Using the plane-wave expansion method, we have calculated and analysed the
changes of photonic band structures arising from two kinds of deformed
lattices, including the stretching and shrinking of lattices. The square
lattice with square air holes and the triangular lattice with circular air
holes are both studied. Calculated results show that the change of lattice
size in some special ranges can enlarge the band gap, which depends strongly
on the filling factor of air holes in photonic crystals; and besides, the
asymmetric band edges will appear with the broken symmetry of lattices. 相似文献
We study the semigroup of the symmetric α-stable process in bounded domains in R2. We obtain a variational formula for the spectral gap, i.e. the difference between two first eigenvalues of the generator of this semigroup. This variational formula allows us to obtain lower bound estimates of the spectral gap for convex planar domains which are symmetric with respect to both coordinate axes. For rectangles, using “midconcavity” of the first eigenfunction (Bañuelos et al., Potential Anal. 24(3): 205–221, 2006), we obtain sharp upper and lower bound estimates of the spectral gap. 相似文献
This paper concerns with the study of a differential variational–hemivariational inequality (DVHVI, for short) in infinite-dimensional Banach spaces. We first introduce the new concept of gap functions for the variational control system of (DVHVI). Then, we consider two kinds of gap functions which are regularized gap function and Moreau–Yosida regularized gap function, respectively, and examine the relevant properties of the gap functions. Moreover, two global error bounds which depend implicitly on the regularized gap function and the Moreau–Yosida regularized gap function, accordingly, are obtained. Finally, in order to illustrate the applicability of the theoretical results, we investigate a coupled dynamic system which is formulated by a nonlinear reaction–diffusion equation described by a time-dependent nonsmooth semipermeability problem. 相似文献
Halogen-functionalized graphenes are utilized as electronic devices and energy materials. In the present paper, the effects of halogen-termination of graphene edge on the structures and electronic states of graphene flakes have been investigated by means of density functional theory (DFT) method. It was found that the ionization potential (Ip) and electron affinity of graphene (EA) are blue-shifted by the halogen termination, while the excitation energy is red-shifted. The drastic change showed a possibility as electronic devices such as field-effect transistors. The change of electronic states caused by the halogen termination of graphene edge was discussed on the basis of the theoretical results. 相似文献
Rectangular arrays of pyramidal recesses coated by silver film are investigated by means of polarization‐resolved nonlinear microscopy at 900 nm fundamental wavelength, demonstrating strong dependence of the dipole‐allowed SHG upon the lattice parameters. The plasmonic band gap causes nearly complete SHG suppression in arrays of 650 nm periodicity, whereas a sharp resonance at 550 nm periodicity is observed due to excitation of band edge Bloch states at fundamental frequency, accompanied by symmetry‐constrained interactions with similar modes at the second‐harmonic frequency. Additionally, coupling with modes at the bottom side of the silver film may lead to extraordinary optical transmission, opening a channel for SHG from the highly nonlinear GaAs substrate. Changing the lattice geometry enables SHG intensity modulation over three orders of magnitude, while the effective nonlinear anisotropy can be continuously switched between the two lattice directions, reaching values as high as ±0.96.