Application of thickness-compensated optical medium in continuous tunable laser

By improving the angle relationship between the cross-sectional shape and the optical path of the optical medium, and using a transparent medium with thickness compensation characteristics, the limitations of the external cavity semiconductor laser in large-scale continuous tunability and frequency stability are solved, and a larger laser frequency tuning range and stability are achieved.

CN120262148AActive Publication Date: 2025-07-04ZHEJIANG GUOSHUI SUB TECHNOLOGY RESEARCH CO LTD
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Patent Information

Application Number
CN202510412031.6
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-04-02
Publication Date
2025-07-04
Estimated Expiration
2045-04-02

AI Technical Summary

Technical Problem

The existing external cavity semiconductor lasers have limitations in achieving large-scale continuous tunability, which can easily cause mode jumps, and the tuning process is complicated, making it difficult to achieve stable single-mode output within a larger tuning range, affecting frequency stability and accuracy, and difficult to meet the needs of high-resolution spectral measurement and precision interference measurement.

Method used

By improving the cross-sectional shape of the optical medium, the thickness has a linear or nonlinear relationship with the angle between the optical path, the length of the resonant cavity is changed, and the cavity mode frequency changes synchronously with the center frequency of the transmission peak of the interference sheet. A transparent medium with thickness compensation characteristics such as a right-angle trapezoid or curved transparent medium is used to achieve continuous tunability of the laser frequency.

Benefits of technology

The continuous tunable range of the laser is expanded, the frequency stability and the stability of the tuning process are improved, and the application needs of high-resolution spectral measurement and precision interference measurement are met.

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Abstract

The invention provides an application of a transparent medium with thickness compensation in a continuous tunable laser, and the cross section of the transparent medium with thickness compensation is in the shape of a right trapezoid, or the front surface of the transparent medium is a curved surface, and the rear surface of the transparent medium is a plane. According to the invention, two different transparent media with thickness compensation characteristics are applied to the external cavity semiconductor laser. Laser emitted by the laser passes through the narrow-band interference sheet, and laser output is achieved under the light feedback of the partially reflecting mirror. According to the invention, the cavity length is changed by adopting the transparent medium with the thickness compensation characteristic, the difference between the cavity mode frequency and the transmission frequency fIF is obtained, and the change of the maximum tunable range of the laser is observed.
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Description

Technical Field

[0001] The present invention relates to the technical field of lasers, and particularly to a laser with an optical medium having thickness compensation and a larger continuously tunable range. Background Art

[0002] With the continuous development of laser technology, external cavity semiconductor lasers have been widely used in fields such as precision manufacturing, lidar, and optical fiber communication due to their wavelength tunability and frequency stability. However, there are still many limitations in achieving a large range of continuous tunability in existing external cavity semiconductor lasers. Traditional tuning methods mainly rely on components such as fiber gratings, piezoelectric mirrors, or optical thin films to adjust the wavelength by changing the cavity length. However, this method is prone to mode hopping phenomena, resulting in limited continuity of wavelength tuning. In addition, it is difficult to achieve stable single-mode output within a large tuning range in the prior art, and the tuning process is complex and vulnerable to external factors such as temperature drift and mechanical vibration, thereby affecting the frequency stability and accuracy of the laser. These limitations make it difficult for current external cavity semiconductor lasers to meet the application requirements with extremely high demands for frequency stability and continuous tunability, such as high-resolution spectroscopic measurement and precision interferometric measurement. Therefore, improving the frequency tunable range of lasers requires not only breakthroughs in device technology but also breakthroughs in tuning methods.

[0003] Chinese Patent Application CN 119394219 A discloses a high-resolution small-angle measurement device based on laser frequency measurement. The measurement device includes a laser. Among them, a compensation medium (transparent solid medium) with a specific thickness and refractive index is placed in the resonant cavity, and it is rotated simultaneously with a narrowband interference filter. While performing interference frequency selection, the cavity length is changed, so that the center frequency of the transmission peak of the interference filter and the cavity mode frequency change simultaneously, enabling the laser frequency to be continuously tuned with high precision, thereby achieving ultra-high-precision continuous measurement of the rotation angle. However, since the thickness of the transparent solid medium is constant, the compensation effect on the cavity mode frequency when it is rotated simultaneously with the narrowband interference filter is limited, thus restricting the range in which the cavity mode frequency and the center frequency of the transmission peak of the interference filter change simultaneously, that is, restricting the angle measurement range of the device. That is, it has become a current technical difficulty to obtain a laser with a larger continuously adjustable range. How to improve the physical structure of the compensation medium to enhance the tunable range is an important research direction at present.

[0004] Therefore, breaking through the limitations of the prior art and further expanding the continuously tunable amount range of the laser while maintaining the original laser structure has important research significance, which will bring significant technological improvements to fields such as optical systems, automatic control, navigation and positioning, and satellite communication, and has broad application prospects. Summary of the Invention

[0005] The object of the present invention is to expand the continuous tunable range of a laser, and to propose a transparent medium with thickness compensation to achieve a laser with a larger continuous tunable range.

[0006] The idea of the present invention is to improve the cross-sectional shape of an optical medium (transparent medium) so that there is a linear or non-linear relationship between its thickness and the angle of the optical path, thereby changing the optical path length of the laser passing through the transparent medium at different angles, that is, the cavity length of the resonant cavity. By selecting the linear or non-linear parameters of the angle between the thickness of the transparent medium and the optical path to control the change amount of the resonant cavity length, the change of the cavity mode frequency caused by the change amount of the resonant cavity length is synchronized with the change of the center frequency of the transmission peak of the interference film caused by the rotation of the interference film, ensuring continuous change of the laser frequency and expanding the mode-hop-free tuning range.

[0007] To this end, the present invention provides a transparent medium with thickness compensation. The cross-sectional shape of the transparent medium with thickness compensation is a right trapezoid. The surface where the oblique waist of the right trapezoid is located is the front surface of the transparent medium, and the surface where the right-angled side of the right trapezoid is located is the rear surface of the transparent medium. The angle between the oblique waist and the right-angled side of the right trapezoid is β. When the transparent medium is in the initial position, the width parallel to the median line and intersecting the laser beam in the right trapezoid is the initial thickness D of the transparent medium g0 , when the change amount of the rotation angle of the transparent medium is θ, the width parallel to the median line and intersecting the laser beam in the right trapezoid is the thickness D' of the transparent medium, and D' = D g0 + Aθ, where A = tanβ and θ is the change amount of the rotation angle of the transparent medium; or,

[0008] The front surface of the transparent medium with thickness compensation is a curved surface and the rear surface is a plane. The cross-sectional shape of the transparent medium is that the front side is a curve. When the change amount of the rotation angle of the transparent medium is θ, the width parallel to the median line and intersecting the laser beam in the cross-sectional shape is the thickness D″ of the transparent medium, and D″ satisfies the relationship θ = aD″ 2 + b, where θ is the change amount of the rotation angle of the transparent medium, and a and b are both constants, as Figure 1 shown in FIGS. A and 1B.

[0009] The present invention also provides an application of the above-mentioned transparent medium with thickness compensation in a continuously tunable laser.

[0010] Furthermore, the present invention also provides a continuously tunable laser with an optically compensating medium having a thickness compensation. The laser includes a laser generating device and a mirror group sequentially arranged on the optical path. A high-precision horizontal rotating table 105 is arranged between the laser generating device and the mirror group. A narrowband interference filter 103 and a transparent medium 104 are fixed on the high-precision horizontal rotating table 105. The light output by the laser generating device is filtered to remove out-of-band light after passing through the narrowband interference filter 103, obtaining narrowband light. The narrowband light returns to the laser diode after passing through the transparent medium 104 and the mirror group. When the oscillation in the cavity reaches the threshold, laser light is output by the mirror group. Among them, the transparent medium 104 is the optically compensating medium having a thickness compensation.

[0011] When the cross-sectional shape of the transparent medium is a right trapezoid, the fixed position of the transparent medium in the laser is such that the height passing through the midpoint of the median line of the right trapezoid is symmetric and non-parallel to the narrowband interference filter with the diameter of the rotating table perpendicular to the optical path as the axis. When the front surface of the transparent medium having a thickness compensation is a curved surface and the rear surface is a plane, the fixed position of the transparent medium in the laser is such that the height passing through the midpoint of the median line of the cross-sectional shape is symmetric and non-parallel to the narrowband interference filter with the diameter of the rotating table perpendicular to the optical path as the axis.

[0012] At this time, in the laser, when the high-precision horizontal rotating table rotates, the narrowband interference filter and the transparent medium rotate synchronously, and the change amount Δf of the resonant cavity mode frequency g satisfies the following relationship:

[0013]

[0014] The resonant cavity mode frequency f g satisfies the following relationship:

[0015]

[0016] Among them, f0 is the cavity mode frequency of the transparent medium at the initial angle α, α is the initial angle between the median line of the cross-sectional shape of the transparent medium and the laser propagation direction, n eff is the refractive index of the transparent medium, L is the initial cavity length, λ0 is the cavity mode wavelength of the transparent medium at the initial angle α (its value is equal to the transmission wavelength λ′0 of the interference filter at the angle (π - α)), and D = D′ or D = D′′.

[0017] Taking white glass as the transparent medium as an example, combined with Figure 1-2 and referring to the laser part in CN 119394219A, its working principle is specifically explained as follows:

[0018] When the initial angle of the white glass is α (i.e., the initial included angle between the median line of the cross-sectional shape of the white glass and the laser propagation direction is α): the initial cavity length Therefore, when the white glass rotates clockwise from α to α - θ, the change in cavity length is:

[0019] where n eff is the refractive index of the white glass, D is the thickness of the white glass, L1 is the length from the output light surface of the laser to the front surface of the white glass, L2 is the length from the rear surface of the white glass to the front surface of the partial mirror, and θ is the rotation angle of the white glass.

[0020] According to the relationship that when the cavity length changes by half a wavelength, the frequency changes by c / 2L:

[0021] The relationship between the resonator cavity jitter ΔL and the change in cavity mode frequency Δf g is:

[0022]

[0023] Given The relationship between the change in cavity mode wavelength Δλ and the rotation angle θ of the white glass satisfies the following:

[0024]

[0025] where λ0 is the cavity mode wavelength of the white glass when the initial angle is α.

[0026] When the cross-sectional shape of the white glass is a right trapezoid, let the thickness of the white glass D′ = D g0 + Aθ, D g0 is the initial thickness of the white glass, θ is the change in the rotation angle of the white glass, A = tanβ is the slope of the linear thickness compensation, and β is the included angle between the oblique waist and the right-angle side of the right trapezoid; that is, the change in cavity mode frequency as the white glass rotates is:

[0027]

[0028] Therefore, when the white glass is placed with an initial angle of α as shown Figure 1 The relationship between the rotation angle θ after the white glass rotates clockwise and the cavity mode frequency f g is:

[0029]

[0030] where f0 is the cavity mode frequency of the white glass when the initial angle is α.

[0031] Similarly, when the front surface of the white glass is a curved surface and the rear surface is a flat surface, and its cross-sectional shape has a curved front side, the thickness D″ of the white glass satisfies the relationship Both a and b are constants; that is, the change in the white glass rotation cavity mode frequency is:

[0032]

[0033] In this case, when the initial angle of the white glass is α, the rotation angle θ of the white glass and the cavity mode frequency f g have the following relationship:

[0034]

[0035] On the other hand, in the present invention, the rotation angle of the narrowband interference filter and the transmission wavelength λ IF have the following relationship expression:

[0036]

[0037] λ′0 is the transmission wavelength of the interference filter at the angle π - α, and n eff2 is the refractive index of the narrowband interference filter. Since the positions of the narrowband interference filter and the transparent medium are axisymmetric with respect to the diameter of the turntable perpendicular to the optical path and are not parallel, when the interference filter rotates clockwise by θ from the initial angle π - α, the angle

[0038] According to the formula the rotation angle of the narrowband interference filter and the transmission frequency f IF have the following relationship:

[0039]

[0040] In the present invention, the laser generating device is a conventional setting in the art and generally includes a laser diode and a first collimating lens sequentially arranged on the optical path. Among them, the working band of the laser diode can be any band. Preferably, from the perspective of facilitating acquisition or saving economy, a 780 nm band laser diode can be used. Those skilled in the art can also select laser diodes with other working wavelengths, such as 420 nm, 850 nm, 1550 nm laser diodes, etc.

[0041] Since the tunable range without mode hopping that can be achieved by the external cavity feedback semiconductor laser with a narrowband filter by tuning the cavity length through feedforward is about ±10 GHz. Therefore, in order to ensure continuous tuning, the frequency difference between the cavity mode frequency f g and the transmission frequency f IF at the same angle should not exceed 10 GHz.

[0042] Compared with the prior art, the present invention applies two different transparent media with thickness compensation characteristics to an external cavity feedback semiconductor laser of a narrowband filter. The laser emitted from the laser passes through a narrowband interference filter to obtain narrowband light, filtering the broadband light emitted by the laser diode into a narrowband light beam. After optical feedback by a partial mirror, when the oscillation in the cavity reaches the threshold, the measured laser is output by the mirror group. It is verified and confirmed by the present invention that by using a transparent medium with thickness compensation characteristics to change the cavity length, under the condition that the frequency difference between the cavity mode frequency f g and the transmission frequency f IF should not exceed 10 GHz, the corresponding angular change range is larger, that is, a larger continuous tunable range is obtained. Description of the Drawings

[0043] Figure 1 A and Figure 1 B are transparent media with thickness compensation;

[0044] Figure 2 is a schematic diagram of the principle of the laser in Embodiment 1;

[0045] Wherein: 101, laser diode, 102, first collimating lens, 103, narrowband interference filter, 104, transparent medium, 105, high-precision horizontal rotating table, 106, rotating table fixing seat, 107, first collimating lens, 108, partial mirror, 109, second collimating lens, 110, mirror.

[0046] Figure 3 is the difference relationship between the change in the cavity mode frequency caused by the rotation angle of the white glass with different thickness compensations and the change in the transmission frequency caused by the simultaneous rotation of the interference filter when the initial angles are 10° and 15°.

[0047] Figure 4 is the relationship between the rotation angle of the white glass with different thicknesses D and f g and the relationship between the different rotation angles of the interference filter and f IF respectively. Detailed Embodiments

[0048] The following embodiments are used to explain the technical solutions of the present invention non-limitingly.

[0049] Embodiment 1 examines the influence of the thickness of transparent solid media with different parameters on the continuous tunable range

[0050] As Figure 2 shown in the figure, the working band of the laser is 780 nm. The device mainly includes a laser diode 101, a first collimating lens 102, a narrowband interference filter 103, and a transparent medium 104 (made of white glass with a refractive index of n eff= 1.5) The focusing lens 107, the partial mirror 108, the second collimating lens 109, and the mirror 110. The high-precision horizontal rotating table 105 is fixed on the rotating table fixing seat 106. Among them, the narrowband interference filter 103 and the transparent medium 104 are fixed on the precision rotating platform 105. Their placement positions are centered on the diameter of the rotating table perpendicular to the optical path, making the narrowband interference filter 103 highly symmetric and non-parallel to the midpoint of the median line of the cross-sectional shape passing through the transparent medium 104.

[0051] The cross-sectional shape of the transparent medium 104 is as Figure 1 shown in A, which is a right trapezoid, and the plane where the right-angled side is located is its rear surface.

[0052] During operation, the light output by the 780 nm laser diode is collimated, the out-of-band light is filtered by the narrowband interference filter, then passes through the transparent solid medium, reaches the partial mirror through the focusing lens and is reflected. When the oscillation in the resonant cavity reaches the threshold, the laser is output by the partial mirror. By simultaneously rotating the interference filter and the transparent solid medium, the central frequency of the transmission peak of the interference filter is synchronized with the cavity mode frequency, realizing continuously tunable output frequency.

[0053] In this embodiment, the continuously tunable range of the laser frequency achieved by setting a transparent medium with thickness compensation is investigated:

[0054] Set the cavity length to 10 cm, the initial angle to α = 10°, λ0 = 780 nm, select transparent solid media with different included angles β between the front surface and the rear surface, and the refractive index of the transparent solid medium is n eff = 1.5, the designed thickness is D′ = 0.048 + θ × A, A = tanβ. Calculate the f g -f IF curves caused by each transparent solid medium and the rotation angle θ of the interference filter when taking different values of A, as shown in Figure 3 (a). Among them,

[0055]

[0056] Among them,

[0057] Through Figure 3 (a), it can be obtained that when the value of A is selected as 0.00417, the angular change range that satisfies the condition that f g -f IF does not exceed ±10 GHz is relatively large. As shown in Figure 4 (a), we respectively plot the cavity mode frequency f g when the thickness D of the optical element is D = D′ = 0.048 + 0.00417θ and D = 0.048 m, and the transmission frequency f IF, observe the tunable amount of the laser, where the abscissa is the change in θ and the ordinate is the frequency.

[0058] The results show that when the frequency difference between the cavity mode frequency and the transmission frequency at the same angle does not exceed the condition of ±10 GHz, that is, f g -f IF does not exceed -1.0×10 10 ~1.0×10 10 Hz, when a conventional transparent medium with a thickness of D = 0.048 (m) is used, the corresponding angular change range is -0.59° to 0.57°, and the corresponding laser frequency tunable range is 3.858×10 14 to 3.862×10 14 Hz (according to Figure 4 (the green dashed line in (a)), the tunable amount is 4×10 11 Hz. When a transparent medium with an included angle between the front surface and the rear surface is used, a larger range can be obtained according to different values of A. For example, when D′ = 0.048 + 0.00417θ, when the frequency difference between the cavity mode frequency and the transmission frequency at the same angle (that is, f g -f IF ) does not exceed the condition of ±10 GHz, the corresponding angular change range is -3.86° to 1.25°, and the corresponding laser frequency tunable range is 3.851×10 14 to 3.864×10 14 Hz (according to Figure 4 (the red dashed line in (a)), the tunable amount is 1.3×10 12 Hz. It can be seen that when the transparent medium adopts the original structure, that is, its front and rear surfaces are parallel, the continuous tunable range of the laser is small, while using the transparent medium with thickness compensation of the present invention can expand the continuous tunable range of the laser.

[0059] Under the same conditions, set the initial angle to α = 15°, design the thickness to be D′ = 0.04575 + θ×A, calculate the values of different A, and draw the f g -f IF curve caused by each transparent solid medium and the interference film when the rotation angle is θ, as shown in Figure 3 (b).

[0060] From Figure 3 (b), it can be obtained that when the value of A is selected as 0.00278, the angular change range that satisfies the condition that f g -f IF does not exceed ±10 GHz is larger. As shown in Figure 4(b), we respectively plot the cavity mode frequency f when the thicknesses of the optical elements are D = D′ = 0.04575 + 0.00278θ and D = 0.04575 m g , as well as the transmission frequency f IF , and observe the tunable range of the laser

[0061] It can be seen that when the condition that the difference between f g -f IF does not exceed ±10 GHz is satisfied, when using a conventional transparent medium with a thickness of D = 0.04575 (m), the corresponding angular change range is -0.59° to 0.56°, and the corresponding tunable range of the laser frequency is from 3.876×10 14 to 3.881×10 14 Hz (according to the blue dashed line in Figure 4 (b)), and the tunable amount is 5×10 11 Hz. When using a transparent medium with an included angle between the front surface and the rear surface, a larger range can be obtained according to different values of A. For example, when D′ = 0.04575 + 0.00278θ, when the condition that the frequency difference between the cavity mode frequency and the transmission frequency at the same angle (i.e., f g -f IF ) does not exceed ±10 GHz is satisfied, the corresponding angular change range is -4.67° to 1.37°, and the corresponding tunable range of the laser frequency is from 3.861×10 14 to 3.884×10 14 Hz (according to the pink dashed line in Figure 4 (b)), and the tunable amount is 2.3×10 12 Hz

[0062] Example 2

[0063] The same settings as in Example 1, the difference is that the transparent medium with a right trapezoidal cross-section is replaced by a transparent medium with a curved front surface and a flat rear surface. When its cross-sectional shape has a curved front side, the thickness D′′ satisfies the relationship Under the conditions that the initial angles are α = 10° and α = 15° respectively, when setting different values of a and b, the curves of f g -f IF caused by each transparent solid medium and the interference film when the rotation angle is θ are plotted, as shown in Figure 3 (c) and (d). Among them,

[0064]

[0065]

[0066] From Figure 3 (c), it can be obtained that when When, it satisfies f g -f IF The angular change range that does not exceed the condition of ±10 GHz is relatively large. As Figure 4 As shown in (c), we respectively plot the thickness of the optical element and the cavity mode frequency f when D = 0.048 m g , as well as the transmission frequency f IF , and observe the laser tunable amount.

[0067] The results show that when the initial angle α = 10° When, when it satisfies f g -f IF Without exceeding the condition of ±10 GHz, the corresponding angular change range is -2.11 to 2.27°, and the laser frequency tunable range is 3.855×10 14 to 3.867×10 14 Hz (according to Figure 4 (the orange dashed line in (c)), and the tunable amount is 1.2×10 12 Hz. It is significantly larger than the continuously tunable range achieved when using conventional transparent media.

[0068] And when the initial angle α = 15° When, when it satisfies f h -f IF Without exceeding ±10 GHz, the corresponding small angular change amount is -3.61 to 1.12°, and the laser frequency tunable range is 3.865×10 14 to 3.883×10 14 Hz (according to Figure 4 (the cyan dashed line in (d)), and the tunable amount is 1.8×10 12 Hz. It is also significantly larger than the continuously tunable range of the laser frequency achieved when using conventional transparent media.

[0069] It can be seen that the transparent medium with thickness compensation of the present invention is applied to the laser, and under the condition that f g -f IF Does not exceed ±10 GHz, the continuously tunable range of the laser can be effectively improved.

Claims

1. A transparent medium with thickness compensation, characterized in that The cross-sectional shape of the transparent medium with thickness compensation is a right trapezoid. The surface where the oblique waist of the right trapezoid is located is the front surface of the transparent medium, the surface where the right-angled side of the right trapezoid is located is the rear surface of the transparent medium, and the included angle between the oblique waist and the right-angled side of the right trapezoid is β. When the transparent medium is in the initial position, the width parallel to the midline within the right trapezoid and intersecting with the laser beam is the initial thickness D of the transparent medium g0 , when the rotation angle change of the transparent medium is θ, the width parallel to the midline within the right trapezoid and intersecting with the laser beam is the thickness D' of the transparent medium, and D' = D g0 + Aθ, where A = tanβ and θ is the rotation angle change of the transparent medium; or The front surface of the transparent medium with thickness compensation is a curved surface, and the rear surface is a plane. The cross-sectional shape of the transparent medium has a curved front side. When the change in the rotation angle of the transparent medium is θ, the width parallel to the median line and intersecting the laser beam within the cross-sectional shape is the thickness D″ of the transparent medium, and D″ satisfies the relationship θ = aD″ 2 + b, where θ is the change in the rotation angle of the transparent medium, and both a and b are constants.

2. Application of the optical medium with thickness compensation according to Claim 1 in a continuously tunable laser.

3. A continuously tunable laser with a transparent medium having thickness compensation, the laser comprising a laser generating device and a mirror group sequentially arranged on an optical path, a high-precision horizontal rotating table (105) is arranged between the laser generating device and the mirror group, a narrowband interference filter (103) and a transparent medium (104) are fixed on the high-precision horizontal rotating table (105), the light output by the laser generating device is filtered to remove out-of-band light after passing through the narrowband interference filter (103) to obtain narrowband light; the narrowband light returns to the laser diode after passing through the transparent medium (104) and the mirror group, and when the intracavity oscillation reaches the threshold, the measured laser is output by the mirror group; characterized in that The transparent medium (104) is the transparent medium with thickness compensation according to Claim 1; When the cross-sectional shape of the transparent medium is a right trapezoid, the fixed position of the transparent medium in the laser is such that the height passing through the midpoint of the median line of the right trapezoid is symmetric and non-parallel to the narrowband interference filter with respect to the diameter of the rotating table perpendicular to the optical path; when the front surface of the transparent medium with thickness compensation is a curved surface and the rear surface is a flat surface, the fixed position of the transparent medium in the laser is such that the height passing through the midpoint of the median line of the cross-sectional shape is symmetric and non-parallel to the narrowband interference filter with respect to the diameter of the rotating table perpendicular to the optical path.

4. The laser according to claim 3, characterized in that When the high-precision horizontal rotating table rotates, the narrowband interference filter and the transparent medium rotate synchronously, and the change amount Δf of the resonant cavity mode frequency g satisfies the following relationship: The resonant cavity mode frequency f g Satisfies the following relationship: Among them, f0 is the cavity mode frequency of the transparent medium at the initial angle α, α is the initial angle between the median line of the cross-sectional shape of the transparent medium and the laser propagation direction, n eff is the refractive index of the transparent medium, λ0 is the cavity mode wavelength of the transparent medium at the initial angle α, and D = D' or D = D".

Citation Information

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