Dispersive Dam-Break Flow of a Photon Fluid

We investigate the temporal photonic analogue of the dam-break phenomenon for shallow water by exploiting a fiber optics setup. We clearly observe the decay of the steplike input (photonic dam) into a pair of oppositely propagating rarefaction wave and dispersive shock wave. Our results show evidence for a critical transition of the dispersive shock into a self-cavitating state. The detailed observation of the cavitating state dynamics allows for a fully quantitative test of the Whitham modulation theory applied to the universal defocusing nonlinear Schrödinger equation.

Figure 1

(a) Snapshots comparing the DSW-RW pair (solid blue curve) obtained from the NLSE with steplike input $E(T,0)=\{P_L+(P_R-P_L)[1+\tanh (T/T_r)]/2{\}}^{1/2}$ (dashed red) with the ideal dispersionless solution of the SWEs (solid black). The oscillations over the top of the RW are due to the Gibbs phenomenon [35]. (b) Wedges in $(T,Z)$ plane corresponding to the RW (fable orange), the DSW (green), and the plateau in between. The boundaries correspond to slopes $\sqrt{k^{\prime \prime }\gamma P_R}{\tau }_j$, $j=4$, 3, 2, 1. Here $k^{\prime \prime }=176{\mathrm{ps}}^2/\mathrm{km}$, $\gamma =3(\mathrm{W}\mathrm{km}{)}^{-1}$, $P_R=1\mathrm{W}$, $P_L=150\mathrm{mW}$, $T_r=10\mathrm{ps}$.

Figure 2

Temporal traces of the whole waveform: (a),(b) experiment; (c),(d) numerics. The left column (a),(c) shows the input; The right column (b),(d) is the output power profile after propagation along the 15 km long fiber. The vertical dashed lines give the predicted delays of the edges of the RW [gray and orange lines, from Eqs. (4)] and the DSW [magenta and green lines, from Eqs. (5)], respectively.

Figure 3

Temporal traces at the fiber output for constant peak power of the photonic dam $P_R=0.8W$ and different background fractions $r$: (a1,a2) 0.15; (b1,b2) 0.11; (c1,c2) 0.03; (d1,d2) 0.01. Left column: experimental results. Right column: numerical simulation based on the NLSE.

Figure 4

(a)–(d) As in Fig. 3, showing a zoom around the spontaneously cavitating state (vacuum point) of the DSW, for $P_R=1$ W and different fractions $r=P_L/P_R$: (a1),(a2) 0.15; (b1),(b2) 0.11; (c1),(c2) 0.07; (d1),(d2) 0.03. (e) Measured delay of the cavitating state vs $r$, compared with prediction from Eq. (6) and numerical simulations of the NLSE. The dashed vertical line stands for the threshold in Eq. (7). Inset: overall RW-DSW dynamics of the case $r=0.05$.