The development of the optical simulation tools is one of the primary tasks of the OSD subsystem. The fields inside AdVirgo are not simple to describe with analytical models, especially in the presence of asymmetries or mirror defects.  

The simulation tools are thus clearly important for the baseline design phase, but an updated and relevant set of simulation tools is also crucial during the construction phase in order to check the design consistency using the real mirrors parameters and results from the pre-commissionned sub-systems (laser, TCS). Furthermore, simulation is a critical tool for the commissioning process. The presence and use of different codes enables crosschecks between them and avoids the risk of errors. Furthermore the development of codes in several laboratories of the Virgo Collaboration allows a more direct control of the results and increases local experience in optical simulation.

Types of simulations

For AdVirgo, three main types of codes are used: FFT codes (DarkF, Siesta and SIS), modal codes (Finesse, LMA-code and MIST) and codes including radiation-pressure (Optickle). DarkF, SIESTA, LMA-code and MIST are developed within the Virgo Col- laboration. SIS and Optickle are developed in LIGO and Finesse in GEO. In addition, standard ray tracing codes (Optocad in 2D and Zemax in 3D) are currently used.

Modal Codes

In the modal codes the electrical field is expanded in a base of Hermite-Gaussian or Laguerre-Gaussian modes. For our purposes one convenient base is the eigenmodes of the perfect and ”cold” (no thermal effect) 3-km arm-cavity. These codes are in general very useful in the early phases of the design, where no big defects are considered, since a low number of modes is required. As it has been showed by works carried out inside the OSD group, when they are used to reproduce marginally stable cavities or small spatial defects, their precision and covergence must be carefully checked.  Examples are Finesse, MIST, and the LMA-code.

FFT Codes

In the FFT codes the electrical field is expanded in plane wave components (through FFT transform). The plane waves are propagated independently through free space and optical components. The steady-state fields are computed by inverse Fourier transform. The advantage of these codes is the fact that no priors on the fields are needed and that they can give precise results. The drawback is that these code are in general slower than the modal codes and their use is probably less effective in the first phases of the design.  Examples are SIS, DarkF, and Siesta.

Radiation Pressure Codes

The existing modal and FFT codes does not contain radiation pressure effects. In order to understand the audio frequency dynamics of the interferometer, it is necessary to include the effects of radiation pressure. This is especially necessary for the design of proper control systems.  An example is Optickle.

Time Domain Simulation

The LIGO developed end-to-end model (E2E) is a time domain modal code which includes many effects, including radiation pressure.  It is extremely slow, but is useful for studying interferometer dynamics (and in particular, transient effects). 

Noise Calculator

The Gravitational Wave Interferometer Noise Calculator (GWINC) does not actually simulate an interferometer, but calculates the contributions of various noise sources and the resulting range (reach) for specific astrophysical sources.