C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, O. Jedrkiewicz, J. Trull
Nonlinear optical media that are normally dispersive, support a new type of localized (nondiffractive and nondispersive) wavepackets that are X-shaped in space and time and have slower than exponential decay. High-intensity X-waves, unlike linear ones, can be formed spontaneously through a trigger mechanism of conical emission, thus playing an important role in experiments.
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A quantum nature of vacuum is expected to affect electromagnetic fields in vacuum as a nonlinear correction, yielding nonlinear Maxwell's equations. We extend the finite-difference time-domain (FDTD) method in the case that the nonlinear electromagnetic Lagrangian is quartic with respect to the electric field and magnetic flux density. With this extension, the nonlinear Maxwell's equations can be numerically solved without making any assumptions on the electromagnetic field. We demonstrate examples of self-modulations of nonlinear electromagnetic waves in a one-dimensional cavity, in particula…
The vacuum is expected to exhibit electromagnetic nonlinearity. We demonstrate the properties of nonlinear electromagnetic wave in a two-dimensional rectangular cavity by calculating the nonlinear correction for two classical standing waves. We apply the linear approximation in a short timescale. A part of the nonlinear correction increases with time. In particular, a one-dimensional second harmonic grows if the cavity size satisfies a specific condition. We also analyze the nonlinear electromagnetic wave in a timescale longer than the applicable limit of the linear approximation. We formulate…
We propose a scheme for realizing subwavelength electromagnetic diode by employing cascading nonlinear meta-atoms. One-way response is demonstrated on a microwave transmission line comprising of three metallic ring resonators acting as meta-atoms and a varactor as the nonlinear medium inclusion. Experiments show that our implementation can operate simultaneously as forward diode and backward diode at different frequencies. A transmission contrast of up to 14.7dB was achieved between forward and backward transmission. Subwavelength size of our diode should be useful for miniaturization of integ…
An analytical method of electromagnetic wave interactions with a general radially anisotropic cloak is established. It is able to deal with arbitrary parameters ($ε_r(r)$, $μ_r(r)$, $ε_t(r)$ and $μ_t(r)$) of a radially anisotropic inhomogeneous shell. The general cloaking condition is proposed from the wave relations for the first time. We derive the parameters of a novel class of spherical nonlinear cloaks and examine its invisibility performance by the proposed method at various nonlinear situations. Spherical metamaterial cloaks with improved invisibility performance is achieved with optima…
We consider propagation of transverse magnetic electromagnetic waves through a nonlinear metamaterial slab, of subwavelength thickness and very small average dielectric permittivity, made up of alternating metal and dielectric nonlinear layers. Exploiting the effective-medium approach, we prove that the output field intensity is a multi-valued function of both the input field intensity and incidence angle so that the transmissivity exhibits a novel kind of multi-stability and a pronounced two-parameter hysteresis behavior. The predicted two-parameter hysteresis physically stems from the fact t…
Translation Matrix Formalism has been used to find an exact analytic solution for linear light propagation in a finite one-dimensional (1D) periodic stratified structure. This modal approach allows to derive a closed formula for the electric field in every point of the structure, by simply imposing a convenient form for the boundary conditions. We show how to apply this result to Second Harmonic Generation (SHG) in the undepleted pump regime.
We present a theory which explains how to achieve an enhancement of nonlinear effects in a thin layer of nonlinear medium by involving a planar periodic structure specially designed to bear a trapped-mode resonant regime. In particular, the possibility of a nonlinear thin metamaterial to produce the bistable response at a relatively low input intensity due to a large quality factor of the trapped-mode resonance is shown. Also a simple design of an all-dielectric low-loss silicon-based planar metamaterial which can provide an extremely sharp resonant reflection and transmission is proposed. The…
Propagation of the TE electromagnetic waves in self-focusing medium is governed by the nonlinear Schroedinger equation. In this paper the stationary solutions of this equation have been systematically presented. The phase-plane method, qualitative analysis, and mechanical interpretation of the differential equations are widely used. It is well known that TE waves can be guided by the single interface between two semi-infinite media, providing that one of the media has a self-focusing (Kerr type) nonlinearity. This special solution is called a spatial soliton. In this paper our interests are no…
We investigate single interface surface plasmon polaritons (SPPs) excited by electromagnetic waves under general electromagnetic boundary conditions that allow for non-zero surface charge and surface current densities. Incorporating these, we derive general conditions for single interface SPPs and solve both the surface source distributions and the surface electromagnetic waves for such SPPs when excited by electromagnetic waves.
We introduce the concept of magnetoelastic metamaterials with electromagnetic properties depending on elastic deformation. We predict a strong nonlinear and bistable response of such metamaterials caused by their structural reshaping in response to the applied electromagnetic field. In addition, we demonstrate experimentally the feasibility of the predicted effect.
We investigate the storage and retrieval of electromagnetic waves using a nonlinear metamaterial, analogous to the electromagnetically induced transparency (EIT) observed in atomic systems. We experimentally demonstrate the storage of the electromagnetic wave by reducing an auxiliary "control" wave; the stored wave is then released by recovering the control wave. We also confirm that the metamaterial can store and reproduce the phase distribution of the original input wave. These effects confirm a remarkable analogy between the metamaterial and an atomic EIT medium.
We propose a multi-field-coupled atomic model that exhibits controllable $symmetric$ and $asymmetric$ evolution of significantly enhanced diffraction peaks in an opto-atomic grating at far-field regime. Such results are obtained by the linear and nonlinear modulation of the intensities of the diffraction peaks as a result of multi-wave-mixing-induced modification of spatially modulated coherence in a closed four-level atomic system. Novelty of the results lies in predicting super symmetric alignment of the diffraction peaks due to the dominance of the amplitude part of the grating-transfer-fun…
An electronic diode is a nonlinear semiconductor circuit component that allows conduction of electrical current in one direction only. A component with similar functionality for electromagnetic waves, an electromagnetic isolator, is based on the Faraday effect of the polarization state rotation and is also a key component of optical and microwave systems. Here we demonstrate a chiral electromagnetic diode, which is a direct analogue of an electronic diode: its functionality is underpinned by an extraordinary strong nonlinear wave propagation effect in the same way as electronic diode function …
The optical nonlinear effects can provide different advanced electromagnetic functionalities, such as wave mixing and phase conjugation, which can be applied in a variety of new applications. However, these effects usually suffer from extremely weak nature and require high input intensity values in order to be excited. Interestingly, the large third order nonlinearity of graphene, along with the strong field confinement stemming from its plasmonic behavior, can be utilized to enhance several relative weak nonlinear effects at infrared (IR) and terahertz (THz) frequencies. Towards this goal, va…
A purely artificial mechanism for optical nonlinearity is proposed based on a metamaterial route. The mechanism is derived from classical electromagnetic interaction in a meta-molecule consisting of a cut-wire meta-atom nested within a split-ring meta-atom. Induced by the localized magnetic field in the split-ring meta-atom, the magnetic force drives an anharmonic oscillation of free electrons in the cut-wire meta-atom, generating an intrinsically nonlinear electromagnetic response. An explicit physical process of a second-order nonlinear behavior is adequately described, which is perfectly de…
Local electromagnetic field enhancement in resonant metamaterials is useful for efficient generation of nonlinear phenomena; however, the field enhancement is suppressed by losses of nonlinear elements in metamaterials. For overcoming this issue, we investigate the nonlinear response of an electromagnetically induced transparency like metasurface loaded with gas as the nonlinear element. To induce nonlinearity in the gas associated with discharges, an electromagnetic wave with a modulated amplitude is incident on the metasurface. The measured waveform and spectrum of the transmitted electromag…
Probing the electromagnetic nonlinearity of vacuum with continuous-wave lasers
本文提出利用共振增强的四波混频技术，在聚焦光学谐振器中实现真空电磁非线性的 tabletop 光学测量，展示了达到 2.5 MW 循环功率的谐振器，为检测真空电磁非线性提供了关键实验步骤。
Scalar and vector electromagnetic solitary waves in nonlinear hyperbolic media
该研究针对双曲非线性介质中的电磁波传播问题，通过Hirota双线性方法推导标量和矢量电磁孤波的精确解析形式，发现双曲横向色散可抑制奇异性形成，且孤波具备传统介质中没有的独特传播特性，为双曲非线性超材料的电磁波传播分析提供支撑。
The propagation of a quasi-harmonic electromagnetic wave in a bulk hyperbolic dielectric metamaterial is considered. If the group velocities dispersion is not taken into account, then wave propagation can be described either by the hyperbolic nonlinear Schrodinger equation or by the hyperbolic Manakov equations. It is shown that the region in the space of wave vectors in which the modulation instability of a spatially homogeneous wave is possible is not limited, in contrast to the case of ordinary media.
The paper explores a theoretical possibility of resonant amplification of electromagnetic modes generated by a nonlinear effect in Euler-Heisenberg electrodynamics. Precisely, we examine the possibility of the amplification for the third harmonics induced by a single electromagnetic mode in radiofrequency cavity, as well as the generation of signal mode of combined frequencies induced by two pump modes ($ω_1$ and $ω_2$) in the cavity. Solving inhomogeneous wave equations for the signal mode, we formulate two resonant conditions for a cavity of arbitrary shape, and apply the obtained formalism …
Nonlinear Tellegen limit
研究磁电介质中非线性磁电耦合产生的新特勒根极限，其场可调，通过在两个磁有序材料系统中展示极限及相图，表明磁点群对称性控制非线性磁电张量结构与电磁不稳定性。
Microscopic quantum theory of nonlinear stimulated scattering of 2D Dirac particles in doped graphene on Coulomb field of impurity ions at the presence of an external strong coherent electromagnetic radiation is developed. We consider high Fermi energies and low frequencies (actually terahertz radiation) to exclude the valence electrons excitations. The Liouville-von Neumann equation for the density matrix is solved analytically, taking into account the interaction of electrons with the scattering potential in the Born approximation. With the help of this solution, the nonlinear inverse-bremss…
Nonlinear metasurfaces based on coupling a locally enhanced plasmonic response to intersubband transitions of n-doped multi-quantum-wells (MQWs) have recently provided second-order susceptibilities orders of magnitude larger than any other nonlinear flat structure measured so far. Here, we present a comprehensive theory to characterize the electromagnetic response of nonlinear processes occurring in ultrathin MQW-based plasmonic metasurfaces, providing a homogeneous model that takes phase-matching at the unit-cell level and the influence of saturation and losses into account. In addition, the …
Third order nonlinear correlation of the electromagnetic vacuum at near-infrared frequencies
本研究结合实验与理论揭示强聚焦近红外飞秒探针的四波混频及其与电磁真空产生的三阶非线性关联，并确定其主导参数区间。
Topological photonics has recently emerged as a route to realize robust optical circuitry, and nonlinear effects are expected to enable tunability of topological states with the light intensity. Here we realize experimentally nonlinear self-induced spectral tuning of the electromagnetic topological edge states in an array of coupled nonlinear resonators in a pump-probe experiment. In a weakly nonlinear regime, we observe that resonators frequencies exhibit spectral shifts, that are concentrated mainly at the edge mode affecting only weakly the bulk modes. For a strong pumping, we describe seve…
We analyze the properties of a nonlinear metamaterial formed by integrating nonlinear components or materials into the capacitive regions of metamaterial elements. A straightforward homogenization procedure leads to general expressions for the nonlinear susceptibilities of the composite metamaterial medium. The expressions are convenient, as they enable inhomogeneous system of scattering elements to be described as a continuous medium using the standard notation of nonlinear optics. We illustrate the validity and accuracy of our theoretical framework by performing measurements on a fabricated …
We propose a method for dynamically controlling the properties of a metamaterial that mimics electromagnetically induced transparency (EIT) by introducing varactor diodes to manipulate the structural symmetry of the metamaterial. Dynamic modulation of the EIT property enables the storage and retrieval of electromagnetic waves. We confirmed that the electromagnetic waves were stored and released, while maintaining the phase distribution in the propagating direction.
Applications of metallic metamaterials have generated significant interest in recent years. Electromagnetic behavior of metamaterials in the optical range is usually characterized by a local-linear response. In this article, we develop a finite-difference time-domain (FDTD) solution of the hydrodynamic model that describes a free electron gas in metals. Extending beyond the local-linear response, the hydrodynamic model enables numerical investigation of nonlocal and nonlinear interactions between electromagnetic waves and metallic metamaterials. By explicitly imposing the current continuity co…
We review the theory for photon-photon scattering in vacuum, and some of the proposals for its experimental search, including the results of our recent works on the subject. We then describe a very simple and sensitive proposal of an experiment and discuss how it can be used at the present (HERCULES) and the future (ELI) ultrahigh power laser facilities either to find the first evidence of photon-photon scattering in vacuum, or to significantly improve the current experimental limits.
The significance of the Lorentz gauge as a constraint on solutions of Maxwellian waves is discussed. It is proved that recent claims of superluminal propagation of electromagnetic waves rely on an erroneous basis.
Electromagnetic signal propagation through lossy media via surface electromagnetic waves
本文建立了任意表面梯度介质中表面电磁波的理论，发现虚部主导的梯度介质中存在新型低损耗表面波解，并展示了从水下通信到紫外纳米光子学的应用。
Kerr rotation signature of nonlinear Maxwell electrodynamics under a uniform electromagnetic background
研究非线性Maxwell电动力学在均匀电磁背景下的Kerr旋转特征，探讨其光学效应与参数关系。
We use blow-up solutions of nonlinear Helmholtz equations to introduce a nonlinear resonance effect that is capable of amplifying electromagnetic waves of particular intensity. To achieve this, we propose a scattering setup consisting of a Kerr slab with a negative (defocusing) Kerr constant placed to the left of a linear slab in such a way that a left-incident coherent TE wave with a specific incidence angle and intensity realizes a blow-up solution of the corresponding Helmholtz equation whenever its wavenumber $k$ takes a certain critical value, $k_\star$. For $k=k_\star$, the solution blow…
We introduce two models of quasi-discrete optical systems: an array of waveguides doped by four-level N-type atoms, and a nonlinear checkerboard pattern, formed by doping with three-level atoms of the Λ-type. The dopant atoms are driven by external fields, to induce the effect of the electromagnetically-induced transparency (EIT). These active systems offer advantages and addition degrees of freedom, in comparison with ordinary passive waveguiding systems. In the array of active waveguides, the driving field may adjust linear and nonlinear propagation regimes for a probe signal. The nonlinear …
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