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FINESSE Frequency Domain Interferometer Simulation

FINESSE Frequency Domain Interferometer Simulation. Versatile simulation software for user-defined i nterferom e ter topologies. Fast, easy to use. Andreas Freise xx . October 2005. Possible Outputs of FINESSE. light power, field amplitudes eigenmodes, beam shape

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FINESSE Frequency Domain Interferometer Simulation

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  1. FINESSEFrequency Domain Interferometer Simulation Versatile simulation software for user-defined interferometer topologies. Fast, easy to use. Andreas Freise xx. October 2005

  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. Components: mirrors, free space, etc. Nodes: connection between components Interferometer Simulation

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

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

  6. Frequency Domain one Fourier frequency one complex output signal

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

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

  9. 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:

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

  11. 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.

  12. 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:

  13. Power Recycling Signals beamsplitter: „tilt“ motion End mirrors with imperfect radius of curvature

  14. Power Recycling Signals

  15. Current and Future Work • Add grating components (for all-reflective interferometer configurations) • Include a correct computation of quantum noise (for interferometers with suspended optics) • Adapt the numerical algorithm so that the programme can be run on a cluster • Add polarisation as a degree of freedom

  16. FINESSE http://www.rzg.mpg.de/~adf/

  17. 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)

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

  19. 1.0 0.1 0.01 TMSR Mode Healing

  20. Higher order modes • Based on TEM Gauss modes, n+m limited by memory and time • Automatic beam tracing through user-defined optical setups • Coupling coefficients for misalignment, mode mismatch (no phase maps, no clipping) • Outputs: • normal detectors • split (or otherwise shapes) detectors • CCD like beam images (for beam or selected fields)

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

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