Nonlinear Zel’dovich Effect: Parametric Amplification from Medium Rotation

The interaction of light with rotating media has attracted recent interest for both fundamental and applied studies including rotational Doppler shift measurements. It is also possible to obtain amplification through the scattering of light with orbital angular momentum from a rotating and absorbing cylinder, as proposed by Zel’dovich more than forty years ago. This amplification mechanism has never been observed experimentally yet has connections to other fields such as Penrose superradiance in rotating black holes. Here we propose a nonlinear optics system whereby incident light carrying orbital angular momentum drives parametric interaction in a rotating medium. The crystal rotation is shown to take the phase-mismatched parametric interaction with negligible energy exchange at zero rotation to amplification for sufficiently large rotation rates. The amplification is shown to result from breaking of anti-$PT$ symmetry induced by the medium rotation.

Figure 1

(a) Parametric gain factor $|\exp (2gL)|$ over the medium length versus the rotation rate $\mathrm{\Omega }$, and (b) the signal gain $G_s$ (dash line) and net gain $G$ (solid line) both as functions of the rotation rate $\mathrm{\Omega }$. For these calculations $m_1=149$ and $m_2=300$. The vertical dashed line indicates ${\mathrm{\Omega }}_p={\omega }_1/\overline{m}=1.2\times 10^{13}\mathrm{rad}{\mathrm{s}}^{-1}$.

Figure 2

Signal gain $G_s$ (dashed line) and net gain $G$ (solid line) both as functions of the scaled rotation rate $\mathrm{\Omega }/{\mathrm{\Omega }}_p$ using (a) the analytic theory and (b) the BPM. For these calculations $m_1=8$ and $m_2=17$, all other parameters being the same as for Fig. 1.