Difference between analytical results and FDTD results for Kerr medium slab

- June 30, 2022 at 8:56 am
  
  ice20390296
  Subscriber
  
  I am running Lumerical FDTD to study the nonlinear refractive index change in a very thin Kerr medium for certain intensity values. I have noticed that after reaching an intensity threshold Δn saturates and the transmission, and reflection (T, R) of the slab no longer changes
  When I compare this with a simple analytical code that solves the problem linearly by simply calculating the nonlinear index change as Δn=In2 and adding the difference to the linear refractive index, naturally the result does not saturate as the refractive index simply changes no matter what source intensity is used.
  Why does the FDTD result saturate?
- June 30, 2022 at 9:47 pm
  
  Guilin Sun
  Ansys Employee
  
  I believe the analytical solution has some limitations and ignore some quantities. Δn=In2 ~=0.69 will be too large to index perturbation, even for the simulation.
  The simulation takes more terms and for such strong nonlinearity, anything can happen.
  I suggest to check the first principle and make sure the analytical solution does not lose any thing, and does not voilate the original assumption.
  - July 1, 2022 at 3:37 pm
    
    ice20390296
    Subscriber
    
    Thank you very much for the reply. If possible could you please explain why the index perturbation is considered too large? At what point should the simulation no longer be considered trustworthy?
    The analytical solution is very basic so I am pretty certain it is not this accurate. But I am curious as to why the simulation behaves in this way.
- November 28, 2022 at 6:41 pm
  
  Guilin Sun
  Ansys Employee
  
  Sorry, I just find your reply. The index perturbation requires delta_n<<1 in order to not excite higher order nonlinearity.

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