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 /spl theta/ from the half-divergence angle /spl theta/ /spl sim/ tan/sup -1/ (/spl lambda///spl pi//spl omega/) with /spl pi//spl omega//sup 2/ being the effective area of the mode in the PCF. For the fiber first presented by Knight et al. (1996), we find a NA /spl sim/ 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.