Fast Simulation of Gaussian-Mode Scattering for Precision Interferometry

Understanding how laser light scatters from realistic mirror surfaces is crucial for the design, com- missioning and operation of precision interferometers, such as the current and next generation of gravitational-wave detectors. Numerical simulations are indispensable tools for this task but their utility can in practice be limited by the computational cost of describing the scattering process. In this paper we present an efficient method to significantly reduce the computational cost of optical simulations that incorporate scattering. This is accomplished by constructing a near optimal representation of the complex, multi-parameter 2D overlap integrals that describe the scattering process (referred to as a reduced order quadrature). We demonstrate our technique by simulating a near-unstable Fabry-Perot cavity and its control signals using similar optics to those installed in one of the LIGO gravitational-wave detectors. We show that using reduced order quadrature reduces the computational time of the numerical simulation from days to minutes (a speed-up of $\approx 2750 \times$) whilst incurring negligible errors. This significantly increases the feasibility of modelling interferometers with realistic imperfections to overcome current limits in state-of-the-art optical systems. Whilst we focus on the Hermite-Gaussian basis for describing the scattering of the optical fields, our method is generic and could be applied with any suitable basis. An implementation of this reduced order quadrature method is provided in the open source interferometer simulation software Finesse.Comment: 15 pages, 11 figure

Experimental demonstration of higher-order Laguerre-Gauss mode interferometry

The compatibility of higher-order Laguerre-Gauss (LG) modes with interferometric technologies commonly used in gravitational wave detectors is investigated. In this paper we present the first experimental results concerning the performance of the LG33 mode in optical resonators. We show that the Pound-Drever-Hall error signal for a LG33 mode in a linear optical resonator is identical to that of the more commonly used LG00 mode, and demonstrate the feedback control of the resonator with a LG33 mode. We succeeded to increase the mode purity of a LG33 mode generated using a spatial-light modulator from 51% to 99% upon transmission through a linear optical resonator. We further report the experimental verification that a triangular optical resonator does not transmit helical LG modes

Quantum-Noise Power Spectrum of Fields with Discrete Classical Components

We present an algorithmic approach to calculate the quantum-noise spectral density of photocurrents generated by optical fields with arbitrary discrete classical spectrum in coherent or squeezed states. The measurement scheme may include an arbitrary number of demodulations of the photocurrent. Thereby, our method is applicable to the general heterodyne detection scheme which is implemented in many experiments. For some of these experiments, e.g. in laser-interferometric gravitational-wave detectors, a reliable prediction of the quantum noise of fields in coherent and squeezed states plays a decisive role in the design phase and detector characterization. Still, our investigation is limited in two ways. First, we only consider coherent and squeezed states of the field and second, we demand that the photocurrent depends linearly on the field's vacuum amplitudes which means that at least one of the classical components is comparatively strong.Comment: 8 pages, 2 figure

Experimental demonstration of a Displacement noise Free Interferometry scheme for gravitational wave detectors showing displacement noise reduction at low frequencies

This paper reports an experimental demonstration of partial displacement noise free laser interferometry in the gravitational wave detection band. The used detuned Fabry-Perot cavity allows the isolation of the mimicked gravitational wave signal from the displacement noise on the cavities input mirror. By properly combining the reflected and transmitted signals from the cavity a reduction of the displacement noise was achieved. Our results represent the first experimental demonstration of this recently proposed displacement noise free laser interferometry scheme. Overall we show that the rejection ratio of the displacement noise to the gravitational wave signal was improved in the frequency range of 10 Hz to 10 kHz with a typical factor of 60.Comment: 5 pages, 3 figure