From: Steven G. Johnson @.>
Sent: Friday, May 13, 2022 2:38 PM
To: NanoComp/photonics-opt-testbed @.>
Cc: Fengwen Wang @.>; Author @.>
Subject: Re: [NanoComp/photonics-opt-testbed] Problem description of the inverse design of slow light waveguide (PR #10)
ε _si=(n_si)^2 =3.476^2
From: Steven G. Johnson @.> Sent: Friday, May 13, 2022 2:38 PM To: NanoComp/photonics-opt-testbed @.> Cc: Fengwen Wang @.>; Author @.> Subject: Re: [NanoComp/photonics-opt-testbed] Problem description of the inverse design of slow light waveguide (PR #10)
@stevengj commented on this pull request.
In slow_light_waveguide/Problem_Description_Slow_light_Waveguide.texhttps://github.com/NanoComp/photonics-opt-testbed/pull/10#discussion_r872353573:
\item Discretization:
408x40 bilinear quadrilateral elements
+\item Regularization:
+
density filter (filter radius: 1/8a) + projection
\item Continuation scheme in the projection
For every $40$th iteration or if ( { $\Delta \rho< 1e-3$ or $\Delta f <1e-3$ } and $\beta < 50$, set $\beta=1.3 \beta$. \
If $\Delta \rho < 1e-4$ or $\Delta f < 1e-4 $, terminate.
+\item Interpolation of the relative permittivity of element $e$:
+
+$\frac{1}{\varepsilon^{\eta}_e} = \left(1- \overline{\rho}^{\eta}e \right)\frac{1}{\varepsilon{\rm{air}}} +\overline{\rho}^{\eta}e \frac{1}{\varepsilon{\rm{Si}}}$
What ε do you use for Si?
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