Fig. 1. A schematic diagram of the photonic bandgap and the optical pulse as a function of position and wavelength. Wavelength components are represented as a rainbow of colors. A representative set of three wavelength component in the optical pulse are shown at different time positions due to group velocity dispersion in the wavelength regime near the photonic bandgap.

Fig. 2. A schematic diagram of the experimental apparatus. The incidents pulse (horizontal red arrow) is focused into the fiber (orange line) and the reflected pulse (vertical arrow) is directed to the fast response photodiode (D) by the beam-splitter (BS). The photo-current is displayed on a sampling oscilloscope. The grating is chirped by a temperature gradient (shown shaded from a hot red to a cold blue), produced by a heater (H) and a cooler (C). The grating bandgap is tuned by applying a strain (S) with a micrometer positioner.

Fig. 3. Transmission spectra for a chirped fiber grating in a series of temperature gradients applied as shown in Figure 2. One end of the fiber is kept at room temperature by the cooler and the other end is at 24 °C (black), 34 °C (red), 44 °C (green), 54 °C (blue), and 64 °C (magenta). Note that the photonic bandgap shift is toward longer wavelengths as the average temperature increases. The incident pulse for the nonlinear propagation experiments is positioned at the short wavelength edge of the grating as shown is Figure 1.

Fig. 4. Experimental (solid curves) reflected pulses from a grating with 0.2 nm bandgap and 0.15 nm chirp over the 6 cm length of the grating. The red curves are in the linear regime with intensities near 1 GW/cm². The blue curves are in the nonlinear regime with intensities near 10 GW/cm² for the experimental data. The simulation (dotted curves) in this case is for a uniform grating with a center wavelength of 1053.2 nm, a chirp of 0.15 nm and a bandgap of 0.3 nm. Both the experimental and simulated fiber in this case had a 3 cm bare fiber section before the grating. The incident pulse wavelength is 1052.8 nm and the intensity is 20GW/cm². Uniform gratings typically give similar results as an apodized grating except that the nonlinear regime is reached at nearly a factor of 2 higher intensity for uniform grating.

Fig. 5. Experimental reflected pulses from a chirped fiber grating with a 0.17 nm bandgap width and a chirp of 0.13 nm over the 6 cm length of the grating. The red curve is for an incident intensity of 3 GW/cm², near the linear regime. The green curve is in the nonlinear regime with an intensity of 6 GW/cm² and the blue curve is further into the nonlinear regime at 9 GW/cm². The total delay of the reflected pulse sequence shown here is approximately 1 ns relative to a small reflection from the incident face of the fiber.

Fig. 6. Numerical simulations of the transmitted and reflected pulses from a chirped grating with parameters corresponding to a 0.3 nm bandgap and chirp of 0.1 nm at intensities in the linear regime a 1 GW/cm² (red curve is multiplied by 10 for comparison with 10 GW/cm²) and nonlinear regime at 10 GW/cm² (green curve) and 20 GW/cm² (blue curve). The incident pulse is shown for the 10 GW/cm² data at a time near 400 ps. Transmitted pulses appear between 900 and 1200 ps and reflected pulses are between 1200 and 1700 ps. The center wavelength for bandgap at the incident face (cool) of the grating is 1053.2 nm. The center wavelength of the incident pulse is 1052.95 nm.

Fig. 7. Numerical simulations in the form of snapshots of the spatial profiles of the forward (red for the nonlinear 15 GW/cm² case and blue for the linear 1 GW/cm² case) and backward (green for the nonlinear 15 GW/cm² case and magenta for the linear 1 GW/cm² case) propagating pulses in movie format (a single frame at a time of 692 ps is shown, open link for full movie). The nonlinear sequence is followed by the linear sequence. The incident pulse width is 80 ps. The snapshots are taken at times of 173, 346, 519, 692, 865, and 1038 ps, relative to the time when the pulse enters the grating. The center wavelength of the grating at the incident (hot) face is 1053.2 nm. The grating chirp is 0.15 nm over the 6 cm length. The center wavelength of the incident pulse is 1053 nm. [Media 1]

Fig. 8. Time dependence of the nonlinearly reflected pulse (blue curve), linearly reflected pulse (red, multiplied by 15 in order to compare with nonlinearly reflected pulse) and incident pulse (green curve) for parameters as given in Figure 7. This simulation can be compared with the experimental results in Figure 5.