Exceptional Points of Degeneracy Induced by Linear Time-Periodic Variation

We present a general theory of exceptional points of degeneracy (EPD) in periodically time-variant systems. We show that even a single resonator with a time-periodic component is able to develop EPDs, contrary to parity-time- (PT) symmetric systems that require two coupled resonators. An EPD is a special point in a system parameter space at which two or more eigenmodes coalesce in both their eigenvalues and eigenvectors into a single degenerate eigenmode. We demonstrate the conditions for EPDs to exist when they are directly induced by time-periodic variation of a system without loss and gain elements. We also show that a single resonator system with zero time-average loss-gain exhibits EPDs with purely real resonance frequencies, yet the resonator energy grows algebraically in time since energy is injected into the system from the time-variation mechanism. Although the introduced concept and formalism are general for any time-periodic system, here, we focus on the occurrence of EPDs in a single LC resonator with time-periodic modulation. These findings have significant importance in various electromagnetic and photonic systems and pave the way for many applications, such as sensors, amplifiers, and modulators. We show a potential application of this time-varying EPD as a highly sensitive sensor

Autonomous linear lossless systems

We define a lossless autonomous system as one having a quadratic differential form associated with it called an energy function, which is positive and which is conserved. We define an oscillatory system as one which has all its trajectories bounded on the entire time axis. In this paper, we show that an autonomous system is lossless if and only if it is oscillatory. Next we discuss a few properties of energy functions of autonomous lossless systems and a suitable way of splitting a given energy function into its kinetic and potential energy components

Guiding structures with multiply connected cross-sections: evolution of propagation in external fields at complex Robin parameters

Properties of the two-dimensional ring and three-dimensional infinitely long straight hollow waveguide with unit width and inner radius $\rho_0$ in the superposition of the longitudinal uniform magnetic field $\bf B$ and Aharonov-Bohm flux are analyzed within the framework of the scalar Helmholtz equation under the assumption that the Robin boundary conditions at the inner and outer confining walls contain extrapolation lengths $\Lambda_{in}$ and $\Lambda_{out}$, respectively, with nonzero imaginary parts. It is shown that, compared to the disk geometry, the annulus opens up additional possibilities of varying magnetization and currents by tuning imaginary components of the Robin parameters on each confining circumference; in particular, the possibility of restoring a lossless longitudinal flux by zeroing imaginary part $E_i$ of the total transverse energy $E$ is discussed. The energy $E$ turns real under special correlation between the imaginary parts of $\Lambda_{in}$ and $\Lambda_{out}$ with the opposite signs what physically corresponds to the equal transverse fluxes through the inner and outer interfaces of the annulus. In the asymptotic case of the very large radius, simple expressions are derived and applied to the analysis of the dependence of the real energy $E$ on $\Lambda_{in}$ and $\Lambda_{out}$. New features also emerge in the magnetic field influence; for example, if, for the quantum disk, the imaginary energy $E_i$ is quenched by the strong intensities $B$, then for the annulus this takes place only when the inner Robin distance $\Lambda_{in}$ is real; otherwise, it almost quadratically depends on $B$ with the corresponding enhancement of the reactive scattering. Closely related problem of the hole in the otherwise uniform medium is also addressed for real and complex extrapolation lengths with the emphasis on the comparative analysis with its dot counterpart.Comment: 37 pages, 9 figure

Refraction enhancement in plasmonics by the coherent control of plasmon resonances

A plasmonic nanoantenna probed by a plane-polarized optical field in a medium with no gain materials can show zero absorption or even amplification, while exhibiting maximal polarizability. This occurs through coupling to an adjacent nanoantenna in a specially designed metamolecule, which is pumped by an orthogonal optical field with phase shift. The introduced scheme is a classical counterpart of an effect known in quantum optics as enhancement of the index of refraction (EIR). In contrary to electromagnetically induced transparency (EIT), where the medium is rendered highly dispersive at the point of zero susceptibility and minimum absorption, in the EIR the system exhibits large susceptibility and low dispersion at the point of zero or negative absorption. The plasmonic analogue of the EIR allows for coherent control over the polarizability and absorption of plasmonic nanoantennas, offering a novel approach to all optical switching and coherent control of transmission, diffraction and polarization conversion properties of plasmonic nanostructures, as well as propagation properties of surface plasmon polaritons on metasurfaces. It may also open up the way for lossless or amplifying propagation of optical waves in zero-index to high refractive index plasmonic metamaterial

On strict passivity and its application to interpolation and Hl control

The authors introduce the L2-system and derive necessary and sufficient conditions for these systems to be strictly passive. Strictly passive L2-systems are characterized as having a representation in terms of a co-J-lossless matrix. A state space proof is developed and provides a Riccati equation characterization of a strictly passive L 2-system, as well as a formula for the co-J-lossless matrix representation. Applications to Nevanlinna-Pick interpolation and an H∞ filtering problem are considere