This chapter focuses on photonic analog of the spin-orbit coupling of electrons occurring inside a graded index medium. Section 9.1 describes two physical mechanisms that can produce changes in the state of polarization of an optical beam. The vectorial form of the wave equation is solved in Section 9.2 to introduce a path-dependent geometrical phase. The photonic analog of the spin-orbit coupling and its implications are also discussed in this section. Section 9.3 considers how the scalar LPlm modes change when the coupling term is taken into account. We treat this term first as a perturbation and then obtain the exact vector modes of a GRIN medium. A quantum approach is used in Section 9.4 to discuss various polarization-dependent effects.

We study further perturbations of the hydrogen atom due to both external and internal magnetic fields. The internal fields give rise to the fine structure of the hydrogen energy levels. The external fields give rise to the Zeeman effect. We also study internal perturbations due to relativistic effects, which are part of the fine structure.

Atoms were at the center of physicists’ interests in the 1920s. It was largely from the effort to understand atomic properties that modern quantum mechanics emerged in this decade. In the 1930s physicists’ concerns expanded to include the nature of atomic nuclei. The constituents of the nucleus were identified, and a start was made in learning what held them together. And as everyone knows, world history was changed in subsequent decades by the military application of nuclear physics.