Molecular sensor based on optical parametric oscillator

Abstract

A sensor includes a resonator including a non-linear material including a non-linear polarizability, the non-linear material configured to convert a pump electromagnetic (EM) wave into a signal EM wave and an idle EM wave, the signal EM wave including a non-linear polarizability, and the idle EM wave including a non-linear polarizability. Wherein at least one of the pump EM wave, the signal EM wave, and / or the idle EM wave is fed back through the non-linear material to form one or more resonant EM waves. And an actuator coupled to the resonator or to a pumping path of the resonator, controlling at least one of a pumping power of the pumping EM wave, a detuning of a frequency pattern of the resonator relative to one or more frequencies of the resonant EM wave, or a phase matching of the non-linear material. An output of the resonator outputs one or more output EM waves including information about a sample coupled to the resonator.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] Pursuant to 35 U.S.C. Section 119(e), this application claims the benefit of co-pending and co-assigned U.S. Provisional Patent Application No. 63 / 342,894, filed on May 17, 2022 by Robert M. Gray, Selina Zhou, Mingchen Liu, Arkadev Roy, and Alireza Marandi, entitled “Molecular Sensor Based on Optical Parametric Oscillator” (Customer Reference Number CIT-8825-P), which is incorporated herein by reference.

[0003] STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH AND DEVELOPMENT

[0004] This invention was made with Government support under Award No. FA9550-20-1-0040 from the Air Force. The Government has certain rights in this invention. Technical Field

[0005] The present invention relates to sensor systems and methods of making and using sensor systems. Background Art

[0006] Mid-infrared (IR) is the main spectral region of interest for molecular sensing, where most molecules exhibit strong spectral fingerprints. Compared to traditional spectroscopic techniques dominated by laboratory analytical equipment or low-cost semiconductor and electrochemical gas sensors, optical gas sensors offer both fast response and high gas specificity, filling the gap between low-cost sensors with poor performance and high-end laboratory equipment [1]. Numerous applications such as medical breath analysis [2] and environmental sensing [3] have prompted efforts to develop mid-infrared broadband coherent spectrometers for multi-class gas sensing, for example using dual-comb spectroscopy [4-6]. However, achieving low-noise, coherent broadband spectrometers in the mid-infrared generally requires addressing significant challenges regarding sources [7] and spectral techniques [8]. Mid-infrared photodetectors also pose obstacles (sensitivity, response time, etc.) to the widespread application of such systems. Therefore, there is a need for more sensitive and faster sensing systems. The present invention meets this need. Summary of the invention

[0007] Illustrative embodiments of the inventive subject matter include, but are not limited to, the following examples.

[0008] 1. A sensor, comprising:

[0009] a resonator comprising a nonlinear material, the nonlinear material comprising a nonlinear susceptibility, the nonlinear material 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;

[0010] an actuator coupled to the resonator or to a pump path of the resonator for controlling or modulating at least one of a pump power of the pump EM wave, a detuning of a frequency mode of the resonator relative to one or more frequencies of the resonating EM wave, or a phase matching of the nonlinear material; and

[0011] The output end of the resonator is used to output one or more output EM waves including information about the sample coupled to the resonator.

[0012] 2. The sensor according to example 1, further comprising:

[0013] a detector coupled to an output of the resonator for detecting an output power of the one or more output EM waves; and

[0014] a computer coupled to the detector, wherein the computer is configured to determine information about the sample based on changes in the output power when the resonating EM wave is coupled to the sample.

[0015] 3. The sensor according to example 2, wherein the computer is configured (e.g., programmed and / or includes circuitry) to:

[0016] determining said information by comparing said output power to a calculated output power calculated using a model of the response of said resonator coupled to said sample interacting with said resonating EM wave, and / or

[0017] The information is determined using a machine learning algorithm trained using training data, wherein:

[0018] The training data includes the associations between:

[0019] the concentration or composition of the sample, and

[0020] the output power as a function of at least one of the pump power, the detuning or the phase matching, and / or

[0021] The information is determined simply by analyzing the changes in the output power.

[0022] 4. The sensor according to any one of Examples 1-3, further comprising an optical parametric oscillator (OPO) comprising the resonator.

[0023] 5. A sensor according to Example 4, wherein the OPO is configured (e.g., phase matched, dispersion engineered, dimensioned and / or controlled by the actuator) to operate at a phase transition between degenerate operation and non-degenerate operation.

[0024] 6. The sensor of example 4, wherein the OPO is configured (e.g., phase matched, dispersion engineered, dimensioned, and / or controlled by the actuator) to:

[0025] operating near a threshold for lasing of said resonant EM wave, and

[0026] The EM includes a synchronizer,

[0027] The sensitivity of the sensor to changes in the sample is enhanced by near-threshold dynamics such as syncon or other soliton formation mechanisms.

[0028] 7. The sensor according to any of examples 4-6, wherein the actuator is configured to change the operation of the OPO from below a threshold (for lasing of the resonant EM wave) to above the threshold.

[0029] 8. The sensor according to any of examples 1-7, wherein the resonator is configured (e.g., phase matched, dispersion engineered, dimensioned, and / or controlled by the actuator) to operate near an oscillation threshold for lasing of the resonant EM wave, where 0.9 ≤ pump power / threshold pump power ≤ 3, or

[0030] The actuator may be configured to set the detuning or the phase matching such that the resonator operates at least at a spectral phase change between degenerate and non-degenerate operation and / or the resonant EM wave includes a syncron.

[0031] 9. The sensor according to any of examples 1-8, wherein the actuator causes the resonant EM wave in the resonator to follow a predictable spectral tuning, and the output EM wave can be used to reconstruct the functionality of a tunable laser spectrometer.

[0032] 10. The sensor of any of Examples 1-9, wherein the actuator is configured to modulate at least one of the pump power, the detuning, or the phase matching to tune a dynamic range, sensitivity, or selectivity of the sensor.

[0033] 11. The sensor according to any of examples 1-10, wherein the information comprises at least a concentration or composition difference of the sample, the sample comprising one or more molecules.

[0034] 12. The sensor of any of Examples 1-11, wherein the information comprises a physical or chemical property of the sample, the sample comprising a solid, a liquid, or a gas.

[0035] 13. A sensor according to any of Examples 1-12, wherein the information is output in real time with sample variation and has a time resolution limited by the modulation / actuation speed of the actuator and the acquisition time of the information (e.g., 1 Hz-1 MHz).

[0036] 14. The sensor according to any of examples 1-13, wherein the actuator comprises at least one of: an actuator configured to tune the length of the resonator, a heater and / or a cooler thermally coupled to the resonator for modulating the phase matching and / or the length of the resonator, an electro-optic modulator that can tune the refractive index of the path length in a cavity, an electro-optic mirror or a beam splitter for controlling the power of the pump EM wave, or a control circuit coupled to a pump source for tuning the frequency or power of the pump EM wave output from the pump source.

[0037] 15. The sensor of any of Examples 1-14, wherein the actuator comprises a scanner that applies one or more ramp functions that modulate at least one of the pump power, the detuning, or the phase matching.

[0038] 16. One or more chips or photonic integrated circuits comprising the sensor of any of Examples 1-15.

[0039] 17. The sensor of any of Examples 1-16, further comprising means for causing the resonant EM wave of the resonator to interact with the sample, wherein the means comprises a sample container positioned to couple the sample to the resonator via an evanescent field, a slot waveguide, an optical fiber, a chamber in the resonator, fluid coupling, free space coupling, or a hollow core fiber.

[0040] 18. The sensor according to any of Examples 1-17, wherein:

[0041] The resonator includes a cavity including a nonlinear material between mirrors, and the cavity includes a sample space for positioning a sample within the cavity.

[0042] 19. The sensor of any of Examples 1-18, wherein the resonator comprises a fiber optic loop coupled to the nonlinear material.

[0043] 20. An analyzer comprising the sensor of any of Examples 1-19, the sensor being configured to output information about the sample, the sample comprising breath, atmospheric concentrations of pollutants or greenhouse gases, or process gases monitored in an industrial environment.

[0044] 21. The sensor of any of examples 1-20, wherein the information comprises a sample concentration within a range that causes saturation of the linear absorption sensor according to Beer Lambert Law.

[0045] 22. A sensing method, comprising:

[0046] coupling a sample to a resonator, the resonator comprising a nonlinear material, the nonlinear material comprising a nonlinear susceptibility, the nonlinear material 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, or the idler EM wave is fed back through the nonlinear material to form one or more resonant EM waves;

[0047] controlling at least one of a pump power of the pump EM wave, a detuning of a frequency mode of the resonator relative to one or more frequencies of the resonating EM wave, or a phase matching of the nonlinear material;

[0048] detecting output power of one or more output EM waves output by the resonator; and

[0049] Information about the samples is calculated from changes in the output power in response to the samples and the modulation.

[0050] 23. A computer-implemented system comprising:

[0051] one or more processors;

[0052] receiving output power of one or more output electromagnetic (EM) waves output from a resonator when the resonator is coupled to a sample, the resonator comprising a nonlinear material, the nonlinear material comprising a nonlinear susceptibility, the nonlinear material 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, or the idler EM wave is fed back through the nonlinear material to form one or more resonant photons;

[0053] controlling modulation / actuation of at least one of a pump power of the pump EM wave, a detuning of a frequency mode of the resonator relative to one or more frequencies of the resonating photons, or a phase matching of the nonlinear material when the sample is coupled to the resonator; and

[0054] Information about the sample is calculated from a change in the output power in response to the sample and the modulation / actuation. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Referring now to the drawings, wherein like reference numerals designate corresponding parts throughout:

[0056] Figure 1: (a) Schematic diagram of the sensor system. (b) Schematic diagram of the sensor system including the OPO. (c) Example output signal from the photodetector as a function of the cavity length of the sensor including the OPO. The peaks correspond to the various resonance conditions in the dual-resonance OPO. (d) OPO output power spectral density at various cavity length detuning values. (e) Output signal (at 4 μm) peak evolution as a function of CO2 concentration.

[0057] Figure 2 : (a) The difference in simulated OPO output power between sensing 4120 and 412ppm CO2. Each "pixel" corresponds to the difference in output power value at different input power (y-axis) and cavity length (x-axis). (b) Simulated OPO output sensing different concentrations of CO2 and N2O at 1.45W input power. (c): Measured 2μm loss signal reflecting the 4um output signal.

[0058] Figure 3 : Overcoming the sensitivity-dynamic range tradeoff imposed by Beer-Lambert’s law using quadratic cavity solitons. a, Schematic illustration of linear absorption sensing governed by Beer-Lambert’s law for light interacting with the sample over a path length, L. b, Linear approaches (light blue region) face fundamental limitations in dynamic range, making it difficult to achieve high sensitivity at large sample concentrations. In contrast, active cavity sensing with quadratic cavity solitons (orange) can achieve high sensitivity at large sample concentrations. c, Schematic illustration of quadratic cavity soliton sensing in the synchrotron state of a synchronously pumped optical parametric oscillator during degeneration. Bright solitons in the signal interact with the sample on each round trip, and the resulting competing nonlinear dynamics generate the signal response measured at the output. d, Specifically, it is shown that stable synchrotron operation requires synchrotron acceleration, which results in a time advance, ΔT, due to gain saturation in the crystal, to balance the round-trip time delay, ΔT RT , and due to the parameter gain to balance the sample loss α and output coupling. T cav , cavity round trip time; T rep , pump repetition period; ΔT, synchronous subgroup advance; ΔT RT , round trip delay; ω, angular frequency; α, absorption coefficient; OC, output coupling; P in , input power; P out , output power; L, path length; Reduced Planck constant.

[0059] Figure 3e -i: Experimental details. e. The experimental setup consists of a 4μm OPO cavity placed inside a cleanroom box, as well as all necessary measurement equipment. f, Calibration curve for mapping the voltage on the pump photodetector to optical power, with the indicated goodness of fit. g, Corresponding calibration curve for the signal. h, Example of raw traces measured by a 4μm photodetector when the round-trip delay in the cavity is scanned at 406ppm (green), 384ppm (orange) and 297ppm (red). The superimposed traces with different shading correspond to the five traces that are averaged to generate the final value. The inset shows a magnified image of the synchondrome peak. i, Experimental data corresponding to three different multiples above the threshold, showing how fine-tuning the pump power can achieve high sensitivity at the desired concentration value. The example trace in h is taken from the data set corresponding to N=2.092. M1, input coupler; M2, output coupler; M3 and M4, concave gold mirrors; OP-GaP, orientation-patterned gallium phosphide crystal; PZT, piezoelectric actuator; MM, magnetic mirror; FTIR, Fourier transform infrared spectrometer; 92:8, membrane beam splitter with 92:8 splitting ratio; PD, photodetector. The formation of the cavity was achieved by supplying nitrogen gas N2 to the cavity. By adjusting the nitrogen flow rate entering the cavity, the concentration of CO2 inside the cavity can be changed. Due to the large size of the purge box and the numerous gas outlets, the internal pressure should be kept approximately constant. The CO2 concentration was monitored using a commercial CO2 sensor (CO2 meter.com K-30), which recorded the real-time measurements on a computer, enabling calibration of the sensing measurements. The measurements were limited by the specifications of the reference sensor and the measurement device; in particular, the reference sensor had a response time spread of 20 s and an accuracy of + / -30 ppm.

[0060] Figure 4 : Secondary cavity soliton enhancement mechanism. a, In near-threshold sensing, the addition of sample leads to an increase in the threshold, resulting in a decrease in the signal power at the sensing point. b, When approaching the threshold, the corresponding signal enhancement grows asymptotically. c, The measured input-output power relationship of the syncron (orange) and conventional (pink) states shows the extremely high slope efficiency and high threshold of the syncron, indicating its potential for near-threshold sensing with high SNR (signal-to-noise ratio). The solid line captures the trend through a linear fit of the experimental data, while the orange dashed line shows the corresponding syncron simulation. dg. Other quality factors of the OPO.

[0061] Figure 5: Soliton dynamics responsible for sensing. a, Experimental power spectrum spectral density shows that despite the relatively narrow absorption characteristics of CO2, the power of the entire syncon spectrum decreases with the addition of sample. b. Like other common multimode lasers, the conventional scheme is in sharp contrast with syncons, because the power in the non-absorbing mode increases with the addition of sample, largely compensating for the losses in the absorption mode. This highlights the importance of the syncon formation dynamics for enhancing near-threshold sensing (despite the wide syncon bandwidth). c, Schematic depiction of the temporal dynamics of cavity soliton formation that implements the sensing enhancement mechanism. The additional losses in the round trip limit the ability of the syncon loss to pump and accelerate, resulting in reduced gain for all modes in the steady state. D. Simulated steady-state pulse position as a function of gas concentration (left). From c, it can be seen that the comparison with the theoretical gain window (right) shows that the syncons move further towards the edge of the gain window with increasing sample concentration.

[0062] Figure 6 : Sensing behavior of secondary cavity solitons. a, Measured output power as a function of CO2 concentration for different multiples above threshold, N, demonstrating the tunability of the high sensitivity region in the approach. The high slope efficiency of the syncon near threshold leads to high sensitivities up to 4.1 mW / ppm, highlighted using the solid trend line. b, Simulations of the response of the syncon to the addition of CO2 at different multiples above threshold show good qualitative agreement with the experimental data. The sensitivity remains constant even for different multiples above threshold for pumping. c, Equivalent path length enhancement calculated for neighboring points in the experiment, showing measured enhancements up to 2491. The solid line shows the enhancement corresponding to the linear fit in b. For a given N, the enhancement grows asymptotically as the threshold is approached. d, Measured sensitivity as a function of CO2 concentration, directly compared with linear sensing (light blue), demonstrating that at high sample concentrations the sensitivity has the potential to be orders of magnitude higher than the linear approach.

[0063] Figure 7: Numerical methods and results. a, Calculated κ, the imaginary part of the complex refractive index, for the CO2 band of interest at atmospheric CO2 levels. b, Corresponding results for n′-1, the real part of the complex refractive index. c: Simulated synchrotron slope efficiency for various values ​​of output coupling; the closest experimental one corresponds to 0.25, shown in orange. By reducing the cavity finesse, the synchrotron threshold and slope efficiency can be increased, which benefits the sensing performance. d, Simulated sensing behavior for three different values ​​of output coupling shown in c, demonstrating higher sensitivity with increasing slope efficiency and threshold. e, Steady-state signal pulse position as a function of pump power, shown to trend toward the center of the gain window as pump power increases. f, Relative steady-state signal pulse position along the fast time axis with increasing CO2 concentration for three different multiples above threshold. Note that the trend observed here is opposite to that in e, illustrating the way gain and loss act as opposing forces for near-threshold synchrotron operation. The relative concentrations of CO2, O2, and H2O vary proportionally, while the relative concentration of N2 increases to compensate.

[0064] Figure 8 : Enhanced calculations for direct comparison with linear absorption sensing. a, Interpolated synchondromic PSD (dashed blue line) plotted on top of the measured PSD (power spectral density) (orange). b: PSD of the calculated spectrum corresponding to the signal with the interpolated spectrum from a to 1.2 m CO2 for three different concentrations. The resulting mode intensity is used to calculate α eff The weight of c, with the baseline linear sensitivity S base and the best linear sensitivity S achieved by path length multiplexing opt Compared to the experimental sensitivity measured for three different folds above the threshold. d, by directly comparing the measured sensitivity and S base The calculated sensitivity enhancement is shown in c. Figure S3b shows the resulting spectra for three different example concentrations. Using the mode intensities from these calculated spectra as weights, together with the provided absorption coefficients, we solve for Δα according to (S12) eff , and the resulting value is substituted into equation (S9) together with the measured values ​​of the intensities I(α) and I(α+Δα) to calculate the equivalent path length enhancement.

[0065] Fig. 9 : Enhanced sensing in a single-mode laser. a, Comparison between the enhancement calculated for the full model including spontaneous emission (orange) and the simplified model ignoring spontaneous emission (blue), showing the strong benefit of near-threshold operation. The y-axis is logarithmic. b, For a given minimum detectable output power P out，det, there are two ways to achieve sensing closer to threshold compared to some reference (line 1). The first is to increase the slope efficiency (line 2), the second is to increase the threshold (line 3). c. Increasing the spontaneous decay rate A (or, equivalently, decreasing B, the stimulated emission rate) can increase the threshold of a laser system without changing the slope efficiency. d. Increasing the output coupling loss α R will increase the threshold and can also benefit slope efficiency. f, adding other losses will increase the threshold but will reduce the slope in the same proportion, thus preventing sensing closer to the detector limit of the threshold.

[0066] Fig.10 : Enhanced sensing of continuous-wave OPOs. a, Comparison between the theoretical enhancement of a continuous-wave OPO in a laser system and that of SMICAS (single-mode intracavity absorption sensing), showing a faster increase for the continuous-wave OPO as N=1 is approached. b, Output intensity versus input intensity for different values ​​of output coupling, showing how both threshold and slope efficiency can be improved by increasing output coupling, providing better signal-to-noise ratio for detector-limited near-threshold sensing in the low-fineness regime. c, Changing the round-trip loss from elements other than output coupling can increase the threshold without reducing the slope efficiency. d, Changing the parameter γ can simultaneously improve both threshold and slope efficiency, benefiting the system in a similar way to output coupling.

[0067] Fig.11 : An OPO sensor built with a dual-resonance OPO (DRO). (a) Example schematic of DRO sensing on a bulk platform; (b) Signal and idler spectra as a function of cavity length tuning, illustrating the different spectral coverage of different OPO peaks; (c) Output signal and idler power measured by a single photodetector as a function of cavity length tuning. Note that each point on the OPO peak in c is the integral of b with respect to wavelength.

[0068] Fig.12 OPO sensors built using a single resonant OPO (SRO). (a) Schematic diagram of an example of SRO sensing on a host platform; (b) Wavelength tuning of the SRO via phase matching tuning (such as temperature tuning of a nonlinear crystal).

[0069] Fig.13 .A flow chart showing a method of manufacturing a sensor system.

[0070] Fig.14 .A flow chart showing the sensing method.

[0071] Fig.15 .A hardware environment for performing one or more computer-implemented methods described herein.

[0072] Fig.16 .A network environment for performing one or more computer-implemented methods described herein. DETAILED DESCRIPTION

[0073] In the following description of the preferred embodiment, reference is made to the accompanying drawings which form a part thereof, in which specific embodiments in which the invention may be implemented are shown by way of illustration. It should be understood that other embodiments may be employed and structural changes may be made without departing from the scope of the invention.

[0074] Technical Description

[0075] Figure 1a A sensor system 100 is shown in accordance with one or more embodiments of the invention. The sensor includes a resonator 102 including a nonlinear material and an actuator 104 coupled to the resonator. When the resonator is appropriately modulated / actuated by the actuator in the presence of a sample coupled to the resonator, one or more output electromagnetic waves from the resonator include information about the sample.

[0076] Example resonators include, but are not limited to, resonators configured for nonlinear 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), with an optical parametric oscillator being one example implementation. The nonlinear material includes a nonlinear 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 nonlinear material to form one or more resonant EM waves. Example materials having a nonlinear susceptibility (e.g., second-order nonlinearity) 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 silicon dioxide. Silicon, silicon nitride, and silicon dioxide, for example, may be used to implement third-order nonlinearity. The nonlinear material may have appropriate phase matching (e.g., periodic poling), dispersion engineering, or length L of the resonator, suitable for (e.g., second order) parametric amplification / conversion processes, converting pump waves into signal waves and idler waves, and / or achieving non-degenerate operation, degenerate operation, near-threshold operation, or other operating modes and states according to the present invention. In one or more examples, a pump wave of a higher frequency (e.g., 2ω or second harmonic)) is converted into a lower frequency idler wave and a lower frequency signal wave (e.g., at frequency ω). The pump EM wave may be output from various electromagnetic radiation sources such as lasers. In some examples, the pump, idler, and signal may include electromagnetic radiation pulses, e.g., femtosecond or picosecond pulses), where the resonator is appropriately dispersion engineered to control walk-off / pulse overlap. In various examples, each optical pulse comprises an electromagnetic radiation pulse having, for example, a center wavelength in the range of 200 nanometers to 10 micrometers.

[0077] An actuator is coupled to the resonator or to a pump path of the resonator for modulating / controlling at least one of a pump power of a pump EM wave, a detuning of a frequency mode of the resonator relative to one or more frequencies of the resonating EM wave, or a phase matching of a nonlinear material. Example actuators include, but are not limited to, an actuator (e.g., a piezoelectric actuator optionally coupled to a translation stage) for tuning the length of the resonator (e.g., directly or via a mirror), a heater or cooler thermally coupled to the resonator for modulating / controlling phase matching and / or the length of the resonator, an electro-optic modulator capable of tuning 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, an amplitude modulator or polarization beam splitter for controlling the power of the pump EM wave, or a control circuit coupled to a pump source for tuning the frequency or power of a pump EM wave output from the pump source.

[0078] exist Figure 1aIn the illustrated embodiment, a detector 112 is coupled to the output of the resonator 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 116 based on changes in the output power when the resonating EM wave is coupled to the sample.

[0079] Figure 1a Also shown is the coupling between the sample and the resonator, which can be achieved in a variety of ways. For example, the resonator can include or be coupled to a cavity, the cavity being used to allow the EM wave and the sample to interact. In one example, the cavity is configured for sensing the sample by evanescent field, waveguide, optical fiber, or fluid coupling. In another example, the cavity includes a cell (housing the sample, such as a gas cell) that forms part of the cavity.

[0080] Other illustrative embodiments and variations of the present invention include, but are not limited to, the following embodiments.

[0081] First Example: Sensor Including an Optical Parametric Oscillator

[0082] Figure 1b A sensor system is shown in which the resonator is an optical parametric oscillator (OPO). More specifically, the OPO includes a nonlinear material in a cavity defined by a mirror M1 and a mirror M2. The sample is coupled to the OPO by placing both the OPO and the sample in a second cavity defined by mirrors OC (output coupler) and IC (input coupler). In this example, where the sample includes carbon dioxide gas, the detector includes a near-infrared light detector (Thorlabs PDAVJ5), and the OPO includes an orientation-patterned gallium phosphide (OP-GaP) nonlinear material in a 4-micron length resonator defined by cavity mirrors M1 and M2, the OPO outputs femtosecond pulses with a wavelength centered at 4 μm

[11] .

[0083] For the dates taken in this example, the samples were contained in a 10 cm path length glass cell with silicon and calcium fluoride windows. The gas chamber in the second cavity was contained in a box to flush out atmospheric gases with nitrogen.

[0084] Figure 1c and Figure 1d The output power and output spectrum as a function of the second cavity detuning are shown respectively. The data show that the output power and spectrum of the OPO depend on the cavity length with extremely high sensitivity [10,12]. Therefore, by using a photodetector to monitor the output power as a function of the cavity round-trip detuning, the spectral characteristic information of the gas molecules in the gas chamber can be extracted with high sensitivity. More specifically, as Figure 1dAs shown, each point on the "detuned peak" is the integration of the OPO power spectrum over all wavelength output spectra at different cavity round-trip lengths. When the target molecule absorption line overlaps with the OPO spectrum, the spectral information is reflected in the shape of these peaks due to absorption and dispersion. These features can be very sensitive to the magnitude of absorption and dispersion and their spectral distribution, which can be used as the basis for molecular sensing.

[0085] Figure 1(e) shows the output signal at different CO2 concentrations, indicating that the amplitude variation of the detuned peak of the output signal as a function of gas concentration can be used to measure gas concentration. While conventional spectral analysis relies on direct measurement of absorption peaks at specific wavelengths, the OPO sensor output provides multiple sources of information between and within multiple detuned peaks containing different spectral information without the need to analyze frequency variations of the spectrum. For example, Figure 1e It shows that the highest output power of the rightmost peak (corresponding to the cavity soliton) decreases with the change of CO2 concentration in the cavity, while the changes of other peaks are opposite. When multiple gases are present, cross-referencing other indicators on the peaks can improve sensitivity and specificity.

[0086] In addition, if Figure 2 As shown, by varying the input pump power (centered around a 2-micron wavelength in this example) and the cavity length, another dimension can be added to the output signal, thereby increasing sensitivity. Figure 2 a was generated by simulating the output signal of the OPO at two different CO2 concentrations (4120ppm and 412ppm) and then taking the difference between them. Each "pixel" corresponds to the power difference in the OPO sensor signal at each pump power (y-axis) and detuning value (x-axis) for these two different concentrations.

[0087] Simulated sensing was performed for 392 and 412 ppm CO and 412 ppm N2O to demonstrate multi-species sensing. Figure 2 b shows the OPO output peaks for various gas concentrations minus the 0 ppm baseline, demonstrating the ability to distinguish between close concentration values ​​and to differentiate between different gas species. In addition, due to the nature of semi-harmonic generation, the distribution of the output signal reflects the loss of the input signal, which enables real-time detection of mid-infrared absorption using a near-infrared detector ( Figure 2 c).

[0088] While this example demonstrates broadband mid-IR gas sensing from ~3.5 μm to ~4.8 μm, this range can be extended by modifying the dispersion and losses within the cavity. Using parametric nanophotonics

[13] , our sensing scheme enables compact on-chip multi-species gas sensors without the need for mid-IR lasers and detectors. The results presented here demonstrate that OPO sensors can enable multi-species, broadband, real-time gas sensing for applications such as, but not limited to, exhaled gas analysis, environmental sensing, and process gas sensing (in industrial settings).

[0089] Second Example: Modulation of OPO Operating State

[0090] a. Sensor architecture and sensing configuration

[0091] The formation dynamics of secondary cavity solitons in OPOs, i.e., time synchronizers, can also be used for molecular sensing 33 The cavity soliton-based sensing mechanism relies on the extremely high sensitivity of the OPO operation to the gain and loss in the soliton state.

[0092] Figure 3 c shows an example sensor configured to sense a gas sample of interest inserted into a dual-resonant synchronously pumped OPO around a degenerate. The OPO includes an optical resonator with a nonlinear material that has a quadratic nonlinearity that provides parametric gain. At degenerate, the nonlinear interaction is phase matched so that the generated signal and idler are at a semi-harmonic of the pump. 35 When the pump repetition period T rep Synchronous pumping occurs when matching the effective signal round trip time in the cavity, while dual-resonance operation means that the OPO allows the signal and idler to resonate in the cavity while the pump is coupled out of the cavity. In this way, the degenerate signal resonating in the cavity is first absorbed by the sample during each round trip and then gains from the pump through a parametric process.

[0093] The syncron is a bright-dark soliton pair of a signal with frequency ω and a pump with frequency 2ω. 38,39 When the round-trip delay is increased relative to conventional operation, cavity syncrons appear in synchronously pumped degenerate OPOs in the high-gain, low-finesse regime, which means that the cold cavity time T cav Relative to the pump repetition period T rep Increase 33 . Figure 3 d shows that stable cavity synchronizer formation requires a dual balance of energy and timing, where gain must equal loss and the synchronizer group is advanced by ΔT, which is (2) Nonlinear interactions in the crystal occur during pumping and must compensate for the round-trip delay ΔT RT, to reestablish synchronization with the pump pulse. The dependence of the timing advance on the pump loss brings these two conditions together, as the gain must be large enough to satisfy the timing condition, resulting in a strong response to gain and loss changes when the syncron is close to the threshold.

[0094] Figure 2 We show that cavity soliton-based sensing mechanisms exploit the interplay between energy and timing in synchronized substates to achieve high sensitivity to samples of interest, in significant contrast to other active cavity schemes. Figure 4 This significantly enhanced sensitivity can be explained by the uniquely large threshold and high slope efficiency of the syncron, as shown in Figure a. At a given pump power, the small amount of loss caused by the sample leads to an increase in the threshold and a corresponding decrease in the output power ΔP. The absolute change in power is proportional to the local slope efficiency at the sensing point, which means that the higher the slope efficiency, the higher the sensitivity.

[0095] In this example, the corresponding path length enhancement formula is:

[0096]

[0097] Among them, 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 some small change in absorption due to the addition of the sample. A model using single-mode laser theory or continuous wave OPO theory shows that when the multiple N above the threshold approaches 1, the path length enhancement will asymptotically approach infinity, as shown schematically Figure 4 b 17 shown.

[0098] This large enhancement near threshold is essentially accompanied by a decrease in the signal-to-noise ratio (SNR). However, the combination of the large slope efficiency, high threshold, and low spontaneous emission rate of the OPO in the synchrotron state makes the SNR decrease extremely slowly. As an example, Figure 4 c shows that the measured synchonite threshold is approximately 2.5 times greater than that of the conventional regime, and the slope efficiency is 3.5 times greater. The net result is that for detector-limited measurements, it is possible to run nearly 9 times closer to threshold at the same output power. This ability to achieve a measurable signal very close to the synchonite threshold can lead to significantly large enhancements, making synchonites an excellent candidate for intracavity sensing.

[0099] b. Features

[0100] a. Procedure for obtaining measurements

[0101] The following results are obtained using a degenerate, synchronously pumped free-space OPO in bow-tie form. 34 . The pump is based on the output of a periodically poled lithium niobate OPO, which provides a pulse train at 2.09μm with a bandwidth of 155nm, a repetition rate of 250MHz and an average power of up to 1.4W. The pulses are coupled in via a dielectric coated mirror with high transmission for the pump and high reflectivity for the signal. The input coupler is placed on a platform with a piezoelectric actuator for tuning the cavity length. The nonlinearity is formed by a 0.5mm, anti-reflection coated, plane-parallel, orientation-patterned gallium phosphide crystal with a poling period of 92.7μm, which allows type-0 phase matching between the pump at 2.09μm and the signal at 4.18μm at room temperature. Two concave gold mirrors with a radius of curvature of 25mm are placed on either side of the crystal for focusing and collimation. The output coupler is a dielectric coated mirror that allows 25% output coupling of the signal near 4.18μm. . A piezoelectric actuator (PZT) on the cavity mirror M1 allows tuning of the cavity length to enter the synchrotron state. The cavity can be locked using a shake and lock protocol.

[0102] The output was passed through a long pass filter and sent to an MCT detector for monitoring. Spectral measurements were performed using a commercial Fourier transform infrared spectrometer. The OPO and all measurement equipment were placed in a nitrogen purged box. To perform sensing measurements, the CO2 concentration was varied by adding N2 to the equipment. The CO2 concentration was referenced to a commercially available CO2 sensor used to calibrate the measurements. At each concentration, five data points were taken and averaged to produce the final result.

[0103] The procedure is as follows. First, a small portion of the 2 μm power is siphoned to the detector ( Figure 3 d). Then use an optical power meter to map the 2 μm power to the detector value to obtain a calibration curve ( Figure 3f ). A similar procedure was used to create calibration curves for the signals in the conventional and synchronized substates in the case of the 4 μm OPO cavity locked and purified, mapping the measured voltage on the photodetector to optical power. Figure 3g An example calibration curve for the synchrotron can be seen in . The R 2 The values ​​are shown in each graph and indicate the goodness of the fit.

[0104] In the sensing measurements, the PZT is continuously scanned by a ramp function provided by a function generator. This enables nearly simultaneous monitoring of all OPO peaks and also allows measurement of the output closer to threshold, where lock-in is typically less stable. The output is measured on a 4 μm photodetector and then mapped to optical power using a calibration curve. Five measurements are taken at each CO2 concentration using a data acquisition unit, triggered on a ramp function used to scan the cavity length. Examples of raw data from the system measurements can be found at Figure 3h , where examples from three different CO2 concentrations are shown, 406ppm (green), 384ppm (orange), and 297ppm (red). Five different traces are superimposed in different hues; they are largely nearly identical, but there are some fluctuations due to the instability of our pump OPO locking and the dynamic nature of our measurements. The inset shows a zoomed-in picture of the syncon peak. By visual comparison with the other peaks, it is clear that the syncon exhibits a significantly more pronounced response to the addition of gas. As mentioned above, we believe that the behavior of the other peaks also contains useful information about the gas being monitored, and therefore will design a sensor in future work to utilize data from all OPO peaks. As discussed in the main text Figure 4 a and Figure 3i As shown, the final output power value at any single concentration value is obtained by averaging the five measured synchronous sub-peaks, finding the maximum voltage of the average measurement, and then mapping it back to optical power through the calibration curve. Figure 3i In Figure 1, we show the output power as a function of concentration at three different multiples above threshold, N = 2.092 (green triangles), N = 1.959 (orange circles), and N = 1.837 (red squares). These three values ​​are significantly closer than those shown above, highlighting the ability to fine-tune the pump power to achieve high sensitivity at any concentration of interest.

[0105] According to references 33 Numerical simulations were performed using the method described in . The nonlinear propagation in the crystal was calculated using the Fourier split-step method to solve the coupled wave equations describing the pump and signal evolution. The round-trip propagation is given by a linear filter, which includes dispersion and frequency-dependent losses. For simulating the sensing behavior, it is important to have an appropriate model for the gas absorption and diffusion during the round-trip process. For this purpose, a Lorentz oscillator model was used with parameters taken from HITRAN 44 .

[0106] b. Results

[0107] Figure 5 a and 5b show the synchronous sub-states at three different CO2 concentrations in the chamber ( Figure 5 a) and traditional state ( Figure 5 b) Experimental spectral data. Figure 5 b shows that cavity soliton-enhanced sensing cannot be achieved in general multimode lasers or conventional OPOs, where other modes that do not experience absorption will compensate for the loss in the absorbing mode, thereby reducing the sample 17 The addition of leads to a limited change in the laser threshold or output power. However, unlike the conventional state, the synchronous substate ( Figure 5 The power in all spectral modes of a) is reduced almost uniformly, demonstrating the possibility of threshold sensing. Moreover, in significant contrast to single-mode lasers, soliton enhancement techniques provide broadband operation, thus relaxing the requirement for fine-tuning the laser line to a single absorption line and providing SNR advantages as well as sensing capabilities in wavelength ranges not normally accessible to lasers, especially in the infrared.

[0108] Figure 5 c schematically shows the formation of soliton pulses with two different absorption values ​​in the resonator after multiple round trips. RT , the newly formed pulse slowly escapes from the gain window determined by the pump pulse and the walk-off length until it grows large enough to experience a strong enough nonlinear acceleration to compensate for the delay. Figure 5 As shown in the measured spectrum in a, despite the relatively narrow absorption spectrum, the small amount of added losses in the signal’s round trip reduces the amount of acceleration and, accordingly, the amount of gain of all spectral modes of the synchron supermode in the steady state (because it interacts with the pump in the nonlinear crystal), resulting in a spectrally uniform reduction in power.

[0109] Figure 5 The simulation in d confirms this dynamic behavior. Figure 5 d shows the steady-state signal pulse position (left) versus the available gain (right) as a function of CO2 concentration at three different multiples above threshold, N = 1.2 (green triangles), N = 1.5 (orange circles), and N = 1.8 (red squares). The gain is calculated as the convolution between the pump pulse shape and the walk-off, with the gain window centered at 0 fs. The approximate gain window edge can be calculated by halving the sum of the pump pulse length and the walk-off length. When sample is added to the cavity, the steady-state position of the signal pulse moves towards the gain window edge due to the reduction in synchron acceleration until it no longer experiences enough gain to resonate. This significant (and drastic) reduction in gain when sample is added to the cavity enables high sensitivity of synchrons near threshold.

[0110] Figure 6a plots the measured synchron output power as the CO2 concentration in the chamber varies. The green triangles, orange circles, and red squares correspond to different multiples of pumping above the threshold (here, N = 1.25, 1.64, and 1.84, respectively). Similar to the input-output power dependence described above, the dependence of the output power on CO2 varies most dramatically near the threshold. The solid line shows a linear fit to the near-threshold data. The slope of the solid line is used to find the sensitivity, and the highest fitted sensitivity calculated is 4.1 mW / ppm. In addition, the data shows that by tuning the pump power, the region of high sensitivity can be changed, enabling the system to have a large dynamic range.

[0111] These observations are consistent with Figure 6 The simulated sensing results in b are consistent, Figure 6 b illustrates the large sensitivity near threshold, and the tuning of the sensitive region by a multiple change above threshold. The calculated sensitivity is shown to be consistent under different pumping conditions. The simulated sensitivity is slightly lower than the experimentally observed result. This difference is mainly due to imperfections in the modeling of the gas response.

[0112] Figure 6 c illustrates the equivalent path length enhancement of the experimental data. eff The enhancement can be calculated by defining it as the effective absorption coefficient produced by a pump with the same bandwidth as the synchrotron (the synchrotron experiences absorption of 1.2 mCO2 at the reference concentration). Based on this definition, The values ​​of neighboring points in the experimental measurements are calculated. The maximum enhancement of 2491 is observed near the critical value in the case of N = 1.84, although similar enhancements are observed near the threshold for the other cases. The solid line shows the difference between the theoretical and the experimental results. Figure 6 The enhancement corresponds to the linear fit of a. The tight fit near threshold illustrates the almost asymptotic trend of the enhancement, with the deviation at lower sample concentrations coming from the observed saturation of the response of syncronons well above threshold.

[0113] Figure 6 d shows the sensitivity in mW / ppm calculated for neighboring points in the experimental measurements. Note that by varying by a factor above 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 approach (bright blue region) is also plotted. A linear cavity of length 1.2 m is modeled, pumped by a pulsed source with an average power of 500 mW and the same bandwidth as our measured syncron, and a path length multiplexing approach is assumed, where the path length enhancement is varied to achieve maximum sensitivity at each point, up to 10 compared to our cavity of finesse of 2. 6The enhancement is 200 times that of the original quartz crystal, and corresponds to a finesse of over 1.5 million. We believe this is a sufficiently large enhancement limit for linear approaches and represents a practically achievable finesse value. As in theory, inverse scaling is observed in this path length multiplexing approach, highlighting the limitations of the dynamic range of linear techniques. In contrast, the syncon sensing mechanism exhibits nearly constant and orders of magnitude higher sensitivity in highly concentrated samples, illustrating how the syncon sensing mechanism breaks the trade-off between sensitivity and dynamic range faced by linear approaches. Therefore, many applications that exploit the syncon sensing technique can benefit from it while avoiding the typical requirement for a high finesse cavity.

[0114] The remarkable sensing performance of the synchonons can be further improved in several ways. In some configurations, as the cavity length is further increased, the OPO exhibits multiple synchonon resonances. These further detuned synchonons can exhibit higher slope efficiencies, leading to potentially greater sensitivity and sensitivity enhancement. 33 In addition, synchonons benefit from operating in a high-gain, low-finesse regime. OPOs implemented using lithium niobate thin-film nanophotonics, where gains up to 100 dB / cm have been demonstrated, could further improve the sensitivity and scalability of molecular sensors. 40，41 Furthermore, other nonlinear behaviors in OPOs, such as spectral phase transitions, can be used as additional means to achieve high sensitivity in OPO intracavity sensing42. OPOs operating in synchronized substates can also be configured for multi-class molecular sensing.

[0115] Third example: numerical values ​​and calculation methods

[0116] In this section, methods for calculating the numerical results presented in the second example, or example methods for performing calculations to determine information about a sample based on the output power, are described. The simulations are mainly based on Ref. 2 The method proposed in .

[0117] 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 a one-way optical parametric amplification (OPA) governed by the coupled wave equations.

[0118]

[0119] where the time coordinate t is set to co-move with the group velocity of the signal wave, and if high-order dispersion is not considered, the pump envelope phase is shifted by π / 2 to ensure a true solution. The subscripts ω and 2ω refer to the signal and pump, respectively. The field envelope is given by E jGiven, where j∈{ω, 2ω}, and normalized so that the instantaneous power is given by |E j | 2 The strength of the nonlinear interaction is given by the nonlinear coupling coefficient Determine, where η0 is the impedance of free space, d eff is the effective nonlinearity, w0 is the Gaussian beam waist inside the crystal (assuming the crystal length is small compared to the confocal parameter), and n j is the refractive index, c is the speed of light. Absorption coefficient α j accounts for the material losses in the crystal. Δβ′ gives the group velocity mismatch between pump and signal. Finally, the dispersion operator Describes the material dispersion experienced by the pump and signal in the crystal.

[0120] The nonlinear step in each round trip is simulated using the split-step Fourier method. For this purpose, the spatial coordinate z corresponding to the propagation distance into the 0.5 mm crystal is divided into 50 walk-off steps. At a given step, the output of the nonlinear interaction is numerically solved using the fourth-order Runge–Kutta method. Then, a linear filter that takes into account the dispersion and losses in the step is applied in the frequency domain. The simulation is performed using reference 3 The fourth-order dispersion is calculated using the Sellmeier equation for GaP.

[0121] After the nonlinear step is completed, we apply an additional linear filter in the frequency domain to account for the round trip propagation of the beam. Specifically, the input to the coupled wave equation for the round trip n+1 is Compared with the output from the previous OPA Related, where L is the length of the crystal, the equation is:

[0122]

[0123] here, and denote the 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 from the mirrors, output coupling, AR coating on the crystal surface, and gas in the cavity. Similarly, at Φ(Ω) = ΔT RT (πc / λ 2ω +Ω)+ΔΦ(Ω), where ΔT RT is the cavity detuning, c is the speed of light, λ 2ω is the pump wavelength. ΔΦ(Ω) contains dispersion terms from various cavity components as well as from the gas.

[0124] The gas model provides an accurate simulation of the sensing behavior. In our simulations, we use the Lorentz oscillator model to calculate the complex refractive index experienced by the signal during the round trip. 4 . Specifically, the exponent n(ω) is given by:

[0125]

[0126] where the indices i and j refer to the upstate and downstate of the transition of interest, respectively, and f ij is the oscillator strength, N j is the density of molecules in the j,q states, q is the electron charge, ε0 is the vacuum dielectric constant, m e is the mass of the electron, ω ij is the center frequency of the transition, γ ij is the line width of the transition. To accurately calculate the response of our experiments, we considered the most abundant atmospheric gases, including N2, O2, H2O, and of course CO2, with parameters taken from the HITRAN database 5 All simulations were assumed to be performed at room temperature and atmospheric pressure. In order to simulate the experimental process of changing the CO2 concentration by nitrogen purge. After calculating the complex refractive index using formula S3, absorption and dispersion can be considered separately from the following relations:

[0127] n(ω)=n′(ω)-iκ(ω)

[0128] where the real part of the refractive index n′(ω) contains the dispersion information, while the imaginary part κ(ω) defines the contribution to the losses. Examples of the imaginary and real parts of the complex refractive index for the CO2 band of interest at atmospheric concentrations can be found in Figure 7 a and Figure 7 b. Interestingly, while most of our theoretical analysis in this example revolves around the effects of losses, we find that an accurate simulation of the sensing behavior also requires a correct model of the dispersion.

[0129] In addition to helping confirm the behavior observed in the experiments, our numerical analysis helps extend these results to different regimes where the sensing performance can be further improved. Figure 7 In c and 7d, we emphasize the importance of low-fineness operation for the observed sensing behavior. As described in the main text and analyzed in part b below, the sensitivity benefits from higher slope efficiency and higher threshold. In the synchrotron regime, both slope efficiency and threshold can be increased by using a low-fineness cavity. Figure 7c shows the output power as a function of input power for output coupling values ​​of 0.1 (green), 0.25 (orange), and 0.4 (red), where the output coupling value of 0.25 roughly corresponds to our experiments. Here, we observe an increase in threshold from about 350nW at an output coupling of 0.1 to about 1200nW at an output coupling of 0.4. In addition, we see that the slope efficiency more than doubles, from 81.3% efficiency to 204%. Correspondingly, we notice a more than fourfold increase in sensitivity, as Figure 7 d. This ability to achieve higher slope efficiency and threshold in the synchrotron state through low-fineness operation is critical to the large sensitivity enhancement that the synchrotron provides.

[0130] Furthermore, our numerical results can help us better understand the nonlinear dynamics in syncon formation, which can be helpful for sensing. Figure 5 c and 5d, it is the interaction of energy and timing conditions that leads to the enhanced sensing behavior of the synchronizer. Figure 5 In d, we show that the dynamic feature that causes the high sensitivity is the movement of the steady-state signal pulse position away from the center of the gain window as loss is added to the cavity. The gain window is determined by the pump pulse and the walk-off length, and can be approximated by convolving the pump pulse (here a sech-shaped pulse of 35 fs duration) with a square pulse of duration equal to the walk-off length Δβ′L (here 72 fs). By finding the “center of mass” of the signal To calculate the steady-state signal pulse position, where P i and t i represents the pulse power and time in the ith Fourier segment. The “centroid” metric helps provide consistency in the measurement results, since the addition of samples tends to distort the temporal characteristics of the pulse.

[0131] To further emphasize the opposing roles of gain and loss, we plot the steady-state pulse position ( Figure 7 e) and the pulse position as a function of concentration ( Figure 7 f). In both cases, the 0fs along the y-axis represents the center of the gain window. Here, we can see that increasing the gain by increasing the pump power pushes the steady-state pulse position toward the center of the gain window, while increasing the loss pulls it away. Thus, we can see how high sensitivity is also enabled by the interplay of energy and timing, which results in a high slope efficiency of the synchrotron state. Figure 7 e The observed jump near 775 mW is an artifact caused by the walk-off nature of the simulation. To mimic the experiment, we usually lock in the detuning value ΔT that gives the maximum power RT, we simulate multiple detuning values ​​and record the one that results in the highest output power. This optimal detuning may change as the pump power is increased, leading to walk-off transitions such as the observed one; however, we expect that for experiments where the detuning can be varied continuously, the behavior should be smooth.

[0132] a. Comparison with Linear Absorption Sensing

[0133] When analyzing the performance of our method, it is helpful to compare it directly with linear absorption sensing (LAS). The analysis in this paper is based on the introduction in Reference 6. We start with the intensity I in The Beer-Lambert law for light passing through a sample with absorption coefficient α and length L states that the output intensity I out Given by the following formula

[0134] I out =I in e -αL

[0135] The most common way to quantify sensitivity enhancement is to consider the path length enhancement. This metric is particularly applicable to cavity-enhanced sensing, where the physical mechanism at work can be directly understood as an increase in the interaction length between light and the sample. In a linear cavity of length L with specular transmittance T and reflectance R (intensity) filled with an absorbing sample, the input-output power relationship is

[0136]

[0137] The approximation made in this paper is to expand the entire expression to the first order of α. where F is the cavity finesse, and using the fact that T ≈ 1-R, we find

[0138]

[0139] Among them, we define is the effective path length. This is the typical Beer-Lambert law, except that the path length L is replaced by L eff Therefore, we can see that the linear cavity is Comparing (S7) with equation (S5), we can find a direct expression for the path length enhancement ξ:

[0140]

[0141] This expression is very useful because it can be used to calculate ξ or equivalently L from the measured value of the intensity effIt can also be generalized to include measurements of some baseline concentration of sample already present in the system. In particular, if the output intensity is measured before and after adding a small amount of sample Δα, the expression becomes:

[0142]

[0143] This is equivalent to equation (1) above, except that in equation (1) we have substituted power for intensity and assumed that the spatial distribution of the beam remains constant between measurements, thus removing the mode area from both the numerator and denominator. It is clear then that the path length enhancement can be easily calculated knowing Δα, the path length L, and the measured value of the change in power when the sample is added. That is, since α = α(ω) is a function of frequency, slightly more care is required to calculate this quantity using only the measured intensity change of a broadband signal. To address this issue, we consider the case of performing LAS with a multimode source containing several frequency modes i, such that I in =∑ i I in，i Then, according to Beer-Lambert's law, each frequency mode is assumed to experience an absorption coefficient α i , the output intensity expression is as follows:

[0144]

[0145] Assume α i L is small, we find

[0146]

[0147] Divide by I in L, and then rearrange it to get α eff The following expression:

[0148]

[0149] α eff is composed of α′ i is given by the weighted sum of s, with the intensities of the various modes (normalized to the total intensity) as weights. Using this expression, equation (S9) can be extended to the case of broadband sources, provided that the spectral shape of the source is known.

[0150] These results allow us to compare between the experimentally measured syncon behavior and the linear approach. To do this, we calculate the equivalent path length enhancement that is necessary for a source with the same spectrum as the syncon at the reference absorption α to experience the same intensity change as further addition of sample Δα in the linear cavity. For this calculation, we first take the experimental syncon spectrum of the CO2 purification cavity measured at 11 ppm ( Figure 8a, orange line), and use interpolation to reconstruct the CO2-free spectrum (blue, dashed line). We then use the CO2 absorption spectrum provided by HITRAN to estimate P i (α i ), that is, assuming that there is no enhancement, the modal absorption coefficient is α i After a sample of 1.2 m of propagation, the modal intensity of the source with a spectrum equivalent to the synchrotron 5 .

[0151] As the main text Figure 4 c, the calculated enhancement effect is very significant, with a value as high as 2491. Using the L defined by equation (S7) eff , we see that this is equivalent to the enhancement provided by a cavity with a finesse of 3912. This is important because it demonstrates that quadratic cavity solitons in a near-threshold low-finess cavity are able to achieve sensitivity enhancements similar to those achieved by linear methods in a high-finess cavity.

[0152] The measurement of path length enhancement as defined in (S9) is primarily useful for quantifying relative power rather than sensitivity. Furthermore, it is difficult to make a fair comparison because the enhancement in the synchronized case does not come from an extension of the path length but from nonlinear dynamics that result in broadband losses. This difficulty is particularly evident in cases where there is already a certain sample baseline level in the cavity, where linear methods typically already experience significant losses in the absorption modes that do not appear in the α-sampling used to calculate α. eff in the synchrotron spectrum. Therefore, for a pump with the same optical properties as our synchrotron OPO output, it is also worthwhile to perform a direct sensitivity comparison with the LAS. Let us start by calculating the sensitivity of the LAS analytically. The sensitivity is the rate of change of the signal with respect to the absorption coefficient I out , is given by the following derivative (S5):

[0153]

[0154] From this we can see that when α = 0, the sensitivity reaches the maximum value I in L. This sensitivity can be quite high due to the large effective path lengths that can be achieved in a high finesse cavity. eff The enhanced sensitivity of the system S enh , with the sensitivity S of the baseline LAS system with path length L base By comparison, the following expression of sensitivity enhancement ζ can be obtained:

[0155]

[0156] Here, we assume that both systems are pumped with the same power. At α = 0, we see that the sensitivity enhancement indeed corresponds exactly to the path length enhancement ξ calculated above. However, when considering the dynamic range, it is clear that for L eff > L, this sensitivity enhancement decays rapidly as α increases. This causes an inherent trade-off between sensitivity and dynamic range in the linear case, since by increasing L (or equivalently, L eff ) achieves higher sensitivity near α = 0, which results in a significant decrease in sensitivity for larger values ​​of α. Therefore, it is also important to directly consider the sensitivity enhancement for the discussion of dynamic range. To make this comparison, we use a linear approach to seek the maximum achievable sensitivity for arbitrary α. By optimizing (S13) with respect to L, we find that when This is the optimized sensitivity:

[0157]

[0158] This optimization sensitivity, which is inversely proportional to α, defines Figure 3 b and Figure 6 The sensitivity limit of the LAS is shown in d. Figure 6 For the comparison plot in d, we assume that the source has the same bandwidth as the syncron and an average power of 500 mW, which is approximately the maximum output power of our system when fully purified. In practice, the asymptotic behavior of the LAS near α = 0 is limited by spatial constraints and the finesse achievable with the available cavity mirrors. For comparison, we assume a cavity length of 1.2 m, the same size as our OPO system, and a maximum path length enhancement of 10 6 , corresponding to a granularity of over 1.5 million. We believe this is a reasonable choice, as such a high granularity is extremely difficult to achieve in practice, especially over such a large bandwidth.

[0159] For our measured data, the sensitivity given by equation (S13) and the sensitivity enhancement (S14) are plotted on our Figure 8 c and 8d’s measurement data. Figure 8 c is very similar to the text Figure 6 d, but here we have simplified the linear region into two lines, the sensitivity limit S opt and baseline sensitivity S base , as mentioned before, they are calculated for a source of the same bandwidth and power as the syncron. Then, Figure 8 d shows the corresponding sensitivity enhancement, which is obtained by comparing our measured sensitivity with S base The maximum sensitivity enhancement is 90. This large sensitivity enhancement can greatly improve the achievable resolution compared to a linear baseline.

[0160] b. Single-mode intracavity absorption sensing

[0161] Here, the theory of single-mode intracavity absorption sensing (SMICAS) is reviewed. We start with the rate equations for the laser system. Defining the mean photon number M, the mean population inversion ρ, the broadband cavity loss γ, the pump rate R, the spontaneous decay rate A of the upper lasing level, and the induced emission rate B per photon per excited atom or molecule, we obtain:

[0162]

[0163] The last term Bρ in equation (S16a) is the average spontaneous emission rate. This term is often omitted in the analysis of single-cavity intracavity absorption sensing. Here, we will give the solution with and without this term in order to discuss its practical significance. Setting both equations to 0 and solving for the steady-state average photon number yields:

[0164]

[0165] When spontaneous emission is not considered, or when When , we can ignore the last term under the root and get:

[0166]

[0167] Intracavity power P int It can be obtained based on the average number of photons M, that is, in is the reduced Planck constant, c is the speed of light, ω is the laser frequency, and we assume that the round-trip length of the free-space cavity is L. Taking the transmittance of the output coupler as T, P can be calculated by out =TP int Calculate the output power P out According to formula (S18), we can derive:

[0168]

[0169] Among them is Total loss, used and Before we proceed, as a final step, we can also rewrite where R is the reflectivity of the output coupler. Similarly, the total loss can be defined as where α tot =α R +α samp +α oth is the collective absorption coefficient, including the output coupling loss α R , the loss α caused by the sample sampand the losses α caused by other intracavity components oth Rewriting equation (S19) in terms of these absorption coefficients yields:

[0170]

[0171] To find the enhancement factor according to formula (S9), we seek the quantity where Δα samp It is a small change in loss due to the presence of the absorber in the cavity. Define ΔP out =P out (α samp )-P out (α samp +Δα samp ) and assume So Using (S20), we can find this quantity as:

[0172]

[0173] We use the multiples above the threshold Finally, we calculate the enhancement Let approximate Δα smap <<α samp

[0174]

[0175] Thus, we see that if the spontaneous emission is negligible, an enhancement can be calculated that asymptotically approaches infinity as the threshold is approached. Fig. 9 a shows the enhancement of the full model calculation using equation (S17) compared to the analytical solution given by equation (S22) neglecting spontaneous emission (using reference 7 The actual laser parameters given in , namely A = 1.7*10 8 s -1 , B=10 -2 s -1 , L = 1m, α R = 0.01, and m -1 ). We set the frequency to ω=4.5*10 14 rad / s, which is equivalent to the center frequency of our OPO output. For these parameters, the agreement is very good, with the main changes occurring very close to N=1, when the simplified model approaches infinity and the full model approaches the peak. In general, the lower the spontaneous emission rate, the better the agreement.

[0176] Therefore, to maximize enhancement, we want our system to operate as close to N=1 as possible. However, we face a signal-to-noise ratio (SNR) trade-off in doing so, since the signal goes to zero as N approaches 1. Intuitively, there are two ways to improve this situation, such as Fig. 9 b. Here, the output power P as a function of the pump rate R out It is shown with a reference line (line 1, medium orange) and compared with two improved lines (line 2, light orange and line 3, dark orange). out，det Shown as a dashed grey line; the grey shaded area below represents the number of photons that could not be detected. det，i (where i∈{1, 2, 3}) indicates that the number of signal photons exceeds P out，det The first avenue of improvement would be to change the slope efficiency, or the rate at which the output power changes with pumping rates above the threshold. As shown in line 2, a higher slope efficiency allows operation closer to the threshold while maintaining a large enough output power to have a large enough SNR. Alternatively, the threshold can be increased, as illustrated in line 3. For the same slope efficiency and output power, a larger threshold will mean a smaller N; in other words, R det，3 / R th，3 <R det，1 / R th，1 With this intuition, we can study equation (S20) to see how each parameter contributes to the tuning enhancement. First, we use P out，det To rewrite equation (S20):

[0177]

[0178] We can then rearrange to solve for R det :

[0179]

[0180] Known We find that the detector is limited to a multiple N above the threshold det It is derived from the following formula:

[0181]

[0182] This expression tells us which parameters we can tune to get closer to the threshold while keeping the signal level the same, thereby improving the SNR of the detector-limited measurement. Here, we can clearly see that while keeping the signal constant, increasing ratio helps to make N det is closer to 1. This is consistent with Fig. 9 c is consistent, Fig. 9c shows the output power as a function of pump rate as A is varied. As A increases, the threshold increases, which should allow operation closer to threshold. Nevertheless, the rates A and B are derived from fundamental properties of the laser system and may be difficult to tune in practice. More notably, the only losses present in equation (S25) are due to the loss due to the output coupling, α R The greater the output coupling, the higher the extraction efficiency, thus increasing the threshold and possibly also benefiting the slope efficiency. Fig. 9 d. In contrast, other intracavity loss mechanisms lead to both an increase in threshold and a decrease in slope efficiency, such as Fig. 9 The net result is that these two effects cancel each other out, resulting in no net gain in terms of operation close to threshold.

[0183] As a final point of comparison, we can find an expression for the sensitivity:

[0184]

[0185] Suppose we have R det Running at a given pump rate, we find:

[0186]

[0187] Among them, S det It is by P out，det The sensitivity at the specified point. As with the SNR when operating near the threshold, we can see that the ratio can benefit absolute sensitivity, further highlighting the benefit of using lasers with low spontaneous emission rates. In addition, we also found that sensitivity is This shows that the dynamic range of ICAS using conventional lasers is the same as we observed in the linear approach; for given system parameters, the maximum achievable sensitivity is inversely proportional to the sample loss. The relationship between this and our discovery in Equation (S22) that the enhancement factor is also inversely proportional to the loss suggests that conventional intracavity absorption sensing using single-mode lasers benefits from high-finess cavities and is best suited for trace gas detection. These conclusions can be used to compare the intracavity absorption spectra in our analysis of CW OPOs in the next section.

[0188] c. ICAS in CW OPO

[0189] While the focus of this work is on the synchrotron regime (a pulsed mode of operation), it is also desirable to have a basic analytical framework for understanding ICAS in OPOs. Continuous-wave (CW) theory can give us such a framework, allowing for direct comparisons with the general laser case presented above. Specifically, here we seek to derive the enhancement factor for ICAS in CW OPOs. Furthermore, we derive expressions for the sensitivities and understand how these quantities vary with key parameters of the OPO. While such analysis using synchrotron theory will be the subject of future work, we believe that this CW analysis can provide a starting point for understanding these important behaviors in OPOs.

[0190] Our derivation in this section will follow Ref. 8 First, we derive an expression for the input-output power relationship, starting from the coupled wave equations for the three-wave mixing process, assuming low losses and low gains. The coupled wave equations for the pump electric field E3, the signal electric field E1, and the idler electric field E2 are given.

[0191]

[0192] where κ i =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, where i∈{1,2,3}. Energy conservation and phase matching require that the pump, signal, and idler frequencies ω i and the wave vector k i With the following relationship:

[0193] ω3=ω2+ω1

[0194] k3=k2+k1+Δk

[0195] We usually achieve a wave vector mismatch Δk≈0 by quasi-phase matching in the crystal. Next, we The solution of the coupled wave equation is postulated under the assumption that is to find the gain and bandwidth of a parametric amplifier of length l. Note that this approximation is almost exact below the threshold and can therefore be used to accurately estimate the threshold gain of the system.

[0196] Our assumptions are as follows:

[0197]

[0198] Substituting into the coupled wave equation, we obtain:

[0199]

[0200] Replace κ i and rearranging the terms yields:

[0201]

[0202] Finally, solving for Γ′ yields:

[0203]

[0204] Thus, we know that Γ′ is the eigenmode that describes the evolution of the field envelope according to our assumption, and consists of two main terms. The first is the loss term, given by the round-trip losses of the signal and idler frequencies defined previously. The second term determines the gain, and we know that one eigenmode grows while the other decays. Setting α1 = α2 = α, we obtain the simplified expression

[0205]

[0206] The solution of the signal field and the idler field is obtained as follows:

[0207]

[0208] Here, g denotes the gain of the field and Γ denotes the maximum achievable gain with perfect phase matching. Having obtained this expression for the field evolution, we now attempt to derive the threshold gain of the OPO. By using equations (S31) and (S34) to find expressions for the evolution of the + and - components of the electric field, we can expand equation (S35) to obtain the following expressions for the electric fields E1(l) and E2(l) at the output of the crystal:

[0209]

[0210] In the case of perfect phase matching, we can take Δk = 0. Then, assuming that the gain is small, the threshold condition (E i (l) = E i (0)), the following expression is obtained:

[0211]

[0212] Simplifying the system yields:

[0213]

[0214] If Γl is also small, and α1l+α2l<<8, we can conclude that:

[0215]

[0216] This is the expression used to find the threshold gain of a CW OPO and essentially boils down to requiring gain to equal loss. Now, we derive an approximation for the oscillator conversion efficiency. We first derive the internal efficiency η from int =(ΔI1+ΔI2) / I 30 Start, where ΔI i =I if -I i0 , which is the intensity change during a single pass through the gain medium. To achieve this, we first assume that dE2 / dz and dE1 / dz are negligible (i.e., the accumulation in a single round trip is small), which gives us the following two pump wave equations:

[0217]

[0218] Here, and + and - refer to the forward and backward propagating fields. Integrating the two equations, assuming that the signal and idler fields are independent of z, yields:

[0219]

[0220] From this we see that the maximum energy transfer from pump to signal and idler occurs at This is consistent with the phase matching relationship. Next, we find that using Substitute the strength We can derive the following relationship between signal and idler power:

[0221]

[0222] The derivation process is as follows:

[0223]

[0224] Between the first and second lines, we use Furthermore, conservation of intensity implies that:

[0225]

[0226] This can be solved to give the input-output power relationship. Let's take it step by step. First, we substitute expressions (S41a) and (S41b) to obtain:

[0227]

[0228] The first two terms on the left cancel, the next two can be combined into a single sine term, and the last two are identical and can therefore be combined. Once this is done, we use expression (S42) with ε 20 and ε 30Re-express everything:

[0229]

[0230] Next, we can divide by the right side, rearrange the terms, and then plug in k3 and the intensity to get:

[0231]

[0232] We define the threshold intensity This is consistent with equation (S39), which is our previous expression for the threshold gain. Note that we can also use I 10 Derive equivalent expressions. Finally, assume Δk = 0 and realize that ΔI2 ≈ a2I 20 :

[0233]

[0234] Here, we define the quantity N = I 30 / I 3，th . Then, combining the two expressions, the internal efficiency is:

[0235]

[0236] This defines the internal efficiency of the CWOPO when it is N times higher than the threshold, taking into account both forward and reverse propagating waves. However, since our OPO is a ring resonant oscillator, the reverse wave does not interact with the gain medium and therefore its contribution can be neglected. If the last term in equation (S42) is left out, the result of repeated calculations is an increase of a factor of 2 in the final expression:

[0237]

[0238] Next, we must find the extraction efficiency η ext , which characterizes the ratio of the strength of the signal and idler generated in the OPO to the OPO output. As before, we will calculate the extraction efficiency of the idler only and infer that the signal extraction efficiency should be similar. Let us assume that the strength of the external coupling of our resonator at the idler is T2. Note that we have already implied this external coupling when calculating the round-trip loss parameters, but we define it separately here so that we can refer to it explicitly.

[0239] Assume that the total internal strength of the resonator is I 2，int , then the output intensity is I 2，out =T2I 2，int . Each round trip, I 2，int will increase by the above calculated amount ΔI2, and Loss. It follows that the internal strength is given by the infinite sum:

[0240]

[0241] Then, the output power is given by:

[0242]

[0243] Therefore, the extraction efficiency is:

[0244]

[0245] The equivalent expression of the signal can be derived. Finally, the signal η1 = η int，1 η ext，1 and idle frequency η2=η int，2 η ext，2 The conversion efficiencies are:

[0246]

[0247] The total conversion efficiency is the sum of the two:

[0248]

[0249] We now want to use this conversion efficiency expression to study the relationship between the system's losses and output power. We will also study the degenerate case, where ω1 = ω2 = ω. To make the statement clear, we will redefine I 1，out +I 2，out =I ω，out , i.e., the degenerate signal, and I3 is defined as I 2ω , i.e. degenerate pumping, we will use the same subscripts for all other quantities. We can then obtain the following signal expression:

[0250]

[0251] From this expression, we can characterize the OPO behavior in the case of single-mode ICAS. First, let's look at the enhancement factor. A small change in loss Δα ω When , the signal changes as follows:

[0252]

[0253] Next, enhance is given by:

[0254]

[0255] This is very similar to the behavior predicted by SM laser theory. However, according to this result, one advantage of the OPO is that behavior, compared to the N-1 behavior exhibited in the SM laser case, which grows to large values ​​far from the threshold, e.g. Fig.10 Here, we can see that CW OPO (orange) grows faster when approaching N=1 compared to SM ICAS (pink).

[0256] In addition to enhancement, we can also look at other scaling behaviors of CW OPO systems, as we did in the case of SM ICAS. First, let us make some simplifications. First, we return to our earlier observation that the output coupling is already implicit in the losses; indeed, the losses α ω It consists of three components, so that α ω =α samp +α R +α oth Here, α samp is the loss from the sample of interest, α R is the loss from the output coupling, making the reflection And α oth is all other round-trip losses in the OPO cavity. Then, Furthermore, we define the parameter It turns out that:

[0257]

[0258] Now let us define the detector-limited output intensity I ω，det The corresponding input intensity I 2ω，det for:

[0259]

[0260] Using this, and noting that the threshold intensity is We find that the output intensity I ω，det The required number of times above the threshold N det Yes: a

[0261]

[0262] Here we see that, unlike the case of the SM laser, the multiple of the OPO above threshold can be approached to unity through tuning of the losses. This is due to the fact that in the OPO case, the losses affect the threshold directly through an offset term rather than through the slope as in the case of the SM laser. Furthermore, we see that tuning the output coupling can provide the greatest benefit, as it can increase both the slope efficiency and the threshold. Finally, increasing γ can also be used to improve the detector-limited sensitivity enhancement, with similar benefits as for the output coupling. These observations are consistent with Fig.10The scaling behavior of equation (S55) plotted in b, 10c and 10d for changes in output coupling, loss and γ parameter, respectively, is consistent. Both output coupling and parameter γ can be tuned to increase both threshold and slope efficiency, while increasing round-trip loss can increase threshold without affecting slope efficiency.

[0263] In addition to looking at the enhancement in detector limits, we can also calculate the sensitivity, which is given here as:

[0264]

[0265] Again, there are significant differences compared to the case of the SM laser. Specifically, the loss terms due to the sample do not appear anywhere in the equations. However, the output coupling and parameter γ can be increased to improve sensitivity, which is consistent with the detector-limited enhancement we see in equation (S57). These results indicate that, unlike the case of the SM laser, the CW OPO can benefit from operation in the low-finesse regime, provided there is sufficient gain above threshold. Furthermore, the lack of reliance on sample losses allows for very high dynamic ranges to be achieved when performing sensing measurements in the OPO system. These differences arise from the different gain mechanisms of the two systems, as shown in their respective rate equations, where the laser gain comes from energy exchange, where atomic transitions lead to the emission of photons, and the parametric gain comes from the interaction between the pump and signal electric fields via quadratic nonlinearities. While understanding the behavior of the synchonons requires more careful treatment than the CW model, these observations are consistent with our experimental findings and further shed light on why the high threshold and slope efficiency of the synchonons can provide large sensitivity enhancements and why we are able to achieve large dynamic ranges in our measurements.

[0266] d. Synchronon Theory

[0267] Synchrons are bright-dark soliton pairs co-propagating in a signal with frequency ω and a pump with frequency 2ω, respectively. By considering the coupled wave equations and retaining only the walk-off and nonlinear coupling terms, the syncronon solutions for a traveling-wave optical parametric amplifier (OPA) operating under degenerate conditions can be easily found. In this section, we follow Ref. 9 We derive the synchrotron solution from the symbol of and use the analytical expression of its dynamic evolution to provide an intuitive explanation for the proposed sensing mechanism. We start with the coupled wave equations for the degenerate field:

[0268]

[0269] Here, κ is the nonlinear coupling coefficient, Δβ′ is the group velocity mismatch, and E ω and E 2ωare the signal field and the pump field, respectively. The time coordinate is defined to move together with the group velocity of the signal wave. Assume that E has an opposite group velocity v. ω (z, t) = E ω (t+vz) and E 2ω =E 2ω The wave solution of the (t+vz) form is given by:

[0270]

[0271] This system of equations can be solved analytically to produce synchronized subsolutions:

[0272]

[0273] In these equations, we define the signal pulse duration τ, the timing advance T experienced due to gain saturation, and the pump amplitude E 2ω，0 The system is reparameterized by the amplitude of the synchronous sub-signal α. Define the small signal gain coefficient γ0 = κE 2ω，0 , we found And T = -γ0τz

[0274] Therefore, we can understand that the syncron is composed of tanh-shaped dark solitons in the pump and sech-shaped bright solitons in the signal, which move together with a group velocity v = γ0τ greater than the signal group velocity. Now, we hope to follow the reference 10 The manifold projection method proposed in , extends this solution to the dynamic regime, thus understanding the effects of gain and loss on the system. We start again with the coupled wave equations and use the method of characteristics to derive the solution for the pump field. We have:

[0275]

[0276] Solving for E 2ω get:

[0277]

[0278] To simplify the integration, we change the variable t′=t+Δβ′(z′-z), thus obtaining:

[0279]

[0280] Now, we invoke the distortion-free gain assumption, that is, for an OPO cavity with mirror reflectivity r and crystal length l, Make varies slowly with z, and γ av satisfy Under the current changes in the variables, this yields Note that the main variation in the signal comes from this exponential term, so it vanishes very quickly for negatively growing t′. We can assume that the lower limit of the integral extends to -∞ to a good approximation:

[0281]

[0282] Next, we can substitute this expression for the pump into the differential equation (S59a) describing the evolution of the signal. This yields:

[0283]

[0284] From here, we assume that the field envelope takes a sech-like form of the syncron given above, but we allow the parameters T, τ, a to vary with z:

[0285]

[0286] Substitute it into E ω In the formula (S66) of (z, t), it is assumed that the pump constant E 2ω，0 ,get:

[0287]

[0288] Defining the right side of equation (S68) as g(z, t), we now perform manifold projection to obtain the evolution equations of the signal pulse parameters. To perform the projection, we must first define an inner product, which we take to be<f|g> =∫f(t)g(t)dt. E sim The total derivative with respect to z is given by:

[0289]

[0290] set up And use the orthogonality of partial derivatives under the inner product definition, such as Where ξ, η∈{T,τ,a} and ξ≠η, we find that the evolution expression of the parameter ξ is as follows:

[0291]

[0292] Applying this to the three parameters of interest, we obtain their evolution equations:

[0293]

[0294] Here, a sim is the steady-state syncron amplitude, given by This system of equations can be solved analytically to obtain the steady-state solutions of T, τ and α, namely:

[0295]

[0296] We can now consider the effects of losses and detuning on the system. Let us consider the round trip delay ΔT RT and the round-trip loss Re -αL , where R is the lumped specular reflection in the round trip and α is the additional loss in the round trip, including the loss due to the presence of the intracavity sample of the resonator with a total length of L. Assuming the length of the nonlinear crystal is l, we obtain the round trip evolution as follows:

[0297]

[0298] When T(n+1)=T(n) and α(n+1)=α(n), the steady state is reached. From this, we can see the two requirements for the formation of synchronizers: the gain must be equal to the loss, so that And the advance of the synchronized subgroup must compensate for the detuning, which means Furthermore, we see the interdependence of these two conditions, since the steady-state center-of-mass position T depends on how quickly the syncron amplitude α saturates to its steady-state value. Since the growth of the amplitude depends on the interplay of gain and loss, the steady-state center-of-mass position is ultimately determined by the gains and losses of the system. Although here we have approximated the pumping as continuous, this interplay becomes very important for pulsed pumping, where the pumping defines a temporal gain window for the signal. In this case, a bright soliton in the signal cannot rise above a threshold if its amplitude does not grow fast enough to satisfy the timing condition before the detuning pulls it out of the gain window. Above the threshold, the bright soliton will experience more or less gain, depending on its steady-state position within the gain window. As Figure 1d and Figure 3 c), these dynamics result in a high slope efficiency of the syncron near threshold and, correspondingly, a high sensitivity of the syncron to the addition of sample to the cavity.

[0299] Example 4: Spectral Analysis Using OPO

[0300] In various examples, OPO sensors can be built using either a dual-resonance OPO (DRO) or a single-resonance OPO (SRO), which have slightly different sensing mechanisms. In a DRO, both the signal and idler frequencies resonate, while in an SRO, only one of the signal or idler frequencies resonates. Although the threshold of a DRO can be much lower than that of an SRO, the necessary overlap of the signal and idler resonances imposes tolerance limits on cavity length and pump frequency fluctuations [1]. Resonating only the signal (or idler) frequency allows an SRO to achieve better output power stability and a wider frequency tuning range.

[0301] First consider the following Fig.11The DRO sensor shown in a, where the cavity and mirrors are designed so that both the signal and idler frequencies resonate within the cavity. The output power is measured by a single photodetector at the output of the SRO, and we can monitor the output power as a function of the OPO tuning parameters such as cavity length. Fig.11 As shown in b, each OPO peak has a different spectral distribution. When we continuously scan the cavity length of the SRO, the output power time trajectory ( Fig.11 c) can allow us to partially reconstruct the intracavity absorption spectrum. For example, if the absorption features of some target molecules are only related to Fig.11 b) overlaps mode 0 and mode 7, which will be reflected as a reduction in photodetector power only on the peaks associated with mode 0 and mode 7. By designing the overall spectral coverage and the spectral overlap between different cavity modes, efficient spectral reconstruction can be performed using only the photodetector signal.

[0302] Next consider Fig.12 An SRO shown in a, where only the signal (orange) is resonating in the cavity, not the idler (green) or pump. The signal power is still measured by a single photodetector at the output of the SRO. At some arbitrary signal frequency, if we monitor the output power as a function of the cavity length, we will not see a walk-off OPO peak as we do with a DRO. Instead, the output signal frequency can be varied by tuning the phase matching (e.g., by temperature tuning of the crystal), effectively tuning the SRO into a tunable source with a narrow linewidth. As an example, pumping the SRO with a near-infrared wavelength can allow the signal to be further tuned into the mid-infrared spectral region.

[0303] Alternatively, instead of directly monitoring the mid-IR signal wavelength at the output of the OPO, we can also measure only the non-resonant near-IR idler frequency, since the absorption features on the signal are also reflected on the idler. Measuring the idler frequency allows the signal to resonate with a higher Q and enable mid-IR sensing using a near-IR source and detector.

[0304] The frequency tuning of the SRO sensor is as follows Fig.12 b, where the curves represent the signal and idler wavelengths at a fixed pump frequency. The degeneracy point corresponds to when the signal and idler wavelengths are equal. As we tune the phase matching, the signal wavelength changes and overlaps with different absorption features of the target molecules inside the gas cell. The absorption within the spectral coverage of the signal wavelength is further enhanced by the resonance, enabling intracavity sensing. Reading the output signal power as a function of the phase matching tuning allows for efficient spectral reconstruction without the use of a spectrometer.

[0305] In one or more embodiments for a single resonant oscillator, the signal or idler may be resonant, and either the pump, a small out-coupled resonant beam, or a non-resonant beam may be measured on a photodetector.

[0306] Process Steps

[0307] a. Manufacturing method

[0308] Fig.13 1 is a flow chart showing a method for manufacturing a sensor system. The method includes the following steps.

[0309] Block 130 represents providing a resonator including a nonlinear material including a nonlinear susceptibility, the nonlinear material configured to convert a pump electromagnetic (EM) wave into a signal EM wave and / or an idler EM wave, wherein at least one of the pump EM wave, the signal EM wave, and / or the idler photons is fed back through the nonlinear material to form one or more resonant EM waves.

[0310] Block 1302 represents coupling an actuator to a resonator or to a pump path of the resonator for at least one of modulating a pump power of a pump EM wave, detuning of a frequency mode of the resonator relative to one or more frequencies of the resonating EM wave, or phase matching of a nonlinear material. The actuator may include or be coupled to a computer or one or more circuits that output signals for controlling the actuator.

[0311] Block 1304 represents optionally coupling a detector (eg, a photodetector) to an output of the resonator for detecting one or more output EM waves that include information about the sample coupled to the resonator.

[0312] Block 1306 represents optionally coupling a computer to the detector.

[0313] Block 1308 represents a coupling device optionally used to couple the sample.

[0314] Box 1310 represents the end result, a sensor or sensor system. The sensor can be implemented in a variety of ways, including but not limited to the following examples (see also Figures 1-16).

[0315] 1. A sensor 100, comprising:

[0316] A resonator 100 comprising a nonlinear material 130, 302 comprising a nonlinear susceptibility, the nonlinear material configured to convert a pump electromagnetic (EM) wave 106 into a signal EM wave 108 and an 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 nonlinear material to form one or more resonant EM waves 111;

[0317] an actuator 104 coupled to the resonator or to a pump path of the resonator for controlling or modulating at least one of a pump power of a pump EM wave, a detuning of a frequency mode of a resonator relative to one or more frequencies of the resonating EM wave, or a phase matching of a nonlinear material; and

[0318] The resonator has an output 120 for outputting one or more output EM waves 122 including information about the sample 116 coupled to the resonator.

[0319] 2. The sensor according to example 1, further comprising:

[0320] a detector 112 coupled to the output of the resonator for detecting an output power of the one or more output EM waves; and

[0321] A computer 114 is coupled to the detector, wherein the computer is configured to determine information about the sample based on changes in output power when the resonating EM wave is coupled to the sample.

[0322] 3. The sensor according to Example 2, wherein the computer is configured to:

[0323] The information is determined by comparing the output power to a calculated output power calculated using a model of the response of a resonator coupled to the sample interacting with the resonating EM wave, and / or:

[0324] The information is determined using a machine learning algorithm trained using training data, wherein:

[0325] The training data includes the associations between:

[0326] the concentration or composition of the sample, and

[0327] said output power as a function of at least one of pump power, detuning or phase matching, and / or

[0328] The information is determined simply by analyzing the change in output power.

[0329] 4. The sensor according to any of Examples 1-3, further comprising an optical parametric oscillator (OPO) 118, 302 comprising a resonator.

[0330] 5. A sensor according to Example 4, wherein the OPO is configured to operate at a phase transition between degenerate operation and non-degenerate operation.

[0331] 6. The sensor of example 4, wherein the OPO 302 is configurable to:

[0332] operating near the threshold for lasing of resonant EM waves, and

[0333] EM includes synchronizers,

[0334] The sensitivity of the sensor to changes in the sample is enhanced by near-threshold dynamics such as syncon or other soliton formation mechanisms.

[0335] 7. The sensor according to any of examples 4-6, wherein the actuator is configured to change the operation of the OPO from below a threshold (for lasing of the resonant EM wave) to above the threshold.

[0336] 8. The sensor according to example 1, wherein the resonator is configurable to operate near an oscillation threshold for laser emission of a resonant EM wave, characterized by 0.9≤pump power / threshold pump power≤3 (e.g., approximately equal to 1), or

[0337] The actuator may be configured to set the detuning or phase matching so that the resonator operates at least at a spectral phase transition between degenerate and non-degenerate operation and / or the resonant EM wave includes a syncron.

[0338] 9. The sensor of any of Examples 1-8, wherein the actuator 104 causes the resonant EM wave in the resonator to follow a predictable spectral tuning, and the output EM wave can be used to reconstruct the functionality of a tunable laser spectrometer. |

[0339] 10. The sensor according to any of examples 1-9, wherein the actuator 104 is configured to modulate at least one of pump power, detuning, or phase matching to tune the dynamic range, sensitivity, or selectivity of the sensor.

[0340] 11. The sensor according to any of examples 1-10, wherein the information comprises at least a concentration or composition difference of a sample comprising one or more molecules, one or more molecular species, or one or more compounds.

[0341] 12. The sensor of any of Examples 1-11, wherein the information comprises a physical or chemical property of the sample, the sample comprising a solid, a liquid, or a gas.

[0342] 13. A sensor according to any of Examples 1-12, wherein information is output in real time with varying samples 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-1 MHz).

[0343] 14. The sensor according to any of examples 1-13, wherein the actuator comprises at least one of: an actuator configured to tune the length of the resonator, a heater and / or a cooler thermally coupled to the resonator for modulating phase matching and / or the length of the resonator, an electro-optic modulator that can tune the refractive index of the path length in the cavity, an electro-optic mirror or a beam splitter for controlling the power of the pump EM wave, or a control circuit coupled to the pump source for tuning the frequency or power of the pump EM wave output from the pump source.

[0344] 15. The sensor of any of examples 1-14, wherein the actuator comprises a scanner that applies one or more ramp functions that modulate at least one of pump power, detuning, or phase matching.

[0345] 16. One or more chips or photonic integrated circuits comprising the sensor or resonator of any of Examples 1-15, or an array of resonators of any of Examples 1-15.

[0346] 17. The sensor of any of Examples 1-16, further comprising a device for causing the resonant EM wave of the resonator to interact with the sample, wherein the device comprises a sample container positioned to couple the sample to the resonator via an evanescent field, a slot waveguide, an optical fiber, a chamber in the resonator, fluid coupling, free space coupling, or a hollow core fiber.

[0347] 18. The sensor according to any of Examples 1-17, wherein:

[0348] The resonator includes a cavity including a nonlinear material between the mirrors, and the cavity includes a sample space for positioning a sample within the cavity.

[0349] 19. The sensor of any of Examples 1-18, wherein the resonator comprises a fiber loop coupled to the nonlinear material.

[0350] 20. An analyzer comprising the sensor of any of Examples 1-19, the sensor being configured to output information about a sample comprising breath, atmospheric concentrations of pollutants or greenhouse gases, or process gases monitored in an industrial environment.

[0351] 21. The sensor of any of examples 1-20, wherein the information includes a sample concentration in a range (eg, parts per trillion to a few percent by volume) that causes saturation of the linear absorption sensor according to Beer-Lambert's law.

[0352] 22. The sensor according to any of examples 1-21, wherein the modulation causes tuning of the narrow linewidth spectrum.

[0353] 23. A sensor according to any of Examples 1-22, wherein the nonlinear material is phase matched, dispersion engineered and / or has a length L tailored for a second-order parametric amplification / conversion process that converts pump waves into signal waves and idler waves, and / or implements non-degenerate operation, degenerate operation, near-threshold operation, or other operating modes and states described in the examples.

[0354] 24. A sensing method comprising:

[0355] coupling the sample to a resonator, the resonator comprising a nonlinear material, the nonlinear material comprising a nonlinear susceptibility, the nonlinear material 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, or the idler EM wave is fed back through the nonlinear material to form one or more resonant EM waves;

[0356] controlling at least one of a pump power of a pump EM wave, a detuning of a frequency mode of a resonator relative to one or more frequencies of a resonating EM wave, or a phase matching of a nonlinear material;

[0357] detecting output power of one or more output EM waves output by the resonator; and

[0358] Information about the sample is calculated from the change in output power in response to the sample and the modulation.

[0359] 25. A computer-implemented system comprising:

[0360] one or more processors;

[0361] receiving output power in response to one or more output electromagnetic (EM) waves output from the resonator when the resonator is coupled to the sample, the resonator comprising a nonlinear material, the nonlinear material comprising a nonlinear susceptibility, the nonlinear material 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, or the idler EM wave is fed back through the nonlinear material to form one or more resonant photons;

[0362] When the sample is coupled to the resonator, controlling modulation of at least one of a pump power of a pump EM wave, a detuning of a frequency mode of the resonator relative to one or more frequencies of the resonator, or a phase matching of a nonlinear material, and

[0363] Information about the sample is calculated from the change in output power in response to the sample and the modulation.

[0364] 24. A molecular sensor based on an optical parametric oscillator (OPO), comprising: an optical parametric oscillator, which is an optical resonator with quadratic nonlinearity, for down-converting pump photons into signal and idler photons; a molecular sample, which may be allowed to flow freely over the optical cavity or contained in an air or microfluidic chamber placed within the cavity; a photodetector for monitoring the sensor output; and the optical cavity coupled to a mechanism for tuning the round-trip delay, which may be provided by a piezoelectric actuator for mechanical tuning or an electro-optic modulator for electrically tuning the refractive index of the optical path. Such tuning may also be effectively achieved outside the cavity by tuning the pump frequency. The cavity may be constructed in free space using multiple mirrors (e.g., in a bow-tie configuration), in an optical fiber, or otherwise.

[0365] 25. A sensor based on an OPO, wherein the OPO is configured to operate using unique nonlinear dynamic behaviors including spectral phase transitions and temporal syncon formation. Spectral phase transitions occur when the OPO transitions from degenerate operation (where both the signal and idler resonate at semi-harmonics of the pump) to non-degenerate operation. These sharp transitions are very sensitive to changes in the loss and dispersion profile of the resonator and are therefore particularly useful for monitoring situations where a sample is added to the cavity. Synchrons are co-propagating bright-dark soliton pairs in the signal and pump that have been shown to form in an OPO operating degenerately under appropriate conditions. A key feature of such an OPO is the high slope efficiency near threshold, which means that the syncrons have a particularly sharp response to increases in intracavity gain and loss and are therefore particularly useful for near-threshold sensing.

[0366] 26. An OPO configured for broadband molecular sensing, such as for use in a variety of tasks ranging from basic research to medical diagnostics and industrial process monitoring.

[0367] 27. A mid-infrared molecular sensor system and method that utilizes the nonlinear dynamics of secondary cavity soliton formation in an optical parametric oscillator to achieve both high sensitivity and large dynamic range when sensing a sample of interest. In one embodiment, the sample is CO2 in 4.18 μm OPO, where simulation results show that the path length is enhanced by 2491 and the sensitivity is improved by several orders of magnitude when the gas concentration is large compared to a linear method. This improvement in sensitivity breaks the fundamental limit on sensitivity imposed by Beer-Lambert's law.

[0368] 28. The sensor of one or more examples wherein the resonator comprises a SRO OPO tuned within a spectral range for performing spectroscopic analysis, wherein the output power as a function of the tuning is used to reconstruct the intracavity absorption spectrum. In one example, the OPO is only a narrow linewidth tunable source.

[0369] 29. The sensor of any of examples 1-28, wherein the sample is in a gas chamber.

[0370] 30. The sensor of any of Examples 1-28, wherein the resonator comprises an optical parametric oscillator comprising an optical parametric amplifier having a cavity therearound.

[0371] 31. A sensor according to any of Examples 1-30, comprising a single resonant OPO, wherein the single resonant OPO comprises a resonator in which a signal or idler frequency can be resonant and any of a pump, a small out-coupled resonant wave, or a non-resonant wave can be measured (e.g., output power) on a photodetector.

[0372] b. Sensing method

[0373] In one example, molecular sensing is accomplished by analyzing the interaction of generated signal and idler photons with a sample in the cavity, where the interaction produces a different response for each resonance of the OPO when the delays are tuned due to the unique frequency content of each resonance. By continuously sweeping the delays and monitoring the power of each resonance on a photodetector, real-time sensor data about the molecular sample of interest can be obtained.

[0374] Figure 8 is a flow chart illustrating a sensing method according to one or more embodiments of the present invention.

[0375] Block 1400 represents coupling a sample to a resonator including a nonlinear material including a nonlinear susceptibility, the nonlinear material 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, or the idler EM wave is fed back through the nonlinear material to form one or more resonant EM waves.

[0376] Block 1402 represents controlling / modulating / actuating at least one of a pump power of a pump EM wave, a detuning of a frequency mode of a resonator relative to one or more frequencies of a resonating EM wave, or a phase matching of a nonlinear material;

[0377] Block 1404 represents detecting the output power of one or more output EM waves output from the resonator.

[0378] Block 1406 represents calculating / determining information about the sample from the change in output power in response to the sample and the modulation. In one or more examples, the computer determines the information by comparing the output power (e.g., amplitude and / or shape) to a calculated output power calculated using a model of the response of a resonator coupled to the sample interacting with the resonating EM wave. In some examples, the computer determines the information using a machine learning algorithm trained using training data, wherein the training data includes a correlation between: (1) a concentration or composition of the sample, and (2) output power as a function of at least one of pump power, detuning, or phase matching.

[0379] Advantages and improvements

[0380] Embodiments of the present invention provide many novel and useful features.

[0381] 1. Broadband molecular sensing can be achieved without performing spectral analysis. This is particularly important in terms of scalability and economy, because traditional spectrometers are usually bulky or expensive, requiring additional components such as gratings, spectral filters, reference light combs (such as dual-comb spectroscopy), or large delays (such as Fourier transform spectroscopy). In OPO-based sensors according to the embodiments described herein, due to the unique frequency components of each OPO resonance, there is effectively a nonlinear mapping from the frequency domain to the time domain in the detected signal. This can achieve broadband sensing that only requires a detector.

[0382] 2. Signal enhancement can be exploited due to the resonator and the gain provided by the quadratic nonlinearity. Linear cavity enhancement is a result of the increase in the effective absorption path length due to multiple passes of the light through the sample in the cavity, while active cavity enhancement also benefits from the near-threshold dynamics in the active cavity due to the interaction of gain and loss.

[0383] 3. Operation and phase transitions as well as in the syncon state. This dynamic enables fundamentally different sensing schemes that can break many limitations of current technologies to achieve high sensitivity, large signal enhancement and considerable dynamic range for mid-IR gas sensing while avoiding the typical requirements of high finesse and high-power operation. Furthermore, syncons can be realized at arbitrary wavelengths, enabling a universal molecular sensing scheme that is particularly useful in wavelength ranges not readily accessible with lasers. For example, for an OPO with 4-micron wavelength output, we have measured near-threshold equivalent path length enhancements of up to 2491 and maximum sensitivities of 4.1 mW / ppm, even at CO2 concentrations up to atmospheric levels. 34 As demonstrated herein, the sensitivity of the synchonons at large gas concentrations is shown to be several orders of magnitude greater than what could theoretically be achieved by a linear approach using a probe with equivalent power and bandwidth to the output of our broadband OPO.

[0384] Due to these features, OPO-based sensors can offer high sensitivity, large dynamic range, and scalability when performing multi-class molecular sensing on samples including gases, liquids, or biological tissues. In particular, with regard to scalability, we emphasize here the exciting possibilities offered by the movement toward integrated photonic instrumentation, due to the strong mode confinement and dispersion engineering in such devices that can provide particularly strong nonlinearities and flexibility. These features can enable us to tailor high-performance sensors to specific application needs. Applications that would particularly benefit include, but are not limited to, those that require precise measurement of a wide range of concentrations.

[0385] Hardware Environment

[0386] Fig.15 1500 (referred to as a computer-implemented system and / or a computer-implemented method) for implementing 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 may be a database computer. The computer 1502 includes a hardware processor 1504A and / or a dedicated hardware processor 1504B (hereinafter optionally collectively referred to as a processor 1504) 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 may include a portable or media viewing / listening 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 device that executes on a variety of platforms and operating systems.

[0387] In one embodiment, computer 1502 is operated by hardware processor 1504A executing instructions defined by computer program 1510 (e.g., for performing calculations described herein or controlling actuation as described herein) under the control of operating system 1508. Computer program 1510 and / or operating system 1508 may be stored in memory 1506 and may interface with users and / or other devices to accept input and commands, and provide output and results based on such input and commands and the instructions defined by computer program 1510 and operating system 1508.

[0388] The output / results may be presented on the display 1522 or provided to another device for presentation or further processing or action. Graphics may be provided by a graphical user interface (GUI) module 1518. Although the GUI module 1518 is depicted as a separate module, the instructions for performing GUI functions may reside or be distributed in the operating system 1508, the computer program 1510, or implemented using dedicated memory and processors. In one or more embodiments, the display 1522 is integrated with / integrated into the computer 1502 and includes a multi-touch device having a touch-sensitive surface (e.g., a tracking capsule or a touch screen) that is capable of recognizing the presence of two or more points of contact with the surface.

[0389] Some or all of the operations performed by the computer 1502 according to the computer program 1510 instructions can be implemented in the special processor 1504B. In this embodiment, some or all of the computer program 1510 instructions can be implemented via firmware instructions stored in a read-only memory (ROM, read-only memory), a programmable read-only memory (PROM, programmable read-only memory) or flash memory or in the memory 1506 in the special processor 1504B. The special processor 1504B can also be hardwired by circuit design to perform some or all operations to implement the present invention. In addition, the special processor 1504B can be a hybrid processor, which includes a dedicated circuit for performing a subset of functions and other circuits for performing more general functions (such as responding to computer program 1510 instructions). In one embodiment, the special processor 1504B is a special integrated circuit (ASIC, specific integrated circuit) or a field programmable gate array, or other circuits (e.g., integrated circuits), or processors for performing artificial intelligence / machine learning.

[0390] The computer 1502 may also implement a compiler 1512 that allows 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 language to be translated into processor 1504 readable code. Alternatively, the compiler 1512 may be an interpreter that directly executes instructions / source code, translates source code into an intermediate representation that is executed, or executes stored precompiled code. Such source code may be written in various programming languages ​​such as JAVA, JAVASCRIPT, PERL, BASIC, etc. After completion, the application or computer program 1510 uses the relationships and logic generated using the compiler 1512 to access and manipulate data received from I / O devices and stored in the memory 1506 of the computer 1502.

[0391] The computer 1502 may also optionally include external communications equipment, such as a modem, satellite link, Ethernet card, or other device for accepting input from other computers 1502 and providing output to them.

[0392] In one embodiment, the instructions implementing the operating system 1508, computer program 1510, and compiler 1512 are tangibly embodied in a non-transitory computer readable medium, such as a data storage device 1520, which may include one or more fixed or removable data storage devices, such as a zip drive, a floppy disk drive 1524, a hard drive, a CD-ROM drive, a tape drive, etc. In addition, the operating system 1508 and the computer program 1510 consist of computer program 1510 instructions that, when accessed, read, and executed by the computer 1502, cause the computer 1502 to perform the steps required to implement and / or use the present invention or to load the instruction program into the memory 1506, thereby creating a special data structure that causes the computer 1502 to operate as a specially programmed computer to perform the method steps described herein. The computer program 1510 and / or operating instructions may also be tangibly embodied in the memory 1506 and / or the data communication device 1530, thereby making a computer program product or article of manufacture according to the present invention. Thus, the terms "article of manufacture," "program storage device," and "computer program product" as used herein are intended to encompass a computer program accessible from any computer-readable device or media.

[0393] Of course, those skilled in the art will recognize that any combination of the above components, or any number of different components, peripherals, and other devices, may be used with the computer 1502 .

[0394] Fig.16A typical distributed / cloud-based computer system 1600 is schematically shown in which a client computer 1602 is connected to a server computer 1606 using a network 1604. A typical combination of resources may include a network 1604, which may include the Internet, a local area network (LAN), a wide area network (WAN), a systems network architecture (SNA) network, etc., and a client 1602 is a personal computer or workstation (such as a Fig.15 ), the server 1606 is a personal computer, workstation, minicomputer or mainframe (such as Fig.151602 and server 1606. The network 1604, such as the Internet, connects the client 1602 to the server computer 1606. The network 1604 can utilize Ethernet, coaxial cable, wireless communication, radio frequency (RF), etc. to connect and provide communication between the client 1602 and the server 1606. In addition, in a cloud-based computing system, resources (e.g., storage, processors, applications, memory, infrastructure, etc.) in the client 1602 and the server computer 1606 can be shared by the client 1602, the server computer 1606, and users across one or more networks. Resources can be shared by multiple users and can be dynamically reallocated based on demand. In this regard, cloud computing can be referred to as a model for implementing access to a shared pool of configurable computing resources. The client 1602 can execute a client application or a web browser and communicate with a server computer 1606 executing a web server 1610. Such a web browser is typically a program such as MICROSOFT INTERNET EXPLORER / EDGE, MOZILLAFIREFOX, OPERA, APPLE SAFARI, GOOGLE CHROME, etc. In addition, the software executed on the client 1602 can be downloaded from the server computer 1606 to the client computer 1602 and installed as a plug-in or ACTIVEX control for the web browser. Therefore, the client 1602 can use ACTIVEX components / component object model (COM) or distributed COM (DCOM) components to provide a user interface on the display of the client 1602. The web server 1610 is typically a program such as Microsoft's Internet Information Server. The web server 1610 can host an active server page (ASP) or internet server application programming interface (ISAPI) application 1612, which can execute scripts. The scripts call objects (called business objects) that perform business logic.The business objects then manipulate the data in the database 1616 through a database management system (DBMS) 1614. Alternatively, the database 1616 may be part of or directly connected to the client 1602, rather than transmitting / obtaining information from the database 1616 through the network 1604. When developers encapsulate business functions into objects, the system may be referred to as a component object model (COM) system. Thus, scripts executed on the web server 1610 (and / or application 1612) call COM objects that implement business logic. In addition, the server 1606 may utilize Microsoft's transaction server (MTS) to access required data stored in the database 1616 via interfaces such as active data objects (ADO), object linking and embedding database OLEDB (object linking and embedding database), or open database connectivity (ODBC).

[0395] In general, these components 1600-1616 all include logic and / or data embodied in and / or retrievable from a device, medium, signal, or carrier, such as a data storage device, a data communication device, a remote computer or a device coupled to a computer via a network or via another data communication device, etc. Furthermore, when this logic and / or data is read, executed, and / or interpreted, it causes the execution of steps necessary to implement and / or use the present invention.

[0396] Although the terms "user computer," "client computer," and / or "server computer" are referred to herein, it will be understood that such computers 1602 and 1606 may be interchangeable and may further include thin client devices with limited or full processing capabilities, such as cellular telephones, notebook computers, pocket computers, multi-touch devices, and / or any other device with appropriate processing, communication, and input / output capabilities.

[0397] Of course, those skilled in the art will recognize that any combination of the above components or any number of different components, peripherals, and other devices may be used with computers 1602 and 1606. Embodiments of the present invention are implemented as a software / CAD application on a client 1602 or server computer 1606. In addition, as described above, the client 1602 or server computer 1606 may include a thin client device or a portable device with a multi-touch based display.

[0398] In one or more examples, a computer-implemented system includes one or more processors that receive 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, the nonlinear material including a nonlinear susceptibility, the nonlinear material 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, or the idler EM wave is fed back through the nonlinear material to form one or more resonant photons; when the sample is coupled to the resonator, control modulation / actuation of at least one of a pump power of the pump EM wave, a detuning of a frequency mode of the resonator relative to one or more frequencies of the resonator, or a phase matching of the nonlinear material, and calculate information about the sample based on a change 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, wherein the application executed by the one or more processors receives the output power and calculates information.

[0399] References

[0400] The following references are incorporated herein by reference.

[0401] References for the first example

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[0414] References for the Second Example

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[0444] 30 Haakestad, M.W., Lamour, T.P., Leindecker, N., Marandi, A. & Vodopyanov, K.L. 使用宽带中红外频率梳源进行腔内痕量分子检测。《美国光学学会B辑》30, 631 - 640(2013)。

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[0456] References for the third example

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[0467] References for the fourth example

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[0469] Summarize

[0470] The description of the preferred embodiments of the present invention ends here. The foregoing description of one or more embodiments of the present invention has been presented for the purpose of illustration and description. The present invention is not exhaustive or to limit the present invention to the precise form disclosed. In light of the above teachings, many modifications and variations are possible. The scope of the present invention is not limited by this detailed description, but is limited by the appended claims.

Claims

1. A sensor, comprising: a resonator comprising a nonlinear material, the nonlinear material comprising a nonlinear susceptibility, the nonlinear material 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 a pump path of the resonator for controlling at least one of a pump power of the pump EM wave, a detuning of a frequency mode of the resonator relative to one or more frequencies of the resonating EM wave, or a phase matching of the nonlinear material; and The output end of the resonator is used to output one or more output EM waves including information about the sample coupled to the resonator.

2. The sensor according to claim 1, further comprising: a detector coupled to the output of the resonator for detecting an output power of the one or more output EM waves; and a computer coupled to the detector, wherein the computer is configured to determine information about the sample based on changes in the output power when the resonating EM wave is coupled to the sample.

3. The sensor according to claim 2, wherein the computer is configured to: determining said information by comparing said output power to a calculated output power calculated using a model of the response of said resonator coupled to said sample interacting with said resonating EM wave, and / or The information is determined using a machine learning algorithm trained using training data, wherein: The training data includes the associations between: the concentration or composition of the sample, and the output power as a function of at least one of the pump power, the detuning or the phase matching, and / or Said information is determined simply by analyzing the variation of said output power.

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

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

6. The sensor of claim 4, wherein the OPO is configured as: operating near a threshold for lasing of said resonant EM wave, and The EM includes a synchronizer, The sensitivity of the sensor to changes in the sample is enhanced by near-threshold dynamics such as syncon or other soliton formation mechanisms.

7. The sensor of claim 4, wherein the actuator changes operation of the OPO from below a threshold for lasing of the resonating EM wave to above the threshold.

8. The sensor of claim 1, wherein the resonator is configurable to operate near an oscillation threshold for lasing of the resonating EM wave, characterized in that 0.9≤Pump power / Threshold pump power≤3, or The actuator can be configured to set the detuning or the phase matching such that the resonator operates at least at a spectral phase change between degenerate and non-degenerate operation and / or the resonant EM wave includes a syncron.

9. The sensor of claim 1, wherein the actuator causes the resonant EM wave in the resonator to follow a predictable spectral tuning, and the output EM wave can be used to reconstruct the functionality of a tunable laser spectrometer.

10. The sensor of claim 1, wherein the actuator is configured to modulate at least one of the pump power, the detuning, or the phase matching to tune a dynamic range, sensitivity, or selectivity of the sensor.

11. The sensor of claim 1, wherein the information comprises at least a concentration or composition difference of the sample, the sample comprising one or more molecules.

12. The sensor of claim 1, wherein the information comprises a physical or chemical property of the sample, the sample comprising a solid, a liquid, or a gas.

13. The sensor of claim 1, wherein the information is output in real time with sample variation and with a time resolution limited by the modulation or actuation speed of the actuator and the acquisition time of the information.

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

15. The sensor of claim 1, wherein the actuator comprises a scanner that applies one or more ramp functions that modulate at least one of the pump power, the detuning, or the phase matching.

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

17. The sensor of claim 1 , further comprising means for causing the resonant EM wave of the resonator to interact with the sample, wherein the means comprises a sample container positioned to couple the sample to the resonator via an evanescent field, a slot waveguide, an optical fiber, a chamber in the resonator, fluid coupling, free space coupling, or a hollow core fiber.

18. The sensor of claim 1, wherein: The resonator includes a cavity including a nonlinear material between mirrors, and the cavity includes a sample space for positioning a sample within the cavity.

19. The sensor of claim 1, wherein the resonator comprises a fiber optic loop coupled to the nonlinear material.

20. An analyzer comprising the sensor of claim 1, the sensor outputting information about the sample, the sample comprising breath, atmospheric concentrations of pollutants or greenhouse gases, or process gases monitored in an industrial environment.

21. The sensor of claim 1, wherein the information includes a concentration of the sample in the range of parts per trillion to a few percent by volume, the concentration causing saturation in a linear absorption sensor according to Beer-Lambert's law.

22. A sensing method comprising: coupling a sample to a resonator, the resonator comprising a nonlinear material, the nonlinear material comprising a nonlinear susceptibility, the nonlinear material 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, or the idler EM wave 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 wave, a detuning of a frequency mode of the resonator relative to one or more frequencies of the resonating EM wave, or a phase matching of the nonlinear material; detecting an output power of one or more output EM waves output by the resonator; as well as Information about the samples is calculated from changes in the output power in response to the samples and the modulation.

23. A computer-implemented system comprising: one or more processors; receiving output power of one or more output electromagnetic (EM) waves output from a resonator when the resonator is coupled to a sample, the resonator comprising a nonlinear material, the nonlinear material comprising a nonlinear susceptibility, the nonlinear material 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, or the idler EM wave is fed back through the nonlinear material to form one or more resonant photons; controlling actuation of at least one of a pump power of the pump EM wave, a detuning of a frequency mode of the resonator relative to one or more frequencies of the resonating photons, or a phase matching of a nonlinear material when the sample is coupled to the resonator; as well as Information about the sample is calculated from a change in the output power in response to the sample and the actuation.

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