Bloch cavity solitons in nonlinear resonators with intracavity photonic crystals

We predict a novel type of cavity solitons, Bloch cavity solitons, existing in nonlinear resonators with the refractive index modulated in both longitudinal and transverse directions and for both focusing (at normal diffraction) and defocusing (at anomalous diffraction) nonlinearities. We develop a modified mean-field theory and analyze the properties of these novel cavity solitons demonstrating, in particular, their substantial narrowing in the zero-diffraction regime.     

Slow vector optical solitons in a cold four-level inverted-Y atomic system

The authors show the formation of slow temporal vector optical solitons in a cold lifetime-broadened four-level inverted-Y atomic system. We demonstrate that Maxwell’s equations for describing two orthogonally polarised components of a low intensity signal field can evolve into two coupled nonlinear Schr?dinger equations, which results in various distortion-free temporal vector optical solitons, such as bright-bright or dark-dark vector solitons. These results are produced from the correct balance between dispersion, self- and cross-phase modulation (SPM and XPM) effects. We also show that the integrable Manakov model can be realised by adjusting the corresponding SPM, XPM and dispersion effects of this inverted-Y atomic system.     

One dimensional photonic band gap material as an omnidirectional reflector

In this article, the reflection properties in one-dimensional dielectric-dielectric photonic band gap (PBG) structure have been studied. We have used SiO₂ as material of low refractive index and Te as a high refractive index material. Reflectivity of proposed PBG structure is plotted as a function of wavelength and angle of incidence and omni-directional PBGs are computed theoretically. To obtain reflectance, we used transfer matrix method for solving Maxwell’s equations for electromagnetic wave in PBG structures. For a large range of frequency, the PBG structure is found to exhibit omni-directional reflection which can be exploited in devices such as optical resonators, mirrors, etc.     

Regime independent coupled-wave equations in anisotropic photorefractive media

An extension to coupled wave theory suitable for all regimes of diffraction is presented. The model assumes that the refractive index grating has an arbitrary profile in one direction and is periodic (but not necessarily sinusoidal) in the other. Higher order diffracted terms are considered and appropriate mismatch terms dealt with. It is shown that this model is analytically equivalent to both the Bragg and Raman–Nath regime coupling models under an appropriate set of assumptions. This model is applied to cases such as optical coupling in liquid crystal cells with photoconductive layers. Its predictions are successfully compared to finite element simulations of the full Maxwell’s equations.     

Properties of optical resonator with a layered metamaterial

The properties of longitudinal and transverse modes of an open optical resonator containing layers of a metamaterial with negative refractive index are studied. Due to the presence of these layers, the metaresonator acquires unique properties compared to a conventional open resonator. Eigenmodes of the metaresonator are studied in which the properties depend on the average dispersion and the average diffraction, which may be either positive, negative, or zero. The conditions of the existence and profiles of the waveguiding modes are obtained. The resonator with zero average diffraction is of particular interest. It is shown that, in this case, the waveguiding mode may have an arbitrary amplitude profile. Under these conditions, the discrete set of the transverse modes becomes continuous, and the eigenfrequencies become independent of the transverse amplitude profile. The resonator’s stability conditions are derived based on the ray-matrix method and diffraction theory. It is shown that insertion of a metamaterial into the resonator substantially affects the region of stability and existence of the waveguiding modes. In particular, the unstable empty resonator can thus be rendered stable.     

Comparison between Weber’s electrodynamics and classical electrodynamics

We present the main aspects of Weber’s electrodynamics and of Maxwell’s equations. We discuss Maxwell’s point of view related to Weber’s electrodynamics. We compare Weber’s force with Lorentz’s force. We analyse the relation between Weber’s law and Maxwell’s equations. Finally, we discuss some experiments performed and proposed with which we can distinguish Weber’s force from Lorentz’s one.     

Normal modes and quality factors of shielded composite dielectric spherical resonators

Electromagnetic field analysis of shielded composite dielectric spherical resonator in which the dielectric sphere is composed of two concentric spheres with different dielectric materials has been made. Characteristic equations for the TE_nmℓ and TM_nmℓ modes have been derived. From these characteristic equations, the resonant frequencies and quality factors have been calculated using numerical method. Computations of the resonant frequencies and quality factors have been made for resonators with parameters suitable for the optical and microware regions. In this paper we have presented the analysis and the results obtained from the numerical computations for shielded composite dielectric spherical resonator in which the dielectric sphere is composed of two concentric spheres with different dielectric materials. Starting from the Maxwell’s equations for such a resonators have been derived and resonant frequencies and quality factor’s have been calculated for the TE_nmℓ and TM_nmℓ modes using numerical method.     

Stabilization of three-dimensional light bullets by a transverse lattice in a Kerr medium with dispersion management

We demonstrate a possibility to stabilize three-dimensional spatiotemporal solitons (“light bullets”) in self-focusing Kerr media by means of a combination of dispersion management in the longitudinal direction (with the group-velocity dispersion alternating between positive and negative values) and periodic modulation of the refractive index in one transverse direction (out of the two). Assuming the usual model based on the paraxial nonlinear Schrödinger equation for the local amplitude of the electromagnetic field, the analysis relies upon the variational approximation (results of direct three-dimensional simulations will be reported in a follow-up). A predicted stability area is identified in the model’s parameter space. It features a minimum of the necessary strength of the transverse modulation of the refractive index, and finite minimum and maximum values of the soliton’s energy. The former feature is also explained analytically.     

Application of microwave amplitude modulation technique to measure spin-lattice and spin-spin relaxation times accurately with a continuous-wave EPR spectrometer: Solution of Bloch’s equations by a matrix technique and least-squares fitting

A matrix technique to calculate signals recorded using the microwave amplitude-modulation technique is described. The calculations are carried out for spin packets, on and off resonance, to take into account inhomogeneous broadening. Both, the transverse component of magnetization representing the continuous-wave signal in a resonator, such as a cross-looped resonator, as well as the signal (electromotive force) induced in a pickup coil oriented parallel to the external magnetic field, are calculated for an arbitrary value of the coefficient of modulation. This is accomplished by solving the relevant Bloch equations in the rotating frame for the case when the amplitude of the microwave field is modulated by a sinusoidal wave, using Fourier expansions of the longitudinal and transverse components of the magnetization in Bloch equations. This results in a series of coupled equations inM _α(n) (α=y,zz), the magnetic moments of vaarious orders, leading to a penta-diagonal matrix of infinite dimension. These equations are then truncated and solved by a fast matrix technique to calculateM _α(n), required to calculate the modulation signals as functions of the amplitudemodulation frequency Ω. It is outlined how to exploit the expressions for the modulation signals to estimate the spin-lattice relaxation timesT ₁ and spin-spin relaxation timesT ₂ accurately by the leastsquares procedure, fitting simultaneously all signals obtained for spin packets, on and off resonance, at various modulation frequencies. Illustrative examples are provided.     

梯度折射率非局域介质中空间孤子振荡行为研究

应用等效粒子近似方法研究了光学空间孤子在带有局域和非局域非线性横向非均匀介质中的传输动力学行为.发现孤子在传播过程中横向的周期性振荡.折射率调制幅度和波导的归一化宽度决定了振荡周期的大小.介质的非局域对振荡振幅有着较小的影响.模拟了孤子传输过程,所得数值结果与理论分析符合很好.此外,模拟传输还发现多孤子束缚态能够在这个模型中稳定传播.这种振荡特性或许可以应用于光学路由器、转换器、开关等.     

Solitons in optical lattices with nonlocal nonlinearity

The propagation of spatial solitons is systematically investigated in nonlocal nonlinear media with an imprinted transverse periodic modulation of the refractive index. Based on the variational principle and the infinitesimal approximation of Maclaurin series expansion, we obtain an analytical solution of such nonlocal spatial solitons and an interesting result that the critical power for such solitons propagation is smaller than that in uniform nonlocal self-focusing media. It is found that there exist thresholds in modulation period and lattice depth for such solitons. A stable spatial soliton propagation is maintained with proper adjustment of the modulation period and the lattice depth.     

Frequency change of partial spherical waves induced by time change of medium permittivity

The transformation of a plane harmonic wave caused by a time jump of the permittivity inside a dielectric sphere is investigated. The exact expressions for the transformed field are obtained as a solution of an initial and boundary value electromagnetic problem for the Maxwell’s equations based on the longitudinal and the transverse spherical vector functions.     

On “Gauge Renormalization” in Classical Electrodynamics

In this paper we pay attention to the inconsistency in the derivation of the symmetric electromagnetic energy–momentum tensor for a system of charged particles from its canonical form, when the homogeneous Maxwell’s equations are applied to the symmetrizing gauge transformation, while the non-homogeneous Maxwell’s equations are used to obtain the motional equation. Applying the appropriate non-homogeneous Maxwell’s equations to both operations, we obtained an additional symmetric term in the tensor, named as “compensating term”. Analyzing the structure of this “compensating term”, we suggested a method of “gauge renormalization”, which allows transforming the divergent terms of classical electrodynamics (infinite self-force, self-energy and self-momentum) to converging integrals. The motional equation obtained for a non-radiating charged particle does not contain its self-force, and the mass parameter includes the sum of mechanical and electromagnetic masses. The motional equation for a radiating particle also contains the sum of mechanical and electromagnetic masses, and does not yield any “runaway solutions”. It has been shown that the energy flux in a free electromagnetic field is guided by the Poynting vector, whereas the energy flux in a bound EM field is described by the generalized Umov’s vector, defined in the paper. The problem of electromagnetic momentum is also examined.     

Analytical model of the enhanced light transmission through subwavelength metal slits: Green’s function formalism versus Rayleigh’s expansion

We present an analytical model of the resonantly enhanced transmission of light through a subwavelength nm-size slit in a thick metal film. The simple formulae for the transmitted electromagnetic fields and the transmission coefficient are derived by using the narrow-slit approximation and the Green’s function formalism for the solution of Maxwell’s equations. The resonance wavelengths are in agreement with the semi-analytical model [Y. Takakura, Phys. Rev. Lett. 86, 5601 (2001)], which solves the wave equations by using the Rayleigh field expansion. Our formulae, however, show great resonant enhancement of a transmitted wave, while the Rayleigh expansion model predicts attenuation. The difference is attributed to the near-field subwavelength diffraction, which is not considered by the Rayleigh-like expansion models. PACS 42.25.Bs; 42.65.Fx; 42.79.Ag; 42.79.Dj     

Modeling of the propagation of electromagnetic waves in 2D labyrinthine photonic structures

The features of electromagnetic wave propagation in photonic structures with a labyrinthine distribution of the refractive index have been analyzed based on the direct numerical solution of Maxwell’s equation. It is shown that the distribution of the energy density of the electromagnetic field is characterized by a complex branching structure, and the transmission nonlinearly depends on the size of the photonic cell.     

Ultra-short scalar and vector solitons in self-inductively transparent media

The analytical form of the one-soliton solutions to the Maxwell–Bloch equations is found without the slowly-varying envelope approximation with application to the ultra-short (few-cycle or sub-cycle) light pulses propagating in media of two-level atoms as well as to fluxons in the long Josephson junctions. Also, we discuss the dynamics of the ultra-short vector solitons propagating in specific three-level media and magnetic-flux transmission lines (of two long Josephson junctions sharing a common superconducting plate). Studies of the (ultra-short) pulse collisions lead to the prediction of pulse stability against the collisions. In particular, the collisions of the ultra-short vector solitons are investigated in detail. Their collision-induced polarization transform is found to be similar to the polarization transform of the vector (Manakov) solitons propagating in self-focusing media.     

Generalized Split-Octonion Electrodynamics

Starting with the usual definitions of octonions and split octonions in terms of Zorn vector matrix realization, we have made an attempt to write the consistent form of generalized Maxwell’s equations in presence of electric and magnetic charges (dyons). We have thus written the generalized potential, generalized field, and generalized current of dyons in terms of split octonions and accordingly the split octonion forms of generalized Dirac Maxwell’s equations are obtained in compact and consistent manner. This theory reproduces the dynamic of electric (magnetic) in the absence of magnetic (electric) charges.     

Solitons in PT–symmetric optical lattices with spatially periodic modulation of nonlinearity

We study the existence and stability of solitons forming in PT–symmetric optical lattices with spatially periodic modulation of the local strength of the nonlinear media. We found that the spatial modulation of the nonlinearity significantly affects the stability of solitons in PT–symmetric optical lattices. With the decrease of the strength of nonlinear refractive index modulation, the soliton's stability domain increases, whereas with the increase of the period of nonlinear refractive index modulation, the corresponding soliton's stability range narrows. In addition, we also investigate the influence of variation of the amplitude of the linear PT–symmetric lattice potential on soliton dynamics, in the presence of spatially periodic modulation of nonlinearity.     

Holographic solitons

We propose a new kind of an optical spatial soliton: the holographic soliton. This soliton consists of two mutually coherent field components that interfere, induce a periodic change in the refractive index, and simultaneously are Bragg diffracted from the grating. Holographic solitons are formed when the broadening tendency of diffraction is balanced by phase modulation that is due to Bragg diffraction from the induced grating. Holographic solitons are solely supported by cross-phase modulation arising from the induced grating, not involving self-phase modulation at all.     

Analysis and Calculations on Dispersion Relation and Coupling Resistance of Periodic Plasma-Cavities

The plasma tensor dielectric permittivity and electromagnetic field accurate expressions in the external axial magnetic field are obtained from the Maxwell’s equations and the double component plasma particle linear movement equations. Further, the flux of energy inside the plasma-cavity drift channel is presented. Based on them, some of the property of cavity passband dispersion and coupling resistance of plasma-filled coupled-cavities slow wave structure in different plasma density and magnetic field conditions is analyzed according to the numerical calculation.