Ultrashort pulse propagation at the photonic band edge: Large tunable group delay with minimal distortion and loss M. Scalora, R. J. Flynn, S. B. Reinhardt, and R. L. Fork Department of Electrical and Computer Engineering, University of Alabama, Huntsville, Alabama 35899 M. J. Bloemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, and J. P. Dowling U.S. Army Missile Command, Weapons Sciences Directorate, AMSMI-RD-WS-ST, Redstone Arsenal, Alabama 35898-5248 R. P. Leavitt U.S. Army Research Laboratory, 2800 Powder Mill Road, Adelphi, Maryland 20783 Received 29 November 1995 We examine optical pulse propagation through a 30-period, GaAs/AlAs, one-dimensional, periodic structure at the photonic band-edge transmission resonance. We predict theoretically—and demonstrate experimentally—an approximate energy, momentum, and form invariance of the transmitted pulse, as well as large group index up to 13.5. The group index is tunable and many orders of magnitude more sensitive to variation in material refractive index than for bulk material. We interpret this observation in terms of time- dependent electromagnetic states of the pulse-crystal system. S1063-651X9650108-X PACS numbers: 42.70.Qs, 42.65.Re, 78.47.+p, 78.66.Fd We report strong theoretical and experimental evidence that an ultrashort optical pulse—incident near the first trans- mission resonance of a compact photonic band-gap PBG structure—excites an unusual state. This state shows marked transient electromagnetic field localization and a close ap- proach to invariant transmission of the pulse. Our simula- tions imply that this unusual combination of properties re- sults from a coherent, resonant, momentum exchange between the ultrashort pulse and the structure. A spatial sepa- ration of the optical electric and magnetic fields mediates this exchange and results in transient energy storage in a quasi- standing-wave within the device. Recent theoretical work by our group demonstrates the existence of a series of N transmission resonances in each pass band for a one-dimensional, N -period, layered structure. Each of these resonances exhibits peak transmittance near unity and large group index 1. The most pronounced com- bination of these properties occurs at the resonances closest to the band gap—the band-edge resonances—where we carry out our experiment. The resulting combination of nearly in- variant transmission and large adjustable group delay for ul- trashort electromagnetic pulses in the linear regime provides a valuable and previously unavailable capability. This current work emerges from our previous studies re- lating to ultrashort pulse propagation 2,3 and atomic emis- sion rates 4,5 in one-dimensional PBG structures—a part of our overall program to develop an understanding of PBG crystals in higher dimensions 6,7. We also note that this combination of efficient transmission and strong transient lo- calization provides a long-sought phenomenon important to optimal optical switching 8. Previous experiments by Chiao and co-workers have investigated the group delay of single-photon pulse propagation through one-dimensional 1D PBG crystals at midgap frequencies 9. But our work here is an investigation of ultrashort pulse propagation at the photonic band-edge resonance. We show in Fig. 1 the theoretical transmittance T dashed and group index n g =c / v , solid of our 30-period GaAs 107.3 nm/AlAs 124.6 nm sample plotted versus midgap-normalized wavelength at the long-wavelength edge of the photonic band gap. We define group delay by FIG. 1. Transmission curve T dashed and the group index n g =c / v g solid, versus midgap-normalized wavelength, for a free- standing, 30-period, 1D, quarter-wave, GaAs/AlAs, PBG structure. In the passband there are a series of 30 resonances where T is nearly unity and n g is also locally maximal. Three of these reso- nances appear here. The absolute maximum in n g is at the band- edge resonance, as shown. left inset: enlarged view of the n g curve solid at the long-wavelength band-edge resonance, with a dotted line representing the bandwidth of 2 ps pulse that fits well within the transmission resonance dashed line. Right inset: simulated comparison of the peak-to-peak group delay of a 2 ps pulse that propagates through the crystal at the band edge solid to a control pulse in bulk material dotted. PHYSICAL REVIEW E AUGUST 1996 VOLUME 54, NUMBER 2 54 1063-651X/96/542/10784/$10.00 R1078 © 1996 The American Physical Society