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The most precise measurement tools of humankind are equipped with ultra-stable lasers. State-of-the-art laser stabilization techniques are based on external cavities, that are limited by noise originated in the coatings of the cavity mirrors. Microstructured mirror coatings (so-called meta-mirrors) are a promising technology to overcome the limitations of coating noise and therewith pave the way towards next-generation ultra-stable lasers. We present the first experimental realization of a 10,000-finesse optical cavity based on a low-noise meta-mirror, representing a milestone in this field. The symbiosis of the presented mirror technology with silicon cavity spacers will result in a 5×10−18 laser stability, which is an order of magnitude improvement.

Ultra-stable laser cavities are the core components of today’s most precise measurement instruments. To design and realize an ultra-stable laser cavity, one must suppress all kinds of noise below the desired frequency stability. The thermal noise of the cavity spacer sets a fundamental limit for the possible stability, especially for cavities operating at room temperature. We present a comprehensive numerical study of thermal cavity spacer noise, accounting for all relevant geometrical parameters. Accelerated by a vast amount of simulation data, a neural network is trained to predict spacer noise precisely for a wide range of all relevant cavity parameters. Based on this neural network, we identified design rules to reduce spacer noise by more than 50% by only changing the cavity geometry. Optimizing the cavity geometry and the material combination can achieve a noise reduction of more than two orders of magnitude without the infrastructural effort of a cryogenic environment.

Thermal noise of optical components is one of the sensitivity limiting effects in gravitational wave detectors, laser stabilization cavities and many other experiments in basic research. However, current methods for the computation of thermal noise are limited for an application in either infinitely large or symmetrically illuminated masses. I present a general method of computing thermal noise of arbitrary finite-sized masses in optical interferometers. The presented approach generalizes state-of-the-art methods for an application in arbitrary shaped optical elements illuminated by arbitrary spatial light distributions. Furthermore, I show the application of the presented approach to compute thermal noise of maladjusted mirrors in Fabry-Perot interferometers. It is shown that the noise can be reduced by off-axis illumination in the case of thin mirrors.

With a relative length measurement precision of better than 10−23, gravitational wave interferometers are the most precise instruments that have ever been built. With this enormous sensitivity many noise sources potentially effect gravitational wave detector sensitivity, each of which must be investigated to ensure confidence in design sensitivity. We present calculations of photoelastic noise as well as thermo refractive noise in the beam splitter and the input test masses in Einstein telescope (ET). It turns out that the amplitude of the photoelastic noise in the ET low-frequency detector is about five orders of magnitude below the maximum design sensitivity and five orders of magnitude below that of the ET high-frequency detector, whereas thermo refractive noise impairs the design sensitivity by approximately 20%.

We theoretically investigate the influence of gravity on laser light in a hemispherical optical cavity, operating on Earth. The propagation of light in such a cavity is modeled by a Gaussian beam, affected by the Earth's gravitational field. On laboratory scale, this field is described by the spacetime of homogeneous gravity, known as Rindler spacetime. In that spacetime, the beam is bent downwards and acquires a height dependent phase shift. As a consequence the phase fronts of the laser light differ from those of a usual Gaussian beam. Assuming that the initial beam enters the cavity along its symmetry axis, these gravitational effects cause variations of the beam phase with every cavity round trip. Detailed calculations are performed to investigate how these phase variations depend on the beam parameters and the cavity setup. Moreover, we discuss the implications of our findings for cavity calibration techniques and cavity-based laser stabilization procedures., 10 pages, 6 figures

The advent of optical metasurfaces, i.e. carefully designed two-dimensional nanostructures, allows unique control of electromagnetic waves. To unlock the full potential of optical metasurfaces to match even complex optical functionalities, machine learning provides elegant solutions. However, these methods struggle to meet the tight requirements when it comes to metasurface devices for the optical performance, as it is the case, for instance, in applications for high-precision optical metrology. Here, we utilize a tandem neural network framework to render a focusing metamirror with high mean and maximum reflectivity of Rmean = 99.993 % and Rmax = 99.9998 %, respectively, and a minimal phase mismatch of Δϕ = 0.016 % that is comparable to state-of-art dielectric mirrors.

As known from Einstein's theory of general relativity, the propagation of light in the presence of a massive object is affected by gravity. In this work, we discuss whether the effect of gravitational light bending can be observed in Earth-based experiments, using high-finesse optical cavities. In order to do this, we theoretically investigate the dynamics of electromagnetic waves in the spacetime of a homogeneous gravitational field and give an analytical expression for the resulting modifications to Gaussian beam propagation. This theoretical framework is used to calculate the intensity profile at the output of a Fabry-P\'erot cavity and to estimate the imprints of Earth's gravity on the cavity output signal. In particular, we found that gravity causes an asymmetry of the output intensity profile. Based on that, we discuss a measurement scheme, that could be realized in facilities like the GEO600 gravitational wave detector and the AEI 10 m detector prototype., Comment: 7 pages, 5 figures, 1 table

Several sources of noise limit the sensitivity of current gravitational wave detectors. Currently, dominant noise sources include quantum noise and thermal Brownian noise, but future detectors will also be limited by other thermal noise channels. In this paper, we study a thermal noise source which is caused by spatial charge carrier density variations in semiconductor materials. We provide an analytical model for the understanding of charge carrier fluctuations under the presence of screening effects and show that charge carrier noise will not be a limiting noise source for third-generation gravitational wave detectors.

We designed, realized, and characterised an imaging Mueller matrix ellipsometry setup for the pixelwise measurement of the Mueller matrices in microscope images. Our setup is capable of performing measurements in reflection as well as in transmission in a broad range of angles of incidence for wavelengths between 400 nm and 700 nm. We compared measurements of specially designed nanostructured samples with AFM and SEM measurements as well as with numerical simulations using the finite element method.

Grating reflectors are a potential low-noise replacement for amorphous multilayer mirrors. We investigate the influence of polarization and refractive index on Brownian thermal noise of binary grating reflectors using Maxwell's stress tensor. Our results demonstrate that the refractive index of the grating material is a critical parameter for thermal noise in these structures. In contrast to multilayer mirrors, a low coating thickness does not necessarily lead to a low thermal noise amplitude for structures with low refractive index. We find that an improved noise performance of grating reflectors requires materials of refractive index ≳2.5. We present a factorized expression for the thermal noise of grating reflectors made of arbitrary materials by simply scaling the noise amplitude with the related material parameters.

We report on key signal contributions in photothermal deflection spectroscopy (PDS) of semiconductors at photon energies below the bandgap energy and show how to extract the actual absorption properties from the measurement data. To this end, we establish a rigorous computation scheme for the deflection signal including semi-analytic raytracing to analyze the underlying physical effects. The computation takes into account linear and nonlinear absorption processes affecting the refractive index and thus leading to a deflection of the probe beam. We find that beside the linear mirage effect, nonlinear absorption mechanisms make a substantial contribution to the signal for strongly focussed pump beams and sample materials with high two-photon absorption coefficients. For example, the measured quadratic absorption contribution exceeds 5% at a pump beam intensity of about ${1.3}\times{10^{5}}\;{W}/{cm^{2}}$ in Si and at ${5}\times{10^{4}}\;{W}/{cm^{2}}$ in GaAs. In addition, our method also includes thermal expansion effects as well as spatial gradients of the attenuation properties. We demonstrate that these effects result in an additional deflection contribution which substantially depends on the distance of the photodetector from the readout point. This distance dependent contribution enhances the surface related PDS signal up to two orders of magnitude and may be misinterpreted as surface absorption if not corrected in the analysis of the measurement data. We verify these findings by PDS measurements on crystalline silicon at a wavelength of 1550 nm and provide guidelines how to extract the actual attenuation coefficient from the PDS signal., Comment: 10 pages, 16 figures, submitted to Journal of Applied Physivs

Accurate metrology of nanostructures gains more and more importance and for efficiency reasons optical methods play a significant role here. Unfortunately, conventional optical microscopy is subject to the well-known resolution limit. The necessity to resolve objects smaller than this limit led to the development of superresolution methods which however are barely used in metrology for practical reasons. Non-imaging indirect optical methods like scatterometry and ellipsometry however are not limited by diffraction and are able to determine the critical dimensions of nanostructures. We investigate the application of different approaches for specifically manipulated near-fields in Mueller matrix ellipsometry to achieve an enhanced sensitivity for polarization based sub-wavelength topological information. To this end, we present first numerical simulations of these approaches. To examine the relationship between structural properties and Mueller matrix elements we designed individual structures based on geometrical shapes of varying parameters as well as small arrays. They are realized by lithography as holes in PMMA resist. First, we characterize SEM images of the structures to validate the fabrication process. Numerical simulations of the Mueller matrices of the structures by finite element method are discussed. Results indicate that conventional Mueller matrix ellipsometry alone is unsuitable but the extension to imaging Mueller matrix microscopy is promising for the characterization of sub-wavelength features.

Collinear photothermal deflection spectroscopy (PDS) is a widely used method for the spatially resolved determination of the optical attenuation coefficient. In this work we rigorously model the signal contributions in PDS on semiconductors below the band gap energy. The dependencies of the PDS signal on selected experimental parameters (pump beam intensity, crossing angle, chopper frequency and distance from the pump beam focus) are computed and compared with previous calculation results that are based on simplified assumptions. We find that for high pump beam intensities and sample materials with high two photon absorption coefficients beside the mirage effect nonlinear absorption mechanisms have a strong impact on the signal. Furthermore, we show that angular deflection effects can significantly enhance the PDS signal. For example, the conical refractive index field due to the pump beam divergence leads to an angular deflection at readout points outside the pump beam focus. Considering these additional signal contributions is crucial to determine proper absorption properties.

Brownian thermal noise is a severe limitation for the sensitivity of many optomechanical high-precision measurement systems. To push the sensitivity limit it is essential to quantify how device geometry and material properties affect thermal noise. As an important building block for optomechanical experiments, we present the analytical calculation of Brownian thermal noise of circular clamped reflective membranes in Fabry Perot cavities. To compute the thermal noise, we investigate the influence of the effective membrane position x (compare Fig. 1(a)) to the eigenfrequency of the cavity.

Spatial light modulators (SLMs) manipulate the polarization, amplitude and phase of incident light beams and are used in diverse applications as beam shaping and steering, digital holography and information processing [1]. Currently, most SLMs are based either on liquid crystal or on MEMS systems such as movable mirror arrays. The first ones have high resolution density and pixel size but low time response in the sub-ms range [2]. While the second ones have faster time responses in the order of hundredths of μs [3] and can be even faster by replacing conventional mirrors with high-contrast gratings (HCG) mirrors [4]. In the last years, other approaches based on metasurfaces and HCGs have been proposed as phase modulators by modulating the refractive index by exploiting the electro-optic or thermo-optic effects or by free-carrier injection [5, 6]. We propose a phase modulator also based on HCGs but exploiting the tunable optomechanical response capable of 2π shift variations and time responses in the order of hundreds of nanoseconds, limited by the mechanical resonance frequency.

We present a concept of a mirror for the application in high-reflectivity low-noise instruments such as interferometers. The concept is based on an etalon with a metasurface (meta-etalon) on the front and a conventional multilayer stack on the rear surface. The etalon in combination with the metasurface enables a dedicated spatial weighing of the relevant thermal noise processes and by this a substantial reduction of the overall read out thermal noise. We exemplary illustrate the benefit of the proposed etalon for thermal noise in two applications: The test masses of the Einstein Telescope gravitational wave detector and a single-crystalline cavity for laser frequency stabilization. In the Einstein Telescope the thermal noise of the etalon even at room temperature outperforms existing concepts for operation temperatures at 10K. For the laser stabilization cavity, a reduction of the modified Allan deviation of an order of magnitude is predicted., Comment: 11 pages, 8 figures, 6 tables

We present the calculation of thermal noise in interferometric gravitational-wave detectors due to the thermal fluctuations of the beam splitter (BS). This work makes use of a recently developed method of the analysis of thermal noise in mirrors from first principles, based on the fluctuation dissipation theorem. The evaluation of BS thermal noise is carried out for the two different grav- itational wave observatories, GEO600 and the Advanced Laser Interferometer Gravitational Wave Observatory (aLIGO). The analysis evaluates thermal noise from both the substrate and the optical reflective and antireflective stacks located on the BS surface. We demonstrate that the fluctuations of both reflecting and anti-reflecting surfaces significantly contribute to the total thermal noise of the BS. The oscillating intensity pattern couples small-scale distortions of the surface to the overall phase readout, and therefore increases the overall thermal noise. In the case of aLIGO, the BS contribution is with $0.3\%$ negligibly small. At a frequency of 500Hz, the BS causes about $10\%$ of GEO600's sensitivity limit. BS noise impairs the feasible sensitivity of the GEO-HF design proposal by about $50\%$.

We investigate a reconfigurable dielectric metasurface merging optomechanical interaction and quasi-bound states in the continuum promising for all-optical light control light. The surface consists of a dimerized high-contrast grating with a compliant bilayer structure. The optical forces induced by a control light field lead to structural deformations changing the optical response. We discuss requirements for the geometry and optical force distribution to enable an efficient optomechanical coupling, which can be exploited to tune reflectivity, phase and polarization of a beam impinging on the metasurface. Numerical results explore some tunable devices as mirrors, saturable output couplers, phase modulators and retarder plates.

We present a method to calculate the power spectral density of Brownian noise in complex optomechanical systems using Levin’s approach of virtual pressure and present first mechanical loss measurements for high-purity GaAs over a wide temperature range from 7K to 250 K. The loss reveals three Debye loss peaks. Each peak corresponds to an Arrhenius-like relaxation process with activation energies of 17.9 meV, 65.4 meV and 123 meV respectively. Additional light induced damping was observed for photon energies below and above the fundamental gap of GaAs in contrast to observations by Okamoto et al.

The optical performance of wire grid polarizers crucially depends on the fabrication accuracy. Reducing the application wavelengths to the ultraviolet spectral range sets the challenge that structural deviations in the range of typically a few nanometers become comparable to the feature sizes of the structure. In this contribution we present a concept to determine structural parameters and structural deviations of DUV wire grid polarizers fabricated with self-aligned double patterning. To this end, we evaluate the properties (i.e the spectral positions, the angular dependence of the spectral positions and widths) of asymmetry induced resonances in the transmittance spectra which occur at wavelengths larger than 380 nm. We derive requirements for measurement setup for nanoscale determination of the structural properties. Our results indicate that the investigation of the angular dependent transmittance at only two different wavelengths and one polarization state is sufficient to determine structural deviations with uncertainties of ±1:7nm for the effective shift of the ridge and ±0:34° for the effective tilt. Thus, the proposed method allows us to retrieve deep subwavelength structural information at the nanoscale with easily accessible transmittance measurements in the visible spectral range.

We propose a bilayer Gamma-shape grating structure as a novel nano-optomechanical system promising for all-optical modulation in a frequency range of a few MHz up to a few 100 MHz.

International audience; Mechanical spectroscopy gives information on the structure of solids and their relaxation mechanisms through the measurements of the elastic constants and the mechanical loss angle of materials. One common way to estimate these quantities is the resonant method where the frequency and the characteristic decay time of oscillations are measured. Since many solid materials can be easily found in the shape of thin disc we have investigated the mechanical loss of these resonators and we have found experimentally that the loss angle dependence on the mode is not trivial but rather follow a distribution of modes into families. We give a model that is able to justify the existence of these families and to predict the level of losses in silicon, silica and brass discs. The model considers the thermoelastic effect and the excess damping caused by the condition of the disc edge. The results of this research are relevant to the research on thin films that are deposited on thin discs like the optical coatings used on the mirrors for the gravitational wave detectors.

Controlling the polarization of light is crucial in numerous applications such as spectroscopy, ellipsometry, photo lithography or industrial vision. Polarization control can be realized by wire grid polarizers (WGPs), which are large aspect ratio, zero order gratings. These elements provide an anisotropic transmittance depending on the polarization direction of the incident light. WGPs’ high attractiveness originates from their large free aperture, while simultaneously being extremely thin. Furthermore, these elements can be easily integrated into other nano-optical devices. Recently, such elements were successfully developed for applications down to the deep ultra violet spectral range. However, at shorter wavelengths the influence of roughness of the structures poses a severe limitation on the feasible optical performance. To tackle this problem, we numerically simulated the impact of line edge roughness on the polarization properties of WPGs. Therefore, we generated edge position data of rough grating lines by means of the Thorsos method and calculated the resulting optical response by finite difference time domain method. With this procedure the influence of standard deviation, correlation length, Hurst exponents and wavelength was investigated. We find that for standard deviations of 2.5 nm and 5.0 nm the polarization contrast is reduced by a factor of 3 and 7, respectively. The polarization contrast shows a minimum for intermediate correlation lengths, while virtually no impact of the Hurst exponent is observed. This is explained by several mechanisms occurring for different ratios between the spatial frequency of the roughness and the frequency of incident light. Our theoretical findings correlate well with experimental results we retrieved with measured roughness parameters of fabricated elements.

We present a formalism to compute Brownian thermal noise in functional optical surfaces such as grating reflectors, photonic crystal slabs or complex metamaterials. Such computations are based on a specific readout variable, typically a surface integral of a dielectric interface displacement weighed by a form factor. This paper shows how to relate this form factor to Maxwell's stress tensor computed on all interfaces of the moving surface. As an example, we examine Brownian thermal noise in monolithic T-shape grating reflectors. The previous computations by Heinert et al. [Heinert et al., PRD 88 (2013)] utilizing a simplified readout form factor produced estimates of thermal noise that are tens of percent higher than those of the exact analysis in the present paper. The relation between the form factor and Maxwell's stress tensor implies a close correlation between the optical properties of functional optical surfaces and thermal noise., Comment: 6 Figures, 7 pages

High-performance nano-optical elements for application wavelengths in the ultraviolet spectral range often require feature sizes of only a few tens of nanometers where line edge roughness (LER) becomes a critical parameter for the optical performance. In this contribution, we explore the influence of LER on the optical performance of wire grid polarizers (WGP) in the far ultraviolet range. Therefore, we present a method, which uses the finite difference time domain method in combination with a comprehensive spatial frequency dependent LER model. The measured LER of 3.6 nm (standard deviation) reduces the WGP's extinction ratio by a factor of 3.6 at a wavelength of 248 nm. We identify a critical range of the correlation length, which maximizes the detrimental effect of LER. The presented method and the results provide the basis for future fabrication technology optimization of WGPs and other optical meta-surfaces in the ultraviolet spectral region or at even shorter wavelengths.

The visibility distance of interferometric gravitational wave detectors is limited by mirror thermal noise at mid-range frequency, where the first coalescence GW signals have been detected and where many others are expected in the next future. In particular, for enhanced second generation and third generation we need to increase the performance of the test mass multilayer reflective coatings. The Virgo collaboration is setting up a coating R&D group on many issues, including especially metrology (loss angle measurements, thermoelastic effect modeling), new materials (new oxides, nitrates, fluoride, new cosputtered mixing and nanolayered composites) completely characterized (optically, mechanically and morphologically), optimization of deposition parameters, with the aim of developing new coating materials and technologies for the AdVirgo upgrades and for future detectors. Another objective is to understand the losses in amorphous materials, framing coating research in the more general context of the physics of glasses and amorphous materials. One of the developed research lines is the study of thermoelastic damping in crystalline materials, that are promising candidates for cryogenic test masses and particularly suitable substrates for coating research. A detailed discussion on models, based on a semi-analytical calculation starting from the heat diffusion equation, for crystalline substrates will be reported. A new study on the changes in thermoelastic loss after coating deposition, with some preliminary results, will be also reported.