A method for calculating the frequency discrimination slope of a PDH frequency stabilization system

Abstract

The present application relates to the technical field of laser frequency stabilization, and discloses a method for calculating the frequency discrimination slope of a PDH frequency stabilization system, comprising the following steps: obtaining the waist position and size of an incident light beam, the waist position and size of a resonant cavity, and the loss and reflectivity of the resonant cavity; determining whether the waist position and size of the incident light beam match the resonant cavity; and then calculating the frequency discrimination slope through different formulas according to the matching of the waist position and size of the incident light beam and the waist position and size of the resonant cavity, which is simpler, and the parameters of each formula are easy to obtain, with high calculation efficiency and high accuracy.

Description

Technical Field

[0001] This invention relates to the field of laser frequency stabilization technology, and in particular to a method for calculating the frequency discrimination slope of a PDH frequency stabilization system. Background Technology

[0002] High-precision Fabry-Perot cavities have wide applications in spectroscopy, optical frequency standards, gravitational wave astronomy, and squeezed state generation. In many high-precision optical cavity experiments, to improve the stability of free-running lasers, the Pound-Dreyfus-Hall (PDH) technique is often used to lock them into an ultra-stable cavity. The basic principle is to demodulate the error signal by detecting the intensity of the reflected light from the resonant cavity. The "approximate slope" of the curve near the resonant point of the error signal is the frequency discrimination slope. In experiments, frequency locking is achieved by using the frequency discrimination slope. Since the frequency discrimination slope directly affects the frequency locking quality, a key parameter of PDH technology is the frequency discrimination slope.

[0003] like Figure 1 As shown, Figure 1 This is a magnified view of the area near the resonance point of the error signal. The horizontal axis represents the frequency detuning, and the vertical axis represents the normalized error signal. The black curve is the "error signal," a key parameter in the PDH frequency stabilization system. The frequency discrimination slope refers to the "approximate slope" of the curve near the resonance point of the error signal (within the dashed box in the figure). Figure 2 for Figure 1 The enlarged view of the curve within the dashed box. Δy refers to the peak-to-peak value of the error signal, and Δx refers to the difference in the horizontal axis corresponding to the peak-to-peak value of the error signal.

[0004] Changes in incident light mode matching directly alter both the transmitted and reflected light fields, and also affect the discrimination slope. These changes include the angle and position of the incident ray, as well as the size and position of the incident beam waist. While the angle and position of the incident ray are relatively easy to align experimentally, aligning the beam waist is more challenging. Therefore, the position and size of the beam waist influence the discrimination slope. From a geometric optics perspective, the incident ray is considered a single "ray," thus only the angle and position of incidence are considered. In contrast, the incident beam is considered from a physical optics perspective, representing a beam of light, requiring consideration of the incident beam waist.

[0005] Figure 3 This is a schematic diagram showing the matching of the incident beam with the beam waist of the resonant cavity. Figure 4 This is a schematic diagram showing the misalignment between the incident beam and the resonant cavity beam waist. Figure 3 In an ideal scenario: the incident beam has a beam waist of ω0, which is transformed into ω after passing through the coupling lens. ′ 0, Figure 4In the case of misalignment, the optical axis of the incident beam on the left does not coincide with the z-axis of the resonant cavity; there is a certain angle γ between them, and a certain distance ε, where ε contains two components, x and y. The beam waist size and position of the incident Gaussian beam on the left deviate from the ideal situation.

[0006] Currently, the calculation of the frequency discrimination slope mainly involves scanning the laser frequency to measure the error signal and then fitting the slope. However, because the linewidth of a free-running semiconductor laser is much larger than that of a resonant cavity, this method is not very accurate and requires a lot of work. Summary of the Invention

[0007] The purpose of this invention is to provide a method for calculating the frequency discrimination slope of a PDH frequency stabilization system that is efficient and accurate.

[0008] To achieve the above objectives, the present invention provides a method for calculating the frequency discrimination slope of a PDH frequency stabilization system, comprising the following steps:

[0009] S1: Obtain the position and size of the incident beam waist;

[0010] S2: Obtain the position and size of the waist of the resonant cavity;

[0011] S3: Obtain the loss and reflectivity of the resonant cavity;

[0012] S4: Determine whether the waist position and size of the incident beam match the resonant cavity; if the waist position and size of the incident beam match the resonant cavity, proceed to step S5; if the waist position of the incident beam matches the resonant cavity, but the waist size of the incident beam does not match the resonant cavity, proceed to step S6; if the waist size of the incident beam matches the resonant cavity, but the waist position of the incident beam does not match the resonant cavity, proceed to step S7; if the waist position and size of the incident beam do not match the resonant cavity, proceed to step S8.

[0013] S5: Frequency discrimination slope Where D is the frequency discrimination slope, P c For sideband power, P s For carrier power, Δv c Line width;

[0014] S6: If the resonant cavity loss is high, then Where D is the frequency discrimination slope, α is the coupling efficiency, and P c For sideband power, P s For carrier power, Δv c Line width;

[0015] If the resonant cavity has low loss and low reflectivity, then Where D is the frequency discrimination slope, α is the coupling efficiency, L is the cavity length, r is the amplitude reflection coefficient of the cavity mirror, and P c For sideband power, P s Where c is the carrier power and c is the speed of light;

[0016] If the resonant cavity has low loss and high reflectivity, then Where D is the frequency discrimination slope, α is the coupling efficiency, L is the cavity length, and P c For sideband power, P s Here, c is the carrier power, r is the speed of light, and r is the amplitude reflection coefficient of the cavity mirror.

[0017] S7: If the resonant cavity loss is high, then Where D is the frequency discrimination slope, α is the coupling efficiency, and P c For sideband power, P s For carrier power, Δv c Line width;

[0018] If the resonant cavity has low loss and low reflectivity, then Where D is the frequency discrimination slope, α is the coupling efficiency, L is the cavity length, r is the amplitude reflection coefficient of the cavity mirror, and P c For sideband power, P s Where c is the carrier power and c is the speed of light;

[0019] If the resonant cavity has low loss and high reflectivity, then Where D is the frequency discrimination slope, α is the coupling efficiency, L is the cavity length, and P c For sideband power, P s Here, c is the carrier power, r is the speed of light, and r is the amplitude reflection coefficient of the cavity mirror.

[0020] S8: If the resonant cavity loss is high, then Where D is the frequency discrimination slope, Δy is the peak-to-peak value of the error signal, and Δx refers to the difference in the horizontal axis corresponding to the peak-to-peak value of the error signal.

[0021] If the resonant cavity has low loss and low reflectivity, then Where D is the frequency discrimination slope, r is the amplitude reflection coefficient of the cavity mirror, Δy is the peak-to-peak value of the error signal, and Δv c Line width;

[0022] If the resonant cavity has low loss and high reflectivity, then Where D is the frequency discrimination slope, L is the cavity length, Δy is the peak-to-peak value of the error signal, c is the speed of light, and r is the amplitude reflection coefficient of the cavity mirror.

[0023] As a preferred option, if the loss of the resonant cavity is less than 10%, it is considered to have low loss; if the loss of the resonant cavity is greater than 10%, it is considered to have high loss.

[0024] As a preferred option, if the reflectivity of the resonant cavity is less than 90%, it is considered to have low reflectivity; if the reflectivity of the resonant cavity is greater than 90%, it is considered to have high reflectivity.

[0025] As a preferred option, the resonant cavity loss includes transmission loss, and the resonant cavity loss is obtained by calculating the transmission loss.

[0026] As a preferred embodiment, the reflectivity of the resonant cavity is the square of the amplitude reflection coefficient of the cavity mirror, that is, the reflectivity of the resonant cavity is r. 2 .

[0027] As a preferred option, the sideband power P c and carrier power P s Obtained by measuring the power of the incident beam.

[0028] P c =J0(β) 2 P0;

[0029] P s =J1(β) 2 P0;

[0030] Where J0 is the 0th order Bezier curve, J1 is the 1st order Bezier curve, β is the modulation depth, and P0 is the power of the incident beam.

[0031] As a preferred embodiment, in step S8, the demodulation signal of the frequency locking module in the PDH frequency stabilization system is connected to an oscilloscope for display, and the peak-to-peak value Δy and the corresponding abscissa difference Δx of the error signal are directly obtained by reading the image displayed on the oscilloscope.

[0032] As a preferred option, the line width Δv c It can be obtained by means of optical cavity ring-down method, laser phase-locked loop method, or frequency modulation sideband as frequency ruler.

[0033] As a preferred option, the coupling efficiency α is measured by the transmission spectrum; wherein, the transmission spectrum is obtained, and the fundamental mode peak value and all mode peak values ​​are obtained from the transmission spectrum. All modes include higher-order modes, and the coupling efficiency α is the ratio of the fundamental mode peak value to the sum of all mode peak values.

[0034] As a preferred option, the coupling efficiency α is measured by the reflection spectrum.

[0035] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0036] This invention analyzes whether the waist position and size of the incident beam match the waist position and size of the resonant cavity. Based on the matching of the waist position and size of the incident beam and the resonant cavity, the frequency discrimination slope is calculated using different formulas. This method is simpler, the parameters of each formula are easy to obtain, and the calculation efficiency and accuracy are high. Attached Figure Description

[0037] Figure 1 This is a magnified schematic diagram of a local area near the resonance point of the error signal.

[0038] Figure 2 for Figure 1 Enlarged view of the curve within the dashed box.

[0039] Figure 3 This is a schematic diagram showing the matching of the incident beam with the resonant cavity beam waist.

[0040] Figure 4 This is a schematic diagram showing the misalignment between the incident beam and the resonant cavity beam waist.

[0041] Figure 5 This is a flowchart illustrating the method for calculating the frequency discrimination slope of the PDH frequency stabilization system according to an embodiment of the present invention. Detailed Implementation

[0042] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and are not intended to limit the scope of the invention.

[0043] Example 1

[0044] like Figure 5 As shown in the figure, a method for calculating the frequency discrimination slope of a PDH frequency stabilization system according to an embodiment of the present invention includes the following steps:

[0045] S1: Obtain the position and size of the incident beam waist;

[0046] S2: Obtain the position and size of the waist of the resonant cavity;

[0047] S3: Obtain the loss and reflectivity of the resonant cavity;

[0048] S4: Determine whether the waist position and size of the incident beam match the resonant cavity; if the waist position and size of the incident beam match the resonant cavity, proceed to step S5; if the waist position of the incident beam matches the resonant cavity, but the waist size of the incident beam does not match the resonant cavity, proceed to step S6; if the waist size of the incident beam matches the resonant cavity, but the waist position of the incident beam does not match the resonant cavity, proceed to step S7; if the waist position and size of the incident beam do not match the resonant cavity, proceed to step S8.

[0049] S5: Where D is the frequency discrimination slope, P c For sideband power, P s For carrier power, Δv c Line width;

[0050] S6: If the resonant cavity loss is high, then Where D is the frequency discrimination slope, α is the coupling efficiency, and P c For sideband power, P s For carrier power, Δv c Line width;

[0051] If the resonant cavity has low loss and low reflectivity, then Where D is the frequency discrimination slope, α is the coupling efficiency, L is the cavity length, r is the amplitude reflection coefficient of the cavity mirror, and P c For sideband power, P s Where c is the carrier power and c is the speed of light;

[0052] If the resonant cavity has low loss and high reflectivity, then Where D is the frequency discrimination slope, α is the coupling efficiency, L is the cavity length, and P c For sideband power, P s Here, c is the carrier power, r is the speed of light, and r is the amplitude reflection coefficient of the cavity mirror.

[0053] S7: If the resonant cavity loss is high, then Where D is the frequency discrimination slope, α is the coupling efficiency, and P c For sideband power, P s For carrier power, Δv c Line width;

[0054] If the resonant cavity has low loss and low reflectivity, then Where D is the frequency discrimination slope, α is the coupling efficiency, L is the cavity length, r is the amplitude reflection coefficient of the cavity mirror, and P c For sideband power, P s Where c is the carrier power and c is the speed of light;

[0055] If the resonant cavity has low loss and high reflectivity, then Where D is the frequency discrimination slope, α is the coupling efficiency, L is the cavity length, and P c For sideband power, P s Here, c is the carrier power, r is the speed of light, and r is the amplitude reflection coefficient of the cavity mirror.

[0056] S8: If the resonant cavity loss is high, then Where D is the frequency discrimination slope, Δy is the peak-to-peak value of the error signal, and Δx refers to the difference in the horizontal axis corresponding to the peak-to-peak value of the error signal.

[0057] If the resonant cavity has low loss and low reflectivity, then Where D is the frequency discrimination slope, r is the amplitude reflection coefficient of the cavity mirror, Δy is the peak-to-peak value of the error signal, and Δv c Line width;

[0058] If the resonant cavity has low loss and high reflectivity, then Where D is the frequency discrimination slope, L is the cavity length, Δy is the peak-to-peak value of the error signal, c is the speed of light, and r is the amplitude reflection coefficient of the cavity mirror.

[0059] This embodiment analyzes whether the waist position and size of the incident beam match the waist position and size of the resonant cavity. Based on the matching of the waist position and size of the incident beam and the resonant cavity, the frequency discrimination slope is calculated using different formulas. This method is simpler, the parameters of each formula are easy to obtain, and the calculation efficiency and accuracy are high.

[0060] Example 2

[0061] The difference between this embodiment and Embodiment 1 is that, based on Embodiment 1, this embodiment provides further explanation of the resonant cavity loss and reflectivity.

[0062] If the resonant cavity loss is less than 10%, it is considered to have low loss; if the resonant cavity loss is greater than 10%, it is considered to have high loss. In this embodiment, if the resonant cavity loss is less than 5%, it is considered to have low loss; if the resonant cavity loss is greater than 5%, it is considered to have high loss.

[0063] If the reflectivity of the resonant cavity is less than 90%, it is considered to have low reflectivity; if the reflectivity of the resonant cavity is greater than 90%, it is considered to have high reflectivity. In this embodiment, if the reflectivity of the resonant cavity is less than 95%, it is considered to have low reflectivity; if the reflectivity of the resonant cavity is greater than 95%, it is considered to have high reflectivity.

[0064] The resonant cavity loss includes transmission loss, which is calculated to obtain the total resonant cavity loss. There are many types of resonant cavity losses, such as diffraction loss, transmission loss, and scattering loss, with transmission loss being the most significant. Therefore, in this embodiment, only the transmission loss needs to be calculated when determining the resonant cavity loss, and the calculated value of the transmission loss is used as the total resonant cavity loss.

[0065] Furthermore, the reflectivity of the resonant cavity is the square of the amplitude reflection coefficient of the cavity mirror, that is, the reflectivity of the resonant cavity is r. 2 .

[0066] The other steps in this embodiment are the same as in Embodiment 1, and will not be repeated here.

[0067] Example 3

[0068] The difference between this embodiment and Embodiment 2 is that, based on Embodiment 2, this embodiment further explains how to obtain each parameter.

[0069] The resonant cavity in this embodiment consists of two identical concave mirrors, which are called cavity mirrors. The amplitude reflection coefficients of the two cavity mirrors are equal, both being r.

[0070] In this embodiment, if the beam waist position and size of the incident beam do not match the resonant cavity, and the resonant cavity has high loss, then only one method can be used. To solve for the frequency discrimination slope, specifically in step S8, the demodulation signal of the frequency locking module in the PDH frequency stabilization system is connected to an oscilloscope for display. The peak-to-peak value Δy and the corresponding abscissa difference Δx of the error signal are directly obtained by reading the image displayed on the oscilloscope.

[0071] If the beam waist position and size of the incident beam do not match the resonant cavity, but the resonant cavity has low loss and low reflectivity, then If the beam waist position and size of the incident beam do not match the resonant cavity, and the resonant cavity has low loss and high reflectivity, then The value of Δy is easy to obtain, but the value of Δx is relatively difficult to obtain. Figure 1 For example, Δy can be directly seen from the graph to be equal to 2, while the value of Δx cannot be directly obtained and requires manipulation of the error signal. However, some frequency-locking modules cannot manipulate the signal, so another step is needed, such as connecting the signal from the frequency-locking module to an oscilloscope for analysis, or even exporting the signal from the oscilloscope to a computer for analysis. Using the solution formula in this embodiment, the measurement of Δx can be avoided. That is, in cases where the beam waist position and size of the incident beam are mismatched with the resonant cavity and the resonant cavity loss is high, the error signal does not need to be connected to an oscilloscope or computer; only the value of Δy in the error signal scanned by the frequency-locking module needs to be read. The frequency discrimination slope can be measured simply by reading Δy.

[0072] When the beam waist position of the incident beam matches the beam waist position of the resonant cavity, or the beam waist size of the incident beam matches the beam waist size of the resonant cavity, or both the beam waist position and size of the incident beam match the beam waist position and size of the resonant cavity, this embodiment utilizes the sideband power P. c Carrier power P s Cavity length L, mirror amplitude reflection coefficient r, and linewidth Δv c This method calculates the frequency discrimination slope, eliminating the need to read the Δy value and thus avoiding the use of error signals. The frequency discrimination slope can be calculated using the parameters of the incident beam and the resonant cavity itself, and it also solves the problem of inaccurate frequency discrimination slope calculation caused by errors in reading Δx and Δy values.

[0073] Specifically, in this embodiment, the sideband power P c and carrier power P s Obtained by measuring the power of the incident beam.

[0074] P c =J0(β) 2 P0;

[0075] P s =J1(β) 2 P0;

[0076] Where J0 is the 0th order Bezier curve, J1 is the 1st order Bezier curve, β is the modulation depth, and P0 is the power of the incident beam.

[0077] Additionally, the line width Δv c It can be obtained by means of optical cavity ring-down method, laser phase-locked loop method, or frequency modulation sideband as frequency ruler.

[0078] The coupling efficiency α is measured using a transmission spectrum. The transmission spectrum is obtained by acquiring the fundamental mode peak value and the peak values ​​of all modes, including higher-order modes. The coupling efficiency α is the ratio of the fundamental mode peak value to the sum of the peak values ​​of all modes. In the transmission spectrum, the highest peak is the fundamental mode peak, and the remaining peaks are the peak values ​​of each mode (including higher-order modes), which is calculated as: fundamental mode peak value / higher-order mode peak value + fundamental mode peak value / first mode peak value + ... + fundamental mode peak value / nth mode peak value.

[0079] Furthermore, it should be noted that the coupling efficiency α can also be measured by the reflection spectrum. The principle is the same as that of the coupling efficiency α measured by the transmission spectrum. Specifically, the reflection spectrum is obtained, and the fundamental mode peak value and all mode peak values ​​are obtained from the reflection spectrum. All modes include higher-order modes. The coupling efficiency α is the ratio of the fundamental mode peak value to the sum of all mode peak values.

[0080] The other steps in this embodiment are the same as in Embodiment 2, and will not be repeated here.

[0081] In summary, the embodiments of the present invention provide a method for calculating the discrimination slope of a PDH frequency stabilization system. This method analyzes whether the beam waist position and size of the incident beam and the beam waist position and size of the resonant cavity match. Based on the matching of the beam waist position and size of the incident beam and the resonant cavity, the discrimination slope is calculated using different formulas. This method is simpler, the parameters of each formula are easy to obtain, and the calculation efficiency and accuracy are high.

[0082] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and substitutions can be made without departing from the technical principles of the present invention, and these improvements and substitutions should also be considered within the scope of protection of the present invention.

Claims

1. A method for calculating the frequency discriminator slope of a PDH frequency stabilized system, characterized in that, The method comprises the following steps: S1: obtaining the waist position and size of the incident light beam; S2: obtaining the waist position and size of the resonant cavity; S3: obtaining the loss and reflectivity of the resonant cavity; S4: judging whether the waist position and size of the incident light beam match the resonant cavity; if the waist position and size of the incident light beam match the resonant cavity, step S5 is performed; if the waist position of the incident light beam matches the resonant cavity but the waist size of the incident light beam does not match the resonant cavity, step S6 is performed; if the waist size of the incident light beam matches the resonant cavity but the waist position of the incident light beam does not match the resonant cavity, step S7 is performed; if the waist position and size of the incident light beam do not match the resonant cavity, step S8 is performed; S5: frequency discriminator slope where D is the frequency discriminator slope, P c is the sideband power, P s is the carrier power, Δν c is the linewidth; S6: if the loss of the resonant cavity is high, then where D is the frequency discrimination slope, a is the coupling efficiency, P c is the sideband power, P s is the carrier power, Δν c is the linewidth; If the loss of the resonant cavity is low and the reflectivity is low, then where D is the frequency discrimination slope, a is the coupling efficiency, L is the cavity length, r is the amplitude reflection coefficient of the cavity mirror, P c is the sideband power, P s is the carrier power, and c is the speed of light. If the loss of the resonant cavity is lower and the reflectivity is higher, then where D is the frequency discrimination slope, a is the coupling efficiency, L is the cavity length, P c is the sideband power, P s is the carrier power, c is the speed of light, and r is the amplitude reflection coefficient of the cavity mirror. S7: if the loss of the resonant cavity is high, then where D is the frequency discrimination slope, a is the coupling efficiency, P c is the sideband power, P s is the carrier power, Δν c is the linewidth; If the loss of the resonant cavity is low and the reflectivity is low, then where D is the frequency discrimination slope, a is the coupling efficiency, L is the cavity length, r is the amplitude reflection coefficient of the cavity mirror, P c is the sideband power, P s is the carrier power, and c is the speed of light. If the loss of the resonant cavity is lower and the reflectivity is higher, then where D is the frequency discrimination slope, a is the coupling efficiency, L is the cavity length, P c is the sideband power, P s is the carrier power, c is the speed of light, and r is the amplitude reflection coefficient of the cavity mirror. S8: if the loss of the resonant cavity is high, then where D is the frequency discrimination slope, Ay is the peak-to-peak value of the error signal, and Δχ refers to the difference in the abscissa corresponding to the peak-to-peak value of the error signal. If the loss of the resonator is low and the reflectivity is low, then where D is the frequency discrimination slope, r is the amplitude reflection coefficient of the cavity mirror, Ay is the peak-to-peak value of the error signal, Δν c is the linewidth; If the loss of the resonator is low and the reflectivity is high, then where D is the frequency discrimination slope, L is the cavity length, Ay is the peak-to-peak value of the error signal, c is the speed of light, and r is the amplitude reflection coefficient of the cavity mirror.

2. The method of claim 1, wherein the frequency offset is calculated by the following equation: ###0001### where f0 is the frequency offset, f is the frequency of the input signal, fref is the reference frequency, and f0 is the frequency of the output signal. If the loss of the resonant cavity is less than 10%, the loss of the resonant cavity is considered to be low; if the loss of the resonant cavity is greater than 10%, the loss of the resonant cavity is considered to be high.

3. The method of claim 1, wherein the frequency offset is calculated by: ###0001### where f0 is the frequency of the reference clock, f is the frequency of the output clock, and T is the period of the output clock. If the reflectivity of the resonant cavity is less than 90%, the reflectivity of the resonant cavity is considered to be low; if the reflectivity of the resonant cavity is greater than 90%, the reflectivity of the resonant cavity is considered to be high.

4. The method of claim 1, wherein the frequency offset is calculated by: ###0001### where f0 is the frequency of the reference clock, f is the frequency of the output clock, and T is the period of the output clock. The loss of the resonant cavity comprises a transmission loss, and the loss of the resonant cavity is obtained by calculating the transmission loss.

5. The method of claim 1, wherein the frequency offset is calculated by the following equation: ###0001### where f0 is the frequency offset, f is the frequency of the input signal, fref is the frequency of the reference signal, and f0 is the frequency of the output signal. The reflectivity of the resonator is the square of the amplitude reflection coefficient of the mirror, i.e. the reflectivity of the resonator is r 2 .

6. The method of claim 1, wherein the frequency offset is calculated by the following equation: ###0001### where f0 is the frequency offset, f is the frequency of the input signal, fref is the reference frequency, and f0 is the frequency of the output signal. Sideband power P c And carrier power P s Obtained by measuring the power of the incident light beam, P c = J0(β) 2 P0; P s = J1(βa) 2 P0; Wherein, J0 is the 0th order Bessel curve, J1 is the 1st order Bessel curve, β is the modulation depth, and P0 is the power of the incident light beam.

7. The method of claim 1, wherein the frequency offset is calculated by: ###0002### where f0 is the frequency of the reference clock, f is the frequency of the output clock, and T is the period of the output clock. In step S8, the demodulation signal of the frequency locking module in the PDH frequency stabilization system is connected to an oscilloscope to display, and the peak-to-peak value Δy of the error signal and the corresponding abscissa difference Δx are directly obtained by reading the image displayed on the oscilloscope.

8. The method of claim 1, wherein the frequency offset is calculated by: ###0002### where f0 is the frequency of the reference clock, f is the frequency of the output clock, and T is the period of the output clock. Line width Δv c Obtained by optical cavity ring-down method or laser phase-locked method or frequency modulation sideband as frequency ruler method.

9. The method of claim 1, wherein the frequency offset is calculated by: ###0002### where f0 is the frequency of the reference clock, f is the frequency of the output clock, and T is the period of the output clock. The coupling efficiency α is measured by a transmission spectrum diagram; wherein, the transmission spectrum diagram is obtained, the fundamental mode peak value and all mode peak values are obtained according to the transmission spectrum diagram, all modes include high-order modes, and the coupling efficiency α is the ratio of the fundamental mode peak value to the sum of all mode peak values.

10. The method of claim 1, wherein the frequency offset is calculated by: ###0002### where f0 is the frequency of the reference clock, f is the frequency of the output clock, and T is the period of the output clock. The coupling efficiency α is measured by a reflection spectrum diagram.

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