Quantum-electrodynamical parametric instability in the incoherent photon gas

We present a theory for the quantum-electrodynamical (QED) parametric scattering instability of an intense photon pulse in an incoherent radiation background. The pump electromagnetic (EM) wave can decay into a scattered daughter EM wave and an acousticlike wave due to the QED vacuum polarization nonlinearity. By a linear instability analysis we obtain a nonlinear dispersion relation for the growth rate of the scattering instability. The nonlinear QED scattering instability can give rise to the exchange of orbital angular momentum between intense Laguerre-Gaussian mode photon pulses and the two daughter waves, which may be a useful method to detect the highly energetic photon gases existing in the vicinity of rotating dense bodies in the Universe, such as pulsars and magnetars. The observation of the scattered waves may reveal information about the twisted acoustic waves in the incoherent photon gas.

Figure 1

The dynamics of the QED scattering instability of intense EM pulses in an incoherent photon gas. The pump pulse $E_p$ decays into scattered waves $E_s$ and acousticlike waves ${\mathcal{E}}_g$. The parameters are $k_s=0.9k_p$ and $k_g=0.1k_p$. At time $t=270/k_{p}c$, the pump $E_p$ depletes and $E_s$ and $E_g$ have amplitude maxima. In the lower right panel, the amplitudes of the $E_p$ (dotted curve), $E_d$ (dashed curve), and ${\mathcal{E}}_g$ (solid curve) at $z=0$ are plotted versus time.

Figure 2

The dynamics of OAM exchange due to the QED scattering instability between the pump EM wave $\lambda \sqrt{{\epsilon }_0{\mathcal{E}}_0}{E}_p$ and scattered EM waves $\lambda \sqrt{{\epsilon }_0{\mathcal{E}}_0}{E}_s$ as well as acousticlike waves $\lambda {\mathcal{E}}_g$ at different times $k_{p}ct=0$, 600, and 800 (upper to lower panels). The parameters are $k_s=0.7k_p$ and $k_g=0.3k_p$.