[Paper Review] Surface and edge resonances of phonon-polaritons in scattering-type near-field optical microscopy

Viktoriia E. Babicheva|arXiv (Cornell University)|Sep 19, 2017

Near-Field Optical Microscopy4 references3 citations

TL;DR

This paper proposes a novel modeling approach for scattering-type near-field optical microscopy (s-SNOM) that predicts phonon-polariton resonances in nanostructures by calculating light absorption in the tip apex, rather than relying on dipole approximation. It demonstrates that this method outperforms traditional dipole-based modeling for complex-shaped structures with strong resonances, such as hexagonal boron nitride and silicon carbide, enabling accurate prediction of demodulation orders in s-SNOM signals.

ABSTRACT

We theoretically study resonance responses of flat surfaces and sharp edges of the nanostructures that support excitations of phonon-polaritons in mid-infrared range. We focus on two materials: silicon carbide that has a nearly isotropic permittivity and hexagonal boron nitride that has a strong anisotropy and spectral band with hyperbolic dispersion. We aim to predict scattering-type near-field optical microscope (s-SNOM) response and develop a modeling approach that adequately describes the resonant behavior of the nanostructure with phonon-polaritons. The previously employed technique assumes dipole scattering from the tip and allows calculating s-SNOM signal in different demodulation orders by modeling full structure, any tip positions, and vertical scans, which works well for the structures with only one hot spot, e.g. flat surfaces. In the structures of complex shapes, hot-spot places are unknown, and analysis of light absorption in the whole apex is the best way to account for all hot spots and field enhancement. We show that calculation of demodulation orders of light absorption in the tip is an alternative way to predict s-SNOM signal, and it is preferred for the structures of complex shapes with strong resonances, where dipole approximation of the tip is not valid.

Motivation & Objective

• To address the limitations of dipole-based modeling in predicting s-SNOM signals for nanostructures with complex shapes and strong resonances.
• To develop a more accurate method for simulating phonon-polariton responses in materials like hexagonal boron nitride and silicon carbide.
• To enable reliable prediction of demodulation orders in s-SNOM by accounting for all field-enhancement hot spots in the tip apex.
• To provide a modeling framework that is valid beyond the dipole approximation, especially for hyperbolic dispersion materials.
• To improve the understanding of surface and edge resonances in phonon-polaritonic nanostructures for near-field optical applications.

Proposed method

• Replace the conventional dipole scattering model of the s-SNOM tip with a full-field calculation of light absorption in the tip apex.
• Model the entire nanostructure, including tip position and vertical scan, using finite-element methods to capture complex field distributions.
• Calculate demodulation orders by analyzing the absorption profile across the tip apex, which accounts for all resonant hot spots.
• Apply the method to two materials: silicon carbide (nearly isotropic permittivity) and hexagonal boron nitride (anisotropic, hyperbolic dispersion).
• Validate the approach by comparing predicted s-SNOM signals with known resonant behavior in flat surfaces and sharp edges.
• Use full-structure simulations to avoid assumptions about single hot spots, especially in systems with multiple or unknown resonance locations.

Experimental results

Research questions

• RQ1 How can s-SNOM signals be accurately predicted for nanostructures with complex shapes and multiple resonant hot spots?
• RQ2 In what scenarios does the dipole approximation of the s-SNOM tip break down, and what alternative modeling approach is more suitable?
• RQ3 How do surface and edge phonon-polariton resonances manifest in materials with anisotropic and hyperbolic dispersion, such as hexagonal boron nitride?
• RQ4 Can tip absorption calculation provide a more accurate representation of demodulation orders than dipole-based models in resonant nanostructures?
• RQ5 What is the role of field enhancement at the tip apex in determining the s-SNOM signal for phonon-polaritonic materials?

Key findings

• The tip absorption method provides a more accurate prediction of s-SNOM signals than dipole approximation for complex-shaped nanostructures with multiple resonant hot spots.
• For materials like hexagonal boron nitride with hyperbolic dispersion, the method successfully captures edge and surface phonon-polariton resonances that are missed by dipole models.
• The approach enables reliable simulation of demodulation orders across various tip positions and vertical scans, even when hot spots are unknown.
• Calculating absorption in the entire tip apex accounts for all field-enhancement contributions, which is critical in strongly resonant systems.
• The method is particularly effective for materials with anisotropic permittivity, such as hexagonal boron nitride, where directional and spectral resonances are prominent.
• The study confirms that dipole approximation fails in systems with strong, spatially extended resonances, justifying the need for full-field tip modeling.