Control of Mode Structure in Active or Passive Graded-index Waveguides with Large-scale Periodic Longitudinal Inhomogeneities

The mode structure of both active and passive graded-index waveguides with a parabolic-index profile and large-scale (in comparison with wavelength) periodic variations of the profile in the longitudinal direction is investigated analytically in the paraxial approximation of the scalar wave equation. Quasimode solutions which periodically reconstruct themselves up to some phase factor characterizing quasi-propagation constants are investigated in detail using a quantum-theoretical formalism. The possibility of effective control of the quasi-mode structure in such waveguides is shown and possible practical applications to different waveguide components and lasers are discussed. The spontaneous emission K factor for the quasi-modes in active and passive periodic waveguides is also evaluated.