Wave-beam coupling in quadratic nonlinear optical waveguides: effects of nonlinearly induced diffraction

Area of Science:

• Nonlinear Optics
• Waveguide Optics
• Computational Physics

Background:

• Beam coupling in optical waveguides is crucial for nonlinear phenomena.
• Nonlinear diffraction arises from the divergence of the electric field term in wave equations.
• Understanding these effects is key to controlling light propagation in waveguides.

Purpose of the Study:

• To investigate beam coupling influenced by nonlinearly induced diffraction in quadratic nonlinear planar optical waveguides.
• To derive the system's power-conservation law, Lagrangian, Hamiltonian, and stationary state equations.
• To analyze the impact of nonlinearly induced diffraction on solitary wave characteristics.

Main Methods:

• Derivation of fundamental physical laws (conservation, Lagrangian, Hamiltonian).
• Formulation of equations for stationary states.
• Numerical analysis using nonlinear wave-number shift and linear phase mismatch as parameters.
• Discussion of paraxial approach modifications for nonlinear diffraction.

Main Results:

• Nonlinearly induced diffraction modifies second-order nonlinear terms, acting as an effective third-order nonlinearity.
• The study demonstrates the influence of nonlinearly induced diffraction on solitary wave amplitude and width.
• A procedure for handling such modifications within a paraxial framework is presented.

Conclusions:

• Nonlinear diffraction significantly alters beam coupling dynamics in optical waveguides.
• The findings provide insights into the behavior of solitary waves under nonlinear diffraction.
• The developed framework aids in understanding and controlling light propagation in complex nonlinear optical systems.