Theory of probing a photonic crystal with transmission near-field optical microscopy

While near-field scanning optical microscopy ~NSOM! can provide optical images with resolution much better than the diffraction limit, analysis and interpretation of these images is often difficult. We present a theory of probing with transmission NSOM that includes the effects of tip field, tip/sample coupling, light propagation through the sample, and light collection. We apply this theory to analyze experimental NSOM images of a nanochannel glass ~NCG! array obtained in transmission mode. The NCG is a triangular array of dielectric rods in a dielectric glass matrix with a two-dimensional photonic band structure. We determine the modes for the NCG photonic crystal and simulate the observed data. The calculations show large contrast at low numerical aperture ~NA! of the collection optics and detailed structure at high NA consistent with the observed images. We present calculations as a function of NA to identify how the NCG photonic modes contribute to and determine the spatial structure in these images. Calculations are presented as a function of tip/sample position, sample index contrast and geometry, and aperture size to identify the factors that determine image formation with transmission NSOM in this experiment. @S0163-1829~98!06128-1#