Exact derivation of the coupling coefficient in corrugated waveguides with rectangular tooth shape

An exact analysis, based on local field expansion, is used in order to calculate the coupling coefficient in corrugated waveguide structures having rectangular tooth shape and small tooth height. In particular, the coupling coefficients for TE field polarization and TM field polarization are derived. It is shown that the expression for the TE coupling is identical with previous results based on the coupled wave formalism and on other techniques as well. This is a consequence of the formal validity of the equivalent index method for TE polarized waves. In the case of TM coupling, the equivalent index method does not hold and the expression for the coupling coefficient deviates significantly from the results obtained by the coupled mode formalism.