Observation of the temporal Bragg-diffraction-induced laser-pulse splitting in a linear photonic crystal

Temporal Bragg-diffraction-induced laser-pulse splitting into two pulses propagating with different group velocities is observed in multilayered linear photonic crystals (PCs). This phenomenon originates from spatially inhomogeneous light localization within the PCs at the Laue scheme of the dynamical Bragg diffraction. In a homogeneous medium at the PC output each pulse is spatially separated into two pulses, propagating in the transmission and diffraction directions, respectively. The experiments are carried out for a one-dimensional porous silicon-based PC consisting of 375 spatial periods of 800 nm thickness using a femtosecond Ti:sapphire laser as a probe. A linear dependence of the time splitting of each pair of transmitted and diffractively reflected pulses on the crystal thickness is demonstrated and is supported by theoretical estimations.

Figure 1

(a) Schematic diagram of doubling of the number of laser pulses caused by splitting of an incident pulse within PC at the Bragg diffraction in the Laue geometry; $T$ and $R$ are transmitted and diffractively reflected pairs of pulses at the PC output; photographs of the laser beam propagating at (b) the exact Bragg angle and (c) tilted to 4° from the Bragg angle.

Figure 2

Measured (solid line) and calculated (dashed lines) autocorrelation functions $I_{0,h_{AC}}\left(\tau \right)$ of laser pulses passed through the PC in the direction (a) of the transmitted wave at 31°and (b) diffracted wave at −31° in the Laue geometry under the fulfillment of the Bragg-diffraction conditions. (Inset) Output intensities of transmitted $I_0\left(t\right)={\left|E_0\left(t\right)\right|}^2$ (solid lines) and diffracted $I_h\left(t\right)={\left|E_h\left(t\right)\right|}^2$ (dashed lines) pulses calculated by Eq. (2). The refractive indexes of the layers are $n_1$ $=$ 1.350 and $n_2$ $=$ 1.455, $d$ $=$ 775 nm, $d_1$/$d$ $=$ 0.45, $z$ $=$ 2 mm, λ $=$ 800 nm, θ $=$ ${\theta }_B$ $=$ 31°, pulse duration is 110 fs, and input pulse size along the $x$ axis is 30 μm.

Figure 3

Experimental measurements of the time delay $t_{12}$($z$) of the transmitted pulses vs PC thickness and $t_{12}$($z$) calculated by Eq. (3) (solid line). Refractive indexes $n_1$ $=$ 1.347 and $n_2$ $=$ 1.460; the other parameters are the same as in Fig. 2. (Inset) Time delay $t_{12}$ vs input power in a PC with the thickness of $z$ $=$ 2.00 $\pm$ 0.03 mm.

Figure 4

Spatial-temporal dynamics of the total pulse field $|E_0(x,z,t)|+|E_h(x,z,t)|$ in the PC calculated by Eqs. (1) and (2) under exact Bragg condition at different instants $t$. The parameters are the same as in Fig. 2.