#### For citation:

Fateev D. В., Mashinsky K. V. Electrodynamic approach for calculating the absorption spectra of plasmons in a rectangle with a two-dimensional electron gas excited by an incident electromagnetic wave. *Izvestiya VUZ. Applied Nonlinear Dynamics*, 2024, vol. 32, iss. 3, pp. 347-356. DOI: 10.18500/0869-6632-003100, EDN: RRNDFW

# Electrodynamic approach for calculating the absorption spectra of plasmons in a rectangle with a two-dimensional electron gas excited by an incident electromagnetic wave

The purpose of this research is to develop an electrodynamic method for calculating the plasmon spectrum in a three-dimensional structure with a two-dimensional electron gas excited by an incident electromagnetic wave.

Methods. The developed method is based on solving integral equations formed with respect to induced currents in the conducting parts of a three-dimensional structure.

Results. The convergence of the method and the calculation time were studied. The conditions for the convergence of calculations of higher plasmon resonances in a rectangular structure with a two-dimensional electron gas are determined. The normal incidence of an arbitrarily polarized electromagnetic wave on a rectangle with a two-dimensional gas is studied. The spectra of the absorption, extinction, forward and back scattering cross sections of the incident wave are calculated.

Conclusion. It is found that in a rectangular structure containing a two-dimensional electron gas, the spectrum of plasmon resonances is modified in comparison with established by two-dimensional models of problem formulation, in which the structure is assumed to be infinite and homogeneous in one of the directions. It has been established that the incident wave most effectively excites fundamental plasmon modes. Plasmonic modes exhibit strong charge accumulation at the edges of the rectangle, which significantly affects the resonant excitation frequencies of plasmonic modes.

- Popov VV. Plasmon excitation and plasmonic detection of terahertz radiation in the gratinggate field-effect-transistor structures. Journal of Infrared, Millimeter, and Terahertz Waves. 2011;32:1178–1191. DOI: 10.1007/s10762-011-9813-6.
- Meziani YM, Handa H, Knap W, Otsuji T, Sano E, Popov VV, Tsymbalov GM, Coquillat D, Teppe F. Room temperature terahertz emission from grating coupled two-dimensional plasmons. Applied Physics Letters. 2008;92(20):201108. DOI: 10.1063/1.2919097.
- Popov VV, Polischuk OV, Shur MS. Resonant excitation of plasma oscillations in a partially gated two-dimensional electron layer. Journal of Applied Physics. 2005;98(3):033510. DOI: 10.1063/ 1.1954890.
- Fateev DV, Mashinsky KV, Polischuk OV, Popov VV. Excitation of propagating plasmons in a periodic graphene structure by incident terahertz waves. Physical Review Applied. 2019;11(6): 064002. DOI: 10.1103/PhysRevApplied.11.064002.
- Marem’yanin KV, Ermolaev DM, Fateev DV, Morozov SV, Maleev NA, Zemlyakov VE, Gavrilenko VI, Popov VV, Shapoval SYu. Wide-aperture detector of terahertz radiation based on GaAs/InGaAs transistor structure with large-area slit grating gate. Technical Physics Letters. 2010;36:365–368. DOI: 10.1134/S106378501004022X.
- Popov VV, Tsymbalov GM, Shur MS, Knap W. The resonant terahertz response of a slot diode with a two-dimensional electron channel. Semiconductors. 2005;39(1):142–146. DOI: 10.1134/ 1.1852665.
- Allen SJ, Jr, Stormer HL, Hwang JCM. Dimensional Resonance of the Two-Dimensional Electron Gas in Selectively Doped GaAs/AlGaAs Heterostructures. Phys. Rev. B. 1983;28:4875. DOI: 10.1103/PhysRevB.28.4875.
- Fetter AL. Magnetoplasmons in a Two-Dimensional Electron Fluid: Disk Geometry. Physical Review B. 1986;33(8):5221. DOI: 10.1103/PhysRevB.33.5221.
- Dahl C, Kotthaus JP, Nickel H, Schlapp W. Magnetoplasma Resonances in Two-Dimensional Electron Rings. Physical Review B. 1993;48:15480. DOI: 10.1103/PhysRevB.48.15480.
- Mikhailov S. Radiative Decay of Collective Excitations in an Array of Quantum Dots. Physical Review B. 1996;54(15):10335. DOI: 10.1103/PhysRevB.54.10335.
- Kovalskii VA , Gubarev SI, Kukushkin IV, Mikhailov SA, Smet JH, von Klitzing K, Wegscheider W. Microwave Response of Two-Dimensional Electron Rings. Physical Review B. 2006;73(19):195302. DOI: 10.1103/physrevb.73.195302.
- Rodionov DA, Zagorodnev IV. Oscillations in Radiative Damping of Plasma Resonances in a Gated Disk of a Two-Dimensional Electron Gas. Physical Review B. 2022;106(23):235431. DOI: 10.1103/PhysRevB.106.235431.
- Zarezin AM, Mylnikov D, Petrov AS , Svintsov D, Gusikhin PA, Kukushkin IV, Muravev VM. Plasmons in a Square of Two-Dimensional Electrons. Physical Review B. 2023;107(7):075414. DOI: 10.1103/PhysRevB.107.075414.
- Dawood A, Park SJ, Parker-Jervis R, Wood C, Li L, Linfield EH, Davies AG, Cunningham JE, Sydoruk O. Effect of Mesa Geometry on Low-Terahertz Frequency Range Plasmons in Two Dimensional Electron Systems. J. Phys. D: Appl. Phys. 2022;55:015103. DOI: 10.1088/1361- 6463/ac2401.
- Mylnikov D, Svintsov D. Limiting Capabilities of Two-Dimensional Plasmonics in Electromagnetic Wave Detection. Physical Review Appl. 2022;17(6):064055. DOI: 10.1103/PhysRevApplied. 17.064055.
- Nikitin AY, Alonso-Gonzalez P, Velez S, Mastel S, Centeno A, Pesquera A, Zurutuza A, Casanova F, Hueso LE, Koppens FHL, Hillenbrand R. Real-Space Mapping of Tailored Sheet and Edge Plasmons in Graphene Nanoresonators. Nat. Photonics. 2016;10:239. DOI: 10.1038/nphoton. 2016.44.
- Popov VV, Yermolaev DM, Maremyanin KV, Zemlyakov VE, Maleev NA, Gavrilenko VI, Bespalov VA, Yegorkin VI, Ustinov VM, Shapoval SYu. Detection of terahertz radiation by tightly concatenated InGaAs field-effect transistors integrated on a single chip. Applied Physics Letters. 2014;104(16):163508. DOI: 10.1063/1.4873540.

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