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FINESSE Frequency Domain Interferometer Simulation

FINESSE Frequency Domain Interferometer Simulation. Andreas Freise European Gravitational Observatory 17 . March 2004. Possible Outputs of FINESSE. light power, field amplitudes eigenmodes, beam shape error/control signals (modulation-demodulation)

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FINESSE Frequency Domain Interferometer Simulation

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  1. FINESSEFrequency Domain Interferometer Simulation Andreas Freise European Gravitational Observatory 17. March 2004

  2. Possible Outputs of FINESSE light power, field amplitudes eigenmodes, beam shape error/control signals (modulation-demodulation) transfer functions, sensitivities, noise couplings alignment error signals, mode matching, etc.

  3. Coupling of light fields: Set of linear equations: Plane Waves – Frequency Domain solved numerically

  4. Frequency Domain Simple cavity: two mirrors + one space (4 nodes) Light source (laser) Output signal (detector)

  5. Frequency Domain one Fourier frequency one complex output signal

  6. Static response phase modulation = sidebands 3 fields, 3 beat signals

  7. Frequency Response infenitesimal phase modulation 9 frequencies, 13 beat signals

  8. start node • Trace beam and set beam parameters Gaussian Beam Parameters • Compute cavity eigenmodes

  9. Mode Mismatch and Misalignment Mode mismatch or misalignemt can be described as light scattering in higher-order spatial modes. Coupling coefficiants for the interferometer matrix are derived by projecting beam 1 on beam 2:

  10. FINESSE: Fast and (fairly) well tested Example: Optical layout of GEO 600 (80 nodes) • The Hermite-Gauss analysis has been validated by: • computing mode-cleaner autoalignment error signals (G. Heinzel) • comparing it to OptoCad (program for tracing Gaussian beams by • R. Schilling) • comparing it to FFT propagation simulations (R. Schilling)

  11. Power Recycling Signals

  12. FINESSE http://www.rzg.mpg.de/~adf/ Windows, Linux /virgo/VCS/1.0/VIRGOSW/Finesse/v0r93/... Linux, AIX

  13. Using Par-Axial Modes Hermite-Gauss modes allow to analyse the optical system with respect to alignment and beam shape. Both misalignment and mismatch of beam shapes (mode mismatch) can be described as scattering of light into higher- order spatial modes. This means that the spatial modes are coupled where an optical component is misaligned and where the beam sizes are not matched.

  14. Gaussian beam parameter q From Plane Waves to Par-Axial Modes The electric field is described as a sum of the frequency components and Hermite-Gauss modes: Example: lowest-order Hermite-Gauss:

  15. Gaussian Beam Parameters Transforming Gaussian beam parameters by optical elements with ABCD matrices: Example: normal incidence transmission through a curved surface:

  16. Frequency Noise Coupling Coupling of a frequency calibration peak into the dark fringe output: Difference between results for TEM00 only and those with higher-order TEM modes: factor  100 phase  90°

  17. 1.0 0.1 0.01 TMSR Mode Healing

  18. with signal recycling: Mode Healing Each recycling cavity minimises the loss due to mode mismatch of the respective other power recycling only:

  19. Typical Tasks ForFINESSE • Error signals, control signals • photo detectors, multiple • mixers • Transfer functions • amplitude-, phase- and • frequency modulations • Shot-noise-limited sensitivities

  20. FINESSE: Versatile simulation software for user-defined interferometer topologies. Fast, easy to use. Higher-order spatial modes: Commissioning of interferometers with high-finesse cavities requires to understand the influences of mode-matching and alignment on control signals and noise couplings.

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