Equifrequency surfaces in a two-dimensional GaN-based photonic crystal

Area of Science:

• Nonlinear Optics
• Photonic Crystals
• Materials Science

Background:

• Quasi-phase matching (QPM) is crucial for efficient nonlinear optical processes like second-harmonic generation (SHG).
• Two-dimensional (2D) photonic crystals offer unique opportunities to tailor light-matter interactions beyond one-dimensional (1D) systems.

Purpose of the Study:

• To determine the angular conditions for achieving quasi-phase matching in 2D photonic crystals for enhanced second-harmonic generation.
• To compare the tuning range of QPM in 2D versus 1D structures.

Main Methods:

• Investigated the equifrequency surfaces of resonant Bloch modes in a 2D periodic GaN/sapphire hole-array photonic crystal.
• Employed a scattering matrix method for theoretical calculations.
• Analyzed the angular dependence of fundamental and second-harmonic frequencies.

Main Results:

• Observed complex equifrequency surface shapes in the 2D photonic crystal, differing significantly from 1D structures.
• Anisotropy of the equifrequency surfaces agreed well with scattering matrix method calculations.
• Identified specific polar and azimuthal angles for QPM in the 2D structure.

Conclusions:

• Established angular conditions for quasi-phase matching in 2D photonic crystals, enabling enhanced second-harmonic generation.
• Demonstrated that 2D structures provide approximately double the fractional bandwidth for frequency tuning compared to 1D structures.
• Highlighted the potential of 2D photonic crystals for broader tuning ranges in nonlinear optical frequency conversion.