Method for calculating conversion ability of gradient-doped single crystal wideband laser frequency doubling

Abstract

The application discloses a calculation method of gradient-doped single crystal wideband laser frequency doubling conversion capacity. Single crystal material with axial gradient refractive index can realize high-efficiency frequency conversion of wideband laser. When a certain gradient-doped single crystal has different refractive index gradient ranges, gradient sizes and single crystal thicknesses, laser wavebands and bandwidths for realizing high-efficiency frequency doubling are different. Through three steps of calculation and comparison of the calculation method, the minimum gradient range and gradient size can be obtained, the blank of theoretical calculation of the gradient-doped single crystal in the field of wideband laser frequency conversion is filled, the refractive index parameter and gradient design of the gradient-doped single crystal are solved, the frequency doubling action distance is prolonged, the single crystal growth difficulty is reduced, the utilization rate and frequency conversion efficiency of the single crystal material are improved, and theoretical guidance is provided for growth of the gradient-doped single crystal.

Description

Technical Field

[0001] This invention relates to the field of calculating the broadband laser frequency conversion capability of gradient refractive index single crystals, and particularly to a method for calculating the broadband laser frequency doubling conversion capability of gradient doped single crystals. Background Technology

[0002] Broadband lasers refer to lasers with a spectrum distributed over a wide frequency range, containing multiple different frequency components and covering a certain wavelength range. Their spectral width can reach several nanometers or even wider, and they exhibit short pulse characteristics, with pulse widths ranging from nanoseconds to femtoseconds. They will have important applications in fields such as optical communication, biomedicine, materials processing, and scientific research. For example, their high peak power and broadband characteristics enable high-precision, high-efficiency material processing of special aircraft parts, as well as micro / nanostructure fabrication and material surface modification. The efficient frequency doubling and third harmonic processes of high-power broadband lasers have been difficult to achieve due to the dispersion characteristics of various single crystals, especially when the pump intensity is approximately 3 GW / cm². 2 The fundamental frequency light has a wavelength of 1053 nm and a bandwidth of 60 nm. The fundamental frequency bandwidth corresponding to a 70% conversion efficiency in the frequency doubling process is about 3.68 nm, while that in the third harmonic process is only 0.04 nm. Therefore, efficient frequency conversion is a huge bottleneck for broadband lasers to move towards engineering applications.

[0003] For traditional narrowband lasers, both harmonic conversion theory and frequency conversion experimental schemes are relatively well-developed. However, birefringence phase matching and quasi-phase matching methods achieve phase matching at a fixed refractive index, and are only applicable to frequency conversion processes with very narrow laser spectral widths. For broadband laser frequency conversion, the single-crystal refractive index must vary within a certain range, or remain almost constant within a certain wavelength band. This requires simultaneous phase matching across multiple wavelengths, i.e., group velocity matching. The commonly used broadband frequency doubling method is return-point matching, which can achieve almost constant single-crystal refractive index within a small band only near the return-point wavelength, but cannot achieve broadband laser frequency conversion at arbitrary wavelengths across the entire transparent band. Therefore, efficient frequency doubling and third-harmonic generation techniques for broadband lasers in arbitrary bands require further research. Numerous parameters govern the refractive index of gradient-doped single crystals, including gradient range, gradient magnitude, single-crystal thickness, broadband laser band, and bandwidth. Currently, it is impossible to quantitatively calculate these parameters or perform theoretical analysis of their logical relationships. Summary of the Invention

[0004] To address the aforementioned technical shortcomings, this invention provides a method for calculating the high-efficiency frequency conversion capability of gradient-doped single-crystal broadband lasers. Single-crystal materials with axially gradient refractive indices can achieve high-efficiency frequency conversion of corresponding wavelength broadband lasers at a specific phase-matching angle. When a single-crystal material has different gradient ranges, gradient magnitudes, and single-crystal thicknesses, the laser band and bandwidth achieving high-efficiency frequency conversion will differ. Knowing the desired laser band and bandwidth for frequency conversion, the method calculates the required gradient range and magnitude of the single crystal through three steps: matching the center wavelength to the center refractive index, matching the maximum wavelength to the minimum refractive index, or matching the minimum wavelength to the maximum refractive index. This characterizes the frequency doubling capability of gradient-doped single-crystal broadband lasers. Similarly, knowing the gradient range and magnitude, the laser band and widest bandwidth capable of high-efficiency frequency conversion can be calculated in reverse.

[0005] The technical solution of this invention is: A method for calculating the frequency doubling conversion capability of a gradient-doped single-crystal broadband laser, given the laser band and broadband laser bandwidth; the method includes: S1. Using the center wavelength of the laser band to match the refractive index at the center position as the broadband laser frequency conversion matching method, the median value of the axial gradient refractive index range of the gradient-doped single crystal is matched with the median value of the broadband laser bandwidth. Then, the lowest refractive index is matched on the side with the maximum wavelength of the broadband laser bandwidth or the highest refractive index is matched on the side with the minimum wavelength of the broadband laser bandwidth. Thus, the first axial gradient refractive index range is obtained. S2. Match the minimum refractive index of the gradient-doped single crystal with the maximum wavelength value of the broadband laser bandwidth, and then find the highest refractive index of the gradient-doped single crystal that matches the minimum wavelength value of the broadband laser bandwidth, thereby obtaining the second axial gradient refractive index range. S3. Match the highest refractive index of the gradient-doped single crystal with the minimum wavelength value of the broadband laser bandwidth, and then find the lowest refractive index of the gradient-doped single crystal that matches the maximum wavelength value of the broadband laser bandwidth. This yields the third axial gradient refractive index range. Take the minimum span among the spans of the first axial gradient refractive index range, the second axial gradient refractive index range, and the third axial gradient refractive index range, and use the minimum span to characterize the broadband laser frequency doubling conversion capability of the gradient-doped single crystal.

[0006] The minimum gradient refractive index range determined above is taken as the gradient range; the gradient magnitude is calculated as gradient range / single crystal thickness; the smaller the gradient magnitude, the longer the frequency doubling distance, which is more beneficial to the frequency doubling conversion capability of gradient-doped single-crystal broadband lasers. The gradient range mentioned above is the span of refractive index variation along the light propagation direction, i.e., the single crystal thickness direction, with dimensionless units; the gradient magnitude is the magnitude of the refractive index variation per unit length along the single crystal thickness direction, with units of cm. -1 Single crystal thickness is the length of a single crystal material along the direction of light propagation, measured in centimeters.

[0007] The aforementioned axial gradient refractive index range refers to the refractive index of a single crystal material increasing or decreasing linearly along the laser propagation direction, i.e., the refractive index exhibits a gradient change. This gradient change is achieved by controlling the elemental composition or structure of the single crystal material itself, making the material a single crystal material that is heterogeneous and has a continuously uniformly changing refractive index.

[0008] The bandwidth of the aforementioned broadband lasers reaches 1nm-10nm, or even tens of nm.

[0009] The aforementioned single crystals are KDP, DKDP, BBO, LBO, KTP, or YVO4. Only single crystals that can achieve birefringence phase matching can achieve the frequency doubling conversion process of broadband lasers by controlling the growth of single crystals to obtain gradient refractive index.

[0010] A method for calculating the bandwidth-to-frequency conversion capability of a gradient-doped single-crystal broadband laser is provided. When a bandwidth-to-frequency light is generated by combining a narrowband fundamental frequency laser and a broadband frequency-doubled laser, for the frequency-doubled laser portion, the minimum axial gradient refractive index range corresponding to the broadband frequency-doubled laser is calculated according to any one of claims 1-4. The minimum axial gradient refractive index range of the broadband bandwidth-to-frequency laser is further calculated by combining the narrowband fundamental frequency laser and the broadband frequency-doubled laser according to any one of claims 1-4.

[0011] A method for calculating the difference frequency conversion capability of gradient-doped single-crystal broadband lasers, wherein when difference frequency light is generated by combining high-frequency fundamental broadband lasers and low-frequency fundamental broadband lasers, the minimum axial gradient refractive index range corresponding to the broadband difference frequency laser is calculated according to any one of claims 1-4.

[0012] A method for calculating the direct third-harmonic conversion capability of a gradient-doped single-crystal broadband laser, wherein when a broadband third-harmonic laser is directly generated from a broadband fundamental frequency laser, the minimum axial gradient refractive index range corresponding to the broadband third-harmonic laser is calculated according to any one of claims 1-4.

[0013] The beneficial effects of this invention are: it enables bidirectional calculation of the gradient range, gradient magnitude, and high-efficiency frequency conversion laser band and bandwidth of any single crystal with axially gradient refractive index; it can calculate the minimum gradient range, thereby minimizing the gradient magnitude; it fills the theoretical calculation gap in the field of broadband laser frequency conversion for gradient-doped single crystals; it solves the problems of refractive index parameters and gradient design for gradient refractive index single crystals; it extends the frequency doubling distance under the same conditions; it reduces the difficulty of single crystal growth; it improves the utilization rate and frequency conversion efficiency of single crystal materials; and it provides theoretical guidance for the growth of gradient refractive index single crystal materials. Attached Figure Description

[0014] Figure 1The range of gradient deuterium content variation in broadband harmonic conversion varies with the deuterium content of a single crystal; (a) 532 nm Type I phase match; (b) 808 nm Type I phase match; (c) 1064 nm Type I phase match; (d) 1064 nm Type II phase match; (e) 1400 nm Type I phase match; (f) 1400 nm Type II phase match; (g) 1053 nm + 530 nm sum-frequency Type II phase match; Figure 2 This is a flowchart illustrating a method for calculating the frequency doubling conversion capability of a gradient-doped single-crystal broadband laser. Detailed Implementation

[0015] The present application will be further described in detail below with reference to the accompanying drawings of the embodiments: A method for calculating the frequency doubling conversion capability of gradient-doped single-crystal broadband lasers, given the laser band and broadband laser bandwidth, such as... Figure 2 As shown, it includes the following three steps: S1. Using the center wavelength of the laser band to match the refractive index at the center position as the broadband laser frequency conversion matching method, the median value of the axial gradient refractive index range of the gradient-doped single crystal is matched with the median value of the broadband laser bandwidth. Then, the lowest refractive index is matched on the side with the maximum wavelength of the broadband laser bandwidth or the highest refractive index is matched on the side with the minimum wavelength of the broadband laser bandwidth. Thus, the first axial gradient refractive index range is obtained. S2. Match the minimum refractive index of the gradient-doped single crystal with the maximum wavelength value of the broadband laser bandwidth, and then find the highest refractive index of the gradient-doped single crystal that matches the minimum wavelength value of the broadband laser bandwidth, thereby obtaining the second axial gradient refractive index range. S3. Match the highest refractive index of the gradient-doped single crystal with the minimum wavelength value of the broadband laser bandwidth, and then find the lowest refractive index of the gradient-doped single crystal that matches the maximum wavelength value of the broadband laser bandwidth. This yields the third axial gradient refractive index range. Take the minimum span among the spans of the first axial gradient refractive index range, the second axial gradient refractive index range, and the third axial gradient refractive index range, and use the minimum span to characterize the broadband laser frequency doubling conversion capability of the gradient-doped single crystal.

[0016] The determined minimum gradient refractive index range is taken as the gradient range; the gradient magnitude is calculated as gradient range / single crystal thickness. A smaller gradient magnitude results in a longer frequency doubling distance, which is more beneficial to the frequency doubling conversion capability of gradient-doped single-crystal broadband lasers. The gradient range is the span of refractive index variation along the light propagation direction, i.e., the single crystal thickness direction, and is dimensionless; the gradient magnitude is the magnitude of the refractive index variation per unit length along the single crystal thickness direction, and is measured in cm. -1 Single crystal thickness is the length of a single crystal material along the direction of light propagation, measured in centimeters.

[0017] The axial gradient refractive index range refers to the refractive index of a single crystal material that increases or decreases linearly along the laser propagation direction, i.e., the refractive index changes in a gradient. This gradient change is achieved by controlling the elemental composition or structure of the single crystal material itself, making the material a single crystal material that is heterogeneous and has a continuously uniform refractive index.

[0018] A specific phase-matching angle refers to the experimental and calculation method being based on a birefringence phase-matching process, i.e., an axially gradient refractive index single crystal can enable broadband lasers with a wide wavelength range to achieve an efficient frequency conversion process at a certain fixed phase-matching angle.

[0019] Broadband lasers, compared to traditional narrowband lasers, have a wider bandwidth, ranging from 1nm to 10nm, or even tens of nm. They have a continuous spectrum within a certain wavelength range, and their spectral shape can be flat-top, Gaussian, etc.

[0020] Single crystals mainly include bulk single crystal materials such as KDP, DKDP, BBO, LBO, KTP or YVO4, which can achieve laser frequency conversion through birefringence phase matching. Only single crystals that can achieve birefringence phase matching can achieve broadband laser frequency doubling conversion by obtaining gradient refractive index through controlling single crystal growth.

[0021] Laser band refers to the wavelength range covered by lasers that can achieve efficient frequency conversion, and bandwidth refers to the width of the laser band, measured in nanometers.

[0022] Similarly, a method for calculating the bandwidth-to-frequency conversion capability of a gradient-doped single-crystal broadband laser involves generating a bandwidth-to-frequency light by combining a narrowband fundamental frequency laser and a broadband frequency-doubled laser. For the frequency-doubled laser portion, the minimum axial gradient refractive index range corresponding to the broadband frequency-doubled laser is calculated according to the method described in any one of claims 1-4. The minimum axial gradient refractive index range of the broadband bandwidth-to-frequency laser is further calculated by combining the narrowband fundamental frequency laser and the broadband frequency-doubled laser according to the method described in any one of claims 1-4.

[0023] Example 1: Potassium dihydrogen phosphate (KDP) and deuterated potassium dihydrogen phosphate (DKDP) single crystals are the only nonlinear optical single crystals to date that can be used in inertial confinement fusion (ICF) engineering, enabling frequency conversion of high-power lasers. Currently, there are challenges in efficient frequency conversion technology for broadband lasers in ICF. Gradient-doped DKDP single crystals can be grown by controlling the deuterium content during the growth of KDP and DKDP single crystals. Since the refractive index of KDP-type single crystals changes linearly with the deuterium content, gradient-doped DKDP single crystals exhibit an axial gradient refractive index. By adjusting the deuterium content of DKDP single crystals, the wavelength range for return point matching can be expanded. The return point wavelength for type I frequency doubling phase matching can be adjusted to between 1034 nm and 1200 nm, and the return point wavelength for type II frequency doubling phase matching to between 1103 nm and 1260 nm. However, broadband laser phase matching cannot be achieved for laser wavelengths outside these ranges.

[0024] Designing gradient-doped deuterium-doped (DKDP) single crystals requires consideration of three parameters: single crystal thickness, deuterium content, and gradient range. Considering linear absorption, the single crystal thickness should be as thin as possible, while still requiring the longest possible harmonic conversion distance for different wavelengths. Therefore, it is necessary to find the smallest possible gradient range within the same thickness that satisfies the bandwidth requirements. Based on this, a suitable single crystal thickness is selected. Calculations are performed using the following laser wavelengths as examples: frequency doubling at 532 nm, 808 nm, 1064 nm, and 1400 nm, and a sum-frequency harmonic at 1053 nm + 530 nm. At 532 nm, only type I phase-matched frequency doubling can be achieved; at 808 nm, 1064 nm, and 1400 nm, both type I and type II phase-matched frequency doubling can be achieved; and at 1053 nm + 530 nm, a type II phase-matched third harmonic harmonic process is achieved. At the 1034 nm turnaround point, KDP single crystals can achieve a 50% frequency doubling efficiency with a fundamental frequency bandwidth of 28 nm, at which point the refractive index difference Δn = 0.000010; and with a fundamental frequency bandwidth of 18 nm, they can achieve an 80% frequency doubling efficiency, at which point the refractive index difference Δn = 0.000005. That is, to achieve a high-efficiency broadband frequency doubling efficiency of over 80%, the refractive index difference Δn < 0.000005.

[0025] The calculation process considered three cases: (1) matching the central deuterium content with the central wavelength, and then finding wavelengths on both sides to match the deuterium content at both ends of the single crystal; (2) matching the lowest deuterium content with the maximum wavelength, and then finding the highest deuterium content that matches the minimum wavelength; (3) matching the highest deuterium content with the minimum wavelength, and then finding the lowest deuterium content that matches the maximum wavelength. The gradient ranges for the above wavelengths (Type I and Type II) were determined using these three methods to minimize the possible gradients. The variation of the 532 nm Type I broadband frequency doubling gradient range with deuterium content is as follows: Figure 1 As shown in (a), the required minimum gradient range is 13%; the 808 nm Class I broadband frequency doubling gradient range varies with deuterium content as follows: Figure 1 As shown in (b), the required minimum gradient range is 11%. The 808 nm Class II broadband frequency doubling case is quite special; calculations show that at this wavelength, the deuterium content cannot be adjusted to achieve an efficient broadband frequency doubling process. The specific reasons and analysis are described later. The results of the 1064 nm Class I broadband frequency doubling gradient range changing with the deuterium content are as follows: Figure 1 As shown in (c), the required minimum gradient range is 0.2%; the variation of the 1064 nm Class II broadband frequency doubling gradient range with deuterium content is as follows. Figure 1 As shown in (d), the required minimum gradient range is 2.6%; the variation of the 1400 nm Class I broadband frequency doubling gradient range with deuterium content is as follows. Figure 1 As shown in (e), the required minimum gradient range is 1.9%; the 1400 nm Class II broadband frequency doubling gradient range varies with deuterium content as follows: Figure 1 As shown in (f), the required minimum gradient range is 2%; the range of the Class II broadband third harmonic gradient at 1053 nm + 530 nm varies with the deuterium content as follows: Figure 1 As shown in (g), the required minimum gradient range is 28%.

[0026] The calculation results show that: (1) The gradient range required for the same bandwidth of harmonic conversion is different at different wavelengths. The gradient range required in the infrared band is very small, especially near the turning point. The broadband frequency doubling characteristic of the turning point itself, combined with the gradient refractive index single crystal, can make the efficient harmonic conversion bandwidth very wide. However, it is difficult to achieve broadband frequency conversion in the ultraviolet band. The broadband and frequency conversion process involves matching three wavelengths, which is also difficult to achieve. (2) The minimum gradient range is not obtained by matching the central wavelength with the central deuterium content. Under different wavelength conditions, it may be by matching the maximum, minimum or a certain wavelength with the corresponding deuterium content to obtain a smaller gradient. (3) The gradient range of single crystals with different deuterium contents at a certain wavelength is also different, and shows different patterns with the change of deuterium content.

Claims

1. A method for calculating the frequency doubling conversion capability of a gradient-doped single-crystal broadband laser, characterized in that, The laser band and broadband laser bandwidth are known; the method includes: S1. Using the center wavelength of the laser band to match the refractive index at the center position as the broadband laser frequency conversion matching method, the median value of the axial gradient refractive index range of the gradient-doped single crystal is matched with the median value of the broadband laser bandwidth. Then, the lowest refractive index is matched on the side with the maximum wavelength of the broadband laser bandwidth or the highest refractive index is matched on the side with the minimum wavelength of the broadband laser bandwidth. Thus, the first axial gradient refractive index range is obtained. S2. Match the minimum refractive index of the gradient-doped single crystal with the maximum wavelength value of the broadband laser bandwidth, and then find the highest refractive index of the gradient-doped single crystal that matches the minimum wavelength value of the broadband laser bandwidth, thereby obtaining the second axial gradient refractive index range. S3. Match the highest refractive index of the gradient-doped single crystal with the minimum wavelength value of the broadband laser bandwidth, and then find the lowest refractive index of the gradient-doped single crystal that matches the maximum wavelength value of the broadband laser bandwidth. This yields the third axial gradient refractive index range. Take the minimum span among the spans of the first axial gradient refractive index range, the second axial gradient refractive index range, and the third axial gradient refractive index range, and use the minimum span to characterize the broadband laser frequency doubling conversion capability of the gradient-doped single crystal.

2. The method for calculating the frequency doubling conversion capability of a gradient-doped single-crystal broadband laser according to claim 1, characterized in that, The determined minimum gradient refractive index range is taken as the gradient range; the gradient magnitude is calculated as gradient range / single crystal thickness; the smaller the gradient magnitude, the longer the frequency doubling distance, which is more beneficial to the frequency doubling conversion capability of gradient-doped single crystal broadband laser; the above gradient range is the span of refractive index variation along the light propagation direction, i.e., the single crystal thickness direction, and the unit is dimensionless; the gradient magnitude is the magnitude of the refractive index variation per unit length along the single crystal thickness direction, and the unit is cm. -1 Single crystal thickness is the length of a single crystal material along the direction of light propagation, measured in centimeters.

3. The method for calculating the frequency doubling conversion capability of a gradient-doped single-crystal broadband laser according to claim 1, characterized in that, The axial gradient refractive index range refers to the refractive index of a single crystal material that increases or decreases linearly along the laser propagation direction, i.e., the refractive index changes in a gradient. This gradient change is achieved by controlling the elemental composition or structure of the single crystal material itself, making the material a single crystal material that is heterogeneous and has a continuously uniform refractive index.

4. The method for calculating the frequency doubling conversion capability of a gradient-doped single-crystal broadband laser according to claim 1, characterized in that, The bandwidth of the broadband laser reaches 1nm-10nm.

5. The method for calculating the frequency doubling conversion capability of a gradient-doped single-crystal broadband laser according to claim 1, characterized in that, The aforementioned single crystals are KDP, DKDP, BBO, LBO, KTP, or YVO4.

6. A method for calculating the bandwidth and frequency conversion capability of a gradient-doped single-crystal broadband laser, characterized in that, When a sum-frequency light is generated by combining a narrowband fundamental frequency laser and a broadband frequency-doubled laser, for the frequency-doubled laser portion, the minimum axial gradient refractive index range corresponding to the broadband frequency-doubled laser is calculated according to the method described in any one of claims 1-4. The minimum axial gradient refractive index range of the sum-frequency light is further calculated by combining the narrowband fundamental frequency laser and the broadband frequency-doubled laser according to the method described in any one of claims 1-4.

7. A method for calculating the difference frequency conversion capability of gradient-doped single-crystal broadband laser, characterized in that, When difference-frequency light is generated by combining high-frequency fundamental broadband laser and low-frequency fundamental broadband laser, the minimum axial gradient refractive index range corresponding to the difference-frequency light is calculated according to the method described in any one of claims 1-4.

8. A method for calculating the direct third-harmonic conversion capability of a gradient-doped single-crystal broadband laser, characterized in that, When broadband third-harmonic laser is directly generated from broadband fundamental frequency laser, the minimum axial gradient refractive index range corresponding to the broadband third-harmonic laser is calculated according to the method described in any one of claims 1-4.

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