Penrose Superradiance in Nonlinear Optics

Particles or waves scattered from a rotating black hole can be amplified through the process of Penrose superradiance, although this cannot currently be observed in an astrophysical setting. Here we theoretically show that analog Penrose superradiance arises naturally in the field of nonlinear optics. A loosely focused signal beam can experience gain or amplification as it glances off a strong vortex pump beam in a nonlinear defocusing medium. Amplification occurs only with the generation and trapping of negative norm modes in the core of the pump vortex, as predicted by Penrose. Our results elucidate a new regime of nonlinear optics involving the notion of an ergoregion, providing further insight into the processes and transient dynamics involved in Penrose superradiance.

Figure 1

Conceptual drawing of the interaction geometry. The signal beam is focused on the collimated pump vortex core. Under conditions corresponding to those identified by Penrose, an idler beam is generated that is trapped inside the pump cortex core and the output signal beam is amplified. The inset shows the pump and signal beam transverse profiles at the input (all beams have the same optical frequency).

Figure 2

For all cases, the pump has OAM $\ell =1$. (a)–(d) For this case, the signal has OAM $n=2$ and idler OAM $q=0$, and Penrose superradiance occurs, $\mathrm{\Delta }K>0$. Cross sections for the intensity profiles $|E_{s,i}(x,y,z){|}^2$ versus $x/w$ and $z/Z_R$ for $y=0$ for the (a) signal and (b) idler, calculated using the linearized theory: (c) Current $J_0(r/w)$ versus radius $r/w$ for $z/Z_R=4$ and (d) reflection ($R-1$) and transmission $T$ versus propagation distance $z/Z_R$. (e)–(h) As in (a)–(d) for signal with OAM $n=-1$ and idler with OAM $q=3$ for which Penrose superradiance is absent, $\mathrm{\Delta }K<0$. (i)–(l) As in (a)–(d) calculated using the full NSE (1). The horizontal dashed white lines in (a),(b),(e),(f) indicate the location of the dimensionless radius $r/w$ of the ergoregion.