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Proceedings Paper

Lasing eigenvalue problems: the electromagnetic modelling of microlasers
Author(s): Trevor Benson; Alexander Nosich; Elena Smotrova; Mikhail Balaban; Phillip Sewell
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Paper Abstract

Comprehensive microcavity laser models should account for several physical mechanisms, e.g. carrier transport, heating and optical confinement, coupled by non-linear effects. Nevertheless, considerable useful information can still be obtained if all non-electromagnetic effects are neglected, often within an additional effective-index reduction to an equivalent 2D problem, and the optical modes viewed as solutions of Maxwell's equations. Integral equation (IE) formulations have many advantages over numerical techniques such as FDTD for the study of such microcavity laser problems. The most notable advantages of an IE approach are computational efficiency, the correct description of cavity boundaries without stair-step errors, and the direct solution of an eigenvalue problem rather than the spectral analysis of a transient signal. Boundary IE (BIE) formulations are more economic that volume IE (VIE) ones, because of their lower dimensionality, but they are only applicable to the constant cavity refractive index case. The Muller BIE, being free of 'defect' frequencies and having smooth or integrable kernels, provides a reliable tool for the modal analysis of microcavities. Whilst such an approach can readily identify complex-valued natural frequencies and Q-factors, the lasing condition is not addressed directly. We have thus suggested using a Muller BIE approach to solve a lasing eigenvalue problem (LEP), i.e. a linear eigenvalue solution in the form of two real-valued numbers (lasing wavelength and threshold information) when macroscopic gain is introduced into the cavity material within an active region. Such an approach yields clear insight into the lasing thresholds of individual cavities with uniform and non-uniform gain, cavities coupled as photonic molecules and cavities equipped with one or more quantum dots.

Paper Details

Date Published: 14 February 2007
PDF: 8 pages
Proc. SPIE 6452, Laser Resonators and Beam Control IX, 64520L (14 February 2007); doi: 10.1117/12.711403
Show Author Affiliations
Trevor Benson, Univ. of Nottingham (United Kingdom)
Alexander Nosich, Institute of Radio-Physics and Electronics (Ukraine)
Elena Smotrova, Institute of Radio-Physics and Electronics (Ukraine)
Mikhail Balaban, Institute of Radio-Physics and Electronics (Ukraine)
Phillip Sewell, Univ. of Nottingham (United Kingdom)

Published in SPIE Proceedings Vol. 6452:
Laser Resonators and Beam Control IX
Alexis V. Kudryashov; Alan H. Paxton; Vladimir S. Ilchenko, Editor(s)

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