Lumopt - Custom Figure of Merit
Lumopt and inverse design are powerful optimization frameworks supported by lumerical. These are based on the adjoint method, and require that you solve the adjoint system to very quickly converge on optimal solutions. See Photonic Inverse Design Overview for more info. Our implementation is currently limited to integrated photonic circuit components as explained in Getting Started with lumopt.
Some users are interested in applying the lumopt methodology to more exotic devices like photodetectors or metasurfaces. The challenge here is that the FOM, and adjoint source would different from the current lumopt implementation which requires a ModeSource and ModeExp monitor for the FOM.
In short would require developing new python classes in lumopt that handle different sources and FOM's. There is no theoretical limitation on doing this, as the physics is the same and much of lumopt would be transferable.We are collectring feedback at the the idea exchange for anyone who would like to see this framework extended to other devices and workflows. Your feedback will help us prioritize development.
Here is a few references that discuss the methodology that would be required, quite clearly, but there is no escaping the fact that it is mathematically quite heavy.
Yu Zhang's thesis
Although I am unable to clarify all the steps I will highlight a few relevant points.
In the time domain your figure of merit( or response function) should take the following form.
Where the integral kernal ϕ(E) depends the design properties you are interested in, and does not depend the fields in the optimization region. In Lumerical we are interested in the power coupling into a guided mode ‘port’. You would have to write your own expression, based on response of interest. If you follow Zhang’s derivation in section 2.4 he arrives at an expression of the adjoint source.
The adjoint system takes on a similar system of equations, with a few approximations.
With a requirement on the adjoint source that.
For a lossy dispersive material you need to reformulate M, and you should refer to section 4.2, but the procedure is the same. Since M should remain invariant to time.