A system of equations for two components of the electric field of a surface wave propagating along the interface between a nonlinear dielectric and topological insulator is derived, based on the dispersion relation for a nonlinear mode. The system is used to show that small disturbances of a steady-state surface wave neither attenuate nor increase over time.
Solitary electromagnetic waves propagating along the waveguides forming a rhombic one-dimensional lattice are considered. Two waveguides that are part of the unit cell are assumed to be made of an optical linear material, while the third waveguide from the same array is composed of material with the cubic nonlinearity. The equations of the coupled waves spreading in each waveguide are solved under some approximation. These solutions represent the breather like solitary waves, which are akin to three component soliton.
Based on the dispersion relation for a wave localised in a thin film of a nonlinear dielectric, which is located on the surface of a topological insulator, we have derived a system of equations that describes the propagation of a surface wave. It is shown that the longitudinal and transverse tangential components of the electric field vector are related due to the nonlinearity of the film and change periodically during propagation. It is found that the rotation period of this vector is determined by the axion charge of the topological dielectric and the nonlinear susceptibility of the thin film.
ЭЛЕКТРОМАГНИТНЫЕ ВОЛНЫ В СРЕДЕ С ТОПОЛОГИЧЕСКИМИ СВОЙСТВАМИ В ПРИСУТСТВИИ ПОСТОЯННОГО МАГНИТНОГО ПОЛЯРассмотрено распространение электромагнитной волны в среде, обладающей топологическими характеристиками в случае, когда в направлении распространения волны приложено постоянной магнитное поле и получены выражения для
The Drude–Lorentz model, which makes it possible to describe a nonlinear response of a dielectric or conducting medium, can be suited for the description of nonlinear nonresonant responses of some exotic media: topological insulators, a Weil semimetal, or a Dirac metal. A generalized Drude–Lorentz model and its simplified version, in which topological effects are taken into account to a minimum extent, are presented. As an example of application of the simplified model, the second-order nonlinear conductivity is derived, which is responsible for the second harmonic generation and the effect of optical rectification. It is shown that the ratio of the topological conductivity to the ordinary linear conductivity contains constants that are proportional to the fine structure constant and the axion field gradient.
The surface waves that propagate along the interface of a dielectric with nonlinear susceptibility of the third order and topological insulator have been considered. The optical nonlinearity of the dielectric ensures the existence of a surface wave. The density of the spin angular momentum of a surface wave has been determined for dielectrics with positive or negative linear permittivity. It has been shown that the spin angular momentum vector has a projection on the normal to the interface, which is different from the usual surface polaritons or plasmon polaritons. The discrete nature of the topological number manifests itself in the discreteness of the values of the normal and tangential components of the spin angular momentum density. The increase in the intensity of the electric field of the wave at the interface of the media changes the value of the spin angular momentum and can lead to its disappearance.
The refraction and reflection phenomena occurring at the boundaries of dielectric waveguides manufactured from the unusual materials have been discussed. Such materials are topological insulators and hyperbolic metamaterials with the electromagnetic properties being different from those for the ordinary dialectics. For example, the polarization of the refracted and reflected waves can be changed; the total internal reflection occurs at small angles of the incident wave that is less than a certain critical angle. As a result, the waveguides acquire new characteristics that distinguish them from the standard dielectric waveguides.
Commonly, a surface wave traveling along the interface between isotropic media has a spin moment that lies in the plane of the interface and is perpendicular to the direction of propagation. Here, we show that, if one of the two media is a topological insulator, the spin moment vector has a component that is normal to the surface of the interface and is proportional to odd integers. The appearance of the normal component of the spin moment is associated with the topological magnetoelectric effect, as a result of which the polarization of the wave changes upon passage through the interface.
The guided waves of a symmetric planar waveguide formed by an isotropic dielectric placed in a hyperbolic medium and having a cubic-nonlinear response are studied theoretically. The optical axis of the hyperbolic medium is directed along the normal to the interfaces between the media. If the permittivity of the waveguide core exceeds the main permittivity for an extraordinary wave in the hyperbolic medium, then each TM mode is characterised by two cut-off frequencies. Dispersion relations for these modes are found in the case of focusing and defocusing core media. The number of the modes possible at a given frequency depends on the radiation intensity. It is shown that zero values of the mode propagation constants are possible in the waveguide, which corresponds to the formation of a standing wave between the boundaries of the waveguide. In addition, in the case of a defocusing waveguide layer, such stopped modes can be obtained with increasing field intensity. The dependences of the propagation constant and the width of the transverse distribution of the mode field on the radiation intensity are found and analysed.
Ekaterina I. Lyashko, Andrei I. Maimistov, 3 and Ildar R. Gabitov 5 Department of General and Applied Physics, Moscow Institute of Physics and Technology, Dolgoprudny, Moscow region, 141700 Russia E-mails: ostroukhova.ei@gmail.com Department of Solid State Physics and Nanostructures, National Nuclear Research University, Moscow Engineering Physics Institute, Moscow, 115409 Russia E-mails: aimaimistov@gmail.com Department of General Physics, Moscow Institute of Physics and Technology, Dolgoprudny, Moscow region, 141700 Russia Department of Mathematics, University of Arizona, Tucson, Arizona, 85721, USA Skolkovo Institute of Science and Technology, Skolkovo Innovation Center, Moscow 143026 Russia E-mails: gabitov@math.arizona.edu (Dated: June 20, 2017)
We have theoretically investigated waveguide modes propagating in a planar waveguide formed by a layer of an isotropic dielectric surrounded by hyperbolic media. The case, when the optical axis of hyperbolic media is perpendicular to the interface, is considered. Dispersion relations are derived for the cases of TE and TM waves. The differences in the characteristics of a hyperbolic and a conventional dielectric waveguide are found. In particular, it is shown that in hyperbolic waveguides for each TM mode there are two cut-off frequencies and the number of propagating modes is always limited.
Interaction of forward and backward waves in a nonlinear medium exhibiting a third-order nonlinearity (the Kerr medium) is investigated theoretically. We have analyzed the propagation of two quasi-harmonic waves with different carrier frequencies, such that the phase velocity at one frequency has the same direction as the group velocity, while the phase and the group velocities at the other frequency have opposite directions. Coupling between the waves in a Kerr medium is caused by cross modulation. It is demonstrated that a steady-state biharmonic wave propagating as a single whole can be formed in this situation.
The dispersion relation determining guided TE and TM modes are found for the slab hyperbolic waveguide. The waveguide is consisting of an isotropic dielectric slab bounded by hyperbolic media. Some differences between the features of the waveguide under consideration and conventional ones are obtained. In particular, in the case of hyperbolic waveguide TM modes have two cutoff frequencies. As a result the number of modes is limited. Both TE and TM modes have nonzero cutoff frequencies, even though waveguide is symmetric one. For the TE and TM modes the Poynting vector component along the wave’s propagation axis could be equal to zero.
We consider the coupled electromagnetic waves propagating in a nonlinear medium, which is featured by a positive and negative refraction indexes. The backward waves can be propagating in this case. The example of the true soliton is discussed. In general case the coupled forward and backward solitary wave can be found. They are analogues to the optical solitons.
