Modulational and Filamentational Instabilities of Intense Photon Pulses and Their Dynamics in a Photon Gas

It is shown that an intense photon pulse interacting nonlinearly with sound waves in a photon gas is subjected to modulational and filamentational instabilities. Starting from a new set of coupled equations governing nonlinear photon-photon interactions, we derive a dispersion relation which depicts the temporal and spatial amplification rates of the modulational and filamentational instabilities. The long term behavior of the modulationally unstable waves renders collapse of a photon beam as well as the formation of cylindrically symmetric photonic solitons. The results can have relevance to the understanding of the nonlinear photonic pulse propagation in astrophysical environments as well as in forthcoming intense laser-matter interaction experiments.

Figure 1

The growth rate $\gamma$ (upper panel) and real frequency ${\Omega }_{\mathrm{R}\mathrm{e}}$ (lower panel) as a function of the wave number $K_{\perp }$ for pump strength $A=0.02$, where $A={ϵ}_0|E_{p0}{|}^2/W$, and different values on $K_x$.

Figure 2

The growth rate $\gamma$ (upper panel) and real frequency ${\Omega }_{\mathrm{R}\mathrm{e}}$ (lower panel) as a function of the wave number $K_{\perp }$ for different pump strengths $A$, where $K_x=0K_{\perp }$.

Figure 3

The normalized photon energy density ${ϵ}_0|E_p{|}^2/W$ as a function of the normalized spatial variables $k_{p}y$ and $k_{p}z$ at different times $k_{p}ct$. We see that initially uniformly distributed photon energy forms localized packages which self-focus and collapse.