Simple Reciprocal Electric Circuit Exhibiting Exceptional Point of Degeneracy

An exceptional point of degeneracy (EPD) occurs when both the eigenvalues and the corresponding eigenvectors of a square matrix coincide and the matrix has a nontrivial Jordan block structure. It is not easy to achieve an EPD exactly. In our prior studies, we synthesized simple conservative (lossless) circuits with evolution matrices featuring EPDs by using two LC loops coupled by a gyrator. In this paper, we advance even a simpler circuit with an EPD consisting of only two LC loops with one capacitor shared. Consequently, this circuit involves only four elements and it is perfectly reciprocal. The shared capacitance and parallel inductance are negative with values determined by explicit formulas which lead to EPD. This circuit can have the same Jordan canonical form as the nonreciprocal circuit we introduced before. This implies that the Jordan canonical form does not necessarily manifest systems' nonreciprocity. It is natural to ask how nonreciprocity is manifested in the system's spectral data. Our analysis of this issue shows that nonreciprocity is manifested explicitly in: (i) the circuit Lagrangian and (ii) the breakdown of certain symmetries in the set of eigenmodes. All our significant theoretical findings were thoroughly tested and confirmed by extensive numerical simulations using commercial circuit simulator software

Analytical Solution for Space-Charge Waves in a Two-Stream Cylindrical Electron Beam

We present an analytical method to compute the wavenumbers and electric fields of the space-charge-wave eigenmodes supported by a two-stream electron beam, consisting of a solid inner cylindrical stream and a coaxial outer annular stream, both contained within a cylindrical metallic tunnel.We extend the analytical model developed by Ramo to the case of two streams. The method accounts for the interaction between the two streams with the presence of the beam-tunnel wall; it can be used to model the complex wavenumbers associated with the two-stream instability and the plasma frequency reduction effects in vacuum electronic amplifiers and other vacuum electronic devices.Comment: 11 pages, 9 figure

Exceptional Points of Degeneracy Directly Induced by Space-Time Modulation of a Single Transmission Line

We demonstrate how exceptional points of degeneracy (EPDs) are induced in a single transmission line (TL) directly by applying periodic space-time modulation to the per-unit-length distributed capacitance. In such space-time modulated (STM)-TL, two eigenmodes coalesce into a single degenerate one, in their eigenvalues (wavenumbers) and eigenvectors (voltage-current states) when the system approaches the EPD condition. The EPD condition is achieved by tuning a parameter in the space-time modulation, such as spatial or temporal modulation frequency, or the modulation depth. We unequivocally demonstrate the occurrence of the EPD by showing that the bifurcation of the wavenumber around the EPD is described by the Puiseux fractional power series expansion. We show that the first order expansion is sufficient to approximate well the dispersion diagram, and how this "exceptional" sensitivity of an STM-TL to tiny changes of any TL or modulation parameter enables a possible application as a highly sensitive TL sensor when operating at an EPD

Parametric Modeling of Serpentine Waveguide Traveling Wave Tubes

A simple and fast model for numerically calculating small-signal gain in serpentine waveguide traveling-wave tubes (TWTs) is described. In the framework of the Pierce model, we consider one-dimensional electron flow along a dispersive single-mode slow-wave structure (SWS), accounting for the space-charge effect. The analytical model accounts for the frequency-dependent phase velocity and characteristic impedance obtained using various equivalent circuit models from the literature, validated by comparison with full-wave eigenmode simulation. The model includes a relation between the modal characteristic impedance and the interaction (Pierce) impedance of the SWS, including also an extra correction factor that accounts for the variation of the electric field distribution and hence of the interaction impedance over the beam cross section. By applying boundary conditions to our generalized Pierce model, we compute both the theoretical gain of a TWT and all the complex-valued wavenumbers of the hot modes versus frequency and compare our results with numerically intensive particle-in-cell (PIC) simulations; the good agreement in the comparison demonstrates the accuracy and simplicity of our generalized model. For various examples where we vary the average electron beam (e-beam) phase velocity, average e-beam current, number of unit cells, and input radio frequency (RF) power, we demonstrate that our model is robust in the small-signal regime.Comment: 16 pages, 14 figure

Reprogrammable graphene-based metasurface mirror with adaptive focal point for THz imaging

Recent emergence of metasurfaces has enabled the development of ultra-thin flat optical components through different wavefront shaping techniques at various wavelengths. However, due to the non-adaptive nature of conventional metasurfaces, the focal point of the resulting optics needs to be fixed at the design stage, thus severely limiting its reconfigurability and applicability. In this paper, we aim to overcome such constraint by presenting a flat reflective component that can be reprogrammed to focus terahertz waves at a desired point in the near-field region. To this end, we first propose a graphene-based unit cell with phase reconfigurability, and then employ the coding metasurface approach to draw the phase profile required to set the focus on the target point. Our results show that the proposed component can operate close to the diffraction limit with high focusing range and low focusing error. We also demonstrate that, through appropriate automation, the reprogrammability of the metamirror could be leveraged to develop compact terahertz scanning and imaging systems, as well as novel reconfigurable components for terahertz wireless communications.Peer ReviewedPostprint (published version