ABSTRACT

In this chapter, we will review some of the properties of optical waves propagating through an unbounded linear medium. We believe that this review will serve as an adequate foundation for the topics in nonlinear optics, to which the entire book is devoted. To this end, we enunciate Maxwell’s equations and derive the wave equation in a linear homogeneous isotropic medium. We define intrinsic impedance, the Poynting vector and irradiance, as well as introduce the concept of polarization. We then expose readers to concepts of plane-wave propagation through anisotropic media, introduce the index ellipsoid, and show an application of electro-optic materials. We also summarize concepts of Fresnel and Fraunhofer diffraction, starting from the paraxial wave equation, and examine the linear propagation of a Gaussian beam. Finally, we expose readers to the important topic of dispersion, which governs the spreading of pulses during propagation in a medium. More importantly, we show how by knowing the dispersion relation, one can deduce the underlying partial differential equation that needs to be solved to find the pulse shapes during propagation. We hope this chapter presents readers with most of the background material required for starting on the rigors of nonlinear optics, which will be formally introduced in Chap. 2. For further reading on related topics, the reader is referred to Cheng (1983), Banerjee and Poon (1991), Goodman (1996), Yariv (1997), and Poon and Banerjee (2001).