Plasmon-polariton distributed-feedback laser pumped by a fast drift current in graphene

We propose a model of a slow surface plasmon-polariton distributed-feedback laser with pump by drift current. The amplification in the dielectric–semiconducting film–dielectric waveguide structure is created by fast drift current in the graphene layer, placed at the semiconductor/dielectric interface. The feedback is provided due to a periodic change in the thickness of the semiconducting film. We have shown that in such a system it is possible to achieve surface plasmon-polariton generation in the terahertz region.

Figure 1

Schematic of a waveguide structure: a semiconducting film with deposited graphene single layer is placed on a semi-infinite dielectric substrate in the case of the semiconducting film (a) of uniform thickness $d$; (b) of spatially modulated thickness with period Λ and modulation depth δd. The direction of the electron flux in the graphene under an applied voltage $U_0$ is indicated by the red arrow.

Figure 2

Frequency dispersion of (a) the SPP phase velocity $V_{\mathrm{ph}}$ (solid orange line), group velocity $V_g$ (dashed violet line), and drift current velocity $V_0$ (dotted green line); (b) amplification coefficient α (solid red line) and absolute value of loss coefficient $|{\beta }^{″}|$ (dashed blue line) for the parameters given in the text. The inset in (a) shows the dispersion of the SPP propagation constant ${\beta }^{\prime }$. Dashed vertical line shows frequency corresponding to condition $V_{\mathrm{ph}}=V_0$. Green area shows frequency interval when $\alpha >|{\beta }^{″}|$, and shaded area corresponds to SPP generation regime (see comments to Fig. 3).

Figure 3

Evolution of the transmission coefficient $T$ with angular frequency ω of SPP and period of the structure Λ. The parameters of the structure are the same as for Fig. 2.

Figure 4

Cross sections of Fig. 3 at two values of the structure period $\mathrm{\Lambda }=70.5\mathrm{nm}$ (solid orange line) and $\mathrm{\Lambda }=72\mathrm{nm}$ (dashed blue line).