I am doing some self-study on photonics and have encountered the following question:
We know that amorphous electronic crystals such as amorphous silicon have a bandgap. Can amorphous photonic crystals also have a bandgap? Roughly how large would the spacing, d, have to be for a bandgap centered around ~ 600 nm?
Here is my solution: Since $n\lambda=2dsin(\theta)$, if $\lambda=600 nm, \theta=\pi/4, n=1,$ then $d=4.24 \times 10^{-7}$.
Could somebody check over my work?