The geometric representation at a fixed frequency of the wavevector (or dispersion) surface $ω(\vec k)$ for lossless, homogeneous dielectric--magnetic uniaxial materials is explored, when the elements of the relative permittivity and permeability tensors of the material can have any sign. Electromagnetic plane waves propagating inside the material can exhibit dispersion surfaces in the form of ellipsoids of revolution, hyperboloids of one sheet, or hyperboloids of two sheets. Furthermore, depending on the relative orientation of the optic axis, the intersections of these surfaces with fixed planes of propagation can be circles, ellipses, hyperbolas, or straight lines. The obtained understanding is used to study the reflection and refraction of electromagnetic plane waves due to a planar interface with an isotropic medium.
In this overview paper, we investigate the dispersion of electromagnetic waves for dissipative and non-dissipative dielectric-magnetic uniaxial mediums. Changing the sign of one component of dielectric permittivity (ε) or magnetic permeability (μ) from positive to negative will lead to sixteen different cases (real or imaginary) for a non-dissipative medium and eight different cases for dissipative one. In a non-dissipative medium, dispersion relations follow the elliptic/hyperbolic relations. This rule completely vanishes regarding the dissipative medium. While the number of dispersion cases …
In this article, we demonstrate experimentally and verified numerically the excitation of Berreman modes that propagate in a dielectric film of uniaxial anisotropic nanoporous alumina grown on an aluminium substrate. It is an air-dielectric-metal asymmetric polaritonic system with a real part of the effective permittivity having a value near zero. The modes are excited at a wavelength lower than the epsilon near zero wavelength region. Minimum reflection is observed for the mid-infrared p-polarized light, while maximum reflection is observed for the s-polarized light. The experimental results …
We present an effective medium description of time-modulated dielectric media. By taking the averaged fields over one modulation period, the relationship between them is derived, defining therefore the different constitutive parameters. In the most general situation, it is found that the effective material is described by means of a spatially and temporally dispersive transverse dielectric function and a constant longitudinal dielectric function. It has been also found that the frequency dependence in the former is weak, in comparison with its wavenumber-dependence (spatial dispersion). Differ…
We analyze surface electromagnetic waves with hyperbolic dispersion supported at the interface between a semi-infinite isotropic medium and an effective uniaxial material. Apart from known types plasmons with hyperbolic dispersion curve, sometimes referred to as Dyakonov plasmons [Z. Jacob and E. E. Narimanov, APL 93, 221109 (2008)], we classify two new types of surface waves with hyperbolic dispersion. One type of such waves, in contrary to Dyakonov plasmons, does not require hyperbolic metamaterials to be involved. These hybrid-polarized plasmon modes with both TE and TM electromagnetic comp…
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 am…
The article demonstrates uncommon manifestation of spatial dispersion in low refractive index contrast 3D periodic dielectric composites with periods of about one tenth of the wavelength. First principles simulations by the well established plane wave method reveal that spatial dispersion leads to appearance of additional optical axes and can compensate anisotropy in certain directions.
Electromagnetic surface waves supported by an isotropic chiral material were investigated via the associated canonical boundary-value problem. Specifically, two scenarios were considered: surface waves guided by the planar interface of an isotropic chiral material and (a) an isotropic dielectric material and (b) a uniaxial dielectric (or plasmonic) material. Both plasmonic and non-plasmonic achiral partnering materials were investigated. In scenario (a) surface waves akin to surface-plasmon-polariton (SPP) waves were excited, while in scenario (b) surface waves akin to Dyakonov waves and akin …
We introduce a practical dielectric metasurface design for microwave frequencies. The metasurface is made of an array of dielectric resonators held together by dielectric connections thus avoiding the need of a mechanical support in the form of a dielectric slab and the spurious multiple reflections that such a slab would generate. The proposed design can be used either for broadband metasurface applications or monochromatic wave transformations. The capabilities of the concept to manipulate the transmission phase and amplitude of the metasurface are supported by numerical and experimental res…
The use of metamaterial as a way to mitigate the negative effects of absorption in metals on the Purcell effect in metal-dielectric structures is investigated. A layered metal-dielectric structure is considered as an anisotropic medium in the long-wavelength limit. The dispersion of the surface plasmon appearing at the boundary between such a structure and a different dielectric material, as well as the position of the peak in the local density of states are studied for various combinations of materials and filling factors of the periodic structure. The calculated frequency dependence of the P…
We reveal extraordinary electromagnetic properties for a general class of uniaxially polarizable media. Depending on parameters, such metamaterials may have wide range of nontrivial shapes of isofrequency contours including lemniscate, diamond and multiply connected curves with connectivity number reaching five. The possibility of the dispersion engineering paves a way to more flexible manipulation of electromagnetic waves. Employing first-principle considerations we prove that uniaxially polarizable media should be described in terms of the nonlocal permittivity tensor which by no means can b…
Diffraction gratings disperse light in a rainbow of colors with the opposite order than refractive prisms, a phenomenon known as negative dispersion. While refractive dispersion can be controlled via material refractive index, diffractive dispersion is fundamentally an interference effect dictated by geometry. Here we show that this fundamental property can be altered using dielectric metasurfaces, and we experimentally demonstrate diffractive gratings and focusing mirrors with positive, zero, and hyper negative dispersion. These optical elements are implemented using a reflective metasurface …
In this paper, we present a quantum theory for field propagation through a three dimensional dielectric when the third order dispersion and the attenuation coefficients are included. A unique Lagrangian is defined leading to the correct equation of motion and the classical Hamiltonian. It is assumed that the dielectric has a combination of inhomogeneity, dispersion and nonlinearity. By employing constraint quantization approach the final Hamiltonian is expanded in terms of properly defined annihilation and creation operators. We obtain the quantum fields (quantum photon-polaritons fields) for …
A single-order transmission diffraction grating based on dispersion engineered all-dielectric metasurfaces is proposed and its wavelength discriminating properties have been theoretically described and confirmed using numerical simulations. The metasurface is designed using a 2D array of all-dielectric resonators, which emulates a Huygens source configuration to achieve a perfect match to free-space in broad bandwidth. Using a holey dielectric nanodisk structure as the unit cell, the resonant wavelength is tapered across the metasurface to engineer the wavelength dependent spatial phase gradie…
We report the prediction of a new type of Dyakonov surface waves that propagate along the flat strip of the interface between two dielectrics with negative anisotropy. It is shown that the surface waves condition is satisfied for negatively anisotropic dielectrics due to specific boundaries of the strip waveguide confined between two metallic plates. Such modes are studied by the perturbation theory in the approximation of weak anisotropy. The existence of Dyakonov surface waves in negative uniaxial crystals motivates us to reconsider the list of materials suitable for their practical implemen…
In this article, we propose and numerically analyze an all dielectric biaxial metamaterial [ADBM] constructed by multilayer pattering of a sub-wavelength ridge array of Silicon and a flat SiO2 layer. The proposed ADBM can support Dyakonov Surface Waves [DSWs] with infinite propagation length which can propagate in a wide angular domain. Though natural uniaxial and biaxial materials and also nanowire all dielectric metamaterials can also support DSWs, the angular existence domain [AED] is limited to a very narrow range. Our proposed ADBM can support can overcome this limitation and it can achie…
We have developed low-dispersion (1480 l/mm), resonance-free, diffraction gratings made of dielectric materials resistant to femtosecond laser damage $(SiO_{2}/HfO_{2})$. A 14 cm diameter sample was fabricated resulting in a mean diffraction efficiency of 99.1% at λ = 810 nm with 0.4% uniformity using equipment which can fabricate gratings up to 1m diagonal. The implementation of these gratings in the compression of 30 fs pulses in an out-of-plane geometry can result in compressor efficiencies of ~95%. The measured laser absorption is 500x lower than current ultrafast petawatt-class compressor…
Dispersion decomposes compound light into monochromatic components at different spatial locations, which needs to be eliminated in imaging but utilized in spectral detection. Metasurfaces provide a unique path to modulate the dispersion only by adjusting the structural parameters without changing the material as required for refractive elements. However, the common linear phase compensation does not conform to the dispersion characteristics of the meta-unit limiting dispersion modulation in broader wavelength bands, which is desired for ultra-broadband or multiband imaging. Here, we propose a …
We investigate electromagnetic propagation in uniaxial dielectrics with a transversely varying orientation of the optic axis, the latter staying orthogonal everywhere to the propagation direction. In such a geometry, the field experiences no refractive index gradients, yet it acquires a transversely-modulated Pancharatnam-Berry phase, that is, a geometric phase originating from a spin-orbit interaction. We show that the periodic evolution of the geometric phase versus propagation gives rise to a longitudinally-invariant effective potential. In certain configurations, this geometric phase can p…
A simple user-friendly software named PRISA has been developed to determine optical constants (refractive index and extinction co-efficient), dispersion parameters (oscillator energy and dispersion energy), absorption co-efficient, band gap and thickness of semiconductor and dielectric thin films from their measured transmission spectrum, only. The thickness, refractive index, and extinction co-efficient of the films have been derived using Envelope method proposed by Swanepoel. The absorption co-efficient in the strong absorption region is calculated using the method proposed by Connel and Le…
Fast, large area patterning of arbitrary structures down to the nanometre scale is of great interest for a range of applications including the semiconductor industry, quantum electronics, nanophotonics and others. It was recently proposed that nanometre-resolution mask lithography can be realised by sending metastable helium atoms through a binary holography mask consisting of a pattern of holes. However, these first calculations were done using a simple scalar wave approach, which did not consider the dispersion force interaction between the atoms and the mask material. To access the true pot…
Electromagnetic Momentum in Dispersive Dielectric Media
当考虑色散效应时，亚伯拉罕和闵可夫斯基关于电介质中电磁动量的表达式都不能给出辐射的吸收体或发射体的正确反冲动量。与电介质中的场相关的总动量密度有三个贡献：（i）场的亚伯拉罕动量密度，（ii）与亚伯拉罕力相关的动量密度，以及（iii）由介质对场的响应的色散部分产生的动量密度，后者显然具有由D.F. Nelson [Phys.Rev.A44，3985（1991）]。所有这三个贡献都需要在电介质中的吸收体或发射体的反冲动量守恒。我们考虑交换的动量和作用在可极化粒子上的力（例如，当光脉冲入射到宿主电介质上时，宿主电介质中的原子或小电介质球），包括电介质的色散以及粒子对场的响应中的色散分量。在慢光介质中，这种力可以大大增加。
We investigate the dispersion relations of TE resonances in different graphene-dielectric structures. Previous work has shown that when a graphene layer is brought into contact with a dielectric material, a gap can appear in its electric band structure. This allows for the formation of TE-plasmons with unusual dispersion relations. In addition, if the dielectric has a finite thickness, graphene strongly modifies the behavior of the waveguiding modes by introducing dissipation above a well-defined cutoff frequency thus providing the possibility of mode filtering. This cutoff and the properties …
In this work, we present an in-depth experimental and numerical study of the short-range THz communications links that use subwavelength dielectric fibers for information transmission and define main challenges and tradeoffs in the link implementation. Particularly, we use air or foam-cladded polypropylene-core subwavelength dielectric THz fibers of various diameters (0.57-1.75 mm) to study link performance as a function of the link length of up to ~10 m, and data bitrates of up to 6 Gbps at the carrier frequency of 128 GHz (2.34 mm wavelength). We find that depending on the fiber diameter, th…
In this letter, we experimentally report an achromatic metalens (AML) operating over a continuous bandwidth in the visible. This is accomplished via dispersion engineering of dielectric phase shifters: titanium dioxide nanopillars tiled on a dielectric spacer layer above a metallic mirror. The AML works in reflection mode with a focal length independent of wavelength from wavelength of 490 nm to 550 nm. We also design a metalens with reverse chromatic dispersion, where the focal length increases as the wavelength increases, contrary to conventional diffractive lenses. The ability to engineer t…
Constraints on transmission, dispersion, and density of states in dielectric multilayers and stepwise potential barriers with arbitrary layer arrangement
We suggest an inverse dispersion method for calculating photonic band diagram for materials with arbitrary frequency-dependent dielectric functions. The method is able to calculate the complex wave vector for a given frequency by solving the eigenvalue problem with a non-Hermitian operator. The analogy with $\cal{PT}$-symmetric Hamiltonians reveals that the operator corresponds to the momentum as a physical quantity and the singularities at the band edges are related to the branch points and responses for the features on the band edges. The method is realized using plane wave expansion techniq…
We develop a consistent quantum description of surface plasmons interacting with quantum emitters and external electromagnetic field. Within the framework of macroscopic electrodynamics in dispersive and absorptive medium, we derive, in the Markov approximation, the canonical Hamiltonian, commutation relations, and coupling parameters for the plasmon modes in metal-dielectric structures of an arbitrary shape whose characteristic size is well below the diffraction limit. We then develop a new quantum approach bridging the macroscopic and canonical schemes which describes the interacting plasmon…
Recent experiments have shown that spatial dispersion may have a conspicuous impact on the response of plasmonic structures. This suggests that in some cases the Drude model should be replaced by more advanced descriptions that take spatial dispersion into account, like the hydrodynamic model. Here we show that nonlocality in the metallic response affects surface plasmons propagating at the interface between a metal and a dielectric with high permittivity. As a direct consequence, any nanoparticle with a radius larger than 20 nm can be expected to be sensitive to spatial dispersion whatever it…
