Linear time invariant system modelling

One of the primary tasks undertaken with Finesse 2 was simulating the frequency domain behaviour of complex optical systems. This involved computing various transfer functions of small signals injected into the system and computing how they affect various outputs. With knowledge of how these small signals behave in an optical system we can then model how classical and quantum noise propagates throughout an optical system and the behaviour of control systems designed to keep the an optical system operating.

Modelling LTI systems is a broad subject and covered in significant and better detail else where. As background reading primarily targeted at modelling LTI systems for sensing and control of interferometers we recommend Chapter 8 Interferometric length sensing and control in [12] — much of this section of the manual will assume physics knowledge from this chapter.

Note

Those with previous experience in modelling LTI responses in Finesse 2 will be familiar with the fsig command that was used to inject a signals. Finesse 3 still keeps the same name fsig but this is now purely the frequency of the small signal excitation Model.fsig.f which globally sets what signal frequency is used. Injecting signals is now done using signal generator components or special analyses like frequency_response.

Finesse 3 introduces a significantly changed interface from Finesse 2 for modelling transfer functions. In this section we will cover these modelling tasks from the basic to more advanced features.

• Modelling transfer functions
  • Operating points: Carrier and signals — DC and AC
  • Computing transfer functions - manual method
• Calculating general transfer functions
  • Setting up the model
  • Calculating the transfer functions
  • Frequency response of the fundamental mode
  • Frequency response between HOMs
• Closing control loops
  • DC control loops - ‘lock’
  • AC control loops
• Using degrees of freedom