Learning Forum

[Aruna_Soibam]

Hello,

I'm plotting the bandstructures of a photonic crystal structure having hexagonal lattice with hole arrays in a silicon slab.

Fig. 1 (a) is the bandstructure of the structure with bandgap ranging from (0.290779 to 0.367144).

Fig 1 (b) is the bandstructure with one row defect in the structure.

From the Fig. 1 (b) how will I understand which modes are supporting in the defect waveguide, and also how can I distinguish the fundamental mode and other higher order modes from the bandstructure.

Thank you.

[Guilin Sun]

Photonics crystal line-defect waveguide is not the regular waveguide that you can define a "fundamental" mode, since it is the bloch mode. You may use different-polarized dipoles and (or) symmstry BCs (if symmetry exists) to isolate the TE and TM modes. and you can find the bloch mode at each eigen frequency: Bloch mode profile - Photonic crystal
Usually, such waveguide will need a regular ridge waveguide as input and output, which has definite, traditional fundamental mode.

[Aruna_Soibam]

Thank you for the reply.
I'm using Electric dipole for TM and Magnetic dipole for TE to plot different bandstructures for TM and TE polarizations.
I was plotting the bandstructures from the paper [1] for single row line defect and 5 rows line defect waveguides, which are shown in the fig below respectively. The bandstructures are coming as a similar trend as that of the paper and we can also differentiate the supported modes.
By using the similar fashion, I plotted the bandstructure in Fig. 1 (b). However, the modes are difficult to differentiate since the modes are pulled down from the upper band; whereas modes are pulled up in [1].
I would like to understand the supported modes in line-defect waveguides through the bandstructure.
[1] O. M. Nawwar et al., ÔÇ£Photonic crystal-based compact hybrid WDM/MDM (De)multiplexer for SOI platforms,ÔÇØ Optics Letters, vol. 43, no. 17, p. 4176, 2018.

[Guilin Sun]

As mentioned previously, the supported modes are on the band structure. Since there are many higher orders, I would suggest that you only simulate up to the order you desire, such as the 2nd order. Once you know the eigen frequency, then you can use a profile monitor with apodization to get the bloch mode. Understanding time apodization in frequency domain monitors

[Aruna_Soibam]

How can I simulate only up to a particular order that I desire? What are the settings to be made?
Can you suggest some examples of that, if available.
Thanks.

[Guilin Sun]

You usually cannot choose the particular order, except that the band gap is clear. But from your current result, you can definitely set the frequency range to the band that you need. Other bands are just noise for you. For example, in this image

It is clear that you only need to simulate the normalized frequency to 0.31 or 0.32 for the first two bands.

[Aruna_Soibam]

Thanks. That helps.
One more thing is that, Is there any option to connect these frequency points (which we observe in the bandstrucure) to form bands while plotting the bandstructure?

[Guilin Sun]

The vertical axis is the normalized frequency, f*a/c from which you can get f. But the plot is from a matrix so you will need to find the peak along a giving k vector and judge which band it is on,