Point source near an anisotropic lens - Revision history

BlazS: /* Case */

2020-09-24T08:46:03Z

‎Case

BlazS: /* Case */

2020-09-24T08:43:33Z

‎Case

BlazS: /* Results */

2020-08-14T07:06:22Z

‎Results

BlazS: /* Results */

2020-08-11T17:02:31Z

‎Results

BlazS: /* Case */

2020-08-11T17:00:48Z

‎Case

BlazS at 16:11, 11 August 2020

2020-08-11T16:11:51Z

BlazS: Created page with " File:FDFD_2D_anizolens_Im.png File:FDFD_2D_anizolens_Re.png "

2020-08-10T02:28:01Z

Created page with "<gallery> File:FDFD_2D_anizolens_Im.png File:FDFD_2D_anizolens_Re.png </gallery>"

New page

<gallery>
File:FDFD_2D_anizolens_Im.png
File:FDFD_2D_anizolens_Re.png
</gallery>

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 \end{equation}
 Where the parameters $a$ and $p$ control the radius of the refinement and how blurred the edge between the two different nodal densities is.
 ==Results==

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 The dielectric function remains a scalar, this has important consequences for the amplitude equation and the boundary condition between the lens and free space around it. The system of equations we are solving is
 \begin{align}
-\nabla \cdot A \nabla v + \mu_z \eps_r \frac{\omega^2}{c_0^2} v = 0 \qquad &\text{in} \quad \Omega  \label{eq:anisoInt} \\
+\nabla \cdot A \nabla E_z^{int} + \mu_z \eps_r \frac{\omega^2}{c_0^2} E_z^{int} = 0 \qquad &\text{in} \quad D  \label{eq:anisoInt} \\
-\nabla^2 u^s + \frac{\omega^2}{c_0^2} u^s  = 0 \qquad &\text{v} \quad \R^2 \setminus \Omega , \label{eq:anisoOut}
+\nabla^2 E_z^s + \frac{\omega^2}{c_0^2} E_z^s  = 0 \qquad &\text{outside} \quad D , \label{eq:anisoOut}
 \end{align}
 where,
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 The problem is two-dimensional because of the form of the permeability tensor, the boundary conditions can be derived from Maxwell's equations. As with isotropic materials, the field and its normal derivative have to be continuous on the boundary however, the (anisotropic) normal derivative is defined in a different way
 \begin{align}
-v - u^s =u^i  \qquad &\text{on} \quad \partial \Omega \label{eq:BC1Aniso} \\
+E_z^{int} - E_z^s =E_z^{inc}  \qquad &\text{on} \quad \partial D \label{eq:BC1Aniso} \\
-\dpar{v}{n_A\!\!\!} - \dpar{u^s}{n} = \dpar{u^i}{n}  \qquad &\text{on} \quad  \partial \Omega, \qquad \text{where} \quad \frac{\partial v}{\partial n_A\!\!\!} = n \cdot A \nabla {v}. \label{eq:BC2}
+\dpar{E_z^{int}}{n_A\!\!\!} - \dpar{E_z^{s}}{n} = \dpar{E_z^{inc}}{n}  \qquad &\text{on} \quad  \partial D, \qquad \text{where} \quad \frac{\partial E_z^{int}}{\partial n_A\!\!\!} = n \cdot A \nabla {E_z^{int}}.
 \end{align}
 The incident field results from a point source and is represented by the Green function of the Helmholtz equation in two dimensions

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 ==Results==
-[[File:FDFD_2D_anizolens_Im.png|800px]]
+[[File:FDFD_2D_anizolens_ImEn.png|800px]]
-[[File:FDFD_2D_anizolens_Re.png|800px]]
+[[File:FDFD_2D_anizolens_ReEn.png|800px]]

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 ==Results==
-<gallery>
-File:FDFD_2D_anizolens_Im.png
+[[File:FDFD_2D_anizolens_Im.png|800px]]
-File:FDFD_2D_anizolens_Re.png
+[[File:FDFD_2D_anizolens_Re.png|800px]]

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 ==Case==
 ==Results==
 <gallery>