Optical frequency compensation method, apparatus, device, medium, and computer program product

Abstract

The present application relates to the technical field of optical frequency compensation, and provides an optical frequency compensation method, device, equipment, medium and computer program product, the method comprising: extracting resonance frequencies of adjacent optical modes of the same mode family; determining a free spectral range value according to the resonance frequencies of the adjacent optical modes of the same mode family; analyzing the change trend of the free spectral range value to obtain a reverse structure compensation amount; and feeding back the physical structure of a target resonator based on the reverse structure compensation amount to compensate for the optical frequency drift locked to the target resonator. Through the active compensation mode, the present application obtains the optical frequency change caused by the geometric thermal expansion of the target resonator cavity, determines the reverse structure compensation amount based on the change trend of the free spectral range value, and feeds back the reverse structure compensation micro stress to the resonator to realize the dynamic compensation of the optical frequency of the target resonator, thereby solving the frequency drift of the resonator caused by thermal expansion.

Description

Technical Field

[0001] This invention relates to the field of optical frequency compensation technology, and in particular to an optical frequency compensation method, apparatus, equipment, medium, and computer program product. Background Technology

[0002] The thermal stability of resonators is crucial for their application. Thermal expansion of the resonator cavity causes changes in its geometric dimensions, a key factor affecting the long-term stability of the resonant frequency. Existing methods to suppress frequency drift caused by thermal expansion include using materials with near-zero thermal expansion coefficients, or sandwiching the resonator within a symmetrical structure to passively offset thermal expansion. However, these methods represent passive compensation in the resonator's structural design; once the structure is set, its compensation capability cannot be dynamically adjusted, making it difficult to adapt to nonlinear temperature disturbances or localized stress problems caused by structural asymmetry. Summary of the Invention

[0003] This invention provides an optical frequency compensation method, apparatus, device, medium, and computer program product to solve the frequency drift problem caused by thermal expansion of existing resonators and to dynamically compensate for the frequency drift caused by thermal expansion of resonators.

[0004] This invention provides an optical frequency compensation method, comprising the following steps:

[0005] Extract the resonant frequencies of adjacent optical modes in the same mode family;

[0006] The free spectral range value is determined based on the resonance frequencies of adjacent optical modes in the same mode family;

[0007] The variation trend of the free spectral range value is analyzed to obtain the reverse structure compensation amount;

[0008] Based on the reverse structure compensation amount, the physical structure of the target resonator is fed back to compensate for the optical frequency drift locked to the target resonator.

[0009] According to the optical frequency compensation method provided by the present invention, the extraction of the resonant frequencies of adjacent optical modes in the same mode family includes:

[0010] Multiple laser sources are used to excite adjacent optical modes of the same mode family in the target resonator;

[0011] The resonant frequencies of adjacent optical modes in the same mode family are read.

[0012] According to the optical frequency compensation method provided by the present invention, determining the free spectral range value based on the resonant frequencies of adjacent optical modes in the same mode family includes:

[0013] Beat frequencies of multiple laser sources in adjacent optical modes of the same mode family locked to the target resonator are used to suppress polarization-dependent common-mode thermal refraction noise and obtain free spectral range values.

[0014] According to the optical frequency compensation method provided by the present invention, the step of analyzing the variation trend of the free spectral range value to obtain the reverse structure compensation amount includes:

[0015] The variation trend of the free spectral range value is tracked and fitted to obtain the variation parameter of the free spectral range value;

[0016] The reverse structure compensation amount is determined based on the aforementioned changing parameters.

[0017] According to the optical frequency compensation method provided by the present invention, the step of feeding back the physical structure of the target resonator based on the reverse structure compensation amount to compensate for the optical frequency drift locked to the target resonator includes:

[0018] Based on the aforementioned reverse structure compensation amount, the piezoelectric actuator is controlled to apply strain to the key structural positions of the target resonator.

[0019] Based on the strain application results, the optical frequency drift locked to the target resonator is compensated.

[0020] According to the optical frequency compensation method provided by the present invention, the step of feeding back the physical structure of the target resonator based on the reverse structure compensation amount to compensate for the optical frequency drift locked to the target resonator includes:

[0021] When the cavity of the target resonator is made of a material with piezoelectric effect, the signal determined based on the reverse structure compensation amount is fed back to the electrodes in the cavity of the target resonator.

[0022] By changing the electric field in the cavity of the target resonator through the electrodes, the mechanical deformation of the target resonator is regulated, thereby compensating for the optical frequency drift locked to the target resonator.

[0023] The present invention also provides an optical frequency compensation device, comprising the following modules:

[0024] The extraction module is used to extract the resonant frequencies of adjacent optical modes in the same mode family;

[0025] The free spectral range value determination module is used to determine the free spectral range value based on the resonance frequencies of adjacent optical modes in the same mode family;

[0026] The reverse structure compensation amount determination module is used to analyze the variation trend of the free spectral range value to obtain the reverse structure compensation amount;

[0027] The optical frequency compensation module is used to provide feedback on the physical structure of the target resonator based on the reverse structure compensation amount, and to compensate for the optical frequency drift locked to the target resonator.

[0028] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and running on the processor, wherein the processor executes the computer program to implement the optical frequency compensation method as described above.

[0029] The present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the optical frequency compensation method as described above.

[0030] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the optical frequency compensation method as described above.

[0031] The optical frequency compensation method, device, equipment, medium, and computer program product provided by this invention propose a method for measuring and controlling frequency drift due to thermal expansion based on changes in the free spectral range. By actively compensating, the optical frequency change caused by the geometric thermal expansion of the target resonator cavity is obtained. The reverse structural compensation amount is determined based on the trend of the free spectral range value. By applying reverse structural compensation micro-stress to the resonator, dynamic compensation of the optical frequency of the target resonator is achieved, thereby solving the frequency drift of the resonator caused by thermal expansion. Attached Figure Description

[0032] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0033] Figure 1 This is one of the flowcharts of the optical frequency compensation method provided by the present invention.

[0034] Figure 2a This is a schematic diagram of the FSR measurement system.

[0035] Figure 2b This is a comparison chart of the allen deviation between FSR measurement data and the RF reference from the rubidium clock.

[0036] Figure 3 This is the second flowchart of the optical frequency compensation method provided by the present invention.

[0037] Figure 4 This is a schematic diagram of the optical frequency compensation device provided by the present invention.

[0038] Figure 5 This is a schematic diagram of the structure of the electronic device provided by the present invention. Detailed Implementation

[0039] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0040] Specifically, determining whether the resonator has experienced optical frequency drift due to thermal expansion requires comprehensive analysis by monitoring the resonant frequency shift and considering temperature changes. The mechanism by which ambient temperature fluctuations cause optical frequency drift is as follows: the resonant frequency of the resonator is determined by the cavity length and the refractive index of the medium. When the temperature changes, the cavity length changes with the temperature, and the refractive index of the medium is affected by the thermo-optical effect. Combining these two factors (cavity length and refractive index of the medium), the optical frequency shift, i.e., the frequency drift, can be obtained. The verification method for the frequency drift is as follows: using a stable laser source as the reference optical path, the reference light is coupled (mixed) with the output light of the resonator to generate a beat frequency signal. The frequency drift is calculated by monitoring the changes in the beat frequency signal. All slow changes in the beat frequency signal are attributed to the structural thermal expansion of the resonator.

[0041] The following is combined with Figures 1-5 This invention describes the optical frequency compensation method, apparatus, device, medium, and computer program product.

[0042] Figure 1 This is one of the flowcharts illustrating the optical frequency compensation method provided by the present invention, such as... Figure 1 As shown, the method includes the following:

[0043] Step 100: Extract the resonant frequencies of adjacent optical modes in the same mode family;

[0044] This invention excites adjacent optical modes of the same mode family in a target resonator (hereinafter referred to as the resonator) using multiple laser sources. The resonant frequencies of the aforementioned adjacent optical modes of the same mode family can be read in real time using a photodetector or a frequency meter.

[0045] (1)

[0046] As shown in Equation 1, the temperature dependence of the resonant frequency of the resonator is described by the thermal refractive index and the thermal expansion coefficient, where, The resonant frequency of the resonator. The resonant frequency is the rate of change with temperature T. The thermal refractive index of the material, This represents the coefficient of thermal expansion of the material. Generally, the coefficient of thermal expansion of optical microresonators is much larger than the coefficient of thermal refractive index, and the resonant frequency drift is dominated by thermal expansion noise.

[0047] Step 200: Determine the free spectral range value based on the resonance frequencies of adjacent optical modes in the same mode family;

[0048] The frequency-locking method (Pound-Drever-Hall, PDH) involves modulating and demodulating the transmission spectrum, generating an error signal, and performing current feedback to lock the laser frequency to an adjacent optical mode within the same mode family. By beating the frequencies of multiple laser sources, since the adjacent optical modes are of the same mode family and polarization state, the beating frequency can suppress polarization-dependent common-mode thermal refractive noise, yielding a free spectral range (FSR). This FSR changes with the thermal expansion of the resonator structure (e.g., changes in length or radius), and can serve as a direct characterization of optical path variation.

[0049] ; (2)

[0050] As shown in Equation 2, the frequency difference between adjacent optical modes in the same mode family is related to the FSR, where, The frequency difference between adjacent optical modes in the same mode family is the free spectral range value (FSR). The free spectral range value of FSR versus temperature The rate of change, that is, the drift of FSR with temperature; R is the speed of light in a vacuum; R is the radius of the optical resonator; and n is the refractive index of the material that makes up the resonator.

[0051] Step 300: Analyze the changing trend of the free spectral range value to obtain the reverse structure compensation amount;

[0052] The FSR signal is input to a controller (e.g., digital logic or analog phase-locked loop circuit) to track and fit the changing trend of the free spectral range value in real time. Based on the amplitude and rate of change of the FSR, the controller calculates the amount of reverse structure compensation that needs to be applied to the target resonator. For example, an error signal is generated by mixing the FSR signal with a local oscillator reference RF source using a low-pass filter. The local oscillator reference RF source can be a rubidium clock.

[0053] FSR measurement system such as Figure 2aAs shown, PZT stands for lead zirconate titanate. WGMR stands for Whispering Gallery Mode Resonator. laser1 and laser2 are both continuous-wave lasers; EOM stands for Electro-Optic Modulator, which applies the required radio frequency phase modulation to generate a PDH error signal; PC stands for Polarization Controller; OC stands for optical circulator; PD stands for photodetector; moku1 and moku2 are both integrated measurement and testing instruments with an internal frequency-locking module. This frequency-locking module is configured to: receive an electrical signal from the photodetector, process the electrical signal based on PDH (Pound-Drever-Hall) technology to generate a PDH error signal, and perform a proportional-integral-derivative (PID) operation on the error signal to generate a feedback signal; the feedback signal is output to the corresponding laser, thereby locking the laser's output frequency to the resonant frequency of the optical resonator (such as WGMR mentioned above).

[0054] This FSR measurement system operates based on the principle of dual-laser PDH frequency locking and beat frequency detection. Through high-precision feedback control, the frequencies of the two lasers are stably locked to different resonant modes of the WGMR, and the free spectral range is calculated using the relationship between mode interval and beat frequency. Specifically, during system operation, the continuous laser outputs from Laser1 and Laser2 first pass through an electro-optic modulator (EOM) to apply radio frequency phase modulation to generate sidebands. The modulated light is then optimized for polarization by a polarization controller (PC) before being injected into the WGMR through a circulator (OC). When the laser frequency is misaligned with the cavity resonant frequency, the reflected light carrying error information is fed into a photodetector (PD) via the circulator, converted into an electrical signal, and sent to the frequency locking module of the Moku device. This module mixes, filters, and demodulates the PDH error signal, generates a feedback signal through PID calculation, and feeds it back to the laser's PZT or current tuning terminal, forming a closed-loop control that forces the laser frequency to track the cavity resonant frequency in real time, achieving ultra-stable locking.

[0055] Once locked, the two laser beams exhibit extremely high frequency stability and each corresponds to a specific mode of WGMR (interval Δm FSRs). The two beams are combined and input into another photodetector to generate a beat frequency signal; the frequency Δν is the frequency difference between the two lasers. Since Δν = Δm × FSR, by accurately measuring Δν (using a frequency counter) and combining it with the known mode interval Δm, the free spectral range value of WGMR, FSR = Δν / Δm, can be calculated.

[0056] Figure 2b The graph shows the allan deviation between the FSR measurement data and the RF-Rb ref referenced to the rubidium clock, illustrating the frequency stability of both over time. The relationship between (Times) and the frequency stability of the FSR is shown. The results indicate that the frequency stability of the FSR is significantly worse than that of the RF reference throughout the entire time range.

[0057] ; (3)

[0058] As shown in Equation 3, the FSR to be measured is compared with the stable reference (f ref The error signal obtained after mixing and low-pass filtering is essentially a baseband representation of phase or frequency error. This is the baseband error signal after phase-sensitive detection. The amplitude gain constant of the phase-detection mixer to baseband link is determined by the mixer conversion factor, the amplitudes of the two inputs, and the low-pass / amplifier gain. f is the instantaneous frequency of the FSR to be measured. ref This is the nominal frequency of the local oscillator reference RF source.

[0059] This represents the phase error between the two signals from 0 to t. This is the static phase offset / phase setpoint.

[0060] (4)

[0061] (5)

[0062] The error signal can be processed by servo control to obtain the feedback signal. As shown in formula (4), the error signal can be processed by the three-term gain algorithm, namely P, I, D, to obtain the feedback signal. , For proportional gain, For integral gain, This is the differential gain. This represents the real-time error value at every instant within the time interval [0, t]. The servo control system LB1005 can implement this feedback control. The LB1005 controller transfer function can be expressed as formula (5), where C is the reverse structure compensation amount. It is the Laplace transform of e(t). It is the representation of the control signal after PI processing in the complex frequency domain, where K is the linear gain of the main gain knob. The scaling factor introduced by the low-frequency gain limitation. The transition frequency is at which the proportional gain is equal to the amplitude of the integral channel. Increasing this frequency will cause the integral action to begin at a higher frequency. For the Laplace operator.

[0063] The LB1005 servo control system processes the feedback signal used to drive the actuator through internal circuitry. The function of the LB1005 servo control system is to treat the error signal generated by mixing as 0, that is, to align the FSR with the local oscillator reference RF source, locking a quantity affected by environmental disturbances to the reference RF. This reduces the impact of ambient temperature on the cavity size of the target resonator and reduces the impact of thermal expansion noise on the laser frequency.

[0064] Step 400: Based on the reverse structure compensation amount, feedback is provided on the physical structure of the target resonator to compensate for the optical frequency drift locked to the target resonator.

[0065] Specifically, the controller outputs a feedback signal to drive the actuator, which can be a piezoelectric ceramic, a micro-electro-mechanical system (MEMS) stress-driven material, or a thermo-optical deformable material, etc., to apply strain to the key structural position of the target resonator, change the actual length or shape of the resonance path, and thus counteract the optical frequency shift caused by thermal expansion.

[0066] (6)

[0067] (7)

[0068] Converting the reverse structural compensation amount into physical strain, it can be expressed by piezoelectric braking as formula (6), where... For reverse strain, is the strain coefficient. If it is a resonant cavity with piezoelectric effect, it can be controlled by an electric field, expressed as formula (7), where, denoted as piezoelectric coefficient, and E as electric field strength.

[0069] This embodiment obtains the optical frequency change caused by the geometric thermal expansion of the target resonator cavity through active compensation, determines the reverse structure compensation amount based on the change trend of the free spectral range value, and achieves dynamic compensation of the optical frequency of the target resonator by feeding back the reverse structure compensation micro-stress to the resonator, thereby solving the frequency drift of the resonator caused by thermal expansion.

[0070] In one embodiment of the optical frequency compensation method provided by the present invention, the extraction of the resonant frequencies of adjacent optical modes in the same mode family includes:

[0071] Step 110: Excite adjacent optical modes of the same mode family in the target resonator using multiple laser sources;

[0072] Step 120: Read the resonant frequencies of adjacent optical modes in the same mode family.

[0073] In practice, the frequency of the laser source is actively locked to an adjacent optical mode within the same mode family. First, resonator design and mode analysis are performed. Based on the target resonator structure, the optical modes are analyzed. The resonant frequencies and spatial field distribution data of each order of optical modes in the longitudinal direction are calculated by solving the Helmholtz equation or using finite element simulation. Based on the calculated resonant frequency data, the required mode frequency band range is determined.

[0074] Next, the laser coupling conditions are optimized based on the calculated spatial field distribution data. Phase matching is achieved by precisely adjusting the laser incident angle and position. For the longitudinal mode, the laser wavelength is adjusted to be close to the calculated resonant frequencies of multiple longitudinal modes (i.e., the resonant frequencies of the longitudinal modes calculated above). The laser is precisely aligned with the field distribution energy concentration area determined by the simulation. At the same time, an adjustable coupler is used to control the coupling strength to ensure that each mode can achieve the best excitation efficiency.

[0075] Then, multi-mode excitation is implemented using the calculated resonant frequency data. A broadband laser source is used to cover the frequency band of the above modes. A sideband covering the resonant frequency interval of adjacent longitudinal modes is generated by frequency modulation. A phase pattern designed based on simulated spatial field distribution data is loaded using a spatial light modulator to match the field distribution of higher-order transverse modes. New frequency components are generated under high power conditions using nonlinear effects such as four-wave mixing.

[0076] During this process, resonator parameters are adjusted simultaneously. Based on the resonant frequency data calculated above, the frequency spacing of different modes is matched with the calculation results through dispersion engineering design. The loss is adjusted to make the quality factor of the target mode close to the target mode, avoiding the dominance of a single mode. At the same time, dynamic tuning techniques such as thermo-optic, electro-optic, or mechanical stress are used to adjust the cavity length or refractive index in real time to precisely control the mode resonant frequency.

[0077] Finally, the resonant frequency was accurately read through verification and optimization. By scanning the laser wavelength and monitoring the transmission spectrum, the observed experimental resonance peak was compared with the calculated resonant frequency sequence. At the same time, the spatial light intensity distribution observed by the charge-coupled device camera (CCD) was quantitatively compared with the spatial field distribution data obtained by simulation. Based on the difference between the experimentally measured resonant frequency, linewidth, and other data and the theoretically calculated values, a proportional-integral-derivative controller (PID controller) or machine learning algorithm was used to implement feedback control, dynamically optimize the laser coupling conditions and resonator parameters, and ensure that the entire measurement device works stably and outputs accurate resonant frequency data.

[0078] This embodiment excites multiple orders of optical modes in a resonator and reads the resonant frequencies of various optical modes in real time, providing data support for subsequent frequency compensation.

[0079] In one embodiment, the optical frequency compensation method provided by this invention, wherein determining the free spectral range value based on the resonant frequencies of adjacent optical modes in the same mode family includes: performing frequency beat analysis on the frequencies of multiple laser sources of adjacent optical modes in the same mode family locked to the target resonator to suppress polarization-dependent common-mode thermal refraction noise, thereby obtaining the free spectral range value. Specifically, this includes:

[0080] Step 210: Lock the frequencies of multiple laser sources to adjacent optical modes of the same mode family;

[0081] Step 220: Beat the frequencies of multiple laser sources to obtain the free spectral range value.

[0082] This invention locks the frequencies of multiple laser sources to adjacent optical modes within the same mode family and beats these laser frequencies to obtain free spectral range values. Specifically, when determining adjacent optical modes within the same mode family, frequency domain analysis is first used to identify mode spacing and spectral characteristics. Vertical modes exhibit an equidistant frequency distribution determined by the cavity length, and the frequency difference between adjacent vertical modes constitutes a free spectral range. This equidistant characteristic can be verified by observing the resonance peaks in the transmission spectrum while scanning the laser wavelength. Radial modes exhibit a non-equidistant distribution due to their frequency spacing being related to the radial quantum number. Adjacent radial modes refer to modes with a radial quantum number difference of 1 at the same angular momentum number. This non-equidistant characteristic requires a high-resolution spectrometer for resolution. The frequency characteristics of folded path modes are determined by the equivalent cavity length of the folded optical path and need to be verified by comparing the optical path simulation results with the measured transmission spectrum. Further spatial domain analysis is used to observe the mode field distribution. The number of nodes in the field distribution of adjacent higher-order modes increases by 1 in transverse modes, while the number of radial nodes in adjacent radial modes differs by 1. These spatial characteristics can be verified by directly observing the light intensity distribution using a CCD camera or a near-field scanning optical microscope. Meanwhile, based on the analysis of mode coupling and competition behavior, when the pump power increases, some adjacent optical modes will experience nonlinear growth due to gain competition, while other modes will be suppressed. If two adjacent optical modes are excited at the same time, the beat frequency signal of their frequency difference can be received by the detector as auxiliary evidence.

[0083] In an optical resonator, the free spectral range, serving as the resonant frequency interval between adjacent optical modes within the same mode family, is determined by its geometry and optical parameters. Multiple resonance peaks can be identified by scanning the input wavelength of the resonator with a tunable laser, recording the transmitted or reflected signals, and then directly measuring the frequency difference between adjacent longitudinal modes to obtain the free spectral range value. This embodiment determines the free spectral range value using the resonant frequencies of adjacent optical modes within the same mode family, providing data support for subsequent frequency compensation.

[0084] In one embodiment of the optical frequency compensation method provided by the present invention, the step of analyzing the variation trend of the free spectral range value to obtain the reverse structure compensation amount includes:

[0085] Step 310: Track and fit the changing trend of the free spectral range value to obtain the changing parameters of the free spectral range value;

[0086] Step 320: Determine the reverse structure compensation amount based on the changed parameters.

[0087] Specifically, this embodiment illustrates the process of optical frequency compensation according to the present invention through the following example. When the ambient temperature changes, the resonator cavity size undergoes thermal expansion or contraction, and the refractive index of the material also changes. Although the thermo-optical effect can usually be compensated by in-cavity power feedback, the radius change caused by the thermal expansion of the resonator cavity directly leads to FSR changes, thereby causing a drift in the repetition frequency of the output optical frequency comb. The fundamental mode and adjacent optical modes in the resonator cavity are excited by pumping with a continuous wave laser. The frequencies of adjacent optical modes in the same mode family are collected using a high-speed photodetector, and the FSR changes between adjacent optical modes are extracted in real time. By performing time-series analysis on the continuously collected free spectral range data, the change rate, change amplitude, and other change parameters are fitted. Based on the pre-established change parameter-strain mapping relationship, the change rate is converted into a strain adjustment rate, and the change amplitude is converted into a reference strain adjustment amount. The two together constitute the inverse structural compensation amount. By using an actuator installed on the resonator cavity, a reference strain adjustment amount is dynamically applied according to the calculated strain adjustment rate, and a corresponding reverse mechanical strain is applied. The structural deformation generated by this strain directly offsets the cavity size change caused by thermal expansion, thereby effectively suppressing the repetition frequency fluctuation dominated by thermodynamic noise in the resonator optical frequency comb system.

[0088] This embodiment obtains the reverse structure compensation amount used to offset optical frequency shift by tracking and analyzing the changing trend of the free spectral range value.

[0089] Figure 3 This is the second flowchart of the optical frequency compensation method provided by the present invention, as shown in Figure 2. The step of feeding back the physical structure of the target resonator based on the reverse structure compensation amount to compensate for the optical frequency drift locked to the target resonator includes:

[0090] Step 410: Based on the reverse structure compensation amount, control the piezoelectric actuator to apply strain to the key structural positions of the target resonator;

[0091] Step 420: Based on the strain application result, compensate for the optical frequency drift locked to the target resonator. That is, based on the strain application result, compensate for the optical frequency corresponding to the target resonator.

[0092] Specifically, this embodiment further illustrates the process of optical frequency compensation of the present invention through the following examples. A dual-fiber coupling structure is adopted, such as single-mode fiber coupling modes with different polarization states and longitudinal orders respectively, to simultaneously excite optical modes with orthogonal polarization and different longitudinal orders, including one set of orthogonal polarization modes (such as TE). 000 With TM 000 ) and 1 group of co-polarized adjacent longitudinal modes (such as TE) 000 With TE 001A three-mode difference frequency architecture was constructed, in which the frequency difference of orthogonal polarization modes is only affected by the change in the material's refractive index (thermo-optic effect), and the spacing between adjacent longitudinal modes with the same polarization, i.e., the FSR, is only affected by the geometrical changes caused by thermal expansion, thereby achieving the separation of the frequency response of the thermo-optic effect and the structural thermal expansion effect. This was achieved using the orthogonal polarization mode TE... 000 With TM 000 The frequency difference between the modes is monitored in real time to detect the temperature change of the mode volume inside the resonator cavity, while the frequency difference between the two modes is also monitored. 000 With TE 001 The variation in the free spectral range reflects the information of the cavity's geometric thermal expansion. The above frequency difference signal and the free spectral range variation signal are fed back to the piezoelectric actuator, which drives the piezoelectric actuator to apply reverse micro-strain according to the reverse structure compensation amount. This actively compensates for the optical frequency shift caused by the thermal expansion of the resonator cavity structure, thereby improving optical frequency stability.

[0093] TE (Transverse Electric) refers to an optical mode where the electric field direction is completely perpendicular to the light propagation direction within the resonator (i.e., the electric field has no component along the propagation direction), and only the magnetic field has a component along the propagation direction. TM (Transverse Magnetic) refers to an optical mode where the magnetic field direction is completely perpendicular to the light propagation direction within the resonator (i.e., the magnetic field has no component along the propagation direction), and only the electric field has a component along the propagation direction. TM and TE modes are orthogonal; in the same resonator, the electric field direction of the TM mode is perpendicular to that of the TE mode. The subscripts after TE and TM (e.g., "000" or "001") represent the radial, poloidal, and circumferential orders of the optical mode. The subscript consists of three numbers: the first number represents the radial order (denoted as p), the middle number represents the poloidal order (denoted as l), and the last number represents the circumferential order (denoted as m). p describes the number of nodes in the field distribution of the optical mode in the radial direction (i.e., the direction of the cross-sectional radius perpendicular to the propagation direction) of the resonator. p=0 indicates no nodes in the radial direction, p=1 indicates one node in the radial direction, and so on. l describes the number of nodes in the field distribution of the optical mode in the poloidal direction (along the spherical / thickness direction) of the resonator. l=0 indicates no nodes in the poloidal direction, l=1 indicates one node in the poloidal direction, and so on. m describes the number of periods in the field distribution of the optical mode in the circumferential direction (i.e., the circumferential direction along the propagation direction) of the resonator. m=0 indicates no phase change along the circumference, m=1 indicates one periodic change along the circumference, and so on.

[0094] For different resonator cavities, such as FP cavities, the PZT can be controlled to change the cavity mirror spacing to compensate for optical path changes caused by thermal expansion; for fiber optic cavities, the fiber can be wound around a circular PZT, and the radial expansion and contraction of the PZT can be used to change the fiber length to achieve compensation. During strain application, the changes in the free spectral range are continuously monitored, and the strain parameters are dynamically adjusted based on the monitoring results to form a closed-loop control circuit.

[0095] The key structural locations mentioned above need to be determined in conjunction with the resonator's structural characteristics. The key structural locations of the FP cavity can be the cavity mirror fixing end or the connection point between the cavity mirror and the cavity support structure. Specifically, the PZT needs to be physically connected to at least one cavity mirror of the FP cavity at this cavity mirror fixing end. When thermal expansion causes the mirror spacing to increase, the PZT applies axial compressive strain to the cavity mirror fixing end, directly shortening the cavity mirror spacing; if thermal expansion causes the mirror spacing to decrease, the PZT applies axial tensile strain to extend the mirror spacing, ultimately achieving optical path compensation.

[0096] The critical structural location of the fiber cavity is the contact area where the optical fiber is wound around the circular PZT, specifically the area where the optical fiber and the outer surface of the circular PZT are in contact. In essence, the optical fiber must be tightly wound around the outer surface of the circular PZT, and this contact area is the critical structural location for strain transfer. When thermal expansion causes the optical fiber to elongate, the PZT contracts radially, and its outer surface applies compressive strain to the wound optical fiber through the contact area, shortening the fiber length. Conversely, if thermal expansion causes the optical fiber to shorten, the PZT expands radially, applying tensile strain to the optical fiber through the contact area, lengthening the fiber.

[0097] This embodiment achieves long-term stability of the resonator's optical frequency by applying a reverse micro-strain based on a value determined by the free spectral range through a driving actuator.

[0098] Based on the aforementioned reverse structure compensation amount, feedback is provided to the physical structure of the target resonator to compensate for the optical frequency drift locked to the target resonator, which may further include:

[0099] Step 430: When the cavity of the target resonator is made of a material with piezoelectric effect, the signal determined based on the reverse structure compensation amount is fed back to the electrodes in the cavity of the target resonator.

[0100] This process is applicable to materials exhibiting the piezoelectric effect. The core characteristic of these materials is that they undergo mechanical deformation under the influence of an external electric field, which is the inverse effect of the piezoelectric effect—that is, the electric field is converted into strain. Unlike traditional solutions that use an external PZT as an actuating device, the resonator cavity itself here possesses both resonance and actuation functions, eliminating the need for an external PZT. Strain control can be achieved simply by pre-setting electrodes within the cavity, offering the technical advantages of not altering the cavity's structure and high adaptability.

[0101] Based on the reverse structural compensation amount obtained from the analysis of FSR variation trends, the controller converts this compensation amount into an electrode driving electrical signal. The signal type is a voltage signal, and the inverse piezoelectric effect response is directly related to the voltage intensity. The signal parameters include voltage amplitude and frequency, which need to be matched with the piezoelectric coefficient of the cavity material, such as the d-coefficient of lithium niobate. 33 The piezoelectric coefficient, reflecting the conversion efficiency between electric field and deformation, ensures that the electrical signal can accurately counteract the geometrical changes required to offset thermal expansion. Metal electrodes, such as gold or silver electrodes, are pre-installed at key locations within the resonator cavity, such as the upper and lower surfaces and radial sidewalls, to ensure conductivity and electric field uniformity. The generated electrode-driving electrical signal is directly connected to these pre-installed electrodes, forming an electrical signal transmission path from the controller to the electrodes to the cavity, replacing the mechanical strain transmission path of the controller-PZT-cavity in traditional solutions.

[0102] Step 440: Change the electric field in the cavity of the target resonator through the electrode, regulate the mechanical deformation of the target resonator, and compensate for the optical frequency drift locked to the target resonator.

[0103] After the electrodes are connected to the driving electrical signal, a uniform external electric field is formed inside the resonator cavity. The direction of the electric field matches the direction of cavity deformation. For example, when the upper and lower electrodes are energized, an electric field perpendicular to the cavity surface is formed, driving the cavity to expand and contract axially. Based on the inverse effect of the piezoelectric effect, the cavity material undergoes mechanical deformation opposite to the direction of thermal expansion under the action of this electric field. For example, when thermal expansion causes the radial radius of the lithium niobate cavity to increase, the optical path length to lengthen, and the FSR to decrease, the external electric field drives the cavity to contract radially, shortening the radius; when thermal expansion causes the axial length of the cavity to lengthen, the external electric field drives the cavity to compress axially, shortening the length, thus achieving the reverse cancellation of the geometric changes caused by thermal expansion.

[0104] Reverse adjustment of the cavity geometry directly alters its effective optical length, where the FSR is inversely proportional to the effective optical length, as shown in the formula: c is the speed of light. For effective optical length. When thermal expansion causes When the electric field increases and the FSR decreases, the electric field-driven deformation causes... Once the initial stable value is restored, the FSR synchronously returns to the target range, ultimately locking the optical frequency of the resonator, offsetting the optical frequency drift caused by thermal expansion, and completing the compensation closed loop.

[0105] Traditional solutions require external actuators such as PZTs and mechanical connection structures. This invention, however, utilizes the piezoelectric effect of the cavity itself to directly control dimensions via electrode-electric field, eliminating the need for additional external actuators and mechanical connections. This significantly simplifies the system structure, making it more suitable for chip-level system packaging requirements and avoiding the shortcomings of traditional solutions that are unsuitable for conventional chip-level system packaging. Furthermore, the response link of electrical signal-electric field-deformation has no mechanical transmission delay, resulting in a response speed faster than external PZTs, reaching microsecond levels (compared to millisecond levels for external PZTs). This allows for faster response to high-frequency temperature fluctuations, meeting the requirements for real-time dynamic adjustment and adapting to environmental fluctuations. This invention only requires pre-setting electrodes within the cavity, without altering the required geometry and material properties for cavity resonance. This avoids the localized stress unevenness problems that can occur with the mechanical clamping of external PZTs, overcoming the difficulty of traditional solutions in handling localized stress unevenness. Moreover, this solution is directly compatible with all resonator materials exhibiting piezoelectric effects, such as lithium niobate and lithium tantalate, eliminating the need to redesign the connection structure of external actuators for different materials. This allows it to be used in different types of optical resonator systems.

[0106] Consistent with the closed-loop logic of FSR sensing, control judgment, and structural feedback, the controller continuously monitors the FSR and dynamically adjusts the parameters of the electrode drive electrical signals, such as voltage amplitude, to precisely control the cavity deformation amplitude and ensure that the FSR remains stable within the target range. For example, when the rate of thermal expansion accelerates and causes the FSR to decrease more rapidly, the controller increases the electrode voltage to enhance the electric field strength and increase the cavity contraction rate; conversely, it decreases the voltage to avoid overcompensation. This dynamic adjustment mechanism further improves the long-term stability of the optical frequency, meeting the needs of photonic systems with extremely high frequency stability requirements, such as high-precision frequency references, narrow-linewidth lasers, and temperature sensors.

[0107] This invention employs an active compensation structure, applying reverse micro-strain via piezoelectric actuator feedback to achieve dynamic compensation of the optical path, thereby suppressing absolute frequency drift. Existing technologies primarily focus on dual-mode differential frequency control to achieve mode volume temperature locking, and thermal expansion noise suppression also relies on passively clamping the microcavity. While this reduces drift, it cannot respond to dynamic temperature changes. This invention, however, utilizes a piezoelectric actuator for nanometer-level closed-loop control of geometric thermal expansion. Specifically, it achieves structured optical path feedback closed-loop control in the packaged state, forming a feedback system. This invention can be seamlessly integrated into existing microcavity-frequency locking systems; differential frequency detection and PZT feedback are readily available and adjustable modules. Without altering the cavity or redesigning the thermal structure, frequency stability can be significantly improved solely through closed-loop feedback PZT, making it particularly suitable for precision measurements, laser frequency stabilization, and chip system applications requiring extremely high absolute optical frequency position.

[0108] The optical frequency compensation device provided by the present invention is described below. The optical frequency compensation device described below can be referred to in correspondence with the optical frequency compensation method described above.

[0109] Please refer to Figure 4 The present invention also provides an optical frequency compensation device, comprising:

[0110] Extraction module 510 is used to extract the resonant frequencies of adjacent optical modes in the same mode family;

[0111] The free spectral range value determination module 520 is used to determine the free spectral range value based on the resonance frequencies of adjacent optical modes in the same mode family;

[0112] The reverse structure compensation amount determination module 530 is used to analyze the changing trend of the free spectral range value to obtain the reverse structure compensation amount;

[0113] The optical frequency compensation module 540 is used to provide feedback on the physical structure of the target resonator based on the reverse structure compensation amount, and to compensate for the optical frequency drift locked to the target resonator.

[0114] Optionally, the extraction module includes:

[0115] The adjacent optical mode excitation unit of the same mode family is used to excite adjacent optical modes of the same mode family in the target resonator through multiple laser sources;

[0116] The resonant frequency reading unit is used to read the resonant frequencies of adjacent optical modes in the same mode family.

[0117] Optionally, the free spectral range value determination module is used to beat the frequencies of multiple laser sources of adjacent optical modes in the same mode family locked to the target resonator, suppress polarization-dependent common-mode thermal refraction noise, and obtain the free spectral range value.

[0118] Optionally, the reverse structure compensation amount determination module includes:

[0119] The trend analysis unit is used to track and fit the trend of the free spectral range value to obtain the change parameters of the free spectral range value;

[0120] A reverse structure compensation amount determination unit is used to determine the reverse structure compensation amount based on the changing parameters.

[0121] Optionally, the optical frequency compensation module includes:

[0122] A strain application control unit is used to control the piezoelectric actuator to apply strain to the structurally critical locations of the target resonator based on the reverse structure compensation amount.

[0123] An optical frequency compensation unit is used to compensate for optical frequency drift locked to the target resonator based on the strain application result.

[0124] Optionally, the optical frequency compensation module further includes:

[0125] An electrode feedback unit is used to feed back a signal determined based on the reverse structure compensation amount to the electrodes in the cavity of the target resonator when the cavity of the target resonator is made of a material with a piezoelectric effect.

[0126] An electric field changing unit is used to change the electric field in the cavity of the target resonator through the electrodes, thereby controlling the target resonator to generate mechanical deformation and compensating for optical frequency drift locked to the target resonator.

[0127] Figure 5 An example is a schematic diagram of the physical structure of an electronic device, such as... Figure 5 As shown, the electronic device may include a processor 610, a communications interface 620, a memory 630, and a communication bus 640. The processor 610, communications interface 620, and memory 630 communicate with each other via the communication bus 640. The processor 610 can call logic instructions in the memory 630 to execute an optical frequency compensation method. This method includes: extracting the resonant frequencies of adjacent optical modes in the same mode family; determining a free spectral range value based on the resonant frequencies of the adjacent optical modes in the same mode family; analyzing the changing trend of the free spectral range value to obtain a reverse structure compensation amount; and, based on the reverse structure compensation amount, providing feedback to the physical structure of the target resonator to compensate for the optical frequency drift locked to the target resonator.

[0128] Furthermore, the logical instructions in the aforementioned memory 630 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0129] On the other hand, the present invention also provides a computer program product, which includes a computer program that can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer can execute the optical frequency compensation method provided by the above methods. The method includes: extracting the resonance frequencies of adjacent optical modes in the same mode family; determining a free spectral range value based on the resonance frequencies of the adjacent optical modes in the same mode family; analyzing the variation trend of the free spectral range value to obtain a reverse structure compensation amount; and feeding back the physical structure of the target resonator based on the reverse structure compensation amount to compensate for the optical frequency drift locked to the target resonator.

[0130] In another aspect, the present invention also provides a non-transitory computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the optical frequency compensation method provided by the above methods. The method includes: extracting the resonant frequencies of adjacent optical modes in the same mode family; determining a free spectral range value based on the resonant frequencies of the adjacent optical modes in the same mode family; analyzing the variation trend of the free spectral range value to obtain a reverse structure compensation amount; and, based on the reverse structure compensation amount, providing feedback on the physical structure of the target resonator to compensate for the optical frequency drift locked to the target resonator.

[0131] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0132] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0133] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. An optical frequency compensation method, characterized in that, include: Extract the resonant frequencies of adjacent optical modes in the same mode family; The free spectral range value is determined based on the resonance frequencies of adjacent optical modes in the same mode family; The variation trend of the free spectral range value is analyzed to obtain the reverse structure compensation amount; Based on the reverse structure compensation amount, the physical structure of the target resonator is fed back to compensate for the optical frequency drift locked to the target resonator.

2. The optical frequency compensation method according to claim 1, characterized in that, The extraction of resonant frequencies of adjacent optical modes in the same mode family includes: Multiple laser sources are used to excite adjacent optical modes of the same mode family in the target resonator; The resonant frequencies of adjacent optical modes in the same mode family are read.

3. The optical frequency compensation method according to claim 2, characterized in that, The step of determining the free spectral range value based on the resonance frequencies of adjacent optical modes in the same mode family includes: Beat frequencies of multiple laser sources in adjacent optical modes of the same mode family locked to the target resonator are used to suppress polarization-dependent common-mode thermal refraction noise and obtain free spectral range values.

4. The optical frequency compensation method according to claim 1, characterized in that, The analysis of the variation trend of the free spectral range value yields the following reverse structure compensation amount: The variation trend of the free spectral range value is tracked and fitted to obtain the variation parameter of the free spectral range value; The reverse structure compensation amount is determined based on the aforementioned changing parameters.

5. The optical frequency compensation method according to claim 1, characterized in that, The step of feeding back the physical structure of the target resonator based on the reverse structure compensation amount to compensate for the optical frequency drift locked to the target resonator includes: Based on the aforementioned reverse structure compensation amount, the piezoelectric actuator is controlled to apply strain to the key structural positions of the target resonator. Based on the strain application results, the optical frequency drift locked to the target resonator is compensated.

6. The optical frequency compensation method according to claim 1, characterized in that, The step of feeding back the physical structure of the target resonator based on the reverse structure compensation amount to compensate for the optical frequency drift locked to the target resonator further includes: When the cavity of the target resonator is made of a material with piezoelectric effect, the signal determined based on the reverse structure compensation amount is fed back to the electrodes in the cavity of the target resonator. By changing the electric field in the cavity of the target resonator through the electrodes, the mechanical deformation of the target resonator is regulated, thereby compensating for the optical frequency drift locked to the target resonator.

7. An optical frequency compensation device, characterized in that, include: The extraction module is used to extract the resonant frequencies of adjacent optical modes in the same mode family; The free spectral range value determination module is used to determine the free spectral range value based on the resonance frequencies of adjacent optical modes in the same mode family; The reverse structure compensation amount determination module is used to analyze the variation trend of the free spectral range value to obtain the reverse structure compensation amount; The optical frequency compensation module is used to provide feedback on the physical structure of the target resonator based on the reverse structure compensation amount, and to compensate for the optical frequency drift locked to the target resonator.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that, When the processor executes the computer program, it implements the optical frequency compensation method as described in any one of claims 1 to 6.

9. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the optical frequency compensation method as described in any one of claims 1 to 6.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the optical frequency compensation method as described in any one of claims 1 to 6.

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