Measurement of Net Group and Reshaping Delays for Optical Pulses in Dispersive Media

We experimentally demonstrate the direct measurement of net group and reshaping delays for arbitrary optical pulses in dispersive media, verifying the earlier prediction of Peatross et al. [Phys. Rev. Lett. 84, 2370 (2000)]. Incoherent pulse propagation in an absorptionless system is well described by net group delay; even the medium causes a great deal of deformation in the transmitted pulse. However, in the case of phase modulated chirping pulses in a resonant absorber, the so-called superluminal or subluminal propagation velocity is strongly influenced by the reshaping delay.

Figure 1

Schematic experimental setup: Beam splitters; BS1, BS2, and BS3. Corner cube reflectors: CC1, CC2, and CC3; second harmonic generating crystal, SHG.

Figure 2

Observed cross correlations (solid curves) of incoherent pulses, at 800 nm, transmitted through ZnSe of (a) 0.0, (b) 10.10, (c) 20.03, and (d) 30.07 mm, in the sample arm. The cross correlation represented by the dashed line in (a) is for coherent pulses at the same wavelength. The horizontal axis for each graph is the absolute delay time ${\tau }_{\mathrm{abs}}$ and labeled in ps. The centers of mass for coherent pulses transmitted through different lengths of ZnSe are (a) 0.0, (b) 58.13, (c) 115.27, and (d) 173.00 ps, while the corresponding ones for incoherent pulses are indicated by downward arrows. Open circles, solid circles, and upward triangles are the eye guides to three major peaks of cross correlations. The cross correlation is seen to widen and deformed significantly, increasing ZnSe thickness, evolving an additional peak shown by the downward triangle in (d).

Figure 3

Observed propagation delays as a function of dye concentration for two different wavelengths (a) 814 and (b) 774 nm. Open circles and open diamonds are propagation delays for chirping and coherent pulses, respectively, while the solid circles represent the measured reshaping delay. Solid, dotted, and dashed lines, respectively, describe the reshaping, total, and net group delays for chirping pulse propagation calculated using Eqs. (1, 2). Inset displays the temporal profile of a transmitted pulse after propagation through a concentration of the dye of $10\times {10}^{-6}\mathrm{M}$ (thin line) along with the initial (thick line) chirping pulse at 814 nm.

Figure 4

Solid circles and solid triangles represent the experimentally observed center wavelengths of the transmitted chirping pulses as a function of dye concentration at the incident wavelengths of 814 and 774 nm, respectively, while the open circles and open triangles represent that for coherent pulses. Inset displays spectral profile of the transmitted chirping pulse after propagation through the dye of $10\times {10}^{-6}\mathrm{M}$ (thin line) along with the initial (thick line) chirping pulse at 814 nm.