Nonlinear waves guided by a dielectric slab

We consider dispersion relations and field structure of TE-polarized guided waves travelling along an asymmetric dielectric slab surrounded by two different nonlinear media. For a given configuration there are four types of guided waves. Three of this four types possess at least one field maximum outside the slab region and have no counterpart in linear waveguide optics. The solutions of the dispersion relations depend now on an additional parameter making them more flexible with respect to the linear limit.     

Exceptional surface wave as a condition of the maximum increase in the intensity of an evanescent electromagnetic wave in a transparent medium

It has been shown that the condition of the maximum increase in the intensity of TM or TE evanescent electromagnetic waves at the interface between two transparent insulators in a static electric (magnetic) field simultaneously determines the dispersion law of the corresponding exceptional surface wave for which the instantaneous energy flux through the interface is zero at any time.     

Near-field distributions of resonant modes in small dielectric objects on flat surfaces

We report numerical simulations of the coupling of waves, either propagating or evanescent, with the eigenmodes of dielectric nanocylinders and nanospheres upon substrates. The multiple interaction of light between these objects and the dielectric surface at which the evanescent waves are created is taken into account. In this way, we present an accurate procedure for predicting and controlling the creation of large field enhancements concentrated both within and near the nanoparticle compared with the angle of incidence and the state of polarization.     

Global transmission diagrams for evanescent waves in a nonlinear hyperbolic metamaterial

A theoretical model of a nonlinear hyperbolic metamaterial is presented in the form of a stack of subwavelength layers of linear plasmonic and nonlinear dielectric materials. A broad picture of the properties of evanescent waves(high-k modes) in this stack is investigated by plotting global transmission diagrams. The presence of nonlinearity strongly modifies these diagrams. The emergence and modification of nonlinear evanescent waves is observed. Some signatures of nonlinear phenomenon such as formation of orbits and trajectories around fixed points are also seen in our work.     

Nonlinear s-polarized surface plasmon polaritons

We have examined the dispersion relations for s-polarized surface plasmon polaritons, guided by (a) the interface between a semi-infinite metal and dielectric medium, and (b) a metal film bounded by semi-infinite dielectric media for situations in which one or more of the dielectric media are characterized by an intensity-dependent refractive index. We found that s-polarized waves satisfy the dispersion relations for very thin metal films bounded by nonlinear dielectric media. These waves exist only for power levels above a threshold that depends on the material parameters. We also comment on the experimental feasibility of observing these waves.     

Transmission enhancement by conversion of evanescent waves into propagating waves

The convolution between spatial modes of two different parts of an optical system can convert evanescent waves into propagating waves. This principle is applied to different optical systems for analyzing various effects in transmission enhancements experiments. We discuss here the differences between the present principle which is related to broadening of resonances and the near-field optical microscopy based on a tunneling effect by a tip detector. The present analysis is applied in particular to two systems: a) transmission enhancement in one slit by coupling the transmitted radiation with transversal Fabry–Pérot electromagnetic (EM) modes, and b) transmission enhancement by coupling between a metallic film with arrays of holes and surface plasmons (SP). The present approach gives more information on transmission enhancement phenomena than that obtained by conventional treatments and can also solve certain disagreements between different theories. The differences between the present process of converting evanescent waves into propagating waves, and that related to the new development of getting a super-resolution by an hyperlens are discussed. PACS 41.20.Jb; 73.20.Mf; 42.79.Dj     

Scattering of waves from nonlinear media with rough surfaces

Abstract

Reflection and scattering of waves from plane and statistically rough interfaces between nonlinear media are studied theoretically. New hysteresis-type dependences of the reflection and transmission coefficients on the amplitude of the incident wave and on the angle of incidence are predicted. Scattering diagrams for diffusely reflected and transmitted fields are calculated. It is found that when the dielectric constant is a steep function of the incident amplitude, nonlinearity suppresses the Bragg resonant scattering mechanism. Smooth roughness of the boundary is shown to enhance the penetration of evanescent waves into nonlinear media.     

Energy-momentum quanta in Fresnel's evanescent wave II

Four generalisations of results appearing in a previous paper, referred to as I, are here produced. (1) Formulas for the field strengths of the evanescent wave generated inside a vacuum sandwiched between two identical refracting media propagating symmetrical incident plane waves; the classical exponential damping factor being then replaced by hyperbolic cosines or sines (according to the field components), an extremely close approximation to a plane tachyon wave is thus obtained; (2) Compact formulas for the case where the evanescent wave is generated by a superposition of plane incident waves with propagation vectors k parallel to a common incidence plane; (3) Compact formulas for the other typical case where the dispersion on k is parallel to the reflecting plane; (4) Formulas for refraction and total reflection of a photon with a non-zero rest mass.We take the opportunity of this paper to review briefly various articles that had escaped us, where a transverse energy flux inside Fresnel's evanescent wave was discussed, and also some recent papers dealing with quantisation of the evanescent wave or related topics.     

On compression of electromagnetic pulses in dielectric plates

The results of theoretical investigation of propagation of electromagnetic wave pulses in nonlinear dielectric plates, taking into account the dispersion introduced by the plate to the maximum possible extent, are presented. The investigation is aimed at obtaining the shortest possible pulses of electromagnetic waves. Pulse compression is based on the collapse of electromagnetic waves in transparent dielectrics with electronic non-linearity. The integral equation for describing the pulse compression is derived, and conditions under which a pulse is compressed relative to time and one of the transverse coordinates are determined. Numerical simulation shows that quite short (on the order of a few femtoseconds) pulses can be obtained in this way.     

Influence of Quantum Effects on the Magnetic Field Behavior in Overdense Plasma

We study the conditions for the anomalous transmission of electromagnetic waves through quantum overdense plasma. We show that this anomalous transmission is triggered due to the excitation of surface waves, as was observed in the classical overdense plasma. The conditions for the excitation of surface waves are obtained by studying the dispersion relation within the framework of quantum hydrodynamics. The corresponding consequences at the classical limits are consistent with the previous studies. In comparison with the classical regimes, the quantum dispersion curve exhibits an asymptotic behavior which indicates significant effects, in particular, at large wavelengths. Herein, to create the required evanescent waves, we consider the quantum plasma to be placed between two ordinary prisms and dielectrics. The effects of the main parameters, such as the permittivity of the prisms and dielectrics and the Fermi velocity, on the rate of the transmission and the magnetic field propagation are also evaluated.     

Spatial separation of the traveling and evanescent parts of dipole radiation

Electric dipole radiation consists of traveling and evanescent plane waves. When radiation is detected in the far field, only the traveling waves will contribute to the intensity distribution, as the evanescent waves decay exponentially. We propose a method to spatially separate the traveling and evanescent waves before detection. It is shown that when the radiation passes through an interface, evanescent waves can be converted into traveling waves and can subsequently be observed in the far field. Let the radiation be observed under angle theta(t) with the normal. Then there exists an angle theta(ac) such that for 0 < or = theta(t) < theta(ac) all intensity originates in traveling waves, whereas for theta(ac) < theta(t) < pi/2 only evanescent waves contribute. It is shown that with this technique and under the appropriate conditions almost all far-field power can be provided by evanescent waves.     

Controlled switching of surface waves in 1D photonic crystals by a thin nonlinear cap layer

In this paper, we investigate the electromagnetic surface waves localized at the interface of the homogeneous dielectric medium and a semi-infinite one-dimensional photonic crystal (1D PC), theoretically. The semi-infinite 1D PC is made of alternative layers of left-handed (LH) and right-handed (RH) materials in the presence of a thin nonlinear cap layer. We consider magnetic permeability and electric permittivity of LH layers being dispersive and non-dispersive. We used an analytical direct matching procedure within the Kronig-Penny model to analyze the dispersion behavior of surface waves with controllable localization. It is shown that the thin nonlinear cap layer acts as a tool to change the backward surface waves to forward ones and vice versa and it plays an important role on the localization of them. Also we show that when the LH layers are chosen dispersive, negative dispersion of surface waves are obtained in a wide range of radiation angle and frequency, and we propose an approach to calculate the applied electric field intensity that leads to switching of surface waves from backward to forward and creating a surface mode with maximum localization.     

Perturbation theory for weakly nonlinear p-polarized surface polaritons

A perturbation theory is developed for weakly nonlinear p-polarized surface polaritons for an interface of two media, one of which is nonlinear. The dependence of the dispersion law of surface waves on the intensity of electric field at the interface has been found. The resulting relations have been compared with the results of recent experiments made by Chen and Carter [1]. This made it possible to define more precisely the value of the nonlinear susceptibility χ⁽³⁾.     

受激拉曼散射对非线性介质波导的时空不稳定性影响

基于非线性包络方程我们研究了平面非线性介质波导中的时空不稳定性,得到了有拉曼散射效应情形下不稳定性调制的增益谱的表达式.结果表明在正常和反常两种群速度色散情形下,拉曼散射效应都会导致出现新的不稳定性区域,并且使原有的每一个谱分量的增益上升从而使谱的范围扩大.并通过分析反常色散情况下四种不同函数分布的非线性色散介质系数对不稳定性增益谱的影响,得到呈双曲函数分布的非线性色散介质最为理想.     

Nonlinear analysis of a wave motion on the surface of a jet moving in a dielectric medium placed in a longitudinal electric field

The possibility of degenerate internal nonlinear resonance interaction between capillary waves with arbitrary symmetry (arbitrary azimuthal numbers) on the surface of a charged cylindrical jet of an ideal incompressible conducting liquid is demonstrated. The jet moves in an ideal incompressible dielectric medium collinearly with an external uniform electrostatic field. It is shown, in particular, that six different resonance situations take place for axisymmetric waves in which primary waves and waves due to the nonlinearity of the equations of hydrodynamics exchange energy.     

Quantum electrodynamics in three-dimensionally periodic structures

Abstract

Recently, the possibility of obtaining ISE in spectral bands of forbidden light propagation (photonic bandgaps) has been suggested by Yablonovitch.¹ These bandgaps are spectral regions admitting only complex wavevectors k (evanescent waves) in any direction, and boundecl by frequencies ω_max((min) at which the dispersion curve ω(k) becomes discontinuous. Because they are associated with definite k (band edges), such hndgaps are delocalized in space, i.e., they inhibit spontaneous emission independently of t.he spatial distribution of emitters in the system. The systems that have been proposed¹ for the demonstration of bandgaps are dielectric superlattices that exhibit strong three-dimensional (3D) periodic moclulations of the dielectric index with a period comparable to half the emission wavelength.     

非线性介质光波导中的传输功率和光学双稳态

本文对结构为非线性包层/线性芯层/非线性衬底的非线性介质光波导的传输特性进行了深入的分析,给出了模场分布函数,色散关系和传输功率的一组形式统一的公式,并对其传输功率的光学双稳态特性进行了讨论.     

Direction and frequency filter basing on an ultra-compact structure consisting of dielectric films

The transmission properties of a two-period structure consisting of dielectric layers and air layers are studied by numeric methods. On the condition of total reflection from dielectric to air layer, the coupling of the evanescent waves in air layers and propagation waves in dielectric layers forms some special transmission bands. Given proper structure parameters, one incident direction only allows one transmission frequency; on the other hand, one transmission frequency only allows one incident direction. This structure can simultaneously achieve frequency filtering and direction filtering.     

非线性平板光波导中TM波的网络分析

用横向等效网络方法分析了非线性平板波导中TM的色散关系和场分布.这种方法基于传输线理论,把非线性介质波导中复杂的电磁场问题等效于电路网络问题,用横向谐振技术得到色散方程.用数值方法计算了不同非线性机制下三层平板非线性波导中的TM波传输特性.     

Simulated Output Images of Near-Field Optics by Volume Integral Equation: Object Placed on the Dielectric Substrate

We investigated near-field optical (NFO) imaging characteristics of a small object placed on a dielectric slab by a computer-code using a three-dimensional volume integral equation with an effective iteration technique called the generalized minimal residual method. A simplified three-dimensional NFO microscope that consists of a small dielectric object placed on the dielectric substrate and a small dielectric sphere as a scanning probe-tip was considered. Calculating two-dimensional output images obtained from scattered far fields, we studied the effect of the substrate on NFO output images, the comparison of NFO output images with electrostatic field around the small object, the dependence of output image characteristics on the wavelength and the difference of imaging characteristics between incident plane waves and incident evanescent waves.