Dyakonov Surface Waves Research Articles

Theory of grating-coupled excitation of Dyakonov surface waves

Excitation of Dyakonov surface waves guided by a plane wave incident on a columnar thin film (CTF) deposited on a surface-relief grating decorating a dielectric substrate was studied using the rigorous coupled-wave approach, when the grating plane, the plane of incidence, and the morphologically significant plane of the CTF are all different. The absorptance for a specific linear polarization state of the incident plane wave was plotted as a function of the polar angle of incidence, at a fixed azimuthal angle, and those absorptance peaks were identified that are independent of the thicknesses of the CTF and the dielectric substrate. The angular locations of these absorptance peaks were correlated with the solution of the canonical boundary-value problem for surface-wave propagation. Dyakonov surface waves can be excited in a wider range of directions in the interface plane by p-polarized illumination than by s-polarized illumination. When the incidence and the grating planes do not coincide, it is possible to excite Dyakonov surfaces for multiple values of the polar angle of incidence.

Dyakonov-like surface waves in anisotropic cylindrical waveguides

Dyakonov surface waves are a well-known example of surface electromagnetic waves propagating along a plane interface between isotropic and anisotropic dielectric media. Here, we investigate the spectrum and radiative losses of Dyakonov waves at the curved interface considering both cases of "positive" and "negative" curvature of anisotropic medium. We demonstrate how Dyakonov waves at a plane interface continuously transform to the leaky or guided modes of an anisotropic cylindrical waveguide and simple derive asymptotic equation for radiative losses. All analytical results are confirmed by solving exact dispersion equation numerically. We believe that our work extends the potential practical application of Dyakonov waves in optics and photonics devices.

Dyakonov Plasmon–Polaritons Propagating along the Surface of a Hyperbolic Metamaterial

Plasmon–polaritons of the type of Dyakonov surface waves propagating along the plane boundary of a hyperbolic metamaterial with an arbitrary orientation of its crystallographic axis are considered. Conditions of the existence of fast, slow, leaking-in, leaking-out, forward, and backward plasmon–polaritons are found. A waveguide in the shape of an asymmetric layer of a hyperbolic metamaterial is examined. An expression for the electromagnetic energy density in this metamaterial is given.

Theory of Dyakonov–Tamm surface waves featuring Dyakonov–Tamm–Voigt surface waves

The propagation of Dyakonov–Tamm (DT) surface waves guided by the planar interface of two nondissipative materials A and B was investigated theoretically and numerically, via the corresponding canonical boundary-value problem. Material A is a homogeneous uniaxial dielectric material whose optic axis lies at an angle χ relative to the interface plane. Material B is an isotropic dielectric material that is periodically nonhomogeneous in the direction normal to the interface. The special case was considered in which the propagation matrix for material A is non-diagonalizable because the corresponding surface wave — named the Dyakonov–Tamm–Voigt (DTV) surface wave — has unusual localization characteristics. The decay of the DTV surface wave is given by the product of a linear function and an exponential function of distance from the interface in material A; in contrast, the fields of conventional DT surface waves decay only exponentially with distance from the interface. Numerical studies revealed that multiple DT surface waves can exist for a fixed propagation direction in the interface plane, depending upon the constitutive parameters of materials A and B. When regarded as functions of the angle of propagation in the interface plane, the multiple DT surface-wave solutions can be organized as continuous branches. A larger number of DT solution branches exist when the degree of anisotropy of material A is greater. If χ=0°, a solitary DTV solution exists for a unique propagation direction on a DT solution branch and should be regarded as the manifestation of an exceptional point. No DTV solutions exist if χ>0°. As the degree of nonhomogeneity of material B decreases, the number of DT solution branches decreases. For most propagation directions in the interface plane, no solutions exist in the limiting case wherein the degree of nonhomogeneity approaches zero; but one solution persists provided that the direction of propagation falls within the angular existence domain of the corresponding Dyakonov surface wave.

Controllable Selective Coupling of Dyakonov Surface Waves at a Liquid-Crystal-Based Interface

Highly directional and lossless surface wave has significant potential applications in the two-dimensional photonic circuits and devices. Here we experimentally demonstrate a selective Dyakonov surface wave coupling at the interface between a transparent polycarbonate material and nematic liquid crystal 5CB. By controlling the anisotropy of the nematic liquid crystal with an applied magnetic field, a single ray at a certain incident angle from a diverged incident beam can be selectively coupled into surface wave. The implementation of this property may lead to a new generation of on-chip integrated optics and two-dimensional photonic devices.

Conformal transformation of Dyakonov surface waves into bound states of cylindrical metamaterials

We put forward the use of transformation optics to map surface waves that exist as one-dimensional modes supported by anisotropic structures into bound states in two-dimensional geometries. Specifically, we show the conformal mapping of Dyakonov waves existing in infinite planar surfaces separating birefringent media into bound modes supported by a cylindrical structure made of suitable metamaterials. In contrast with the original Dyakonov waves, the resulting fiber-like modes are highly dispersive, may exist as fundamental as well as higher-order states, feature helical wave fronts, and exhibit a lower and upper frequency cutoff. The program we put forward can be applied to all wave phenomena currently known to occur only in planar geometries in different types of anisotropic media.

Electromagnetic surface waves guided by a twist discontinuity in a uniaxial dielectric with optic axis lying in the discontinuity plane

ABSTRACTA method for calculating the eigenwaves in a “semi-infinite” uniaxial dielectric medium (UDM) is proposed. The term “semi-infinite” medium implies the presence of at least one flat boundary of such medium. This method allowed writing out all the components of the total fields in UDM. With the help of that analytical representation of the fields, the problem of the propagation of Dyakonov surface waves guided by the planar interface of two identical UDM with their optic axes lying in the interface plane was investigated to derive an exact analytical expression for the phase speed, when the direction of propagation bisects the angle formed by the two optic axes. On the basis of the solutions found, the energy characteristics were studied, which demonstrated the presence of the flux of average over a period power of the Dyakonov wave along the coordinate axes lying in the plane of UDM boundary.

Dyakonov-Voigt surface waves.

Electromagnetic surface waves guided by the planar interface of an isotropic dielectric medium and a uniaxial dielectric medium, both non-dissipative, were considered, the optic axis of the uniaxial medium lying in the interface plane. Whereas this interface is known to support the propagation of Dyakonov surface waves when certain constraints are satisfied by the constitutive parameters of the two partnering mediums, we identified a different set of constraints that allow the propagation of surface waves of a new type. The fields of the new surface waves, named Dyakonov–Voigt (DV) surface waves, decay as the product of a linear and an exponential function of the distance from the interface in the anisotropic medium, whereas the fields of the Dyakonov surface waves decay only exponentially in the anisotropic medium. In contrast to Dyakonov surface waves, the wavenumber of a DV surface wave can be found analytically. Also, unlike Dyakonov surface waves, DV surface waves propagate only in one direction in each quadrant of the interface plane.

Dyakonov surface waves at the interface of nanocomposites with spherical and ellipsoidal inclusions

The dispersion properties of different types of surface electromagnetic waves which are supported by the interface of two nanocomposite materials with inclusions of different shape are studied theoretically and numerically. Both nanocomposites are made of doped n-type semiconductor inclusions which are evenly distributed in a transparent dielectric matrix. First nanocomposite contains semiconductor inclusions of spherical shape and can be represented as isotropic material with scalar effective dielectric permittivity. Second nanocomposite contains semiconductor inclusions of ellipsoidal shape and can be modeled as a uniaxial anisotropic crystal with two different principal effective permittivity components. Influence of physical and geometrical parameters of the nanocomposites on dispersion properties of surface waves is studied. It is shown that when dissipations in the semiconductor inclusions are taken into account the angular spectrum of Dyakonov surface wave existence becomes wider, and several dispersion curves of surface modes can simultaneously exist.

Surface polaritons and Dyakonov-like surface waves in an isotropic-anisotropic nanocomposite system

The properties of surface polaritons as well as Dyakonov surface waves at the plane interface between a nanocomposite made of doped semiconductor spherical inclusions distributed in a transparent matrix and a nanocomposite made of the identical transparent matrix but with doped semiconductor inclusions of ellipsoidal shape are studied. Electrodynamic Maxwell-Garnett model is applied to simulate the effective resonance permittivity of both nanocomposites. The nanocomposite with spherical inclusions represents an isotropic medium, while the nanocomposite with ellipsoidal inclusions can be described as uniaxial material. It is shown, that by properly choosing the physical and geometrical parameters of the corresponding composites, like the volume fractions and materials of nanoinclusions, the effective control over surface plasmon-polaritons and Dyakonov-like surface waves properties is possible.

Terahertz Dyakonov plasmon surface waves supported by a plasma/TiO2 interface

A Dyakonov plasmon surface wave (DPSW), which is a special case of Dyakonov surface wave (DSW), is studied theoretically at the interface of an isotropic plasma and a uniaxial rutile ${\mathrm{TiO}}_{2}$ in the terahertz (THz) frequencies. DPSW has the combination of properties of both DSW and surface plasmon polariton (SPP) such as directionality (of DSW) and high localization degree (of SPP). The existence conditions for propagation of the DPSW in this structure are found to be extremely relaxed compared to DSW existing in dielectric media. DPSWs in comparison to common SPPs are composed of four evanescent waves: transverse electric and transverse magnetic in the isotropic plasma cover, and ordinary and extraordinary waves in the uniaxial rutile ${\mathrm{TiO}}_{2}$ crystal substrate. Frequency tunability, localization degree, directionality, and hybridization factor of the DPSWs for three cases of THz frequencies are investigated. It is also demonstrated that the presence of the plasma medium with tunable permittivity can lead to novel applications of DPSWs in such structures.

Electromagnetic surface waves guided by a plane interface between a porous nanocomposite and a hypercrystal

Dispersion properties of surface electromagnetic waves localized at the plane interface between a nanocomposite made of a semiconductor inclusions evenly distributed in a transparent matrix and a hypercrystal, formed by an alternating dielectric and hyperbolic layers are studied. Electrodynamic Maxwell Garnett model is applied to simulate the effective resonance permittivity of the nanocomposite. In the subwavelength approximation the hypercrystal is represented as the uniaxial media with two different principal permittivity tensor components. The particular attention is devoted to the study of dispersion properties of hybrid Dyakonov surface waves. It is shown that by properly choosing physical and geometrical parameters of the corresponding composites, like volume fractions of nano-inclusions, thicknesses of hyperbolic and dielectric layers, and materials used, the effective control over the properties of supported surface modes is possible.

Dyakonov waves in biaxial anisotropic crystals

We present the general analytical theory for Dyakonov surface waves at the interface of a biaxial anisotropic dielectric with an isotropic medium. We demonstrate that these surface waves can be divided into todo distinct classes, with qualitatively different spatial behavior. We obtain explicit expressions for the Dyakonov waves dispersion and the parameter range for their existence.

Simultaneous existence of amplified and attenuated Dyakonov surface waves

The propagation of Dyakonov surface waves guided by the planar interface of (i) an isotropic dielectric material and (ii) a homogenized uniaxial dielectric composite material comprising both passive and active component materials was theoretically investigated, under the assumption that the optic axis of the uniaxial partnering material lies wholly in the interface plane. For a certain range of the volume fraction of the active component material, the uniaxial partnering material is neither wholly dissipative nor wholly active and the Dyakonov surface waves propagating in certain directions amplify but the Dyakonov surface waves propagating in other directions attenuate.

Leaky property of the Dyakonov-like wave at the surface of a semi-infinite metal-dielectric multilayered structure.

We investigate the Dyakonov-like surface wave (DLSW) at the interface of a dielectric and a metal-dielectric multilayered (MDM) structure when this MDM structure serves as an elliptic medium according to the effective medium approximation (EMA). Different from the conventional Dyakonov surface waves, we find that this kind of DLSW possesses an unexpected leaky property due to an additional hyperbolic-like wave in the MDM structure, resulting in a significant increase of propagation loss compared to the results estimated by a simple effective model based on the EMA. Moreover, such leaky property is found to be sensitive to the period of the MDM structure. Thus, to diminish this non-negligible leaky loss, one can suppress the amplitude of the leaky component by designing the MDM structure with a smaller period. On the other hand, as the MDM structure sometimes can also support an additional elliptic-like dispersion when it is regarded as a hyperbolic medium, we discuss this condition for completeness. Based on this elliptic-like dispersion, an apparent leaky property is observed in the resultant DLSW. This DLSW propagates with a wider range of propagation direction but suffers from a poor field confinement to the interface it is propagating along.

Experimental Observation of Dyakonov Plasmons in the Mid-Infrared

In this work, we report on observation of Dyakonov plasmons at an interface with a hyperbolic metamaterial in the mid-IR. The hyperbolic metamaterial is implemented as a CMOS-compatible high aspect ratio grating structure with aluminium-doped ZnO (AZO) ridges grown by atomic layer deposition in deep trench silicon matrix. The dispersion of Dyakonov plasmons is characterized by the attenuated total reflection method in the Otto configuration. We demonstrate that Dyakonov plasmons propagate in a broad range of directions (a few tens of degrees) in contrast to the classical Dyakonov surface waves (about one tenth of degree). The obtained results provide useful guidelines for practical implementations of structures supporting Dyakonov plasmons in the mid-IR.

Terahertz Dyakonov surface waves in plasma metamaterials.

Metamaterials in which plasmas are included have significant properties that may not be found in ordinary metamaterials. The permittivity function of these engineered materials can be rapidly manipulated by applying external electric and magnetic field or changing the gas pressure, temperature, and collisional frequency. We investigate the conditions necessary for the existence of Dyakonov surface waves (DSWs) propagating along the interface of a plasma metamaterial (PMM) and an isotropic dielectric material in the terahertz region. We assume the PMM to be a multilayer structure that consists of plasma and background isotropic material alternately. The influence of considering the plasma collisional loss in the DSW dispersion curve is studied. We demonstrate that the angular regions in which the DSW propagation is allowed can be tuned and significantly expanded. We also show that the large birefringence represented by the PMM allows DSWs to exist within large angular existence domains and levels of localization similar to plasmons, thus making these surface waves available for practical applications.

Experimental observation of Dyakonov plasmons in the mid-infrared

AbstractIn this work, we report on observation of Dyakonov plasmons at an interface with a hyperbolic metamaterial in the mid-IR. The hyperbolic metamaterial is implemented as a CMOS-compatible high aspect ratio grating structure with aluminium-doped ZnO (AZO) ridges grown by atomic layer deposition in deep trench silicon matrix. The dispersion of Dyakonov plasmons is characterized by the attenuated total reflection method in the Otto configuration. We demonstrate that Dyakonov plasmons propagate in a broad range of directions (a few tens of degrees) in contrast to the classical Dyakonov surface waves (about one tenth of degree). The obtained results provide useful guidelines for practical implementations of structures supporting Dyakonov plasmons in the mid-IR.

Determination of dissipative Dyakonov surface waves using a finite element method based eigenvalue algorithm.

A full-vectorial finite element method is developed to analyze the surface waves propagating at the interface between two media which could be dissipative particularly. The dissipative wave possessing a complex-valued propagation constant can be determined precisely for any given propagation direction and thus the property of losses could be thoroughly analyzed. Besides, by applying a special characteristic of the implicit circular block matrix, we reduce the computational consumptions in the analysis. By utilizing this method, the Dyakonov surface wave (DSW) at the interface between a dielectric and a metal-dielectric multilayered (MDM) structure which serves as a hyperbolic medium is discussed. Its propagation loss is smaller for larger period of the MDM structure but its field becomes less confined to the interface.

Compound Dyakonov modes at a symmetric uniaxial-isotropic-uniaxial planar structure

Compound Dyakonov modes supported by a symmetric uniaxial-isotropic-uniaxial planar structure are investigated, of which the uniaxial layers have the identical principal values of the relative permittivity tensor and optic axis orientation. By solving the canonical boundary-value problem, two branches of compound Dyakonov modes are obtained with symmetric and antisymmetric field distributions respectively. The shapes of the field distributions are proven to be closely related to the reflectance of TE polarized waves at the interfaces of the structure. The relevant characteristics of propagation constants, field distributions, propagation direction ranges and polarization states are numerically calculated. The results show that these characteristics are highly affected by the thickness and the permittivity of the middle isotropic layer, the antisymmetric modes will cutoff when the thickness decreases below critical value and the polarization states of symmetric modes will vary significantly from Dyakonov surface waves due to the strong coupling.