The University of Southampton
University of Southampton Institutional Repository

Time delay distribution in Bragg gratings

Time delay distribution in Bragg gratings
Time delay distribution in Bragg gratings
A layer-by-layer analysis of the time delay of both reflected and transmitted light in one-dimensional photonic band-gap structures is developed and applied to uniform Bragg gratings. An effective Fabry-Pérot cavity is associated with every layer along the Bragg grating, multiple paths with a well defined layer traversal time are identified, and the average time is computed, introducing an appropriate weighting factor that accounts for interference between different paths. The analysis presented leads directly to a complex-valued time delay whose real part is shown to be equivalent to the classic phase time delay. Physical meaning is also given to the imaginary part. The local dwell time, interpreted as the average time spent by light in the layer independently of the final (transmitted or reflected) state, is proved analytically to be related to the energy density distribution when small index change gratings are considered. The time delay evolution is derived at different wavelengths and the nonuniform distribution along the grating is discussed. Nonintuitive features such as superluminal transmission time delay for propagation inside the band gap and negative reflection time delay close to transmission resonances are addressed. Finally, the effect of introducing a small perturbation in the structure is shown to be directly related to the local time delay and is proposed as a possible experimental measurement scheme for both its real and imaginary parts.
1539-3755
036604-[13pp]
Ghiringhelli, F.
773894f2-f092-452f-84ae-98e3b64aca3f
Zervas, M.N.
1840a474-dd50-4a55-ab74-6f086aa3f701
Ghiringhelli, F.
773894f2-f092-452f-84ae-98e3b64aca3f
Zervas, M.N.
1840a474-dd50-4a55-ab74-6f086aa3f701

Ghiringhelli, F. and Zervas, M.N. (2002) Time delay distribution in Bragg gratings. Physical Review E, 65 (3), 036604-[13pp]. (doi:10.1103/PhysRevE.65.036604).

Record type: Article

Abstract

A layer-by-layer analysis of the time delay of both reflected and transmitted light in one-dimensional photonic band-gap structures is developed and applied to uniform Bragg gratings. An effective Fabry-Pérot cavity is associated with every layer along the Bragg grating, multiple paths with a well defined layer traversal time are identified, and the average time is computed, introducing an appropriate weighting factor that accounts for interference between different paths. The analysis presented leads directly to a complex-valued time delay whose real part is shown to be equivalent to the classic phase time delay. Physical meaning is also given to the imaginary part. The local dwell time, interpreted as the average time spent by light in the layer independently of the final (transmitted or reflected) state, is proved analytically to be related to the energy density distribution when small index change gratings are considered. The time delay evolution is derived at different wavelengths and the nonuniform distribution along the grating is discussed. Nonintuitive features such as superluminal transmission time delay for propagation inside the band gap and negative reflection time delay close to transmission resonances are addressed. Finally, the effect of introducing a small perturbation in the structure is shown to be directly related to the local time delay and is proposed as a possible experimental measurement scheme for both its real and imaginary parts.

This record has no associated files available for download.

More information

Published date: 2002

Identifiers

Local EPrints ID: 13806
URI: http://eprints.soton.ac.uk/id/eprint/13806
ISSN: 1539-3755
PURE UUID: af1f8324-2d5c-4b35-a05a-5fbcb857e7e9
ORCID for M.N. Zervas: ORCID iD orcid.org/0000-0002-0651-4059

Catalogue record

Date deposited: 07 Jan 2005
Last modified: 09 Jan 2022 02:40

Export record

Altmetrics

Contributors

Author: F. Ghiringhelli
Author: M.N. Zervas ORCID iD

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×