The paper by Yeh, Yariv, and Hong presents a comprehensive theory for the propagation of electromagnetic radiation in periodically stratified media, including finite, semi-infinite, and infinite media. The authors use the diagonalization of the unit cell translation operator to derive exact solutions for Bloch waves, dispersion relations, and band structures. They introduce new phenomena with applications in integrated optics and laser technology, such as Bragg waveguides, birefringence, phase matching, and optical surface waves. The theory is formally similar to the quantum theory of electrons in crystals, utilizing concepts like Bloch modes, forbidden gaps, evanescent waves, and surface waves. The paper also discusses the reflectivity of multilayer films, the dispersion relation between frequency and wavevector, and the behavior of electromagnetic waves in periodic media with alternating gain and loss. The authors provide analytic expressions for reflectivity, mode dispersion relations, and field distributions in various types of waveguides, including symmetric and asymmetric multichannel waveguides. They also explore the existence of electromagnetic surface waves guided by the boundary of a semi-infinite periodic multilayer dielectric medium. The paper concludes with a discussion of the analogies between the optics of periodic layered media and solid-state physics, highlighting the potential for further applications in phase matching and electro-optical modulation.The paper by Yeh, Yariv, and Hong presents a comprehensive theory for the propagation of electromagnetic radiation in periodically stratified media, including finite, semi-infinite, and infinite media. The authors use the diagonalization of the unit cell translation operator to derive exact solutions for Bloch waves, dispersion relations, and band structures. They introduce new phenomena with applications in integrated optics and laser technology, such as Bragg waveguides, birefringence, phase matching, and optical surface waves. The theory is formally similar to the quantum theory of electrons in crystals, utilizing concepts like Bloch modes, forbidden gaps, evanescent waves, and surface waves. The paper also discusses the reflectivity of multilayer films, the dispersion relation between frequency and wavevector, and the behavior of electromagnetic waves in periodic media with alternating gain and loss. The authors provide analytic expressions for reflectivity, mode dispersion relations, and field distributions in various types of waveguides, including symmetric and asymmetric multichannel waveguides. They also explore the existence of electromagnetic surface waves guided by the boundary of a semi-infinite periodic multilayer dielectric medium. The paper concludes with a discussion of the analogies between the optics of periodic layered media and solid-state physics, highlighting the potential for further applications in phase matching and electro-optical modulation.