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Microwave Remote Sensing Based on Maxwell Equations
Published in Maged Marghany, Automatic Detection Algorithms of Oil Spill in Radar Images, 2019
In this regard, the considerations of electromagnetic waves leads to the theory of relativity in the first stage. Indeed, Maxwellian electrodynamics is considered as a basic law of relativity physics. Therefore, it defines light rays as electromagnetic waves. In this sense, the trajectory of a light ray in a vacuum can be placed on the light-cone. Thus, the speed of light becomes a diagonal line in the light-cone diagram. We can therefore present the electromagnetic waves coded in satellite data with a different time in the light-cone diagram (Fig. 1.12) [6,9,18].
Silicon Photonics
Published in Paul R. Prucnal, Bhavin J. Shastri, Malvin Carl Teich, Neuromorphic Photonics, 2017
Paul R. Prucnal, Bhavin J. Shastri, Malvin Carl Teich
In general, optical coupling between two modes requires energy and phase-matching. In a periodic dielectric structure with period ∧ in the x direction, however, modes with propagation vectors that differ by Δkx=2πmΛ will also exchange energy (where m is an integer). Suppose a silicon slab in air has a mode with a dispersion function given by ω = ωwg(kx) as in Fig. 7.5. A free-space plane wave in the x direction is described by ω = ckx where k0 is the vacuum wavelength. This relation is referred to as the light line. Other unguided, unbound plane waves at a continuum of angles are described by ω=ck0=ckxsinθ, where θ is measured perpendicular to the direction of propagation. This region is referred to as the light cone. The very reason that guided modes are bound in a silicon slab is that the dispersion function lies below the light cone. By introducing a periodic grating in some region of the waveguide, suddenly the bound mode can couple with an unbound plane wave, such that () ωg(kx)=ckx+2πmΛsinθ, which has a finite number of solutions at a given ω, corresponding to different diffraction orders. This equation creates a design condition on coupling angle θ that maximizes coupling efficiency for the desired wavelength range.
Bulk-edge correspondence in open photonic systems
Published in Waves in Random and Complex Media, 2021
Recently, many important discoveries have been made in non-hermitian [10] and/or parity-time symmetric [11], and/or open quantum systems [12]. The discoveries include periodic tables in topological phases [13], non-hermitian skin effect [14], interaction effects [15]. This paper is closely related to several issues in open quantum systems. However, in studying such a system, possible issues relevant to the light cone are completely absent. The light cone is inherent in photonic systems and gives severe constraints on them. For instance, the light cone separates the momentum space into two distinct regions, inside and outside the light cone. Inside the light cone, photons can leak to outer space, whereas outside the light cone, photons are totally internal reflected. The Brillouin zone folding in PhCs further complexifies the momentum space. Such a complexity is usually not taken into account in the study of open quantum systems. Therefore, the issues on the light cone may give some insights to open quantum systems.
Stability estimate in the determination of a time-dependent coefficient for hyperbolic equation by partial Dirichlet-to-Neumann map
Published in Applicable Analysis, 2019
Mourad Bellassoued, Imen Rassas
Let r>0 such that . For T>2r, we set and we consider the annular domain and we define respectively the forward and backward light cone Note also Further, given M>0 and , we introduce the sets of admissible potential q: and for given , we set and The first main result of this paper can be stated as follows:
The two-dimensional hybrid surface plasma micro-cavity
Published in Journal of Modern Optics, 2018
Tong Kai, Wang Mei-yu, Wang Fu-cheng, Guo Jia
The TM band gap characteristic of the micro-cavity structure is caused by the difference of the effective refractive index between the mixed mode and the surface plasma wave mode of the silver surface. The characteristic of the TM mode band gap calculation can be effectively limited by the symmetry of the vertical direction in the simulation analysis of the band structure of the micro-cavity. The dispersion relation of the two-dimensional micro-cavity structure in the first Brillouin zone is analyzed by 3D-FDTD method and the simulation result is shown in Figure 3. The wave vector is represented by the abscissa and the normalized frequency is represented by the ordinate. The band L and band U can be characterized by the square line and the triangle point line, respectively. The band gap is composed of band L, band U and the frequency range enclosed by the light line. The light cone is represented by the region above the light line. As shown in Figure 3, there is a band gap within the scope of the normalized frequency of 0.234–0.27.