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 provi
de 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.
We present a first-principles method to compute radiation properties of ultra-high quality factor photonic crystal cavities. Our Frequency-domain Approach for Radiation (FAR) can compute the far-field radiation pattern and quality factor of cavity mo
des $sim 100$ times more rapidly than conventional finite-difference time domain calculations. It also provides a simple rule for engineering the cavitys far-field radiation pattern.
