Numerical Aperture of Single-Mode Photonic Crystal Fibers

We consider the problem of radiation into free space from the end-facet of a single-mode photonic crystal fiber (PCF). We calculate the numerical aperture NA=sin theta from the half-divergence angle theta ~ tan^{-1}(lambda/pi w) with pi w^2 being the effective area of the mode in the PCF. For the fiber first presented by Knight et al. we find a numerical aperture NA ~ 0.07 which compares to standard fiber technology. We also study the effect of different hole sizes and demonstrate that the PCF technology provides a large freedom for NA-engineering. Comparing to experiments we find good agreement.