Lasing Action from Quasi‐Propagating Modes

Abstract

longitudinal beam profiles, [1,2] and because of their increased rotational symmetry, 2D cavities enable multimode lasing, [3,4] vortex polarization, and annular-shaped beams. [2,5] Most lasing work on 2D photonic crystals exploits band edges at high symmetry points (e.g., Γ, X, and M points of a square lattice) in reciprocal space for optical feedback. [6][7][8][9] Since standing waves at these points are biaxially confined, solutions to their wave equation are critically constrained, which limits lasing action to discrete wavelengths and directions. [10] However, 2D photonic crystals can also be considered as lines of 1D arrays, where in-plane scattered waves are decomposed along two orthogonal directions. [2,10,11] In this picture, quasi-propagating photonic modes are slow traveling waves and can be interpreted as uniaxially confined standing waves that propagate along high-symmetry directions (e.g., Γ-M, Γ-X, and M-X). The additional degree of freedom from propagation enables the band edge states to span a continuum of energies and wavevectors. [10,12,13] Although quasi-propagating modes are predicted to support optical feedback, [10,13,14] lasing action via 2D cavities remains primarily focused on that from high symmetry points.Strongly scattering 2D plasmonic nanoparticle (NP) lattices that can trap light in-plane support hybrid photonic-plasmonic modes known as surface lattice resonances (SLRs). [15,16] Feedback from SLRs has enabled nanoscale lasing from NP lattice cavities integrated with index-matched emitter gain materials such as organic dyes in solvents and upconversion NP thin films. [17][18][19][20] NP lattices integrated with high-refractiveindex emissive materials such as colloidal quantum dot films have also demonstrated lasing from transverse electric (TE) and transverse magnetic (TM) waveguide-hybridized SLRs (W TE -SLRs and W TM -SLRs). [21][22][23] Because of the mode structure of the waveguide component, W-SLRs can excite large volumes of active material for lasing. [22,24] For either SLR or W-SLR modes, however, feedback for lasing is from biaxially confined standing waves [21,23,[25][26][27] since their losses are lower than quasipropagating modes. [2,28,29] Lasing from quasi-propagating modes should be possible; we hypothesize that they have been elusive due to insufficient gain coefficients (≈10-200 cm −1 ). [30,31] Although engineered gain materials such as gradient-shell quantum dots [32] or dyes with minimized triplet states [33] may offer higher gain, their syntheses are challenging. In contrast, lead halide perovskite nanocrystals (NCs) can be readily Band edges at the high symmetry points in reciprocal space of periodic structures hold special interest in materials engineering for their high density of states. In optical metamaterials, standing waves found at these points have facilitated lasing, bound-states-in-the-continuum, and Bose-Einstein condensation. However, because high symmetry points by definition are localized, properties associated with them are limited to specific e...

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