We derive a frequency-domain-based approach for radiation (FAR) from double-heterostructure cavity (DHC) modes. We use this to compute the quality factors and radiation patterns of DHC modes. The semi-analytic nature of our method enables us to provide a general relationship between the radiation pattern of the cavity and its geometry. We use this to provide general designs for ultrahigh quality factor DHCs with radiation patterns that are engineered to emit vertically.
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