BlochFamily¶

Type:	section
Appearance:	simple
Excludes:	PropagatingModes

The BlochFamily multiple source allows a comfortable definition of all incident plane waves sharing the same Bloch phase in periodic geometries. As discussed here, periodic structures support a set of discrete diffraction orders, or Fourier modes that are linked to the reciprocal grid in k space. This source definition sets up plane wave illuminations incident from all these discrete directions separately for s and p polarization. A table containing the K and Amplitude vector of the different illumination is exported if the OutputFileName is provided.

MultipleSources {
  BlochFamily {
   Lambda0 = 800e-9
   Sigma = [0 0]
   Incidence = Both
   OutputFileName = "sourceTable.jcm"
}

In the following we focus on the two-fold periodic case only. From the grid the two lattice vectors $\pvec{a}_{\perp, 1}$ and $\pvec{a}_{\perp, 2}$ with their respective reciprocal grid vectors $\pvec{b}_{\perp, 1}$ , $\pvec{b}_{\perp, 2}$ are determined automatically. The same holds for $\varepsilon_\pm$ and $\mu_\pm$ , the corresponding scalar permittivities and permeabilities in the lower and upper half spaces, respectively. The angular wave number is given by $k_\pm=\omega \sqrt{\varepsilon_\pm \mu_\pm}$ .

Using reciprocal grid vectors the transversal components $\pvec{k}_{\perp, n_1, n_2} = n_1 \pvec{b}_{\perp, 1}+n_2 \pvec{b}_{\perp, 2} + k_{\perp, \mathrm{B}}$ of the k-vector is determined for given integers $n_1,n_2$ . By prescribing the transversal component of the Bloch vector $\pvec{k}_{\mathrm{B}}$ (this can set using Sigma), the illuminations can be translated in reciprocal space. This remaining normal component $k_z$ is determined by $k_z = \pm\sqrt{k_\pm^2-|\pvec{k_\perp}|^2}$ in the appropriate half spaces.