Thermal noise in optical cavities revisited

Thomas Kessler; Thomas Legero; Uwe Sterr

doi:10.1364/JOSAB.29.000178

Thermal noise in optical cavities revisited

Thomas Kessler, Thomas Legero, and Uwe Sterr

Journal of the Optical Society of America B
Vol. 29,
Issue 1,
pp. 178-184
(2012)
•https://doi.org/10.1364/JOSAB.29.000178

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Thomas Kessler, Thomas Legero, and Uwe Sterr, "Thermal noise in optical cavities revisited," J. Opt. Soc. Am. B 29, 178-184 (2012)

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Related Topics
Table of Contents Category
- Instrumentation, Measurement, and Metrology
Optics & Photonics Topics
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The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Fabry-Perot (120.2230)
- Metrology (120.3940)
- Laser stabilization (140.3425)
- Glass and other amorphous materials (160.2750)
- Resonators (230.5750)

About this Article
History
- Original Manuscript: June 29, 2011
- Manuscript Accepted: October 18, 2011
- Published: December 16, 2011

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Abstract

Thermal noise of optical reference cavities sets a fundamental limit to the frequency instability of ultrastable lasers. Using Levin’s formulation of the fluctuation-dissipation theorem, we correct the analytical estimate for the spacer contribution given by Numata et al. [Phys. Rev. Lett. 93, 250602 (2004)]. For detailed analysis, finite- element calculations of the thermal noise focusing on the spacer geometry, support structure, and the usage of different materials have been carried out. We find that the increased dissipation close to the contact area between spacer and mirrors can contribute significantly to the thermal noise. From an estimate of the support structure contribution, we give guidelines for a low-noise mounting of the cavity. For mixed-material cavities, we show that the thermal expansion can be compensated without deteriorating the thermal noise.

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$R_{sp}$	spacer radius	$16 mm$
L	spacer length	$100 mm$
$r_{sp}$	spacer central bore radius	$5.5 mm$
$D_{sb}$	substrate diameter	$25.4 mm$
$h_{sb}$	substrate thickness	$6.3 mm$
$d_{ct}$	coating thickness	$2 μm$
w	beam waist ( $1 / e^{2}$ radius)	$240 μm$
E	Young’s modulus ULE (FS)	$67.6 (73.0) GPa$
ν	Poisson’s ratio ULE (FS)	0.17 (0.16)
$ϕ_{ct}$	loss angle coating	$4 \cdot 10^{- 4}$
$1 / ϕ$	quality factor ULE (FS)	$6 \cdot 10^{4}$ ( $10^{6}$ )
T	temperature	$293 K$
$k_{B}$	Boltzmann’s constant	$1.381 \cdot 10^{- 23} J / K$

	Spacer	Substrate	Coating
Analytic result	1.04	16.89	0.126
FEM calculation	1.50	16.99	0.127

$A_{sup}$	area	$2 {mm}^{2}$	[16]
$d_{sup}$	thickness	$0.7 mm$	[16]
$E_{sup}$	Young’s modulus	$0.8 MPa$
$ν_{sup}$	Poisson’s ratio	0.27
$G_{sup}$	shear modulus	$E_{sup} / (2 + 2 ν_{sup}) = 0.31 MPa$	[44]
$ϕ_{sup}$	loss angle	0.33	[44, 45]

$R_{sp}$	spacer radius	$16 mm$
L	spacer length	$100 mm$
$r_{sp}$	spacer central bore radius	$5.5 mm$
$D_{sb}$	substrate diameter	$25.4 mm$
$h_{sb}$	substrate thickness	$6.3 mm$
$d_{ct}$	coating thickness	$2 μm$
w	beam waist ( $1 / e^{2}$ radius)	$240 μm$
E	Young’s modulus ULE (FS)	$67.6 (73.0) GPa$
ν	Poisson’s ratio ULE (FS)	0.17 (0.16)
$ϕ_{ct}$	loss angle coating	$4 \cdot 10^{- 4}$
$1 / ϕ$	quality factor ULE (FS)	$6 \cdot 10^{4}$ ( $10^{6}$ )
T	temperature	$293 K$
$k_{B}$	Boltzmann’s constant	$1.381 \cdot 10^{- 23} J / K$

	Spacer	Substrate	Coating
Analytic result	1.04	16.89	0.126
FEM calculation	1.50	16.99	0.127

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