Reflection Phase Shift of One-dimensional Plasmon Polaritons in Carbon Nanotubes

TL;DR

This study explores the reflection phase shift of one-dimensional plasmon polaritons in carbon nanotubes through experiments and theory, revealing a wavelength and diameter-dependent phase shift that differs from 2D systems, with implications for nanoscale polaritonic devices.

Contribution

The paper provides the first combined experimental and theoretical analysis of RPS in 1D plasmon polaritons in carbon nanotubes, highlighting its dependence on wavelength and diameter.

Findings

RPS is non-zero and depends on nanotube parameters.

Theoretical model explains RPS via evanescent fields beyond nanotube ends.

RPS varies with the ratio of wavelength to nanotube diameter.

Abstract

We investigated, both experimentally and theoretically, the reflection phase shift (RPS) of one-dimensional plasmon polaritons. We launched 1D plasmon polaritons in carbon nanotube and probed the plasmon interference pattern using scanning near-field optical microscopy (SNOM) technique, through which a non-zero phase shift was observed. We further developed a theory to understand the nonzero phase shift of 1D polaritons, and found that the RPS can be understood by considering the evanescent field beyond the nanotube end. Interesting, our theory shows a strong dependence of RPS on polaritons wavelength and nanotube diameter, which is in stark contrast to 2D plasmon polaritons in graphene where the RPS is a constant. In short wave region, the RPS of 1D polaritons only depends on a dimensionless variable -- the ratio between polaritons wavelength and nanotube diameter. These results provide fundamental insights into the reflection of polaritons in 1D system, and could facilitate the design of ultrasmall 1D polaritonic devices, such as resonators, interferometers.