Spatial dispersion and energy in strong chiral medium

Since the discovery of backward-wave materials, people have tried to realize strong chiral medium, which is traditionally thought impossible mainly for the reason of energy and spatial dispersion. We compare the two most popular descriptions of chiral medium. After analyzing several possible reasons for the traditional restriction, we show that strong chirality parameter leads to positive energy without any frequency-band limitation in the weak spatial dispersion. Moreover, strong chirality does not result in a strong spatial dispersion, which occurs only around the traditional limit point. For strong spatial dispersion where higher-order terms of spatial dispersion need to be considered, the energy conversation is also valid. Finally, we show that strong chirality need to be realized from the conjugated type of spatial dispersion.Comment: 6 pages, 2 figure

Breaking the challenge of signal integrity using time-domain spoof surface plasmon polaritons

In modern integrated circuits and wireless communication systems/devices, three key features need to be solved simultaneously to reach higher performance and more compact size: signal integrity, interference suppression, and miniaturization. However, the above-mentioned requests are almost contradictory using the traditional techniques. To overcome this challenge, here we propose time-domain spoof surface plasmon polaritons (SPPs) as the carrier of signals. By designing a special plasmonic waveguide constructed by printing two narrow corrugated metallic strips on the top and bottom surfaces of a dielectric substrate with mirror symmetry, we show that spoof SPPs are supported from very low frequency to the cutoff frequency with strong subwavelength effects, which can be converted to the time-domain SPPs. When two such plasmonic waveguides are tightly packed with deep-subwavelength separation, which commonly happens in the integrated circuits and wireless communications due to limited space, we demonstrate theoretically and experimentally that SPP signals on such two plasmonic waveguides have better propagation performance and much less mutual coupling than the conventional signals on two traditional microstrip lines with the same size and separation. Hence the proposed method can achieve significant interference suppression in very compact space, providing a potential solution to break the challenge of signal integrity

Negative reflections of electromagnetic waves in chiral media

We investigate the reflection properties of electromagnetic/optical waves in isotropic chiral media. When the chiral parameter is strong enough, we show that an unusual \emph{negative reflection} occurs at the interface of the chiral medium and a perfectly conducting plane, where the incident wave and one of reflected eigenwaves lie in the same side of the boundary normal. Using such a property, we further demonstrate that such a conducting plane can be used for focusing in the strong chiral medium. The related equations under paraxial optics approximation are deduced. In a special case of chiral medium, the chiral nihility, one of the bi-reflections disappears and only single reflected eigenwave exists, which goes exactly opposite to the incident wave. Hence the incident and reflected electric fields will cancel each other to yield a zero total electric field. In another word, any electromagnetic waves entering the chiral nihility with perfectly conducting plane will disappear.Comment: 5 pages, 5 figure

Quasi-Perron-Frobenius property of a class of saddle point matrices

The saddle point matrices arising from many scientific computing fields have block structure $W= \left(\begin{array}{cc} A & B\\ B^T & C \end{array} \right)$, where the sub-block $A$ is symmetric and positive definite, and $C$ is symmetric and semi-nonnegative definite. In this article we report a unobtrusive but potentially theoretically valuable conclusion that under some conditions, especially when $C$ is a zero matrix, the spectral radius of $W$ must be the maximum eigenvalue of $W$. This characterization approximates to the famous Perron-Frobenius property, and is called quasi-Perron-Frobenius property in this paper. In numerical tests we observe the saddle point matrices derived from some mixed finite element methods for computing the stationary Stokes equation. The numerical results confirm the theoretical analysis, and also indicate that the assumed condition to make the saddle point matrices possess quasi-Perron-Frobenius property is only sufficient rather than necessary