On the performance limits of coatings for gravitational wave detectors made of alternating layers of two materials

Abstract

The coating design for mirrors used in interferometric detectors of gravitational waves currently consists of stacks of two alternating dielectric materials with different refractive indexes. In order to explore the performance limits of such coatings, we have formulated and solved the design problem as a multiobjective optimization problem consisting in the minimization of both coating transmittance and thermal noise. An algorithm of global optimization (Borg MOEA) has been used without any a priori assumption on the number and thicknesses of the layers in the coating. The algorithm yields to a Pareto tradeoff boundary exhibiting a continuous, decreasing and non convex (bump-like) profile, bounded from below by an exponential curve which can be written in explicit closed form in the transmittance-noise plane. The lower bound curve has the same expression of the relation between transmittance and noise for the quarter wavelength design where the noise coefficient of the high refractive index material assumes a smaller equivalent value. An application of this result allowing to reduce the computational burden of the search procedure is reported and discussed.

Temperature‐mediated excitation of defect modes in a periodic structure at terahertz frequencies

“…In Figures 2 and 3, the real and imaginary parts of the relative permittivity, Re(ε D ) and Im(ε D ), respectively, are displayed as functions of both temperature T [−100, 100] C and frequency f = 2πω [3,7] THz.…”

“…They can be used as adaptation devices, for example, as coatings that reduce the reflectivity of a surface. 1,2 At the opposite, such structures can be designed to increase reflectivity and can be used as optical mirrors to achieve high reflectivity either at a fixed wavelength 3 or in a broad frequency range. 4 Various other applications are possible, for example, as beam splitters, 5,6 filters that transmit (or reflect) parts of the spectrum, [7][8][9][10] polarizers, 11 plasmonic devices, 12 to improve Raman spectroscopy, 13 to localize field, [14][15][16] and so on.…”

“…25 Other materials with features suitable for applications of multilayers include some polymers that show excellent transparency at terahertz. In particular, polymethylpentene (TPX, more precisely, poly-4methylpentene-1) is a semicrystalline polymer with negligible absorptance and with a refractive index which is Abbreviations: InSb, indium antimonide; SiO 2 , silica; TPX, polymethylpentene practically constant in the range [3,7] THz. 26 In addition, the TPX refractive index is particularly low (≈1.5), making it suitable for use in multilayers as the low refraction index medium.…”

Emergence and Evolution of Crystallization in TiO2 Thin Films: A Structural and Morphological Study

“…This exciting and rich set of material properties has made TiO 2 a valuable candidate for applications in many fields, as well as for fundamental science investigations. To date, the market demand on TiO 2 -based devices for photocatalysis [1][2][3][4], sensors [5,6], optical reflective coatings for highly innovative 2 of 18 applications [7,8] (innovative mirrors for gravitational wave interferometers, among the others [9][10][11][12]), solar cells [13][14][15], metal insulator semiconductor industry [16], self-cleaning application [17][18][19], water purification processes [20], has been systematically growing, especially for thin films and nanostructures. In addition, a constant effort has been made in setting up reliable computational techniques, mainly based on density functional theory (DFT), to predict and describe the properties of TiO 2 , not only in its crystalline forms, but also in the amorphous phase, as well as to simulate the amorphous to crystalline phase transition [21][22][23].…”

Demonstration of the Multimaterial Coating Concept to Reduce Thermal Noise in Gravitational-Wave Detectors

“…The coatings currently used in Advanced LIGO and Advanced Virgo are made from silica (SiO 2 ) and tantala doped with titania (TiO 2 ∶Ta 2 O 5 ) [7,8,[11][12][13][14]. Many approaches to develop coatings with reduced thermal noise and low optical absorption at the ppm level are being investigated, such as understanding correlations between atomic structure and material properties [15][16][17][18][19], elevated temperature deposition [20], different dopants and doping concentrations [13,21], nanolayer structures [22,23], crystalline coatings [24], alternative amorphous materials [21,25,26], and optimizing the layer thicknesses [27].…”