Fig. 3.

Enhancing transmitted power at selected time. a, b Temporal shapes of the output pulse when the spatially integrated intensity (power) is optimized at arrival time (a) t₀ = −5 ps and (b) t₀ = 16.1 ps. Red solid lines are the measured pulse shapes with optimized input wavefronts, the blue dotted lines are predicted from measured correlations C₂(t, t′). They exhibit strong enhancement compared to the mean eigenvalues of $u^{†}\left(t\right)u\left(t\right)$, which represents the mean output pulse shape for random input wavefronts (black dash-dotted lines). Transmitted powers are all normalized by the peak power of the transmitted pulse with random input wavefronts. The insets are spatial intensity patterns at t₀ for the optimized wavefront (upper panel) and a random wavefront (lower panel). The speckle grains at t₀ = −5 ps are larger than those at t₀ = 16.1 ps, due to larger contributions from the lower-order modes at earlier arrival time. c Temporal shapes of pulses optimized at different t₀, ranging from −20 ps to 25 ps. The target time of a and b are marked by the white dashed lines. d Enhancement factor η of the transmitted power at the target arrival time t₀. Blue squares: measured enhancement. Black circles: enhancement predicted from C₂(t). Error bars represent the standard deviation among four measurements of the fiber in different bending configurations. Red dashed line indicates four times enhancement if C₂(t) = 0