Analytical models of transient thermoelastic deformations of mirrors heated by high power cw laser beams

Hello, P.; Vinet, J.-Y.

doi:10.1051/jphys:0199000510200224300

Cited by 59 publications

(50 citation statements)

References 8 publications

(22 reference statements)

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“…The second term of u z (r) is the Saint-Venant term, in which Y is the mirror Young's modulus. The calculation of B is given by Hello and Vinet [15] 9 . This term acts to make the thermal deformation more convex.…”

Section: Summary and Discussionmentioning

confidence: 99%

“…We follow a well-known derivation by Hello and Vinet [15] and recent expansion by Vinet [27] which allows one to calculate the thermoelastic deformation induced in any axially symmetric mirror heated by absorption of an axially symmetric transmitted beam.…”

Section: Appendix a Thermoelastic Deformationmentioning

confidence: 99%

“…SIS can also calculate the signal sideband induced by small motions of the mirrors. Surface deformations, such as thermal deformation (using the Hello-Vinet approximation [15]), measured aberrations, randomly generated profile errors and micro-roughness can also be included.…”

Section: Simulation Toolsmentioning

confidence: 99%

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Thermal distortions of non-Gaussian beams in Fabry–Perot cavities

Miller¹,

Willems²,

Yamamoto³

et al. 2008

Class. Quantum Grav.

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Thermal effects are already important in currently operating interferometric gravitational wave detectors. Planned upgrades of these detectors involve increasing optical power to combat quantum shot noise. We consider the ramifications of this increased power for one particular class of laser beamswide, flat-topped, mesa beams. In particular we model a single mesa beam Fabry-Perot cavity having thermoelastically deformed mirrors. We calculate the intensity profile of the fundamental cavity eigenmode in the presence of thermal perturbations, and the associated changes in thermal noise. We also outline an idealized method of correcting for such effects. At each stage we contrast our results with those of a comparable Gaussian beam cavity. Although we focus on mesa beams the techniques described are applicable to any azimuthally symmetric system.

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Section: Summary and Discussionmentioning

confidence: 99%

Section: Appendix a Thermoelastic Deformationmentioning

confidence: 99%

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Thermal distortions of non-Gaussian beams in Fabry–Perot cavities

Miller¹,

Willems²,

Yamamoto³

et al. 2008

Class. Quantum Grav.

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show abstract

“…The thermal variation of the material refractive index and the elastic thermal expansion at the mirror surfaces are the two dominant thermal aberrations. Hello and Vinet [13,14] predicted both the steady state and transient temperature distribution throughout a cylindrical mirror for the case where the change in temperature due to absorption of optical power remains small compared to the external ambient temperature. The time evolution of the thermal aberration per unit total absorbed power for a concentric laser beam passing through a cylindrical test mass of radius a and height h, is given by an infinite sum of exponentials as follows: are the thermo-optical coefficient, the thermal conductivity, the emissivity, and the density of the test mass material, respectively, and is the StefanBoltzmann constant.…”

mentioning

confidence: 99%

“…Figure 1 [7] shows the core optical components of an advanced interferometer, with shading showing the temperature build up in the core optical components. Thermal lensing arises whenever absorbed light in an optical substrate or coating creates a temperature gradient, which, via thermal expansion and the thermo-optic coefficient, leads to wave front distortion of the optical modes of the interferometer [9][10][11][12][13][14][15].…”

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confidence: 99%

Compensation of Strong Thermal Lensing in High-Optical-Power Cavities

Zhao

Degallaix

et al. 2006

Phys. Rev. Lett.

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In an experiment to simulate the conditions in high optical power advanced gravitational wave detectors, we show for the first time that the time evolution of strong thermal lenses follows the predicted infinite sum of exponentials (approximated by a double exponential), and that such lenses can be compensated using an intracavity compensation plate heated on its cylindrical surface. We show that high finesse 1400 can be achieved in cavities with internal compensation plates, and that mode matching can be maintained. The experiment achieves a wave front distortion similar to that expected for the input test mass substrate in the Advanced Laser Interferometer Gravitational Wave Observatory, and shows that thermal compensation schemes are viable. It is also shown that the measurements allow a direct measurement of substrate optical absorption in the test mass and the compensation plate.

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Optimized high power laser mirror design for low quality degradation and beam analysis

Ach¹,

Viöl²

2005

Laser Phys. Lett.

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The thermally induced deformation of different copper mirrors for infrared laser beams was simulated using a finite element method. The deformation is highly dependent on the mirror design. Several mirror designs with different cooling arrangements have been simulated. A mirror design with a set of straight cooling channels and a stiff body shows the least deformation. The cooling channel diameter, spacing, surface distance and overall mirror thickness were varied at this design and the surface deformation was compared. The mirror design not only influences the overall expansion of the mirror but also the shape of the surface deformation. The optimized mirror geometry provides small quality degradation at beam guidance and the possibility of an online beam monitoring method by measurement of the local surface deformation. The method can serve as a device for online and beam position detection. Deformation of the surface of metallic laser mirrors with different cooling techniques. 5 mm thick flat backside cooled mirror, 5 mm thick mirror with backside honeycomb structure, mirror with 5 mm surface layer, cooling channels and stiff body

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Analytical models of transient thermoelastic deformations of mirrors heated by high power cw laser beams

Cited by 59 publications

References 8 publications

Thermal distortions of non-Gaussian beams in Fabry–Perot cavities

Thermal distortions of non-Gaussian beams in Fabry–Perot cavities

Compensation of Strong Thermal Lensing in High-Optical-Power Cavities

Optimized high power laser mirror design for low quality degradation and beam analysis

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