Optics

Cover Page
ABOUT THE AUTHOR
Title Page
Copyright Page
Preface
CONTENTS
Part
1. History of Optics
References
2. What Is Light?
2.1 Introduction
2.2 The Corpuscular Model
2.3 The Wave Model
2.4 The Particle Nature of Radiation
2.5 Wave Nature of Matter
2.6 The Uncertainty Principle
2.7 The Single-Slit Diffraction Experiment
2.8 The Probabilistic Interpretation of Matter Waves
2.9 An Understanding of Interference Experiments
2.10 The Polarization of a Photon
2.11 The Time-Energy Uncertainty Relation
Summary
Problems
Solutions
References and Suggested Readings
Part 1 Geometrical Optics
3. Fermat’s Principle and Its Applications
3.1 Introduction
3.2 Laws of Reflection and Refraction from Fermat’s Principle
3.3 Ray Paths in an Inhomogeneous Medium
3.4 The Ray Equation and its Solutions
3.5 Refraction of Rays at the Interface between an Isotropic Medium and an Anisotropic Medium
Summary
Problems
References and Suggested Readings
4. Refraction and Reflection by Spherical Surfaces
4.1 Introduction
4.2 Refraction at a Single Spherical Surface
4.3 Reflection by a Single Spherical Surface
4.4 The Thin Lens
4.5 The Principal Foci and Focal Lengths of a Lens
4.6 The Newton Formula
4.7 Lateral Magnification
4.8 Aplanatic Points of a Sphere
4.9 The Cartesian Oval
4.10 Geometrical Proof for the Existence of Aplanatic Points
4.11 The Sine Condition
Summary
Problems
References and Suggested Readings
5. The Matrix Method in Paraxial Optics
5.1 Introduction
5.2 The Matrix Method
5.3 Unit Planes
5.4 Nodal Planes
5.5 A System of Two Thin Lenses
Summary
Problems
References and Suggested Readings
6. Aberrations
6.1 Introduction
6.2 Chromatic Aberration
6.3 Monochromatic Aberrations
Summary
Problems
References and Suggested Readings
Part 2 Vibrations and Waves
7. Simple Harmonic Motion, Forced Vibrations, and Origin of Refractive Index
7.1 Introduction
7.2 Simple Harmonic Motion
7.3 Damped Simple Harmonic Motion
7.4 Forced Vibrations
7.5 Origin of Refractive Index
7.6 Rayleigh Scattering
Summary
Problems
References and Suggested Readings
8. Fourier Series and Applications
8.1 Introduction
8.2 Transverse Vibrations of a Plucked String
8.3 Application of Fourier Series in Forced Vibrations
8.4 The Fourier Integral
Summary
Problems
References and Suggested Readings
9. The Dirac Delta Function and Fourier Transforms
9.1 Introduction
9.2 Representations of the Dirac Delta Function
9.3 Integral Representation of the Delta Function
9.4 Delta Function as a Distribution
9.5 Fourier Integral Theorem
9.6 The Two- and Three-Dimensional Fourier Transform
Summary
Problems
10. Group Velocity and Pulse Dispersion
10.1 Introduction
10.2 Group Velocity
10.3 Group Velocity of a Wave Packet
10.4 Self Phase Modulation
Summary
Problems
References and Suggested Readings
11. Wave Propagation and the Wave Equation
11.1 Introduction
11.2 Sinusoidal Waves: Concept of Frequency and Wavelength
11.3 Types of Waves
11.4 Energy Transport in Wave Motion
11.5 The One-Dimensional Wave Equation
11.6 Transverse Vibrations of a Stretched String
11.7 Longitudinal Sound Waves in a Solid
11.8 Longitudinal Waves in a Gas
11.9 The General Solution of the One-Dimensional Wave Equation
Summary
Problems
References and Suggested Readings
12. Huygens’ Principle and Its Applications
12.1 Introduction
12.2 Huygens’ Theory
12.3 Rectilinear Propagation
12.4 Application of Huygens’ Principle to Study Refraction and Reflection
Summary
Problems
References and Suggested Readings
Part 3 Interference
13. Superposition of Waves
13.1 Introduction
13.2 Stationary Waves on a String
13.3 Stationary Waves on a String Whose Ends are Fixed
13.4 Stationary Light Waves: Ives’ and Wiener’s Experiments
13.5 Superposition of Two Sinusoidal Waves
13.6 The Graphical Method for Studying Superposition of Sinusoidal Waves
13.7 The Complex Representation
Summary
Problems
References and Suggested Readings
14. Two-Beam Interference by Division of Wave Front
14.1 Introduction
14.2 Interference Pattern Produced on the Surface of Water
14.3 Coherence
14.4 Interference of Light Waves
14.5 The Interference Pattern
14.6 The Intensity Distribution
14.7 Fresnel’s Two-Mirror Arrangement
14.8 Fresnel Biprism
14.9 Interference with White Light
14.10 Displacement of Fringes
14.11 Lloyd’s Mirror Arrangement
14.12 Phase Change on Reflection
Summary
Problems
References and Suggested Readings
15. Interference by Division of Amplitude
15.1 Introduction
15.2 Interference by a Plane Parallel Film When Illuminated by a Plane Wave
15.3 The Cosine Law
15.4 Nonreflecting Films
15.5 High Reflectivity by Thin Film Deposition
15.6 Reflection by a Periodic Structure
15.7 Interference by a Plane Parallel Film When Illuminated by a Point Source
15.8 Interference by a Film with Two Nonparallel Reflecting Surfaces
15.9 Colors of Thin Films
15.10 Newton’s Rings
15.11 The Michelson Interferometer
Summary
Problems
References and Suggested Readings
16. Multiple-Beam Interferometry
16.1 Introduction
16.2 Multiple Reflections from a Plane Parallel Film
16.3 The Fabry–Perot Etalon
16.4 The Fabry–Perot Interferometer
16.5 Resolving Power
16.6 The Lummer–Gehrcke Plate
16.7 Interference Filters
Summary
Problems
References and Suggested Readings
17. Coherence
17.1 Introduction
17.2 The Line Width
17.3 The Spatial Coherence
17.4 Michelson Stellar Interferometer
17.5 Optical Beats
17.6 Coherence Time and Line Width via Fourier Analysis
17.7 Complex Degree of Coherence and Fringe Visibility in Young’s Double-Hole Experiment
17.8 Fourier Transform Spectroscopy
Summary
Problems
References and Suggested Readings
Part 4 Diffraction
18. Fraunhofer Diffraction I
18.1 Introduction
18.2 Single-Slit Diffraction Pattern
18.3 Diffraction by a Circular Aperture
18.4 Directionality of Laser Beams
18.5 Limit of Resolution
18.6 Two-Slit Fraunhofer Diffraction Pattern
18.7 N-Slit Fraunhofer Diffraction Pattern
18.8 The Diffraction Grating
18.9 Oblique Incidence
18.10 X-ray Diffraction
18.11 The Self-Focusing Phenomenon
18.12 Optical Media Technology—An Essay
Summary
Problems
References and Suggested Readings
19. Fraunhofer Diffraction II and Fourier Optics
19.1 Introduction
19.2 The Fresnel Diffraction Integral
19.3 Uniform Amplitude and Phase Distribution
19.4 The Fraunhofer Approximation
19.5 Fraunhofer Diffraction by a Long Narrow Slit
19.6 Fraunhofer Diffraction by a Rectangular Aperture
19.7 Fraunhofer Diffraction by a Circular Aperture
19.8 Array of Identical Apertures
19.9 Spatial Frequency Filtering
19.10 The Fourier Transforming Property of a Thin Lens
Summary
Problems
References and Suggested Readings
20. Fresnel Diffraction
20.1 Introduction
20.2 Fresnel Half-Period Zones
20.3 The Zone Plate
20.4 Fresnel Diffraction—A More Rigorous Approach
20.5 Gaussian Beam Propagation
20.6 Diffraction by a Straight edge
20.7 Diffraction of a Plane Wave by a Long Narrow Slit and Transition to the Fraunhofer Region
Summary
Problems
References and Suggested Readings
21. Holography
21.1 Introduction
21.2 Theory
21.3 Requirements
21.4 Some Applications
Summary
Problems
References and Suggested Readings
Part 5 Electromagnetic Character of Light
22. Polarization and Double Refraction
22.1 Introduction
22.2 Production of Polarized Light
22.3 Malus’ Law
22.4 Superposition of Two Disturbances
22.5 The Phenomenon of Double Refraction
22.6 Interference of Polarized Light: Quarter Wave Plates and Half Wave Plates
22.7 Analysis of Polarized Light
22.8 Optical Activity
22.9 Change in the SOP (State of Polarization) of a Light Beam Propagating Through an Elliptic Core Single-Mode Optical Fiber
22.10 Wollaston Prism
22.11 Rochon Prism
22.12 Plane Wave Propagation in Anisotropic Media
22.13 Ray Velocity and Ray Refractive Index
22.14 Jones’ Calculus
22.15 Faraday Rotation
22.16 Theory of Optical Activity
Summary
Problems
References and Suggested Readings
23. Electromagnetic Waves
23.1 Maxwell’s Equations
23.2 Plane Waves in a Dielectric
23.3 The Three-Dimensional Wave Equation in a Dielectric
23.4 The Poynting Vector
23.5 Energy Density and Intensity of an Electromagnetic Wave
23.6 Radiation Pressure
23.7 The Wave Equation in a Conducting Medium
23.8 The Continuity Conditions
23.9 Physical Significance of Maxwell’s Equations
Summary
Problems
References and Suggested Readings
24. Reflection and Refraction of Electromagnetic Waves
24.1 Introduction
24.2 Reflection and Defraction at an Interface of Two Dielectrics
24.3 Reflection by a Conducting Medium
24.4 Reflectivity of a Dielectric Film
Summary
Problems
References and Suggested Readings
Part 6 Photons
25. The Particle Nature of Radiation
25.1 Introduction
25.2 The Photoelectric Effect
25.3 The Compton Effect
25.4 The Photon Mass
25.5 Angular Momentum of a Photon
Summary
Problems
References and Suggested Readings
Part 7 Lasers and Fiber Optics
26. Lasers: An Introduction
26.1 Introduction
26.2 The Fiber Laser
26.3 The Ruby Laser
26.4 The He-Ne Laser
26.5 Optical Resonators
26.6 Einstein Coefficients and Optical Amplification
26.7 The Line Shape Function
26.8 Typical Parameters for a Ruby Laser
26.9 Monochromaticity of the Laser Beam
26.10 Raman Amplification and Raman Laser
Summary
Problems
References and Suggested Readings
27. Optical Waveguides I: Optical Fiber Basics Using Ray Optics
27.1 Introduction
27.2 Some Historical Remarks
27.3 Total Internal Reflection
27.4 The Optical Fiber
27.5 Why Glass Fibers?
27.6 The Coherent Bundle
27.7 The Numerical Aperture
27.8 Attenuation in Optical Fibers
27.9 Multimode Fibers
27.10 Pulse Dispersion in Multimode Optical Fibers
27.11 Dispersion and Maximum Bit Rates
27.12 General Expression for Ray Dispersion Corresponding to a Power Law Profile
27.13 Plastic Optical Fibers
27.14 Fiber-Optic Sensors
Problems
References and Suggested Readings
28. Optical Waveguides II: Basic Waveguide Theory and Concept of Modes
28.1 Introduction
28.2 TE Modes of a Symmetric Step Index Planar Waveguide
28.3 Physical Understanding of Modes
28.4 TM Modes of a Symmetric Step Index Planar Waveguide
28.5 TE Modes of a Parabolic Index Planar Waveguide
28.6 Waveguide Theory and Quantum Mechanics
Problems
References and Suggested Readings
29. Optical Waveguides III: Single-Mode Fibers
29.1 Introduction
29.2 Basic Equations
29.3 Guided Modes of a Step Index Fiber
29.4 Single-Mode Fiber
29.5 Pulse Dispersion in Single-Mode Fibers
29.6 Dispersion Compensating Fibers
Problems
References and Suggested Readings
Part 8 Special Theory of Relativity
30. Special Theory of Relativity I: Time Dilation and Length Contraction
30.1 Introduction
30.2 Speed of Light for a Moving Source
30.3 Time Dilation
30.4 The Mu Meson Experiment
30.5 The Length Contraction
30.6 Understanding the Mu Meson Experiment via Length Contraction
30.7 Length Contraction of a Moving Train
30.8 Simultaneity of Two Events
30.9 The Twin Paradox
30.10 The Michelson–Morley Experiment
30.11 Brief Historical Remarks
Problems
References and Suggested Readings
31. Special Theory of Relativity II: Mass-Energy Relationship and Lorentz Transformations
31.1 Introduction
31.2 The Mass-Energy Relationship
31.3 The Doppler Shift
31.4 The Lorentz Transformation
31.5 Addition of Velocities
References and Suggested Readings
Appendix A: Gamma Functions and Integrals Involving Gaussian Functions
Appendix B: Evaluation of the Integral
Appendix C: The Reflectivity of a Fiber Bragg Grating
Appendix D: Diffraction of a Gaussian Beam
Appendix E: TE and TM Modes in Planar Waveguides
Appendix F: Solution for the Parabolic Index Waveguide
Appendix G: Invariance of the Wave Equation Under Lorentz Transformation
Name Index
Subject Index