- #1

jgk5141

- 6

- 0

In 1D Photonic crystals, a defect can be introduced to create a defect/resonance mode and enable transmission. At first considerations, the thickness of the single defect layer determines the transmission frequency. Moreover, if it is a half-wavelength layer it will enable a resonance condition (this is where the analogy of fabry-perot comes in) at that wavelength and allow transmission in the forbidden band (photonics band gap) of the original photonic crystal. However, when performing simulations (Transfer Matrix Method), and the simulation starts to vary farther from the ideal, then it becomes clear that the performance of the structure is dictated by a much more complex scattering problem. For example, if multiple defects are introduced at different points within the photonic crystal the multiple transmission peaks appear within the stop-band. Even if all of these defects are at the same thickness, the resonances are at different frequencies. I have attached a screen shot of double-cavity structure that is a good example of something that would display this.

An analogy that first comes to mind is the tight-binding model and this seems to be a good starting point, but I cannot find a good starting point for this idea within the field of photonics. Trying to understand this phenomenon, I came across several topics such as Couple-mode theory (CMT), quasi-modes, quasi-normal modes, Wannier functions, and more.

What I am trying to understand is first, the fundamental question of why do these optical modes couple? And second, how can I predict the frequencies of these coupled modes prior to any simulation? I want to develop this theoretical intuition without just brute-forcing my simulations until I get the desired results. Any help our guidance in this area would be greatly appreciated. Please let me know if more information is needed.

An analogy that first comes to mind is the tight-binding model and this seems to be a good starting point, but I cannot find a good starting point for this idea within the field of photonics. Trying to understand this phenomenon, I came across several topics such as Couple-mode theory (CMT), quasi-modes, quasi-normal modes, Wannier functions, and more.

What I am trying to understand is first, the fundamental question of why do these optical modes couple? And second, how can I predict the frequencies of these coupled modes prior to any simulation? I want to develop this theoretical intuition without just brute-forcing my simulations until I get the desired results. Any help our guidance in this area would be greatly appreciated. Please let me know if more information is needed.