Interferometry with high-order Laguerre-gaussian modes for the gravitational wave detections – LAGUERRE

The precision optical interferometry is in general performed with gaussian beams, such as the ones emitted by lasers. The use of higher-order Laguerre-Gaussian beams generates new technical difficulties, ranging from the efficient production of these modes starting from standard lasers, to the interferometry itself and to the specific use in giant Michelson interferometric detectors used for gravitational-wave detection. In the LAGUERRE project we have studied all these problems with a table-top prototype and with optical numerical simulations.

We have first produced a Laguerre-Gaussian (LG) mode with a good purity and efficiency, starting from a phase plate and a Fabry-Perot cavity, used as a spatial filter. Then, we have sent this mode in a table-top Michelson interferometer with Fabry-Perot cavities in the arms, a similar scheme to the one used in gravitational-wave detectors. During our experimental research we did not found any fundamental issue in using LG modes in gravitational-wave detectors, except the higher requirements in optical quality of the mirrors with respect to the ones necessary for Gaussian modes. This effect, found through numerical simulations by other research groups, is due to the degeneracy of LG modes with modes of the same order, an effect that is not present in fundamental gaussian modes. The requirements on mirror quality are today not achievable with the present mirror manufacturing technology and make the use of LG modes not yet possible. In our experiment we have measured the effect of degeneracy, which is in agreement with the simulations. Moreover, we have studied (in collaboration with another research group) a thermal compensation method to reduce the mirror defects. This technique has allowed to partially decrease the effects of degeneracy, and it deserves more study to understand its use in gravitational-wave detectors.

In conclusion, the use of LG modes is not yet possible, due to the degeneracy problem. The LG modes could be implemented in the medium-long term future, if the mirror surface quality will increase and/or if the thermal compensation techniques will be demonstrated.

A.Gatto et al. Fabry-Pérot-Michelson interferometer using higher-order Laguerre-Gauss modes, Phys. Rev. D 90, 122011)

The gravitational wave radiation is one of the most important consequences of the Einstein’s theory of General Relativity. The direct detection of gravitationnal waves (GW) will not only give a strong confirmation of the theory but it will open a new window to observe the universe, complementary to the electromagnetic one.

The first generation of gravitational wave detectors, such GEO, LIGO and Virgo are under operation and they have collected several years of data. Due to the small rate of the astrophysical events accessible with the current sensitivities, the detection is possible but not probable. A 2nd generation GW detectors (Advanced Virgo and Advanced LIGO), with an order of magnitude better sensitivity, is under preparation and it will probably be operated around 2015. Furthermore, the design study of a third generation detector, The Einstein Telescope, has been funded by the European Union and the project is part of the ASPERA roadmap.

The thermal noise is one of the main noise sources of the detector. It is due to the Brownian vibrations of the materials of the mirrors and of the suspension wires and its reduction is the subject of this research project. The main technique to reduce the thermal noise is the use of materials with very high quality factors. The use of a cryogenic detector has also been proposed, but this option is considered not enough mature for advanced Virgo and maybe considered for a third generation detectors. Another way to decrease the effect of thermal noise is to reduce the coupling between the mirror thermal noise itself and the beam sensing the position of the mirror. This is naturally done by an increase the beam size with respect to the mirror dimensions, thus averaging the thermal noise on a bigger surface. The limitation of this technique relies, of course, in the mirror dimensions.

The Gaussian beams, currently used in the interferometric detectors and in almost all the experiments which uses coherent source of electromagnetic radiation, concentrate almost all the power in a small region around the center (the beam radius), but with long tails which make necessary the use of mirrors much larger than the beam radius. To overcome to this problem the use of non gaussian beams has been proposed.

The Laguerre-Gauss (LG) modes are a solution of the propagation equation of the electromagnetic waves, in the paraxial approximation. High-order LG modes have a ring structure allowing a more uniform power distribution on the mirror’s surface and then a reduction of the thermal noise. Furthermore, having spherical wavefronts, these beams can be used with spherical mirrors. Furthermore, due to their wider power distribution, the LG modes will also allow to decrease the mirrors deformation due to the power transferred from the beam to the mirror materials. This thermal lensing effect is one of the main problems in the current gravitational wave interferometers.

In conclusion, the great interest of the LG modes are on their possibility to decrease the thermal noise and the thermal deformations of the mirrors with a minimum impact on the detector configuration, but only changing the shape of the beam before it enters in the interferometer. The goal of the LAGUERRE project is to demonstrate the feasibility of this technique. First, we plan to produce high-order Laguerre-Gaussian modes with high efficiency and purity. Then, we plan to build a table-top LG interferometer with a similar optical scheme of the GW detectors.