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# Quantum Optics for Engineers

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## 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

**Introduction**Introduction

Brief Historical Perspective

Principles of Quantum Mechanics

The Feynman Lectures on Physics

Photon

Quantum Optics

Quantum Optics for Engineers

**Planck’s Quantum Energy Equation**

Introduction

Planck’s Equation and Wave Optics

**Uncertainty Principle**

Heisenberg Uncertainty Principle

Wave–Particle Duality

Feynman Approximation

Interferometric Approximation

Minimum Uncertainty Principle

Generalized Uncertainty Principle

Additional Versions of the Heisenberg Uncertainty Principle

Applications of the Uncertainty Principle in Optics

**Dirac Quantum Optics**

Dirac Notation in Optics

Dirac Quantum Principles

Interference and the Interferometric Equation

Coherent and Semicoherent Interferograms

Interferometric Equation in Two and Three Dimensions

Classical and Quantum Alternatives

**Interference, Diffraction, Refraction, and Reflection via the Dirac Notation**

Introduction

Interference and Diffraction

Positive and Negative Refraction

Reflection

Succinct Description of Optics

**Generalized Multiple-Prism Dispersion**

Introduction

Generalized Multiple-Prism Dispersion

Double-Pass Generalized Multiple-Prism Dispersion

Multiple-Return-Pass Generalized Multiple-Prism Dispersion

Multiple-Prism Dispersion and Laser Pulse Compression

**Dirac Notation Identities**

Useful Identities

Linear Operations

**Laser Excitation**

Introduction

Brief Laser Overview

Laser Excitation

Excitation and Emission Dynamics

Quantum Transition Probabilities and Cross Sections

**Laser Oscillators Described via the Dirac Notation**

Introduction

Transverse and Longitudinal Modes

Laser Cavity Equation: An Intuitive Approach

Laser Cavity Equation via the Interferometric Equation

**Interferometry via the Dirac Notation**

Interference

*à la*Dirac

Hanbury Brown–Twiss Interferometer

Two-Beam Interferometers

Multiple-Beam Interferometers

*N*-Slit Interferometer as a Wavelength Meter

Ramsey Interferometer

**Secure Interferometric Communications in Free Space**

Introduction

Theory

**-Slit Interferometer for Secure Free-Space Optical Communications**

*N*Interferometric Characters

Propagation in Terrestrial Free Space

Discussion

**Schrödinger’s Equation**

Introduction

Schrödinger’s Mind

Heuristic Explicit Approach to Schrödinger’s Equation

Schrödinger’s Equation via the Dirac Notation

Time-Independent Schrödinger’s Equation

Introduction to the Hydrogen Equation

**Introduction to Feynman Path Integrals**

Introduction

Classical Action

Quantum Link

Propagation through a Slit and the Uncertainty Principle

Feynman Diagrams in Optics

**Matrix Aspects of Quantum Mechanics**

Introduction

Introduction to Vector and Matrix Algebra

Quantum Operators

Pauli Matrices

Introduction to the Density Matrix

**Classical Polarization**

Introduction

Maxwell Equations

Polarization and Reflection

Jones Calculus

Polarizing Prisms

Polarization Rotators

**Quantum Polarization**

Introduction

Linear Polarization

Polarization as a Two-State System

Density Matrix Notation

**Entangled Polarizations: Probability Amplitudes and Experimental Configurations**

Introduction

Hamiltonian Approach

Interferometric Approach

Pryce–Ward–Snyder Probability Amplitude of Entanglement

Pryce–Ward–Snyder Probability

Pryce–Ward Experimental Arrangement

Wu–Shaknov Experiment

Conclusion

**Quantum Computing**

Introduction

Interferometric Computer

Classical Logic Gates

Qubits

Quantum Logic

**Quantum Cryptography and Teleportation**

Introduction

Quantum Cryptography

Quantum Teleportation

**Quantum Measurements**

Introduction

Interferometric Irreversible Measurements

Quantum Nondemolition Measurements

Soft Polarization Measurements

Soft Intersection of Interferometric Characters

**Interpretational Issues in Quantum Mechanics**

Introduction

EPR

Bohm Polarization Projection of the EPR Argument

Bell’s Inequalities

Some Prominent Quantum Physicists on Issues of Interpretation

Eisenberg’s Uncertainty Principle and EPR

van Kampen’s Quantum Theorems

On Probabilities and Probability Amplitudes

Comment on the Interpretational Issue

**Appendix A: Survey of Laser Emission Characteristics**

Appendix B: Brief Survey of Laser Resonators and Laser Cavities

Appendix C: Ray Transfer Matrices

Appendix D: Multiple-Prism Dispersion Series

Appendix E: Complex Numbers

Appendix F: Trigonometric Identities

Appendix G: Calculus Basics

Appendix H: Poincaré’s Space

Appendix I:

Appendix J:

Appendix K: Physical Constants and Optical Quantities

Appendix B: Brief Survey of Laser Resonators and Laser Cavities

Appendix C: Ray Transfer Matrices

Appendix D: Multiple-Prism Dispersion Series

Appendix E: Complex Numbers

Appendix F: Trigonometric Identities

Appendix G: Calculus Basics

Appendix H: Poincaré’s Space

Appendix I:

*N*-Slit Interferometric CalculationsAppendix J:

*N*-Slit Interferometric Calculations—Numerical ApproachAppendix K: Physical Constants and Optical Quantities

## Reviews

"Duarte's book is a welcome addition to the family of optics texts because he stresses fundamental connections between classical and quantum optics. His review of the bedrock theory and experiments of several of the founders of quantum physics provides an instructive transition to recent developments in quantum optics, such as photon entanglement. Perhaps the most appealing aspect of this book is the treatment of classical optical concepts and phenomena in terms of a quantum formalism...Both graduate students and the experienced researcher will find this treatment of quantum optics to be illuminating and valuable...I look forward to having a copy in my personal library."

—Professor J. Gary Eden, Electrical and Computer Engineering, University of Illinois

"Quantum Optics for Engineersis an original and unique book that describes classical and quantum optical phenomena, and the synergy between these two subjects, from an interferometric perspective. Dirac’s notation is used ... [to] provide a lucid explanation of quantum polarization entanglement. The book will serve engineers with a minimum knowledge of quantum mechanics ... to understand modern experiments with lasers, optical communications, and the intriguing world of quantum entanglement."

––Ignacio E. Olivares, Universidad de Santiago de Chile"

Quantum Optics for Engineersprovides a transparent and succinct description of the fundamentals of quantum optics using Dirac’s notation and ample illustrations. Particularly valuable is the explanation and elucidation of quantum entanglement from an interferometric perspective. The cohesiveness provided by the unified use of Dirac’s notation, emphasizing physics rather than mathematics, is particularly useful for those trained in engineering. This will be a valuable asset to any optical engineer’s library."

––Anne M. Miller, RR Donnelley, USA"This book is a concise and comprehensive presentation of numerous fundamental concepts related to the light nature and its interaction with matter. A very structured and logical route reveals step by step the rigorous theory of quantum optics. To some extent, the whole project can be fairly defined as unique. One of the heaviest tools in quantum optics, operator representation, is introduced in a very clear and straightforward way. Nature foundations and rather complicated mathematical tools are brought in a very elegant manner such that readers suddenly find themselves as experts in areas they would consider untouchable magic. The intriguing world of quantum entanglement is revealed via many practical examples."

––Sergei Popov, Royal Institute of Technology, Sweden