Abstract
Third harmonic generation of terahertz radiation is expected to occur in monolayer graphene due to the nonlinear relationship between the crystal momentum and the current density. In this work, we calculate the terahertz nonlinear response of monolayer graphene inside a parallel-plate waveguide including pump depletion, self-phase, and cross-phase modulation. To overcome the phase mismatching between the pump field and third-harmonic field at high input fields due to self-phase and cross-phase modulation, we design a waveguide with two dielectric layers with different indices of refraction. We find that, by tuning the relative thicknesses of the two layers, we are able to improve phase matching and thereby increase the power efficiency of the system by more than a factor of two at high powers. With this approach, we find that despite the loss in this system, for an incident frequency of 2 THz, we are able to achieve power efficiencies of 75% for graphene with low Fermi energies of 20 meV and up to 35% when the Fermi energy is 100 meV.
Highlights
Graphene, as a zero-bandgap two-dimensional semiconductor with a linear electron band dispersion near the Dirac points, has the potential to exhibit very interesting nonlinear optical properties.1–4 The linear dispersion relation of the electrons near the Dirac points leads to a constant electron speed.5–7 the intraband current induced in graphene by terahertz (THz) fields displays clipping as the amplitude of the incident field increases, which generates odd harmonics in the current and transmitted electric field.8–12 Exploiting the nonlinear response of graphene enables one to produce higher frequency THz radiation through the generation of harmonics
We develop a coupled-mode theory including all propagating lossy modes to calculate the power efficiency for third-harmonic generation in a parallel-plate waveguide (PPW) and use this model to examine the impact of these effects on the power conversion efficiency
We have developed a coupled-mode theory for the propagating lossy modes of the pump and third harmonic fields in a PPW to calculate third harmonic generation, including pump depletion, self-phase modulation (SFM), and XFM
Summary
As a zero-bandgap two-dimensional semiconductor with a linear electron band dispersion near the Dirac points, has the potential to exhibit very interesting nonlinear optical properties. The linear dispersion relation of the electrons near the Dirac points leads to a constant electron speed. the intraband current induced in graphene by terahertz (THz) fields displays clipping as the amplitude of the incident field increases, which generates odd harmonics in the current and transmitted electric field. Exploiting the nonlinear response of graphene enables one to produce higher frequency THz radiation through the generation of harmonics. We have shown in previous work that this configuration can increase the power efficiency of the system by more than a factor of 100, relative to the results for the normal-incidence configuration, and that the power efficiency is relatively insensitive to the plate separation but depends strongly on the Fermi energy.. We develop a coupled-mode theory including all propagating lossy modes to calculate the power efficiency for third-harmonic generation in a PPW and use this model to examine the impact of these effects on the power conversion efficiency.. One goal in this work is to optimize the thickness of the dielectric layers and the Fermi energy of the graphene to obtain phase matching and thereby maximize the generated third-harmonic electric field.
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