An exploration of open coupled-cavity lasers: from exceptional points to dynamics
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Date
2020-12-24
Authors
O'Connor, Christopher P.J.
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Publisher
University College Cork
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Abstract
In optical communications, there is an increase in demand for investigation of multisection laser cavities, which are involved in the development of Photonic Integrated Circuits or PICs. The requirement for such circuits results from, for example, the increase in demand for faster internet devices, which means improving the infrastructure involved. PICs are useful for such advancements as instead of an electrical circuit, these use optical devices such as lasers. Furthermore, these laser cavities are closely interacting or strongly coupled as they are of millimetre to submillimetre scales. Due to the size and complexity of these devices, they are not yet fully understood. Previous work has shown some interesting behaviour with these strongly coupled cavities. For example, the existence of exceptional points, where two modes coalesce, and also the possibility for a laser mode to go below threshold with increasing population inversion in a cavity, all in the steady state. However, for these types of devices, there is currently no full dynamical model that considers the complexity of strongly coupled cavities, with only outgoing light at the boundary of the laser.
Thus, the aim of this thesis is to investigate three important areas. The first is to understand the steady state situation further and improve upon what is known already. We introduce a new basis to do this and create a threshold condition, which is used to explore the complexities of coupled cavities. With this, we further address the occurrence of these exceptional points and give a more in-depth insight into the interesting effects that occur. The second area is to introduce a new, elegant approach in solving the electromagnetic field equation for the steady state, while still considering the geometrical features of a multisection laser. We introduce a second formalism for laser equations at threshold, which is shown to be a projection of a loxodromic spiral on a Riemann sphere with the use of Mobius transformations. With this, we investigate the threshold branches of multisection laser devices and discover a different type of exceptional point, where instead, the branches merge rather than modes. Furthermore, this new approach removes the need for unnecessary information while retaining the important physical characteristics to explain a coupled cavity laser. Lastly, a dynamical model that represents a strongly coupled laser with outgoing boundary conditions is introduced by connecting the classical electromagnetic field to the quantum mechanical description for the active medium. We go beyond the steady state by introducing a time-dependent scaling term for the electromagnetic field, which scales with the population inversion equations to provide a physically explained self-consistent set of dynamical equations. This model confirms results seen in the steady state situation. It also expands upon the steady state to show possible dynamical properties which are a result of the close interactions between both cavities, while crucially considering open boundary conditions while using the spatial profile for the active medium.
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Keywords
Laser physics , Photonic integrated circuits , Laser dynamics , Semiclassical laser theory , Applied mathematics , Exceptional points , Steady-state ab-initio laser theory
Citation
O'Connor, C. P. J. 2020. An exploration of open coupled-cavity lasers: from exceptional points to dynamics. PhD Thesis, University College Cork.