Temporal Boundary Solitons and Extreme Superthermal Light Statistics

We discover the formation of a temporal boundary soliton (TBS) in close proximity of a temporal boundary, moving in a nonlinear optical medium, upon high-intensity pulse collision with the boundary. We show that the emergent TBS is unstable to perturbations caused by the cross-phase modulation between the TBS and the other soliton products of the collision and that such instability triggers colossal intensity fluctuations of the reflected pulse ensemble with unprecedented magnitudes of the normalized autocorrelation function for an even weakly fluctuating input pulse.

Figure 1

Evolution of the intensity (a1)–(d1) and the spectrum (a2)–(d2) of an incident Gaussian pulse of width $t_p=0.6\mathrm{ps}$ and input peak power $P_0$: $P_0=80\mathrm{W}$ (a1),(a2), $P_0=250\mathrm{W}$ (b1),(b2), $P_0=593.8\mathrm{W}$ (c1),(c2), and $P_0=709.4\mathrm{W}$ (d1),(d2) as functions of the propagation distance $z$ in the reference frame moving with the temporal boundary as the pulse propagates inside the nonlinear medium with the temporal boundary at $t_b=5\mathrm{ps}$. The intensity and spectral distributions are displayed as functions of the time $\tau =t-z/v_b$ in the TB reference frame and the shifted frequency $\mathrm{\Omega }=\omega -{\omega }_0$ relative to the carrier frequency ${\omega }_0$ corresponding to the communication wavelength $\lambda =1.55\mu \mathrm{m}$ of a standard silica-glass fiber.

Figure 2

Normalized intensity autocorrelation function of an ensemble of input Gaussian pulses with the average peak power at the source $⟨P_0⟩$: $⟨P_0⟩=80$ (a), $⟨P_0⟩=250$ (b), $⟨P_0⟩=593.8$ (c), and $⟨P_0⟩=709.4\mathrm{W}$ (d) as a function of time $\tau$ in the reference frame moving with the TB at $t_b=5\mathrm{ps}$, evaluated at the receiver plane a distance $z_{*}=100\mathrm{m}$ away from the source.

Figure 3

Illustrating the shape of the normalized autocorrelation function. (a) The gray area corresponds to the time interval at the receiver where TBS and/or other soliton fission products are likely to arrive. (b) The broad normalized autocorrelation function $g^{(2)}(\tau )$, corresponding to a pulse ensemble with $⟨P_0⟩=250\mathrm{W}$ and 3% noise level, evaluated at $z_{*}=100$, exhibits a main peak and several secondary peaks of comparable magnitude. (c) The red area corresponds to the time interval at the receiver where exceptionally rare TBSs, which propagate all the way along the TB toward the receiver plane, arrive. (d) The normalized intensity autocorrelation function, corresponding to a pulse ensemble with $⟨P_0⟩=593.8\mathrm{W}$ and 3% noise level, evaluated at $z_{*}=100$, features a tall and narrow spike residing on a broad pedestal comprised of a multitude of much lower peaks of comparable heights.

Figure 4

Normalized intensity autocorrelation function of an ensemble of input Gaussian pulses with the average peak power at the source $⟨P_0⟩=593.8\mathrm{W}$ and 3% (a), 5% (b), and 10% (c) noise level as a function of time $\tau$ in the reference frame moving with the TB, evaluated at $z_{*}=100\mathrm{m}$.