Azimuthal and radial modulation of double-four-wave mixing in a coherently driven graphene ensemble

We investigate in detail the azimuthal and radial modulation (i.e., the azimuthal order l(j) and radial order p(j) with j= 1, 2) of double-four-wave mixing (double-FWM) by use of two higher-order Laguerre-Gaussian (LG) beams in a Landau quantized graphene ensemble. A pair of weak probe pulses in the graphene ensemble interacts with two LG beams and thus two vortex FWM fields with the opposite vorticity are subsequently generated. In combination with numerical simulations, we reveal that (i) there appear l(1) + l(2) periods of phase jumps in the phase profiles under any conditions; (ii) p + 1 concentric rings emerge in the intensity profile and the strength is mainly concentrated on the inner ring when the two LG beams have the same radial orders (i.e., p(1)=p(2)=p); (iii) there are p raised narrow rings occurring in the phase profile in the case of p(1)= p(2)=p and l(1) not equal l(2), and the raised narrow rings would disappear when p(1)=p(2) and l(1)=l(2); (iv) p(max) + 1 concentric rings appear in the intensity profile, meanwhile, vertical bar p(1) - p(2)vertical bar convex discs and p(min) raised narrow rings emerge in the phase diagram in the case of p(1) not equal p(2), here p(max) = max(p(1), p(2)) and p(min) = min(p(1), p(2)). Moreover, the two generated FWM fields have the same results, and the difference is that the phase jumps are completely opposite. These findings may have potential application in graphene-based nonlinear optical device by using LG beams with adjustable mode orders. (C) 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Automated summary

The study investigates the azimuthal and radial modulation of double-four-wave mixing by using higher-order Laguerre-Gaussian beams in Landau quantized graphene ensemble. The findings reveal unique phase and intensity profiles, including phase jumps, concentric rings, and raised narrow rings, depending on the radial orders and azimuthal orders of the beams. The potential applications of these results in graphene-based nonlinear optical devices using LG beams with adjustable mode orders are highlighted.