arXiv subjects

Claude Amra

Publications and source records attributed to Claude Amra.

16 recordsLinked to original sources

arXiv2026

Designing a low-loss high reflectivity mirror for gravitational waves detectors by combining a dielectric metasurface and a multilayer stack

The design of low-mechanical-loss, high reflectivity mirrors is crucial in the development of the next generation of gravitational-wave observatories. Currently, the amorphous multilayer reflective coatings which are deposited at the surface of the test masses in interferometric gravitational-wave detectors present a major limiting factor in detector sensitivity due to their thermal noise. These coatings require a large number of thin layers to achieve ultra-high reflectivity. However, the thermal noise generated by this type of stack increases with the number of layers used. These dielectric mirrors represent a very mature technology, with current research producing only incremental improvements, highlighting the need for new technical solutions that can address this specific issue. Here, we provide insights into the expected performance of mirrors that combine a resonant metasurface with a multilayer stack. The suggested mirror design ensures the high reflectivity required for interferometric gravitational wave detectors, while using fewer layers of properly selected materials. As a result, it significantly reduces the total coating thickness, making it a promising option for reducing thermal noise as well.

physics.optics↗

arXiv2024

Comparison of arm cavity optical losses for the two wavelengths of the Einstein Telescope gravitational wave detector

A new generation of gravitational wave detectors is currently being designed with the likely use of a different laser wavelength compared to current instruments. The estimation of the optical losses for this new wavelength is particularly relevant to derive the detector sensitivity and also to anticipate the optical performances of future instruments. In this article, we measured the absorption and angle-resolved scattering of several mirror samples in order to compare optical losses at a wavelength of 1064 and 1550\ nm. In addition, we have carried out simulations of the Einstein Telescope arm cavities at 1064 and 1550\ nm taking into account losses due to surface low-spatial frequency flatness. Our results suggest that optical losses as measured at 1064\ nm are about twice as large as those at 1550\ nm as predicted with a simple model.

physics.optics↗

arXiv2024

Stable Phase Retrieval with Mirror Descent

In this paper, we aim to reconstruct an n-dimensional real vector from m phaseless measurements corrupted by an additive noise. We extend the noiseless framework developed in [15], based on mirror descent (or Bregman gradient descent), to deal with noisy measurements and prove that the procedure is stable to (small enough) additive noise. In the deterministic case, we show that mirror descent converges to a critical point of the phase retrieval problem, and if the algorithm is well initialized and the noise is small enough, the critical point is near the true vector up to a global sign change. When the measurements are i.i.d Gaussian and the signal-to-noise ratio is large enough, we provide global convergence guarantees that ensure that with high probability, mirror descent converges to a global minimizer near the true vector (up to a global sign change), as soon as the number of measurements m is large enough. The sample complexity bound can be improved if a spectral method is used to provide a good initial guess. We complement our theoretical study with several numerical results showing that mirror descent is both a computationally and statistically efficient scheme to solve the phase retrieval problem.

math.OC↗

arXiv2023

Low-coherence interferometric measurement of the spectral dependence of the light field backscattered by optical interfaces

In this paper, we show how the combined use of low coherence interferometry, balanced detection and data processing comparable to that used in Fourier transform spectrometry allows us to characterize with ultimate resolutions (sub-ppm in level, 0.2 nm in wavelength and 5 mdeg in angle) the retro-reflection and retro-scattering response of both sides of a 2 mm thick silica wafer.

physics.optics↗

arXiv2022

Low coherence interferometric detection of the spectral dependence of the retro-reflection coefficient of an anti-reflective coated interface

The measurement of very low reflection coefficients of anti-reflective coated interfaces has become a key issue for the realization of precision instruments such as the giant interferometers used for the detection of gravitational waves. We propose in this paper a method, based on low coherence interferometry and balanced detection, which not only allows to obtain the spectral dependence of this reflection coefficient in amplitude and phase, with a sensitivity of the order of 0.1 ppm and a spectral resolution of 0.2 nm, but also to eliminate any spurious influence related to the possible presence of uncoated interfaces. This method also implements a data processing similar to that used in Fourier transform spectrometry. After establishing the formulas that control the accuracy and the signal-to-noise ratio of this method, we present the results that provide a complete demonstration of its successful operation in various experimental conditions.

physics.optics↗

arXiv2022

Provable Phase Retrieval with Mirror Descent

In this paper, we consider the problem of phase retrieval, which consists of recovering an $n$-dimensional real vector from the magnitude of its $m$ linear measurements. We propose a mirror descent (or Bregman gradient descent) algorithm based on a wisely chosen Bregman divergence, hence allowing to remove the classical global Lipschitz continuity requirement on the gradient of the non-convex phase retrieval objective to be minimized. We apply the mirror descent for two random measurements: the \iid standard Gaussian and those obtained by multiple structured illuminations through Coded Diffraction Patterns (CDP). For the Gaussian case, we show that when the number of measurements $m$ is large enough, then with high probability, for almost all initializers, the algorithm recovers the original vector up to a global sign change. For both measurements, the mirror descent exhibits a local linear convergence behaviour with a dimension-independent convergence rate. Our theoretical results are finally illustrated with various numerical experiments, including an application to the reconstruction of images in precision optics.

math.OC↗

arXiv2017

Anomalous refraction phenomena in a transparent slab

An exact formulation of the propagation of a monochromatic wave packet impinging upon a transparent, homogeneous, isotropic and parallel slab at oblique incidence is presented. Approximate formulas are derived for low divergence Gaussian light beams. These formulas show the presence of anomalous refraction phenomena at any slab thickness, including negative refraction and flat lensing effects, induced by the reflection on the rear face.

physics.optics↗

arXiv2015

Thermal concentrator homogenized with solar-shaped mantle

We propose solar-shaped thermal concentrators designed with orthoradial layers and obtained in practice through the homogenization of an ideal thermal concentrator. Considering the spectral regime of the heat equation, we quantitatively evaluate at different pulsations the effectiveness of the homogenized concentrators by comparing the thermal flux existing in an ideal concentrator and the thermal flux in an homogenized concentrator. Dependence on the pulsation is shown to be negligible and plotting the effectiveness of the homogenized concentrators as a function of the number of orthoradial layers $N$, we determine the number of layers needed to achieve a certain effectiveness. Significantly high numbers $N$(ranging from a hundred to tens of thousands layers) are found highlighting the fact that achieving high effectiveness demands a high level of engineering of the homogenized concentrator.

physics.comp-ph↗

arXiv2015

Optical scatter of quantum noise filter cavity optics

Optical cavities to filter squeezed light for quantum noise reduction require optics with very low scattering losses. We report on measured light scattering from two super-polished fused silica optics before and after applying highly-reflective ion-beam sputtered dielectric coatings. We used an imaging scatterometer that illuminates the sample with a linearly polarized 1064 nm wavelength laser at a fixed angle of incidence and records images of back scatter for azimuthal angles in the plane of the laser beam. We extract from these images the bidirectional reflectance distribution function (BRDF) of the optics with and without coating and estimate their integrated scatter. We find that application of these coatings led to a more than 50% increase of the integrated wide-angle scatter, to 5.00+/-0.30 and 3.38+/-0.20 ppm for the two coated samples. In addition, the BRDF function of the coated optics takes on a pattern of maxima versus azimuthal angle. We compare with a scattering model to show that this is qualitatively consistent with roughness scattering from the coating layer interfaces. These results are part of a broader study to understand and minimize optical loss in quantum noise filter cavities for interferometric gravitational-wave detectors. The scattering measured for these samples is acceptable for the 16 m long filter cavities envisioned for the Laser Interferometer Gravitational-wave Observatory (LIGO), though reducing the loss further would improve LIGO's quantum-noise limited performance.

physics.optics↗

arXiv2015

Analogies between optical propagation and heat diffusion: Applications to micro-cavities, gratings and cloaks

A new analogy between optical propagation and heat diffusion in heterogeneous anisotropic media has been proposed recently [S. Guenneau, C. Amra, and D. Veynante, Optics Express Vol. 20, 8207-8218 (2012)]. A detailed derivation of this unconventional correspondence is presented and developed. In time harmonic regime, all thermal parameters are related to optical ones in artificial metallic media, thus making possible to use numerical codes developed for optics. Then the optical admittance formalism is extended to heat conduction in multilayered structures. The concepts of planar micro-cavities, diffraction gratings, and planar transformation optics for heat conduction are addressed. Results and limitations of the analogy are emphasized.

physics.optics↗

arXiv2014

Spectral efficiency of engineered thermal cloaks in the frequency regime

We analyse basic thermal cloaks designed via different geometric transforms applied to thermal cloaking. We evaluate quantitatively the efficiency of these heterogeneous anisotropic thermal cloaks through the calculation of the standard deviation of the isotherms. The study addresses the frequency regime and we point out the cloak's spectral efficiencies. We find that all these cloaks have comparable efficiency irrespective of whether or not they have singular conductivity at their inner boundary. However, approximate cloaking with multi-layered cloak critically depends upon the homogenization algorithm and a large number of thin layers (at least fifty) is required to reduce substantially the standard deviation of the isotherms.

cond-mat.mtrl-sci↗

arXiv2014

Absorbing Backside Anti-reflecting Layers for high contrast imaging in fluid cells

The single Anti-Reflecting (AR) layer is a classical problem in optics. When all materials are pure dielectrics, the solution is the so-called lambda/4 layer. Here we examine the case of absorbing layers between non absorbing media. We find a solution for any layer absorption coefficient provided that the light goes from the higher towards the lower index medium, which characterizes backside layers. We describe these AR absorbing (ARA) layers through generalized index and thickness conditions. They are most often ultrathin, and have important applications for high contrast imaging in fluid cells.

physics.optics↗

arXiv2014

Phase retrieval of reflection and transmission coefficients from Kramers-Kronig relations

Analytic and passivity properties of reflection and transmission coefficients of thin-film multilayered stacks are investigated. Using a rigorous formalism based on the inverse Helmholtz operator, properties associated to causality principle and passivity are established when both temporal frequency and spatial wavevector are continued in the complex plane. This result extends the range of situations where the Kramers-Kronig relations can be used to deduce the phase from the intensity. In particular, it is rigorously shown that Kramers-Kronig relations for reflection and transmission coefficients remain valid at a fixed angle of incidence. Possibilities to exploit the new relationships are discussed.

physics.optics↗

arXiv2013

Optical properties of multilayer optics including negative index materials

Negative indices are revisited through the thin-film admittance formalism. Effective indices and phase delay associated with wave propagation through negative index layers are carefully defined and computational rules easily implementable in standard thin-film software are derived from this approach. This admittance formalism is then used to recover the main features of the perfect lens and to highlight the benefit of such negative index materials to improve the performances of quarter-wavelength Bragg mirrors and Fabry-Perot band-pass filters.

physics.optics↗

arXiv2013

Negative Index Materials: The Key to "White" Multilayer Fabry-Perot

The use of negative index materials is highly efficient for tayloring the spectral dispersion properties of a quarter-wavelength Bragg mirror and for obtaining a resonant behavior of a multilayer Fabry-Perot cavity over a very large spectral range. An optimization method is proposed and validated on some first promising devices.

physics.optics↗

arXiv2011

Light repolarization by scattering media

The polarization of a coherent depolarized incident light beam passing through a disordered medium is investigated. The local polarization of the scattered far field and the probability density function are calculated and show an excellent agreement with experiment. It is demonstrated that complex media may confer high degree of polarization (0.75 DOP average) to the incident unpolarized light.

physics.optics↗