Phase-matching and Peak Nonlinearity Enhanced Third-Harmonic Generation in Graphene Plasmonic Coupler

Strong nonlinear optical effects generally require giant optical fields interacting with the nonlinear media. Doped graphene hosts electrically tunable plasmons with long lifetimes that interact strongly with light. We investigate a graphene plasmonic coupler and explore two mechanisms to pursue highly efficient third-harmonic generation (THG): (1) phase matching of graphene plasmons at fundamental- and third-harmonic frequencies and (2) peak third-order nonlinear susceptibility of doped graphene. The third-harmonic wave is mainly converted from the evanescent mode of the incident light and the THG efficiency is found to be enhanced by over 10 orders of magnitude compared with a bare monolayer graphene. The significantly enhanced nonlinear optical responses in the graphene plasmonic coupler make this configuration an ideal platform for the development of alternative frequency generators and for signal processing at midinfrared and terahertz frequencies.

Figure 1

The configuration of the graphene plasmonic coupler. (a) 3D schematic illustration. FF wave at a frequency of ω (red arrow) illuminating from the left-side nanoribbon is converted to a TH wave at a frequency of 3ω (blue arrow) in the right side. (b) 2D structure consisting of graphene nanoribbons with different doping levels sandwiched between dielectric media with relative permittivities of ε₁, ε₂, and ε₃. The corresponding chemical doping levels are E_F0, E_F1, and E_F2. W = 8 nm, C = 2 nm, and E_F0 = 1 eV are fixed.

Figure 2

THG assisted by PMC with stimulated plasmons producing high electric field enhancement. Electric field profiles of E_z in the x-y plane under PMC pairs between (a) 0th FF and (b) 0th TH modes, (d) 1st FF and (e) 0th TH modes, and (g) 0th FF and (h) 1st TH modes. (c),(f),(i) Effective mode index (n_eff) at FF and TH and the THG conversion efficiency (η) for the corresponding three PMC pairs as a function of the dielectric permittivity ε₃. Black: FF mode, red: TH mode, and blue: conversion efficiency.

Figure 3

THG conversion efficiency over the propagation distance under PMC (black, left y axis) and non-PMC (blue, right y axis) conditions for (a) 0th FF and 0th TH modes pair, (b) 1st FF and 0th TH modes pair, and (c) 0th FF and 1st TH modes pair.

Figure 4

Total (black line), real (Re, red line) and imaginary (Im, blue line) parts of the graphene χ⁽³⁾ at 6 µm under different doping levels.

Figure 5

THG conversion efficiency along the propagation distance for 0th FF and 0th TH (black line), 1st FF and 0th TH (red line), and 0th FF and 1st TH (blue line) PMC pairs.

Figure 6

Normalized THG conversion efficiency of left-peak χ⁽³⁾ case at PMC for 0th FF and 0th TH as a function of (a) background graphene Fermi level E_F0 with fixed C = 2 nm, and (b) separation C at E_F0 = 1 eV.