We have investigated the generation of highly pure higher-order Laguerre-Gauss (LG) beams at high laser power of order 100 W, the same regime that will be used by second-generation gravitational wave ...interferometers such as Advanced LIGO. We report on the generation of a helical-type LG33 mode with a purity of order 97% at a power of 83 W, the highest power ever reported in literature for a higher-order LG mode. This is a fundamental step in proving technical readiness for use of LG beams in gravitational wave interferometers of future generations.
Brownian noise of dielectric mirror coatings is expected to be one of the limiting noise sources, at the peak sensitivity, of next generation ground based interferometric gravitational wave (GW) ...detectors. The use of higher-order Laguerre-Gauss (LG) beams has been suggested to reduce the effect of coating thermal noise in future generations of gravitational wave detectors. In this paper we describe the first test of interferometry with higher-order LG beams in an environment similar to a full-scale gravitational wave detector. We compare the interferometric performance of higher-order LG modes and the fundamental mode beams, injected into a 10 m long suspended cavity that features a finesse of 612, a value chosen to be typical of future gravitational wave detectors. We found that the expected mode degeneracy of the injected LG3, 3 beam was resolved into a multiple peak structure, and that the cavity length control signal featured several nearby zero crossings. The break up of the mode degeneracy is due to an astigmatism (defined as |Rcy − Rcx|) of 5.25 ± 0.5 cm on one of our cavity mirrors with a radius of curvature (Rc) of 15 m. This observation agrees well with numerical simulations developed with the FINESSE software. We also report on how these higher-order mode beams respond to the misalignment and mode mismatch present in our 10 m cavity. In general we found the LG3, 3 beam to be considerably more susceptible to astigmatism and mode mismatch than a conventional fundamental mode beam. Therefore the potential application of higher-order Laguerre-Gauss beams in future gravitational wave detectors will impose much more stringent requirements on both mode matching and mirror astigmatism.
Higher order Laguerre-Gauss (LG) beams have been proposed for use in future generation gravitational wave detectors for their potential to reduce the effects of the thermal noise of the test masses. ...However, it has been reported that due to the degeneracy of higher order modes using these beams will be extremely challenging. Our aim was to quantify these degeneracy effects. We present a new analytical approximation to compute the coupling between different LG modes, verified with simulation results of realistic arm cavities. This method is applied to Advanced LIGO mirror maps and used to derive requirements for mirrors for the use of the LG33 beam.
Diffraction gratings have been proposed as replacements for transmissive optical elements in the next generation of gravitational wave detectors. However, they couple additional alignment noise to ...phase noise, and current models are based on unrealistic plane-wave expansion theories. There is a need for a description of grating-related phase noise which is compatible with standard interferometer tools. In this paper we investigate the grating-related phase shift by presenting a fully analytical Gaussian model for the phase accumulation of a displaced beam when diffracted from a grating. We consider a first-order modal decomposition as the method employed by simulation tools for off-axis beams. We show that the phase distribution of a typical displaced beam and a decomposed beam is accurate to within 3.9 × 10−8 radians. However, we find that the grating-related phase noise is not present, and this is further validated experimentally by the absence of a phase shift in beams with different modes. The phase noise must therefore be implemented manually into existing interferometer simulation tools.
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