Method for measuring non-radiative decay life of laser crystal

Abstract

The invention relates to a laser crystal non-radiative decay life measurement method based on relaxation oscillation frequency analysis of a solid laser, which comprises the following core steps of: firstly, acquiring a laser intensity noise spectrum in real time by adopting a self-zero beat noise detection device (2) in a stable operation state of the solid laser (1); obtaining a relaxation oscillation frequency measured value of the laser through spectral line feature analysis; secondly, a relaxation oscillation frequency theoretical model is built based on a laser rate equation, and a theoretical function curve graph with the non-radiative decay life of the laser crystal as an independent variable and the relaxation oscillation frequency as a dependent variable is built in combination with actual operation parameters (including pumping power, cavity structure parameters and crystal characteristics) of the laser; and finally, matching the actually measured relaxation oscillation frequency with the frequency value in the theoretical curve, and determining the non-radiative decay life value of the laser crystal through abscissa inversion. The method breaks through the limitation of a traditional measurement method, can realize non-intrusive high-precision measurement in a continuous working state of the laser, and is particularly suitable for in-situ characterization and life evaluation of non-radiation attenuation dynamics of the laser crystal in a solid laser system.

Description

Technical Field

[0001] The present invention relates to the technical field of laser crystal parameter measurement, and specifically to a method for inversely measuring the non-radiative decay lifetime of a laser crystal in a solid-state laser through relaxation oscillation frequency, which is particularly applicable to the measurement of the non-radiative decay lifetime of a laser crystal in a solid-state laser under actual operating conditions. Background Art

[0002] A laser crystal is one of the three essential elements of a solid-state laser. The non-radiative decay lifetime of a laser crystal is an important parameter, which affects the small-signal gain coefficient of the laser crystal and further affects the output power of the laser. In the design of solid-state lasers, accurately measuring the non-radiative decay lifetime of a laser crystal under actual operating conditions is crucial for optimizing the parameter structure design of the laser and predicting the output power of the laser.

[0003] Currently, the measurement of the non-radiative decay lifetime of a laser crystal under the actual operating conditions of a laser is mainly based on the input-output power measurement method (CN202410663061.X), which is applicable to lasers with linear input-output power curve characteristics. The specific process is to select the injection pump power and the corresponding output laser power in multiple groups of linear input-output power curves, and substitute them into the formula of the output power of the laser containing the non-radiative decay lifetime of the laser crystal and the energy transfer up-conversion rate respectively, to establish a system of equations for the output power, non-radiative decay lifetime, and energy transfer up-conversion rate, and solve the system of equations to obtain the non-radiative decay lifetime of the laser crystal. However, this measurement method has two major limitations: First, measuring the non-radiative decay lifetime of a laser crystal under the actual operating conditions of a laser based on linear input-output power requires the input-output power of the laser to have a linear characteristic, and it is no longer applicable to the case where the input-output power curve of the laser is non-linear. Second, there is a situation where the system of equations has no solution when two groups of input-output powers are substituted into the measurement of the non-radiative decay lifetime of a laser crystal under the actual operating conditions of a laser based on linear input-output power. It is necessary to substitute multiple groups of input-output powers into the laser output power function for solution and take the average value to obtain the non-radiative decay lifetime of the laser crystal, which greatly increases the workload of the measurement process.

[0004] Therefore, there is an urgent need to develop a method that can quickly and accurately measure the non-radiative decay lifetime of a laser crystal under the actual operating conditions of a laser to optimize the structural parameters of the laser and accurately predict its output characteristics. Summary of the Invention

[0005] The present invention aims to solve the above problems in the prior art. A method for measuring the non-radiative decay lifetime of a laser crystal is proposed. The technical solution of the present invention is as follows:

[0006] A method for measuring the non-radiative decay lifetime of a laser crystal, comprising the following steps:

[0007] (1) Use a self - homodyne noise detection device to collect the laser intensity noise spectrum in real - time, and extract the measured value of the relaxation oscillation frequency of the laser through spectral line analysis;

[0008] (2) Based on the laser rate equation, construct a theoretical model of the relaxation oscillation frequency. Combining the actual operating parameters of the laser, including pump power, cavity structure parameters, and crystal characteristics, establish a theoretical function curve graph with the non - radiative decay lifetime of the laser crystal as the independent variable and the relaxation oscillation frequency as the dependent variable;

[0009] (3) Match the measured relaxation oscillation frequency value in step (1) with the frequency value in the theoretical curve in step (2), and determine the corresponding non - radiative decay lifetime value through abscissa inversion to achieve accurate measurement of the actual lifetime of the laser crystal under stable operating conditions.

[0010] Furthermore, in the theoretical function curve graph with the non - radiative decay lifetime of the laser crystal as the independent variable and the relaxation oscillation frequency as the dependent variable, the value of ω off is calculated using formula (1):

[0011]

[0012] where α is the number of photons in the cavity, expressed as:

[0013]

[0014] where is the spontaneous emission rate of the lower energy level, τ nr is the non - radiative decay lifetime, is the spontaneous emission rate of the upper energy level, τ f is the fluorescence lifetime of the inverted population in the upper energy level, j 2 is the probability distribution of the ground - state particles, j 2 is expressed as: where Γ is the pump rate, and Γ is expressed as: where p in is the laser diode pump power in the laser when measuring the laser intensity noise, η t is the pump light transmission efficiency η a = 1 - exp(-aL 1 ) is the absorption efficiency of the gain medium, a is the absorption coefficient of the gain medium for the pump laser, is the quantum efficiency, v l is the output laser frequency, v p is the pump laser frequency, h is Planck's constant, N lm is the number of doped ions utilized in the laser medium, expressed as: N lm = ρ lm*V m , where V m is the mode volume of the pump laser at the laser crystal, expressed as: where ω p is the beam waist radius of the pump laser at the center of the laser crystal, λ p is the wavelength of the pump laser; z represents the axial position coordinate along the length direction of the laser crystal.

[0015] where the total cavity decay rate κ of the laser is expressed as:

[0016] κ = κ m + κ l , (3)

[0017] where is the cavity decay rate caused by the output mirror coupling mirror of the laser, is the cavity decay rate caused by the loss inside the laser cavity, is the lifetime of the oscillating laser in the laser resonator, L 2 is the cavity length for a single round trip of light in the resonator;

[0018]

[0019] where g is the stimulated emission rate of the coupling between the atomic transition of the laser crystal in the laser and the cavity mode of the laser, σ s is the laser stimulated emission cross section, ρ lm = ρ c * c w is the doped atom density in the gain medium, ρ c is the atom density corresponding to a doping atom concentration of 1.0%, c w is the doping concentration of the gain medium, c is the speed of light, L 1 is the doped length of the atoms in the laser crystal, and n is the refractive index of the laser crystal.

[0020] Furthermore, the laser crystal to be measured is integrated into the solid laser resonator as the gain medium. During the noise measurement process, the laser needs to maintain a stable operating state, specifically manifested as: the pump source current fluctuation is less than ±0.5%, the operating temperature is controlled within the range of ±0.1 °C, and the continuous output power fluctuation is lower than ±1%;

[0021] The self-heterodyne noise detection device is composed of a high-sensitivity photodetector, a low-noise transimpedance amplifier, and a spectrum analyzer. Its detection bandwidth covers the 10 Hz - 10 MHz frequency band, and it can collect the laser intensity noise spectrum in real time and analyze the relaxation oscillation peak frequency, with a frequency resolution better than 1 kHz;

[0022] The theoretical model is constructed based on the laser rate equation. By introducing the non-radiative transition rate parameter of the crystal, a quantitative relationship between the relaxation oscillation frequency and the non-radiative decay lifetime is established. In the model, the actual cavity loss, pump efficiency, and crystal thermal effect parameters are calibrated.

[0023] Further, the theoretical model of the relaxation oscillation frequency is constructed based on the laser rate equation, specifically including: the relaxation oscillation frequency The number of photons in the cavity The total cavity decay rate κ of the laser = κ m +κ l , the stimulated emission rate of the coupling between the atomic transition of the laser crystal and the cavity mode of the laser The advantages and beneficial effects of the present invention are as follows:

[0024] The present invention proposes a method that is simple to operate, accurate in results, and easy to accurately measure the non-radiative decay lifetime of a laser crystal under the actual operating conditions of a solid-state laser.

[0025] Its core principle lies in that the relaxation oscillation frequency of a solid-state laser is a function of the number of photons in the cavity in the full quantum noise model, and the change in the number of photons is restricted by the physical mechanism of the non-radiative decay lifetime of the laser crystal. In specific implementation, first, under the stable operating state of the laser, the intensity noise spectrum is obtained in real time through a self-homodyne noise detection system and the relaxation oscillation characteristic frequency is extracted; then, a theoretical model is constructed based on the laser rate equation, and combined with measured parameters such as pump power and cavity loss, a quantitative mapping curve between the non-radiative decay lifetime and the relaxation oscillation frequency is established; finally, through the matching inversion of the experimentally measured frequency value and the theoretical curve, the actual non-radiative decay lifetime of the laser crystal under dynamic working conditions is directly determined, realizing the in-situ precise correlation between the operating state and physical parameters.

[0026] 1. Based on the dynamic correlation mechanism between relaxation oscillation frequency and quantum noise

[0027] The core innovation of the present invention is to establish a quantitative mapping relationship between the relaxation oscillation frequency and the non-radiative decay lifetime in the full quantum noise model. Traditional methods rely on static testing or off-line analysis, while the present invention directly extracts the non-radiative decay lifetime through the intensity noise spectrum during the dynamic operation of the laser. Its ingenuity lies in using the sensitivity of the relaxation oscillation frequency to the change in the number of photons in the cavity to convert the quantum noise fluctuation into an observable signal. This design makes the measurement process fully synchronized with the actual working state of the laser, overcomes the problem of parameter distortion caused by traditional methods deviating from the dynamic working conditions, thus significantly improving the measurement accuracy, and without the need for an additional excitation source, realizing "zero-interference" in-situ detection.

[0028] 2. Self-homodyne noise detection and characteristic frequency extraction technology

[0029] To achieve non-invasive measurement, the present invention uses a self-zero detection system to capture the laser intensity noise spectrum in real time, and accurately extracts the relaxation oscillation characteristic frequency through an adaptive filtering algorithm. Unlike traditional methods that rely on external modulation or destructive sampling, this technology only uses the inherent quantum noise of the laser as an information carrier, cleverly avoiding interference with the laser packaging structure or operating mode. Its advantages are: data collection can be completed in a single measurement, it is compatible with packaged lasers, and the equipment cost is reduced by more than 60%, providing a feasible solution for rapid detection of production lines and service life monitoring.

[0030] 3. Multi-parameter coupling inversion algorithm and universal model design

[0031] In view of the nonlinear response of the input-output characteristics of the laser, the present invention simultaneously introduces measured parameters such as pump power, cavity loss, and mode matching efficiency into the theoretical model, and constructs a generalized mapping curve library of radiation-free decay lifetime and relaxation oscillation frequency. Through intelligent matching and inversion of experimental data and theoretical curves, the algorithm can automatically compensate for the influence of laser type differences and power fluctuations. Its innovation lies in: using the Bayesian optimization framework to achieve multi-parameter decoupling, solving the failure problem of traditional single variable models in high power or nonlinear ranges, expanding the measurement application range to the 10mW-10kW power range, and is effective for both continuous / pulsed laser systems.

[0032] 4. Dynamic in-situ detection and full-scenario adaptation capabilities

[0033] This invention has made a breakthrough in embedding the non-radiative attenuation lifetime measurement into the laser operation process, supporting real-time dynamic monitoring of each stage of debugging, packaging, and service. Compared with the limitations of traditional methods that require disassembly of the crystal or interruption of laser output, this technology can synchronously complete the extraction of lifetime parameters while the laser is working normally through in-situ noise signal analysis. Its unique value lies in: for the first time, it realizes the scenario compatibility of "measuring while running" - the crystal performance can be optimized during the laboratory debugging stage, the production line can perform full inspection and quality control, and the crystal aging can be warned during the service period, providing a disruptive tool for the full life cycle management of the laser system.

[0034] The present invention uses a quantum noise-driven measurement mechanism, non-invasive signal chain design, and a multi-physics field coupling inversion algorithm to push the radiation-free attenuation lifetime test from the "static offline" era to the "dynamic in-situ" era, solving the core problem of high-precision, full-working condition, and full-scenario compatibility, opening up a new paradigm for laser crystal performance evaluation and laser reliability research. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 The present invention provides a preferred embodiment scheme;

[0036] Figure 2Schematic diagram of the structure of the measurement device for the non-radiative decay lifetime of the laser crystal in the solid-state laser in the embodiment

[0037] Figure 3 Intensity noise spectral diagram obtained by the laser measured using the self-homodyne noise detection device

[0038] Figure 4 Non-radiative decay lifetime τ of the laser crystal under actual operating conditions of the solid-state laser nr And relaxation oscillation frequency ω of the laser off Function curve diagram Specific implementation manner

[0039] Next, the technical solutions in the embodiments of the present invention will be clearly and detailedly described in conjunction with the accompanying drawings in the embodiments of the present invention. The described embodiments are only a part of the embodiments of the present invention

[0040] The technical solution of the present invention to solve the above technical problems is

[0041] The present invention proposes a method with simple operation, accurate results, and easy to accurately measure the non-radiative decay lifetime of the laser crystal under the actual operating state of the solid-state laser

[0042] Its core principle lies in: the relaxation oscillation frequency of the solid-state laser has a functional relationship with the number of photons in the cavity in the full quantum noise model, and the change in the number of photons is restricted by the physical mechanism of the non-radiative decay lifetime of the laser crystal. During specific implementation, first, under the stable operating state of the laser, the intensity noise spectrum is obtained in real time through the self-homodyne noise detection system, and the relaxation oscillation characteristic frequency is extracted; then, a theoretical model is constructed based on the laser rate equation, and combined with measured parameters such as pump power and cavity loss, a quantitative mapping curve between the non-radiative decay lifetime and the relaxation oscillation frequency is established; finally, through the matching inversion of the experimentally measured frequency value and the theoretical curve, the actual non-radiative decay lifetime of the laser crystal under dynamic working conditions is directly determined, realizing the in-situ precise correlation between the operating state and physical parameters

[0043] According to the full quantum noise theory model of the laser, under the stable operating state of the laser, the relaxation oscillation frequency ω of the laser off Is expressed as

[0044]

[0045] Among them, α is the number of photons in the cavity, which is expressed as

[0046]

[0047] Among them Is the spontaneous emission rate of the lower energy level, τ nr Is the non-radiative decay lifetime is the spontaneous emission rate of the upper energy level, τ f is the fluorescence lifetime of the inverted particles in the upper energy level, j 2 is the probability distribution of the ground state particle number, j 2 is expressed as: where Γ is the pumping rate, and Γ is expressed as: where p in is the pump power of the laser diode in the laser when measuring the intensity noise of the laser, η t is the pump light transmission efficiency (the ratio of the pump light power entering the gain medium to the pump light power output by the laser diode, η a = 1 - exp(-aL 1 ) is the absorption efficiency of the gain medium, and a is the absorption coefficient of the gain medium for the pump laser, is the quantum efficiency, v l is the output laser frequency, v p is the pump laser frequency, h is the Planck constant, N lm is the number of doped ions utilized in the laser medium, and is expressed as: N lm = ρ lm *V m where V m is the mode volume of the pump laser at the laser crystal, and is expressed as: where ω p is the beam waist radius of the pump laser at the center of the laser crystal, λ p is the wavelength of the pump laser, and z represents the axial position coordinate along the length direction of the laser crystal.

[0048] where the total cavity decay rate κ of the laser is expressed as:

[0049] κ = κ m + κ l , (3)

[0050] where is the cavity decay rate caused by the output mirror coupling mirror of the laser, is the cavity decay rate caused by the loss inside the laser cavity, is the lifetime of the oscillating laser in the laser resonator, L 2 is the cavity length for a single round trip of light in the resonator.

[0051] In formula (1), g is the stimulated emission rate of the atomic transition of the laser crystal coupled with the laser cavity mode, and is expressed as:

[0052]

[0053] where σ s is the stimulated emission cross section of the laser, ρ lm = ρc *c w is the doping atom density in the gain medium, ρ c is the atom density corresponding to a doping atom concentration of 1.0%, c w is the doping concentration of the gain medium, c is the speed of light, L 1 is the atomic doping length of the laser crystal, and n is the refractive index of the laser crystal;

[0054] As shown in formulas (1)-(4), when the pump power and cavity structure parameters of the laser are fixed, there is a clear functional mapping relationship between the relaxation oscillation frequency and the non-radiative decay lifetime of the laser crystal. Based on this, when the laser is in a stable operating state (constant parameters), a theoretical response curve with the non-radiative decay lifetime as the independent variable and the relaxation oscillation frequency as the dependent variable can be constructed according to parameters such as the actual pumping conditions and the cavity loss coefficient.

[0055] During the experiment, in the stable operating state of the laser, the laser intensity noise spectrum is obtained in real time through a self-homodyne noise detection device, and the measured characteristic value of the relaxation oscillation frequency is analyzed from it. The measured frequency is matched with the frequency parameter in the theoretical response curve. When the two reach numerical consistency, the actual non-radiative decay lifetime value of the laser crystal under the current pumping conditions can be obtained by inverting the value of the corresponding abscissa, realizing the direct correlation measurement of the operating state and physical parameters.

[0056] The present invention provides a method for measuring the non-radiative decay lifetime of a laser crystal in the actual working state of a solid laser, and the specific steps are as follows:

[0057] 1. Noise spectrum analysis: Use a self-homodyne noise detection device to measure the laser intensity noise spectrum in real time, and extract the measured value of the relaxation oscillation frequency of the laser through the spectral peak characteristics;

[0058] 2. Theoretical modeling: Based on the actual parameters of the laser (pump power, cavity loss, etc.), construct a theoretical response curve with the non-radiative decay lifetime as the independent variable and the relaxation oscillation frequency as the dependent variable;

[0059] 3. Parameter inversion: Match the measured frequency with the theoretical curve, and directly obtain the actual non-radiative decay lifetime of the laser crystal under the current working conditions through the abscissa mapping.

[0060] Figure 1 is the overall implementation architecture schematic diagram of the method of the present invention. In the stable operating state of the solid laser, a self-homodyne noise detection device (including a high-bandwidth photodetector and a spectrum analyzer) is used to collect the laser intensity noise spectrum in real time.

[0061] Figure 2The structural configuration of the four-mirror ring cavity continuous 1047nm solid-state laser in this embodiment: The resonator consists of a four-mirror butterfly-shaped ring cavity, where the lenses (4) and (5) are convex-concave lenses with a radius of curvature R = 1500mm, and (6) and (7) are plano-concave lenses with a radius of curvature R = -100mm. The input coupling mirror (4) is coated with a dichroic film with high transmittance (T 880nm >99.5%) at 880nm / high reflectance (R 1047nm >99.7%) at 1047nm, (5) and (6) are coated with a 1047nm high-reflectance film (R 1047nm >99.7%), and the output coupling mirror (7) is coated with a 1047nm partial transmission film (T 1047nm = 20%). The pump source (1) uses an 880nm fiber-coupled laser diode (core diameter 400μm, NA = 0.22), and after passing through the coupling system (3), it is focused on the waist spot with a diameter of 0.49mm at the center of the laser crystal (8). The laser crystal (8) is a 30mm long Nd:YLF doped with 1at.% Nd +3 (S1, S2: AR 880nm；1047nm ). To eliminate the spatial hole burning effect, an optical isolator (9) composed of a 6mm long terbium gallium garnet (TGG) crystal and a half-wave plate is used in the resonator to ensure unidirectional traveling wave operation, and the total cavity length is 450mm.

[0062] The experiment was carried out under the condition of stable injection of 50W pump power. Figure 3 The measured intensity noise spectrum is shown, and its relaxation oscillation peak is located at 161kHz. A theoretical model is constructed based on the actual parameters of the laser: the length of the laser crystal L 1 = 3×10 -2 m, the single round-trip cavity length of the laser L 2 = 0.45m, the refractive index of the laser crystal n = 1.47, the fluorescence lifetime τ f = 485×10 -6 s, the doping concentration of Nd ions in the laser crystal c +3 = 1at.%, Avogadro's constant n w = 6.02×10 a = 6.02×10 23 , the speed of light c = 2.997×10m / s, Planck's constant h = 6.63×10 -34 , the beam waist radius ω of the pump laser at the center of the laser crystal p = 0.49mm, the absorption coefficient a of the gain medium for the pump laser = 130 / m, the transmittance t of the output coupling mirror = 0.2, the intracavity loss δ of the laser = 0.04, the transmission efficiency η of the pump laser t = 0.98, the measured absorption efficiency η of the crystal for the pump laser a = 0.73, the quantum efficiency η q= 0.841, the pump power P of the laser diode in = 50 W, the pump laser wavelength λ p = 880×10 -9 m, the pump laser frequency Laser frequency λ l = 1047×10 -9 m, the doped atom density ρ in the gain medium lm = ρ c *c w = 1.4*10 26 *c w .

[0063] Based on the actual parameters of the above laser, a quantitative mapping curve is made with the non-radiative decay lifetime τ nr of the laser crystal as the independent variable and the relaxation oscillation frequency ω off of the laser as the dependent variable, as shown in Figure 4 . When the theoretical curve intersects with the actual measured relaxation oscillation frequency value of 161 kHz, the corresponding abscissa τ nr = 22 μs is the actual non-radiative decay lifetime of the crystal under the 50 W pump condition.

[0064] The systems, devices, modules or units illustrated in the above embodiments can be specifically implemented by computer chips or entities, or by products with certain functions.

[0065] It should also be noted that the term "including", "comprising" or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, commodity or device including a series of elements not only includes those elements, but also includes other elements not explicitly listed, or elements inherent to such process, method, commodity or device. Without further limitation, an element defined by the statement "including a..." does not exclude the existence of another identical element in the process, method, commodity or device including the said element.

[0066] The above embodiments should be understood as being only for the purpose of illustrating the present invention and not for limiting the protection scope of the present invention. After reading the content recorded in the present invention, those skilled in the art can make various changes or modifications to the present invention, and these equivalent changes and modifications also fall within the scope defined by the claims of the present invention.

Claims

1. A method for measuring the non-radiative decay lifetime of a laser crystal, characterized in that: The following steps are involved: (1) Using a self-zero-beat noise detection device to collect the laser intensity noise spectrum in real time, and extracting the measured value of the laser relaxation oscillation frequency through spectral line analysis; (2) Based on the laser rate equation, a theoretical model of relaxation oscillation frequency is constructed. Combined with the actual operating parameters of the laser, including pump power, cavity structure parameters and crystal characteristics, a theoretical function curve is established with the non-radiative decay lifetime of the laser crystal as the independent variable and the relaxation oscillation frequency as the dependent variable. (3) Matching the relaxation oscillation frequency value measured in step (1) with the frequency value in the theoretical curve of step (2), determining the corresponding non-radiative decay lifetime value by horizontal coordinate inversion, and realizing accurate measurement of the actual lifetime of the laser crystal under stable working state.

2. A method for measuring the radiation-free decay lifetime of a laser crystal according to claim 1, characterized in that: In the theoretical function curve with the non-radiative decay lifetime of the laser crystal as the independent variable and the relaxation oscillation frequency as the dependent variable, ω off The value of is calculated using formula (1): Where α is the number of photons in the cavity, expressed as: in, is the spontaneous emission rate of the lower energy level, τ nr is the radiation-free decay lifetime, is the spontaneous emission rate of the upper energy level, τ f is the fluorescence lifetime of the upper energy level inversion particle, j2 is the probability of the ground state particle number distribution, and j2 is expressed as: Where Γ is the pump rate and Γ is expressed as: Among them, p in is the laser diode pump power in the laser corresponding to the measurement of laser intensity noise, η t is the pump light transmission efficiency η a =1-exp(-aL1) is the absorption efficiency of the gain medium, a is the absorption coefficient of the gain medium to the pump laser, is the quantum efficiency, v l is the output laser frequency, v p is the pump laser frequency, h is Planck's constant, N lm is the number of doping ions used in the laser medium, expressed as: N lm =ρ lm *V m , where V m is the mode volume of the pump laser at the laser crystal, expressed as: Among them, ω p is the waist radius of the pump laser at the center of the laser crystal, λ p is the wavelength of the pump laser; z represents the axial position coordinate along the length direction of the laser crystal; The total cavity decay rate κ of the laser is expressed as: k=k m +k l , (3) in, is the cavity decay rate caused by the laser output mirror and coupling mirror, is the cavity decay rate caused by the laser cavity loss, is the lifetime of the oscillating laser in the laser resonant cavity, L2 is the cavity length of a single round trip of the light in the resonant cavity; Where g is the rate of stimulated emission of light coupled between the atomic transition of the laser crystal and the laser cavity mode, σ s is the laser stimulated emission cross section, ρ lm =ρ c *c w is the density of doped atoms in the gain medium, ρ c is the atomic density corresponding to the doping atomic concentration of 1.0%, c w is the doping concentration of the gain medium, c is the speed of light, L1 is the atomic doping length of the laser crystal, and n is the refractive index of the laser crystal.

3. The method for measuring the non-radiative decay lifetime of a laser crystal according to claim 1, characterized in that: The laser crystal under test is integrated into the solid laser resonant cavity as a gain medium. During the noise measurement process, the laser needs to maintain a stable operating state, which is specifically manifested as: the pump source current fluctuation is less than ±0.5%, the operating temperature is controlled within the range of ±0.1°C, and the continuous output power fluctuation is less than ±1%; The self-zero-beat noise detection device is composed of a high-sensitivity photodetector, a low-noise transimpedance amplifier and a spectrum analyzer. Its detection bandwidth covers the frequency band of 10 Hz-10 MHz, and can collect the laser intensity noise spectrum and analyze the relaxation oscillation peak frequency in real time, with a frequency resolution better than 1 kHz. The theoretical model is constructed based on the laser rate equation. By introducing the crystal non-radiative transition rate parameter, a quantitative relationship between the relaxation oscillation frequency and the non-radiative decay lifetime is established. The actual cavity loss, pump efficiency and crystal thermal effect parameters are calibrated in the model.

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