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

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 (N A) of the collection optics and detailed structure at high N A consistent with the observed images. We present calculations as a function of N A to identify how the NCG photonic modes contribute to and 1 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.

Near-field second-harmonic generation of semiconductor quantum dots

“…Previously, the Bethe-Bouwkamp model has been used to calculate the tip field and to analyze experimental near-field images. 21 However, in this model the effect of the finite thickness of the metal cladding on the tip field is neglected. Also, the tip has been modeled frequently as a singleradiating dipole 22 for the simplicity of calculations and the clarity of the physical picture.…”

“…5 and 6 except that a fundamental frequency of បϭ0.93 eV is employed. Note that, in the Bethe-Bouwkamp model, 4,21,31,32 the tip core is vacuum and the metal cladding is a perfect conductor with infinite extension in the xy plane but zero extension along the z direction. We see from Figs.…”

Spectral Domain Analysis of a Circular Nano-Aperture Illuminating a Planar Layered Sample

“…The sources of these partial fields are determined by the spectrum of the BB equivalent magnetic current of the aperture. Consequently, the spectral domain approach based on the BB model has frequently been used in the SNOM context [7][8][9][10][11][12][13][14][15][16][17], and some of these works included the effect of a nearby planar material sample in the formulation. Baida and Van Labeke [15] also converted the Cartesian Fourier transform representation into a more efficient Fourier-Bessel transform representation, which replaces the two-dimensional Fourier-type integrals by one-dimensional Hankel transforms.…”

Near-field scanning optical microscopy of photonic crystal nanocavities

“…On the other hand, near-field scanning optical microscopy ͑NSOM͒ has recently been used as a powerful alternative method to analyze local electromagnetic field distributions in fabricated nanophotonic structures. [9][10][11][12][13][14][15][16][17] Gérard et al 14 reported NSOM measurements of active PPC with spectral emission in the infrared region and Shin et al 15 reported the near-field investigation of the lasing modes in PPC lasers. However, in both studies, uncoated optical fibers were used and, therefore, it was not possible to obtain high spatially resolved near-field images of the field distribution inside the cavity.…”

“…Similar results were predicted by theory. 10 Also, spectra obtained using microphotoluminescence ͓Fig. 5͑c͔͒ show the presence of dielectric bands at ϭ1555 nm.…”