Two-Dimensional Coupled Wave Theory for Triangular Lattice TM-polarised Photonic Crystal Surface Emitting Lasers

Matthew N. Robinson; Stephen J. Sweeney; Richard A. Hogg

doi:10.1109/JSTQE.2024.3502794

Two-Dimensional Coupled Wave Theory for Triangular Lattice TM-polarised Photonic Crystal Surface Emitting Lasers

Matthew N. Robinson, Stephen J. Sweeney, Richard A. Hogg

Aston Institute of Photonic Technologies (AiPT)

University of Glasgow

Research output: Contribution to journal › Article › peer-review

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Abstract

This paper presents a coupled-wave analysis of triangular-lattice photonic crystal surface emitting lasers (PCSELs) with transverse magnetic polarization. Six plane waves coupled by Bragg diffraction describe the two-dimensional optical coupling. Resonant mode frequencies are calculated for a lattice of circular holes at various fill factors and compared to the plane-wave expansion method. Analytical equations for coupling constants and mode frequencies are derived, and mode degeneracy as a function of fill factor is examined. Comparision to a square lattice TM mode PCSEL shows improved in-plane 2D coupling. The general equations for arbitrary unit cell dielectric functions are discussed, with predictions of the lasing mode supported by finite device calculations.

Original language	English
Article number	1700811
Number of pages	11
Journal	IEEE Journal of Selected Topics in Quantum Electronics
Volume	31
Issue number	2
Early online date	20 Nov 2024
DOIs	https://doi.org/10.1109/JSTQE.2024.3502794
Publication status	Published - Mar 2025

Bibliographical note

Copyright © 2024, IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

Funding

This work was supported by the EPSRC and SFI through the PIADS CDT under Grant EP/S023321/1.

Funders	Funder number
Engineering and Physical Sciences Research Council
Science Foundation Ireland	EP/S023321/1

Keywords

Lattices
Continuous wavelet transforms
Couplings
Vectors
Photonic crystals
Surface emitting lasers
Mathematical models
Laser modes
Distributed feedback devices
Three-dimensional displays

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10.1109/JSTQE.2024.3502794

MN Robinson et al_AAM_Two-Dimensional_Coupled_Wave_Theory_for_Triangular_Lattice_TM-polarised_Photonic_Crystal_Surface_Emitting_Lasers
Copyright © 2024, IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Accepted author manuscript, 7 MBLicence: Unspecified

Cite this

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title = "Two-Dimensional Coupled Wave Theory for Triangular Lattice TM-polarised Photonic Crystal Surface Emitting Lasers",

abstract = "This paper presents a coupled-wave analysis of triangular-lattice photonic crystal surface emitting lasers (PCSELs) with transverse magnetic polarization. Six plane waves coupled by Bragg diffraction describe the two-dimensional optical coupling. Resonant mode frequencies are calculated for a lattice of circular holes at various fill factors and compared to the plane-wave expansion method. Analytical equations for coupling constants and mode frequencies are derived, and mode degeneracy as a function of fill factor is examined. Comparision to a square lattice TM mode PCSEL shows improved in-plane 2D coupling. The general equations for arbitrary unit cell dielectric functions are discussed, with predictions of the lasing mode supported by finite device calculations.",

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author = "Robinson, {Matthew N.} and Sweeney, {Stephen J.} and Hogg, {Richard A.}",

note = "Copyright {\textcopyright} 2024, IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.",

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AU - Sweeney, Stephen J.

AU - Hogg, Richard A.

N1 - Copyright © 2024, IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

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N2 - This paper presents a coupled-wave analysis of triangular-lattice photonic crystal surface emitting lasers (PCSELs) with transverse magnetic polarization. Six plane waves coupled by Bragg diffraction describe the two-dimensional optical coupling. Resonant mode frequencies are calculated for a lattice of circular holes at various fill factors and compared to the plane-wave expansion method. Analytical equations for coupling constants and mode frequencies are derived, and mode degeneracy as a function of fill factor is examined. Comparision to a square lattice TM mode PCSEL shows improved in-plane 2D coupling. The general equations for arbitrary unit cell dielectric functions are discussed, with predictions of the lasing mode supported by finite device calculations.

AB - This paper presents a coupled-wave analysis of triangular-lattice photonic crystal surface emitting lasers (PCSELs) with transverse magnetic polarization. Six plane waves coupled by Bragg diffraction describe the two-dimensional optical coupling. Resonant mode frequencies are calculated for a lattice of circular holes at various fill factors and compared to the plane-wave expansion method. Analytical equations for coupling constants and mode frequencies are derived, and mode degeneracy as a function of fill factor is examined. Comparision to a square lattice TM mode PCSEL shows improved in-plane 2D coupling. The general equations for arbitrary unit cell dielectric functions are discussed, with predictions of the lasing mode supported by finite device calculations.

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KW - Couplings

KW - Vectors

KW - Photonic crystals

KW - Surface emitting lasers

KW - Mathematical models

KW - Laser modes

KW - Distributed feedback devices

KW - Three-dimensional displays

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JO - IEEE Journal of Selected Topics in Quantum Electronics

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Two-Dimensional Coupled Wave Theory for Triangular Lattice TM-polarised Photonic Crystal Surface Emitting Lasers

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