IEEE Researchers Provide Mathematical Solutions to Study 2D Light Interaction in Photonic Crystal Lasers

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Laser diodes are semiconductors that generate light and amplify it using repeated reflection or 'optical feedback'. Once the light has achieved desirable optical gain, laser diodes release it as powerful laser beams. Photonic crystal surface-emitting lasers (PCSELs) are advanced laser diodes where the optical gain is typically distributed laterally to the propagating light within a photonic crystal (PC) structure. They differ from traditional lasers by separating gain, feedback, and emission functions, offering scalable single-mode power and innovative designs.

In a paper that was recently published in Volume 31, Issue 2 of the IEEE Journal of Selected Topics in Quantum Electronics on 20 November, 2024, researchers have developed a method to numerically simulate the interaction of light waves within PCSELs. The researchers examined how light waves interact within a triangular-lattice PCSEL, where the PC forms a triangular grid structure. They found that the two-dimensional light wave interaction or 'coupling' within triangular-lattice PCSEL was stronger than that in square lattice PCSEL. This increased coupling offers greater optical feedback, which is beneficial for efficient lasing.

The researchers focused on six plane light waves propagating through the crystal and coupling through a process called Bragg diffraction. They then performed numerical simulations of 2D coupling of these plane wave in triangular-lattice PCSEL. Finally, they compared the 2D coupling with those seen in square lattice PCSEL.

The team derived analytical equations for both mode frequencies and coupling constants, which can be used alongside experimental band structure measurements to aid the design of transverse magnetic (TM) triangular lattice PCSELs. 'These equations improve in-plane 2D coupling for TM-mode triangular-lattice PCSELs, which is particularly beneficial for low-index contrast devices', notes Professor Stephen John Sweeney, a senior IEEE member and co-author of the study.

The researchers also derived the general form of the coupled wave equations for unit cells in the crystal lattice, which can further aid the experimental design of PCSELs with superior efficiency. Additionally, the team identified the 'fundamental lasing mode' of triangular-lattice PCSEL, which is the pattern of the electromagnetic field that offers the most efficient laser output.

The findings establish parallels between TM and transverse electric (TE) polarisation behaviours, while emphasizing the unique advantages TM modes offer in certain configurations, particularly in low index contrast devices.

The derived analytical models and coupling equations provide a foundation for experimental optimization of photonic crystal structures, enabling targeted enhancements in device efficiency and performance.