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

TL;DR

This paper develops a comprehensive theory for transmission near-field optical microscopy (NSOM) imaging of photonic crystals, analyzing experimental images of a nanochannel glass array and identifying factors influencing image formation.

Contribution

It introduces a detailed theoretical framework for transmission NSOM imaging of photonic structures, including tip effects and light propagation, validated by experimental data.

Findings

Large contrast at low NA in NSOM images

Detailed structural features at high NA

Identification of factors affecting image formation

Abstract

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 imaging 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.