Reflection Phase Shift Of One-dimensional Plasmon Polaritons In Carbon Nanotubes

The reflection phase shift(RPS)of propagating electromagnetic modes at interfaces is a fundamental physical concept.The reflection phenomena of the traditional plane wave propagating in a three-dimensional dielectric environment are well described by Fresnel reflection and transmission coefficients.However,the RPS of polaritons,which are propagating electromagnetic modes confined in low-dimensional materials,has not received much attention for a long time.With the emergence of lowdimensional materials in recent years,such as graphene,hexagonal boron nitride,and carbon nanotube,it has been possible to achieve high-quality polaritons in experiments,which provides a golden opportunity to study the RPS of polaritons in low-dimensional systems.The RPS of two-dimensional(2D)polaritons has already been studied.We investigated,both experimentally and theoretically,the reflection phase shift(RPS)of onedimensional plasmon polaritons in carbon nanotubes.Experimentally,we launched one-dimensional(1D)plasmon polaritons in carbon nanotubes and probed the plasmon interference pattern using a scanning near-field optical microscopy technique,through which a nonzero phase shift was observed.Plasmon polaritons confined in metallic carbon nanotubes exhibit an extraordinary quality.The sharp AFM tip enabled optical excitation of plasmons due to its large near-field momentum.We fabricated high-quality plasmons in carbon nanotube,and determined its RPS with the wavelength of incident infrared light ranging from 7.7 ?m to9.6 ?m.Theoretically,we investigated the RPS of one-dimensional plasmon polaritons using a combination of analytical calculations and COMSOL simulations.We first recreated the reflection phenomena of 1D polaritons in a carbon nanotube system by solving Maxwells equation numerically with COMSOL.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.Interestingly,our theory shows a strong dependence of RPS on polaritons wavelength and nanotube diameter,which is in stark contrast to two-dimensional plasmon polaritons in graphene where the RPS is a constant.In the 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 the 1D system,and could facilitate the design of ultrasmall 1D polaritonic devices,such as resonators and interferometers.