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
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.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
