Post on 01-Apr-2015
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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
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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: