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Periodic wavelength-scale surface patterns have long been used in the context of lasing and spontaneous emission to enhance emission by light trapping (distributed Bragg resonances). Buried within these well-known devices, however, are theoretical mysteries that are still being unravelled. A periodic surface grating actually creates a continuum of resonant modes, so what determines which single mode (if any) lases? Technically, what determines the stability of a periodic lasing mode: is it only the finite size of a surface that allows single-mode lasing, or can it arise for arbitrarily large structures? More generally, if one continuously deforms an unpatterned surface to maximize light emission, how is the symmetry broken and what optimal structures arise? We address these questions by combining new computational techniques for modeling and large-scale optimization of incoherent emission and lasing with new analytical results arising from perturbation and stability theory.
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