Introduction to Finesse

Finesse is a simulation program for interferometers. The user can build any kind of virtual interferometer using the following components:

  • lasers, with user-defined power, wavelength and shape of the output beam;

  • free spaces with arbitrary index of refraction;

  • mirrors and beam splitters, with flat or spherical surfaces;

  • modulators to change amplitude and phase of the laser light;

  • amplitude or power detectors with the possibility of demodulating the detected signal with one or more given demodulation frequencies;

  • lenses and isolators.

For a given optical setup, the program computes the light field amplitudes at every point in the interferometer assuming a steady state. To do so, the interferometer description is translated into a set of linear equations that are solved numerically. For convenience, a number of standard analyses can be performed automatically by the program, namely computing modulation-demodulation error signals and transfer functions. Finesse can perform the analysis using plane waves or Hermite-Gauss modes. The latter allows computation of the effects of mode matching and misalignments. In addition, error signals for automatic alignment systems can be simulated.

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Fig. 1 A schematic diagram of a laser interferometer which can be modelled using Finesse (in this case a Fabry-Perot cavity with a Pound-Drever-Hall control scheme).

Literally every parameter of the interferometer description can be tuned during the simulation. The typical output is a plot of a photodetector signal as a function of one or two parameters of the interferometer (e.g. arm length, mirror reflectivity, modulation frequency, mirror alignment). Optional text output provides information about the optical setup including, but not limited to, mode mismatch coefficients, eigenmodes of cavities and beam sizes.

Finesse provides a fast and versatile tool that has proven to be very useful during design and commissioning of interferometric gravitational wave detectors. However, the program has been designed to allow the analysis of arbitrary, user-defined optical setups. In addition, it is easy to install and easy to use. Therefore Finesse is very well suited to study basic optical properties, like, for example, the power enhancement in a resonating cavity or modulation-demodulation methods.

Motivation and History

The search for gravitational waves with interferometric detectors has led to a new type of laser interferometer: new topologies are formed combining known interferometer types. In addition, the search for gravitational waves requires optical systems with a very long baseline, large circulating power and an enormous stability. The properties of this new class of laser interferometers have been the subject of extensive research.

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Fig. 2 Bird’s eye view of the GEO 600 gravitational wave detector near Hannover, Germany. Image courtesy of Harald Lück, Albert Einstein Institute Hannover.

Several prototype interferometers have been built during the last few decades to investigate their performance in detecting gravitational waves. The optical systems, Fabry-Perot cavities, a Michelson interferometer and combinations thereof are in principle simple and have been used in many fields of science for many decades. The sensitivity required for the detection of the expected small signal amplitudes of gravitational waves, however, has put new constraints on the design of laser interferometers. The work of the gravitational wave research groups has led to a new exploration of the theoretical analysis of laser interferometers. Especially, the clever combination of known interferometers has produced new types of interferometric detectors that offer an optimised sensitivity for detecting gravitational waves. Work on prototype interferometers has shown that the models describing the optical system become very complex even though they are based on simple principles. Consequently, computer programs have been developed to automate the computational part of the analysis. To date, several programs for analysing optical systems are available to the gravitational wave community [2].

The idea for Finesse was first raised in 1997, when (Andreas) was visiting the Max-Planck-Institute for Quantum Optics in Garching, to assist Gerhard Heinzel with his work on Dual Recycling at the 30 m prototype interferometer. We were using optical simulations which were rather slow and not very flexible. At the same time Gerhard Heinzel had developed a linear circuit simulation Liso that used a numerical algorithm to solve the set of linear equations representing an electronic circuit. The similarities of the two computational tasks and the outstanding performance of Liso lead to the idea to use the same methods for an optical simulation. Gerhard Heinzel kindly allowed me to copy the Liso source code which saved me much time and trouble in the beginning.

In the following years Finesse was continually developed during my work at the university in Hannover within the GEO project [3][4].

Finesse has been most frequently utilised during the commissioning of GEO 600, some of these simulation results have been published in [5][6][7][8] and in [9].

More recently Finesse has been used during the commissioning of Advanced LIGO. Finesse is now actively developed as an open source project and it is now widely used in many other projects; the Finesse home page lists more than 100 documents citing it [10].