A generic approach to boundary reflection in periodic media

Waves in periodic media, whose propagation is governed by nearest neighbour interaction, are investigated. The reflection and transmission coefficients are derived for a plane wave incident from medium 1 upon medium 2, without invoking common approximations. The derivation is valid for a class of waves including magneto- and electro-inductive waves, waves on short loaded dipoles, nanoparticles, coupled waveguides and acoustic waves in monatomic media. For this last case hitherto unknown microscopic reflection and transmission coefficients are derived and shown to reduce in the continuous limit to the well-known expressions in terms of acoustic impedances.     

Attenuation of electromagnetic wave propagation in sandstorms incorporating charged sand particles

A theoretical approach for predicting the attenuation of microwave propagation in sandstorms is presented, with electric charges generated on the sand grains taken into account. It is found that the effect of electric charges distributed partially on the sand surface is notable. The calculated attenuation is in good agreement with that measured in certain conditions. The distribution of electric charges on the surface of sand grains, which is not easy to measure, can be approximately determined by measuring the attenuation value of electromagnetic waves. Some effects of sand radius, dielectric permittivity, frequency of electromagnetic wave, and visibility of sandstorms on the attenuation are also discussed quantitatively. Finally, a new electric parameter is introduced to describe the roles of scattering, absorption and effect of charges in attenuation.     

Superluminal electromagnetic focus wave modes

A particular transformation of coordinates, associated with superluminal X-pulses, leaves the wave equation invariant and changes focus wave modes into superluminal focus wave pulses. Rather simple and manageable expressions for TM electromagnetic waves allow the investigation of these new localized solutions of Maxwell's equations. Received 11 June 2002 / Received in final form 27 August 2002 Published online 31 December 2002     

Kramers-Kronig relations and the barrier interaction time problem

It is shown that the two characteristic interaction times and for classical electromagnetic waves with an arbitrarily shaped barrier are not independent quantities, but are connected by Kramers-Kronig relations for the real and imaginary components of a causal magnitude. The corresponding macroscopic sum rule for the complex time is also derived. An analogy between the interaction time problem and an electrical circuit with capacitive and conducting frequency dependent components is established. Received: 21 July 1998     

New localized Superluminal solutions to the wave equations with finite total energies and arbitrary frequencies

By a generalized bidirectional decomposition method, we obtain new Superluminal localized solutions to the wave equation (for the electromagnetic case, in particular) which are suitable for arbitrary frequency bands; several of them being endowed with finite total energy. We construct, among the others, an infinite family of generalizations of the so-called “X-shaped" waves. Results of this kind may find application in the other fields in which an essential role is played by a wave-equation (like acoustics, seismology, geophysics, gravitation, elementary particle physics, etc.). Received 23 June 2002 Published online 24 September 2002 RID="a" ID="a"Work partially supported by MIUR and INFN (Italy), and by FAPESP (Brazil). This paper did first appear as e-print physics/0109062 [and as preprint INFN/FM-01/02 (I.N.F.N.; Frascati, 2001)]. RID="b" ID="b"e-mail: recami@mi.infn.it     

Effects of a finite screening length on the absorption of electromagnetic waves

When an electromagnetic wave impinges on a semiconductor or ionic conductor having a sizeable screening length, it induces diffusion currents in addition to the ohmic currents, which affects the propagation in heterostructures or composite media involving such materials. In the simple geometries and in the low frequency regime studied here, the absorption may be either enhanced or reduced, depending on the parameters, and effects precluded for metals are predicted: extinction of the reflection by a plane wall, complete absorption of an electric multipolar wave by a sphere, disappearance of the scattering by a small sphere, vanishing of both reflection and transmission coefficients for a slab. If the screening length is larger than the skin depth, a slab with intermediate thickness may have a large transparency, and a thick piece of material is expected to be cooled down by the wave near the interface and overheated deeper inside. Received: 29 July 1997 / Revised: 24 November 1997 / Accepted: 20 February 1998     

Generalization of Brittingham's localized solutions to the wave equation

A family of localized solutions of Brittingham's type is constructed for different cylindric coordinates. We use method of incomplete separation of variables with zero separation constant and, then, the Bateman transformation, which enables us to obtain solutions in the form of relatively undistorted progressing waves containing two arbitrary functions, each of which depends on a specific phase function. Received 23 March 2001     

Effective magnetic properties of a composite material with circular conductive elements

Effective magnetic properties of a composite meta-material consisting of periodically arranged circular conductive elements are studied theoretically. A general expression for the effective bulk permeability is obtained with mutual effects and lattice ordering being taken into account. The resonance frequency of the permeability is found to be strongly dependent on the size and shape of the unit cell. Frequency dispersion of the permeability is studied with special attention paid to the frequency range, where negative values of the permeability are possible. Corresponding recommendations for optimisation of the meta-materials with negative permeability are made. The results are confirmed by numerical simulations of the finite structure behaviour in an external magnetic field. Received 19 April 2002 Published online 31 July 2002     

Omnidirectional zero-\bar {\mathsf n} gap in symmetrical Fibonacci sequences composed of positive and negative refractive index materials

The band structures of symmetrical Fibonacci sequences (SFS) composed of positive and negative refractive index materials are studied with a transfer matrix method. A new type of omnidirectional zero- gaps is found in the SFS. In contrast to the Bragg gaps, such an omnidirectional zero- gap is insensitive to the incident angles and polarization, and is invariant upon the change of the ratio of the thicknesses of two media. It is found that omnidirectional zero- gap exists in all the SFS, and it is rather stable and independence of the structure sequence.     

New phases of zinc under pressure from first principles

A procedure for finding the many stable phases of an element under hydrostatic pressure p is discussed and applied to zinc. Five new phases are found with several different Bravais symmetries under the constraint of one atom per cell and their stabilities as functions of p calculated. The procedure seems generalizable to find all the phases in all Bravais symmetries in a given range of pressure. In particular fcc Zn, which is unstable at p = 0, is shown to be very stable above 320 kbar to at least 1000 kbar. In agreement with Müller et al. [Phys. Rev. B 60, 16448 (1999)], a rhombohedral (rh) phase is found to be stable at p = 0, and several more rh phases are found at pressures up to 320 kbar. The Gibbs free energies of all phases are evaluated as functions of p, and the pressures of thermodynamically favored phase transitions are found. The behavior of Zn is compared to similar behavior of vanadium, which also shows stable rh phases and cubic phase instability in a range of pressure; the bcc phase instability is also healed by additional pressure.     

Millimeter-wave whispering gallery modes in an ellipsoidal dielectric resonator with a small ellipticity

It is found that, when the shape of a dielectric sphere (hemisphere) operating under the whispering gallery mode conditions is perturbed by a surface curvature gradient (ellipticity), the unloaded Q factor of the sphere degrades and its resonance frequencies change. It is shown theoretically and experimentally that an elliptic irregularity removes frequency degeneracy of whispering gallery modes at millimeter waves.     

Semiclassical steady-state analysis of a degenerate two-photon laser

The steady-state analysis of a single-mode two-photon laser are treated semiclassically by using the Maxwell-Bloch equations. The theory is applied to a ring-laser model. We find similarities and significant differences between the one- and two-photon polarizations of the medium, population inversion and mode-pulling formula. The population inversion and the longitudinal variation of the steady-state modulus of the field are studied numerically. Received: 1 March 1999 / Received in final form: 8 April 1999     

Resonant modes and inter-well coupling in photonic quantum well with negative index materials

The transfer matrix method was used to study the resonant modes in photonic quantum well by stacking different photonic crystals consisting of positive index materials and negative index materials. The eigenfrequency equation for the resonant modes is derived. It is found that these resonant modes are omnidirectional, and the number of resonant modes is equal to the period number of photonic quantum wells. Moreover, the resonant modes become N-fold splitting in the N photonic quantum wells. The splitting intervals increase with the deceasing of photonic barrier thickness due to the coupling among the wells.     

微波谐振器系统的调谐实验研究

圆台谐振腔和微波产生及传输装置可以形成一套和外界独立的微波谐振器系统.由于壁面上电磁压强差的作用,圆台谐振腔可能产生净电磁力,这需要从实验上给予证明.为此首先应对独立的微波谐振器系统进行调谐实验研究,使系统时刻处于谐振状态,这是实验证明净电磁力存在的重要保证.为此,本文对圆台谐振腔进行低信号调谐实验,同时配合调谐元件,准确地调试2.45 GHz频率下的谐振状态,分析温度对谐振状态的影响.实验结果表明该微波谐振器谐振频率2.44895 GHz、品质因数117495.0823,而且当腔体壁温升高时谐振频率减小、品质因数出现周期性振荡.     

Propagation of partially polarized, partially coherent beams in uniaxial crystals orthogonal to the optical axis

The propagation of partially polarized and partially coherent beams in uniaxial crystals orthogonal to the optical axis is investigated. The analytical formulae for the elements of the cross-spectral density matrix of partially polarized and partially coherent beams propagating through uniaxial crystals orthogonal to the optical are derived. The numerical results show that the degree of polarization decreases with the increase of the ratio of extraordinary to ordinary refractive indices at a certain propagation distance, and the influence of uniaxial crystals on the degree of coherent is not so evident. And the beams spread more rapidly in the direction parallel to the optical axis than orthogonal to the optical axis in positive crystal with the propagation distance increasing.     

Trifurcation of band-gap structure and coexistence of lattice-like states and critical states in piezoelectric period-doubling superlattices

We study the propagation of electromagnetic wave in piezoelectric period-doubling superlattices with using the generalized 4 × 4 transfer matrix method, and the dynamics of electromagnetic wave and acoustic wave is treated on equal footing. The band-gap structure trifurcates, which is understood within the framework of perturbation theory under periodic boundary condition. The uncoupled phononic branch of field distributions is Bloch-wave-like. For the coupled polaritonic branch, the lattice-like field distributions, for which Thue-Morse sequence is famous, also manifest in this piezoelectric period-doubling system and coexist with critical states. They can be characterized as extended if the superlattice size considered is large enough. In fact, our study suggests that such lattice-like field distributions are common phenomena in piezoelectric superlattices irrespective of lattice types and depend only on the frequency and domain widths, they reflect the intrinsic symmetry of the transfer matrices for the particular domain setting and frequency.     

Microwave propagation parameters in magnetic fluids

Complex dielectric permittivity and complex magnetic permeability measurements of two magnetic fluids (as microwave propagation media), in the approximate range 0.2-5GHz were performed. The two samples consisted of magnetite nanoparticles, dispersed in kerosene and in water, respectively. Based on the dielectric and magnetic measurements, the frequency (f ) dependence of the attenuation parameter, , the phase constant, , the propagation constant, , the intrinsic impedance, Z_m, the refractive index, n , the reflection coefficient, R , the wavelength, and the skin depth, , of the investigated samples were determined.     

Omnidirectional reflection and flat-top transmissionin Thue-Morse quasicrystal with single-negative materials

By means of transfer matrix method, we investigate the transmittance and reflectance of Thue-Morse (T-M) structure composed of negative-permittivity and negative-permeability materials. It is shown that the width and location of an omnidirectional reflectance band remain invariant with the change of generation order, and that the omnidirectional reflectance band is determined by both TE and TM polarization, which different completely from that in dielectric T-M structure. Moreover, a flat-top total transmission band occurs around the same frequency in which the general zero average permittivity and permeability are both satisfied in T-M structure. The basis for these phenomena are presented and discussed.