The finding of Photon Hall effect (PHE) on metal surface is an important progress in photonics, but it will be more practical if PHE can be realized in line-type waveguide. In this paper, we suggested a way to realize PHE in two-dimensional photonic crystal (PC) waveguide. Numerical simulation results show that the propagating direction and strength of light in the PC waveguide can be controlled by the polarization state of incident light. Different from the PHE on metal surface, the PHE in PC waveguide can be driven not only by circularly polarized light, but also by linearly polarized light. The PHE in PC waveguide can be attributed to the interference of the two component waves excited by the incident light.
By means of a noncommutative differential calculus on function space of discrete Abelian groups and that of the regular lattice with equal spacing as well as the discrete symplectic geometry and a kind of classical mechanical systems with separable Hamiitonian of the type H(p, q) = T(p) + V(q) on regular lattice, we introduce the discrete symplectic algorithm, i.e., the phase-space discrete counterpart of the symplectic algorithm including original symplectic schemes and the jet-symplectic schemes in terms of the discrete time jet bundle formalism, on the regular lattice. We show some numerical calculation examples and compare the results of different schemes.
The adiabatic process is an old topic, which does not excite energy transitions and entropy changes in quantum systems. For undergraduate students, these two properties are easily accepted intuitively, but the general proof is complicated. Unlike ordinary textbooks, we use the principle of energy conservation in a one-dimensional infinite well to prove these properties. This paper will enable students to deepen their views on quantum mechanics and statistical physics.
A general method is proposed to describe the energy levels of the interface states in one-dimensional photonic crystal (PC) heterojunction [Formula: see text] containing dispersive or non-dispersion materials. We found that the finite energy levels of the interface states for the finite configuration can be described totally by the dispersion relation of the PC with a periodic unit [Formula: see text]. It is further found that this method is also applicable for the case of defect modes. We believe our method can be used to guide the practical application.
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