Discussion Forum

I am trying to further develop the Band-Gap Analysis of a Photonic Crystal [application ID: 798] model to conduct for a certain photonic crystal I'm designing. And I would appreciate any help or advice that anyone can provide. Thanks in advance!

The original model is found here.

Context

This model investigates the wave propagation in a photonic crystal that consists of GaAs pillars [70 nm radius] placed equidistant from each other [375 nm square lattice primitive cell side length]. Because it has a repeated pattern, only one pillar is needed for the simulation.

I want to use the same model but for a photonic crystal made of SiO2 that consists of Air pillars placed equidistant from each other. Again, because it has a repeated pattern, only one pillar is needed.

The complications for this [that I'm aware of] or the aspects I'm unsure of, raise the following questions:

Q1. Dispersion function

The dispersion relation for the refractive index of GaAs, in the original model [application ID: 798], is defined as an analytical function [as it used more than once]. This is expressed, using Global>Analytic, as: -3.3285e5[1/m]*c_const/f+3.8359.

Where, [I believe] 'c_const' is the speed of light in vacuum constant [approximatley 300E6 m/s] and 'f' is frequency [Hz]. However, I'm unsure what the values -3.3285e5[1/m] or +3.8359 represent.

As I understand it, this equation is used to determine the dispersion of light in the medium. Commonly, the optical dispersion of a medium is estimated using the Sellmeier equation. But the usual form of the equation is very different than the above equation.

Of course, my material is SiO2, with Air holes. And so I will need to define an expression for this arrangement for the analytical function. Can anyone advise further?

Q2. Photonic crystal configuration

The original model [application ID: 798] uses a unit cell composed of a stiff inner core and a softer outer matrix material. As stated above, I want to model a photonic crystal made from SiO2 with Air pillars, thus, a soft inner core and a stiffer outer matrix material. Can anyone advise if this arrangement causes any impact that requires a setting/parameter/etc change to the model?

Q3. Band numbers

The original model [application ID: 798] uses a parametric sweep to calculate the dispersion relations for the five lowest bands [1 - 5]. Can anyone explain why? And perhaps advise what bands I should consider for my photonic crystal?

Q4. Wave vector, k, magnitude

Lastly, the original model [application ID: 798] uses an Auxiliary sweep to scan the fraction of the wave vector, k, magnitude from 0 to 0.5 (half the Brillouin zone). And later, using a Stationary Solver>Paramteric> Continuation the Tuning of step size is selected to make sure the solver takes small enough steps when starting the sweep. With values set as: the initial step size = 0.0001; minimum step size = 0.0001; and maximum step size = 0.01.

Considering the photonic crystal I want to model, can anyone advise what k value and what step sizes to use for the sweep?