enable a fundamentally different sensing scheme that can achieve high sensitivity, significant signal enhancement, and a substantial dynamic range for mid-infrared gas sensing while avoiding the requirements of typical high-finesse, high-power operation and breaking many of the limits of current technology. Furthermore, the ability to achieve simaltons at any wavelength enables a universal molecular sensing scheme that is useful particularly in wavelength regions where lasers are not readily available. For example, in an OPO with a 4-micron wavelength output, an equivalent path length improvement of 2491 near the threshold and a maximum sensitivity of 4.1 mW / ppm even at atmospheric-level CO2 concentrations were measured. 34 . As shown herein, this sensitivity of simaltons at high gas concentrations has been shown to be orders of magnitude greater than that theoretically achievable by a linear method using a probe with power and bandwidth equivalent to the output of our broadband OPO.

[0370] These features enable OPO-based sensors to provide high sensitivity, a wide dynamic range, and scalability in performing multi-molecular sensing of samples including gases, liquids, or biological tissues. Particularly in terms of scalability, the particularly strong non-linearity and flexibility obtained by mode confinement and dispersion control in these devices highlight the interesting possibilities brought about by the movement towards integrated photonics. These features can enable the creation of high-performance sensors tailored to a given application of interest. Particularly advantageous applications include, but are not limited to, those requiring precise measurement over a wide range of concentrations.

[0371] Hardware environment FIG. 15 is an exemplary hardware and software environment 1500 (referred to as a computer-implemented system and / or a computer-implemented method) used in the implementation of one or more embodiments of the present invention. The hardware and software environment includes a computer 1502 and may include peripheral devices. The computer 1502 may be a user / client computer, a server computer, or a database computer. The computer 1502 includes a hardware processor 1504A and / or a special-purpose hardware processor 1504B (hereinafter collectively referred to as the processor 1504 for the sake of alternative), and a memory 1506 such as a random access memory (RAM). The computer 1502 may be coupled to and / or integrated with other devices including input / output (I / O) devices such as a keyboard 1514, a cursor control device 1516 (e.g., a mouse, a touch screen, a multi-touch device, etc.), and a printer 1528. In one or more embodiments, the computer 1502 may be coupled to or include a portable or media viewing device 1532 (e.g., a cellular device, a personal digital assistant, etc.). In yet another embodiment, the computer 1502 may include a multi-touch device, a mobile phone, or other Internet-enabled devices that are executed on various platforms and operating systems.

[0372] In one embodiment, the computer 1502 operates by the hardware processor 1504A executing instructions defined by a computer program 1510 (e.g., for performing the calculations or operations described herein) under the control of an operating system 1508. The computer program 1510 and / or the operating system 1508 are stored in the memory 1506, interface with a user and / or other devices to receive inputs and commands, and provide outputs and results based on such inputs and commands and the instructions defined by the computer program 1510 and the operating system 1508.

[0373] The output / result can be presented on the display 1522 or provided to another device for presentation or further processing or operation. The image can be provided via the graphical user interface (GUI) module 1518. Although the GUI module 1518 is depicted as a separate module, the instructions for performing the GUI functions can be resident or distributed in the operating system 1508, the computer program 1510, or implemented with a specific-purpose memory and processor. In one or more embodiments, the display 1522 is integrated with the computer 1502 and includes a multi-touch device having a touch-sensing surface (e.g., a trackpad or a touch screen) capable of recognizing the presence of two or more contact points with a surface.

[0374] Some or all of the operations performed by the computer 1502 in accordance with the computer program 1510 instructions can be implemented with a specific-purpose processor 1504B. In this embodiment, some or all of the computer program 1510 instructions can be implemented via read-only memory (ROM), programmable read-only memory (PROM), or flash memory within the specific-purpose processor 1504B, or firmware instructions stored in the memory 1506. The special-purpose processor 1504B can be hardwired through circuit design to perform some or all of the operations for implementing the present invention. Further, the specific-purpose processor 1504B can be a hybrid processor including dedicated circuitry for performing a subset of functions and other circuitry for performing more general functions such as responding to the computer program 1510 instructions. In one embodiment, the specific-purpose processor 1504B is an application-specific integrated circuit (ASIC) or a field-programmable gate array, or other circuitry (e.g., an integrated circuit), or a processor for performing artificial intelligence / machine learning.

[0375] Computer 1502 can also implement a compiler 1512 that enables translating an application or computer program 1510 written in a programming language such as C, C++, assembly, SQL, PYTHON, PROLOG, MATLAB, RUBY, RAILS, HASKELL, or other languages into code readable by processor 1504. Alternatively, compiler 1512 can be an interpreter that directly executes the instruction / source code, translates the source code into an intermediate representation to be executed, or executes pre-compiled code stored. Such source code can be written in various programming languages such as JAVA, JAVASCRIPT, PERL, BASIC, etc. After completion, application or computer program 1510 accesses and operates on data received from an I / O device and stored in memory 1506 of computer 1502 using the relationships and logic generated using compiler 1512.

[0376] Computer 1502 optionally further includes an external communication device such as a modem, satellite link, Ethernet card, or other device for receiving input from another computer 1502 and providing output to another computer 1502.

[0377] In one embodiment, the instructions implementing the operating system 1508, computer program 1510, and compiler 1512 are tangibly embodied on a non-transitory computer-readable medium, such as data storage device 1520, which may include one or more fixed or removable data storage devices such as a zip drive, floppy disk drive 1524, hard drive, CD-ROM drive, tape drive, and the like. Further, the operating system 1508 and computer program 1510, when accessed, read, and executed by computer 1502, cause computer 1502 to perform the steps necessary for the implementation and / or use of the present invention or load an instruction program into memory 1506, and thus create a specific purpose data structure that operates computer 1502 as a specially programmed computer for performing the method steps described herein. The computer program 1510 and / or operating instructions may also be tangibly embodied in memory 1506 and / or data communication device 1530 to create a computer program product or manufactured article according to the present invention. Thus, as used herein, the terms "manufactured article," "program storage device," and "computer program product" are intended to encompass a computer program accessible from any computer-readable device or medium.

[0378] Of course, those skilled in the art will recognize that the above components, or any number of different components, peripheral devices, and other devices may be used in combination with computer 1502.

[0379] FIG. 16 schematically shows a typical distributed / cloud-based computer system 1600 that connects client computer 1602 to server computer 1606 using network 1604. A typical combination of resources may include network 1604, which consists of the Internet, LAN (Local Area Network), WAN (Wide Area Network), SNA (System Network Architecture) network, etc., client 1602 (described in FIG. 15), which is a personal computer or a workstation, and server 1606 (described in FIG. 15), which is a personal computer, a workstation, a minicomputer, or a mainframe. However, it should be noted that different networks such as cellular networks (e.g., GSM [Global System for Mobile Communications], etc.), satellite-based networks, or any other type of network may be used to connect client 1602 and server 1606 according to embodiments of the present invention. Network 1604, such as the Internet, connects client 1602 to server computer 1606. Network 1604 can utilize Ethernet, coaxial cable, wireless communication, radio frequency (RF), etc. to connect and provide communication between client 1602 and server 1606. Further, in a cloud-based computing system, resources of client 1602 and server computer 1606 (e.g., storage, processor, application, memory, infrastructure, etc.) can be shared by client 1602, server computer 1606, and users via one or more networks. Resources can be shared by multiple users and dynamically reallocated according to demand. In this regard, cloud computing can be referred to as a model for enabling access to a shared pool of configurable computing resources. Client 1602 can execute a client application or a web browser and communicate with server computer 1606 that executes web server 1610.Such web browsers are usually programs such as MICROSOFT INTERNET EXPLORER / EDGE, MOZILLA FIREFOX, OPERA, APPLE SAFARI, GOOGLE CHROME, etc. Further, the software executed on the client 1602 can be downloaded from the server computer 1606 to the client computer 1602 and installed as a plugin or ACTIVEX control of the web browser. Thus, the client 1602 can utilize the ACTIVEX component / component object model (COM) or distributed COM (DCOM) component to provide a user interface on the display of the client 1602. The web server 1610 is usually a program such as MICROSOFT’S INTERNET INFORMATION SERVER. The web server 1610 can host an ASP (Active Server Page) or ISAPI (Internet Server Application Programming Interface) application 1612, which may be executing scripts. The scripts call objects (referred to as business objects) that execute business logic. The business objects manipulate data in the database 1616 via a database management system (DBMS) 1614. Alternatively, the database 1616 can be part of the client 1602 or directly connected to the client 1602 instead of communicating / retrieving information from the database 1616 via the network 1604. When developers encapsulate business functions into objects, the system can be referred to as a component object model (COM) system. Thus, the scripts executed on the web server 1610 (and / or the application 1612) call COM objects that implement business logic.Further, the server 1606 may access the necessary data stored in the database 1616 via an interface such as ADO (Active Data Objects), OLE DB (Object Linking and Embedding DataBase), or ODBC (Open DataBase Connectivity) using MTS (MICROSOFT’S TRANSACTION SERVER).

[0380] Generally, all of these components 1600 to 1616 are embodied as and / or include logic and / or data that can be obtained from devices, media, signals, or carriers, such as data storage devices, data communication devices, remote computers, or devices coupled to a computer via a network or another data communication device. Further, when this logic and / or data is read, executed, and / or interpreted, steps necessary for the implementation and / or use of the present invention are executed as a result.

[0381] In this specification, reference is made to the terms "user computer", "client computer", and / or "server computer", but such computers 1602 and 1606 may be interchangeable and may further include thin client devices, mobile phones, notebook computers, pocket computers, multi-touch devices, and other portable devices having limited or full processing capabilities, and / or any other devices having appropriate processing, communication, and input / output functions.

[0382] Of course, those skilled in the art will recognize that any combination of the above components, or any number of different components, peripheral devices, and other devices may be used with computers 1602 and 1606. Embodiments of the present invention are implemented as software / CAD applications on client 1602 or server computer 1606. Further, as described above, client 1602 or server computer 1606 may include a sink client device or a portable device having a multi-touch-based display.

[0383] In one or more examples, a computer-implemented system includes one or more processors that receive the output power of one or more output electromagnetic (EM) waves output from a resonator when the resonator is coupled to a sample, the resonator including a non-linear material having a non-linear susceptibility configured to convert a pump electromagnetic (EM) wave into a signal EM wave and an idler EM wave, at least one of the pump EM wave, the signal EM wave, and the idler EM wave being fed back through the non-linear material to form one or more resonant photons, the processor controlling at least one of modulation / actuation of the pump power of the pump EM wave, the detuning of the frequency mode of the resonator with respect to one or more frequencies of the resonant EM waves, and the phase matching of the non-linear material upon coupling of the sample to the resonator, and the processor calculating information about the sample from changes in the output power in response to the sample and the modulation / actuation. In one or more examples, a computer includes one or more processors, one or more memories, and an application / program stored in the one or more memories, and the application executed by the one or more processors receives the output power and calculates information.

[0384] References The following references are incorporated herein by reference. References for Example 1 1 J. Hodgkinson and R. P. Tatam, Meas. Sci. Technol. 24, 012004 (2012). 2 Appl. physics. B 124, 161 (2018). 3 Optica 6, 165 - 168 (2019). 4 Nat. Photonics 12, 202 - 208 (2018). 5 Nat. Photonics 12, 209 - 214 (2018). 6 arXiv 2107.08333 (2021). 7. Nat. Photonics 6, 440 - 449 (2012). 7 Science 371, eabe0722 (2021). 8 Optica 3, 324 - 327 (2016). 9 Phys. Rev. A 94, 063809 (2016). 10 Conf. on Lasers Electro - Optics p. SF3R.4 (2020). 11 Nat. Commun. 12, 835 (2021). 12 Optica 9, 303 - 308 (2022). References for Example 2 1 Hodgkinson, J. & Tatam, R. P. Optical gas sensing: a review. Measurement Science and Technology 24, 012004 (2012). 2. Yang, Z., Albrow - Owen, T., Cai, W. & Hasan, T. Miniaturization of optical spectrometers. Science 371, eabe0722 (2021). 2 O'Keefe, A. & Deacon, D. A. Cavity ring-down optical spectrometer for absorption measurements using pulsed laser sources. Review of scientific instruments 59, 2544-2551 (1988). 3 Gagliardi, G. & Loock, H.-P. Cavity-enhanced spectroscopy and sensing (Springer, 2014). 4 Thorpe, M. J., Moll, K. D., Jones, R. J., Safdi, B. & Ye, J. Broadband cavity ringdown spectroscopy for sensitive and rapid molecular detection. Science 311, 1595-1599 (2006). 5 Bernhardt, B. et al. Cavity-enhanced dual-comb spectroscopy. Nature photonics 4, 55-57 (2010). 6 Reber, M. A., Chen, Y. & Allison, T. K. Cavity-enhanced ultrafast spectroscopy: ultrafast meets ultrasensitive. Optica 3, 311-317 (2016). 7 Foltynowicz, A., Ban, T., Masrowski, P., Adler, F. & Ye, J. Quantum-noise-limited optical frequency comb spectroscopy. Physical review letters 107, 233002 (2011). 8 Langridge, J. et al. Cavity enhanced absorption spectroscopy of multiple trace gas species using a supercontinuum radiation source. Optics Express 16, 10178-10188 (2008). 9 Zondlo, M. A., Paige, M. E., Massick, S. M. & Silver, J. A. Vertical cavity laser hygrometer for the National Science Foundation Gulfstream-V aircraft. Journal of Geophysical Research: Atmospheres 115 (2010). 10 Lou, X., Feng, Y., Yang, S. & Dong, Y. Ultra-wide-dynamic-range gas sensing by optical pathlength multiplexed absorption spectroscopy. Photonics Research 9, 193-201 (2021). 11 Altmann, J., Baumgart, R. & Weitkamp, C. Two-mirror multipass absorption cell. Applied Optics 20, 995-999(1981). 12 Tuzson, B., Mangold, M., Looser, H., Manninen, A. & Emmenegger, L. Compact multipass optical cell for laser spectroscopy. Optics letters 38, 257-259 (2013). 13 Dong, M. et al. Double-range near-infrared acetylene detection using a dual spot-ring Herriott cell (DSR-HC). Optics Express 26, 12081-12091 (2018). 14 Antonov, E., Koloshnikov, V. & Mironenko, V. Quantitative measurement of small absorption coefficients in intracavity absorption spectroscopy using a cw dye laser. Optics Communications 15, 99-103 (1975). 15 Goldman, A. & Cheskis, S. Intracavity laser absorption spectroscopy of sooting acetylene / air flames. Applied Physics B 92, 281-286 (2008). 16 Baev, V. M., Latz, T. & Toschek, P. E. Laser intracavity absorption spectroscopy. Applied Physics B 69, 171-202 (1999). 17 Trager, F., Neumann, R., Kowalski, J. & Putlitz, G. z. Intracavity atomic beam laser spectrometer for low intensity spectral lines. Applied physics 12, 19-22 (1977). 19. Kleist, E. & Bettermann, H. Intracavity absorption measurements from liquid samples in an Ar+-ion laser. Optics letters 13, 449-451 (1988). 18 Gilmore, D., Cvijin, P. V. & Atkinson, G. Intracavity absorption spectroscopy with a titanium: sapphire laser. Optics communications 77, 385-389 (1990). 19 Belkin, M. A. et al. Intra-cavity absorption spectroscopy with narrow-ridge microfluidic quantum cascade lasers. Optics Express 15, 11262-11271 (2007). 20 Garnache, A., Kachanov, A., Stoeckel, F. & Houdre, R. Diode-pumped broadband verticalexternal-cavity surface-emitting semiconductor laser applied to high-sensitivity intracavity absorption spectroscopy. JOSA B 17, 1589-1598 (2000). 21 Lohden, B. et al. Fiber laser intracavity absorption spectroscopy for in situ multicomponent gas analysis in the atmosphere and combustion environments. Applied Physics B 102, 331-344 (2011). 22 Zhang, Y. et al. Investigation of erbium-doped fiber laser intra-cavity absorption sensor for gas detection. Optics Communications 232, 295-301 (2004). 23 Fjodorow, P., Hellmig, O. & Baev, V. M. A broadband Tm / Ho-doped fiber laser tunable from 1.8 to 2.09 μm for intracavity absorption spectroscopy. Applied Physics B 124, 1-8 (2018). 24 Stark, A. et al. Intracavity absorption spectroscopy with thulium-doped fibre laser. Optics communications 215, 113-123 (2003). 25 Fjodorow, P. et al. Room-temperature Fe: ZnSe laser tunable in the spectral range of 3.75.3 μm applied for intracavity absorption spectroscopy of CO2isotopes, CO and N2O. Optics Express 29, 12033-12048 (2021). 26 Melentiev, P. et al. Plasmonic nanolaser for intracavity spectroscopy and sensorics. Applied Physics Letters 111, 213104 (2017). 27 Brunner, W. & Paul, H. The optical parametric oscillator as a means for intracavity absorption spectroscopy. Optics Communications 19, 253-256 (1976). 28 Babin, A. A., Petryakov, V. N. & Fredman, G. Feasibility of using singly resonant parametric oscillators for intracavity infrared spectroscopy. Soviet Journal of Quantum Electronics 11, 664(1981). 29 Boller, K.-J. & Schroder, T. Demonstration of broadband intracavity spectroscopy in a pulsed optical parametric oscillator made of β-barium borate. JOSA B 10, 1778-1784 (1993). 30 Haakestad, M. W., Lamour, T. P., Leindecker, N., Marandi, A. & Vodopyanov, K. L. Intracavity trace molecular detection with a broadband mid-IR frequency comb source. JOSA B 30, 631-640 (2013). 31 Jankowski, M. et al. Temporal simultons in optical parametric oscillators. Physical Review Letters 120, 053904 (2018). 34. Liu, M. et al. High-Power Mid-IR Few-Cycle Frequency Comb from Quadratic Solitons in an Optical Parametric Oscillator. Laser & Photonics Reviews 16, 2200453. eprint: https : / / onlinelibrary.wiley.com / doi / pdf / 10.1002 / lpor. 202200453. https: / / onlinelibrary·wiley.com / doi / abs / 10.1002 / lpor. 202200453(2022). 32 Marandi, A., Ingold, K. A., Jankowski, M. & Byer, R. L. Cascaded half-harmonic generation of femtosecond frequency combs in the mid-infrared. Optica 3, 324-327 (2016). 33 Marandi, A., Leindecker, N. C., Pervak, V., Byer, R. L. & Vodopyanov, K. L. Coherence properties of a broadband femtosecond mid-IR optical parametric oscillator operating at degeneracy. Optics express 20, 7255-7262 (2012). 34 Muraviev, A., Smolski, V., Loparo, Z. & Vodopyanov, K. Massively parallel sensing of trace molecules and their isotopologues with broadband subharmonic mid-infrared frequency combs. Nature Photonics 12, 209-214 (2018). 35 Akhmanov, S. et al. Nonstationary nonlinear optical effects and ultrashort light pulse formation. IEEE Journal of Quantum Electronics 4, 598-605 (1968). 36 Trillo, S. Bright and dark simultons in second-harmonic generation. Optics letters 21, 1111-1113 (1996). 37 Ledezma, L. et al. Intense optical parametric amplification in dispersion-engineered nanophotonic lithium niobate waveguides. Optica 9, 303-308. https: / / opg.optica.org / optica / abstract. cfm?URI=optica-9-3-303 (Mar. 2022). 38 Ledezma, L. et al. Widely-tunable optical parametric oscillator in lithium niobate nanophotonics. arXiv preprint arXiv:2203.11482 (2022). 39 Roy, A., Jahani, S., Langrock, C., Fejer, M. & Marandi, A. Spectral phase transitions in optical parametric oscillators. Nature communications 12, 1-9 (2021). 40 Zhou, S., Gray, R., Liu, M., Roy, A. & Marandi, A. Towards gas sensing without spectroscopy using mid-infrared optical parametric oscillators in Optical Sensors (2022), SM1E-1. 41 Gordon, I. et al. The HITRAN2020 molecular spectroscopic database. Journal of Quantitative Spectroscopy and Radiative Transfer 277, 107949 (2022). References for Example 3 1 Liu, M. et al. High-Power Mid-IR Few-Cycle Frequency Comb from Quadratic Solitons in an Optical Parametric Oscillator. Laser & Photonics Reviews 16, 2200453. eprint: https : / / onlinelibrary.wiley.com / doi / pdf / 10.1002 / lpor. 202200453. https: / / onlinelibrary.wiley.com / doi / abs / 10.1002 / lpor. 202200453. 2 Jankowski, M. et al. Temporal simultons in optical parametric oscillators. Physical Review Letters 120, 053904 (2018). 3 Wei, J. et al. Temperature dependent Sellmeier equation for the refractive index of GaP. Optical Materials Express 8, 485-490 (2018). 4 Demtroder, W. Laser spectroscopy 1: basic principles (Springer, 2014). 5 Gordon, I. et al. The HITRAN2020 molecular spectroscopic database. Journal of Quantitative Spectroscopy and Radiative Transfer 277, 107949 (2022). 6 Romanini, D., Ventrillard, I., Mejean, G., Morville, J. & Kerstel, E. in Cavity-Enhanced Spectroscopy and Sensing 1-60 (Springer, 2014). 7 Baev, V. M., Latz, T. & Toschek, P. E. Laser intracavity absorption spectroscopy. Applied Physics B 69, 171-202 (1999). 8 Byer, R. L. Optical parametric oscillators. Quantum electronics: A treatise 1 (1975). 9 Jankowski, M. Pulse Formation and Frequency Conversion in Dispersion-Enginered Nonlinear Waveguides and Resonators (Stanford University, 2020). 10 Hamerly, R. et al. Reduced models and design principles for half-harmonic generation in synchronously pumped optical parametric oscillators. Physical Review A 94, 063809 (2016). References for Example 4 [1] S. T. Yang, R. C. Eckardt, and R. L. Byer, "Power and spectral characteristics of continuous-wave parametric oscillators: the doubly to singly resonant transition," J. Opt. Soc. Am. B 10, 1684-1695 (1993)

[0385] Conclusion The above is the description of the preferred embodiments of the present invention. The above description of one or more embodiments of the present invention is presented for purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise forms disclosed. Many modifications and variations are possible in light of the above teachings. It is intended that the scope of the present invention be defined not by this detailed description but by the appended claims.

Claims

1. A sensor comprising: a resonator including a nonlinear material having a nonlinear susceptibility configured to convert pump electromagnetic (EM) waves into signal EM waves and idler EM waves, wherein at least one of the pump EM waves, the signal EM waves, and / or the idler EM waves is fed back through the nonlinear material to form one or more resonant EM waves; an actuator coupled to the resonator or a pump path to the resonator, configured to control at least one of pump power of the pump EM waves, detuning of a frequency mode of the resonator with respect to one or more frequencies of the resonant EM waves, and phase matching of the nonlinear material; an output of the resonator that outputs one or more output EM waves including information about a sample coupled to the resonator; A sensor comprising the above.

2. The sensor according to claim 1, further comprising: a detector coupled to the output of the resonator, configured to detect output power of the one or more output EM waves; a computer coupled to the detector, configured to determine the information about the sample from a change in the output power when the resonant EM waves are coupled to the sample. A sensor further comprising the above.

3. The sensor according to claim 2, wherein the computer is configured to: determine the information by comparing the output power with a calculated output power calculated using a model of the response of the resonator coupled to the sample that interacts with the resonant EM waves, and / or determine the information using a machine learning algorithm trained with training data including an association of the concentration or composition of the sample with the output power as a function of at least one of the pump power, the detuning, and the phase matching, and / or determine the information only by analyzing a change in the output power. A sensor configured as above.

4. The sensor according to claim 1, further comprising an optical parametric oscillator (OPO) including the resonator.

5. The sensor according to claim 4, wherein the OPO is configured to operate during a phase transition between a degenerate operation and a non-degenerate operation.

6. The sensor according to claim 4, wherein the OPO is configured to operate near a laser oscillation threshold of the resonant EM waves, and the EM includes simaltons. A sensor configured such that the sensitivity of the sensor to changes in the sample is improved by near-threshold dynamics such as simaltons or other soliton formation mechanisms.

7. The sensor according to claim 4, wherein the actuator is configured to change the operation of the OPO from below the threshold (of the laser oscillation of the resonant EM wave) to above the threshold.

8. In the sensor according to claim 1, the resonator is configured to operate near the oscillation threshold of the laser oscillation of the resonant EM wave, characterized in that 0.9 ≦ pump power / threshold pump power ≦ 3, or The actuator is configured such that the resonator operates at least during a spectral phase transition between a degenerate operation and a non-degenerate operation and / or the detuning or the phase matching is set such that the resonant EM wave includes simaltons.

9. In the sensor according to claim 1, the actuator can cause the resonant EM wave of the resonator to follow a predictable spectral tuning and reproduce the function of a wavelength-variable laser spectrometer using the output EM wave.

10. In the sensor according to claim 1, the actuator is configured to modulate at least one of the pump power, the detuning, and the phase matching to adjust the dynamic range, sensitivity, or selectivity of the sensor.

11. In the sensor according to claim 1, the information includes at least the concentration or composition differentiation of the sample containing one or more molecules.

12. In the sensor according to claim 1, the information includes the physical or chemical properties of the sample containing a solid, a liquid, or a gas.

13. In the sensor according to claim 1, the information is output in real time along with the change in the sample and with a time resolution limited by the modulation / operation speed of the actuator and the acquisition time of the information.

14. The sensor according to claim 1, wherein the actuator includes an actuator configured to adjust the length of the resonator, a heater and / or a cooler thermally coupled to the resonator to modulate the phase matching and / or the length of the resonator, an electro-optic modulator capable of adjusting the refractive index of the path length in the cavity, an electro-optic mirror or beam splitter for controlling the power of the pump EM wave, and at least one of a control circuit coupled to the pump source to adjust the frequency or power of the pump EM wave output from the pump source.

15. The sensor according to claim 1, wherein the actuator includes a scanner that applies one or more ramp functions for modulating at least one of the pump power, the detuning, and the phase matching.

16. One or more chips or photonic integrated circuits comprising the sensor according to claim 1.

17. The sensor according to claim 1, further comprising means for interacting the resonant EM wave of the resonator with the sample, the means including a sample container positioned to couple the sample to the resonator via an evanescent field, a slot waveguide, an optical fiber, the chamber of the resonator, a fluidic coupling, a free space coupling, or a hollow core fiber.

18. In the sensor according to claim 1, the resonator includes a cavity containing the nonlinear material between mirrors, the cavity including a sample space for positioning the sample within the cavity.

19. The sensor according to claim 1, wherein the resonator includes an optical fiber loop coupled to the nonlinear material.

20. An analyzer comprising the sensor according to claim 1, the analyzer being configured to output information about a sample including the concentration of the sample in the range of pptv to several percent that causes saturation of the linear absorption sensor according to Lambert-Beer's law.

21. The sensor according to claim 1, wherein the information includes the concentration of the sample in the range of pptv to several percent that causes saturation of the linear absorption sensor according to Lambert-Beer's law.

22. A sensing method, coupling a sample to a resonator comprising a nonlinear material having a nonlinear susceptibility configured to convert pump electromagnetic (EM) waves into signal EM waves and idler EM waves, wherein at least one of the pump EM waves, the signal EM waves, and the idler EM waves is fed back through the nonlinear material to form one or more resonant EM waves; controlling at least one of a pump power of the pump EM waves, a detuning of a frequency mode of the resonator with respect to one or more frequencies of the resonant EM waves, and a phase matching of the nonlinear material; detecting an output power of one or more output EM waves output from the resonator; calculating information about the sample from changes in the output power in response to the sample and the modulation; A method comprising.

23. A computer-implemented system, comprising: one or more processors configured to receive an output power of one or more output electromagnetic (EM) waves output from the resonator when the resonator is coupled to a sample, the resonator comprising a nonlinear material having a nonlinear susceptibility configured to convert pump EM waves into signal EM waves and idler EM waves, wherein at least one of the pump EM waves, the signal EM waves, and / or the idler EM waves is fed back through the nonlinear material to form one or more resonant photons; the processor controls at least one of an operation of a pump power of the pump EM waves, a detuning of a frequency mode of the resonator with respect to one or more frequencies of the resonant photons, and a phase matching of the nonlinear material when the sample is coupled to the resonator, and the processor calculates information about the sample from changes in the output power in response to the sample and the operation. A computer-implemented system.

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