A Field Theory Approach to Photonics.

Format:

Book

Author/Creator:

Ornigotti, Marco.

Series:

IOP Ebooks Series

Language:

English

Subjects (All):

Photonics.

Field theory (Physics).

Physical Description:

1 online resource (258 pages)

Edition:

1st ed.

Place of Publication:

Bristol : Institute of Physics Publishing, 2025.

Summary:

Starting with the familiar classical electrodynamics framework of Maxwell's equations and the light-matter interaction in the dipole approximation, this 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:

Intro

Author biography

Marco Ornigotti

Notation and conventions

Chapter Introduction

References

Chapter 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

2.3.1 Green's function in cylindrical coordinates

2.4 Paraxial approximation and Gaussian beams

2.4.1 Hermite and Laguerre-Gaussian beams

2.5 The paraxial propagator

2.6 Light-matter interaction

2.6.1 Electromagnetic scalar and vector potentials

2.6.2 Electromagnetic potentials in the presence of matter

2.6.3 Multipole expansion of the electromagnetic field

2.6.4 Electric versus magnetic dipoles

2.6.5 Interaction Hamiltonian and minimal coupling

2.6.6 Dipole interaction Hamiltonian

Chapter Field theory in a nutshell

3.1 Lagrangian, Hamiltonian, and Noether's theorem

3.1.1 Lagrangian dynamics

3.1.2 Equivalent Lagrangians

3.1.3 Lagrangian density for a scalar paraxial field

3.1.4 Hamiltonian dynamics

3.1.5 Noether theorem and conserved quantities

3.1.6 Conserved quantities and their continuity equations

3.2 Noether theorem for internal symmetries of the field

Chapter Electromagnetic field theory

4.1 A preliminary discussion

4.2 The Lagrangian for the electromagnetic field

4.2.1 Gauge invariance and the choice of gauge

4.3 The Hamiltonian for the electromagnetic field

4.4 Conserved quantities of the electromagnetic field

4.4.1 Electromagnetic stress-energy tensor

4.4.2 Physical meaning of the components of Tμν

4.5 Orbital and spin angular momentum of the electromagnetic field

4.5.1 SAM and circular polarisation

4.5.2 OAM and twisted phase fronts.

4.6 Helicity, chirality and spin angular momentum

4.6.1 The second electromagnetic potential

4.6.2 Dual electromagnetism, helicity density and optical spin

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

Chapter Quantum field theory in a nutshell

5.1 Hamiltonian mechanics revisited

5.2 Canonical quantisation

5.2.1 Fock space for quantum fields

5.3 Interacting field-Hamiltonian formalism

5.4 Feynman diagrams

5.4.1 The Feynman propagator

5.4.2 Wick's theorem and the Feynman rules

5.5 Path integral quantisation

5.5.1 Path integral for a free field

5.6 Interacting fields-path integral formalism

Appendix A: The quantum harmonic oscillator

Appendix B: Gaussian integrals of fields

Chapter Quantum theory of the electromagnetic field

6.1 Part I: canonical quantisation of the electromagnetic field

6.1.1 Single-mode electromagnetic Fock states

6.1.2 Single-mode electromagnetic coherent states

6.1.3 Quantisation and optical beams

6.2 Part II: quantum nonlinear optics in canonical formalism

6.2.1 Second-order nonlinearities

6.2.2 Transition probability

6.2.3 Quantum state of the field after the interaction

6.2.4 Third-order nonlinearities

6.3 Part III: path integrals quantisation of the electromagnetic field

6.3.1 Faddeev-Popov quantisation

6.3.2 A more intuitive approach to Faddeev-Popov quantisation

6.3.3 Partition function for the electromagnetic field

6.4 Feynman propagator for the electromagnetic field

6.4.1 Feynman propagator in canonical formalism

6.4.2 Feynman propagator in path integral formalism.

Appendix A: Coherent states of the quantum harmonic oscillator

Appendix B: A primer on Grassmann variables and fields

Chapter Applications of path integrals in photonics

7.1 Part I: path integrals in photonics

7.1.1 Light propagation in inhomogeneous media

7.1.2 Path integrals in nonlinear optics

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

7.2.1 Path integrals description of light-matter interaction

7.2.2 Dielectric function from path integrals

7.2.3 Dressed electromagnetic propagator

7.2.4 Field operators and noise currents

7.2.5 Quantum nonlinear optics using path integrals

7.2.6 Feynman diagrams from path integrals for interacting theories

7.2.7 Second-order nonlinearities-quantum pump

7.2.8 Second-order nonlinearities-undepleted pump

7.2.9 Third-order nonlinearities

7.2.10 High-order and cascaded nonlinearities

Appendix A: Derivation of equations (7.20a)

Appendix B: Schwinger-Dyson equation for the dressed propagator

Appendix C: Derivation of equation (7.142)

Chapter Light-matter interaction in 2D materials

8.1 A primer on graphene

8.1.1 The crystalline structure of graphene

8.1.2 Graphene Hamiltonian

8.1.3 Low energy Hamiltonian for graphene

8.1.4 Dirac equation from graphene Hamiltonian

8.2 Light-matter interaction on a plane

8.3 Optical conductivity of graphene

8.3.1 Current correlator from effective action

8.3.2 Current correlator from direct path integration

8.3.3 DC conductivity of graphene

8.4 Extension to other materials and nonlinear properties

References.

Notes:

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Other Format:

Print version: Ornigotti, Marco A Field Theory Approach to Photonics

ISBN:

9780750357890

OCLC:

1528362628