Diacritical study of light, electrons and sound scattering by particles and holes

F Javier García De Abajo,Francisco Meseguer,Héctor Estrada

doi:10.1088/1367-2630/11/9/093013

Abstract

We discuss the differences and similarities in the interaction of scalar and vector wave fields with particles and holes. Analytical results are provided for the transmission of isolated and arrayed small holes as well as surface modes in hole arrays for light, electrons and sound. In contrast to the optical case, small-hole arrays in perforated perfect screens cannot produce acoustic or electronic surface-bound states. However, unlike electrons and light, sound is transmitted through individual holes approximately in proportion to their area, regardless of their size. We discuss these issues with a systematic analysis that allows one to explore both common properties and unique behavior in wave phenomena for different material realizations.

Highlights

Scientists have been fascinated by wave phenomena and the many common aspects shared by different physical realizations of propagating oscillatory motion, unique behavior is accompanying each of them [1]
Z→±0 we find that (i) the expression (3) has vanishing normal derivative in the screen outside S, satisfying the boundary conditions for Fig. 3(a), and (ii) ψscat(r) + exp(ik · R + ikzz) vanishes at S, so that it represents the solution for an electron wave function incident on the complementary screen [Fig. 3(b)]
This means that the transmittance of sound through a drilled screen coincides with the reflectance of electrons on the complementary disk(s)

Summary

INTRODUCTION

Scientists have been fascinated by wave phenomena and the many common aspects shared by different physical realizations of propagating oscillatory motion, unique behavior is accompanying each of them [1]. Electrons, and sound are prototypical examples of waves that reveal profound differences, even at the level of a single-particle, classical description. This discussion is preceded by a rich literature dating back to the nineteenth century [1, 2, 3, 4, 5, 6, 7, 8, 9]. We demonstrate that hole arrays in thin screens cannot sustain acoustic or electronic surface-trapped modes, in contrast to the optical case These results provide essential tools for exploring other common properties and unique behavior in wave phenomena, some of which are outlined in the concluding paragraph.

INDIVIDUAL HOLES

Re Im

BOUND STATES IN HOLE ARRAYS

PARTICLE ARRAYS

SUMMARY

Noticing that