Frequency discrimination slope calculation method of PDH frequency stabilization system

Abstract

The invention relates to the technical field of laser frequency stabilization, and discloses a frequency discrimination slope calculation method for a PDH frequency stabilization system, and the method comprises the following steps: obtaining the beam waist position and size of an incident beam, the beam waist position and size of a resonant cavity, and obtaining the loss and reflectivity of the resonant cavity; judging whether the beam waist position and the size of the incident beam are matched with those of the resonant cavity or not; then, according to the beam waist position and size of the incident light beam and the matching condition of the beam waist position and size of the resonant cavity, the frequency discrimination slope is calculated through different formulas, the method is simpler, parameters of all the formulas are easy to obtain, the calculation efficiency is high, and the accuracy is high.

Description

Technical Field

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

[0002] High-precision Fabry-Perot cavities are widely used in spectroscopy, optical frequency standards, gravitational wave astronomy, and compressed state generation. In many high-precision optical cavity experiments, in order to improve the stability of free-running lasers, Pound-Drever-Hall (PDH) technology is usually used to lock them in ultra-stable cavities. The basic principle is to detect the reflected light intensity of the resonant cavity and demodulate the error signal. The "approximate slope" of the curve near the resonance point of the error signal is the discrimination slope. The discrimination slope is used to achieve frequency locking in the experiment, and the discrimination slope will directly affect the quality of frequency locking. Therefore, a key parameter of the PDH technology is the discrimination slope.

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

[0004] Changes in the incident light mode matching will not only directly change the transmitted light field and the reflected light field, but will also affect the discrimination slope. Changes in the incident light mode matching include the angle and position of the incident light and the size and position of the incident light waist. The angle and position of the incident light are relatively easy to align during the experiment, but the waist alignment is difficult. Therefore, the position and size of the waist have an impact on the discrimination slope. The incident light is considered from the perspective of geometric optics, and the incident light is considered to be a "light ray", so there are only the incident angle and position; while the incident light beam is considered from the perspective of physical optics, and the incident light is considered to be a beam of light, that is, a "light beam", and the waist of the incident light needs to be considered.

[0005] Figure 3 is a schematic diagram of the matching between the incident beam and the resonant cavity waist. Figure 4 Schematic diagram of the misalignment between the incident light beam and the resonant cavity waist. Figure 3 For the ideal case: the waist size of the incident beam is ω0, and after the coupling lens, the waist size is transformed into ω ′ 0, Figure 4This is a misalignment situation. The optical axis of the incident light beam on the left does not coincide with the z-axis of the resonant cavity. There is a certain angle γ and a certain distance ε. ε contains two components, x and y. The waist size and waist position of the incident Gaussian beam on the left are somewhat different from the ideal situation.

[0006] At present, the calculation of the frequency discrimination slope is mainly to measure the error signal by scanning the laser frequency, and then fit the slope. However, because the line width of the free-running semiconductor laser is much larger than the line width of the resonant cavity, this method is not accurate and requires a lot of work. Summary of the invention

[0007] The purpose of the present invention is to provide a method for calculating the discrimination slope of a PDH frequency stabilization system with high efficiency and high accuracy.

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

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

[0010] S2: Get the beam waist position and size 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 light beam match the resonant cavity; if the waist position and size of the incident light beam match the resonant cavity, proceed to step S5; 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, proceed to step S6; 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, proceed to step S7; if the waist position and size of the incident light beam do not match the resonant cavity, proceed to step S8;

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

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

[0015] If the resonant cavity has low loss and low reflectivity, then Where D is the 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 is the sideband power, P s is the carrier power, c is the speed of light;

[0016] If the resonant cavity has low loss and high reflectivity, then Where D is the discrimination slope, α 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;

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

[0018] If the resonant cavity has low loss and low reflectivity, then Where D is the 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 is the sideband power, P s is the carrier power, c is the speed of light;

[0019] If the resonant cavity has low loss and high reflectivity, then Where D is the discrimination slope, α 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;

[0020] S8: If the loss of the resonant cavity 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 horizontal coordinate difference 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 is the line width;

[0022] If the resonant cavity has low loss and high reflectivity, then Where D is the 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 solution, if the loss of the resonant cavity is less than 10%, it is considered that the loss of the resonant cavity is low; if the loss of the resonant cavity is greater than 10%, it is considered that the loss of the resonant cavity is high.

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

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

[0026] As a preferred solution, 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 solution, the sideband power P c and carrier power P s By measuring the power of the incident beam,

[0028] P c =J0(β) 2 P0;

[0029] P s =J1(β) 2 P0;

[0030] 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.

[0031] As a preferred solution, in step S8, the demodulated 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 of the error signal and the corresponding horizontal coordinate difference Δx are directly obtained by reading the image displayed on the oscilloscope.

[0032] As a preferred solution, the line width Δv c It is obtained by using the cavity ring-down method, laser phase-locking method or frequency modulation sideband as the frequency ruler.

[0033] As a preferred embodiment, the coupling efficiency α is measured by a transmission spectrum diagram; wherein, the transmission spectrum diagram is obtained, and the fundamental mode peak and all mode peaks 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 to the sum of all mode peaks.

[0034] As a preferred solution, the coupling efficiency α is measured through a reflection spectrum diagram.

[0035] Compared with the prior art, the present invention has the following beneficial effects:

[0036] The present invention analyzes whether the waist position and size of the incident light beam and the waist position and size of the resonant cavity match, and obtains the 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. The method is simpler, and the parameters of each formula are easy to obtain, with high calculation efficiency and accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 It is a local enlarged schematic diagram near the resonance point of the error signal.

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

[0039] Figure 3 Schematic diagram of the matching of the incident light beam and the resonant cavity waist.

[0040] Figure 4 Schematic diagram of the misalignment between the incident light beam and the resonant cavity waist.

[0041] Figure 5 The present invention is a flowchart of a method for calculating a discrimination slope of a PDH frequency stabilization system according to an embodiment of the present invention. DETAILED DESCRIPTION

[0042] The specific implementation of the present invention is further described in detail below in conjunction with the accompanying drawings and examples. The following examples are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

[0043] Embodiment 1

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

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

[0046] S2: Get the beam waist position and size 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 light beam match the resonant cavity; if the waist position and size of the incident light beam match the resonant cavity, proceed to step S5; 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, proceed to step S6; 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, proceed to step S7; if the waist position and size of the incident light beam do not match the resonant cavity, proceed to step S8;

[0049] S5: Where D is the demodulation slope, P c is the sideband power, P s is the carrier power, Δv c is the line width;

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

[0051] If the resonant cavity has low loss and low reflectivity, then Where D is the 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 is the sideband power, P s is the carrier power, c is the speed of light;

[0052] If the resonant cavity has low loss and high reflectivity, then Where D is the discrimination slope, α 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;

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

[0054] If the resonant cavity has low loss and low reflectivity, then Where D is the 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 is the sideband power, P s is the carrier power, c is the speed of light;

[0055] If the resonant cavity has low loss and high reflectivity, then Where D is the discrimination slope, α 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;

[0056] S8: If the loss of the resonant cavity 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 horizontal coordinate difference 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 is the line width;

[0058] If the resonant cavity has low loss and high reflectivity, then Where D is the 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 light beam match the waist position and size of the resonant cavity, and calculates the 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. This is simpler, and the parameters of each formula are easy to obtain, with high calculation efficiency and accuracy.

[0060] Embodiment 2

[0061] The difference between this embodiment and the first embodiment is that, based on the first embodiment, this embodiment further illustrates the loss and reflectivity of the resonant cavity.

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

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

[0064] The loss of the resonant cavity includes the transmission loss, and the loss of the resonant cavity is obtained by calculating the transmission loss. There are many losses in the resonant cavity, such as diffraction loss, transmission loss, scattering loss, etc., among which the most important is the transmission loss. Therefore, when calculating the loss of the resonant cavity in this embodiment, only the transmission loss needs to be calculated, and the calculated value of the transmission loss is regarded as the loss of the entire resonant cavity.

[0065] In addition, 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 of this embodiment are the same as those of the first embodiment and will not be described again here.

[0067] Embodiment 3

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

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

[0070] In this embodiment, if the waist position and size of the incident light beam do not match the resonant cavity, and the loss of the resonant cavity is high, then only To solve the demodulation slope, specifically, in step S8, the demodulated 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 of the error signal and the corresponding horizontal coordinate difference Δx are directly obtained by reading the image displayed on the oscilloscope.

[0071] If the incident beam waist position and size do not match the resonant cavity, but the resonant cavity has low loss and low reflectivity, then If the incident beam waist position and size 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, it can be directly seen from the figure that Δy is equal to 2, while the value of Δx cannot be directly obtained, and the error signal needs to be operated. However, some frequency locking modules cannot operate the signal, so another step is required, such as connecting the signal of the frequency locking module to an oscilloscope for analysis, or even exporting the signal on the oscilloscope to a computer for analysis. By using the solution formula of this embodiment, the measurement of Δx can be avoided. That is, in the case where the waist position and size of the incident light beam do not match the resonant cavity and the loss of the resonant cavity is high, the error signal does not need to be connected to the oscilloscope or computer, and it is only necessary to read the value of Δy in the error signal scanned by the frequency locking module, and the frequency discrimination slope can be measured only by reading Δy.

[0072] When the waist position of the incident light beam matches the waist position of the resonant cavity, or the waist size of the incident light beam matches the waist size of the resonant cavity, or the waist position and size of the incident light beam match the waist position and size of the resonant cavity, this embodiment uses the sideband power P c , carrier power P s , cavity length L, the amplitude reflection coefficient r and line width Δv of the cavity mirror c To calculate the discrimination slope, the need to read the Δy value mentioned above is eliminated, and there is no need to use the error signal. The discrimination slope can be calculated through the parameters of the incident light beam and the resonant cavity itself, and the problem of inaccurate calculation of the discrimination slope caused by errors in reading the Δx and Δy values ​​is also solved.

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

[0074] P c =J0(β) 2 P0;

[0075] P s =J1(β) 2 P0;

[0076] 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.

[0077] In addition, the line width Δv c It is obtained by using the cavity ring-down method, laser phase-locking method or frequency modulation sideband as the frequency ruler.

[0078] The coupling efficiency α is measured through the transmission spectrum; wherein, the transmission spectrum is obtained, and the fundamental mode peak and all mode peaks are obtained according to the transmission spectrum. All modes include high-order modes, and the coupling efficiency α is the sum of the fundamental mode peak and all mode peaks. In the transmission spectrum, the highest peak is the fundamental mode, and the remaining peaks are the peaks of each mode (including high-order modes), that is, the fundamental mode peak / high-order mode peak+fundamental mode peak / first mode peak+…+fundamental mode peak / nth mode peak.

[0079] In addition, it should be pointed out that the coupling efficiency α can also be measured through the reflection spectrum diagram. The principle is the same as that of measuring the coupling efficiency α through the transmission spectrum diagram. Specifically, obtain the reflection spectrum diagram, and take the fundamental mode peak value and all mode peak values ​​on the reflection spectrum diagram. All modes include high-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 of this embodiment are the same as those of the second embodiment and will not be described again here.

[0081] In summary, the embodiment of the present invention provides a method for calculating the discrimination slope of a PDH frequency stabilization system, which analyzes whether the waist position and size of the incident light beam and the waist position and size of the resonant cavity match, and calculates the 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. The method is simpler, and the parameters of each formula are easy to obtain, with high calculation efficiency and accuracy.

[0082] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and substitutions can be made without departing from the technical principles of the present invention. These improvements and substitutions should also be regarded as the scope of protection of the present invention.

Claims

1. A method for calculating the discrimination slope of a PDH frequency stabilization system, characterized in that: The steps include: S1: Get the waist position and size of the incident light beam; S2: Get the beam waist position and size of the resonant cavity; S3: Obtain the loss and reflectivity of the resonant cavity; S4: Determine 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, proceed to step S5; 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, proceed to step S6; 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, proceed to step S7; if the waist position and size of the incident light beam do not match the resonant cavity, proceed to step S8; S5: Frequency discrimination slope Where D is the demodulation slope, P c is the sideband power, P s is the carrier power, Δν c is the line width; S6: If the loss of the resonant cavity is high, then Where D is the discrimination slope, α is the coupling efficiency, P c is the sideband power, P s is the carrier power, Δν c is the line width; If the resonant cavity has low loss and low reflectivity, then Where D is the 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 is the sideband power, P s is the carrier power, c is the speed of light; If the resonant cavity has low loss and high reflectivity, then Where D is the discrimination slope, α 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 discrimination slope, α is the coupling efficiency, P c is the sideband power, P s is the carrier power, Δν c is the line width; If the resonant cavity has low loss and low reflectivity, then Where D is the 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 is the sideband power, P s is the carrier power, c is the speed of light; If the resonant cavity has low loss and high reflectivity, then Where D is the discrimination slope, α 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, Δy is the peak-to-peak value of the error signal, and Δx refers to the horizontal coordinate difference corresponding to the peak-to-peak value of the error signal; 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 Δν c is the line width; If the resonant cavity has low loss and high reflectivity, then Where D is the 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.

2. The method for calculating the discrimination slope of the PDH frequency stabilization system according to claim 1, characterized in that: If the loss of the resonant cavity is less than 10%, it is considered that the loss of the resonant cavity is low; if the loss of the resonant cavity is greater than 10%, it is considered that the loss of the resonant cavity is high.

3. The method for calculating the discrimination slope of the PDH frequency stabilization system according to claim 1, characterized in that: If the reflectivity of the resonant cavity is less than 90%, it is considered that the reflectivity of the resonant cavity is low; if the reflectivity of the resonant cavity is greater than 90%, it is considered that the reflectivity of the resonant cavity is high.

4. The method for calculating the discrimination slope of the PDH frequency stabilization system according to claim 1, characterized in that: The loss of the resonant cavity includes the transmission loss, and the loss of the resonant cavity is obtained by calculating the transmission loss.

5. The method for calculating the discrimination slope of the PDH frequency stabilization system according to claim 1, characterized in that: 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 .

6. The method for calculating the discrimination slope of the PDH frequency stabilization system according to claim 1, characterized in that: Sideband power P c and carrier power P s By measuring the power of the incident beam, P c =J0(β) 2 P0; P s =J1(va) 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 for calculating the discrimination slope of the PDH frequency stabilization system according to claim 1, characterized in that: In step S8, the demodulated 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 of the error signal and the corresponding horizontal coordinate difference Δx are directly obtained by reading the image displayed on the oscilloscope.

8. The method for calculating the discrimination slope of the PDH frequency stabilization system according to claim 1, characterized in that: Line width Δv c It is obtained by using the cavity ring-down method, laser phase-locking method or frequency modulation sideband as the frequency ruler.

9. The method for calculating the discrimination slope of a PDH frequency stabilization system according to claim 1, characterized in that: The coupling efficiency α is measured through a transmission spectrum diagram; wherein, the transmission spectrum diagram is obtained, and the fundamental mode peak and all mode peaks are obtained according to the transmission spectrum diagram. All modes include high-order modes, and the coupling efficiency α is the sum of the fundamental mode peak and all mode peaks.

10. The method for calculating the discrimination slope of the PDH frequency stabilization system according to claim 1, characterized in that: The coupling efficiency α is measured by the reflection spectrum.

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