Multimaterial optical coatings are a promising viable option to meet the challenging requirements (in terms of transmittance, absorbance, and thermal noise) of next-generation gravitational wave ...detector mirrors. In this paper we focus on ternary coatings consisting of quarter-wavelength-thick layers, where a third material (H^{′}) is added to the two presently in use, namely, silica (L) and titania-doped tantala (H), featuring higher dielectric contrast (against silica) and lower thermal noise (compared with titania-doped tantala), but higher optical losses. We seek the optimal material sequences, featuring minimal thermal (Brownian) noise under prescribed transmittance and absorbance constraints, by exhaustive simulation over all possible configurations, for different values of the optical density and extinction coefficient of the third material, including the case of amorphous silicon and silicon nitride operating at ambient and cryogenic temperatures. In all cases studied, the optimal designs consist of a stack of (H^{′}|L) doublets topped by a stack of (H|L) doublets, confirming previous heuristic assumptions, and the achievable coating noise power spectral density reduction factor ranges from ∼0.5 at 290 K down to ∼0.1 at 20 K. The robustness of the found optimal designs against layer thickness deposition errors and uncertainties and/or fluctuations in the optical losses of the third material is also investigated. Possible margins for further thermal noise reduction by layer thickness optimization, and strategies to implement it, are discussed.
Simple algorithms for retrieving free-space antenna field or directivity patterns from complex (field) or real (intensity) measurements taken in ideal reverberation environments are introduced and ...discussed.
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 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.
•Solution of the design optimization problem of two-materials coatings for Gravitational Wave detectors.•Pareto front computation by (state of art) multi-objective optimizations algorithm (Borg MOEA).•Analytic expression bounding the Pareto fronts.•Noise reduction in realistic Gravitational Waves detectors.
A triadic Cantor fractal multi-layer is a stack of two different dielectric materials whose thicknesses are determined according to the triadic Cantor fractal scheme. When inserted in a rectangular ...waveguide, the spectral response of a triadic Cantor multi-layer can be tailored to feature a narrow single transmission peak in the waveguide single-mode frequency range, with a low insertion loss and a high rejection level of forbidden frequencies. The experimental characterization of alumina-polystyrene and plexiglass-polystyrene Cantor multi-layers inserted in a WR90 waveguide (Hewlett-Packard, USA) matches thoroughly with the results of the theoretical modeling and demonstrates that triadic Cantor multi-layers can be used to realize feasible narrow-band microwave filters.
Ray chaos, manifested by the exponential divergence of trajectories in an originally thin ray bundle, can occur even in linear electromagnetic propagation environments, due to the inherent ...nonlinearity of ray-tracing maps. In this paper, we present a novel (two-dimensional) test example of such an environment which embodies intimately coupled refractive wave-trapping and periodicity-induced multiple scattering phenomenologies, and which is amenable to explicit full-wave analysis. Though strictly nonchaotic, it is demonstrated that under appropriate conditions which are inferred from a comprehensive parametric database generated via the above-noted rigorous reference solution, the high-frequency wave dynamics exhibits trends toward irregularity and other peculiar characteristics; these features can be interpreted as "ray-chaotic footprints", and they are usually not observed in geometries characterized by "regular" ray behavior. In this connection, known analogies from other disciplines (particularly quantum physics) are briefly reviewed and related to the proposed test configuration. Moreover, theoretical implications and open issues are discussed, and potential applications are conjectured.
Multifrequency numerical simulations of the light-coupling efficiency of a prismatic bioinspired compound lens (BCL) of silicon atop a thick silicon substrate were carried out within the framework of ...geometrical optics. Comparison was made with untextured and groove-textured silicon substrates as well as with untextured silicon substrates with a double-layer anti-reflection (DLAR) coating. Taking into account the broadband nature and the sea-level spectral irradiance of the insolation flux, and averaging over all admissible directions and both linear polarization states of the incident light, we found that the light-coupling efficiency can be almost doubled with respect to the untextured silicon substrate and enhanced by about a third with respect to a DLAR-coated untextured silicon substrate, by adopting a DLAR-coated silicon BCL.
We study a simple (ray optical, scalar) model of mode-stirred electromagnetic reverberating enclosures. Extensive numerical simulations reveal consistently that spatial-field homogenization and ...(wide-sense) deterministic chaos occur together, as the time-harmonic peak displacement of the mode-stirring wall becomes comparable to the electromagnetic wavelength. Reverberation properties can thus be synthetically gauged by Lyapounov exponents. Semiquantitative design optimization criteria are obtained and possible generalizations are discussed.
An efficient numerical method is proposed and implemented for the analysis of propagation characteristics of single-mode optical fibers with arbitrary refractive index profile. The method follows the ...concept of the so-called model-based parameter estimation, and the Pade algorithm is used to construct a low-order rational approximant of the spectral domain Green's function, obtained by solving a hierarchy of static problems. The sought eigenfrequency and field distribution are then estimated by computing, respectively, the dominant pole and the related residual of the rational approximant. A number of profiles are analyzed and experiments show that very accurate results can be cheaply obtained through this technique.
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