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  • July 2012

Optics InfoBase > Spotlight on Optics > Unified theoretical model for calculating laser-induced wavefront distortion in optical materials


Unified theoretical model for calculating laser-induced wavefront distortion in optical materials

Published in JOSA B, Vol. 29 Issue 7, pp.1772-1777 (2012)
by Luis C. Malacarne, Nelson G. C. Astrath, and Mauro L. Baesso

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Spotlight summary: One of the great advantages of laser sources is the high quality of their output beams, which are close to diffraction-limited Gaussian beams. A high beam quality can be important in a wide range of applications, e.g. when strong focusing is required, when a large working distance is necessary for a given optical system design, etc.

However, a laser beam’s high power density results in significant thermal loading of the laser’s elements due to optical absorption, even if this absorption is negligible in usual conditions. Indeed, thermal lensing and thermally-induced birefringence due to temperature gradients, generated through non-radiative relaxation of absorbed energy, can seriously affect a laser’s performance and modify the quality of its beam. For example, scaling the output power of diode-pumped solid-state lasers is a key issue for laser source designers: thermally-induced distortion of the laser crystal is a primary limiting factor on average power scaling in such systems. Further, even passive components suffer from laser-induced heating if the average laser power is sufficiently high: the unavoidable absorption within the bulk and on the surfaces of an element raises its temperature (where laser beam passes the element) and, thus, results in the development of a thermal lens through the thermo-optic effect, thermal expansion, and the stress-optic effect.

The method for determining wave-front distortions due to thermal lensing in an element requires computation of the temperature and thermal stress distributions under thermal load and the corresponding optical path distortions suffered for each polarization of light passing through the element.

Within certain approximations regarding the element’s geometry and low optical absorption, the temperature and thermally-induced stress distributions may be expressed in an analytic form that simplifies significantly the final solution. To the best of my knowledge, before publication of this article by L.C. Malacarne et al. in the Journal of the Optical Society of America B, only two major theoretical models for the analytical determination of optical distortions in heated elements were used: (i) the approximation of long rods (plane-strain model) and (ii) the approximation of thin windows (plane-stress model). The authors of this paper obtained a solution for this problem in analytic terms, irrespective to the thickness of the element, and showed that this solution is in excellent agreement with both the plane-strain and plane-stress limiting cases. For laser source designers, this means that no more special codes, based on e.g. finite elements, for the calculation of the thermal lensing effect in passive laser elements might be necessary. Hereafter, it would be nice to see a generalized solution for elements with moderate absorption (e.g. passive absorbers, laser media) and azimuthal anisotropy (e.g. laser crystals).

--Andrey N. Kuzmin



Technical Division: Light–Matter Interactions
ToC Category: Optics at Surfaces
OCIS Codes: (240.6700) Optics at surfaces : Surfaces
(350.5340) Other areas of optics : Photothermal effects
(350.6830) Other areas of optics : Thermal lensing


Posted on July 20, 2012

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