Analytical treatment of the thermal problem in axially pumped solid-state lasers

Usievich, B. A.; Sychugov, V A; Pigeon, Florent; Tishchenko, A.V.

doi:10.1109/3.945327

Cited by 27 publications

(14 citation statements)

References 5 publications

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“…2a and b, respectively, according to the analytical expression (6). The temperature increase in the longitudinal direction is in a range of 2.73 -2.78 K at different radii.…”

Section: A Typical Examplementioning

confidence: 99%

“…This model results in relatively large error, since the coolant temperature rise along the flow direction has been ignored. Multi-dimensional analytical solutions have been derived by Belostotskii and Kudryashev [3], Farrukh, et al [4], Hello, et al [5], Usievich, et al [6], Chénais, et al [7]. However, the longitudinal variation of coolant temperature has not been taken into account in these analytical models.…”

Section: Introductionmentioning

confidence: 98%

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A study of the axisymmetric thermal strain in a laser rod with longitudinal temperature rise

Huai

2009

Applied Thermal Engineering

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“…2a and b, respectively, according to the analytical expression (6). The temperature increase in the longitudinal direction is in a range of 2.73 -2.78 K at different radii.…”

Section: A Typical Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

A study of the axisymmetric thermal strain in a laser rod with longitudinal temperature rise

Huai

2009

Applied Thermal Engineering

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“…As another example, the thermal models have also been used to study the diffraction images of thermal lenses [27].…”

Section: Introductionmentioning

confidence: 99%

Analytical solutions for anisotropic time-dependent heat equations with Robin boundary condition for cubic-shaped solid-state laser crystals

Sabaeian

2012

Appl. Opt.

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The problem of finding analytical solutions for time-dependent or time-independent heat equations, especially for solid-state laser media, has required a lot of work in the field of thermal effects. However, to calculate the temperature distributions analytically, researchers often have to make some approximations or employ complex methods. In this work, we present full analytical solutions for anisotropic time-dependent heat equations in the Cartesian coordinates with various source terms corresponding to various pumping schemes. Moreover, the most general boundary condition of Robin (or impedance boundary condition), corresponding to the convection cooling mechanism, was applied. This general condition can be easily switched to constant temperature and thermal insulation as special cases. To this end, we first proposed a general approach to solving time-dependent heat equations with an arbitrary heat source. We then applied our approach to explore the temperature distribution for three cases: steady-state pumping or long transient, single-shot pumping or short transient, and repetitively pulsed pumping. Our results show the possibility of an easier and more accurate approach to analytical calculations of the thermal dispersion, thermal stresses (strains), thermal bending, thermal phase shift, and other thermal effects.

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“…The analytical treatment of this thermal problem is rather complicated. The expression for temperature distribution obtained using the Dinis series (see [13][14][15] and refs. therein) is described by the infinite sum of cumbersome terms with Bessel functions, and is, therefore, inconvenient for practical applications.…”

Section: Introductionmentioning

confidence: 99%

Numerical treatment of the temperature distribution in end-pumped composite laser rods

Dement'ev¹

2007

Lithuanian J. Phys.

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Analytical and numerical studies of the thermal characteristics of conventional and composite laser rods in laser-diode endpumped geometry are reported in detail using Nd : YAG rods as an example. It has been shown that taking into account the temperature dependence of the heat conductivity, the change of the temperature in the active element can be significantly higher compared to the data for the temperature-independent heat conductivity coefficient. It has been found that the dependence of heat conductivity on temperature causes the non-parabolic heat distribution even in the region inside the pump beam with the top hat intensity distribution. It has also been shown by direct numerical simulations that the undoped entrance section of the composite rod significantly reduces the peak temperature rise inside the crystal.

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Analytical treatment of the thermal problem in axially pumped solid-state lasers

Cited by 27 publications

References 5 publications

A study of the axisymmetric thermal strain in a laser rod with longitudinal temperature rise

A study of the axisymmetric thermal strain in a laser rod with longitudinal temperature rise

Analytical solutions for anisotropic time-dependent heat equations with Robin boundary condition for cubic-shaped solid-state laser crystals

Numerical treatment of the temperature distribution in end-pumped composite laser rods

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