Field form of perturbation theory for calculating the matrix elements of operators between the states of two degenerate atomic levels. I

It is shown that the calculation of the matrix elements between degenerate states of arbitrary atomicmolecular systems can be reduced to a calculation of the matrix elements for some auxiliary operator. The perturbation theory for this calculation can be given a field form, and its matrix elements can be expressed in terms of the contributions from special Feynman diagrams. The exact rules are formulated for constructing the contributions from these diagrams.     

Reflectance spectra and photonic band gaps of a one-dimensional photonic crystal based on a silicon-air periodic structure

The reflectance spectra of a one-dimensional photonic crystal based on a silicon-air periodic structure are calculated. A map of photonic band gaps is plotted, which makes it possible to deliberately choose the geometric parameters of the structure (the thickness of silicon partitions D _Si and the period A) for different ranges of the wavelength λ. To obtain structures with a photonic band gap in the range A/λ=0.15–0.5, the main region (as rule, corresponding to the lowest frequencies) can be used, and, taking into account the secondary photonic band gaps, the range A/λ can be extended to 1 and even more. In addition, it is found that, in the range D _Si/A=0.4–0.9, the secondary band gaps may be wider than the main ones (on the frequency scale). The influence of the filling factor D _Si/A on the formation of the edges of spectral bands is revealed.