Vanishing tilt-to-length coupling for a singular case in two-beam laser interferometers with Gaussian beams

The omnipresent tilt-to-length coupling in two-beam laser interferometers, frequently a nuisance in precision measurements, vanishes for the singular case of two beams with identical parameters and complete detection of both beams without clipping. This effect has been observed numerically and is explained in this manuscript by the cancellation of two very different effects of equal magnitude and opposite sign. This paper was published in Applied Optics and is made available as an electronic reprint with the permission of OSA. The paper can be found at the following URL on the OSA website: [http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-54-5-1010]. Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law

Laser development and stabilization for the spaceborne interferometric gravitational wave detector LISA

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Sub-pm/Hz\mathrm{\mathbf{\sqrt{\rm Hz}}} non-reciprocal noise in the LISA backlink fiber

The future space-based gravitational wave detector Laser Interferometer Space Antenna (LISA) requires bidirectional exchange of light between its two optical benches on board of each of its three satellites. The current baseline foresees a polarization-maintaining single-mode fiber for this backlink connection. Phase changes which are common in both directions do not enter the science measurement, but differential ("non-reciprocal") phase fluctuations directly do and must thus be guaranteed to be small enough. We have built a setup consisting of a Zerodur$^{\rm TM}$ baseplate with fused silica components attached to it using hydroxide-catalysis bonding and demonstrated the reciprocity of a polarization-maintaining single-mode fiber at the 1 pm/$\sqrt{\textrm{Hz}}$ level as is required for LISA. We used balanced detection to reduce the influence of parasitic optical beams on the reciprocity measurement and a fiber length stabilization to avoid nonlinear effects in our phase measurement system (phase meter). For LISA, a different phase meter is planned to be used that does not show this nonlinearity. We corrected the influence of beam angle changes and temperature changes on the reciprocity measurement in post-processing

A brief comparison of optical pathlength difference and various definitions for the interferometric phase

To this paper we discuss that the phase readout in low noise laser interferometers can significantly deviate from the underlying optical pathlength difference (OPD). The cross coupling of beam tilt to the interferometric phase readout is compared to the OPD. For such a system it is shown that the amount of tilt to phase readout coupling depends strongly on the involved beams and their parameters, as well as on the detector properties and the precise definition of the phase. The unique single element photodiode phase is therefore compared to three common phase definitions for quadrant diodes. It is shown that neither phase definition globally shows the least amount of cross coupling of angular itDeutsches Zentrum für Luft- und Raumfahrt (DLR)/No 50 OQ 130

EOM sideband phase characteristics for the spaceborne gravitational wave detector LISA

The Laser Interferometer Space Antenna (LISA) is a joint ESA/NASA mission proposed to observe gravitational waves. One important noise source in the LISA phase measurement will be on-board reference oscillators. An inter-spacecraft clock tone transfer chain will be necessary to remove this non-negligible phase noise in post processing. One of the primary components of this chain are electro-optic modulators (EOMs). At modulation frequencies of 2 GHz, we characterise the excess phase noise of a fibre-coupled integrated EOM in the LISA measurement band (0.1 mHz to 1 Hz). The upper phase noise limit was found to be almost an order of magnitude better than required by the LISA mission. In addition, the EOM's phase dependence on temperature and optical power was determined. The measured coefficients are within a few milliradians per kelvin and per watt respectively and thereby negligible with the expected on-board temperature and laser power stability.DLR/50 OQ 0601DFG/EXC/QUES

Measurement of the non-reciprocal phase noise of a polarization maintaining single-mode optical fiber

Polarization maintaining single-mode optical fibers are key components in the interferometry of the Laser Interferometer Space Antenna (LISA). LISA's measurement principle relies on the availability of space qualified fibers of this type which influence the phase of light with a wavelength of 1064 nm passing in opposite directions through them with differences smaller than 6 prad/. We present a measurement scheme suitable to sense these non-reciprocal phase changes, as well as results obtained using this setup on samples of commercially available fibers. The experimental setup for the fiber characterization consists of a quasi-monolithic interferometer which constitutes a representative cut-out of the local interferometry on-board LISA concerning the fiber. Several noise sources are identified and improvements to the setup are presented to overcome them. The noise level achieved using this setup is between approximately 40 prad/ and 400 prad/ in the frequency range between 1 mHz and 1 Hz. It is also verified that this noise level is limited by the setup and not introduced by the fiber.DLR/50 OQ 060

Sub-system mechanical design for an eLISA optical bench

We present the design and development status of the opto-mechanical sub-systems that will be used in an experimental demonstration of imaging systems for eLISA. An optical bench test bed design incorporates a Zerodur® baseplate with lenses, photodetectors, and other opto-mechanics that must be both adjustable - with an accuracy of a few micrometers - and stable over a 0 to 40°C temperature range. The alignment of a multi-lens imaging system and the characterisation of the system in multiple degrees of freedom is particularly challenging. We describe the mechanical design of the precision mechanisms, including thermally stable flexure-based optical mounts and complex multi-lens, multi-axis adjuster mechanisms, and update on the integration of the mechanisms on the optical bench

Readout for intersatellite laser interferometry: Measuring low frequency phase fluctuations of HF signals with microradian precision

Precision phase readout of optical beat note signals is one of the core techniques required for intersatellite laser interferometry. Future space based gravitational wave detectors like eLISA require such a readout over a wide range of MHz frequencies, due to orbit induced Doppler shifts, with a precision in the order of $\mu \textrm{rad}/\sqrt{\textrm{Hz}}$ at frequencies between $0.1\,\textrm{mHz}$ and $1\,\textrm{Hz}$. In this paper, we present phase readout systems, so-called phasemeters, that are able to achieve such precisions and we discuss various means that have been employed to reduce noise in the analogue circuit domain and during digitisation. We also discuss the influence of some non-linear noise sources in the analogue domain of such phasemeters. And finally, we present the performance that was achieved during testing of the elegant breadboard model of the LISA phasemeter, that was developed in the scope of an ESA technology development activity.Comment: submitted to Review of Scientific Instruments on April 30th 201

Lasers for LISA: Overview and phase characteristics

We have investigated two alternative laser systems for the Laser Interferometer Space Antenna (LISA). One consisted of the laser of LISA's technology precursor LISA Pathfinder and a fiber amplifier originally designed for a laser communication terminal onboard TerraSar-X. The other consisted of a commercial fiber distributed feedback (DFB) laser seeding a fiber amplifier. We have shown that the TerraSar-X amplifier can emit more than 1W without the onset of stimulated Brillouin scattering as required by LISA. We have measured power noise and frequency noise of the LISA Pathfinder laser (LPL) and the fiber laser. The fiber laser shows comparable or even lower power noise than the LPL. LISA will use electro-optical modulators (EOMs) between seed laser and amplifier for clock noise comparison between spacecraft. This scheme requires that the excess noise added by the amplifiers be negligible. We have investigated the phase characteristics of two fiber amplifiers emitting 1 W and found them to be compatible with the LISA requirement on amplifier differential phase noise.DLR/50 OQ 0501DLR/50 OQ 060