Basic Optics

Principles and Concepts
 
 
Elsevier (Verlag)
  • 1. Auflage
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  • erschienen am 29. August 2016
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  • 1010 Seiten
 
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978-0-12-809307-8 (ISBN)
 

Basic Optics: Principles and Concepts addresses in great details the basic principles of the science of optics, and their related concepts. The book provides a lucid and coherent presentation of an extensive range of concepts from the field of optics, which is of central relevance to several broad areas of science including physics, chemistry, and biology.

With its extensive range of discourse, the book's content arms scientists and students with knowledge of the essential concepts of classical and modern optics. It can be used as a reference book and also as a supplementary text by students at the college and university levels and will, at the same time, be of considerable use to researchers and teachers.

The book is composed of nine chapters and includes a great deal of material not covered in many of the more well-known textbooks on the subject. The science of optics has undergone major changes in the last fifty years due to developments in the areas of the optics of metamaterials, Fourier optics, statistical optics, quantum optics, and nonlinear optics, all of which find their places in the book, with a clear presentation of their basic principles. Even the more traditional areas of ray optics and wave optics are elaborated within the framework of electromagnetic theory, at a level more fundamental than what one finds in many of the currently available textbooks. Thus, the eikonal approximation leading to ray optics, the Lagrangian and Hamiltonian formulations of ray optics, the quantum theoretic interpretation of interference, the vector and dyadic diffraction theories, the geometrical theory of diffraction, and similar other topics of basic relevance are presented in clear terms.

The presentation is lucid and elegant, capturing the essential magic and charm of physics.

All this taken together makes the book a unique text, of major contemporary relevance, in the field of optics.

Avijit Lahiri is a well known researcher, teacher, and author, with publications in several areas of physics, and with a broad range of current interests including physics and the philosophy of science.


  • Provides extensive and thoroughly exhaustive coverage of classical and modern optics
  • Offers a lucid presentation in understandable language, rendering the abstract and difficult concepts of physics in an easy, accessible way
  • Develops all concepts from elementary levels to advanced stages
  • Includes a sequential description of all needed mathematical tools
  • Relates fundamental concepts to areas of current research interest


Professor Avijit Lahiri obtained his Ph.D. from Calcutta University in 1975. He was engaged in teaching physics and research over a long period of 36 years. He published work in several areas of theoretical physics in international peer reviewed journals, including those published by Elsevier. He lectured widely on numerous topics in physics and mathematics, both to a general audience and to specialists. For the last fifteen years he devoted himself to book writing and authored five books.
  • Englisch
  • Saint Louis
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  • USA
Elsevier Science
  • 19,87 MB
978-0-12-809307-8 (9780128093078)
0128093072 (0128093072)
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  • Front Cover
  • Basic Optics: Principles and Concepts
  • Copyright
  • Dedication
  • Contents
  • Acknowledgments
  • Chapter 1: Electromagnetic Theory and Optics
  • 1.1 Introduction
  • 1.2 Maxwell's Equations in Material Media and in Free Space
  • 1.2.1 Electromagnetic Field Variables
  • 1.2.1.1 Digression: The naming of the field variables
  • 1.2.1.2 Digression: The naming of the field variables and their space-time variations in optics
  • 1.2.2 Maxwell's Equations
  • 1.2.3 Material Media and the Constitutive Relations
  • 1.2.3.1 Linear media
  • Digression: tensors and tensor fields
  • 1.2.3.2 Nonlinear media
  • 1.2.4 Integral Form of Maxwell's Equations
  • 1.2.5 Boundary Conditions Across a Surface
  • 1.2.6 The Electromagnetic Field in Free Space
  • 1.2.7 Microscopic and Macroscopic Variables for a Material Medium
  • 1.3 Digression: Vector Differential Operators
  • 1.3.1 Curvilinear Coordinates
  • 1.3.2 The Differential Operators
  • 1.4 Electromagnetic Potentials
  • 1.4.1 Gauge Transformations
  • 1.4.2 The Lorentz Gauge and the Inhomogeneous Wave Equation
  • 1.4.3 The Homogeneous Wave Equation in a Source-Free Region
  • 1.5 The Hertz Vector Representation
  • 1.6 The Principle of Superposition
  • 1.7 The Complex Representation
  • 1.8 Energy Density and Energy Flux
  • 1.8.1 Energy Density
  • 1.8.2 Poynting's Theorem: The Poynting Vector
  • 1.8.3 Intensity at a Point
  • 1.9 Optical Fields: An Overview
  • 1.10 The Uniqueness Theorem
  • 1.11 Simple Solutions to Maxwell's Equations
  • 1.11.1 Overview
  • 1.11.2 Harmonic Time Dependence
  • 1.11.2.1 Fictitious magnetic charges and currents
  • 1.11.2.2 The Helmholtz equations
  • 1.12 The Monochromatic Plane Wave
  • 1.12.1 Monochromatic Plane Waves in Free Space
  • 1.12.2 Plane Waves in an Isotropic Dielectric
  • 1.12.3 Energy Density and Intensity for a Monochromatic Plane Wave
  • 1.13 States of Polarization of a Plane Wave
  • 1.13.1 Linear, Circular, and Elliptic Polarization
  • 1.13.2 States of Polarization: Summary
  • 1.13.3 Intensity of a Polarized Plane Wave
  • 1.13.4 Polarized and Unpolarized Waves
  • 1.14 Reflection and Refraction at a Planar Interface
  • 1.14.1 The Fields and the Boundary Conditions
  • 1.14.2 The Laws of Reflection and Refraction
  • 1.14.3 The Fresnel Formulae
  • 1.14.3.1 Setting up the problem
  • 1.14.3.2 Perpendicular polarization
  • Phase change in reflection
  • 1.14.3.3 Parallel polarization: Brewster's angle
  • Brewster's angle
  • Parallel polarization: Phase change on reflection
  • The case of normal incidence
  • 1.15 Total Internal Reflection
  • 1.16 Plane Waves: Significance in Electromagnetic Theory and Optics
  • 1.17 Electromagnetic Waves in Dispersive Media
  • 1.17.1 Susceptibility and Refractive Index in an Isotropic Dielectric
  • 1.17.1.1 Introduction: The context
  • 1.17.1.2 Dispersion: The basic equations
  • 1.17.2 Dispersion: Further Considerations
  • 1.17.2.1 The local field: Clausius-Mossotti relation
  • 1.17.2.2 Dispersion: The general formula
  • 1.17.2.3 The distribution of resonant frequencies
  • 1.17.2.4 Types of microscopic response
  • 1.17.2.5 The quantum theory of atomic susceptibilities
  • 1.17.2.6 Low-frequency and high-frequency limits in dispersion
  • 1.17.2.7 Wave propagation in conducting media
  • 1.17.2.8 Dispersion as coherent scattering
  • 1.17.2.9 Dispersion and absorption: A consequence of causality
  • 1.17.2.10 Magnetic permeability: Absence of dispersion
  • 1.17.2.11 Dispersion and absorption in water
  • 1.17.2.12 Negative refractive index
  • 1.17.3 Conducting Media: Absorption and Reflection
  • 1.17.3.1 Absorption in a conducting medium
  • 1.17.3.2 Reflection from the surface of a conductor
  • 1.17.4 Group Velocity
  • Digression: Frequency as a function of the wave vector for isotropic and anisotropic media
  • 1.17.5 Energy Density in a Dispersive Medium
  • 1.17.6 Group Velocity and Velocity of Energy Propagation
  • 1.17.7 Group Velocity, Signal Velocity, and Causality
  • 1.17.7.1 Introduction
  • 1.17.7.2 Velocity of energy propagation and ray velocity
  • 1.17.7.3 Wave propagation: The work of Sommerfeld and Brillouin
  • 1.17.7.4 Superluminal group velocity: Defining the signal velocity
  • 1.18 Stationary Waves
  • 1.19 Spherical Waves
  • 1.19.1 The Scalar Wave Equation and Its Spherical Wave Solutions
  • 1.19.2 Vector Spherical Waves
  • 1.19.3 Electric and Magnetic Dipole Fields
  • 1.19.3.1 The field of an oscillating electric dipole
  • 1.19.3.2 The oscillating magnetic dipole
  • 1.19.3.3 The dipole field produced by a pinhole
  • 1.20 Cylindrical Waves
  • 1.20.1 Cylindrical Wave Solutions of the Scalar Wave Equation
  • 1.20.2 Vector Cylindrical Waves
  • 1.20.2.1 Cylindrical waves produced by narrow slits
  • 1.21 Wave Propagation in Anisotropic Media
  • 1.21.1 Introduction
  • 1.21.2 Propagation of a Plane Wave: The Basics
  • 1.21.3 The Phase Velocity Surface
  • 1.21.4 The Ray Velocity Surface
  • 1.21.5 The Wave Vector and the Ray Vector
  • 1.21.6 Polarization of the Field Vectors
  • 1.21.7 The Two Ellipsoids
  • 1.21.7.1 The index ellipsoid
  • 1.21.7.2 The ray ellipsoid
  • 1.21.8 Uniaxial and Biaxial Media
  • 1.21.9 Propagation in a Uniaxial Medium
  • 1.21.10 Double Refraction
  • 1.22 Wave Propagation in Metamaterials
  • 1.22.1 Electric and Magnetic Response in Dielectrics and Conductors
  • 1.22.2 Response in Metamaterials
  • 1.22.3 `Left-Handed' Metamaterials and Negative Refractive Index
  • 1.22.4 Negative Refractive Index: General Criteria
  • 1.22.5 Metamaterials in Optics and in Electromagnetic Phenomena
  • 1.22.6 Transformation Optics: The Basic Idea
  • 1.23 Coherent and Incoherent Waves
  • Chapter 2: Foundations of Ray Optics
  • 2.1 Introduction
  • 2.2 The Eikonal Approximation
  • 2.2.1 The Eikonal Function
  • 2.2.2 The Eikonal Equation
  • 2.2.3 The Field Vectors e and h
  • 2.2.4 Energy Density and the Poynting Vector
  • 2.2.4.1 The energy density
  • 2.2.4.2 Eikonal approximation as a local plane wave description
  • 2.2.4.3 Spherical and cylindrical dipole fields
  • 2.2.4.4 The Poynting vector and intensity
  • 2.2.5 The Geometrical Wavefront and the Ray Path
  • 2.2.6 Intensity and Its Variation Along a Ray Path
  • 2.2.7 Optical Path Length
  • 2.2.7.1 Optical path length along an arbitrary path
  • 2.2.7.2 The optical path length along a ray path
  • 2.2.7.3 Path length and phase difference
  • 2.2.7.4 The scalar approach: Phase difference and optical path length
  • 2.2.8 The Transport of Field Vectors Along a Ray Path
  • 2.2.9 The Laws of Reflection and Refraction
  • 2.2.10 The Fresnel Formulae for Reflection and Refraction
  • 2.2.11 Reflection and Refraction: A Digression
  • 2.2.12 The Eikonal Approximation: Summary
  • 2.3 Characterizing the Ray Paths: Fermat's Principle
  • 2.3.1 Introduction
  • 2.3.2 Digression: Basic Ideas in the Calculus of Variations
  • 2.3.2.1 Integrals along a path and their variation
  • 2.3.2.2 Parameterization of varied paths
  • 2.3.2.3 First-order and higher-order variations in I
  • 2.3.2.4 Euler equations in the calculus of variations
  • 2.3.3 The Ray Equation and Fermat's Principle
  • 2.3.4 Digression: The Lagrangian and Hamiltonian Formulations
  • 2.3.5 Fermat's Principle and Ray Optics
  • 2.3.5.1 Fermat's principle and the laws of reflection and refraction
  • 2.3.5.2 Ray produced backward: Defining the optical path
  • 2.3.6 The Nature of Stationarity in Fermat's Principle
  • 2.3.6.1 Stationarity related to signs of a set of eigenvalues
  • 2.3.6.2 Transitions in the nature of stationarity
  • 2.3.6.3 Transitions in the nature of stationarity: Example
  • 2.3.7 Families of Ray Paths: Caustics and Conjugate Points
  • 2.3.8 Caustics and Conjugate Points: Examples
  • 2.3.8.1 The spherical mirror: Equation of the caustic
  • 2.3.8.2 Refraction at a planar surface
  • 2.3.8.3 Reflection at a planar surface
  • 2.3.9 Fermat's Principle and the Path Integral
  • 2.3.9.1 The path integral in quantum theory
  • 2.3.9.2 Path integral and geometrical optics
  • 2.3.9.3 Fermat's principle, diffraction, and the path integral
  • 2.4 Geometrical Optics: The Luneburg-Kline Approach
  • 2.5 Principles of Ray Optics: An Overview
  • Chapter 3: Ray Optics: Optical Systems and Optical Imaging
  • 3.1 Introduction
  • 3.2 Gaussian Optics
  • 3.2.1 Gaussian Optics: Introduction
  • 3.2.2 Sign Convention in Ray Optics
  • 3.2.3 The Ray Coordinates
  • 3.2.3.1 Meridional and skew rays
  • 3.2.3.2 Reduced angles and distances: The ray coordinates
  • 3.2.4 Transfer Matrices
  • 3.2.4.1 The translation matrix
  • 3.2.4.2 The refraction and reflection matrices
  • 3.2.5 The System Matrix
  • 3.2.6 Condition for Image Formation: The Conjugation Matrix
  • 3.2.6.1 Real and virtual images
  • 3.2.6.2 The condition for image formation
  • 3.2.6.3 Succession of intermediate images
  • 3.2.7 Transverse and Angular Magnifications
  • 3.2.7.1 The transverse magnification
  • 3.2.7.2 The angular magnification
  • 3.2.7.3 The Lagrange invariant
  • 3.2.8 The Cardinal Points
  • 3.2.8.1 The principal planes
  • 3.2.8.2 The focal planes
  • 3.2.8.3 The nodal points
  • 3.3 Gaussian Optics: Examples
  • 3.3.1 A Single Refracting Surface
  • 3.3.2 A Thin Lens
  • 3.3.3 A Thick Lens
  • 3.3.3.1 Thick lens: The general case
  • 3.3.3.2 A spherical lens
  • 3.3.4 A Combination of Two Thin Lenses
  • 3.4 Nonsymmetric Systems: Linear Optics
  • 3.4.1 Nonsymmetric Systems: Introduction
  • 3.4.2 Ray Coordinates and Transfer Matrices in Linear Optics
  • 3.4.3 Transfer Matrices of Linear Optics: The Symplectic Group
  • 3.4.4 The Restriction to Gaussian Optics
  • 3.5 Hamiltonian Optics: Introduction to Characteristic Functions
  • 3.5.1 Characteristic Functions: The Basic Idea
  • 3.5.2 The Point Characteristic and the Canonical Variables
  • 3.6 Image Formation by an Optical System
  • 3.6.1 Stigmatic Imaging: Maxwell's Theorem
  • 3.6.2 Perfect Imaging
  • 3.6.3 Maxwell's Fish-Eye
  • 3.6.4 Stigmatic Imaging of Points
  • 3.6.4.1 Off-axis points: Abbe's sine condition
  • 3.6.4.2 On-axis points: The Herschel condition
  • 3.6.5 Astigmatic Pencils of Rays: The Focal Lines
  • 3.7 Aberrations in Imaging Systems
  • 3.7.1 Types of Aberration
  • 3.7.2 Ray Aberration and Wave Aberration
  • 3.7.2.1 Aberration measures: Introduction
  • Digression: Entrance and exit pupils of an optical system
  • 3.7.2.2 Ray aberration
  • Digression: Summary of notation used
  • 3.7.2.3 Wave aberration
  • 3.7.2.4 Relating ray aberration to wave aberration
  • 3.7.2.5 The wave aberration function in the Seidel approximation
  • Digression-Longitudinal ray aberration: Light spot diagrams
  • 3.7.2.6 The effect of defocus on ray aberration measures
  • 3.7.3 The Seidel Aberrations
  • 3.7.3.1 Spherical aberration
  • 3.7.3.2 Coma
  • 3.7.3.3 Astigmatism
  • 3.7.3.4 Field curvature
  • 3.7.3.5 Distortion
  • 3.7.4 Calculating the Seidel Coefficients
  • 3.7.4.1 The general approach
  • 3.7.4.2 The Seidel sums of a thin lens
  • Pupil at lens position
  • Pupil positioned away from the lens
  • 3.7.5 Chromatic Aberration
  • 3.7.5.1 The dispersive power
  • 3.7.5.2 The achromatic doublet
  • 3.7.5.3 The secondary spectrum
  • 3.7.5.4 Longitudinal and lateral chromatic aberration
  • 3.7.5.5 Chromatic aberration measures for a thin lens
  • 3.7.6 Lens Combinations: Reduction of Aberrations
  • 3.7.7 Aberrations and Diffraction
  • 3.8 Optical Instruments
  • 3.8.1 Introducing a Number of Commonly Used Terms
  • 3.8.1.1 Object space, image space
  • 3.8.1.2 Entrance pupil, exit pupil, aperture
  • 3.8.1.3 Vignetting
  • 3.8.1.4 Principal ray
  • 3.8.1.5 Entrance window, exit window, field of view
  • 3.8.2 Eyepieces
  • 3.8.3 The Telescope
  • 3.8.3.1 Working principle
  • 3.8.3.2 The telescope objective
  • 3.8.4 The Compound Microscope
  • 3.8.4.1 Working principle
  • 3.8.4.2 The microscope objective
  • 3.8.5 The Camera
  • Chapter 4: Interference
  • 4.1 Interference: The Basic Idea
  • 4.2 An Interference Setup: The Double Slit
  • 4.2.1 Describing the Setup
  • 4.2.2 The Field Vectors
  • 4.2.3 The Intensity
  • 4.2.4 Interference Fringes
  • 4.2.5 The Simplifying Assumptions
  • 4.3 Michelson's Interferometer With a Monochromatic Plane Wave
  • 4.3.1 The Basic Setup
  • 4.3.2 Linearly Polarized Incident Wave
  • 4.3.2.1 The field vectors
  • 4.3.2.2 The superposed field and the intensity
  • 4.3.3 Incident Wave in an Arbitrary State of Polarization
  • 4.3.3.1 Polarized and unpolarized waves: The field vectors
  • 4.3.3.2 The intensity expression
  • 4.4 Coherence Characteristics, States of Polarization, and Interference Patterns
  • 4.5 The Use of Scalar Waves and Ray Paths in Interference
  • 4.5.1 The Scalar Wave Approach
  • 4.5.2 The Use of Ray Paths in Interference
  • 4.5.3 The Double-Hole Setup: Young's Fringes
  • 4.5.3.1 The setup
  • 4.5.3.2 The superposition
  • 4.5.3.3 The intensity
  • 4.5.3.4 The fringe pattern
  • 4.5.4 Virtual Sources in Interference
  • 4.5.5 Temporal and Spatial Coherence in Interference
  • 4.5.5.1 Temporal coherence
  • 4.5.5.2 Spatial coherence
  • 4.5.5.3 Extended quasi-monochromatic source
  • 4.6 Interference by Division of the Wavefront
  • 4.6.1 Monochromatic Point Sources and Extended Fringe Systems
  • 4.6.2 Young's Double-Slit Setup With a Linearly Extended Source
  • 4.7 Interference by Division of Amplitude
  • 4.7.1 Thin Film Interference
  • 4.7.1.1 Thin film: The phase difference and the intensity
  • 4.7.1.2 Thin film interference: Loss of temporal coherence
  • 4.7.1.3 The loss of spatial coherence: Localized fringes
  • General considerations
  • Fringes localized on the film
  • Fringes localized at infinity
  • 4.7.1.4 Thin film interference: Summary
  • 4.7.2 Fringes of Equal Thickness: Newton's Rings
  • 4.7.3 Fringes of Equal Inclination
  • 4.7.3.1 Michelson's interferometer
  • 4.7.3.2 The Mach-Zehnder interferometer
  • 4.8 The Stellar Interferometer
  • 4.9 Multiple Beam Interference
  • 4.9.1 Multiple Beam Interference: The Basic Idea
  • 4.9.2 Nearly Normal Incidence: The Fabry-Pérot Interferometer
  • 4.9.3 Incidence Near the Critical Angle: The Lummer-Gehrcke Interferometer
  • 4.10 Applications of Interferometers
  • 4.11 Interference as a Quantum Phenomenon
  • Chapter 5: Diffraction and Scattering
  • 5.1 Introduction
  • 5.1.1 The Diffraction Problem in Electromagnetic Theory and Optics
  • 5.1.2 Apertures and Obstacles
  • 5.1.3 Diffraction by Apertures
  • 5.1.4 Fresnel and Fraunhofer Setups
  • 5.2 Diffraction Theory: The Basics
  • 5.3 Diffraction of Scalar Waves
  • 5.3.1 The Basics: Scalar Helmholtz Equation
  • 5.3.2 Kirchhoff's Diffraction Formula
  • 5.3.2.1 How the formula is arrived at
  • 5.3.2.2 Kirchhoff's formula: Limitations
  • 5.3.3 Scalar Diffraction: Rayleigh-Sommerfeld Theory
  • 5.3.4 Scalar Diffraction: The Intensity Formula
  • 5.3.5 Diffraction of Non-monochromatic Waves
  • 5.3.6 Scalar Diffraction: Diffracted Ray Paths
  • 5.3.7 History: Huygens-Fresnel Theory
  • 5.3.7.1 What the theory is about
  • 5.3.7.2 Huygens-Fresnel principle of wave propagation
  • 5.3.8 Scalar Theory: Fresnel Diffraction
  • 5.3.8.1 Fresnel diffraction by a rectangular aperture
  • 5.3.8.2 Fresnel diffraction by a slit
  • 5.3.8.3 Fresnel diffraction by a straight edge
  • 5.3.9 Scalar Theory: Fraunhofer Diffraction
  • 5.3.9.1 Fraunhofer diffraction: Linearity of phase in aperture coordinates
  • 5.3.9.2 Fraunhofer diffraction by a rectangular aperture
  • 5.3.9.3 Fraunhofer diffraction by a circular aperture
  • 5.3.9.4 Fraunhofer diffraction by a long slit
  • Monochromatic plane wave incident normally on the slit
  • Incident radiation produced by a slit source and a collimating lens
  • 5.3.9.5 Fraunhofer diffraction by a double slit
  • 5.3.9.6 Fraunhofer diffraction by a grating
  • 5.3.10 Fraunhofer Diffraction as a Fourier Transformation of the `Aperture Function'
  • 5.3.10.1 Introducing the aperture function
  • 5.3.10.2 Fraunhofer diffraction as a Fourier transformation
  • 5.4 Wave Propagation and Diffraction: The Angular Spectrum Representation
  • 5.4.1 Diffraction and Wave Propagation
  • 5.4.2 Wave Propagation: The Angular Spectrum Representation
  • 5.5 Diffraction of Electromagnetic Waves: Vector Kirchhoff Theory
  • 5.5.1 Stratton-Chu Formulae
  • 5.5.2 Franz Formulae
  • 5.6 Dyadic Green's Functions in the Diffraction of Electromagnetic Waves
  • 5.6.1 The Algebra and Calculus of Dyadics
  • 5.6.2 Dyadic Green's Functions as Fields due to Unit Current Sources
  • 5.6.3 Fields due to Localized Current Sources
  • 5.6.4 The Diffraction Problem
  • 5.6.4.1 A splitting of the field vectors
  • 5.6.4.2 The parity of the field vectors with respect to the PEC screen
  • 5.6.5 Green's Dyadics in Diffraction
  • 5.6.5.1 The formal solution to the diffraction problem
  • 5.6.5.2 The aperture field
  • 5.7 The Smythe Formula
  • 5.8 Babinet's Principle
  • 5.9 Diffraction by a Straight Edge: The Exact Solution
  • 5.9.1 Two-Dimensional Diffraction Problems
  • 5.9.2 The Angular Spectrum Representation
  • 5.9.3 The Solution
  • 5.9.4 Interpreting the Solution
  • 5.9.4.1 The regions of interest
  • 5.9.4.2 Features of the exact solution
  • 5.10 The Slit Problem
  • 5.10.1 Stating the Problem
  • 5.10.2 Electric Vector Parallel to the Length of the Slit
  • 5.10.3 Magnetic Vector Parallel to the Length of the Slit
  • 5.10.4 The Problem of the Narrow Slit: An Overview
  • 5.11 The Circular Aperture
  • 5.11.1 The Geometry
  • 5.11.2 The Smythe Formula With Kirchhoff's Boundary Condition
  • 5.11.3 Comparison With the Scalar Diffraction Results
  • 5.11.4 A Useful Integral Formula: The Hertz Vector Representation
  • 5.11.5 The Long-Wavelength Limit: The Bethe Approach
  • 5.11.6 Improvements on Bethe's Solution
  • 5.11.7 The Long-Wavelength Limit in Optics
  • 5.12 The Geometrical Theory of Diffraction (GTD)
  • 5.12.1 The Background
  • 5.12.2 The Diffracted Rays
  • 5.12.3 The Diffracted Field and the Diffraction Coefficient
  • 5.12.4 Illustration: The Straight-Edge Problem
  • 5.12.5 Multiple Diffraction
  • 5.12.6 Diffraction From Corners, Vertices, and Boundary Surfaces
  • 5.12.7 GTD: Summary and Overview
  • 5.13 Diffraction Theory: A Brief Overview
  • 5.14 Diffraction Theory of Aberrations
  • 5.15 Diffraction With Partially Coherent Radiation
  • 5.16 Scattering in Electromagnetic Theory and Optics: An Introduction
  • 5.16.1 Rayleigh Scattering
  • 5.16.1.1 Rayleigh scattering: The basics
  • 5.16.1.2 Rayleigh scattering by a single scatterer
  • 5.16.1.3 Rayleigh scattering from a dielectric sphere
  • 5.16.1.4 Rayleigh scattering from a perfectly conducting sphere
  • 5.16.1.5 Rayleigh scattering from a pinhole
  • 5.16.1.6 Rayleigh scattering by atoms and molecules: The quantum description
  • 5.16.1.7 Rayleigh scattering by an assembly of scatterers
  • Rayleigh scattering by a dilute gas
  • Rayleigh scattering in denser fluids
  • The blue of the sky
  • Rayleigh scattering in optical fibers
  • 5.16.2 Mie Scattering
  • 5.16.3 Raman Scattering
  • Chapter 6: Fourier Optics
  • 6.1 Introduction
  • 6.2 Fundamentals of Fourier Transformation
  • 6.2.1 The Fourier Transform and Its Inverse
  • 6.2.2 Spatial Frequencies: The Two-Dimensional Transform
  • 6.2.3 Examples
  • 6.2.4 Parseval's Identity
  • 6.2.5 The Convolution Theorem
  • 6.2.5.1 Statement of the theorem
  • 6.2.5.2 Point spread function and convolution: Graphical illustration
  • 6.2.5.3 Corollary: The autocorrelation theorem
  • 6.2.5.4 Autocorrelation: Graphical illustration
  • 6.2.5.5 The cross correlation
  • 6.3 Fresnel Propagation
  • 6.3.1 Wave Propagation in the Fresnel Approximation
  • 6.3.2 Fresnel Propagation and the Angular Spectrum
  • 6.3.3 Digression: The Gaussian Beam
  • 6.3.4 The Fraunhofer Limit
  • 6.4 Phase Transformation by a Thin Lens: Lens as a Fourier Transformer
  • 6.4.1 Phase Transformation by a Thin Lens
  • 6.4.2 Thin Lens as a Fourier Transformer
  • 6.4.2.1 Input placed against the lens
  • 6.4.2.2 Input in front of the lens
  • 6.4.2.3 Input behind the lens
  • 6.5 The Operators
  • 6.6 Image Formation by a Thin Positive Lens With Coherent Light
  • 6.7 Frequency Analysis of Optical Imaging
  • 6.7.1 Frequency Response in Coherent Imaging
  • 6.7.1.1 The convolution
  • 6.7.1.2 The transfer function
  • 6.7.1.3 The pupil as a two-dimensional filter
  • 6.7.1.4 The transfer function and the aberrations
  • 6.7.2 Frequency Response in Incoherent Imaging
  • 6.7.2.1 The envelope function
  • 6.7.2.2 The intensity and the convolution
  • 6.7.2.3 The optical transfer function
  • 6.7.2.4 The pupil and the optical transfer function
  • 6.7.2.5 Incoherent imaging: The effect of aberrations
  • 6.8 Fourier Optics: Applications
  • 6.8.1 Transformation From the Input Plane to the Output Plane: Summary
  • 6.8.2 Applications of Fourier Optics: Introduction
  • 6.8.3 The Phase Contrast Microscope
  • 6.8.4 Spatial Frequency Filtering
  • 6.8.5 The 4f Correlator
  • 6.8.6 Optical Character Recognition
  • 6.9 Digression: Holography
  • 6.9.1 Holography: The Basic Idea
  • 6.9.2 The Segregation
  • 6.9.2.1 Rotational transformation of a field
  • 6.9.2.2 An improved holographic setup
  • Chapter 7: Optical Coherence: Statistical Optics
  • 7.1 Introduction: Statistical Features of Electromagnetic Fields
  • 7.2 Microscopic Features of an Optical Source: Stochastic Processes
  • 7.2.1 The Basic Idea
  • 7.2.2 Elementary Event
  • 7.2.3 Stochastic Process
  • 7.2.4 Stochastic Process: An Example
  • 7.3 Joint Probability Distributions and Ensemble Averages: The Autocorrelation Function
  • 7.3.1 Joint Probability Distribution Functions
  • 7.3.2 The Autocorrelation Function
  • 7.3.3 Time Averages
  • 7.4 Stationary and Wide-Sense Stationary Processes
  • 7.4.1 Stationary Random Process: Definition
  • 7.4.2 Wide-Sense Stationarity
  • 7.4.3 Stationary Random Process: Example
  • 7.4.4 Ergodicity
  • 7.4.4.1 Ergodicity: Definition
  • 7.4.4.2 Ergodicity and stationarity
  • 7.4.4.3 Ergodicity and stationarity: Simple examples
  • 7.5 Cross Correlation Between Two Real Random Processes
  • 7.6 Complex Random Processes
  • 7.7 Power Spectrum of a Real Random Process
  • 7.7.1 Wiener-Kinchin Theorem
  • 7.8 The Cross-Spectral Density of Two Real Processes
  • 7.9 The Analytic Signal
  • 7.9.1 The Analytic Signal: Definition
  • 7.9.2 The Imaginary Part
  • 7.9.3 Complex Stochastic Processes Defined by Analytic Signals
  • 7.9.4 Analytic Signal: The Spectral Density
  • 7.9.5 Cross Correlation of Two Complex Random Processes
  • 7.9.6 Cross-Spectral Density of Two Complex Random Processes
  • 7.10 Gaussian Random Processes
  • 7.10.1 The Central Limit Theorem and the Gaussian Distribution
  • 7.10.2 Gaussian Distributions in Optics
  • 7.10.3 Gaussian Processes: Statistical Features
  • 7.11 Statistical Characteristics of Optical Signals: Introduction
  • 7.11.1 Statistical Fluctuations of the Optical Field: The Classical and the Quantum Descriptions
  • 7.11.2 Optical Correlations of Various Orders
  • 7.11.2.1 Correlation functions: Introduction
  • 7.11.2.2 Correlation functions for a parallel beam
  • 7.11.3 Quasi-Monochromatic Sources of Light
  • 7.11.3.1 Monochromatic and quasi-monochromatic sources
  • 7.11.3.2 Coherent quasi-monochromatic source
  • 7.11.3.3 Incoherent quasi-monochromatic source
  • 7.11.3.4 Quasi-monochromatic signal: An example
  • 7.11.3.5 Chaotic light
  • 7.12 Intensity Fluctuations at a Point
  • 7.12.1 Polarized Chaotic Light
  • 7.12.1.1 Instantaneous intensity: The negative exponential distribution
  • 7.12.2 Unpolarized Chaotic Light
  • 7.13 Partially Polarized Light: States of Polarization and Intensity Fluctuations
  • 7.13.1 Vector-valued Real and Complex Random Processes for the Electromagnetic Field
  • 7.13.2 Introduction to the Coherence Matrix
  • 7.13.3 States of Polarization and Their Transformation
  • 7.13.3.1 Stokes parameters
  • 7.13.3.2 The degree of polarization
  • 7.13.3.3 The transformation matrices
  • 7.13.4 Fluctuations of Instantaneous Intensity
  • 7.14 First-Order Coherence Effects
  • 7.14.1 First-Order Coherence: Introduction
  • 7.14.2 Propagation of Partially Coherent Radiation Past an Aperture
  • 7.14.3 The Huygens-Fresnel Principle for Partially Coherent Radiation
  • 7.14.4 The Mutual Coherence Function and the Degree of Coherence
  • 7.14.5 The Double-Hole Setup
  • 7.14.5.1 The intensity
  • 7.14.5.2 The fringe pattern
  • 7.14.6 The Mutual Coherence Function in Diffraction
  • 7.15 Propagation of Mutual Coherence
  • 7.15.1 The Wave Equations
  • 7.15.2 The Helmholtz Equations
  • 7.15.3 Solution to the Dirichlet Problem
  • 7.15.4 Propagation of Mutual Intensity
  • 7.16 Van Cittert-Zernike Theorem
  • 7.17 First-Order Coherence in Stellar Interferometry
  • 7.18 Image Formation With Partially Coherent Light
  • 7.18.1 Transformation of Mutual Intensity
  • 7.18.2 Mutual Intensity Transfer Function
  • 7.18.3 Spatial Frequency Components of Intensity
  • 7.18.4 The Illuminating System
  • 7.18.5 Working Out the Image Intensity: The Basic Principle
  • 7.19 Photocounting: The Semiclassical Approach
  • 7.19.1 Photocount Fluctuations: Introduction
  • 7.19.2 The Instantaneous Counting Rate
  • 7.19.3 Counting Statistics
  • 7.19.3.1 Photocount distribution for a field with negligible fluctuations
  • 7.19.3.2 Photocount distribution in a fluctuating field
  • A. Observation time (T) long compared with the coherence time
  • B. Observation time (T) short compared with the coherence time
  • 7.20 Intensity Correlations
  • 7.20.1 Intensity Correlations: Introduction
  • 7.20.2 The Second-Order Correlation Function and Degree of Coherence
  • 7.20.3 The Hanbury Brown-Twiss Setup
  • 7.20.4 Photocurrent Correlations
  • 7.20.5 Digression: Cross-Spectral Purity
  • 7.20.6 Photocurrent Correlation and the Degree of Coherence
  • Chapter 8: Quantum Optics
  • 8.1 Introduction: The Classical and the Quantum
  • 8.2 The Classical Description of Systems
  • 8.2.1 The Phase Space: Pure States and Observables
  • 8.2.2 Mixed Classical States: Distribution Functions
  • 8.2.3 Composite Systems and Reduced States
  • 8.3 The Quantum Description
  • 8.3.1 State Vectors and the State Space
  • 8.3.1.1 The representation of states by vectors: The Hilbert space
  • 8.3.1.2 The inner product and the norm
  • 8.3.1.3 The wave function representing a state vector
  • 8.3.1.4 State spaces of finite dimensions
  • 8.3.2 Linear Operators
  • 8.3.2.1 Eigenvalues and eigenvectors
  • 8.3.2.2 Hermitian operators
  • 8.3.2.3 Change of basis: Unitary transformations
  • 8.3.3 Observations in Quantum Theory
  • 8.3.4 Superposed States
  • 8.3.5 The Coordinate and Momentum Representations
  • 8.3.5.1 The two representations
  • 8.3.5.2 The fundamental commutation relation and the transformation formula
  • 8.3.5.3 The wave functions and the basic operators
  • 8.3.5.4 Generalization
  • 8.3.5.5 Probability density
  • 8.3.6 Projection Operators and Their Completeness
  • 8.3.7 Simultaneous Measurements
  • 8.3.8 The Hamiltonian Operator and the Energy Representation
  • 8.3.9 Pure States and Their Time Evolution: The Schrödinger Equation
  • 8.3.9.1 Conserved dynamical variables
  • 8.3.10 Mixed States in Quantum Theory
  • 8.3.11 The Three Pictures
  • 8.3.12 Composite Systems and Reduced States
  • 8.3.13 Quantum Correlations: Entanglement
  • 8.3.14 Electromagnetic Field: The Quantum View
  • 8.4 The Harmonic Oscillator
  • 8.4.1 The Number States: Creation and Annihilation Operators
  • 8.4.2 The Coherent State
  • 8.4.2.1 Minimum uncertainty
  • 8.4.2.2 The quadrature operators
  • Digression: Coherent state for an arbitrary 1D system
  • 8.4.2.3 Coherent state: Characteristic features
  • 8.4.2.4 Poisson distribution
  • 8.4.3 Squeezed States
  • 8.4.3.1 Quadrature squeezing: The squeezed coherent state
  • 8.4.3.2 Squeezed states: Definition and construction
  • The first approach
  • The second approach
  • 8.4.3.3 Squeezed states: Characteristic features
  • Time evolution
  • Number distribution in a squeezed state
  • 8.4.4 Harmonic Oscillator: Classical and Nonclassical States
  • 8.4.4.1 The basic idea
  • 8.4.4.2 Sudarshan-Glauber P-representation
  • 8.5 The Free Electromagnetic Field in a Box: Classical Description
  • 8.5.1 Periodic Boundary Condition in a Box: Plane Wave Modes
  • 8.5.2 The Electromagnetic Field in a Cavity
  • 8.5.3 Summary: Eigenmode Expansion of the Electromagnetic Field
  • 8.6 Quantization of the Electromagnetic Field
  • 8.6.1 Mode Expansion of the Field Hamiltonian
  • 8.6.2 Annihilation and Creation Operators: Commutation Relations
  • 8.6.3 Energy Spectrum: Photons
  • 8.7 States of the Electromagnetic Field
  • 8.7.1 Single-Mode States
  • 8.7.2 Multimode States
  • 8.8 Statistical Features of Observables
  • 8.8.1 Photon Number Distribution
  • 8.8.1.1 Single-mode number states and coherent states
  • 8.8.1.2 Single-mode chaotic states
  • 8.8.1.3 Photon number distribution in a single-mode squeezed state
  • 8.8.2 Electric Field Fluctuations
  • 8.8.2.1 The single-mode field operator
  • 8.8.2.2 Field fluctuations in number states
  • 8.8.2.3 Coherent state: Amplitude and phase fluctuations
  • 8.8.2.4 Field fluctuations in a squeezed state
  • 8.8.2.5 Field fluctuations in a single-mode chaotic state
  • 8.8.3 Fluctuations in Multimode States
  • 8.9 The Continuous-Mode Description
  • 8.9.1 Continuous-Mode Description: The Basics
  • 8.9.2 Continuous-Mode Number States
  • 8.9.3 Continuous-Mode Coherent States
  • 8.9.4 Continuous-mode Chaotic States
  • 8.9.5 Photon Pair States
  • 8.9.6 Continuous-Mode Squeezed States
  • 8.10 The P-Representation of an Optical Field
  • 8.10.1 P-Representations of Single-Mode Field States
  • 8.10.2 Optical Equivalence Theorem
  • 8.11 Field Transformation by Optical Devices
  • 8.11.1 The Beam Splitter
  • 8.11.2 The Mach-Zehnder Interferometer
  • 8.12 Atom-Field Interaction
  • 8.12.1 Matter and Radiation: A and B Coefficients
  • 8.12.2 The Atom Interacting With a Classical Electromagnetic Field
  • 8.12.2.1 Atom-field interaction in semiclassical theory: Introduction
  • 8.12.2.2 Classical field: The interaction Hamiltonian
  • 8.12.2.3 Weak interaction: Results of perturbation theory
  • 8.12.2.4 Digression: Fermi's golden rule
  • 8.12.2.5 Rabi oscillations: Two-level atom in a classical field
  • 8.12.2.6 Induced transition: Einstein's B coefficients
  • 8.12.3 The Atom and the Quantized Field: The Jaynes-Cummings Model
  • 8.12.3.1 The Hamiltonian
  • 8.12.3.2 The oscillations
  • 8.12.3.3 Collapse and revival
  • 8.12.3.4 The dressed states
  • 8.12.4 Quantum Theory of the A and B Coefficients
  • 8.13 The Laser: Principles of Operation
  • 8.13.1 The Basic Idea of the Laser
  • 8.13.2 The Three-Level and Four-Level Schemes
  • 8.13.3 Continuous Wave Operation: Rate Equations
  • 8.13.4 Output Photon Flux
  • 8.13.5 Fluctuation Properties of Laser Light
  • 8.14 Quantum Theory of Photocounting
  • 8.14.1 Photodetection Probability
  • 8.14.2 Photocount Distribution
  • 8.15 Quantum Correlation Functions
  • 8.16 First-Order Coherence
  • 8.16.1 First-Order Correlation: Classical Coherence Characteristics
  • 8.16.2 First-Order Quantum Coherence
  • 8.16.2.1 Interference: The intensity formula
  • 8.16.2.2 Quantum first-order degree of coherence
  • Single-mode field states
  • Multimode field states
  • Continuous-mode states
  • 8.17 Second-Order Coherence
  • 8.17.1 Introduction: Classical Coherence and Its Limitations
  • 8.17.2 Second-Order Quantum Coherence
  • 8.17.3 Second-Order Degree of Coherence
  • 8.17.3.1 Single-mode states
  • 8.17.3.2 Continuous-mode states
  • 8.17.4 Photon Antibunching
  • 8.18 Two-Photon Interference
  • 8.19 Homodyne Detection
  • 8.20 Cavity Quantum Electrodynamics
  • 8.20.1 CQED: Introduction
  • 8.20.2 Atom in a Cavity: The Relevant Parameters
  • 8.20.3 The Weak Coupling Regime
  • 8.20.3.1 The cavity-controlled decay rate
  • 8.20.3.2 Vacuum energy shift in a cavity
  • 8.20.3.3 Modification of the cavity refractive index
  • 8.20.4 Open Systems in Quantum Optics
  • 8.20.4.1 Open systems: The master equation
  • 8.20.4.2 Master equation: The standard form
  • 8.20.4.3 Example: Decay of the two-level atom
  • 8.20.4.4 Example: Decay of the cavity field
  • 8.20.4.5 Master equation for the atom-cavity system
  • 8.20.5 The Strong Coupling Regime
  • 8.21 Quantum Optics and Quantum Information
  • 8.21.1 Information Processing: Classical and Quantum
  • 8.21.2 Realization of Qubits and Quantum Gates
  • 8.21.2.1 Quantum information hardware: Introduction
  • 8.21.2.2 Quantum optics hardware: The ion trap
  • 8.21.2.3 Quantum optics hardware: The high-Q cavity
  • 8.21.2.4 Quantum optics hardware: Photonic qubits
  • Chapter 9: Nonlinear Optics
  • 9.1 Introduction
  • 9.2 The Basic Equations
  • 9.2.1 The Electric Field Strength
  • 9.2.2 The Polarization
  • 9.2.3 The Response: Time Domain Description
  • 9.2.4 The Response: Frequency Domain Description
  • 9.2.4.1 Frequency domain: The basic formula
  • 9.2.4.2 The second order of nonlinearity
  • 9.2.4.3 A simple example
  • 9.2.4.4 Phase matching: The basic principle
  • 9.2.4.5 Nonlinearities of higher order
  • 9.2.4.6 Symmetries of the susceptibility tensor
  • 9.3 Nonlinear Optical Processes: Schematic Description
  • 9.3.1 The Basic Scheme
  • 9.3.2 Virtual Levels
  • 9.4 The Theoretical Calculation of Susceptibilities
  • 9.4.1 Theory of Nonlinear Susceptibilities: Introduction
  • 9.4.2 Nonlinear Susceptibilities: The Density Operator Formalism
  • 9.4.2.1 Atomic interactions and the density operator
  • 9.4.2.2 The evolution equation and its perturbative solution
  • 9.4.2.3 The linear susceptibility
  • 9.4.2.4 Nonlinear susceptibilities
  • The second-order susceptibility
  • The third-order susceptibility
  • 9.4.3 Atomic Susceptibilities: The Classical and Quantum Theories
  • 9.4.3.1 The linear susceptibility in the two theories
  • 9.4.3.2 Anharmonic oscillations and nonlinear susceptibilities
  • 9.4.3.3 Approximate formulae for the susceptibilities
  • 9.5 The Wave Equation in a Nonlinear Medium
  • 9.6 Second-Order Processes
  • 9.6.1 Sum-Frequency Generation
  • 9.6.2 Three-Wave Processes: The Manley-Rowe Relations
  • 9.6.3 Difference-Frequency Generation and Optical Parametric Amplification
  • 9.6.4 The Optical Parametric Oscillator
  • 9.6.5 Second-Harmonic Generation
  • 9.6.6 Parametric Down Conversion
  • 9.7 Third-Order Processes
  • 9.7.1 Third-Order Nonlinearity: Introduction
  • 9.7.2 Optical Kerr Effect
  • 9.8 The Quantized Field in a Nonlinear Medium
  • 9.8.1 Quantum Theory: Second-Harmonic Generation
  • 9.8.2 Quantum Theory: Parametric Down Conversion
  • Bibliography
  • Note for Bibliography
  • Index
  • Back Cover

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