Exact analytic solutions to the nonlinear wave equation for a saturable Kerr-like medium: modes of nonlinear optical waveguides and couplers

Exact analytic solutions to the nonlinear wave equation for a lossless saturable Kerr-like medium are found. The nonlinearity is an intensity-dependent refractive index which saturates according to the model n/sup 2/=n/sub 0//sup 2//spl plusmn/a|E|/sup 2//(1+b|E|/sup 2/). The solutions to the wave equation are used to determine the TE power-dependent dispersion relations, and therefore the guided modes, of a single waveguide structure and of a directional coupler whose coupling medium is the nonlinear saturable material. Although the interaction between the sinh- and cosh-like modes of the coupler, and therefore the coupling length, is not treated in this work, it is shown that the critical power, defined in the literature to be the level of input power above which 100% of the power cannot be switched between the guides of a coupler, is a mathematical misinterpretation in both saturable media as well as in nonsaturable Kerr media. The absence of a critical power in single waveguide structures is also demonstrated. Parameters of GaAs-based waveguides and of a GaAs-GaAlAs MQW coupling medium are used in the numerical analysis. >

[1]  J. D. Begin,et al.  An analysis of a planar optical directional coupler with a lossless Kerr-like coupling medium , 1990 .

[2]  E. Popov,et al.  Dispersion characteristics of multilayer waveguides , 1985 .

[3]  L. Esaki,et al.  A bird's-eye view on the evolution of semiconductor superlattices and quantum wells , 1986 .

[4]  Robert C. Gauthier,et al.  Nonlinear guided waves coupled nonlinearly in a planar GaAs/GaAlAs multiple quantum well structure , 1986 .

[5]  H. Haug,et al.  Basic mechanisms of the optical nonlinearities of semiconductors near the band edge , 1985 .

[6]  Falk Lederer,et al.  Generalized dispersion relations for nonlinear slab-guided waves , 1985 .

[7]  D. Mihalache,et al.  TM-polarized nonlinear slab-guided waves in saturable media , 1986 .

[8]  D. Marcuse,et al.  The coupling of degenerate modes in two parallel dielectric waveguides , 1971 .

[9]  C. Burrus,et al.  Novel hybrid optically bistable switch: The quantum well self‐electro‐optic effect device , 1984 .

[10]  D. Chemla,et al.  Optical Stark effect on excitons in GaAs quantum wells. , 1986, Optics letters.

[11]  G. Stegeman,et al.  Saturation of guided wave index with power in nonlinear planar waveguides , 1987 .

[12]  W. Wiegmann,et al.  131 ps optical modulation in semiconductor multiple quantum wells (MQW's) , 1985, IEEE Journal of Quantum Electronics.

[13]  S. Al-bader,et al.  Guided waves in nonlinear saturable self-focusing thin films , 1987 .

[14]  S. M. Jensen.  The Nonlinear Coherent Coupler , 1982 .

[15]  B. Weiss,et al.  Modal propagation within MQW waveguides , 1989 .

[16]  P. Egan,et al.  Optically nonlinear waves in thin films , 1986 .

[17]  Richard A. Soref,et al.  Electro‐optical switching in a GaAs multiple quantum well directional coupler , 1989 .

[18]  Antonetti,et al.  "Dressed excitons" in a multiple-quantum-well structure: Evidence for an optical Stark effect with femtosecond response time. , 1986, Physical review letters.