An analysis of a planar optical directional coupler with a lossless Kerr-like coupling medium

The nonlinear all-optically controlled coupling characteristics are studied analytically and numerically for two planar optical waveguides coupled through a lossless Kerr-like slab. The exact dispersion equation for this waveguiding structure is derived in terms of Jacobian elliptic functions. The optical intensity-dependent coupling length is described as a combination of symmetriclike and antisymmetriclike modes of propagation, derived from the nonlinear combination of the independent modes of the structure. A simple analytical formula is derived for the critical power, defined as the power above which the antisymmetric mode disappears and complete energy transfer between the two waveguides is no longer possible. The analysis provides insight into the complicated nature of the waveguiding structure behavior, and it shows one possible approach to solving difficult propagation problems in nonlinear optical waveguides of this or similar configuration