Abstract:
We discuss the possible existance of transverse optical plasma modes in superlattices consisting of Josephson coupled superconducting layers. These modes appear as resonances in the current-current correlation function, as opposed to the usual plasmons which are poles in the density-density channel. We consider both bilayer superlattices, and single layer lattices with a spread of interlayer Josephson couplings. We show that our model is in quantitative agreement with the recent experimental observation by a number of groups of a peak at the Josephson plasma frequency in the optical conductivity of La$_{1.85}$Sr$_{0.15}$CuO$_4$

Abstract:
In this work, we generalize the theory of localized surface plasmons to the case of high-Tc cuprate superconductors, spatially confined in the form of small spherical particles. At variance from ordinary metals, cuprate superconductors are characterized by a low-energy bulk excitation known as the Josephson plasma wave (JPW), arising from interlayer tunneling of the condensate along the c-axis. The effect of the JPW is revealed in a characteristic spectrum of surface excitations, which we call Josephson surface plasmons. Our results, which apply to any material with a strongly anisotropic electromagnetic response, are worked out in detail for the case of multilayered superconductors supporting both low-frequency (acoustic) and transverse-optical JPW. Spatial confinement of the Josephson plasma waves may represent a new degree of freedom to engineer their frequencies and to explore the link between interlayer tunnelling and high-Tc superconductivity.

Abstract:
An introduction is given to collective modes in layered, high Tc superconductors. An experimental demonstration is treated of the mechanism proposed by Anderson whereby photons travelling inside the superconductor become massive, when the U(1) gauge symmetry is broken in the superconductor to which the photons are coupled. Using the Ferrell-Tinkham sumrule the photon mass is shown to have a simple relation to the spectral weight of the condensate. Various forms of Josephson plasmons can exist in single-layer, and bi-layecuprates. In the bi-layer cuprates a transverse optical plasma mode can be observed as a peak in the c-axis optical conductivity. This mode appears as a consequence of the existence of two different intrinsic Josephson couplings between the CuO2 layers. It is strongly related to a collective oscillation corresponding to small fluctuations of the relative phases of the two condensates, which has been predicted in 1966 by A.J. Leggett for superconductors with two bands of charge carriers. A description is given of optical data of the high Tc cuprates demonstrating the presence of these and similar collective modes.

Abstract:
The electrodynamic features of the multiband model are examined using the transverse equation of motion approach in order to give the explanation of several long-standing problems. It turns out that the exact summation of the most singular terms in powers of $1/\omega^{n}$ leads to the total optical conductivity which, in the zero-frequency limit, reduces to the results of the Boltzmann equation, for both the metallic and semiconducting two-band regime. The detailed calculations are carried out for the quasi-one-dimensional (Q1D) two-band model corresponding to imperfect charge-density-wave (CDW) nesting. It is also shown that the present treatment of the impurity scattering processes gives the DC conductivity of the ordered CDW state in agreement with the experimental observation. Finally, the DC and optical conductivity are calculated numerically for a few typical Q1D cases.

Abstract:
We predict the existence of transverse electric (TE) plasmons in bilayer graphene. We find that their plasmonic properties are much more pronounced in bilayer than in monolayer graphene, in a sense that they can get more localized at frequencies just below $\hbar\omega=0.4$~eV for adequate doping values. This is a consequence of the perfectly nested bands in bilayer graphene which are separated by $\sim 0.4$~eV.

Abstract:
We calculate the linear transverse current current response function for graphene at finite temperature and chemical potential. Within the Random Phase Approximation, we then discuss general aspects of transverse plasmons beyond the local response such as their dependence on temperature and on the surrounding dielectric media. We find, e.g., maximal confinement of this mode for a homogeneous dielectric media with refractive index $n\simeq 40$. Confinement can further be enhanced by placing the graphene sheet inside an optical cavity, but there exists a critical width below which no transverse mode can be sustained. For zero doping and finite temperature, there are no well-defined transverse plasmonic excitations in contrast to the longitudinal channel. We also discuss the absorption of electromagnetic radiation in single and double-layer systems for $s$ and $p$ polarizations and point out that the theoretical limit of 50% is reached for $s$-polarized light with incident angle of $\theta\approx89^o$.

Abstract:
Feasibility of usage of surface plasmons in a new design of an integrated optical isolator has been studied. In the case of surface plasmons propagating at a boundary between a transition metal and a double-layer dielectric, there is a significant difference of optical loss for surface plasmons propagating in opposite directions. Utilizing this structure, it is feasible to fabricate a competitive plasmonic isolator, which benefits from a broad wavelength operational bandwidth and a good technological compatibility for integration into the Photonic Integrated Circuits (PIC). The linear dispersion relation was derived for plasmons propagating in a multilayer magneto-optical slab.

Abstract:
This paper analytically investigates the nonlinear behaviour of transverse plasmons in pair plasmas on the basis of the nonlinear governing equations obtained from Vlasov--Maxwell equations. It shows that high frequency transverse plasmons are modulationally unstable with respect to the uniform state of the pair plasma. Such an instability would cause wave field collapse into a localized region. During the collapse process, ponderomotive expulsion is greatly enhanced for the increase of wave field strength, leading to the formation of localized density cavitons which are significant for the future experimental research in the interaction between high frequency electromagnetic waves and pair plasmas.

Abstract:
The origin and properties of the transverse non-reciprocal magneto-optical (nMO) effect were studied. The transverse nMO effect occurs in the case when light propagates perpendicularly to the magnetic field. It was demonstrated that light can experience the transverse nMO effect only when it propagates in the vicinity of a boundary between two materials and the optical field at least in one material is evanescent. The transverse nMO effect is pronounced in the cases of surface plasmons and waveguiding modes. The magnitude of the transverse nMO effect is comparable to or greater than the magnitude of the longitudinal nMO effect. In the case of surface plasmons propagating at a boundary between the transition metal and the dielectric it is possible to magnify the transverse nMO effect and the magneto-optical figure-of-merit may increase from a few percents to above 100%. The scalar dispersion relation, which describes the transverse MO effect in cases of waveguide modes and surface plasmons propagating in a multilayer MO slab, was derived.

Abstract:
Phase slips in a one-dimensional closed array of Josephson junctions hybridize the persistent current states (PCS) and plasmon branches of excitations. The interference between phase slips passing through different junctions of the array makes the hybridization sensitive to the charges of the superconducting islands comprising the array. This in turn results in the Aharonov-Casher effect for plasmons, which in absence of phase slips are insensitive to island charges.