The dispersion relations for surface plasmon in a nonlinear-metal-nonlinear dielectric structure

In the asymmetric and symmetric nonlinear-metal-nonlinear dielectric structures, this paper studies the analytic dispersion relation for surface plasmon in a system consisting of a thin metallic film covered on two sides media of intensity-dependent refractive indexes by applying a generalised first integral approach. Especially in the symmetric waveguide structure, two possible modes can exist: the odd mode and the even mode. The dispersion relations of the two modes are obtained. Due to the nonlinear dielectric, the squared magnitude of the electric field at the interface appears and alters the dispersion relations. Numerical results are compared to those from a certain approximate treatment.     

五层对称人工超常材料结构的表面等离子体激元

研究了由左手材料、负介电材料、常规介电材料所构成的几种五层对称结构表面等离子体激元的特性.讨论了表面等离子体激元的存在区域、色散关系、以及p和s偏振的表面色散曲线枝,发现表面模的性质强烈依赖于系统的组成材料及其组合方式|层数越多,表面色散曲线枝也越多,处在频率通带的表面极化模态也越多|在五层结构中有p和s两种偏振的表面等离子体激元,在共振时,可导致p波和s波强透射.此外,通过使用衰减全反射方法,探讨了激发并观察表面等离子体激元的可能性.     

Surface plasmon polariton at the interface of dielectric and graphene medium using Kerr effect

We theoretically investigate the control of surface plasmon polariton(SPP) generated at the interface of dielectric and graphene medium under Kerr nonlinearity. The controlled Kerr nonlinear signal of probe light beam in a dielectric medium is used to generate SPPs at the interface of dielectric and graphene medium. The positive, negative absorption, and dispersion properties of SPPs are modified and controlled by the control and Kerr fields. A large amplification(negative absorption) is noted for SPPs under the Kerr nonlinearity. The normal/anomalous slope of dispersion and propagation length of SPPs is modified and controlled with Kerr nonlinearity. This leads to significant variation in slow and fast SPP propagation. The controlled slow and fast SPP propagation may predict significant applications in nano-photonics, optical tweezers, photovoltaic devices, plasmonster, and sensing technology.     

非对称型Kerr类介质膜漏波导中的非线性导波

本文研究了特定边界条件下非对称型Kerr类介质膜漏波导中TE₀光波的传播特性。计算结果表明,介质膜厚存在一临界值。临界值之上没有导波存在,临界值之下能同时存在强场TE₀模和弱场TE₀模,它们具有不同的传播波数。这两个模的膜内传播功率、场强峰值位置随膜厚和光场频率的变化各不相同,色散关系也有极大差别。在对称极限之下,弱场TE₀模的色散为零。 关键词：     

Cherenkov terahertz radiation from Dirac semimetals surface plasmon polaritons excited by an electron beam

We demonstrate a physical mechanism for terahertz(THz) generation from surface plasmon polaritons(SPPs). In a structure with a bulk Dirac semimetals(BDSs) film deposited on a dielectric substrate, the energy of the asymmetric SPP mode can be significantly enhanced to cross the light line of the substrate due to the SPP-coupling between the interfaces of the film. Therefore, the SPPs can be immediately transformed into Cherenkov radiation without removing the wavevector mismatch. Additionally, the symmetric SPP mode can also be dramatically lifted to cross the substrate light line when a buffer layer with low permittivity relative to the substrate is introduced. In this case, dual-frequency THz radiation from the two SPP modes can be generated simultaneously. The radiation intensity is significantly enhanced by over two orders due to the field enhancement of the SPPs. The radiation frequency can be tuned in the THz frequency regime by adjusting the beam energy and the chemical potential of the BDSs. Our results could find potential applications in developing room temperature, tunable, coherent, and intense THz radiation sources to cover the entire THz band.     

Effects of saturation on optical bistability with coupled surface plasmons

We present exact numerical results for a symmetric layered medium (prism/Ag film/nonlinear dielectric/Ag film/prism) where the middle dielectric slab is assumed to have a saturation-type nonlinearity. We show bistable behaviour in the power dependence of the reflectivity ofp-polarized light under the condition when coupled surface modes are excited in the structure. Moreover, we study the effect of saturation on the bistable behaviour to show that multivalued character is inhibited by saturation effects. The field distributions corresponding to the minimum reflectivity states of the nonlinear structure are also presented.     

Nonlinear photonic crystals: III. Cubic nonlinearity

Abstract

Weakly nonlinear interactions between wavepackets in a lossless periodic dielectric medium are studied based on the classical Maxwell equations with a cubic nonlinearity. We consider nonlinear processes such that: (i) the amplitude of the wave component due to the nonlinearity does not exceed the amplitude of its linear component; (ii) the spatial range of a probing wavepacket is much smaller than the dimension of the medium sample, and it is not too small compared with the dimension of the primitive cell. These nonlinear processes are naturally described in terms of the cubic interaction phase function based on the dispersion relations of the underlying linear periodic medium. It turns out that only a few quadruplets of modes have significant nonlinear interactions. They are singled out by a system of selection rules including the group velocity, frequency and phase matching conditions. It turns out that the intrinsic symmetries of the cubic interaction phase stemming from assumed inversion symmetry of the dispersion relations play a significant role in the cubic nonlinear interactions. We also study canonical forms of the cubic interaction phase leading to a complete quantitative classification of all possible significant cubic interactions. The classification is ultimately based on a universal system of indices reflecting the intensity of nonlinear interactions.     

Plasma modes in low-dimensional electron system over surface of liquid helium

The collective plasma modes in a quasi-two-dimensional (Q2D) electron system located over the free surface of liquid helium are studied theoretically within many-body dielectric formalism. The dispersion of modes is considered both over bulk liquid and over helium film where the essential modification of interelectron interaction occurs due to screening effects in the substrate with a large value of dielectric constant. It is shown that the plasma spectrum consists of longitudinal and transverse branches which dispersion laws depend on the values of the dielectric constant of helium and the film thickness. For the helium film covering metal, the longitudinal mode is acoustic differing of that for the surface electron (SE) system over bulk helium.     

Plasmon-Assisted Phase-Matched Second- and Third-Harmonic Generation in Single-Negative Heterostructures

Dispersion relations of surface plasmon polaritons （SPPs） in sandwiched optical systems are studied. The system is actually a kind of SPP waveguides, with two kinds of single negative material （SNG） as core and cladding layers, respectively. Since both TM and TE polarized SPPs can be excited in the structure, the dispersion of SPPs becomes more abundant and leads to colorful nonlinear opticM properties. The authors demonstrate the effective phase-matched second and third-harmonic generation （SHG, THG） assisted by the coupled SPPs. A cascaded second-order nonlinear process can Mso be achieved in the structure when the thickness of the core layer is properly selected, leading to the simultaneous SHG and THG. Further investigations show that much easier phase-matching can be fulfilled in the SNG waveguide array. Our results would be of potential use for surface-enhanced frequency conversion device such as light emitters or lasers.     

Propagation of surface plasmon polaritons in anisotropic MIM and IMI structures

Electromagnetic wave propagation through waveguide structures consisting of anisotropic dielectric layers, assisted by surface plasmon-polaritons (SPPs) is theoretically studied. Dispersion relations corresponding to both short range and long range coupled SPP modes in metal/insulator/metal (MIM) and insulator/metal/insulator (IMI) structures, taking into consideration the anisotropy of the insulator, are derived and numerically solved. The dispersion has a prominent dependence on the anisotropy of the dielectric environment. The dependence of propagation on the misalignments of the optic axes of the insulator has also been investigated.     

三层不对称人工电磁材料界面处表面等离子体激元的理论研究

从P和S偏振出发.研究了由常规材料/左手材料/负介电常数材料、及常规材料/左手材料/负磁导率材料这两种三层不对称结构界面上表面等离子体激元(Surface plasmon polaritons,SPPs)的存在区域、色散曲线及其激发.观察到表面等离子体激元的性质强烈地依赖于人工电磁材料的组成参量,例如介质板的厚度和等离子体的频率.最后,使用衰减全反射(Attenuated total reflection,ATR)技术,探究了激发和观察表面等离子体激元的可能性.并针对P和s偏振两种情况计算了衰减全反射光谱.     

Nonlinear photonic crystals: II. Interaction classification for quadratic nonlinearities

Weakly nonlinear interactions between wavepackets in lossless periodic dielectric media are studied based on the classical nonlinear Maxwell equations. We consider nonlinear processes such that: (i) the amplitude of the wave component due to the nonlinearity does not exceed the amplitude of its linear component; (ii) the spatial range of a probing wavepacket is much smaller than the dimension of the medium sample, and it is not too small compared with the dimension of the primitive cell. These nonlinear processes are naturally described in terms of the Bloch modes and the dispersion relations of the underlying linear periodic medium. It turns out that only a few triads of modes have significant nonlinear interactions. They are singled out by the frequency and phase matching conditions and, as we show, by an additional selection rule: the group velocity matching condition. The latter condition is the most important selection rule for the nonlinear regimes. We give a complete quantitative classification of all possible significant interactions for quadratic nonlinearities. The classification is based on a universal system of indices reflecting the intensity of nonlinear interactions. The obtained classification points to the second harmonic generation as being one of the stronger nonlinear interactions, and often the strongest one.     

Surface plasmon polaritons of symmetric and asymmetric metamaterial slabs

The p and s-polarized surface plasmon polaritons (SPPs) of symmetric and asymmetric slabs formed arbitrarily by four types of conventional materials: dielectrics, negative dielectric permittivity materials, negative magnetic permeability materials, and left-handed materials are comprehensively analysed. The existence regions, dispersion relations, and excitation of SPPs in different frequency regions are investigated in detail. For symmetric slabs, the numbers and the frequency positions of surface polariton branches are quite different. At the same time, the pairs of the p or s-polarized SPP branches occur in the same frequency range. For asymmetric slabs, the SPP branches in mid- and high-frequency ranges are greatly different. In addition, the slab thickness has a great effect on SPPs of asymmetric and symmetric slabs. The attenuated total reflection spectra for the cases of p and s polarizations in these slabs are also calculated.     

Optical modes in a plasmonic waveguide with electrically anisotropic metamaterial

We study the optical modes in a plasmonic waveguide with electrically anisotropic metamaterial and dielectric, including symmetric (anti-symmetric) photonic mode and symmetric (anti-symmetric) plasmonic mode. The dispersion curves for these modes are derived, and a graphical method is used to calculate the solution of symmetric photonic mode and anti-symmetric plasmonic mode. By simulation results the conditions of the existence for these modes are deduced in each case.     

Extraordinary THz transmission through subwavelength semiconductor slits under antiparallel external magnetic fields

We theoretically study the resonant transmission of electromagnetic waves at the THz frequencies through subwavelength semiconductor slits under external static magnetic fields. The dispersion relations of the surface plasmon polaritons (SPPs) inside a subwavelength slit are analytically derived. It is found that the SPPs propagating along one direction and its reverse are symmetric when parallel external magnetic fields are applied, but are asymmetric when antiparallel external magnetic fields are applied. The transmission properties of periodic subwavelength semiconductor slit arrays with the antiparallel magnetic fields in each unit cell are investigated by the mode expansion technique. The two significant transmission characteristics are observed: (i) The resonant peaks are redshifted with increasing external magnetic fields; (ii) The transmissions in the two opposite directions through the slit arrays are asymmetric. The origin of the transmission asymmetry is reasonably explained by the magnetic-field induced asymmetric SPP propagation losses.     

Nonlinear photonic crystals: II. Interaction classification for quadratic nonlinearities

Abstract

Weakly nonlinear interactions between wavepackets in lossless periodic dielectric media are studied based on the classical nonlinear Maxwell equations. We consider nonlinear processes such that: (i) the amplitude of the wave component due to the nonlinearity does not exceed the amplitude of its linear component; (ii) the spatial range of a probing wavepacket is much smaller than the dimension of the medium sample, and it is not too small compared with the dimension of the primitive cell. These nonlinear processes are naturally described in terms of the Bloch modes and the dispersion relations of the underlying linear periodic medium. It turns out that only a few triads of modes have significant nonlinear interactions. They are singled out by the frequency and phase matching conditions and, as we show, by an additional selection rule: the group velocity matching condition. The latter condition is the most important selection rule for the nonlinear regimes. We give a complete quantitative classification of all possible significant interactions for quadratic nonlinearities. The classification is based on a universal system of indices reflecting the intensity of nonlinear interactions. The obtained classification points to the second harmonic generation as being one of the stronger nonlinear interactions, and often the strongest one.     

Active modulation of plasmonic signal with a subwavelength metal/nonlinear dielectric material/metal structure

<正>Light propagation through a metal/nonlinear dielectric material/metal(M-NL-M) structure is numerically studied.The design parameters of the M-NL-M structure are found with the waveguide theory so that the structure only supports the symmetric surface plasmon polaritons(SPP(0)) mode and the antisymmetric surface plasmon polaritons(SPP(1)) mode.The coupling between the two modes within the M-NL-M structure is exploited.Through controlling the propagation constants of the two modes with the intensity-dependent dielectric constant of the nonlinear Kerr material,an effective all-optical control of plasmonic signal modulator can be realized with this M-NL-M structure.     

Optically nonlinear phonon-polariton modes in a three-layered structure

A theory is presented for the propagation of phonon-polariton modes arising when phonons are coupled to electromagnetic waves in multilayered structures. A multi-layered structure consists of a thin film surrounded symmetrically by a bounding media. Numerical calculations are given for s-polarized phonon-polariton modes in the case where the bounding media are assumed to be semi-infinite layers with nonlinear dielectric functions of ionic crystal type supporting optical phonon modes and the thin film is characterized by a Kerr-type nonlinear dielectric function. The phonon-polaritons were found to have distinct branches characteristic of optical phonons and showing features that are different from those of plasmon-polaritons [S. Baher, M.G. Cottam, Surf. Rev. Lett. 10 (2003) 13]. The parameters that modify the modes are the in-plane wave vector, the thickness of the film, the phonon frequency and the nonlinearity of each layer. It was found that by increasing the film thickness and nonlinearity coefficient, the curves move to the left and the number of the branches increases without changing the pattern of the curves.     

Propagation and stability of the stationary stripe nonlinear guided waves in a symmetric structure with a nonlinear film

Abstact The propagation and stability of the stationary stripe nonlinear guided waves in an antiwaveguide symmetric layered structure containing a nonlinear film are simulated numerically. The symmetric, antisymmetric and asymmetric modes are considered, in both Kerr-law and saturable instantaneous self-focusing nonlinearity cases. The numerical calculations support the statement that stationary stripe nonlinear guided waves are always unstable on propagation for Kerr-law nonlinearities and the use of saturable nonlinear films leads to stability on propagation for effective indices corresponding to the ascending branches of the nonlinear dispersion curves.     

Plasmon polariton modes guided by a metal film of finite width

The properties of purely bound plasmon-polariton modes guided by a symmetric thin metal film of finite width are described for what is believed to be the first time, and a suitable mode nomenclature for identifying them is proposed. The dispersion characteristics of the modes as a function of film thickness are presented. It has been found that long-range plasmon-polariton modes exist in a symmetric film structure and that one of them may be suitable for optical signal transmission.