Compact lasers that can produce a range of beam patterns are important for progress in several areas, including the improvement of optical tweezers, ultra-high-density optical memory and microfluidics. Here we engineer photonic crystals to generate semiconductor lasers that produce a range of beam patterns while maintaining stable single-mode oscillation. Our results could contribute to the realization of compact lasers that are capable of producing diverse beam patterns on demand.

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We present a useful framework based on the coupled-wave theory, through which we can survey the resonant modes of TM polarization in 2D photonic-crystal lasers and understand their properties in detail. Through numerical calculations, we clarify their threshold gains, deviations from the Bragg frequency and field distributions. We find that the lasing mode can be selected by manipulating the hole-filling factor or the boundary reflection.

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We propose a coupled-wave model for a square-lattice two-dimensional (2D) photonic crystal (PC) with a transverse electric mode. A set of coupled-wave equations is obtained from this model and it is shown that 2D optical coupling occurs between four light waves propagating in the Γ-X direction via higher-order waves propagating in the Γ-M direction. The expressions for the resonant mode frequencies derived from the coupled-wave equations describe the characteristics of experimental results for the band-edge frequencies of the 2D PC laser.

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