Monochromatic Plane Waves and Scalar Helmholtz Equations

This lecture covers the theory of monochromatic plane waves in Cartesian coordinates, focusing on the solutions of the scalar Helmholtz equations. The instructor explains the decoupled nature of the equations and their application in electromagnetic wave analysis. Various exercises and examples are provided to illustrate the concepts, including amplitude polarization and vector analysis. The lecture emphasizes the mathematical formalism required to describe wave propagation in the absence of sources, with a particular focus on the Helmoltz equation. The session concludes with a discussion on the interpretation of solutions in the frequency domain and practical applications in wave sector analysis.