Modes of shallow photonic crystal waveguides: Semi-analytic treatment

Mahmoodian, S; Poulton, CG; Dossou, KB; McPhedran, RC; Botten, LC; De Sterke, CM

Modes of shallow photonic crystal waveguides: Semi-analytic treatment

Mahmoodian, S Poulton, CG

Dossou, KB

McPhedran, RC Botten, LC

De Sterke, CM

Permalink

Publication Type:: Journal Article
Citation:: Optics Express, 2009, 17 (22), pp. 19629 - 19643
Issue Date:: 2009-01-01

Open Access

Copyright Clearance Process

Recently Added
In Progress
Open Access

This item is open access.

Adobe PDF

Download full textAdobe PDF (669.15 kB)

View on publisher's site

View statistics

Full metadata record

Field	Value	Language
dc.contributor.author	Mahmoodian, S	en_US
dc.contributor.author	Poulton, CG https://orcid.org/0000-0002-2707-3424	en_US
dc.contributor.author	Dossou, KB https://orcid.org/0000-0002-2342-8945	en_US
dc.contributor.author	McPhedran, RC	en_US
dc.contributor.author	Botten, LC https://orcid.org/0000-0001-6471-6954	en_US
dc.contributor.author	De Sterke, CM	en_US
dc.date.issued	2009-01-01	en_US
dc.identifier.citation	Optics Express, 2009, 17 (22), pp. 19629 - 19643	en_US
dc.identifier.uri	http://hdl.handle.net/10453/9493
dc.description.abstract	We investigate the formation of photonic crystal waveguide (PCW) modes within the framework of perturbation theory. We derive a differential equation governing the envelope of PCW modes constructed from weak perturbations using an effective mass formulation based on the Luttinger-Kohn method from solid-state physics. The solution of this equation gives the frequency of the mode and its field. The differential equation lends itself to simple analytic approximations which reduce the problem to that of solving slab waveguide modes. By using this model, we demonstrate that the nature of the projected band structure and corresponding Bloch functions are central to the behaviour of PCW modes. With this understanding, we explain why the odd mode in a hexagonal PCW spans the entire Brillouin zone while the even mode is cut off. © 2009 Optical Society of America.	en_US
dc.relation.ispartof	Optics Express	en_US
dc.relation.isbasedon	10.1364/OE.17.019629	en_US
dc.rights	© 2009 Optical Society of America. Users may use, reuse, and build upon the article, or use the article for text or data mining, so long as such uses are for non-commercial purposes and appropriate attribution is maintained. All other rights are reserved.	en_US
dc.subject.classification	Optics	en_US
dc.subject.mesh	Crystallization	en_US
dc.subject.mesh	Refractometry	en_US
dc.subject.mesh	Sensitivity and Specificity	en_US
dc.subject.mesh	Reproducibility of Results	en_US
dc.subject.mesh	Equipment Design	en_US
dc.subject.mesh	Equipment Failure Analysis	en_US
dc.subject.mesh	Light	en_US
dc.subject.mesh	Scattering, Radiation	en_US
dc.subject.mesh	Models, Theoretical	en_US
dc.subject.mesh	Manufactured Materials	en_US
dc.subject.mesh	Computer-Aided Design	en_US
dc.subject.mesh	Computer Simulation	en_US
dc.title	Modes of shallow photonic crystal waveguides: Semi-analytic treatment	en_US
dc.type	Journal Article
utslib.citation.volume	22	en_US
utslib.citation.volume	17	en_US
utslib.for	0205 Optical Physics	en_US
utslib.for	0906 Electrical and Electronic Engineering	en_US
utslib.for	1005 Communications Technologies	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
pubs.organisational-group	/University of Technology Sydney/Faculty of Science/School of Mathematical and Physical Sciences
utslib.copyright.status	open_access
pubs.issue	22	en_US
pubs.publication-status	Published	en_US
pubs.volume	17	en_US

Abstract:

We investigate the formation of photonic crystal waveguide (PCW) modes within the framework of perturbation theory. We derive a differential equation governing the envelope of PCW modes constructed from weak perturbations using an effective mass formulation based on the Luttinger-Kohn method from solid-state physics. The solution of this equation gives the frequency of the mode and its field. The differential equation lends itself to simple analytic approximations which reduce the problem to that of solving slab waveguide modes. By using this model, we demonstrate that the nature of the projected band structure and corresponding Bloch functions are central to the behaviour of PCW modes. With this understanding, we explain why the odd mode in a hexagonal PCW spans the entire Brillouin zone while the even mode is cut off. © 2009 Optical Society of America.

Please use this identifier to cite or link to this item:

http://hdl.handle.net/10453/9493