finesse frequency domain interferometer simulation
DESCRIPTION
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) - PowerPoint PPT PresentationTRANSCRIPT
FINESSEFINESSE
Frequency Domain Interferometer Simulation
Andreas Freise
European Gravitational Observatory
17. March 2004
5. September 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
5. September 2003 Andreas Freise
Plane Waves – Frequency Domain
Coupling of light fields:
Set of linear equations: solved numerically
5. September 2003 Andreas Freise
Frequency Domain
Simple cavity: two mirrors + one space (4 nodes)
Light source (laser)
Output signal (detector)
5. September 2003 Andreas Freise
Static response
phase modulation = sidebands
3 fields, 3 beat signals
5. September 2003 Andreas Freise
Frequency Response
infenitesimal phase modulation
9 frequencies, 13 beat signals
5. September 2003 Andreas Freise
Gaussian Beam Parameters
Compute cavity eigenmodes
start node
Trace beam and set beam parameters
5. September 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:
5. September 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)
5. September 2003 Andreas Freise
FINESSEFINESSE
http://www.rzg.mpg.de/~adf/
/virgo/VCS/1.0/VIRGOSW/Finesse/v0r93/...
Windows, Linux
Linux, AIX
5. September 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.
5. September 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
5. September 2003 Andreas Freise
Gaussian Beam Parameters
Example: normal incidence transmission through a curved surface:
Transforming Gaussian beam parameters by optical elements with ABCD matrices:
5. September 2003 Andreas Freise
Frequency Noise Coupling
Coupling of a frequency calibration peak into the dark fringe output:
Difference between results forTEM00 only and those withhigher-order TEM modes: factor 100 phase 90°
5. September 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:
5. September 2003 Andreas Freise
Error signals, control signals
photo detectors, multiple
mixers
Transfer functions
amplitude-, phase- and
frequency modulations
Shot-noise-limited
sensitivities
Typical Tasks For FINESSE
5. September 2003 Andreas Freise
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.