A field theory approach to photonics Marco Ornigotti

Format:

Book

Author/Creator:

Ornigotti, Marco, author.

Contributor:

Institute of Physics (Great Britain), publisher.

Language:

English

Subjects (All):

Photonics.

Field theory (Physics).

Physical Description:

1 online resource

Place of Publication:

IOP Publishing 2025

Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) IOP Publishing [2025]

Biography/History:

Marco Ornigotti is a theoretical physicist interested in the fundamental aspects of light-matter interaction at both the classical and quantum scale and in unravelling the hidden connections between photonics and other disciplines of physics. He received his Master's degree in photonics and PhD in physics from Polytechnic Institute of Milan, and the habilitation in theoretical physics from Friedrich Schiller University. Marco spent several years in Germany for his Postdoc, first at the Max Planck Institute for the Science of Light at Friedrich Schiller University Jena, and University of Rostock. Since 2019 he joined Tampere University, where he is now Associate Professor and leads the Theoretical Optics and Photonics group, whose main research interest concerns the interaction of structured light with matter, with particular emphasis on 2D, and epsilon-near-zero materials

Summary:

This book provides an introduction to the use of field theory (both in its classical and quantum formulation) to approach problems in optics and photonics, with specific emphasis on path integral methods. Starting with the familiar classical electrodynamics framework of Maxwell's equations and the light-matter interaction in the dipole approximation, the book slowly guides the reader through a journey that will touch several different aspects of photonics and field theory, including quantisation, nonlinear optics, path integrals, and its application to problems in photonics and 2D materials

Contents:

1. Introduction

part I. Classical theory of light. 2. Electromagnetic field and light-matter interaction

2.1. Maxwell's equations, wave equation, and the Helmholtz equation

2.2. The propagator for the Helmholtz equation

2.3. Helmholtz equation in cylindrical coordinates : Bessel beams

2.4. Paraxial approximation and Gaussian beams

2.5. The paraxial propagator

2.6. Light-matter interaction

3. Field theory in a nutshell

3.1. Lagrangian, Hamiltonian, and Noether's theorem

3.2. Noether theorem for internal symmetries of the field

4. Electromagnetic field theory

4.1. A preliminary discussion

4.2. The Lagrangian for the electromagnetic field

4.3. The Hamiltonian for the electromagnetic field

4.4. Conserved quantities of the electromagnetic field

4.5. Orbital and spin angular momentum of the electromagnetic field

4.6. Helicity, chirality and spin angular momentum

4.7. Field theory description of light-matter interaction

4.8. Electrodynamics in curved spacetime and transformation optics

Appendix A. Derivation of equation (4.68)

Appendix B. Derivation of the Power-Zienau-Wooley transformation

part II. Quantum theory of light. 5. Quantum field theory in a nutshell

5.1. Hamiltonian mechanics revisited

5.2. Canonical quantisation

5.3. Interacting field

Hamiltonian formalism

5.4. Feynman diagrams

5.5. Path integral quantisation

5.6. Interacting fields

path integral formalism

Appendix A. The quantum harmonic oscillator

Appendix B. Gaussian integrals of fields

6. Quantum theory of the electromagnetic field

6.1. Part I : canonical quantisation of the electromagnetic field

6.2. Part II : quantum nonlinear optics in canonical formalism

6.3. Part III : path integrals quantisation of the electromagnetic field

6.4. Feynman propagator for the electromagnetic field

Appendix A. Coherent states of the quantum harmonic oscillator

Appendix B. A primer on Grassmann variables and fields

part III. Path integrals for classical and quantum optics applications. 7. Applications of path integrals in photonics

7.1. Part I : path integrals in photonics

7.2. Part II : quantum field theory, path integrals and photonics

Appendix A. Derivation of equations (7.20a)

Appendix B. Schwinger-Dyson equation for the dressed propagator

Appendix C. Derivation of equation (7.142)

8. Light-matter interaction in 2D materials

8.1. A primer on graphene

8.2. Light-matter interaction on a plane

8.3. Optical conductivity of graphene

8.4. Extension to other materials and nonlinear properties

Notes:

"Version: 20250701"--Title page verso

Includes bibliographical references

Online resource; title from PDF title page (viewed on August 1, 2025)

Other Format:

Print version A field theory approach to photonics

ISBN:

9780750357890

9780750357883

OCLC:

1522005485

Access Restriction:

Restricted for use by site license