In an isotropic, homogeneous, nondissipative, dielectric-magnetic medium that is simply moving with respect to an inertial reference frame, planewave solutions of the Maxwell curl postulates can be such that the phase velocity and the time-averaged Poynting vector are mutually orthogonal. Orthogonal-phase-velocity propagation thus adds to the conventional positive-phase-velocity propagation and the recently discovered negative-phase-velocity propagation that is associated with the phenomenon of negative refraction.
In this paper we will analyze the propagation of the angular spectrum of the electromagnetic field through a finite length uniaxial crystal. We solve the boundary conditions of the fields at an interface of an isotropic medium and an uniaxial anisotropic medium with the optical axis in an arbitrary direction and soon after we choose the optical axis in a plane formed by the direction of propagation (z-axis) and the x-axis . We show how the couplings occur between the components of the field and in what situations we can give a vector or scalar treatment for the propagation
The quasi-one-dimensional rhombic array of the waveguides is considered. System of equations describing coupled waves in the waveguide in the linear limit is solved exactly. The electric field distribution was found both for the diffractionless (or dispersionless) flat band modes and for the dispersive modes.
In this work, we present a simplified but comprehensive derivation of all the key concepts and main results concerning light pulse propagation in dielectric media, including a brief extension to the case of active media and laser oscillation. Clarifications of the concepts of slow light and "superluminality" are provided, and a detailed discussion on the concept of transform-limited pulses is also included in the Appendix.
The propagation of light through bianisotropic materials is studied in the geometrical optics approximation. For that purpose, we use the quartic general dispersion equation specified by the Tamm-Rubilar tensor, which is cubic in the electromagnetic response tensor of the medium. A collection of different and remarkable Fresnel (wave) surfaces is gathered, and unified via the projective geometry of Kummer surfaces.
The propagation of a quasi-harmonic electromagnetic wave in a bulk hyperbolic dielectric metamaterial is considered. If the group velocities dispersion is not taken into account, then wave propagation can be described either by the hyperbolic nonlinear Schrodinger equation or by the hyperbolic Manakov equations. It is shown that the region in the space of wave vectors in which the modulation instability of a spatially homogeneous wave is possible is not limited, in contrast to the case of ordinary media.
Propagation of ultrashort electromagnetic wave packets in free space beyond the paraxial and slowly-varying-envelope approximations : a time-domain approach
We present a bi-orthogonal approach for modeling the response of localized electromagnetic resonators using quasinormal modes, which represent the natural, dissipative eigenmodes of the system with complex frequencies. For many problems of interest in optics and nanophotonics, the quasinormal modes constitute a powerful modeling tool, and the bi-orthogonal approach provides a coherent, precise, and accessible derivation of the associated theory, enabling an illustrative connection between different modeling approaches that exist in the literature.
We study the propagation of three-dimensional (3D) bipolar ultrashort electromagnetic pulses in an inhomogeneous array of semiconductor carbon nanotubes. The heterogeneity is represented by a planar region with an increased concentration of conduction electrons. The evolution of the electromagnetic field and electron concentration in the sample are governed by the Maxwell's equations and continuity equation. In particular, non-uniformity of the electromagnetic field along the axis of the nanotubes is taken into account. We demonstrate that, depending on values of parameters of the electromagne…
A method is proposed for the analysis of the propagation of electromagnetic waves through a homogeneous slab of a medium with Drude-Lorentz dispersion behavior, and excited by a causal sinusoidal source. An expression of the time dependent field, free from branch-cuts in the plane of complex frequencies, is established. This method provides the complete temporal response in both the steady-state and transient regimes in terms of discrete poles contributions. The Sommerfeld and Brillouin precursors are retrieved and the corresponding set of poles are identified. In addition, the contribution in…
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…
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 …
Quantum-statistical effects occur during the propagation of electromagnetic (EM) waves inside the dielectric media or metamaterials, which include a large class of nanophotonic and plasmonic waveguides with dissipation and noise. Exploiting the formal analogy between the Schrodinger equation and the Maxwell equations for dielectric linear media, we rigorously derive the effective Hamiltonian operator which describes such propagation. This operator turns out to be essentially non-Hermitian in general, and pseudo-Hermitian in some special cases. Using the density operator approach for general no…
Ultra-BroadBand Electromagnetic Control Using a Triple Circular Ring Metasurface: Surface Wave Propagation, Beam Steering, and RCS reduction (50-100 Ghz)
Sylhet Engineering College（锡尔赫特工程学院）；North South University（北南大学）；Mahdy Research Academy（马迪研究院）
We present an extension of the canonical coupled mode theory of electromagnetic waves to the case of pulses and spatio-temporal perturbations in complex media. Unlike previous attempts to derive such a model, our approach involves no approximation, and does not impose any restriction on the spatio-temporal profile. Moreover, the effect of modal dispersion on mode evolution and on the coupling to other modes is fully taken into account. Thus, our approach can yield any required accuracy by retaining as many terms in the expansion as needed. It also avoids various artifacts of previous derivatio…
Free-Space Propagation and Skyrmion Topology of Toroidal Electromagnetic Pulses
Institute of Applied Physics, University of Electronic Science and Technology of China（电子科技大学应用物理研究所）；Yangtze Delta Region Institute (Huzhou), University of Electronic Science and Technology of China（电子科技大学长三角研究院（湖州））；Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University（南洋理工大学物理与数学科学学院物理学与应用物理学部）；Centre for Disruptive Photonic Technologies, The Photonics Institute, Nanyang Technological University（南洋理工大学光子研究院破坏性光子技术研究中心）；Optoelectronics Research Centre & Centre for Photonic Metamaterials, University of Southampton（南安普顿大学光电子研究中心及光子超材料中心）
We explicitly solve the equations for the propagation of an electromagnetic wave up to the subleading order geometric optics expansion in the Kerr spacetime. This is done in two nontrivial steps. We first construct a set of parallel propagated null tetrad in Kerr spacetime. Two of the components of such tetrad give the propagation and polarization of an electromagnetic wave in geometric optics approximation. Then we use the parallel propagated tetrad to solve the modified trajectory equation in Kerr spacetime. We obtain the wavelength-dependent deviation of the trajectory of electromagnetic wa…
Analytically, without magnetostatic approximation, the problem of electromagnetic wave propagation along arbitrary direction in a tangentially magnetized bihyrotropic layer has been solved. It is found that one can bring the Maxwell equations for this problem to the fourth order differential equation and the obtained biquadratic characteristic equation determines two different wave numbers kx21 and kx22 describing the wave distribution over the layer thickness. The dispersion equation describing wave propagation in the bihyrotropic layer was obtained for the case of real kx21 and kx22 values. …
The diffraction of electromagnetic waves at the surface periodic structures accompanied by strong anomalous effects in different diffraction orders is considered in great detail for high-contrast interfaces. We restrict our discussion to the TM polarization of the incident wave (the magnetic field is orthogonal to the plane of incidence) and the simplest geometry when the plane of incidence is orthogonal to the grating grooves. The most attention is focused on the strong maxima and minima of the energy flux density accompanying specific grazing propagation of some diffraction order. Relation t…
Characterizing electromagnetic wave propagation in nonlinear and inhomogeneous media is of great interest from both theoretical and practical perspectives, even though it is extremely complicated. In fact, it is still an unresolved issue to find the exact solutions to the nonlinear waves in the orthogonal curvilinear coordinates. In this paper, we present an analytic method to handle the problem of electromagnetic waves propagation in arbitrarily nonlinear and particularly inhomogeneous media without dispersion. Through the exact solutions of the (1+1)-dimensional nonlinear Maxwell equations, …
A first comprehensive treatment on complex eigenmodes is presented for general lossy traveling-wave electromagnetic structures where the per unit length propagation phase shift ($β$) dependent complex eigenfrequencies $Ω(β)$ are mapped to the frequency dependent complex propagation constant $γ(ω_0)$ for variety of electromagnetic structures. Rigorous procedures are presented to first compute the complex eigenmodes of both uniform and periodic electromagnetic structures which are confirmed using full-wave simulations and known analytical results. Two mapping procedures are further presented for…
The propagation of electromagnetic waves trapped within dielectric and magnetic layers is considered. The description within the three-dimensional theory is compared with the simplified analysis in two dimensions. Two distinct media configurations with different topology are dealt with: a plane slab and a hollow cylinder. Choosing the appropriate values for the geometrical parameters (layer thickness, radius of the cylinder) and for the electromagnetic properties of the media one can trap exactly one mode corresponding to that obtained within the two-dimensional electromagnetism. However, the …
A theory for the characterization of the fourth moment of electromagnetic wave beams is presented in the case when the source is partially coherent. A Gaussian-Schell model is used for the partially coherent random source. The white-noise paraxial regime is considered, which holds when the wavelength is much smaller than the correlation radius of the source, the beam radius of the source, and the correlation length of the medium, which are themselves much smaller than the propagation distance. The complex wave amplitude field can then be described by the Itô-Schrödinger equation. This equation…
A synoptic view on the long-established theory of light propagation in crystalline dielectrics is presented, providing a new exact solution for the microscopic local electromagnetic field thus disclosing the role of the divergence-free (transversal) and curl-free (longitudinal) parts of the electromagnetic field inside a material as a function of the density of polarizable atoms. Our results enable fast and efficient calculation of the photonic bandstructure and also the (non-local) dielectric tensor, solely with the crystalline symmetry and atom-individual polarizabilities as input.
