Wave functions for high-symmetry, thin microstrip antennas and two-dimensional quantum boxes

Abstract

For a spinless quantum particle in a one-dimensional box or an electromagnetic wave in a one-dimensional cavity, the respective Dirichlet and Neumann boundary conditions both lead to non-degenerate wave functions. However, in two spatial dimensions, the symmetry of the box or microstrip antenna is an important feature that has often been overlooked in the literature. In the high-symmetry cases of a disk, square, or equilateral triangle, the wave functions for each of those two boundary conditions are grouped into two distinct classes, which are one- and two-dimensional representations of the respective point groups, $C_{\infty v}$, $C_{4v}$, and $C_{3v}$. Here we present visualizations of representative wave functions for both boundary conditions and both one- and two-dimensional representations of those point groups. For the one-dimensional representations, color contour plots of the wave functions are presented. For the two-dimensional representations, the infinite degeneracies are presented as common nodal points and/or lines, the patterns of which are invariant under all operations of the respective point group. The wave functions with the Neumann boundary conditions have important consequences for the coherent terahertz emission from the intrinsic Josephson junctions in the high-temperature superconductor Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta }$: the enhancement of the output power from electromagnetic cavity resonances is only strong for wave functions that are not degenerate.

arXiv comment18 pages, 23 figures

References in corpus (15)

• Coherent THz emission of Bi_2Sr_2CaCu_2O_8 intrinsic Josephson junction stacks in the hot spot regime
• Hot spots and waves in Bi2Sr2CaCu2O8 intrinsic Josephson junction stacks -a study by Low Temperature Scanning Laser Microscopy
• Geometrical Resonance Conditions for THz Radiation from the Intrinsic Josephson Junctions in Bi2Sr2CaCu2O8+d
• Pristine and intercalated transition metal dichalcogenide superconductors
• Powerful terahertz emission from Bi2Sr2CaCu2O8+delta mesa arrays
• Broadly Tunable Sub-terahertz Emission from Internal Branches of the Current-voltage Characteristics of Superconducting Bi2Sr2CaCu2O8+d Single Crystals
• Nodeless pairing in superconducting copper-oxide monolayer films on Bi2Sr2CaCu2O8+δ
• Evidence for a Dual-Source Mechanism of THz Radiation from Rectangular Mesas of Single Crystalline \bm{$\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{r}}_2\mathrm{CaC}{\mathrm{u}}_2{\mathrm{O}}_{8+\delta }$} Intrinsic Josephson Junctions
• Radiation from a Josephson STAR-emitter
• Presence of $s$-wave pairing in Josephson junctions made of twisted ultrathin Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+x}$ flakes
• Local SiC photoluminescence evidence of non-mutualistic hot spot formation and sub-THz coherent emission from a rectangular Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta }$ mesa
• Angular dependence of the radiation power of a Josephson STAR-emitter
• Cavity mode waves during terahertz radiation from rectangular Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta }$ mesas
• Monolithic superconducting emitter of tunable circularly polarized terahertz radiation
• Control of Circularly Polarized THz Wave from Intrinsic Josephson Junctions by Local Heating

Cited by in corpus (2)

• Terahertz emission from mutually synchronized standalone Bi2Sr2CaCu2O8+x intrinsic-Josephson-junction stacks
• Angular dependence of the upper critical induction of clean $s$- and $d_{x^2-y^2}$-wave superconductors with self-consistent ellipsoidal effective mass and Zeeman anisotropies