In Chapter 1, we reviewed important concepts in scalar diffraction theory and statistical optics. While incredibly insightful and an accurate approximation (in many practical scenarios), scalar statistical optics misses important physical phenomena, such as partial polarization and coherence-induced polarization changes. Here, we generalize the scalar concepts discussed in Chapter 1 to account for light being an electromagnetic wave. Following the outline of Chapter 1, we begin with a brief review of electromagnetic diffraction theory. Using the electromagnetic form of the plane wave spectrum, we derive the Rayleigh–Sommerfeld electromagnetic diffraction integrals for both the electric and magnetic fields. We discuss the paraxial near-field and non-paraxial far-field approximations to these integrals and their affect on polarization. Moving away from diffraction, we conclude the section by examining polarization in a more general context. We review the polarization ellipse, Jones vectors and matrices, Stokes parameters, Mueller matrices, and finally, the Poincaré sphere, as these concepts will be useful in our subsequent analyses of random electromagnetic beams. |
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