Modulation-free locking method and device based on spatial mode mismatch of optical resonator

Abstract

This invention relates to the field of optical resonator locking technology, and discloses a modulation-free optical resonator locking method and apparatus based on optical field spatial mode mismatch, aiming to solve the problems of complexity and noise introduction in traditional PDH locking technology systems. This method uses the superposition field of the spatial fundamental mode and the second-order transverse mode excited by mode mismatch as the input light field of the optical cavity. After breaking the mode orthogonality through pinhole clipping, the reflected light is split and a controllable Gouy phase shift is introduced. Two photodetectors detect the signals and differentially process them to generate an error signal, thus achieving optical resonator locking. This invention requires no external modulation and demodulation components, has a simple structure, high stability, and locking effect comparable to traditional PDH methods. It has low requirements for spot centering and partition consistency, providing a simple and effective way to achieve cavity frequency stabilization in precision optical systems, and is suitable for fields such as laser frequency stabilization and precision measurement.

Description

Technical Field

[0001] This invention relates to the field of optical resonator locking technology, and more specifically to a modulation-free locking method and apparatus for optical resonators based on optical field spatial mode mismatch. Background Technology

[0002] Optical resonant cavities are core components in fields such as laser frequency stabilization, precision measurement, and optical sensing. Their cavity length must be stably locked at the resonant position of the incident laser to fully utilize their high sensitivity. Generating a stable, sensitive, and noise-resistant cavity length error signal is crucial for achieving cavity length locking. Currently, the most commonly used optical cavity locking method is the Pound-Drever-Hall (PDH) technique. This technique relies on radio frequency modulation and demodulation of the optical field, requiring a large number of modulation and demodulation components. This results in extremely high noise performance requirements for electronic components and photodetectors, and a complex system structure. Furthermore, residual amplitude modulation noise is inevitably introduced during the phase modulation process, severely affecting the locking accuracy of the optical cavity.

[0003] To address the aforementioned issues, modulation-free cavity locking technology has gradually developed, among which modulation-free cavity locking technology based on higher-order spatial transverse modes has attracted widespread attention. Tilt locking is a commonly used method in modulation-free cavity locking, but this method generates error signals based on the interference between the fundamental mode and the first-order spatial mode, which is severely affected by optical field pointing noise. Another method is to use a second-order Laguerre-Gaussian (LG) mode excited by mode mismatch as an alternative reference for cavity locking. Although this can reduce optical field pointing noise, it requires the use of custom detectors such as four-quadrant detectors or bullseye detectors, which is not conducive to practical application and promotion.

[0004] Therefore, there is a need for an optical resonator locking scheme that is simple in structure, highly stable, requires no external modulation and demodulation, and can be implemented using conventional optical components, in order to solve the problems of system complexity, noise interference, and high requirements for detectors in the existing technology. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of existing optical resonator locking technologies, such as system complexity, susceptibility to noise interference, and reliance on custom detectors, and to provide a modulation-free locking method for optical resonators based on optical field spatial mode mismatch, so as to achieve modulation-free locking of optical resonators with simple structure and high long-term stability.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a modulation-free optical resonator locking method based on optical field spatial mode mismatch, comprising the following steps: Step 1: Input the fundamental mode light field into the optical resonator, and use the superimposed light field of the spatial fundamental mode and the second transverse mode excited by mode mismatch as the input light field of the optical resonator; Step 2: Cut the reflected light from the optical resonant cavity using a small aperture; Step 3: Split the reflected light after the pinhole is cut into two paths, and use two photodetectors to detect the two beams respectively; simultaneously control the Gouy phase shifts corresponding to the fundamental modes of the two beams to be respectively... and π; Step 4: Perform differential processing on the output signals of the two photodetectors to generate an error signal, and adjust the cavity length of the optical resonant cavity based on the error signal to lock it.

[0007] The spatial fundamental mode is The second-order transverse modulus is mold.

[0008] In step 1, the position of the waist spot of the incident laser is adjusted to deviate from the beam waist position of the optical resonator, thereby introducing mode mismatch to excite the fundamental mode and the second-order transverse mode in the cavity, forming a superimposed optical field of the fundamental mode and the second-order transverse mode.

[0009] In step 3, a phase-shifting lens is set in one path, and the position of the phase-shifting lens and the corresponding photodetector is adjusted to make its Gouy phase shift π. In the other path, the position of the corresponding photodetector is adjusted to make its Gouy phase shift π / 2.

[0010] Furthermore, the present invention also provides a modulation-free optical resonator locking device based on optical field spatial mode mismatch, for implementing the modulation-free optical resonator locking method based on optical field spatial mode mismatch as described in the claims, comprising: a laser source, a cavity matching lens, a pinhole aperture, a beam splitter, a phase shifting lens, a first photodetector, and a second photodetector. The light output from the laser source is incident on the optical resonant cavity after passing through the cavity matching lens. The fundamental mode and the second-order transverse mode in space are generated in the optical resonant cavity based on mode mismatch excitation. The reflected light from the optical resonant cavity is split into two beams by the beam splitter after passing through the cavity matching lens and the pinhole aperture. One beam is directly detected by the first photodetector, and the other beam is detected by the second photodetector after passing through the phase-shifting lens. The output terminals of the first and second photodetectors are connected to a differential processing circuit, the output terminal of the differential processing circuit is connected to a frequency locking module, and the output terminal of the frequency locking module is connected to a cavity length control module of the optical resonant cavity.

[0011] The frequency locking module includes a PID controller and a high-voltage amplifier. The input terminal of the PID controller is connected to the differential processing circuit, the output terminal of the PID controller is connected to the high-voltage amplifier, and the output terminal of the high-voltage amplifier is connected to the cavity length control module of the optical resonant cavity.

[0012] The aperture radius of the pinhole aperture is equal to the radius of the light spot. times.

[0013] The placement of the first photodetector satisfies the following conditions: ; The positions of the phase-shifting lens and the second photodetector satisfy the following conditions: ; in, This indicates the distance between the cavity-matching lens and the position of the first waist spot closest to the optical resonant cavity. This indicates the distance from the cavity-matching lens to the position of the second waist spot on the other side. This indicates the distance between the second waist spot position on the other side of the cavity matching lens and the first photodetector. This indicates the distance between the position of the second waist spot on the other side of the cavity-matching lens and the phase-shifting lens. This indicates the distance between the phase-shifting lens and the third waist spot position on the output side, where the second photodetector is located.

[0014] The beam splitter is a 50 / 50 beam splitter, and the optical resonant cavity is an FP cavity.

[0015] The first and second photodetectors are single-quadrant DC photodetectors.

[0016] Compared with the prior art, the present invention has the following advantages: 1. No external modulation and demodulation components required: This invention adopts a modulation-free cavity-locking scheme, which avoids the use of a large number of modulation and demodulation components in the traditional PDH method, and at the same time eliminates the residual amplitude modulation noise introduced during the optical field phase modulation process. The system structure is simple and highly stable.

[0017] 2. Relying on conventional optical components, it is highly practical: Compared with the existing four-quadrant / segmentation detection scheme based on spatial modes, the present invention only uses conventional optical components and a single-quadrant DC detector, which has lower requirements for spot centering and partition consistency. The detection system does not require special design and can independently adjust the light intensity, making the implementation process more flexible and simple, which is conducive to practical application and promotion.

[0018] 3. Excellent locking effect: This invention destroys the orthogonality of modes by spatial trimming, and combines controllable Gouy phase shift with dual detector differential structure. The generated error signal exhibits clear bipolar characteristics near the resonance point. The zero crossover point is at the same height as the center of the cavity transmission peak. The locking effect is comparable to the traditional PDH method, and it has good noise resistance.

[0019] 4. Wide range of applications: The present invention has a compact structure and high stability, and can be widely used in precision optical systems that require cavity frequency stabilization, such as laser frequency stabilization, precision measurement, and optical sensing. It is especially suitable for scenarios with high requirements for system complexity and stability. Attached Figure Description

[0020] Figure 1 This is a schematic diagram illustrating the principle of a modulation-free optical resonator locking method based on optical field spatial mode mismatch, as provided in Embodiment 1 of the present invention. Figure 2 This is a schematic diagram of a modulation-free optical resonator locking device based on optical field spatial mode mismatch provided in Embodiment 2 of the present invention; Figure 3 This is a graph showing the relationship between the interference intensity of the fundamental mode and the second-order transverse mode in this invention and the size of the pinhole; the horizontal axis is the ratio of the pinhole radius to the spot radius, and the vertical axis is the relative interference intensity; Figure 4 This is a theoretical simulation diagram of the transmission signal of the optical resonator and the detection signals of the two photodetectors in this invention; where DCA represents the detection signal of the first photodetector, DCB represents the detection signal of the second photodetector, and DCA-DCB represents the error signal obtained by differential processing. Figure 5 This is the experimental optical path diagram used in the embodiments of the present invention; Figure 6 The diagram shows the output signals of the two photodetectors and the transmission signal of the optical resonant cavity obtained in the experiment. Figure 7 The error signal and transmission signal diagrams corresponding to the fundamental mode obtained by differential processing in the experiment are shown. Figure 8 This is a comparison chart of the power spectral density of the lock-in error signal between the present invention and the traditional PDH method.

[0021] In the diagram: 1 is the laser source, 2 is the optical resonant cavity, 3 is the pinhole aperture, 4 is the beam splitter, 5 is the cavity matching lens, 6 is the first photodetector, 7 is the second photodetector, 8 is the PID controller, 9 is the differential processing circuit, 10 is the mixer, 11 is the phase-shifting lens, 12 is the light guide device, 13 is the high-voltage amplifier; 14 is the PDH cavity-locking device, 15 is the electro-optic modulator, 16 is the mixer, 17 is the low-pass filter, 18 is the third photodetector, and 19 is the local oscillator. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0023] Example 1 like Figure 1 As shown, Embodiment 1 of the present invention provides a modulation-free optical resonator locking method based on optical field spatial mode mismatch, comprising the following steps: Step 1: Input the fundamental mode light field into the optical resonator, and use the superimposed light field of the spatial fundamental mode and the second transverse mode excited by mode mismatch as the input light field of the optical resonator.

[0024] Specifically, in this embodiment, the spatial fundamental mode used is The second-order transverse modulus is mold.

[0025] Specifically, in step 1, the position of the waist spot of the incident laser is adjusted to deviate from the beam waist position of the optical resonant cavity, thereby introducing mode mismatch to excite the cavity fundamental mode and the spatial second-order transverse mode, forming a superimposed optical field of the spatial fundamental mode and the second-order transverse mode.

[0026] Step 2: Clip the reflected light from the optical resonant cavity using a pinhole aperture. Specifically, the reflected light can be clipped using a pinhole aperture.

[0027] Step 3: Split the reflected light after the pinhole is cut into two paths, and use two photodetectors to detect the two beams respectively; at the same time, control the Gouy phase shifts corresponding to the fundamental modes of the two paths to be π / 2 and π respectively.

[0028] In this embodiment, by controlling the Gouy phase shifts corresponding to the base films of the two paths to be π / 2 and π respectively, the Gouy phase shift difference between the second-order transverse mode and the fundamental mode in the first path can be π, and the Gouy phase shift difference between the second-order transverse mode and the fundamental mode in the second path can be 2π. That is, compared with the first path, the second-order transverse mode and the fundamental mode in the second path can accumulate an additional π Gouy phase shift difference, thereby making the signs of the two interference signals opposite, providing a basis for the subsequent generation of a clear zero-crossing bipolar distribution error signal.

[0029] In step 3, a phase-shifting lens is set in one path, and the position of the phase-shifting lens and the corresponding photodetector is adjusted to make the fundamental mode Gouy phase shift π. In the other path, the position of the corresponding photodetector is adjusted to make the fundamental mode Gouy phase shift π / 2.

[0030] Step 4: Perform differential processing on the output signals of the two photodetectors to generate an error signal, and adjust the cavity length of the optical resonant cavity based on the error signal to lock it.

[0031] Example 2 like Figure 2As shown, Embodiment 2 of the present invention provides a modulation-free optical resonator locking device based on optical field spatial mode mismatch, used to implement the modulation-free optical resonator locking method based on optical field spatial mode mismatch described in Embodiment 1, including: laser source 1, cavity matching lens 5, pinhole aperture 3, beam splitter 4, phase shift lens 10, first photodetector 6, second photodetector 7, differential processing circuit 9, and frequency locking module.

[0032] The light output from the laser source 1 is incident on the optical resonant cavity 2 after passing through the cavity matching lens 5. Within the optical resonant cavity 2, the fundamental mode and the second-order spatial transverse mode are generated based on mode mismatch excitation. The reflected light from the optical resonant cavity 2 is split into two beams by the beam splitter 4 after passing through the cavity matching lens 5 and the pinhole aperture 3. One beam is directly detected by the first photodetector 6, and the other beam is detected by the second photodetector 7 after passing through the phase shift lens 10. The output terminals of the first photodetector 6 and the second photodetector 7 are connected to the differential processing circuit 9. The output terminal of the differential processing circuit 9 is connected to the frequency locking module. The output terminal of the frequency locking module is connected to the cavity length control module of the optical resonant cavity 2.

[0033] Specifically, the frequency locking module includes a PID controller 8 and a high-voltage amplifier 13. The input terminal of the PID controller 8 is connected to the differential processing circuit 9, and the output terminal of the PID controller 8 is connected to the high-voltage amplifier 13. The output terminal of the high-voltage amplifier 13 is connected to the cavity length control module of the optical resonant cavity 2. The cavity length control module of the optical resonant cavity 2 can be a piezoelectric ceramic mounted on the cavity mirror.

[0034] Furthermore, in this embodiment, a light guide device 12 may also be included, which is disposed between the laser source 1 and the cavity matching lens 5, for separating the light incident on the cavity matching lens 5 from the light reflected by the cavity matching lens 5. Specifically, the light guide device 12 may be a polarizing beam splitter prism, and a half-wave plate may be disposed between it and the laser source 1, and a quarter-wave plate may be disposed between it and the cavity matching lens 5.

[0035] Specifically, in this embodiment, as Figure 3 The diagram shows the relationship between the interference intensity of the fundamental mode and the second-order transverse mode as a function of the aperture size. Therefore, in this embodiment, the aperture radius of the aperture stop 3 is taken to be equal to the spot radius. This can maximize the intensity of the interference signal. For example... Figure 4 As shown, (a) represents the detection signal and differential signal of the two photodetectors obtained from theoretical simulation, and (b) represents the transmission signal of the optical resonant cavity 2 obtained from theoretical simulation. In this embodiment, the detuning range between the laser sweep frequency range and the resonant frequency of the optical resonant cavity 2 is set to -1600 to 400 MHz to ensure that the error signal exhibits a clear zero-crossing bipolar distribution.

[0036] Specifically, in this embodiment, in the first signal detected by the first photodetector 6, the position of the first photodetector 6 should such that the Gouy phase shift of the fundamental mode is... That is, the placement of the first photodetector 6 satisfies the following conditions: (1) Furthermore, in the second signal detected by the second photodetector, the positions of the phase-shifting lens 10 and the second photodetector 7 should such that the Gouy phase shift corresponding to the fundamental mode is π, that is, the following condition must be satisfied: (2) in, This represents the Gouy phase shift from the first waist spot to the cavity-matching lens 5. This represents the Gouy phase shift from cavity-matched lens 5 to the second waist spot. This represents the Gouy phase shift from the second waist spot to the first photodetector 6. This indicates the Gouy phase shift from the second waist spot to the phase-shifting lens 10. Let Gouy phase shift be the distance from phase-shifting lens 10 to the third waist spot. Therefore, we have: (3) (4) in, This indicates the distance between the cavity matching lens 5 and the first waist spot near the optical resonant cavity. This indicates the distance from the cavity-matching lens 5 to the position of the second waist spot on the other side. This indicates the distance between the second waist spot on the other side of the cavity matching lens 5 and the first photodetector 6. This indicates the distance between the second waist spot on the other side of the cavity matching lens 5 and the phase shift lens 10. The distance between the phase-shifting lens 10 and the third waist spot on the output side is indicated, and the second photodetector 7 is positioned at the third waist spot location. Here, the first waist spot refers to the waist spot of the beam reflected by the optical resonant cavity 2, the second waist spot refers to the waist spot of the beam formed after the reflected light passes through the cavity matching lens 5, and the third waist spot location refers to the waist spot of the beam after passing through the phase-shifting lens 10. , and These represent the Rayleigh lengths of the beams corresponding to the first waist spot, the second waist spot, and the third waist spot, respectively.

[0037] Specifically, in this embodiment, the beam splitter is a 50 / 50 beam splitter, and the optical resonant cavity 2 is an FP cavity.

[0038] Specifically, in this embodiment, the first photodetector 6 and the second photodetector 7 are single-quadrant DC photodetectors.

[0039] In this embodiment, based on Figure 5 The optical path diagram shown is used to build an experimental optical path to compare the locking method of the present invention with the PDH locking method. The PDH locking device 14 involved in the PDH locking cavity includes an electro-optic modulator 15, a local oscillator 19, a mixer 16, a low-pass filter 17 and a third photodetector 18, and also requires a PID controller 8 and a high-voltage amplifier 13.

[0040] Optical path calibration: Calibrate the coaxiality of all optical components to ensure that the incident beam can be accurately injected into the optical resonant cavity and that the reflected light is uniformly incident on the beam splitter after being clipped by the pinhole aperture. Optical path calibration: Adjust the coaxiality of the pinhole aperture, beam splitter, lens, and detector to ensure that the reflected beam is uniformly incident on the beam splitter after being clipped by the pinhole aperture and that the light intensity distribution of the two detection optical paths is symmetrical.

[0041] Mode mismatch control and parameter setting: Adjust the relative positions of the laser source and the optical resonator to deviate the waist position of the incident laser from the beam waist position of the cavity, introducing mode mismatch to excite the fundamental mode and the second-order transverse mode in space, forming a superimposed input light field; set a small aperture of appropriate size and adjust its position to destroy the full-section orthogonality of the transverse modes; according to Figure 3 Based on the theoretical simulation results, the laser output power and detector response parameters are set to ensure that the signal acquisition range covers the target detuning range.

[0042] Signal Acquisition and Verification: After turning on laser source 1, the cavity length of optical resonant cavity 2 is scanned. Two signals are simultaneously acquired through two photodetectors and recorded. Figure 6 The signals of the three detectors shown are as follows: DCA in (a) is the output signal of the first detector, DCB is the output signal of the second detector, and TransDC in (b) is the cavity transmission signal detected by the third detector. It was observed that the signals of the first detector and the second detector are reversed at the fundamental mode and the second-order mode, which is consistent with the Gouy phase shift modulation effect in the theoretical analysis.

[0043] Error signal generation and verification: The output signals of detectors A and B are connected to the differential processing circuit 9. The resulting fundamental mode corresponding error signal and transmission signal are as follows: Figure 7 As shown, (a) is the error signal and (b) is the transmission signal. The error signal exhibits a clear bipolar distribution, and the zero-crossing point of the error signal coincides with the center position of the cavity transmission peak, proving that it can accurately characterize the resonance condition of the cavity and thus can be effectively used for cavity length locking.

[0044] Cavity Lock-in and Stability Test: Figure 7The error signal shown is input to the PID controller 8. Appropriate proportional, integral, and derivative parameters are set, and the PZT end of the optical resonant cavity 2 is adjusted to achieve stable locking of the cavity length at the laser resonance position. Subsequently, the conventional PDH cavity locking device is started, and 12.5MHz phase modulation is applied to complete the comparison locking test. Locking performance comparison analysis: The power spectral density of the error signals of the two locking methods was collected, combined with, for example... Figure 8 As shown in the figure, the analysis shows that the noise spectrum characteristics of the two are basically the same in the wide frequency band, and the locking stability is comparable. In addition, the present invention can not only avoid residual amplitude modulation noise and have better long-term operation stability, but also eliminates the need for modulation and demodulation components, resulting in lower system complexity.

[0045] 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 or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A modulation-free optical resonator locking method based on optical field spatial mode mismatch, characterized in that, Includes the following steps: Step 1: Input the fundamental mode light field into the optical resonator, and use the superimposed light field of the spatial fundamental mode and the second transverse mode excited by mode mismatch as the input light field of the optical resonator; Step 2: Cut the reflected light from the optical resonant cavity using a small aperture; Step 3: Split the reflected light after the pinhole is cut into two paths, and use two photodetectors to detect the two beams respectively; simultaneously control the Gouy phase shifts corresponding to the fundamental modes of the two beams to be respectively... and π; Step 4: Perform differential processing on the output signals of the two photodetectors to generate an error signal, and adjust the cavity length of the optical resonant cavity based on the error signal to lock it.

2. The method for locking a modulation-free optical resonator based on optical field spatial mode mismatch according to claim 1, characterized in that, The spatial fundamental mode is The second-order transverse modulus is mold.

3. The method for locking a modulation-free optical resonator based on optical field spatial mode mismatch according to claim 1, characterized in that, In step 1, the position of the waist spot of the incident laser is adjusted to deviate from the beam waist position of the optical resonator, thereby introducing mode mismatch to excite the fundamental mode and the second-order transverse mode in the cavity, forming a superimposed optical field of the fundamental mode and the second-order transverse mode.

4. The method for locking a modulation-free optical resonator based on optical field spatial mode mismatch according to claim 1, characterized in that, In step 3, a phase-shifting lens is set in one path, and the position of the phase-shifting lens and the corresponding photodetector is adjusted to make its Gouy phase shift π. In the other path, the position of the corresponding photodetector is adjusted to make its Gouy phase shift π / 2.

5. A modulation-free optical resonator locking device based on optical field spatial mode mismatch, used to implement the modulation-free optical resonator locking method based on optical field spatial mode mismatch as described in any one of claims 1-3, characterized in that, include: Laser source (1), cavity matching lens (5), pinhole aperture (3), beam splitter (4), phase shift lens (10), first photodetector (6), second photodetector (7); The light output from the laser source (1) is incident on the optical resonant cavity (2) after passing through the cavity matching lens (5). The fundamental mode and the second-order transverse mode in space are generated in the optical resonant cavity (2) based on mode mismatch excitation. The reflected light from the optical resonant cavity (2) is split into two beams by the beam splitter (4) after passing through the cavity matching lens (5) and the pinhole aperture (3). One beam is directly detected by the first photodetector (6), and the other beam is detected by the second photodetector (7) after passing through the phase shift lens (10). The output terminals of the first photodetector (6) and the second photodetector (7) are connected to the differential processing circuit (9), the output terminal of the differential processing circuit (9) is connected to the frequency locking module, and the output terminal of the frequency locking module is connected to the cavity length control module of the optical resonant cavity (2).

6. A modulation-free optical resonator locking device based on optical field spatial mode mismatch according to claim 5, characterized in that, The frequency locking module includes a PID controller (8) and a high voltage amplifier (13). The input terminal of the PID controller (8) is connected to the differential processing circuit (9), and the output terminal of the PID controller (8) is connected to the high voltage amplifier (13). The output terminal of the high voltage amplifier (13) is connected to the cavity length control module of the optical resonant cavity (2).

7. A modulation-free optical resonator locking device based on optical field spatial mode mismatch according to claim 5, characterized in that, The aperture radius of the pinhole aperture (3) is equal to the light spot radius. times.

8. A modulation-free optical resonator locking device based on optical field spatial mode mismatch according to claim 5, characterized in that, The placement of the first photodetector (6) satisfies the following conditions: - + = ； The positions of the phase-shifting lens (10) and the second photodetector (7) satisfy the following conditions: - + - = ； in, This indicates the distance between the cavity matching lens (5) and the position of the first waist spot near the optical resonant cavity. This indicates the distance from the cavity-matching lens (5) to the position of the second waist spot on the other side. This indicates the distance between the second waist spot position on the other side of the cavity matching lens (5) and the first photodetector (6). This indicates the distance between the position of the second waist spot on the other side of the cavity matching lens (5) and the phase shift lens (10). The distance between the phase-shifting lens (10) and the third waist spot position on the output side is indicated, and the second photodetector (7) is set at the third waist spot position.

9. A modulation-free optical resonator locking device based on optical field spatial mode mismatch according to claim 5, characterized in that, The beam splitter is a 50 / 50 beam splitter, and the optical resonant cavity (2) is an FP cavity.

10. A modulation-free optical resonator locking device based on optical field spatial mode mismatch according to claim 5, characterized in that, The first photodetector (6) and the second photodetector (7) are single-quadrant DC photodetectors.

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