Contemporary Optics

With the advent of lasers, numerous applications of it such as optical information processing, holography, and optical communication have evolved. These applications have made the study of optics essential for scientists and engineers. The present volume, intended for senior under­ graduate and first-year graduate students, introduces basic concepts neces­ sary for an understanding of many of these applications. The book has grown out of lectures given at the Master's level to students of applied optics at the Indian Institute of Technology, New Delhi. Chapters 1-3 deal with geometrical optics, where we develop the theory behind the tracing of rays and calculation of aberrations. The formulas for aberrations are derived from first principles. We use the method in­ volving Luneburg's treatment starting from Hamilton's equations since we believe that this method is easy to understand. Chapters 4--8 discuss the more important aspects of contemporary physical optics, namely, diffraction, coherence, Fourier optics, and holog­ raphy. The basis for discussion is the scalar wave equation. A number of applications of spatial frequency filtering and holography are also discussed. With the availability of high-power laser beams, a large number of nonlinear optical phenomena have been studied. Of the various nonlinear phenomena, the self-focusing (or defocusing) of light beams due to the nonlinear dependence of the dielectric constant on intensity has received considerable attention. In Chapter 9 we discuss in detail the steady-state self-focusing of light beams.

1. Paraxial Ray Optics.- 1.1. Introduction.- 1.2. Fermat’s Principle.- 1.3. Lagrangian Formulation.- 1.4 Hamiltonian Formulation.- 1.5. Application of the Hamiltonian Formulation to the Study of Paraxial Lens Optics.- 1.5.1. A Single Refracting Surface.- 1.5.2. Thin Lens.- 1.5.3. Thick Lens.- 1.6. Eikonal Approximation.- 1.6.1. Derivation of the Eikonal Equation.- 1.6.2. The Eikonal Equation and Fermat’s Principle.- 1.7. Wave Optics as Quantized Geometrical Optics.- 2. Geometrical Theory of Third-Order Aberrations.- 2.1. Introduction.- 2.2. Expressions for Third-Order Aberrations.- 2.3. Physical Significance of the Coefficients A, B, C, D, and E.- 2.3.1. Spherical Aberration.- 2.3.2. Coma.- 2.3.3. Astigmatism and Curvature of Field.- 2.3.4. Distortion.- 2.4. The Coefficients Hij in Terms of Refractive-Index Variation.- 2.5. Aberrations of Graded-Index Media.- 2.6. Aberrations in Systems Possessing Finite Discontinuities in Refractive Index.- 2.6.1. A Plane Glass Surface.- 2.6.2. Aberration of a Thin Lens.- 2.7. Chromatic Aberration.- 3. Characteristic Functions.- 3.1. Introduction.- 3.2. Point Characteristic function.- 3.2.1. Definition and Properties.- 3.2.2. Abbe Sine Condition.- 3.3. Mixed Characteristic function.- 3.3.1. Definition and Properties.- 3.3.2. Third-Order Aberration of Rotationally Symmetric Systems.- 3.4. Angle Characteristic function.- 3.5. Explicit Evaluation of Characteristic Functions.- 3.5.1. Mixed Characteristic Function for a Plane Surface of Refraction.- 3.5.2. Angle Characteristic of a Spherical Surface of Refraction.- 4. Diffraction.- 4.1. Introduction.- 4.2. The Spherical Wave.- 4.3. Integral Theorem of Helmholtz and Kirchhoff.- 4.4. The Fresnel-Kirchhoff Diffraction Formula.- 4.5. Fraunhofer and Fresnel Diffraction.- 4.6. Fraunhofer Diffraction by a Rectangular Aperture.- 4.7. Fraunhofer Diffraction by a Circular Aperture.- 4.8. Distribution of Intensity in the Airy Pattern.- 4.9. Fresnel Diffraction by a Circular Aperture.- 4.10. Fresnel Diffraction by a Single Slit.- 4.11. Diffraction of Waves Having Amplitude Distribution along the Wavefront.- 4.12. Babinet’s Principle.- 4.13. Periodic Apertures.- 4.14. Intensity Distribution near the Focal Plane.- 4.15. Optical Resonators.- 5. Partially Coherent Light.- 5.1. Introduction.- 5.2. Complex Representation.- 5.3. Mutual Coherence Function and Degree of Coherence.- 5.4. Quasi-Monochromatic Sources.- 5.5. Van Cittert-Zernike Theorem.- 5.6. Differential Equations Satisfied by ?12(?).- 5.7. Partial Polarization.- 5.7.1. The Coherency Matrix.- 5.7.2. Degree of Polarization.- 5.7.3. Measurement of the Elements of J.- 5.7.4. Optical Devices.- 6. Fourier Optics I. Spatial Frequency Filtering.- 6.1. Introduction.- 6.2. Fraunhofer and Fresnel Diffraction Approximations.- 6.3. Effect of a Thin Lens on an Incident Field Distribution.- 6.4. Lens as a Fourier-Transforming element.- 6.5. Spatial Frequency Filtering and Its Applications.- 6.5.1. Phase Contrast Microscopy.- 6.5.2. Cross-Correlation.- 6.5.3. Character Recognition.- 6.5.4. Multichannel Operation.- 6.5.5. Matrix Multiplication.- 7. Fourier Optics II. Optical Transfer Functions.- 7.1. Introduction.- 7.2. The Point-Spread function.- 7.3. Point-Spread Function of a Thin Lens.- 7.4. Frequency Analysis.- 7.5. Coherence and Resolution.- 8. Holography.- 8.1. Introduction.- 8.2. The Underlying Principle.- 8.3. Interference between Two Plane Waves.- 8.4. Point Source Holograms.- 8.5. Diffuse Illumination of the Object.- 8.6. Fourier Transform Holograms.- 8.6.1. Resolution in Fresnel and Fourier Transform Holograms.- 8.6.2. Lensless Fourier Transform Holograms.- 8.7. Volume Holograms.- 8.8. Applications of Holography.- 8.8.1. Three-Dimensional Reconstruction.- 8.8.2. Interferometry.- 8.8.3. Microscopy.- 8.8.4. Imaging through Aberrating Media.- 9. Self-Focusing.- 9.1. Introduction.- 9.2. Elementary Theory of Self-Focusing.- 9.3. More Rigorous Theory for Self-Focusing.- 9.4. Thermal Self-Focusing/Defocusing of Laser Beams.- 9.5. Solution of the Scalar Wave Equation with Weak Nonlinearity.- 9.6. General Problems on the Calculation of the Nonlinear Dielectric Constant.- 10. Graded-Index Waveguides.- 10.1. Introduction.- 10.2. Modal Analysis.- 10.3. Propagation through a Selfoc Fiber.- 10.3.1. Propagation of a Gaussian Beam Launched Symmetrically about the Axis.- 10.3.2. Propagation of a Gaussian Beam Launched at an Off-Axis Point Parallel to the Axis.- 10.4. Pulse Propagation.- 10.5. Fabrication.- 11. Evanescent Waves and the Goos-Hänchen Effect.- 11.1. Introduction.- 11.2. Existence of Evanescent Waves.- 11.3. Total Internal Reflection of a Bounded Beam.- 11.4. Physical Understanding of the Goos-Hänchen Shift.- 11.5. The Goos-Hänchen Effect in a Planar Waveguide.- 11.6. Prism-Film Coupler.- Appendix A. The Dirac Delta Function.- B. The Fourier Transform.- C. Solution of Equation (10.2–12).- References.