Please enable JavaScript to view this site.

Application Gallery

The goal of this example is to demonstrate how to simulate the Bloch mode profile of a periodic structure, including degenerate modes.

 

Solvers

FDTD

Associated files

bloch_mode.fsp

bloch_mode_bandstructure.lsf

bloch_mode.lsf

See also

Photonic Crystals

Bandstructure

Making a CW movie

Apodization

Square 3D

Bloch_title_figure

 

Here we use a 3D cubic lattice structure composed of a simple cubic lattice of spheres with lattice period 500 nm. The spheres are composed of a material with refractive index = 3, and radius = 130 nm. The bandstructure for this lattice is shown below. To generate the band diagram, open bloch_mode.fsp run the bloch_mode_bandstructure.lsf. If there is no sweep data, enable the dipole_cloud and bandstructure analysis group to run all the sweep. Please refer to bandstructure calculation for more details.

 

bloch_mode_profile_bandstructure_zoom50

 

Now we extract the Bloch modes of the 2 lowest order modes at the Brillouin zone edge (kx = p/a) from a single simulation. We know that these modes have frequencies 256 THz and 281 THz when (kx, ky, kx) = (0.5, 0, 0), at the 20th sweep point. We also know that the Bloch mode can be written as \( E_{k+a}(x)=\exp (i k a) u_{k}(x) \). Our goal is to extract uk(x).

 

Load the file bloch_mode.fsp. This example uses two 3D frequency profile monitors to determine the field profiles of the modes. Each monitor is set to the frequency of one of the modes and uses the time apodization feature to correctly extract the field profile information at that frequency using Fourier transforms.

 

Due to the symmetry of the problem, each of the bands calculated in the bandstructure above is doubly degenerate, one mode for each polarization. Thus care must be taken to excite only one of these Bloch modes. By placing a point dipole source on a symmetry plane of the lattice, one mode of a specific polarization may be excited directly. Note that it is very important, when degenerate modes are present, to use symmetry properties to determine where to place the point dipole sources. Otherwise you will extract the field profile corresponding to a linear combination of all the degenerate modes!

 

After running the simulation project, open the script prompt and run the script file bloch_mode.lsf. This will calculate |uk(x)|2 for the modes at the two frequencies and plot cross sections of them. The results are shown below:

 

lower frequency

symmetry: sy = +1, sz = -1

upper frequency

symmetry: sy = +1, sz = -1

bloch_mode_profile_256thz_xy_zoom80

bloch_mode_profile_281thz_xy_zoom80

bloch_mode_profile_256thz_xz_zoom80

bloch_mode_profile_281thz_xz_zoom80

Copyright Lumerical Inc. | Privacy | Site Map