Guided Modes in the Plane Array of Optical Waveguides

It is known that for an isolated dielectric cylinder waveguide there exists the cutoff frequency $\omega_\ast$ below which there is no guided mode. It is shown in the paper that the infinite plane periodic array of such waveguides possesses the guided modes in the frequency domain which is below the frequency $\omega_\ast$. In the case of a finite array, the modes in this frequency domain are weakly radiating ones, but their quality factor $Q$ increases with the number of waveguides $N$ as $Q(N)\sim N^3$. This dependence is obtained both numerically, using the multiple scattering formalism, and is justified with a simple analytical model

The effect of Aharanov-Bohm phase on the magnetic-field dependence of two-pulse echos in glasses at low temperatures

The anomalous response of glasses in the echo amplitude experiment is explained in the presence of a magnetic field. We have considered the low energy excitations in terms of an effective two level system. The effective model is constructed on the flip-flop configuration of two interacting two level systems. The magnetic field affects the tunneling amplitude through the Aharanov-Bohm effect. The effective model has a lower scale of energy in addition to the new distribution of tunneling parameters which depend on the interaction. We are able to explain some features of echo amplitude versus a magnetic field, namely, the dephasing effect at low magnetic fields, dependence on the strength of the electric field, pulse separation effect and the influence of temperature. However this model fails to explain the isotope effects which essentially can be explained by the nuclear quadrupole moment. We will finally discuss the features of our results.Comment: 8 pages, 7 figure

Effect of nuclear quadrupole interactions on the dynamics of two-level systems in glasses

The standard tunneling model describes quite satisfactorily the thermal properties of amorphous solids at temperatures $T<1K$ in terms of an ensemble of two-level systems possessing logarithmically uniform distribution over their tunneling amplitudes and uniform distribution over their asymmetry energies. In particular, this distribution explains the observable logarithmic temperature dependence of the dielectric constant. Yet, experiments have shown that at ultralow temperatures $T<5mK$ such a temperature behavior breaks down and the dielectric constant becomes temperature independent (plateau effect). In this letter we suggest an explanation of this behavior exploiting the effect of the nuclear quadrupole interaction on tunneling. We show that below a temperature corresponding to the characteristic energy of the nuclear quadrupole interaction the effective tunneling amplitude is reduced by a small overlap factor of the nuclear quadrupole ground states in the left and right potential wells of the tunneling system. It is just this reduction that explains the plateau effect . We predict that the application of a sufficiently large magnetic field $B>10T$ should restore the logarithmic dependence because of the suppression of the nuclear quadrupole interaction.Comment: To appear in the Physical Review Letter