Photonic crystal surface emitting lasers (PCSEL) are of interest in order to achieve large area single mode operation, excellent beam quality, and high output powers. Coherent PCSEL arrays have also been realised and lasing mode control of PCSELs has been demonstrated by using external in-plane feedback.
However, the design and analysis of PCSELs has been limited by current modelling techniques. The plane wave expansion method is only applicable to infinite structures whilst the finite difference time domain method is computationally intensive especially when modelling large area, three dimensional finite devices. Other analytical approach, such as coupled mode analysis, leads to significant mathematical complication. None of these are well suited to accurately describing complex PCSEL devices, nor the effect of in-plane feedback.
We introduce a general quasi-analytical model based on the separation of variables and a quasi-scalar field distribution. The multilayer planar structure in the growth direction is accounted for by computing the effective indices corresponding to the in-plane bound guided modes. This operation results in a sculpted, periodic index distribution. Next, by first assuming index uniformity along the z-axis, a piecewise constant multilayer periodic media results. An effective wave impedance of the waves supported in this structure are then computed and used to construct the 3D device. In this way, the final device characteristics account for the 2D periodic photonic crystal media.
We compare our modelling to other methods, and various experimental reports. In particular we focus upon the effect of external in-plane feedback on PCSELs.
Pavlo Ivanov, Richard A. Hogg, Richard J. Taylor, David T. D. Childs, and Guangrui Li, "Effective index modelling of photonic crystal surface-emitting lasers (Conference Presentation)," Proc. SPIE 10526, Physics and Simulation of Optoelectronic Devices XXVI, 105260O (Presented at SPIE OPTO: January 30, 2018; Published: 14 March 2018); https://doi.org/10.1117/12.2290680.5751402732001.
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