FINESSEFINESSE 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

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 opticalcomponent is misaligned and where the beam sizes are notmatched.

11. July 2003 Andreas Freise

Mode Mismatch and Misalignment

Mode mismatch or misalignemt can be described as light scatteringin 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 imperfectradius 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

FINESSEFINESSE

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

11. July 2003 Andreas Freise

FINESSE: Fast and (fairly) well tested

TEM order O matrix elements (effective)computation time (100 data points)

0 ~25000 340 <1 sec

5 ~11000000 83000 400 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:

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Mode Healing

1.0 0.1 0.01

TMSR

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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: