Lasing eigenvalue problems: the electromagnetic modelling of microlasers

Trevor Benson; Alexander Nosich; Elena Smotrova; Mikhail Balaban; Phillip Sewell

doi:10.1117/12.711403

14 February 2007 Lasing eigenvalue problems: the electromagnetic modelling of microlasers

Trevor Benson, Alexander Nosich, Elena Smotrova, Mikhail Balaban, Phillip Sewell

Proceedings Volume 6452, Laser Resonators and Beam Control IX; 64520L (2007) https://doi.org/10.1117/12.711403
Event: Lasers and Applications in Science and Engineering, 2007, San Jose, California, United States

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.

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Trevor Benson, Alexander Nosich, Elena Smotrova, Mikhail Balaban, and Phillip Sewell "Lasing eigenvalue problems: the electromagnetic modelling of microlasers", Proc. SPIE 6452, Laser Resonators and Beam Control IX, 64520L (14 February 2007); https://doi.org/10.1117/12.711403

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KEYWORDS

Electromagnetism

Refractive index

Optical microcavities

Modeling

Error analysis

Finite-difference time-domain method

Modal analysis

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