ABSTRACT
This chapter follows a staged approach by first looking at spatial effects following with an analysis of temporal effects. Linear optical properties of materials play a large role in determining nonlinear effects, the linear propagation effects for more general types of electromagnetic waves also play a critical role in determining the efficiency of nonlinear effects. Specifically, the chapter derives a more general wave equation that first includes diffraction and the Poynting vector walk-off and then temporal effects. It also provides a presentation of diffraction and walk-off effects in the wave equation. After an illustration on the balance between dispersion and nonlinearity and between diffraction and nonlinearity, the chapter discusses the special case of a thin sample exhibiting no group-velocity dispersion (GVD). The incorporation of temporal effects into the slowly varying envelope approximation (SVEA) equations is also discussed.
