KTP crystal adiabatic frequency doubling method based on photoelectric effect

Abstract

The application discloses a KTP crystal adiabatic frequency doubling method based on photoelectric effect and belongs to the technical field of nonlinear optical frequency conversion. The KTP crystal is processed into a wedge-shaped crystal with linearly changed thickness along a light transmission direction, and the thickness of the wedge-shaped crystal linearly increases from an incident end to an emission end. Continuous parallel flat electrodes are prepared on upper and lower inclined surfaces of the wedge-shaped crystal, a single constant high-voltage pulse is applied to the flat electrodes, a spatially monotonically decreasing gradient electric field is formed in the wedge-shaped crystal by using continuous changes of the flat electrode spacing along the light transmission direction, and based on the spatially monotonically decreasing gradient electric field formed in the wedge-shaped crystal, a phase mismatch amount between fundamental frequency light and frequency doubled light monotonically and smoothly changes from a negative value to a positive value along the light transmission direction and satisfies an adiabatic stability criterion, and enters an adiabatic state. The application generates a monotonically and gradually changed electric field along the light transmission direction through the trapezoidal flat electrodes, so that the system enters the adiabatic state and realizes high-efficiency conversion of the fundamental frequency light into the frequency doubled light.

Description

Technical Field

[0001] This invention relates to the field of nonlinear optical frequency conversion technology, and in particular to a KTP crystal adiabatic frequency doubling method based on the photoelectric effect. Background Technology

[0002] Second harmonic generation (SHG) is the core method for achieving laser frequency up-conversion. Traditional SHG technology relies on meeting strict phase-matching conditions, i.e., the difference in propagation constants between the fundamental and harmonic frequencies is zero. However, this technology has the following inherent drawbacks: a narrow range of permissible parameters, sensitivity to crystal temperature fluctuations and incident angle deviations, making it difficult to operate under wide temperature or broad spectral line conditions; and a low efficiency limit, as the energy oscillates periodically between the fundamental and harmonic frequencies due to phase mismatch accumulation caused by dispersion, making it difficult to exceed 70% for single-pass conversion efficiency.

[0003] Recent studies have shown that if the phase mismatch can be monotonically and smoothly varied from a large negative value to a large positive value along the direction of light propagation, the system will enter an adiabatic state. In this state, energy flows in one direction, and theoretically, 100% pump depletion can be achieved.

[0004] Currently, the main approaches to achieving spatial gradual change in phase mismatch and their drawbacks are as follows:

[0005] The temperature gradient method sets a huge temperature difference at both ends of the crystal, such as between the heating end and the cooling end. The required temperature difference is extremely large, and thermal stress can easily cause the crystal to crack; thermal equilibrium is established very slowly.

[0006] The segmented / aperiodic polarization method uses photolithography to create a variable-period ferroelectric domain structure inside a crystal. The manufacturing process is extremely complex and costly. Once fabricated, the phase matching curve is fixed and cannot be dynamically adjusted. Summary of the Invention

[0007] The purpose of this invention is to overcome the shortcomings of the prior art and provide a KTP crystal adiabatic frequency doubling method based on the photoelectric effect. This method can utilize a wedge-shaped KTP crystal in conjunction with a single high-voltage pulse source to naturally form a continuous gradient electric field through the geometric structure, thereby perfectly satisfying the adiabatic frequency transformation conditions.

[0008] To achieve the above objectives, the present invention is implemented using the following technical solution:

[0009] This invention provides a method for adiabatic frequency doubling of KTP crystals based on the photoelectric effect, comprising:

[0010] The KTP crystal is processed into a wedge-shaped crystal with a linearly varying thickness along the light transmission direction. The thickness of the wedge-shaped crystal increases linearly from the incident end to the exit end.

[0011] A continuous parallel plate electrode is prepared on the upper and lower inclined surfaces of the wedge-shaped crystal. A single constant high voltage pulse is applied to the plate electrode. By utilizing the continuous change in the spacing between the plate electrodes along the light transmission direction, a spatially monotonically decreasing gradient electric field is formed inside the wedge-shaped crystal.

[0012] Based on the spatially monotonically decreasing gradient electric field formed inside the wedge-shaped crystal, the phase mismatch between the fundamental frequency light and the second-order light is driven to change monotonically and smoothly from a negative value to a positive value along the light transmission direction, and the adiabatic stability criterion is satisfied, so the system enters the adiabatic state.

[0013] Optionally, the slope of the thickness variation of the wedge-shaped crystal is expressed as:

[0014] ;

[0015] in, Indicates the length of the light transmission direction The slope of the thickness variation of the lower wedge-shaped crystal; Indicates the thickness of the wedge-shaped crystal at the incident end; Indicates the thickness of the wedge-shaped crystal at the exit end; Indicates the total length of the light transmission direction.

[0016] Optionally, the monotonically decreasing gradient electric field formed inside the wedge-shaped crystal is expressed as:

[0017] ;

[0018] in, Indicates the length of the light transmission direction The spatially monotonically decreasing gradient electric field formed inside the lower wedge-shaped crystal; Indicates a single, constant high-voltage pulse; Indicates the length of the light transmission direction The slope of the thickness variation of the lower wedge-shaped crystal.

[0019] Optionally, based on the spatially monotonically decreasing gradient electric field formed inside the wedge-shaped crystal, the phase mismatch between the fundamental frequency light and the second-order harmonic light is driven to monotonically and smoothly change from a negative value to a positive value along the light transmission direction, including:

[0020] Based on the linear electro-optic effect of KTP crystal, the refractive index of the wedge crystal is changed by the monotonically decreasing gradient electric field formed inside the wedge crystal, thereby driving the refractive index change of the fundamental frequency light and the frequency harmonic light.

[0021] The change in refractive index of the fundamental and harmonic light drives the phase mismatch between the fundamental and harmonic light to change monotonically and smoothly from a negative value to a positive value along the light transmission direction.

[0022] Optionally, the phase mismatch between the fundamental frequency light and the frequency-doubled light is expressed as:

[0023] ;

[0024] In the formula, ;

[0025] in, This indicates the phase mismatch between the fundamental frequency light and the frequency-doubled light; This represents the initial phase mismatch when no electric field is applied. Indicates the photoelectric tuning coefficient; Indicates the length of the light transmission direction The spatially monotonically decreasing gradient electric field formed inside the lower wedge-shaped crystal; This indicates the wavelength of the fundamental frequency light in a vacuum; This represents the refractive index of the fundamental frequency o-ray in a wedge-shaped crystal; This represents the refractive index of the fundamental e-ray in a wedge-shaped crystal; Both represent the linear electro-optic coefficients of the wedge-shaped crystal.

[0026] Optionally, the phase mismatch between the fundamental frequency light and the frequency-doubled light crosses the matching point and satisfies the boundary conditions;

[0027] The boundary conditions are expressed as follows:

[0028] ;

[0029] ;

[0030] In the formula, ;

[0031] in, , These represent light transmission direction lengths of 0 and 0 respectively. The phase mismatch between the fundamental frequency light and the second harmonic light; Indicates the total length in the direction of light transmission; Represents the characteristic length of the system; This represents the speed of light in a vacuum. Represents the vacuum permittivity; This represents the average refractive index of the fundamental frequency light in the wedge-shaped crystal; This represents the average refractive index of the frequency-doubled light in the wedge-shaped crystal; This indicates the wavelength of the fundamental frequency light in a vacuum; This indicates the wavelength of frequency-doubled light in a vacuum; Indicates the effective nonlinear coefficient of the wedge-shaped crystal; It represents the intensity of the incident fundamental frequency light.

[0032] Optionally, the adiabatic stability criterion is expressed as:

[0033] .

[0034] Optionally, the single constant high-voltage pulse is a nanosecond-level high-voltage pulse, and a digital delay generator is used to make the leading edge of the single constant high-voltage pulse advance before the laser pulse turns on and the trailing edge lag after the laser pulse turns off.

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

[0036] This invention utilizes the linear electro-optic effect of KTP crystals to generate a monotonically gradually changing electric field along the light transmission direction through trapezoidal plate electrodes with spatial gradient characteristics. This brings the system into an adiabatic state, achieving a high-efficiency conversion from fundamental frequency light to frequency-doubled light. Only a single-channel high-voltage source is required, eliminating the need for complex voltage divider networks or multi-channel synchronous control, significantly reducing system cost and failure rate. The maximum surface electric field is far below the damage resistance threshold of KTP crystals. Combined with the pulsed operating mode, the crystal has almost no risk of electrical breakdown. It abandons the large temperature gradient method, allowing the crystal to operate near room temperature without the risk of thermally induced birefringence and cracking. By finely adjusting the applied voltage, the phase mismatch curve can be linearly shifted, thus adapting to incident lasers with different center wavelengths or peak powers. It can be widely used in lidar, biomedicine, quantum optics, and high-power green lasers. Attached Figure Description

[0037] Figure 1 A schematic flowchart of the KTP crystal adiabatic frequency doubling method based on the photoelectric effect provided in an embodiment of the present invention;

[0038] Figure 2 This is a schematic diagram of the structure of a wedge-shaped crystal and its upper and lower inclined surfaces used to prepare a continuous parallel flat plate electrode, as provided in an embodiment of the present invention. Detailed Implementation

[0039] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the embodiments of the present invention and the specific features in the embodiments are detailed descriptions of the technical solution of the present invention, rather than limitations thereof. In the absence of conflict, the embodiments of the present invention and the technical features in the embodiments can be combined with each other.

[0040] The term "and / or" simply describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A alone, A and B simultaneously, or B alone. Additionally, the character " / " generally indicates that the preceding and following related objects have an "or" relationship.

[0041] Example 1

[0042] like Figure 1As shown, this embodiment provides a KTP crystal adiabatic frequency doubling method based on the photoelectric effect, including the following steps:

[0043] Step 1: Process the KTP crystal into a wedge-shaped crystal with linearly varying thickness along the light transmission direction, specifically as follows:

[0044] Potassium titanium phosphate (KTP) crystals were processed into wedge-shaped crystals with linearly varying thickness along the light transmission direction. The KTP crystals were then cut along a specific direction at an angle of [insert angle here]. KTP crystals are wedge-shaped along the light transmission direction, i.e., trapezoidal prisms.

[0045] The thickness of the wedge-shaped crystal increases linearly from the incident end to the exit end. Let the thickness at the incident end, i.e., the thin end, be... The thickness of the exit end, i.e., the thick end, is Because the thickness of the wedge-shaped crystal varies linearly along the z-axis, the length in the light transmission direction... The slope of the thickness variation of the lower wedge crystal Represented as:

[0046] ;

[0047] in, Indicates the total length of the light transmission direction.

[0048] In this embodiment, as Figure 2 As shown, the total length in the light transmission direction The thickness at the incident end is 30mm. The thickness at the exit end is 3mm. It is 10mm.

[0049] Step 2: Prepare continuous parallel planar electrodes and apply a single constant high-voltage pulse to form a gradient electric field, specifically:

[0050] A continuous parallel plate electrode is prepared on the upper and lower inclined surfaces of a wedge-shaped crystal, and a single constant high voltage pulse is applied to the plate electrode.

[0051] A continuous parallel metal plate electrode is plated on the upper and lower inclined surfaces of a wedge-shaped crystal, and the same single constant high-voltage pulse is applied. In this embodiment, a single constant high-voltage pulse The amplitude is 22.45kV and the pulse width is 20ns.

[0052] By utilizing the continuous variation in the spacing between the planar electrodes along the light transmission direction, a spatially monotonically decreasing gradient electric field is formed inside the wedge-shaped crystal, with the length along the light transmission direction... The monotonically decreasing gradient electric field formed inside the lower wedge-shaped crystal Represented as:

[0053] .

[0054] Step 3: Naturally generate a continuous gradient electric field through geometric structure to satisfy the adiabatic frequency transformation condition, specifically:

[0055] Based on the spatially monotonically decreasing gradient electric field formed inside the wedge-shaped crystal, the phase mismatch between the fundamental frequency light and the second-order light is driven to change monotonically and smoothly from a negative value to a positive value along the light transmission direction, and the adiabatic stability criterion is satisfied, so the system enters the adiabatic state.

[0056] Based on the linear electro-optic effect of KTP crystal, the refractive index of the wedge crystal is driven to change by the monotonically decreasing gradient electric field formed inside the wedge crystal, thereby driving the refractive index change of the fundamental frequency light and the second-order harmonic light; the fundamental frequency light includes the fundamental o-light and e-light.

[0057] The change in refractive index of the fundamental and harmonic light drives the phase mismatch between the fundamental and harmonic light to change monotonically and smoothly from a negative value to a positive value along the light transmission direction.

[0058] Photoelectric tuning coefficient Represented as:

[0059] ;

[0060] in, This indicates the wavelength of the fundamental frequency light in a vacuum; This represents the refractive index of the fundamental frequency o-ray in a wedge-shaped crystal; This represents the refractive index of the fundamental e-ray in a wedge-shaped crystal; Both represent the linear electro-optic coefficients of the wedge-shaped crystal.

[0061] In this embodiment, the physical properties of the KTP crystal at 1064 nm are substituted, i.e. , , , We can obtain:

[0062] ;

[0063] at this time It is dimensionless.

[0064] The phase mismatch between the fundamental frequency light and the second harmonic light Represented as:

[0065] ;

[0066] in, This represents the initial phase mismatch when no electric field is applied.

[0067] According to Yaakobi's self-resonance theory, the characteristic length of the system... Determined by light intensity and nonlinear coefficients, i.e., the characteristic length of the system. Represented as:

[0068] ;

[0069] in, This represents the speed of light in a vacuum. Represents the vacuum permittivity; This represents the average refractive index of the fundamental frequency light in the wedge-shaped crystal; This represents the average refractive index of the frequency-doubled light in the wedge-shaped crystal; This indicates the wavelength of the fundamental frequency light in a vacuum; This indicates the wavelength of frequency-doubled light in a vacuum; Indicates the effective nonlinear coefficient of the wedge-shaped crystal; It represents the intensity of the incident fundamental frequency light.

[0070] In this embodiment, the parameter substituted is light intensity. , , , The calculation yields:

[0071] .

[0072] To achieve complete pump depletion, the phase mismatch between the fundamental frequency light and the second-harmonic light must cross the matching point, i.e. And it satisfies the boundary conditions.

[0073] The boundary conditions are expressed as follows:

[0074] ;

[0075] ;

[0076] in, , These represent light transmission direction lengths of 0 and 0 respectively. The phase mismatch between the fundamental frequency light and the frequency harmonic light. The length in the direction of light transmission at the incident end. , The length in the light transmission direction at the output end. .

[0077] In this embodiment, , .

[0078] To allow sufficient margin for future construction, this plan is designed as follows:

[0079] .

[0080] Total change .

[0081] The adiabatic stability criterion is expressed as:

[0082] .

[0083] In this embodiment, It meets the requirements for deep insulation.

[0084] Therefore, due to Monotonically increasing, therefore the field strength Monotonically decreasing. (Based on the formula) ,when When decreasing, It automatically increases, thereby achieving a linear increase in phase mismatch.

[0085] To prevent cumulative damage caused by long-term high-voltage DC action on the crystal, a single constant high-voltage pulse is used, which is a nanosecond-level high-voltage pulse. A digital delay generator is used to make the leading edge of the single constant high-voltage pulse start earlier than the laser pulse and the trailing edge lag behind the laser pulse.

[0086] In this embodiment, a high-voltage pulse power supply outputs a 22.45 kV, 20 ns pulse voltage and is electrically connected to a trapezoidal electrode; a synchronization delay controller is used to receive the laser synchronization signal and trigger the high-voltage pulse output; the maximum output voltage of the high-voltage pulse power supply is not less than 25 kV, and both the pulse rise and fall edges are less than 5 ns.

[0087] The high-voltage pulse width is 20 ns, and the laser pulse width is 10 ns. Using a digital delay generator, the leading edge of the single constant high-voltage pulse is turned on 5 ns before the laser pulse, and the trailing edge is turned off 5 ns after the laser pulse. That is, the laser passes completely within the middle 10 ns window of the electric field flat-top period. The equivalent high-voltage action time is only 20 ns, the average power consumption is extremely low, and the field strength is far below the breakdown threshold, which greatly improves the long-term working life of the crystal.

[0088] In this embodiment, the KTP crystal is fabricated into a wedge shape with a length of 30 mm, and the thickness linearly increases from 3 mm at the incident end to 10 mm at the output end. A single high-voltage pulse of 22.45 kV and 20 ns is applied using trapezoidal electrodes plated on the upper and lower slopes. By continuously varying the electrode spacing, a monotonically decreasing gradient electric field is formed within the crystal, driving the phase mismatch to smoothly cross from -500 m⁻¹ to +1400 m⁻¹, strictly meeting the self-resonant adiabatic condition, with a theoretical conversion efficiency exceeding 90%. The 20 ns high-voltage pulse width completely covers the 10 ns laser pulse, and the maximum field strength is only 7.02 V / μm, far below the KTP breakdown threshold. The structure is extremely simple, safe, and reliable, solving the problems of abrupt changes in field strength and large temperature gradient stress in traditional segmented electrodes. It is suitable for high-efficiency broadband green lasers and for expanding the temperature tolerance range of frequency conversion.

[0089] Example 2

[0090] Based on Example 1, this example introduces an experimental example of a KTP crystal adiabatic frequency doubling method based on the photoelectric effect:

[0091] High optical quality KTP crystal rods are selected, along the phase matching direction. Cutting. The translucent surface undergoes fine polishing to achieve a surface shape accuracy of [insert accuracy here]. The parallelism is better than 10 seconds. The two sides of the crystal are processed into trapezoidal bevels to ensure a light transmission length of 30mm, a thickness of 3mm at the thin end with a tolerance of ±0.02mm, and a thickness of 10mm at the thick end with a tolerance of ±0.02mm.

[0092] Electrodes are deposited on a trapezoidal bevel using magnetron sputtering. A 20nm thick chromium (Cr) underlayer enhances adhesion, while a 200nm thick gold (Au) outer layer reduces contact resistance. Electrode edges should be precisely aligned with crystal edges to prevent tip discharge.

[0093] A dual-color antireflection coating is deposited on the two light-transmitting end faces of the crystal, namely AR@1064nm & 532nm, with residual reflectance <0.5%@1064nm and <0.3%@532nm.

[0094] The crystal was placed in a small semiconductor refrigeration temperature control furnace with a temperature control setpoint of 25.0℃ and a temperature control accuracy of ±0.1℃ to eliminate the interference of ambient temperature fluctuations on the refractive index.

[0095] Connect the trapezoidal electrode to a high-voltage pulse power supply. The maximum output is 25kV, and the pulse width is adjustable to 20ns.

[0096] Connect the laser, outputting a 1064nm pulse width of 10ns, and the synchronous output signal to the digital delay generator.

[0097] The digital delay generator outputs two channels: one to trigger a high-voltage power source, and the other to be used as an oscilloscope trigger.

[0098] The high voltage is set to delay the laser synchronization signal by +5ns to ensure that the field strength has stabilized by the time the laser arrives.

[0099] Start the laser and high voltage source.

[0100] The 532nm green light output was measured using a power meter at the 30mm output end.

[0101] Theoretically, 1W of incident 1064nm fundamental frequency light can output >0.9W of 532nm frequency-doubled light.

[0102] When the center wavelength of the incident laser shifts to 1064.5nm, the original It will no longer be -500 m⁻¹. At this point, there is no need to replace the crystal; simply fine-tune the high voltage amplitude from 22.45 kV to 22.0 kV or 23.0 kV, and the entire voltage can be shifted according to the offset direction. The curve allows the system to re-enter the adiabatic range, which verifies that the invention has excellent dynamic tuning capability.

[0103] When the laser repetition frequency is increased to 100kHz, the repetition frequency of the high-voltage pulse is synchronously increased to 100kHz. Due to the pulse width of only 20ns and the duty cycle of only 0.2%, the average output power of the high-voltage source is extremely low, which will not cause cumulative heating of the crystal and can still work stably.

[0104] This embodiment utilizes the linear electro-optic effect of KTP crystals, namely the Pockels effect, to generate a monotonically gradually changing electric field along the light transmission direction through a trapezoidal plate electrode with spatial gradient characteristics. This causes the system to enter an adiabatic state, achieving a high-efficiency conversion from 1064nm fundamental frequency light to 532nm frequency-doubled light. It can be widely used in fields such as lidar, biomedicine, quantum optics, and high-power green lasers.

[0105] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.

Claims

1. A method for adiabatic frequency doubling of KTP crystals based on the photoelectric effect, characterized in that, include: The KTP crystal is processed into a wedge-shaped crystal with a linearly varying thickness along the light transmission direction. The thickness of the wedge-shaped crystal increases linearly from the incident end to the exit end. A continuous parallel plate electrode is prepared on the upper and lower inclined surfaces of the wedge-shaped crystal. A single constant high voltage pulse is applied to the plate electrode. By utilizing the continuous change in the spacing between the plate electrodes along the light transmission direction, a spatially monotonically decreasing gradient electric field is formed inside the wedge-shaped crystal. Based on the spatially monotonically decreasing gradient electric field formed inside the wedge-shaped crystal, the phase mismatch between the fundamental frequency light and the second-order light is driven to change monotonically and smoothly from a negative value to a positive value along the light transmission direction, and the adiabatic stability criterion is satisfied, so the system enters the adiabatic state.

2. The KTP crystal adiabatic frequency doubling method based on the photoelectric effect according to claim 1, characterized in that, The slope of the thickness variation of the wedge-shaped crystal is expressed as: ； in, Indicates the length of the light transmission direction The slope of the thickness variation of the lower wedge-shaped crystal; Indicates the thickness of the wedge-shaped crystal at the incident end; Indicates the thickness of the wedge-shaped crystal at the exit end; Indicates the total length of the light transmission direction.

3. The KTP crystal adiabatic frequency doubling method based on the photoelectric effect according to claim 1, characterized in that, The monotonically decreasing gradient electric field formed inside the wedge-shaped crystal is expressed as: ； in, Indicates the length of the light transmission direction The spatially monotonically decreasing gradient electric field formed inside the lower wedge-shaped crystal; Indicates a single, constant high-voltage pulse; Indicates the length of the light transmission direction The slope of the thickness variation of the lower wedge-shaped crystal.

4. The KTP crystal adiabatic frequency doubling method based on the photoelectric effect according to claim 1, characterized in that, Based on the spatially monotonically decreasing gradient electric field formed inside the wedge-shaped crystal, the phase mismatch between the fundamental frequency light and the second-order harmonic light is driven to monotonically and smoothly change from a negative value to a positive value along the light transmission direction, including: Based on the linear electro-optic effect of KTP crystal, the refractive index of the wedge crystal is changed by the monotonically decreasing gradient electric field formed inside the wedge crystal, thereby driving the refractive index change of the fundamental frequency light and the frequency harmonic light. The change in refractive index of the fundamental and harmonic light drives the phase mismatch between the fundamental and harmonic light to change monotonically and smoothly from a negative value to a positive value along the light transmission direction.

5. The KTP crystal adiabatic frequency doubling method based on the photoelectric effect according to claim 1, characterized in that, The phase mismatch between the fundamental frequency light and the frequency-doubled light is expressed as: ； In the formula, ; in, This indicates the phase mismatch between the fundamental frequency light and the frequency-doubled light; This represents the initial phase mismatch when no electric field is applied. Indicates the photoelectric tuning coefficient; Indicates the length of the light transmission direction The spatially monotonically decreasing gradient electric field formed inside the lower wedge-shaped crystal; This indicates the wavelength of the fundamental frequency light in a vacuum; This represents the refractive index of the fundamental frequency o-ray in a wedge-shaped crystal; This represents the refractive index of the fundamental e-ray in a wedge-shaped crystal; Both represent the linear electro-optic coefficients of the wedge-shaped crystal.

6. The KTP crystal adiabatic frequency doubling method based on the photoelectric effect according to claim 4, characterized in that, The phase mismatch between the fundamental frequency light and the frequency-doubled light crosses the matching point and satisfies the boundary conditions; The boundary conditions are expressed as follows: ； ； In the formula, ; in, , These represent light transmission direction lengths of 0 and 0 respectively. The phase mismatch between the fundamental frequency light and the second harmonic light; Indicates the total length in the direction of light transmission; Represents the characteristic length of the system; This represents the speed of light in a vacuum. Represents the vacuum permittivity; This represents the average refractive index of the fundamental frequency light in the wedge-shaped crystal; This represents the average refractive index of the frequency-doubled light in the wedge-shaped crystal; This indicates the wavelength of the fundamental frequency light in a vacuum; This indicates the wavelength of frequency-doubled light in a vacuum; Indicates the effective nonlinear coefficient of the wedge-shaped crystal; It represents the intensity of the incident fundamental frequency light.

7. The KTP crystal adiabatic frequency doubling method based on the photoelectric effect according to claim 6, characterized in that, The adiabatic stability criterion is expressed as follows: 。 8. The KTP crystal adiabatic frequency doubling method based on the photoelectric effect according to claim 1, characterized in that, The single constant high-voltage pulse adopts a nanosecond-level high-voltage pulse and uses a digital delay generator to make the leading edge of the single constant high-voltage pulse advance before the laser pulse turns on and the trailing edge lag after the laser pulse turns off.

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