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Introduction

This study explores the impact of thermal noise on the sensitivity of interferometers, particularly at low frequencies around 100 Hz, and investigates the potential advantages of utilizing high-order Laguerre-Gauss (LG) modes over traditional flat beams. It discusses the production methods for flat beams and "Mexican hat" mirrors while evaluating their thermal noise characteristics. The results suggest that high-order LG modes can significantly reduce thermal noise compared to conventional configurations, allowing for the maintenance of sensitivity through standard spherical optics, albeit with stricter alignment requirements.

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Introduction

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  1. Thermal noise and high order Laguerre-Gauss modesJ-Y. Vinet, B. Mours, E. TournefierGWADW meeting, Isola d’ElbaMay 27th – Jun 2nd , 2006

  2. Introduction • Mirror thermal noise will limit the interferometers sensitivities around few 100 Hz • Thermal noise is smaller with more uniformly distributed power => Spherical-spherical cavities instead of flat-spherical cavities (Virgo case) => Flat beams • Flat beam issues: • Production of flat beams • Production of “Mexican hat” mirrors • More coating thermal noise? • What can be gained with high order Laguerre-Gauss modes? - Advantage: use classical mirrors

  3. Mirror thermal noise Loss angle Mirror bulk thermal noise estimated with the BHV model(Phys. Lett A 246 (1998) 227) Displacement noise PSD: U: Strain energy of the mirror under a pressure distribution having the profile of the readout beam Thermal noise smaller for flatter profiles LG(0,0)w0=5cm LG(0,3)w0=5cm LG(2,2)w0=5cm Flat w=11.3 cm LG(5,5)

  4. m=0, 1, 2, 3, 4, 5 a/w for 1 ppm losses Diffraction losses a/w = Mirror radius / beam waist Order n of LG(n,m) Diffraction losses • Potential problem with high order modes: diffraction losses • Ensure that diffraction losses stay below 1 ppm a/ spherical-spherical cavities with Virgo type mirrors (35 cm) b/ for each mode adjust the beam size so that diffraction losses = 1 ppm 1 ppm

  5. TEM00 w=6.7cm Flat beam w=11.3cm Thermal noise reduction Reduction of thermal noise with respect to present Virgo configuration Ratio of thermal noise for: LG(n,m) in spherical-spherical cavity / TEM00 w=2cm m=0, 1, 2, 3, 4, 5 Thermal noise reduction Order n of LG(n,m) => Thermal noise reduced by a factor 3 to 5 with respect to present Virgo configuration => Can reach results even better than flat beams !

  6. Advantages / Issues • Optics: • Mirrors uniformity on large diameter • Large but standard optics (spherical mirrors, mode cleaners,…) • Cavities compatible with TEM00 beam • Production of high order Laguerre-Gauss modes: • With a fiber laser: Bragg fibers can produce LG modes? • Diffractive optical elements (DOE) ? • Error signals: • Longitudinal locking: in principle no difference with TEM00 • Alignment: higher order modes more sensitive to misalignments

  7. Alignment/matching issues • Mis-alignments • Beam waist mis-matching Dominantly couples to non-degenerated modes => can be cleaned up by output mode cleaner Losses larger than for (0,0) mode => more stringent constraints on misalignments / matching Example LG(2,2) vs (0,0) mode: - alignment: should be 2-3 times more precise - waist: should be 4 times more precisely matched Coupling to cavity LG(0,0) w0=5cm LG(2,2) w0=5cm misalignment X (cm)

  8. Conclusions • High order LG modes seem to be a good alternative to flat beams • Thermal noise can be comparable to or even lower than flat beams • Standard spherical optics can be used • Losses: slightly larger constraints on alignment than with TEM00 • Not too risky: optics compatible with standard TEM00 beam

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