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Advantages of High Order Laguerre-Gauss Modes in Thermal Noise Reduction

Explore the benefits of utilizing high order Laguerre-Gauss modes to reduce thermal noise in interferometers. Detailed discussion on mirror thermal noise limitations, diffraction losses, and production methods. Discover how these modes offer comparable or lower thermal noise compared to flat beams, with standard spherical optics. Learn about alignment and matching challenges and how output mode cleaners can help mitigate losses. Find out why high order modes are a promising alternative to flat beams for enhancing interferometer sensitivity.

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Advantages of High Order Laguerre-Gauss Modes in Thermal Noise Reduction

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

  5. TEM00 w0=6.7cm Flat beam w=11.3cm Thermal noise reduction Reduction of thermal noise with respect to present Virgo configuration Ratio of thermal noise: 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 configurations => Can reach results even better than flat beams with w=11.3 cm !

  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 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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