Linking topological features of the Hofstadter model to optical diffraction figures

In two, three and even four spatial dimensions, the transverse responses experienced by a charged particle on a lattice in a uniform magnetic field are fully controlled by topological invariants called Chern numbers, which characterize the energy bands of the underlying Hofstadter Hamiltonian. These remarkable features, solely arising from the magnetic translational symmetry, are captured by Diophantine equations which relate the fraction of occupied states, the magnetic flux and the Chern numbers of the system bands. Here we investigate the close analogy between the topological properties of Hofstadter Hamiltonians and the diffraction figures resulting from optical gratings. In particular, we show that there is a one-to-one relation between the above mentioned Diophantine equation and the Bragg condition determining the far-field positions of the optical diffraction peaks. As an interesting consequence of this mapping, we discuss how the robustness of diffraction figures to structural disorder in the grating is a direct analogy of the robustness of transverse conductance in the Quantum Hall effect.

Электромагнитные волны в волноводе с периодически модулированным магнитодиэлектрическим заполнением

The propagation of electromagnetic waves in an ideal regular waveguide, filling of which is periodically modulated in space and time, is considered. It is assumed that the modulation depths are small and the modulation of the waveguide filling does not lead to the interaction between different waveguide modes. Wave equations are obtained for transverse-electric (TE) and transverse-magnetic (TM) fields in the waveguide with respect to the longitudinal components of the magnetic and electric vectors, respectively, are obtained. They represent second order partial differential equations with periodic coefficients. By changing the variables these equations are reduced to ordinary differential equations with periodic coefficients of the Mathieu-Hill type. Solutions of these equations are found in the first approximation with respect to small modulation depths in the region of “weak” interaction between the signal wave and the modulation wave (the Wulff-Bragg condition is not satisfied). The obtained results show that TE and TM fields in the waveguide in the above approximation are represented as the sum of three space-time harmonics (zero and plus and minus first) with complicated amplitudes and frequencies.

Variation in altitude of high-frequency enhanced plasma line by the pump near the 5th electron gyro-harmonic

During an ionospheric heating campaign carried out at the European Incoherent Scatter Scientific Association (EISCAT), the ultra high frequency incoherent scatter (IS) radar observed a systematic variation in the altitude of the high-frequency enhanced plasma line (HFPL), which behaves depending on the pump frequency. Specifically, the HFPL altitude becomes lower when the pump lies above the 5th gyro-harmonic. The analysis shows that the enhanced electron temperature plays a decisive role in the descent in the HFPL altitude. That is, on the traveling path of the enhanced Langmuir wave, the enhanced electron temperature can only be matched by the low electron density at a lower altitude so that the Bragg condition can be satisfied, as expected from the dispersion relation of Langmuir wave.

SURFACE-RELIEF THREE-PORT OUTPUT WITH A CONNECTING LAYER GRATING UNDER THE SECOND BRAGG CONDITION

A three-port surface-relief grating with a connecting layer under the second Bragg condition is put forward and designed for the free space application in this paper. Such grating can function as a beam splitter, which can split the polarized light into the [Formula: see text]2nd order and the [Formula: see text]1st order and the 0th order based on the optimum grating profile parameters. By using rigorous coupled-wave analysis, a highly-efficient polarization-dependent connecting-layer-based grating can be obtained with the optimum different depths and thicknesses with the grating duty cycle of 0.65 and grating period of 1150[Formula: see text]nm. On the basis of the designed grating profile parameters, a modal method can explain the propagating process. Compared with the conventional surface-relief fused-silica grating, the diffraction efficiencies for TE polarization in three orders are improved. Therefore, the novel conception of the grating under the second Bragg condition is significant for further applications such as interferometer with improved efficiency for TE polarization.

Chemically-resolved determination of hydrogenated graphene–substrate interaction

Selective photo-electron emission from hydrogenated graphene driven by standing wave field at Bragg condition.

The real part of the dispersion surface in X-ray dynamical diffraction in the Laue case for perfect crystals

The real part of the dispersion surface in X-ray dynamical diffraction in the Laue case for perfect crystals is analysed using a Riemann surface. In the conventional two-beam approximation, each branch or wing of the dispersion surface is specified by one sheet of the Riemann surface. The characteristic features of the dispersion surface are analytically revealed using four parameters, which are the real and imaginary parts of two quantities that specify the degree of departure from the exact Bragg condition and the reflection strength. The present analytical method is generally applicable, irrespective of the magnitudes of the parameters with no approximation. Characteristic features of the dispersion surface are also revealed by geometrical considerations with respect to the Riemann surface.