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H-case: Color map of the focusing ability as a function of f/d and frequency. Here, d = 1000 μm, μ c = 1 eV, T =300 K, τ = 1 ps
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Background
The scattering of H- and E-polarized plane waves by a two-dimensional (2-D) parabolic reflector made of graphene and placed in the free space is studied numerically. Methods
To obtain accurate results we use the Method of Analytical Regularization. ResultsThe total scattering cross-section and the absorption cross-section are computed, t...
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Citations
... By following this procedure in [13,14] the graphene strip, disc, and infinite strip grating problems are simulated with a high level of accuracy using Nystrom method and MAR. The focusing effect of a graphene reflector in free space is studied in [15,16] by using MAR method based on the RHP technique. Then, in [17], a graphene reflector with a dielectric substrate case is simulated as a more realistic geometry. ...
... In spite of all the aforementioned literature, most of the studied geometries are related to the planar reflectors, and the tunable graphene reflector having curved profile is studied very rarely compared to the planar ones. For example, in [16], the focusing effect of a graphene parabolic reflector is studied, and the results show that the control of field level is problematic above lower THz regions. In the present study, the graphene parabolic reflector is numerically modelled in microwaves depending on the problem parameters with the high accuracy provided by the RHP-based MAR method. ...
... As graphene is dominantly resistive at microwave range, it is a lossy material. In the modelling of the scattering performance of reflector, another important characteristic is absorption cross-section (ACS), which can be found from the optical theorem [7,16]. ...
The studied configuration is a two-dimensional, very thin parabolic reflector made of graphene and illuminated by an H-polarized electromagnetic plane wave. We present basic scattering and focusing properties of such a graphene reflector depending on the graphene parameters at microwave frequencies, using the resistive boundary condition for very thin sheets. The scattering is formulated as an electromagnetic boundary-value problem; it is transformed to a singular integral equation that is further treated with the method of analytical regularization (MAR) based on the known solution of the Riemann–Hilbert Problem (RHP). The numerical results are computed by using a Fredholm second-kind matrix equation that guarantees convergence and provides easily controlled accuracy. Compared to THz range, in microwaves, the scattering pattern of reflector and the field level at geometrical focus can be controlled in a wide range by adjusting the chemical potential of graphene. Even though here no dielectric substrate supporting the graphene is considered, the practical realization can also be possible as a thin layer graphene material in GHz range. As we demonstrate, the variation of the chemical potential from 0 to 1 eV can improve the focusing ability within the factor of three. The high accuracy of the used method and the full wave formulation of the problem support our findings.
... Graphene is a novel ultra-thin material that has unique electronic and optical properties [1][2][3]. Today, the patterned graphene shapes such as strips, disks and gratings of them are actively studied in the optical and terahertz wave ranges, where they can be useful as components of novel plasmon waveguides, antennas, sensors and filters [4][5][6][7][8]. This interest is due to the fact that graphene has very good electron conductance, which can be tuned by a DC bias [1][2][3][4][5][6][7][8][9], that makes the mentioned devices tunable as well. ...
... Today, the patterned graphene shapes such as strips, disks and gratings of them are actively studied in the optical and terahertz wave ranges, where they can be useful as components of novel plasmon waveguides, antennas, sensors and filters [4][5][6][7][8]. This interest is due to the fact that graphene has very good electron conductance, which can be tuned by a DC bias [1][2][3][4][5][6][7][8][9], that makes the mentioned devices tunable as well. A sheet of graphene is able to support the plasmon guided wave in the infrared and terahertz ranges [2]. ...
We implement the Lasing Eigenvalue Problem (LEP) approach to study the electromagnetic field in the presence of a circular quantum wire (QW) made of a gain material and wrapped in graphene cover and a dimer of two identical graphene-covered QWs, at the threshold of stationary emission. LEP delivers the mode-specific eigenvalue pairs, namely the frequencies and the threshold values of the QW gain index for the plasmon and the wire modes of such nanolasers. In our analysis, we use quantum Kubo formalism for the graphene conductivity and classical Maxwell boundary-value problem for the field functions. The technique involves the resistive boundary conditions, the separation of variables in the local coordinates, and, for the dimer, the addition theorem for the cylindrical functions. For single-wire plasmonic laser, we derive approximate engineering expressions for the lasing frequencies and threshold values of the gain index that complement the full-wave computations. For the dimer, we derive separate determinantal equations for four different classes of symmetry of the lasing supermodes and solve them numerically. Our investigation of the mode frequencies and thresholds versus the graphene and QW parameters shows that plasmon modes or, for the dimer, plasmon supermodes have lower frequencies and thresholds than the wire modes provided that the QW radius is smaller than 10 μm, however in thicker wires they are comparable. Only the plasmon-mode characteristics are well-tunable using the graphene chemical potential. In the dimer, all lasing supermodes form closely located quartets, however, they quickly approach the single-wire case if the inter-wire separation becomes comparable to the radius. These results open a way for building essentially single-mode plasmonic nanolasers and their arrays and suggests certain engineering rules for their design.
... The largest deviations appear at lower frequencies. This proves that at high frequencies a gridded reflector becomes more and more transparent in either polarization regime, similarly to the reflectors made of graphene (Oguzer et al. 2017;Oguzer and Altintas 2021). ...
We consider the two-dimensional (2-D) scattering of the TE- and TM-polarized plane electromagnetic waves from a discrete grid-like parabolic reflector consisting of parallel circular perfectly electrically conducting (PEC) wires at oblique incidence. Our analysis is performed in the exact formulation, fully taking into account the wave interactions between the wires. We use the method of separation of variables in the local cylindrical coordinate systems in combination with Graf’s addition formulas for cylindrical functions. The near field in the vicinity of the reflector is calculated at different angles of incidence. The dependences of the maximum field amplitude in the focal area and the position of this maximum on the angle of incidence are plotted. The far field scattered patterns, total scattering cross-sections and backward scattering cross-sections are calculated and discussed.
... Параболічні відбивачі -найпопулярніші і широко використовувані відбивачі для фокусування електромагнітних хвиль [1]. Разом із традиційними суцільними відбивачами в сучасних антенах часто використовуються відбивачі з сітчастих та гнучких матеріалів [2][3][4]. ...
Розглянуто проблему розсіяння пласких хвиль дискретним параболічним рефлектором (ДПР), виготовленим з рівновіддалено розташованих кремнієвих ниток. Досліджено фокусуючу здатність таких відбивачів як у випадку Е-, так і Н-поляризації. Для моделювання цієї задачі ми використовуємо метод часткового розділення змінних разом з регуляризацією, що приводить до матричного рівняння Фредгольма другого роду для коефіцієнтів розкладання функції поля. Цей факт гарантує збіжність розв’язку та прогнозованої точності наших розрахунків. Ми чисельно вивчаємо відбиваючі характеристики ДПР та їхню фокусуючу здатність разом з картинами ближнього поля та значеннями функції поля у зоні фокусування.
... They include the methods of expansion in terms of the eigenfunctions of the Helmholtz equation and integral transformations as well as the method of analytical regularisation (MAR) [33,[37][38][39][40]. In the past years, the MAR has been used to study a wide variety of timeharmonic scattering problems associated with PEC and imperfect scatterers [41][42][43][44][45][46][47][48][49][50][51][52][53]. The main merit of the MAR is that it ends up with the Fredholm second kind matrix equations, which have the convergence guaranteed by the Fredholm theorems. ...
... whereb ðχÞ mτ are known coefficients. The function U ðχÞ mτ ðθ; φÞ in Equations (26) and (45) depends on the conical structure geometry, and the function Φ iτ ðt; rÞ (46) is completely defined by the source type. ...
Abstract An initial‐boundary value problem for the transient electromagnetic field in the presence of a complicated‐shape scatterer is studied. The considered biconical zero‐thickness and perfectly conducting surface with periodic longitudinal slots has many special cases, each of which is of separate practical interest. A new analytical‐numerical technique is presented that is based on the Mehler–Fock integral transform and the method of analytical regularisation. The source of excitation of the slotted bicone is a radial electric dipole with an arbitrary time dependence on the field. The proposed method makes it possible to obtain an analytical and numerical solution of the problem to carry out a qualitative and numerical analysis, and to study the characteristic features of the main scattering. Due to the use of the method, the initial‐boundary value problem is reduced to a Fredholm type of the second kind system of linear algebraic equations (SLAE‐2). The dependences of the condition number on the problem parameters and the estimation of the SLAE‐2 convergence with larger truncation orders are given. The far‐field radiation patterns are plotted for various values of the problem parameters, the behaviour of the near field at the apex of the slotted cone is studied, and the regime of the slot wave propagation is analysed.
... Infinite graphene-strip grating in the free space was also studied by the MAR-RHP in [9]. In [18], a 2-D parabolic graphene reflector in the free space is modelled using MAR-RHP in the H-polarization case and inverse Fourier transform in the E-case. The SPwave resonances are observed in H-wave scattering and absorption, and also the focusing ability (FA) is studied as a function of the parameters. ...
... In the present study, the scattering and absorption crosssections (ACSs) and FA are analyzed in the E-polarization case for a thin parabolic dielectric reflector covered with graphene layers from both sides. Our main interest is in the comparison of how the focusing of a THz wave by such a composite reflector can be worse or better than by purely dielectric [19] and purely graphene [18] ones. To model a thin dielectric reflector, in [19] (see also [20]), we use the generalized boundary condition (GBC) with Mitzner [21] and Karlsson [22] type electric and magnetic resistivities on the median line of the reflector. ...
... Firstly, the formulation details are explained, and then a set of coupled SIEs for the effective electric and magnetic currents are derived. Their discretization is done similarly to [9,[16][17][18][19][20], and then the numerical results are presented; they cover the frequency dependences of the total scattering and ACSs and FA. Conclusions are summarized in the final section. ...
Abstract We consider two‐dimensional (2‐D) thin dielectric parabolic reflector, covered with graphene from both sides, illuminated symmetrically by an E‐polarized electromagnetic plane wave. Our aim is to estimate the focussing ability of such a composite reflector depending on the graphene parameters. We use a version of the two‐side generalized boundary condition, modified for a thin multilayer case. The scattering is formulated as an electromagnetic boundary‐value problem; it is cast to a set of two coupled singular integral equations that are further subjected to analytical regularisation based on the known Riemann–Hilbert problem solution. Thanks to this procedure, the numerical results are computed from a Fredholm second‐kind matrix equation that guarantees convergence and provides easily controlled accuracy. In the lower part of the THz range, high values of the focusing ability are observed even for a thin reflector; they are greater than for a purely dielectric reflector and a free standing graphene reflector. On the other hand, a regime of almost full transparency, intrinsic for the dielectric layer, can spoil focusing ability. Novel aspect is that the location in frequency of this effect can be controlled, in wide range, by changing the chemical potential of graphene.
... Plasmon-mode resonances in the scattering and absorption by the gratings of coplanar graphene strips were analyzed in [19]- [21]. The accurately studied curved graphene configurations are restricted to fully covered circular dielectric rod [22]- [24] and parabolic reflector in air [25]. ...
In this article, we consider the radiation characteristics of a THz antenna made of a circular dielectric rod decorated with conformal graphene strip and illuminated by the field of a line magnetic current. The strip has arbitrary angular size and location and its surface impedance is characterized with Kubo theory. Our mathematically accurate analysis uses a dedicated hypersingular integral equation for the current induced on the strip. Discretization of this equation is carried out by the Nystrom-type method, which has a guaranteed convergence. We study the dependences of the powers radiated and absorbed in this configuration and also the directivity of antenna emission, in wide frequency range from 0 to 10 THz. They show very interesting interplay between the broadband inverse photonic-jet effect of lens-like dielectric rod and two types of resonances: on the moderate-Q plasmon modes of graphene strip and on the extremely high-Q whispering-gallery modes of the circular rod.
... Partially covered thin arbitrary cross-section rod was approximately treated in [32]. MAR-based analysis of the focusing efficiency of 2-D parabolic graphene reflector in the free space was presented in [33]. ...
... To validate our code, we have compared it with another full-wave convergent technique, the method of analytical regularization based on the Riemann-Hilbert Problem solution [14,33]. The results are identical within any desired number of digits and thus are not shown here -see [37] for details. ...
... The resonances on the m-even plasmon modes are absent because in the case of symmetric strip location they are not excited, i.e. remain "dark." What is interesting, if 0 2 360 , then the third plasmon mode smoothly transforms to the first plasmon mode of fully covered circular rod [28], where the resonances follow (33), however, with 2 instead of and 0 . ...
We analyse, using integral equations and a previously developed in-house numerical algorithm, the scattering and absorption of the H -polarized plane wave by a metasurface consisting of a double-layer grating of flat graphene strips placed into a lossless dielectric slab. The algorithm is meshless and its convergence is guaranteed mathematically. It is a version of the method of analytical preconditioning; namely, it uses the set of weighted Chebyshev polynomials as expansion functions in the discretization of a hypersingular electric field integral equation for the on-strip current. Then the computational error is controlled by the matrix size and can be reduced to machine precision. Using this advanced tool, we plot the frequency dependences, in a huge range from 1 GHz to 10 THz, of the transmittance, reflectance and absorbance of such a metasurface. This accurate analysis reveals resonances on several types of natural modes, best understood via visualization of in-resonance near-fields. In addition to plasmon-mode resonances, special attention is paid to the ultra-high- Q resonances on the lattice modes, which are absent on the free-standing graphene strip gratings.
... [12][13][14] Apart from commercial codes, their modeling has been done with several convergent methods: regularizing method-of-moments, the Riemann-Hilbert Problem (RHP) method, and Nystrom-type discretization with Chebyshev quadratures. [15][16][17][18][19][20][21] Application of these mathematically grounded methods allows finding the solutions to the considered problems with controlled accuracy within a reasonable time of computation. ...
... 8-10 and its waveguiding properties in Ref. 15. Plasmon-assisted resonances in the scattering and absorption by infinite and finite gratings of coplanar graphene strips under normal and inclined incidence were analyzed in Refs. [15][16][17][18][19] Focusing ability of a parabolic graphene reflector in the free space was considered in Ref. 20. Still most frequently graphene is placed on top of the dielectric layer, which provides better mechanical rigidity. ...
We consider the scattering of an H-polarized plane wave by an infinite dielectric rod with a conformal graphene strip of arbitrary angular width, placed at the rod rear side. Our analysis is based on the hypersingular integral equation for the current induced on the strip. Discretization of this equation is carried out by the Nystrom-type method, which has a guaranteed convergence. This meshless trusted computational instrument enables us to plot the dependences of the absorption cross section and the total scattering cross section on the strip angular width and the frequency, in a wide range from 1 GHz to 6 THz. We concentrate our analysis on studying the interplay between the broadband photonic-jet effect of the dielectric rod and the reasonably high-Q resonances on the plasmon modes of the graphene strip. It is found that as the photonic jet becomes brighter with higher frequencies, the plasmon-mode resonances become more intensive as well.
... This has enabled finding the numerical solutions to the considered problems with controlled accuracy within reasonable time of computation. A 2-D parabolic graphene reflector was considered in [15]. ...
