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

11. July 2003 Andreas Freise

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

11. July 2003 Andreas Freise Interferometer Simulation Components: mirrors, free space, etc. Nodes: connection between components

11. July 2003 Andreas Freise Plane Waves – Frequency Domain Coupling of light fields: Set of linear equations: solved numerically

11. July 2003 Andreas Freise Frequency Domain Simple cavity: two mirrors + one space (4 nodes) Light source (laser) Output signal (detector)

11. July 2003 Andreas Freise Frequency Domain one Fourier frequency one complex output signal

11. July 2003 Andreas Freise Static response phase modulation = sidebands 3 fields, 3 beat signals

11. July 2003 Andreas Freise Frequency Response infenitesimal phase modulation 9 frequencies, 13 beat signals

11. July 2003 Andreas Freise 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: Gaussian beam parameter q

11. July 2003 Andreas Freise Gaussian Beam Parameters  Compute cavity eigenmodes start node  Trace beam and set beam parameters

11. July 2003 Andreas Freise 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.

11. July 2003 Andreas Freise 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:

11. July 2003 Andreas Freise Power Recycling Signals End mirrors with imperfect radius of curvature beamsplitter: „tilt“ motion

11. July 2003 Andreas Freise Power Recycling Signals

11. July 2003 Andreas Freise 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

11. July 2003 Andreas Freise FINESSE

11. July 2003 Andreas Freise FINESSE: Fast and (fairly) well tested TEM order Omatrix elements(effective) computation time (100 data points) 0~ <1 sec 5~ sec 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. July 2003 Andreas Freise Mode Healing power recycling only: Each recycling cavity minimises the loss due to mode mismatch of the respective other with signal recycling:

11. July 2003 Andreas Freise Mode Healing T MSR

11. July 2003 Andreas Freise 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)

11. July 2003 Andreas Freise Gaussian Beam Parameters Example: normal incidence transmission through a curved surface: Transforming Gaussian beam parameters by optical elements with ABCD matrices: