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Terahertz radiation generation by laser-resonant excitation of terahertz surface magnetoplasmons on a graphene-n-InSb semiconductor interface

Rohit Kumar Srivastav, Mrityunjay Kundu

arXiv:2503.14532v1cond-mat.mes-hallphysics.opticsphysics.plasm-ph

TL;DR

The paper addresses THz surface-magnetoplasmon generation on a rippled graphene–n-InSb interface, a configuration not previously investigated in detail under a magnetic field. It uses laser-driven linear mode conversion, with the resulting amplitude varying with magnetic field, graphene Fermi energy, semiconductor temperature, and incidence angle.

  • Problem

    THz surface-magnetoplasmon generation by linear mode conversion on a rippled graphene–n-InSb surface under an external magnetic field had not been investigated in detail.

    Source: §I · p. 1

  • Method

    An obliquely incident p-polarized laser drives oscillatory electron velocity that couples to modulated density and generates a current source for resonant THz surface-magnetoplasmons.

    Source: §I · p. 2, §II · p. 2

  • Results

    The THz surface-magnetoplasmon amplitude decreases with increasing magnetic field, increases with graphene Fermi energy, and peaks near grazing incidence; higher temperature may also yield higher field intensity.

    Source: §IV · p. 5, §V · p. 6

  • Takeaways & Limitations

    The approach offers control of THz surface-magnetoplasmon amplitude through graphene Fermi energy, semiconductor temperature, magnetic field, and laser incidence angle for actively tunable THz plasmonic devices.

    Source: §V · p. 6

Abstract

from arXiv · show

We propose a method for the laser-excitation of terahertz surface magnetoplasmons via the linear mode conversion of terahertz radiation on a graphene sheet deposited on an n-type semiconductor in presence of an external magnetic field parallel to the semiconductor surface. An obliquely incident p-polarized laser beam interacting with the graphene n-InSb semiconductor surface, imparts linear oscillatory velocity to the free electrons. This oscillatory velocity couples with the modulated electron density to generate a linear current density, which resonantly excites terahertz surface magnetoplasmons. It is shown that the amplitude of terahertz surface magnetoplasmons wave can be tuned by adjusting the external magnetic field ($\text{B}_{0}$), the graphene's Fermi energy ($\text{E}_\text{F}$), the semiconductor's temperature (T), and the incident angle ($\theta$) of laser. This mechanism has the potential to enable the development of an actively tunable plasmonic device.

I. INTRODUCTION

Graphene and n-InSb offer a platform for THz surface-plasmon excitation, while magnetic-field effects and temperature-dependent electron density make semiconductor surface modes tunable. This work addresses the unexamined use of linear mode conversion to excite THz surface magnetoplasmons on a rippled graphene–n-InSb interface.

I. INTRODUCTION

  • Graphene and n-InSb are presented as alternatives for THz plasmonics because their plasma frequency lies in the THz range and semiconductor dispersion responds strongly to magnetic field.The cited n-InSb and graphene electron densities are on the order of 10^23 m^-3 and 10^12 m^-2, respectively.Source: §I · p. 1
  • The generation of THz radiation by linear mode conversion on a rippled graphene–n-InSb surface under an external magnetic field had not been investigated in detail.The work examines a surface-parallel magnetic field and a p-polarized incident laser.Source: §I · p. 1
  • The study examines how magnetic field, semiconductor temperature, graphene Fermi energy, and laser incidence angle affect THz surface-magnetoplasmon excitation.The paper derives the linear current density and wave amplitude before presenting results and conclusions.Source: §I · pp. 1–2
  • Graphene provides conductivity that supports strong surface-plasmon waves, while the ripple supplies the extra wave number for resonant THz surface-magnetoplasmon excitation.The magnetic-field configuration produces asymmetric dispersion, which the authors use to excite the modes.Source: §I · p. 2
  • The authors report a low-magnetic-field, low-Fermi-energy parameter space where dispersion curves reverse direction with increasing field and Fermi energy relative to earlier works.They associate this regime with generation below approximately 6 THz.Source: §I · p. 2

II. LINEAR CURRENT DENSITY: THE SOURCE OF THz

An obliquely incident p-polarized laser produces an oscillatory electron velocity at a rippled graphene–n-InSb surface. Coupling that velocity to the modulated electron density creates a current source that propagates with a shifted wave number and excites THz surface magnetoplasmons.

II. LINEAR CURRENT DENSITY: THE SOURCE OF THz

  • The model assumes a rippled electron density n = (n0/2) + nq, with nq = (n0/2)cos(qz), and graphene conductivity σg = (ie^2EF)/(πħ^2(ω0 + iν)) when EF ≫ ħω0.Here q and a denote ripple wave number and amplitude; n-InSb is treated as under-dense, with ω0 > ωp.Source: §II · p. 2
  • The transmitted laser field depends on the transmission coefficient Ttr, which incorporates graphene conductivity through σg.The incident p-polarized beam has frequency ω0 and wave-vector components k0x and k0z, and the magnetic field B0 points along y.Source: §II · p. 2
  • The laser gives free electrons a first-order oscillatory velocity that couples with the modulated density to produce an oscillatory current density.The current propagates at ω = ω0 with kz = k0z + q and acts as a THz source.Source: §II · p. 2

MAGNETOPLASMONS WAVE: DISPERSION, AMPLITUDE

The paper derives a dispersion relation for terahertz surface magnetoplasmons (SMPs) on rippled graphene–n-InSb and examines how Fermi energy, magnetic field, and ripple phase matching shape the dispersion. The curves shift differently across the lower- and higher-Fermi-energy regimes.

MAGNETOPLASMONS WAVE: DISPERSION, AMPLITUDE

  • The SMP dispersion relation follows from electromagnetic field equations and graphene’s surface-current jump condition at the interface.The field solution uses the n-InSb permittivity components and graphene conductivity; the current source is localized to the rippled region.Source: MAGNETOPLASMONS WAVE: DISPERSION,… · pp. 2–3
  • At EF = 80–1000 meV and Ωce = 0.1, SMP dispersion first moves away from the light-line as EF rises, then turns back toward it at higher EF.The higher-EF results, particularly above EF ∼400 meV, resemble those in Refs..Source: MAGNETOPLASMONS WAVE: DISPERSION,… · p. 3, Figure 2 · p. 3
  • For EF = 20–110 meV at Ωce = 0.04, increasing EF or Ωce shifts the SMP dispersion farther from the free-space light-line.Figure 3 compares EF sweeps at fixed Ωce with Ωce sweeps at fixed EF.Source: MAGNETOPLASMONS WAVE: DISPERSION,… · pp. 3–4, Figure 3 · p. 3
  • Resonant excitation requires phase matching through ripple wave number q, whose dispersion is examined against frequency while varying EF, Ωce, and incident angle θ.The text reports that q ∝ kz makes the EF and Ωce trends nearly quantitatively similar to those in Figure 3, while θ adds an angular dependence.Source: MAGNETOPLASMONS WAVE: DISPERSION,… · p. 4

A. Approximate terahertz SMP field

The approximate SMP-field treatment assumes a fixed mode structure with an amplitude varying along the propagation direction. It uses a WKB-based procedure to determine field strength relative to the incident laser, with the ratio depending on transmission, ripple height, and illumination length.

A. Approximate terahertz SMP field

  • The approximation holds the SMP mode structure constant while allowing its amplitude to vary with z.The derivation then substitutes kz → (kz − i∂/∂z), applies a WKB approximation, and projects the equation onto ψ*(x).Source: A. Approximate terahertz SMP field · p. 4
  • Figure 4 compares normalized ripple wave number Q with normalized SMP frequency Ω while varying EF, Ωce, or θ.Each parameter sweep holds the other stated quantities fixed as indicated in the caption.Source: Figure 4 · p. 4
  • The THz SMP-to-laser field-strength ratio is directly proportional to transmission coefficient Ttr, ripple height h, and illumination length d.The amplitude is obtained by integrating over the illumination length.Source: A. Approximate terahertz SMP field · pp. 4–5

IV. RESULTS AND DISCUSSION

The reported THz SMP field amplitude varies with magnetic field, graphene Fermi energy, incident angle, and semiconductor temperature. The authors report nearly 100 times the normalized amplitude reported for p-polarized optical rectification.

IV. RESULTS AND DISCUSSION

  • |El/E0| decreases as Ωce increases for THz frequencies of 2, 3, 4, and 5 THz at EF = 120 meV and θ = 82.83°.The authors attribute the decrease to restricted electron motion as the external magnetic field increases.Source: §IV · p. 5, Figure 5 · p. 5
  • |El/E0| increases with graphene Fermi energy for each of the four THz frequencies at Ωce = 0.04 and θ = 82.83°.Source: §IV · p. 5, Figure 6 · p. 5
  • |El/E0| rises with incident angle, peaks near grazing incidence depending on THz frequency, then falls; no THz is generated at normal incidence.The authors select θ = 82.83° for Figures 5 and 6 to obtain the maximum effect.Source: §IV · p. 5
  • Nearly 100 times the |El/E0| ≈ 10^-4 amplitude reported for p-polarized optical rectification was obtained using linear mode conversion.The comparison is reported for results shown in Figures 5, 6, and 7.Source: §IV · p. 5
  • At temperatures from 300 to 360 K, |El/E0| decreases with increasing Ωce; the authors suggest low magnetic field and higher temperature may lead to higher THz field intensity.The plotted case uses ω = 5 THz, EF = 120 meV, and θ = 82.83°.Source: §IV · p. 5

V. CONCLUSION

The conclusion links THz surface magnetoplasmon amplitude to graphene Fermi energy, THz frequency, semiconductor temperature, and resonance, and identifies these as controls for the proposed tunable scheme.

V. CONCLUSION

  • The study examines excitation over approximately 2–5 THz, graphene Fermi energies of 20–140 meV, and magnetic fields from 0 to 896.5 Gauss; amplitude can be controlled through EF, T, B0, and laser incidence angle θ.Source: §V · pp. 5–6
  • THz SMP amplitude grows with graphene Fermi energy as the normalized propagation constant Kz increases.For kz >> ω/c, the conclusion also states that amplitude grows with Kz.Source: §V · pp. 5–6
  • THz SMP field strength grows with THz frequency as the required ripple wave number Q increases.Source: §V · p. 6
  • THz SMP amplitude grows as n-InSb temperature increases, alongside increases in electron density n0 and plasma frequency ωp.The stated proportionality is |El/E0| ∝ ωp^2 ∝ T^(3/2)exp(0.26/kBT).Source: §V · p. 6
  • Generated THz SMP amplitude reaches a maximum at a normalized THz frequency where SMP resonance occurs.Source: §V · p. 6

A. Conflict of interest

The authors report no conflicts of interest.

B. Conflict of interest

B. Author Contributions

Rohit Kumar Srivastav and Mrityunjay Kundu developed the work; Srivastav prepared the figures and original draft, while Kundu reviewed and edited the final manuscript.

B. Author Contributions

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