arXiv subjects

Maxim Durach

Publications and source records attributed to Maxim Durach.

At least 19 recordsLinked to original sources

arXiv2026

Multilayer Babinet metamaterial to initiate nonreciprocal topological phenomena and generalized Faraday rotation

Multilayers of Babinet complementary periodic structures constructed with miniarrays of spherical plasmonic nanoresonators were optimized to ensure Generalized Faraday Rotation. Nonreciprocal rotation and asymmetric transmission were achieved in spectrally overlapping regions due to the reach physics involving (i) symmetry breaking via coupled localized modes, (ii) Brillouin zone-folding stemmed from constituent sub-lattices forming in-plane twisted coupled loops, (iii) interlayer coupling between Babinet complementary patterns. The nanophotonical phenomena include (i) quasi-BIC resonances, (ii) hierarchically coupled localized and propagating modes that results in time-periodic Floquet modulation, (iii) initialization of synthetic potentials tuneable independently via intra and inter-layer parameters. The unique bianisotropic composites result in a synthetic vector gauge and emulated magnetic field manifesting itself in tilted-precessing magnetic dipoles and the accompanying modulation being time-periodic, inherently ensures a synthetic dimension. The asymmetric transmission is enhanced in the classical sense along quantized flat bands, and in mixed and forward bases inside finite wavelength-and-tilting intervals overlapping with nonreciprocal polarization rotation. The transmitted pulse re-shaping proves beating of nearby resonant modes, the loss can be compensated with active ad-layers thereby resulting in Faraday isolator capability. The multilayers synthetize topological phenomena in high-dimensional synthetic parameter spaces.

physics.optics↗

arXiv2026

Propagation Maps, Maradona Exceptional Points, and Pele Singularities in Anisotropic, Tellegen, Chiral, Moving-Medium, Omega and Other Isotropy-Broken Materials

Anisotropic, Tellegen, chiral, moving-medium-type, omega, gyrotropic, hyperbolic, and multi-hyperbolic materials form an important class of isotropy-broken photonic media in which wave propagation can no longer be characterized by the Fresnel wave surface alone. Here we show that Fresnel wave surfaces can be converted into propagation maps that organize positive- and negative-phase-velocity propagation together with attenuation and amplification. In Hermitian media, the boundary between forward and backward propagation forms the Michelangelo silhouette separatrix. This separatrix is also a continuous locus of Maradona exceptional points, where the index-of-refraction operator becomes defective even though the material medium remains Hermitian. In non-Hermitian media, the attenuation-amplification boundary forms the Caravaggio chiaroscuro separatrix. The associated Pele singularities occur where the handedness remains continuous while the gain-loss character changes sign. Their physical importance is revealed by the momentum-resolved density of states: at these points, the Lorentzian linewidth of the non-Hermitian momentum-resolved density of states (DOS) collapses, producing sharp DOS peaks whose sign reverses across the separatrix. Thus, Pele singularities are threshold-like gain-loss singularities of the Fresnel wave-surface propagation map, generated by non-Hermitian linewidth collapse. The result is a compact geometric language for describing how handedness, degeneracy, loss, gain, and momentum-resolved DOS are organized in isotropy-broken electromagnetic materials.

physics.optics↗

arXiv2025

Beyond Fresnel Wave Surfaces: Off-Shell Photonic Density of States and Near-Fields in Isotropy-Broken Materials with Loss or Gain

Fresnel wave surfaces, or isofrequency light shells, provide a powerful framework for describing electromagnetic wave propagation in anisotropic media, yet their applicability is restricted to reciprocal, lossless materials and far-field radiation. This paper extends the concept by incorporating near-field effects and non-Hermitian responses arising in media with loss, gain, or non-reciprocity. Using the Om-potential approach to macroscopic electromagnetism, we reinterpret near fields as off-shell electromagnetic modes, in analogy with off-shell states in quantum field theory. We show that photonic density of states (PDOS) distributions near Fresnel surfaces acquire Lorentzian broadening in non-reciprocal media, directly linking this effect to the Beer-Bouguer-Lambert law of exponential attenuation or amplification. Furthermore, we demonstrate how Abraham and Minkowski momenta, locked to light shells in the far field, naturally shift to characterize source structures in the near-field regime. This unified treatment bridges the gap between sources and radiation, on-shell and off-shell modes, and reciprocal and non-reciprocal responses. The framework provides both fundamental insight into structured light and practical tools for the design of emitters and metamaterial platforms relevant to emerging technologies such as 6G communications, photonic density-of-states engineering, and non-Hermitian photonics.

physics.optics↗

arXiv2025

Om-Theory of Macroscopic Electromagnetism: Greener Vibes for Isotropy-Broken Media

The applicability ranges of macroscopic and microscopic electromagnetisms are opposite. While microscopic electromagnetism deals with point sources, singular fields, and discrete atomistic materials, macroscopic electromagnetism concerns smooth average distributions of sources, fields, and homogenized effective metamaterials. Greens function method - GFM - involves finding fields of point sources and applying superposition principle to find fields of distributed sources. When utilized to solve microscopic problems GFM is perfectly within the applicability range. Extension of GFM to simple macroscopic problems is convenient, but not fully logically sound, since point sources and singular fields are technically not a subject of macroscopic electromagnetism. This explains the difficulty of both finding the Greens functions and applying superposition principle in complex isotropy-broken media, which are very different from microscopic environments. In this manuscript, we lay out a path to solution of macroscopic Maxwells equations for distributed sources bypassing GFM, by introducing inverse approach and a method based on Om-potential which we describe here. To the researchers of electromagnetism this provides access to powerful analytical tools and a broad new space of solutions for Maxwells equations.

cond-mat.other↗

arXiv2024

Biaxial Gaussian Beams, Hermite-Gaussian Beams, and Laguerre-Gaussian Vortex Beams in Isotropy-Broken Materials

We develop the paraxial approximation for electromagnetic fields in arbitrary isotropy-broken media in terms of the ray-wave tilt and the curvature of materials Fresnel wave surfaces. We obtain solutions of the paraxial equation in the form of biaxial Gaussian beams, which is a novel class of electromagnetic field distributions in generic isotropy-broken materials. Such beams have been previously observed experimentally and numerically in hyperbolic metamaterials but evaded theoretical analysis in the literature up to now. The biaxial Gaussian beams have two axes: one in the direction of Abraham momentum, corresponding to the ray propagation, and another in the direction of Minkowski momentum, corresponding to the wave propagation, in agreement with the recent theory of refraction, ray-wave tilt, and hidden momentum [Durach, 2024, Ref. 1]. We show that the curvature of the wavefronts in the biaxial Gaussian beams correspond to the curvature of the Fresnel wave surface at the central wave vector of the beam. We obtain the higher-order modes of the biaxial beams, including the biaxial Hermite-Gaussian and Laguerre-Gaussian vortex beams, which opens avenues toward studies of optical angular momentum (OAM) in isotropy-broken media, including generic anisotropic and bianisotropic materials.

physics.optics↗

arXiv2024

Theory of Refraction, Ray-Wave Tilt, Hidden Momentum, and Apparent Topological Phases in Isotropy-Broken Materials based on Electromagnetism of Moving Media

One of the problems of physics arguably greater in stature than even mathematical Hilberts problems is the mysterious nature of electromagnetic momentum in materials. In this paper we show that the difference between the Minkowski and Abraham momenta, which is composed of the Roentgen and Shockley hidden momenta, is directly related to the phenomenon of refraction and the tilt of rays from the wavefront propagation direction. We demonstrate that individual electromagnetic waves with non-unit indices of refraction n appear as quasistatic high-k waves to an observer in the proper frames of the waves. When Lorentz transformed into the material rest frames these high-k waves are Fresnel-Fizeau dragged from rest to their phase velocities and acquire longitudinal hidden momentum and related refractive properties. On the material level all electromagnetic waves belong to Fresnel wave surfaces topologically classified according to hyperbolic phases by Durach and determined from the electromagnetic material parameters. To moving observers, material parameters appear modified, which leads not only to the alterations of Fresnel wave surfaces, but even the topological classes of the materials may appear differently in moving frames. We discuss the phenomenon of the electromagnetic momentum tilt, defined as non-zero angle between Abraham and Minkowski momenta or equivalently between the rays and the wavefront propagation direction. We show that momentum tilt is only possible in isotropy-broken media, where E and H fields can be longitudinally polarized in presence of electric and magnetic bound charge waves. The momentum tilt can be understood as differential aberration of rays and waves when observed in material rest frame.

physics.optics↗

arXiv2023

Electromagnetic Scattering by Bianisotropic Spheres

Electromagnetic fields in bulk bianisotropic media can be represented using plane waves whose k-vectors can be found using the index of refraction operator method and belong to the Fresnel wave surfaces that fall into one of the 5 hyperbolic classes that are used as the taxonomy of bianisotropic media [Durach et al., Appl. Sci., Opt. Comm. (2020), PIER (2022)]. It has been demonstrated that, alternatively, the linear combinations of vector spherical harmonics can be used as a set of solutions of vector Helmholtz equation in gyroelectric, gyromagnetic, and gyrotropic anisotropic media to develop Mie theory of scattering by anisotropic spheres [Lin, Chui, Phys. Rev. E (2004), Li, Ong, Zheng, Phys. Rev. E (2012)]. In this paper we introduce electromagnetic orbitals for bianisotropic media as linear combinations of vector spherical harmonics, which represent a set of solutions of Maxwells equations in bianisotropic media. Using these bianisotropic orbitals we develop a theory of scattering of electromagnetic radiation by bianisotropic spheres with arbitrary effective material parameters and sizes. As a by-product we obtain a simple expression for the expansion of a vector plane wave over vector spherical harmonics (cf. Sarkar, Halas, Phys. Rev. E (1997)). We obtain the polarizability expressions in Rayleigh limit of our theory in agreement with the previous results of the electrostatic approximation [Lakhtakia, J. Phys (1990), Sihvola, Mic. Opt. Tech. Lett. (1994)].

physics.optics↗

arXiv2021

On Fresnel-Airy Equations, Fabry-Perot Resonances and Surface Electromagnetic Waves in Arbitrary Bianisotropic Metamaterials, including with Multi-Hyperbolic Fresnel Wave Surfaces

We introduce a theory of optical responses of bianisotropic layers with arbitrary effective medium parameters, which results in generalized Fresnel-Airy equations for reflection and transmission coefficients at all incidence directions and polarizations. The poles of these equations provide explicit expressions for the dispersion of Fabry-Perot resonances and surface electromatic waves in bianisotropic layers and interfaces. The existence conditions of these resonances are topologically related to the zeros of the high-k characteristic function h(k)=0 of bulk bianisotropic materials and Durach et al. taxonomy of bianisotropic media according to the hyperbolic topological classes [Applied Sciences, 10(3), 763 (2020); Optics Communications, 476, 126349 (2020)].

physics.optics↗

arXiv2020

Tetra-hyperbolic and tri-hyperbolic optical phases in anisotropic metamaterials without magnetoelectric coupling due to hybridization of plasmonic and magnetic Bloch high-k polaritons

In this paper we reveal the physics behind the formation of tri- and tetra-hyperbolic phases in anisotropic metamaterials without magnetoelectric coupling and describe the anti-crossing splitting phenomenon in the hyperbolic dispersion which arises due to the hybridization of the plasmonic and magnetic Bloch high-k polaritons. This considerably deepens the understanding of the high-k polaritons and the topology of the optical iso-frequency surfaces in k-space and will find applications in optical nano-resolution imaging and emission rate and directivity control. To accomplish this, we develop a range of new techniques of theoretical optics for bianisotropic materials, including the quadratic index of refraction operator method, suitable to study the high-k polaritons with finite indices of refraction and the explicit expression for the characteristic matrix in generic bianisotropic media. We introduce the spatial stratification approach for the electric and magnetic responses of anisotropic homogeneous media to analyze the underlying Bloch waves. We believe that the formalisms developed here can be useful for the researchers in the field of theoretical optics of anisotropic and bianisotropic media in the future.

physics.optics↗

arXiv2019

Tri- & Tetra-Hyperbolic Iso-frequncy Topologies Complete Classification of Bi-Anisotropic Materials

We describe novel topological phases of iso-frequency k-space surfaces in bi-anisotropic optical materials - tri- and tetra-hyperbolic materials, which are induced by introduction of chirality. This completes the classification of iso-frequency topologies for bi-anisotropic materials, since as we show all optical materials belong to one of the following topological classes: tetra-, tri-, bi-, mono- or non-hyperbolic. We show that phase transitions between these classes occur in the k-space directions with zero group velocity at high k-vectors. This classification is based on the sets of high-k polaritons (HKPs), supported by materials. We obtain the equation describing these sets and characterize the longitudinal polarization impedance of HKPs.

physics.optics↗

arXiv2018

Additional Waves and Additional Boundary Conditions in Local Quartic Metamaterials

Additional electromagnetic waves and additional boundary conditions (ABCs) in non-local materials attracted a lot of attention in the past. Here we report the possibility of additional propagating and evanescent waves in local anisotropic and bi-anisotropic linear materials. We investigate the possible options for ABCs and describe how to complement the conventional 4 Maxwells boundary conditions in the situations when there are more than 4 waves that need to be matched at the boundary of local and linear quartic metamaterials. We show that these ABCs must depend on the properties of the interface and require the introduction of the additional effective material parameters describing this interface, such as surface conductivities.

physics.optics↗

arXiv2018

Complete 72-Parametric Classification of New and Old Kinds of Surface Plasmon Waves

We propose a general and complete classification of all possible new and old kinds of surface plasmon waves that can propagate at boundaries of arbitrary linear, local bi-anisotropic media, including the quartic metamaterials. For arbitrary frequency, wavelength, propagation direction, penetration depths and fields of the proposed surface plasmon waves we found the dispersion condition and determined the 72-parametric class of media that support a particular surface plasmon. A member of each class is a pair of anisotropic materials without magnetoelectric couplings.

physics.optics↗

arXiv2017

The Inverse Problem of Quartic Photonics

We propose an approach to engineer quartic metamaterials starting from the desired photonic states. We apply our method to the design of the high-k asymptotics of metamaterials, extreme non-reciprocity and complex bi-anisotropic media.

physics.optics↗

arXiv2017

Spin Angular Momentum Transfer and Plasmogalvanic Phenomena

We introduce the continuity equation for the electromagnetic spin angular momentum (SAM) in matter and discuss the torque associated with the SAM transfer in terms of effective spin forces acting in a material. In plasmonic metal, these spin forces result in plasmogalvanic phenomenon which is pinning the plasmon-induced electromotive force to atomically-thin layer at the metal interface.

cond-mat.mtrl-sci↗

arXiv2016

Optical Neutrality: Invisibility without Cloaking

We show that it is possible to design an invisible wavelength-sized metal-dielectric metamaterial object without evoking cloaking. Our approach is an extension of the neutral inclusion concept by Zhou and Hu [Phys.Rev.E 74, 026607 (2006)] to Mie scatterers. We demonstrate that an increase of metal fraction in the metamaterial leads to a transition from dielectric-like to metal-like scattering, which proceeds through invisibility or optical neutrality of the scatterer. Formally this is due to cancellation of multiple scattering orders, similarly to plasmonic cloaking introduced by Alu and Engheta [Phys.Rev.E 72, 016623 (2005)], but without introduction of the separation of the scatterer into cloak and hidden regions.

physics.optics↗

arXiv2016

On Nature of Plasmon Drag Effect

Light-matter momentum transfer in plasmonic materials is theoretically discussed in the framework of plasmonic pressure mechanism taking into account non-equilibrium electron dynamics and thermalization process. We show that our approach explains the experimentally observed relationship between the plasmon-related electromotive force and absorption and allows one to correctly predict the magnitude of the plasmon drag emf in flat metal films. We extend our theory to metal films with modulated profiles and show that the simple relationship between plasmonic energy and momentum transfer holds at relatively small amplitudes of height modulation and an approximation of laminar electron drift. Theoretical groundwork is laid for further investigations of shape-controlled plasmon drag in nanostructured metal.

physics.optics↗

arXiv2015

Ultimately Thin Metasurface Wave Plates

Optical properties of a metasurface which can be considered a monolayer of two classical uniaxial metamaterials, parallel-plate and nanorod arrays, are investigated. It is shown that such metasurface acts as an ultimately thin sub-50 nm wave plate. This is achieved via an interplay of epsilon-near-zero and epsilon-near-pole behavior along different axes in the plane of the metasurface allowing for extremely rapid phase difference accumulation in very thin metasurface layers. These effects are shown to not be disrupted by non-locality and can be applied to the design of ultrathin wave plates, Pancharatnam-Berry phase optical elements and plasmon-carrying optical torque wrench devices.

physics.optics↗

arXiv2015

Abatement of Computational Issues Associated with Dark Modes in Optical Metamaterials

Optical fields in metamaterial nanostructures can be separated into bright modes, whose dispersion is typically described by effective medium parameters, and dark fluctuating fields. Such combination of propagating and evanescent modes poses a serious numerical complication due to poorly conditioned systems of equations for the amplitudes of the modes. We propose a numerical scheme based on a transfer matrix approach, which resolves this issue for a parallel plate metal-dielectric metamaterial, and demonstrate its effectiveness.

physics.optics↗