Correct use of the photoelastic effect for the description of thermally induced refractive index change is discussed and the analytical relations between thermo-optic coefficients at zero stresses and zero strains are found for all classes of cubic crystals. These relations may be useful for the investigation of thermal effects in very promising sesquioxide class m3 laser crystals. An accepted set of elasto-optical coefficients of the YAG crystal and an alternative one found in the literature were used in numerical simulations. Significant differences in the calculated thermo-optic coefficients and induced birefringence are found using different sets of these coefficients. Misunderstandings related with the so-called photoelastic coefficients are resolved and new expressions for these coefficients are found. It is shown that the incorrect use of these coefficients for different pump beam distributions can lead to significant discrepancies for thermally induced birefringence. It is also shown that common use of the generalized thermo-optic coefficients significantly overestimates the values of optical power of thermal lenses when they are applied to the laser rods with lengths several times longer than their diameter.

On the use of photoelastic effect and plane strain or plane stress approximations for the description of thermal lensing

Temperature dependences of the thermo-optical coefficients of YAG crystals are often neglected when thermal lensing in laser rods is investigated, though their influence is very significant. It is especially significant for transversally non-uniform thermal loading. An analytical solution of the heat transfer equation with only the radial heat flow is found in the integral form, which is very convenient for numerical simulations. Uniform, top-hat, parabolic, Gaussian, super-Gaussian and annular heat source distributions are used in the calculations. The generalization of the thermally-induced refractive index change for long enough [1 1 1]-cut YAG rods to the case of temperature-dependent YAG parameters is developed and applied to the calculation of the corresponding optical path differences. Different definitions of the optical power of the aberrated thermal lens (TL) are discussed in detail. It is shown that for each of the heat source distributions, the temperature dependences of the YAG parameters significantly increase (1.5–1.8 times) the paraxial optical power of the induced TL.

Modeling of thermal lensing in a [1 1 1]-cut Nd:YAG rod with temperature-dependent parameters and different pumping profiles

Temperature dependences of the thermal conductivity and thermo-optic coefficient are often neglected when thermal lensing in laser crystals is investigated, though their influence is very significant. In this paper, the general solution of heat transfer equation with temperature dependent thermal conductivity is found in an integral form, which is very convenient for analytical and numerical analysis. Using this solution, the possibility to eliminate spherical aberration by a proper choice of the pump parabolicity parameter is investigated in detail. The inaccuracies in the definition of optical path differences used in a few previous works for the case of temperature dependent thermo-optic coefficient are explained. It is shown that the use of a correct definition increases the value of the parabolic coefficient at which the elimination of spherical aberrations may be realized as compared with the original work of Hodgson and Weber. It is also found that nearly the same shapes of pumping are required for elimination of spherical aberrations for both radial and tangential polarization.

/pdf/conditions-for-reducing-spherical-thermal-aberrations-in-4vtq4mpqrz.pdf

Conditions for reducing spherical thermal aberrations in transversally pumped YAG rods

Master Oscillator Power Amplifier (MOPA) systems find extensive use in laser development to increase the optical power of laser emissions from a Master Oscillator (MO). Commonly used are the cylindrical rod MOPAs that are optically excited using a multimode fiber-coupled (FC) diode laser emission in an end-pumped configuration. Current analytical 3D models that incorporate thermal effects, gain saturation, and iterative Fourier beam propagation methods, collectively, rely on static approximations of the evolution of the FC pump beam profile over the longitudinal volume of the amplifier crystal. Furthermore, in general, the spectral behavior of the FC diode emission is assumed to be static, and the thermal wavelength shift is not accounted for in the simulation. In this work, we demonstrate a novel approach for accurate modeling of the multimode FC pump beam emission as a complex field using a phase-only Gaussian to flat-top (FT) diffractive optical element, thus allowing for the inclusion of the pump beam into the iterative propagation method. Additionally, we present a method for precise calibration of the model using simple experimental measurements of the diode emission spectrum. The theoretical model is experimentally validated using an end-pumped Nd:YAG crystal rod to perform single-pass amplification of a Gaussian beam, showing excellent agreement with predicted output powers over the calibrated range of pump powers. Furthermore, we provide experimental data that exhibits a strong correlation between the Gaussian to FT phase-only transformation and the multimode FC diode evolution in free-space propagation.

Improving performance prediction of diode end-pumped solid-state Nd:YAG rod amplifiers by incorporating pump mode evolution.

An algorithm for determining the thermal stress in round cylindrical monocrystals by means of the integral photoelasticity method is analyzed. Transillumination in a cross section of a sample is assumed. The optical problem is solved within the framework of the paraxial approximation assuming weak birefringence. Reconstruction is based on the measurement of characteristic parameters of the polarized light propagated through the sample.

Polarization tomography of residual stress in monocrystals of YAG

Using correct expressions for piezo-optic and elasto-optic effects, the analytical relations between thermal coefficients of the refractive index at zero stress and zero strain have been established for YAG-type cubic crystals. Using the plane strain and plane stress approximations, analytical expressions for thermal radial and tangential changes of the refractive index have been found. The relations between different expressions for photoelastic coefficients are established. Examples of the inconsistent usage of generalised thermo-optic coefficients are discussed. It is shown that their values are often significantly overestimated when the results of the plane stress approximation are applied to a laser rod with a length larger than its diameter.

http://iopscience.iop.org/article/10.1088/1054-660X/25/9/095004/pdf

Relationships between different expressions of thermo-optic and photoelastic coefficients of YAG crystal

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Relationships between different expressions of thermo-optic and photoelastic coefficients of YAG crystal