Application of the Complex Coupled-Mode Theory to Optical Fiber Grating Structures

The complex coupled-mode theory (CMT) is applied to optical fiber grating structures of circular cross section. The radiative fields are treated in terms of discrete complex modes similarly to the guided modes in the conventional CMT. The number of modes that contribute to the couplings may be effectively reduced by considering the phase-matching condition. Therefore, simple analytical expressions for mode amplitudes and powers are obtained. Examples of the Bragg gratings with various outer cladding refractive indexes, e.g., lower, equal to and higher than the inner cladding refractive index, are investigated and show excellent agreement with rigorous numerical solutions.