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Investigating the Radial Photonic Band Structure of Second-Order Circular Gratings Using FDTD and Hankel Transform
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DOI：10.1109/JSTQE.2026.3676074.png)
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Abstract
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Second-order circular gratings enable precise control of azimuthal modes and far-field symmetry in surface-emitting laser devices due to their rotational symmetry. In this study, we present a comprehensive analysis of the photonic band structures along the radial direction of circular gratings using a novel method combining Finite-Difference Time-Domain (FDTD) simulations with the Hankel transform. This method establishes a band-structure-level description of radial dispersion in circularly symmetric gratings. Energy bands were extracted by exciting the gratings at the center and sampling the radial field distribution via time-domain monitors. We systematically investigated the impact of field polarization, number of periods, duty cycle, and etch depth of gratings on the dispersion relation, revealing that both the width and spectral position of the bandgap are highly tunable by these parameters. To validate our model, angle-resolved spectroscopy was performed on fabricated GaN-based circular gratings with multiple quantum wells. The obtained band structures show clear photonic bandgaps and symmetric dispersion around the high-symmetry points, confirming the existence of radial photonic bands. These findings provide a foundation for the design of novel surface emitting lasers that leverage the band-edge properties of second-order circular gratings.
Keywords:
Circular gratings
Hankel transform
GaN laser
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