This page contains materials for the time domain simulation of the dual recycling Michelson cavity. The formulation of calculating the fields in the DRM cavity is provided in a LIGO document, T040062. For now, only scalar field is included in the calculation. This calculation includes up to the first order of time dependence of all physics quantities, mirror motions and input and internal fields. This is important to study the frequency noise issues, which appears as time dependent phases. This note is a pdf file based on a mathematica notebook, and the notebook itself is available on request.

A matlab code has been developed for fast prototyping based on this formulation. This version dated April 13, 2004, has been validated by comparing with the calculation using primitive modules of e2e. This matlab code is designed to calculate the time evolution of fields for any given mirror motions and input fields, it can be used as a part of a more complete dual recycling cavity simulation with mechanics and control systems. This matlab code and e2e box files are available for download with simple README files.

There are a few major steps for the future.

- Fully validate the code, and make it more efficient by eliminating terms unnecessary for the practical case.
- Write an e2e primitive so that full time domain simulation can be done in the e2e environment
- Extend the calculation to use modal model so that beam profile can be simulated.

Hiro Yamamoto : hiro@ligo.caltech.edu

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