FINESSEFINESSE

Frequency Domain Interferometer Simulation

Andreas Freise

European Gravitational Observatory

17. March 2004

5. September 2003 Andreas Freise

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

Frequency Domain

one Fourier frequency

one complex output signal

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

Power Recycling Signals

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

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

1.0 0.1 0.01

TMSR

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.