This chapter focuses on the impact of partial coherence on the propagation of optical beams inside a GRIN medium. Section 11.1 introduces the basic coherence-related concepts needed to understand the later material. Section 11.2 uses the evolution of cross-spectral density to study whether periodic self-imaging, an intrinsic property of a GRIN medium, is affected by partial coherence of an incoming beam. Section 11.3 employs the Gaussian-Schell model to discuss how the optical spectrum, the spectral intensity, and the degree of coherence associated with a Gaussian beam change with the beam’s propagation inside a GRIN medium. The focus of Section 11.4 is on Gaussian beams that are only partially polarized. The concept of the polarization matrix is used to study how the degree of polarization evolves when such a partially coherent Gaussian beam is transmitted through a GRIN medium

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.

Propagation of electromagnetic waves inside a GRIN medium is studied in this chapter. Section 2.1 starts with Maxwell’s equations and uses them to derive a wave equation in the frequency domain. A mode based technique is used in Section 2.2 for solving the wave equation for a GRIN device fabricated with a parabolic index profile. The properties of both the Hermite’Gauss and the Laguerre-Gauss modes are discussed. Section 2.3 is devoted to other power-law index profiles and employs the Wentzel-Kramers Brillouin method to discuss the properties of modes supported by them. We discuss in Section 2.4 the relative efficiency with which different modes are excited by an optical beam incident on a GRIN medium. The intermodal dispersive effects that become important for pulsed beams are also covered. Section 2.5 describes several non-modal techniques that can be used for studying wave propagation in GRIN media.

The focus of this chapter is on longitudinal variations of the refractive index and how such variations affect the propagation of light inside a GRIN medium. Section 7.1 describes the ray-optics and wave-optics techniques that can be used for this purpose. Section 7.2 focuses on tapered GRIN fibers and describes the impact of tapering on the periodic self-imaging for a few different tapering profiles. The analogy between a GRIN medium and a harmonic oscillator is exploited in Section 7.3 by employing several quantum-physics techniques for solving the GRIN problem. Section 7.4 is devoted to the case of periodic variations in the refractive index that are induced by changing the core’s radius of a GRIN fiber along its length in a periodic fashion.

The focus of this chapter is on focusing and self-imaging of optical beams occurring in a graded-index rod. Section 3.1 provides a geometrical-optics perspective and shows why optical rays follow a curved path inside a GRIN medium. The modes of such a medium are used in Section 3.2 to find a propagation kernel and use it discuss the phenomenon of self-imaging. Section 3.3 is devoted to studying how a GRIN rod can be used as a flat lens to focus an incoming optical beam. Imaging characteristics of such a lens are also considered in this section. Several important applications of GRIN devices are discussed in Section 3.4.

Considerable effort has been directed toward developing new types of artificial materials known now as photonic crystals and metamaterials. Even though the initial focus was not on creating a spatially varying refractive index, it was soon realized that such materials can be fabricated with an index gradient in one or more dimensions. In this chapter, we focus on the novel GRIN devices whose design is based on photonic crystals and metamaterials. Section 10.1 introduces the basic concepts needed to understand the physics behind these two types of materials. Section 10.2 is devoted to GRIN structures based on the concept of photonic crystals. Metamaterials designed with an index gradient are discussed in Section 10.3. The focus of Section 10.4 is on a subgroup of metamaterials, known as metasurfaces, which contain nanoscale objects made with dielectric or metallic materials and are thinner than the wavelength of radiation they are intended for.

The focus in this chapter is on intensity-dependent changes in the refractive index of a GRIN medium, responsible for the Kerr effect. In Section 5.1, we consider self-focusing of an optical beam inside a GRIN medium. Pulsed beams are considered in Section 5.2, where we derive a nonlinear propagation equation and discuss the phenomena of self- and cross-phase modulations. Section 5.3 is devoted to modulation instability and the formation of multimode solitons. Intermodal nonlinear effects are considered in Section 5.4 with emphasis on four-wave mixing and stimulated Raman scattering. Nonlinear applications discussed in Section 5.5 include supercontinuuum generation, spatial beam cleanup, and second harmonic generation.

In Part I we examined the form and function ofthe major families of power electronic converters.Our goal was to show how the intended powerconversion function is achieved in each case byappropriate configuration of the circuitcomponents and by proper operation of theswitches. Throughout those earlier chapters, ourconcern was with nominal operating conditions, that is,the ideal operating conditions in which aconverter is designed to perform its primaryconversion function. As nominal operation in mostpower electronic circuits involves a periodic steady state, wefocused on situations in which circuit operationand behavior are the same from cycle to cycle.

Power magnetics are often constrained by loss.Consequently, the ability to accurately predictthe loss of a magnetic component is extremelyvaluable for design. The techniques for modelingmagnetics loss introduced in the previous chaptersare useful, but do not adequately cover allsituations. In this chapter we introduce refinedmethods to predict winding and core losses inmagnetic components, with particular emphasis onfactors (such as proximity effect) that becomedominant at high frequencies and on cases wherethe waveforms are not purely dc or sinusoidal.

We add transformers to the topology of ahigh-frequency converter for three reasons: toprovide electrical isolation between two (or more)external systems; to reduce the component stressesthat result when the input/output conversion ratiois far from unity; and to create multiple relatedoutputs in a simple manner. (We showed therelationship between switch-stress factor and theconversion ratio in Fig. 5.26.) There are manyways in which we can include the transformer inthe topology of a dc/dc converter; we present anddiscuss some of them in this chapter.

Power electronic circuits change the characterof electrical energy: from dc or ac to ac or dc,from one voltage level or frequency to another, orin some other way. We refer to such circuitsgenerically as converters, staticconverters (because they contain nomoving parts), powerprocessors, or powerconditioners. The part of the system thatactually manipulates the flow of energy is thepower circuit. It isthe scaffold for the system’s other components,such as the control circuit or the thermalmanagement parts.

The rapid switching transitions of a powerconverter are potential sources of electromagneticinterference (EMI), both for the converter itselfand for the systems to which it is connected.Adequate filtering at the input and output of theconverter is important, both to obtain acceptableperformance and to prevent interference with otherequipment. In this chapter, we consider thesources of EMI in a converter, how EMI is measuredand modeled, and how it can be mitigated, with afocus on conducted (rather than radiated) EMI.

The previous chapters on magnetics provided thekey concepts needed to analyze, model, and designmagnetic components such as inductors andtransformers. The purpose of this chapter is torefine and extend the methods introduced there,with a focus on techniques for magnetic componentdesign. In particular, we introduce design methodsand sizing considerations for efficientlyconverging on an appropriate design. Thisincludes, for example, approximate methods forsizing the magnetic core for an inductor ortransformer, and metrics for comparing magneticmaterials.