I am not clear about what this exactly means. I know that there are forbidden bands in PCW, but what exactly means tunning the edges of such band to atomic transitions frequencies D1 and D2? and how can that infer that atoms are localized inside the waveguide by optical dipole forces?
In Photonics Crystal waveguide, you have for each light frequency corresponding k wave vector. IF so, they call it a band. Usually, one operates at the lower band of the PCW. The task is to make the PCW so, that it could translate modes with a frequency of light equal to this transition. You can do it by varying the shape of you PCW or it's materials.
Other case, is photonics crystal cavity. In it, you place your atom inside this cavity, but due to the PC band structure, only modes with allowed frequency are transmitted from it, forming a fabry-perrot resonator.
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