A method for designing a concentration gradient of a gain medium of a laser amplifier and a gain medium of a laser amplifier

Abstract

The application discloses a concentration gradient design method of a laser amplifier gain medium and the laser amplifier gain medium, and relates to the technical field of laser amplification, and aims to solve the heat effect problem that heat distribution is uneven due to uneven pump light absorption distribution of the laser amplifier gain medium. Technical points of the application include: according to the heat conduction equation, the phase difference of each section of the crystal corresponding to the seed light passing through the pump light region when the laser amplifier amplifies the seed light is calculated and obtained; according to the phase difference of each section of the crystal through which the seed light passes being equal, the phase difference of each section of the crystal corresponding to the seed light passing through the pump light region is set to be equal; the absorption coefficient of each section of the crystal is obtained by iterative solution using simulation software; and the concentration gradient of each section of the crystal is calculated and obtained according to the relationship between the absorption coefficient and the concentration gradient. According to the application, the concentration distribution of the laser amplifier crystal is designed according to the depolarization generated by the seed light passing through the amplification laser medium, so that the purpose of reducing the thermal depolarization effect from the root is achieved.

Description

Technical Field

[0001] This invention relates to the field of laser amplification technology, specifically to a method for designing the concentration gradient of a laser amplifier gain medium and a laser amplifier gain medium. Background Technology

[0002] High-energy, high-repetition-rate lasers with high beam quality have important applications in industrial production, such as shock strengthening and laser cutting; and in the military field, such as laser weapons and laser guidance. However, MOPA amplification structures, which are mainly based on traditional uniformly concentrated rod-shaped or bulk crystals, are limited by many factors such as the thermal effect of the gain medium and the fracture stress limit, making it difficult to significantly increase their operating repetition frequency and power, and also affecting the output beam quality.

[0003] In end-pumped conditions, conventional uniformly doped crystals exhibit significant temperature gradients due to the uneven distribution of pump energy along the propagation direction. This leads to severe thermal effects, noticeably reducing system efficiency, beam quality, and laser system stability. Reducing crystal concentration decreases pump light absorption, thus affecting high-power laser output; increased external cooling and changes in cavity shape increase system complexity. Summary of the Invention

[0004] To address this issue, the present invention proposes a concentration gradient design method for laser amplifier gain media and a laser amplifier gain media, in order to solve the problem of uneven heat distribution and severe thermal effects caused by uneven pump light absorption distribution in laser amplifier gain media.

[0005] According to one aspect of the present invention, a method for designing the concentration gradient of a laser amplifier gain medium is provided, the method comprising the following steps:

[0006] If the depolarization values ​​of each segment of the laser amplifier crystal are set to be equal, then the phase difference of the seed light passing through each segment of the crystal is determined to be equal based on the relationship between the depolarization values ​​and the phase difference of the seed light passing through the crystal.

[0007] The phase difference of each crystal segment when the seed light passes through the pump light region is obtained by calculating the phase conduction equation based on the heat conduction equation.

[0008] Based on the fact that the phase difference of the seed light is equal when it passes through each segment of the crystal, the settings are configured so that the phase difference of the corresponding segments of the crystal is equal when the seed light passes through the pump light region.

[0009] The absorption coefficient of the first segment of the crystal and the length of each segment are set, and the absorption coefficient of each segment of the crystal is obtained by iterative solution using simulation software.

[0010] The concentration gradient of each segment of the crystal is calculated based on the relationship between the absorption coefficient and the concentration gradient.

[0011] Furthermore, the relationship between the depolarization value and the phase difference of the seed light passing through the crystal is expressed as:

[0012]

[0013] In the formula, D pol Indicates the debias value; r a θ represents the radius of the seed light; θ represents the various angles of the seed light, which are generally circular with angles ranging from 0 to 2π; ψ(r) represents the phase difference of the seed light as it passes through the crystal.

[0014] Furthermore, the phase difference of each segment of the crystal corresponding to the seed light passing through the pump light region is expressed as follows:

[0015]

[0016]

[0017] In the formula, ψ1(r) represents the phase difference of the seed light after passing through the first segment of the crystal; r represents the radius of the seed light; λ s L1 represents the wavelength of the seed light; n0 represents the length of the first segment of the crystal; p represents the refractive index of the crystal; 11 p 12 p 44 It is the elastic optical coefficient; P represents the pump power; η h Indicates heat load; α T ν represents the linear expansion coefficient; α1 represents the absorption coefficient of the first segment of the crystal; Kc represents the thermal conductivity; z represents the position of the crystal; ω p Rc represents the pump light radius; Rc represents the crystal radius; r > ω p ;ψ i (r) represents the phase difference of the seed light after passing through the i-th segment of the crystal; L i α represents the length of the i-th segment of the crystal and the total length of all preceding segments; i The value represents the absorption coefficient of the i-th segment of the crystal; l k This represents the length of the k-th segment of the crystal.

[0018] Furthermore, the phase difference between each segment of the crystal is set to be equal when the seed light passes through the pump light region, as expressed in the following way:

[0019]

[0020] Furthermore, the lengths of each segment of the crystal are set to be equal or unequal.

[0021] Furthermore, the simulation software is MATLAB simulation software.

[0022] According to another aspect of the present invention, a laser amplifier gain medium is also provided, wherein the gain medium is a laser crystal, and the concentration gradient of the laser crystal is determined according to the concentration gradient design method described above.

[0023] The beneficial technical effects of this invention are:

[0024] This invention designs the concentration distribution of the laser amplifier crystal based on the depolarization generated by the seed light through the amplified laser medium, thereby reducing the thermal depolarization effect at its source. It also reduces the possibility of crystal breakage due to exceeding the thermal stress limit, achieving uniform and stable amplification of the seed light, and is more suitable for high repetition rate and high power laser amplification. Attached Figure Description

[0025] The above and other objects, features, and advantages of exemplary embodiments of the present invention will become readily apparent from the following detailed description taken in conjunction with the accompanying drawings. Several embodiments of the invention are illustrated in the drawings by way of example and not limitation, wherein:

[0026] Figure 1 This is a flowchart of a method for designing the concentration gradient of a laser amplifier gain medium according to an embodiment of the present invention.

[0027] Figure 2 These are example results from embodiments of the present invention; wherein, (a) corresponds to the longitudinal temperature distribution of the crystal when the pump power is 100W; (b) corresponds to the relationship between the crystal thermal focal length and the pump power; (c) corresponds to the seed light depolarization value; and (d) corresponds to the absorption power distribution. Detailed Implementation

[0028] The principles and spirit of the invention will now be described with reference to several exemplary embodiments. It should be understood that these embodiments are given merely to enable those skilled in the art to better understand and implement the invention, and are not intended to limit the scope of the invention in any way. Rather, these embodiments are provided to make this disclosure more thorough and complete, and to fully convey the scope of this disclosure to those skilled in the art.

[0029] Those skilled in the art will recognize that embodiments of the present invention can be implemented as a system, apparatus, device, method, or computer program product. Therefore, this disclosure can be specifically implemented in the following forms: entirely hardware, entirely software (including firmware, resident software, microcode, etc.), or a combination of hardware and software. It should be understood herein that any number of elements in the accompanying drawings is for illustrative purposes only and not as a limitation, and any naming is for distinction only and has no limiting meaning.

[0030] This invention proposes a concentration gradient design method for the gain medium of a laser amplifier, which is also a crystal design method for an end-pumped laser amplifier. The main purpose is to solve the problem of uneven heat distribution caused by uneven pump light absorption in laser amplifiers, so as to reduce the serious thermal effect problem in high-power laser amplifiers.

[0031] Since the primary means of realizing high-power lasers is laser amplification, and laser amplifiers are the main means of realizing laser amplification, the thermal load of the solid laser medium determines the thermal stress limit of the material, affecting the energy storage of the gain medium and causing thermal distortion. The resulting heat energy limits the further amplification of the seed light by the laser amplifier. Therefore, this invention designs the crystal concentration distribution based on the depolarization generated by the seed light through the amplified laser medium, thereby reducing the thermal depolarization effect at its source. This also reduces the possibility of crystal breakage due to exceeding the thermal stress limit, achieving uniform and stable amplification of the seed light, making it more suitable for high-repetition-rate, high-power laser amplification.

[0032] like Figure 1 As shown, the method includes the following steps:

[0033] Step 1: Set the depolarization values ​​of each segment of the laser amplifier crystal to be equal. Then, based on the relationship between the depolarization values ​​and the phase difference of the seed light passing through the crystal, determine that the phase difference of the seed light passing through each segment of the crystal is equal.

[0034] Step 2: Calculate the phase difference of each segment of the crystal when the seed light passes through the pump light region, based on the heat conduction equation;

[0035] Step 3: Based on the fact that the phase difference of the seed light is equal when it passes through each segment of the crystal, set the crystal so that the phase difference of the corresponding segments is equal when the seed light passes through the pump light region.

[0036] Step 4: Set the absorption coefficient of the first segment of the crystal and the length of each segment of the crystal, and use simulation software to iteratively solve for the absorption coefficient of each segment of the crystal;

[0037] Step 5: Calculate the concentration gradient of each segment of the crystal based on the relationship between the absorption coefficient and the concentration gradient.

[0038] The present invention will be described in detail through the following embodiments.

[0039] Currently, gradient-doped crystals are designed with the following methods: identical absorption power per segment, identical thermal focal length per segment, identical maximum temperature per segment, and identical gain distribution. To minimize amplifier depolarization, gradient-doped crystals are designed with equal depolarization per segment. Since the change in the beam radius of the seed beam within the crystal is negligible in most cases, and according to the design principles of solid-state laser mode matching, the laser has higher output power when the seed beam is slightly greater than or equal to the pump beam, but in practical applications, the seed beam and pump beam are almost never completely equal. Therefore, only the case where the seed beam radius is greater than the pump beam is considered.

[0040] In step one, the depolarization value of each segment of the laser amplifier crystal is set to be equal, and the thermal depolarization caused by each segment of the crystal is:

[0041]

[0042] The above formula takes into account the pump light variation, but in reality, the pump light radius generally does not remain constant. Based on the relationship between the depolarization value and the phase difference of the seed light passing through the crystal, the thermal depolarization caused by each segment of the crystal is equivalent to the phase difference of the seed light passing through each segment of the crystal being equal:

[0043] ψ1(r)=ψ i (r),i=1,2,3,…,n (2)

[0044] In step two, since the phase difference between the seed light passing through the pump light region and the region outside the pump light illumination is different, the phase difference of each crystal segment corresponding to the seed light passing through the pump light region is calculated according to the heat conduction equation; wherein, the phase difference corresponding to the first crystal segment is expressed as:

[0045]

[0046] Where, ω p The pump light radius is r > ω. p This indicates that the seed light passes through the pump light region; 0 < r < ω p The z represents the area outside the seed light's illumination by the pump light; z represents each position in the crystal.

[0047] The phase difference corresponding to the i-th segment of the crystal is represented as:

[0048]

[0049] In the formula, L i This represents the length of the i-th segment of the crystal and the total length of all preceding segments of the crystal.

[0050] As an example, the derivation process is as follows:

[0051] The heat conduction equation is:

[0052]

[0053] The temperature difference formula, derived from the heat conduction equation, is as follows:

[0054]

[0055] In the formula, α(z) is a function of the crystal absorption coefficient. Then, the elastic strain can be calculated. For isotropic materials, the difference in elastic strain between the radial and tangential directions is:

[0056]

[0057] The thermally induced birefringence in the

[111] direction can be calculated from the elastic strain difference as follows:

[0058]

[0059] Due to the change in thermal refractive index, the final phase difference changes as follows:

[0060]

[0061] According to formulas (5)-(9), the phase difference expressions of formulas (3) and (4) can be obtained.

[0062] After obtaining the phase difference, depolarization can be expressed as:

[0063]

[0064] In the formula, r a θ represents the radius of the seed light; θ represents the various angles of the seed light. The seed light is generally circular, with angles ranging from 0 to 2π. It can be seen that since all other values ​​in formula (10) are constants, the depolarization value is only related to the phase difference. That is, based on the relationship between the depolarization value and the phase difference of the seed light passing through the crystal, it can be determined that the phase difference of the seed light passing through each segment of the crystal is equal.

[0065] Furthermore, neglecting the thermal focusing effect within the crystal, it is assumed that the seed light radius remains constant during the amplification process, i.e., r a Since the pump spot variation has already been considered in the phase difference calculation, the debiasing value can be calculated by taking ω in the integration interval as a constant. p ω can be set as a constant for calculation. p To obtain the average pump spot radius, substituting equations (5)-(9) into equation (10) yields the depolarization value:

[0066]

[0067] in,

[0068]

[0069] P h =P abs η h P abs To absorb power, η h For heat load, λ p , λ s These represent the wavelengths of the pump light and the seed light, respectively; α T The linear expansion coefficient is 7.5 × 10⁻⁶. -6 K -1 ), where ν is Poisson's ratio (0.25), n0 is the crystal refractive index (1.82), and K c R represents the thermal conductivity (0.014 W / (mm·K) for YAG). c p is the crystal radius. 11 p 12 and p 44 These are the elastic optical coefficients, with approximate values ​​of -0.029, 0.0091, and -0.0615. These are all crystal parameters for Nd:YAG.

[0070] Depend on This allows P in formula (6) to be used. h Substitution, where P is the pump power, yields:

[0071]

[0072] In step three, since the phase difference of the seed light when it passes through the pump light irradiation area is much larger than that outside the pump light irradiation area, to simplify the calculation, based on the assumption that the phase difference of the seed light is equal across all segments of the crystal, the phase difference of the seed light when it passes through the pump light irradiation area is set to be equal across all segments of the crystal, i.e., r > ω. p At that time, ψ1(r)=ψ i (r), after reduction, we get:

[0073]

[0074] in, l k ω is the length of the k-th segment of the crystal; p (z)=ω p0 +θ p |z-z0| takes the light incident end of the crystal as the origin, ω p0 Let z0 be the pump beam waist radius, z0 be the pump beam waist position, and θ be the pump beam waist position. p It is the divergence angle. According to ω... p (z) can be used to obtain the radius of the light spot at each position.

[0075] In step four, the absorption coefficient of the first segment of the crystal and the lengths of each segment are set. The absorption coefficients of each segment are then obtained iteratively using the simulation software Matlab. Different lengths will result in different optimal absorption coefficients; generally, they can be designed to be of equal length. The pump light radius can be changed according to the actual situation, and different pump light radii have a significant impact on the final crystal parameters.

[0076] In step five, the concentration gradient of each segment of the crystal is calculated based on the relationship between the absorption coefficient and the concentration gradient. The relationship between the absorption coefficient and the concentration gradient is approximately linear. For common Nd:YAG crystals, the relationship between the absorption coefficient and the concentration gradient when pumped at 808 nm can be expressed as: α = 736n + 6, where α is the absorption coefficient and n is the crystal concentration.

[0077] The lengths of each segment of the crystal are set to be equal or unequal. Table 1 provides example design parameters.

[0078] Table 1 Crystal parameters

[0079]

[0080] Figure 2 Examples of 2-segment and 3-segment bonded crystals are shown, with the same total number of doped particles and total length. Figure 2 In the figures (a), (b), (c), and (d), respectively, the longitudinal temperature distribution of the crystal, the relationship between the crystal's thermal focal length and pump power, and the distribution of depolarization value and absorption power are shown. It can be seen that the design method of this invention effectively reduces the thermal effect and temperature gradient of the laser amplifier, reduces the thermal lensing effect (thermal focal length) and thermal depolarization effect of the crystal, and lowers the maximum temperature with a more uniform temperature distribution. Figure (d) shows the pump light absorption distribution. Due to the low concentration at the front end of the gradient-doped crystal, the absorption at the front end of the traditional uniform-concentration crystal is much greater than that at the back end. Therefore, this invention makes the front-end pump light absorption much smaller than that of the traditional uniform-concentration crystal, while the back end has a high concentration and absorption much greater than that of the uniform-concentration crystal, ultimately resulting in a more uniform pump light absorption distribution. Since the crystal of the amplifier generally needs to withstand very high pump power, thus generating a lot of heat, this invention can also reduce the possibility of the crystal breaking due to excessive thermal stress.

[0081] In summary, this invention reduces thermal effects and increases the maximum total energy storage of the crystal through internal crystal design. In single-end pumping, this is mainly achieved by increasing the energy storage density at the crystal center and rear end. In double-end pumping, it is mainly achieved by increasing the energy storage density at the crystal center, allowing the temperature distribution to reach an approximately balanced state, thereby reducing thermal effects. This invention primarily targets multi-segment crystals. Its main feature is the calculation of a concentration distribution value that ensures equal depolarization values ​​for the seed light passing through any segment of the amplifying crystal. Crystals of different concentrations are then combined using a bonding method based on this concentration distribution. Because the absorption of pump light is related to the crystal concentration—higher concentration means more energy absorbed and more heat generated—the concentration distribution exhibits a gradient, with higher concentrations further away from the pump light.

[0082] Another embodiment of the present invention also proposes a laser amplifier gain medium, wherein the gain medium is a laser crystal, and the concentration gradient of the laser crystal is determined according to the concentration gradient design method described in the above embodiments.

[0083] Although the operations of the method of the invention are described in a specific order in the accompanying drawings, this does not require or imply that the operations must be performed in that specific order, or that all the operations shown must be performed to achieve the desired result. Additionally or alternatively, certain steps may be omitted, multiple steps may be combined into one step, and / or one step may be broken down into multiple steps.

[0084] While the spirit and principles of the invention have been described with reference to several specific embodiments, it should be understood that the invention is not limited to the disclosed specific embodiments, and the division of aspects does not imply that features in these aspects cannot be combined for benefit; such division is merely for ease of description. The invention is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims.

Claims

1. A method for designing the concentration gradient of a laser amplifier gain medium, characterized in that, Includes the following steps: If the depolarization values ​​of each segment of the laser amplifier crystal are set to be equal, then the equal phase difference of the seed light passing through each segment of the crystal is determined by the relationship between the depolarization values ​​and the phase difference of the seed light passing through the crystal. The relationship between the depolarization values ​​and the phase difference of the seed light passing through the crystal is expressed as follows: In the formula, D pol Indicates the debias value; r a denoted by θ, which represents the maximum value of the seed light radius; r represents the seed light radius; θ represents the various angles of the seed light, ranging from 0 to 2π; ψ(r) represents the phase difference of the seed light as it passes through the crystal. The phase difference of each crystal segment when the seed light passes through the pump light region is calculated based on the heat conduction equation; the phase difference of each crystal segment when the seed light passes through the pump light region is expressed as: In the formula, ψ1(r) represents the phase difference of the seed light after passing through the first segment of the crystal; ψ i (r) represents the phase difference of the seed light after passing through the i-th segment of the crystal; r represents the radius of the seed light; λ s L represents the wavelength of the seed light; L1 represents the length of the first segment of the crystal; L i The length of the i-th segment of the crystal is represented by ni and the total length of all preceding segments; n0 represents the refractive index of the crystal; pi 11 p 12 p 44 It is the elastic optical coefficient; P represents the pump power; η h Indicates heat load; α T ν represents the linear expansion coefficient; ν represents Poisson's ratio; α1 represents the absorption coefficient of the first segment of the crystal; α i K represents the absorption coefficient of the i-th segment of the crystal; c ω represents thermal conductivity; z represents the position of the crystal; ω represents the position of the crystal. p R represents the pump light radius; c Indicates the crystal radius; r > ω p ;l k Indicates the length of the k-th segment of the crystal; Based on the fact that the phase difference of the seed light is equal across all segments of the crystal, the settings are configured such that the phase difference of the seed light is equal across all segments of the crystal when it passes through the pump light region. The absorption coefficient of the first segment of the crystal and the length of each segment are set, and the absorption coefficient of each segment of the crystal is obtained by iterative solution using simulation software. The concentration gradient of each segment of the crystal is calculated based on the relationship between the absorption coefficient and the concentration gradient.

2. The method for designing the concentration gradient of a laser amplifier gain medium according to claim 1, characterized in that, The setting ensures that the phase difference between each segment of the crystal is equal when the seed light passes through the pump light region, which is represented as follows:

3. The method for designing the concentration gradient of a laser amplifier gain medium according to claim 1, characterized in that, The lengths of each segment of the crystal are set to be equal or unequal.

4. The method for designing the concentration gradient of a laser amplifier gain medium according to claim 1, characterized in that, The simulation software is MATLAB.

5. A laser amplifier gain medium, wherein the gain medium is a laser crystal, characterized in that, The concentration gradient of the laser crystal is determined according to the concentration gradient design method as described in any one of claims 1-4.

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