Photothermal and thermo-refractive effects in high reflectivity mirrors at room and cryogenic temperature

Increasing requirements in the sensitivity of interferometric measurements is a common feature of several research fields, from gravitational wave detection to quantum optics. This motivates refined studies of high reflectivity mirrors and of noise sources that are tightly related to their structure. In this work we present an experimental characterization of photothermal and thermo-refractive effects in high reflectivity mirrors, i.e., of the variations in the position of their effective reflection plane due to weak residual power absorption. The measurements are performed by modulating the impinging power in the range 10Hz÷100kHz. The experimental results are compared with an expressly derived theoretical model in order to fully understand the phenomena and exploit them to extract useful effective thermo-mechanical parameters of the coating. The measurements are extended to cryogenic temperature, where most high sensitivity experiments are performed (or planned in future versions) and where characteriza...

[1]  M. Pinard,et al.  Thermoelastic effects at low temperatures and quantum limits in displacement measurements , 2001 .

[2]  John L. Hall,et al.  Laser phase and frequency stabilization using an optical resonator , 1983 .

[3]  W. Cheng,et al.  Effect of thermal stresses on temperature dependence of refractive index for Ta2O5 dielectric films , 1999 .

[4]  J. A. Morrison,et al.  The heat capacity of pure silicon and germanium and properties of their vibrational frequency spectra , 1959 .

[5]  K. K. Kelley,et al.  The Specific Heats at Low Temperatures of Tantalum Oxide and Tantalum Carbide1 , 1940 .

[6]  Andrew G. Glen,et al.  APPL , 2001 .

[7]  J. Wortman,et al.  Young's Modulus, Shear Modulus, and Poisson's Ratio in Silicon and Germanium , 1965 .

[8]  Douglas B. Leviton,et al.  Temperature-dependent absolute refractive index measurements of synthetic fused silica , 2006, SPIE Astronomical Telescopes + Instrumentation.

[9]  M. Gorodetsky Thermal noises and noise compensation in high-reflection multilayer coating , 2008, 0809.0438.

[10]  L. Conti,et al.  Experimental measurement of the dynamic photothermal effect in Fabry-Perot cavities for gravitational wave detectors. , 2002, Physical review letters.

[11]  Wei Cheng,et al.  Temperature dependence of refractive index of Ta2O5 Dielectric Films , 1997 .

[12]  M. M. Fejer,et al.  Thermoelastic dissipation in inhomogeneous media: loss measurements and displacement noise in coated test masses for interferometric gravitational wave detectors , 2004 .

[13]  Michael L. Gorodetsky,et al.  Thermo-refractive noise in gravitational wave antennae , 2000 .

[14]  Yasumasa Okada,et al.  Precise determination of lattice parameter and thermal expansion coefficient of silicon between 300 and 1500 K , 1984 .

[15]  L. Pinard,et al.  A study of coating mechanical and optical losses in view of reducing mirror thermal noise in gravitational wave detectors , 2010 .

[16]  R. Pohl,et al.  Thermal Conductivity and Specific Heat of Noncrystalline Solids , 1971 .

[17]  C. Tien,et al.  Simultaneous determination of the thermal expansion coefficient and the elastic modulus of Ta2O5 thin film using phase shifting interferometry , 2000 .

[18]  Takayuki Tomaru,et al.  Cryogenic cooling of a sapphire mirror-suspension for interferometric gravitational wave detectors , 1998 .

[19]  G. K. White,et al.  Linear thermal expansion measurements on silicon from 6 to 340 K , 1977 .

[20]  C. Swenson,et al.  Tunneling models and the experimental thermal expansivities of fused silica and poly(methylmethacrylate) (PMMA) below 4 K , 1979 .

[21]  Mehmet Naci Inci Simultaneous measurements of thermal optical and linear thermal expansion coefficients of Ta2O5 films , 2003, International Commission for Optics.

[22]  G. A. Slack,et al.  Thermal Conductivity of Silicon and Germanium from 3°K to the Melting Point , 1964 .

[23]  L. Conti,et al.  Wideband dual sphere detector of gravitational waves. , 2000, Physical review letters.

[24]  C. Fang-Yen,et al.  Optical bistability induced by mirror absorption: measurement of absorption coefficients at the sub-ppm level. , 1997, Optics letters.

[25]  広 久保田,et al.  Principle of Optics , 1960 .

[26]  P. D. Maycock,et al.  Thermal Conductivity of Silicon from 300 to 1400°K , 1963 .

[27]  Mack,et al.  Low-temperature behavior of vitreous silica containing neon solute. , 1985, Physical review. B, Condensed matter.

[28]  Enhanced photothermal displacement spectroscopy for thin-film characterization using a Fabry-Perot resonator , 2003, cond-mat/0310194.

[29]  T. Briant,et al.  Observation of back-action noise cancellation in interferometric and weak force measurements. , 2007, Physical review letters.

[30]  G. White Thermal Expansion of Vitreous Silica at Low Temperatures , 1975 .

[31]  A. Heidmann,et al.  Experimental investigation of dynamic photo-thermal effect , 2006 .

[32]  Martin M. Fejer,et al.  Experimental measurements of mechanical dissipation associated with dielectric coatings formed using SiO2, Ta2O5 and Al2O3 , 2006 .

[33]  M. Fejer,et al.  Thermo-optic noise in coated mirrors for high-precision optical measurements , 2008, 0807.4774.