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Quantum Optics for Engineers

Book Description

Quantum Optics for Engineers provides a transparent and methodical introduction to quantum optics via the Dirac's bra–ket notation with an emphasis on practical applications and basic aspects of quantum mechanics such as Heisenberg's uncertainty principle and Schrodinger's equation.

Self-contained and using mainly first-year calculus and algebra tools, the book:

  • Illustrates the interferometric quantum origin of fundamental optical principles such as diffraction, refraction, and reflection
  • Provides a transparent introduction, via Dirac's notation, to the probability amplitude of quantum entanglement
  • Explains applications of the probability amplitude of quantum entanglement to optical communications, quantum cryptography, quantum teleportation, and quantum computing.

Quantum Optics for Engineers is succinct, transparent, and practical, revealing the intriguing world of quantum entanglement via many practical examples. Ample illustrations are used throughout its presentation and the theory is presented in a methodical, detailed approach.

Table of Contents

  1. Cover
  2. Half Title
  3. Title Page
  4. Copyright Page
  5. Dedication
  6. Table of Contents
  7. List of Figures
  8. List of Tables
  9. Preface
  10. Author
  11. 1. Introduction
    1. 1.1 Introduction
    2. 1.2 Brief Historical Perspective
    3. 1.3 Principles of Quantum Mechanics
    4. 1.4 The Feynman Lectures on Physics
    5. 1.5 Photon
    6. 1.6 Quantum Optics
    7. 1.7 Quantum Optics for Engineers
    8. References
  12. 2. Planck’s Quantum Energy Equation
    1. 2.1 Introduction
    2. 2.2 Planck’s Equation and Wave Optics
    3. References
  13. 3. Uncertainty Principle
    1. 3.1 Heisenberg Uncertainty Principle
    2. 3.2 Wave–Particle Duality
    3. 3.3 Feynman Approximation
      1. 3.3.1 Example
    4. 3.4 Interferometric Approximation
    5. 3.5 Minimum Uncertainty Principle
    6. 3.6 Generalized Uncertainty Principle
    7. 3.7 Additional Versions of the Heisenberg Uncertainty Principle
      1. 3.7.1 Example
    8. 3.8 Applications of the Uncertainty Principle in Optics
      1. 3.8.1 Beam Divergence
      2. 3.8.2 Beam Divergence and Astronomy
      3. 3.8.3 Uncertainty Principle and the Cavity Linewidth Equation
      4. 3.8.4 Tuning Laser Microcavities
      5. 3.8.5 Sub-Microcavities
    9. Problems
    10. References
  14. 4. Dirac Quantum Optics
    1. 4.1 Dirac Notation in Optics
    2. 4.2 Dirac Quantum Principles
    3. 4.3 Interference and the Interferometric Equation
      1. 4.3.1 Examples: Double-, Triple-, Quadruple-, and Quintuple-Slit Interference
      2. 4.3.2 Geometry of the N-Slit Interferometer
      3. 4.3.3 Diffraction Grating Equation
      4. 4.3.4 N-Slit Interferometer Experiment
    4. 4.4 Coherent and Semicoherent Interferograms
    5. 4.5 Interferometric Equation in Two and Three Dimensions
    6. 4.6 Classical and Quantum Alternatives
    7. Problems
    8. References
  15. 5. Interference, Diffraction, Refraction, and Reflection via the Dirac Notation
    1. 5.1 Introduction
    2. 5.2 Interference and Diffraction
      1. 5.2.1 Generalized Diffraction
      2. 5.2.2 Positive Diffraction
    3. 5.3 Positive and Negative Refraction
      1. 5.3.1 Focusing
    4. 5.4 Reflection
    5. 5.5 Succinct Description of Optics
    6. Problems
    7. References
  16. 6. Generalized Multiple-Prism Dispersion
    1. 6.1 Introduction
    2. 6.2 Generalized Multiple-Prism Dispersion
      1. 6.2.1 Example: Generalized Single-Prism Dispersion
    3. 6.3 Double-Pass Generalized Multiple-Prism Dispersion
      1. 6.3.1 Design of Zero-Dispersion Multiple-Prism Beam Expanders
    4. 6.4 Multiple-Return-Pass Generalized Multiple-Prism Dispersion
      1. 6.4.1 Multiple-Prism Beam Compressors
    5. 6.5 Multiple-Prism Dispersion and Laser Pulse Compression
      1. 6.5.1 Example: Single-Prism Pulse Compressor
      2. 6.5.2 Example: Double-Prism Pulse Compressor
      3. 6.5.3 Example: Four-Prism Pulse Compressor
    6. Problems
    7. References
  17. 7. Dirac Notation Identities
    1. 7.1 Useful Identities
      1. 7.1.1 Example
    2. 7.2 Linear Operations
      1. 7.2.1 Example
    3. Problems
    4. References
  18. 8. Laser Excitation
    1. 8.1 Introduction
    2. 8.2 Brief Laser Overview
      1. 8.2.1 Laser Optics
    3. 8.3 Laser Excitation
      1. 8.3.1 Electrically Excited Gas Lasers
      2. 8.3.2 Optically Pumped Gas and Liquid Lasers
      3. 8.3.3 Optically Pumped Solid-State Lasers
      4. 8.3.4 Electrically Excited Semiconductor Lasers
    4. 8.4 Excitation and Emission Dynamics
      1. 8.4.1 Rate Equations for a Two-Level System
      2. 8.4.2 Dynamics of a Multiple-Level System
      3. 8.4.3 Long-Pulse Approximation
      4. 8.4.4 Example
    5. 8.5 Quantum Transition Probabilities and Cross Sections
      1. 8.5.1 Long-Pulse Approximation
    6. Problems
    7. References
  19. 9. Laser Oscillators Described via the Dirac Notation
    1. 9.1 Introduction
    2. 9.2 Transverse and Longitudinal Modes
      1. 9.2.1 Transverse-Mode Structure
      2. 9.2.2 Double- and Single-Longitudinal-Mode Emission
        1. 9.2.2.1 Example
    3. 9.3 Laser Cavity Equation: An Intuitive Approach
    4. 9.4 Laser Cavity Equation via the Interferometric Equation
    5. Problems
    6. References
  20. 10. Interferometry via the Dirac Notation
    1. 10.1 Interference à la Dirac
    2. 10.2 Hanbury Brown–Twiss Interferometer
    3. 10.3 Two-Beam Interferometers
      1. 10.3.1 Sagnac Interferometer
      2. 10.3.2 Mach–Zehnder Interferometer
      3. 10.3.3 Michelson Interferometer
    4. 10.4 Multiple-Beam Interferometers
    5. 10.5 N-Slit Interferometer as a Wavelength Meter
    6. 10.6 Ramsey Interferometer
    7. Problems
    8. References
  21. 11. Secure Interferometric Communications in Free Space
    1. 11.1 Introduction
    2. 11.2 Theory
    3. 11.3 N-Slit Interferometer for Secure Free-Space Optical Communications
    4. 11.4 Interferometric Characters
    5. 11.5 Propagation in Terrestrial Free Space
      1. 11.5.1 Clear-Air Turbulence
    6. 11.6 Discussion
    7. Problems
    8. References
  22. 12. Schrödinger’s Equation
    1. 12.1 Introduction
    2. 12.2 Schrödinger’s Mind
    3. 12.3 Heuristic Explicit Approach to Schrödinger’s Equation
    4. 12.4 Schrödinger’s Equation via the Dirac Notation
    5. 12.5 Time-Independent Schrödinger’s Equation
      1. 12.5.1 Quantized Energy Levels
      2. 12.5.2 Semiconductor Emission
      3. 12.5.3 Quantum Wells
      4. 12.5.4 Quantum Cascade Lasers
      5. 12.5.5 Quantum Dots
    6. 12.6 Introduction to the Hydrogen Equation
    7. Problems
    8. References
  23. 13. Introduction to Feynman Path Integrals
    1. 13.1 Introduction
    2. 13.2 Classical Action
    3. 13.3 Quantum Link
    4. 13.4 Propagation through a Slit and the Uncertainty Principle
      1. 13.4.1 Discussion
    5. 13.5 Feynman Diagrams in Optics
    6. Problems
    7. References
  24. 14. Matrix Aspects of Quantum Mechanics
    1. 14.1 Introduction
    2. 14.2 Introduction to Vector and Matrix Algebra
      1. 14.2.1 Vector Algebra
      2. 14.2.2 Matrix Algebra
    3. 14.3 Quantum Operators
      1. 14.3.1 Position Operator
      2. 14.3.2 Momentum Operator
      3. 14.3.3 Example
      4. 14.3.4 Energy Operator
      5. 14.3.5 Heisenberg Equation of Motion
    4. 14.4 Pauli Matrices
      1. 14.4.1 Pauli Matrices for Spin One-Half Particles
    5. 14.5 Introduction to the Density Matrix
      1. 14.5.1 Examples
      2. 14.5.2 Transitions via the Density Matrix
    6. Problems
    7. References
  25. 15. Classical Polarization
    1. 15.1 Introduction
    2. 15.2 Maxwell Equations
    3. 15.3 Polarization and Reflection
      1. 15.3.1 Plane of Incidence
    4. 15.4 Jones Calculus
      1. 15.4.1 Example
    5. 15.5 Polarizing Prisms
      1. 15.5.1 Transmission Efficiency in Multiple-Prism Arrays
      2. 15.5.2 Induced Polarization in a Double-Prism Beam Expander
      3. 15.5.3 Double-Refraction Polarizers
      4. 15.5.4 Attenuation of the Intensity of Laser Beams Using Polarization
    6. 15.6 Polarization Rotators
      1. 15.6.1 Birefringent Polarization Rotators
        1. 15.6.1.1 Example
      2. 15.6.2 Broadband Prismatic Polarization Rotators
        1. 15.6.2.1 Example
    7. Problems
    8. References
  26. 16. Quantum Polarization
    1. 16.1 Introduction
    2. 16.2 Linear Polarization
      1. 16.2.1 Example
    3. 16.3 Polarization as a Two-State System
      1. 16.3.1 Diagonal Polarization
      2. 16.3.2 Circular Polarization
    4. 16.4 Density Matrix Notation
      1. 16.4.1 Stokes Parameters and Pauli Matrices
      2. 16.4.2 Density Matrix and Circular Polarization
      3. 16.4.3 Example
    5. Problems
    6. References
  27. 17. Entangled Polarizations: Probability Amplitudes and Experimental Configurations
    1. 17.1 Introduction
    2. 17.2 Hamiltonian Approach
      1. 17.2.1 Example
    3. 17.3 Interferometric Approach
    4. 17.4 Pryce–Ward–Snyder Probability Amplitude of Entanglement
    5. 17.5 Pryce–Ward–Snyder Probability
    6. 17.6 Pryce–Ward Experimental Arrangement
    7. 17.7 Wu–Shaknov Experiment
      1. 17.7.1 Relevance of the Pryce–Ward Theory and the Wu–Shaknov Experiment to EPR
    8. 17.8 Conclusion
    9. Problems
    10. References
  28. 18. Quantum Computing
    1. 18.1 Introduction
    2. 18.2 Interferometric Computer
    3. 18.3 Classical Logic Gates
    4. 18.4 Qubits
    5. 18.5 Quantum Logic
      1. 18.5.1 Pauli Matrices and Quantum Logic
      2. 18.5.2 Quantum Gates
    6. Problems
    7. References
  29. 19. Quantum Cryptography and Teleportation
    1. 19.1 Introduction
    2. 19.2 Quantum Cryptography
      1. 19.2.1 Bennett and Brassard Approach
      2. 19.2.2 Polarization Entanglement Approach
    3. 19.3 Quantum Teleportation
    4. Problems
    5. References
  30. 20. Quantum Measurements
    1. 20.1 Introduction
    2. 20.2 Interferometric Irreversible Measurements
      1. 20.2.1 Additional Irreversible Quantum Measurements
    3. 20.3 Quantum Nondemolition Measurements
    4. 20.4 Soft Polarization Measurements
    5. 20.5 Soft Intersection of Interferometric Characters
      1. 20.5.1 Comparison between Theoretical and Measured N-Slit Interferograms
      2. 20.5.2 Soft Interferometric Probing
      3. 20.5.3 Mechanics of Soft Interferometric Probing
      4. 20.5.4 Discussion
    6. Problems
    7. References
  31. 21. Interpretational Issues in Quantum Mechanics
    1. 21.1 Introduction
    2. 21.2 EPR
    3. 21.3 Bohm Polarization Projection of the EPR Argument
    4. 21.4 Bell’s Inequalities
      1. 21.4.1 Example
      2. 21.4.2 Discussion
    5. 21.5 Some Prominent Quantum Physicists on Issues of Interpretation
    6. 21.6 Heisenberg’s Uncertainty Principle and EPR
    7. 21.7 van Kampen’s Quantum Theorems
    8. 21.8 On Probabilities and Probability Amplitudes
    9. 21.9 Comment on the Interpretational Issue
    10. Problems
    11. References
  32. Appendix A: Survey of Laser Emission Characteristics
  33. Appendix B: Brief Survey of Laser Resonators and Laser Cavities
  34. Appendix C: Ray Transfer Matrices
  35. Appendix D: Multiple-Prism Dispersion Series
  36. Appendix E: Complex Numbers
  37. Appendix F: Trigonometric Identities
  38. Appendix G: Calculus Basics
  39. Appendix H: Poincaré’s Space
  40. Appendix I: N-Slit Interferometric Calculations
  41. Appendix J: N-Slit Interferometric Calculations—Numerical Approach
  42. Appendix K: Physical Constants and Optical Quantities
  43. Index