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Real-space Hopfield diagonalization of inhomogeneous dispersive media

Real-space Hopfield diagonalization of inhomogeneous dispersive media
Real-space Hopfield diagonalization of inhomogeneous dispersive media
We introduce a real-space technique able to extend the standard Hopfield approach commonly used in quantum polaritonics to the case of inhomogeneous lossless materials interacting with the electromagnetic field. We derive the creation and annihilation polaritonic operators for the system normal modes as linear, space-dependent superpositions of the microscopic light and matter fields. We prove their completeness and invert the Hopfield transformation expressing the microscopic fields as functions of the polaritonic operators. As an example, we apply our approach to the case of a planar interface between vacuum and a polar dielectric, showing how we can consistently treat both propagative and surface modes, and express their nonlinear interactions, arising from phonon anharmonicity, as polaritonic scattering terms. We also show that our theory, including the proof of completeness, can be naturally extended to the case of dissipative materials.
1550-235X
1-9
Gubbin, Christopher
09b75073-7a9a-4443-9a84-1458ec2535e9
Maier, Stefan A.
950db919-e145-48b5-bd73-196de02e46fe
De Liberato, Simone
5942e45f-3115-4027-8653-a82667ed8473
Gubbin, Christopher
09b75073-7a9a-4443-9a84-1458ec2535e9
Maier, Stefan A.
950db919-e145-48b5-bd73-196de02e46fe
De Liberato, Simone
5942e45f-3115-4027-8653-a82667ed8473

Gubbin, Christopher, Maier, Stefan A. and De Liberato, Simone (2016) Real-space Hopfield diagonalization of inhomogeneous dispersive media. Physical Review B, 94, 1-9. (doi:10.1103/PhysRevB.94.205301).

Record type: Article

Abstract

We introduce a real-space technique able to extend the standard Hopfield approach commonly used in quantum polaritonics to the case of inhomogeneous lossless materials interacting with the electromagnetic field. We derive the creation and annihilation polaritonic operators for the system normal modes as linear, space-dependent superpositions of the microscopic light and matter fields. We prove their completeness and invert the Hopfield transformation expressing the microscopic fields as functions of the polaritonic operators. As an example, we apply our approach to the case of a planar interface between vacuum and a polar dielectric, showing how we can consistently treat both propagative and surface modes, and express their nonlinear interactions, arising from phonon anharmonicity, as polaritonic scattering terms. We also show that our theory, including the proof of completeness, can be naturally extended to the case of dissipative materials.

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Accepted/In Press date: 13 October 2016
e-pub ahead of print date: 3 November 2016
Organisations: Quantum, Light & Matter Group

Identifiers

Local EPrints ID: 401900
URI: http://eprints.soton.ac.uk/id/eprint/401900
ISSN: 1550-235X
PURE UUID: ea55f1bb-8c1f-4eda-9b83-576ca598bf80
ORCID for Christopher Gubbin: ORCID iD orcid.org/0000-0003-3988-028X
ORCID for Simone De Liberato: ORCID iD orcid.org/0000-0002-4851-2633

Catalogue record

Date deposited: 24 Oct 2016 15:28
Last modified: 07 Oct 2020 04:54

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Contributors

Author: Christopher Gubbin ORCID iD
Author: Stefan A. Maier

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