Large negative and positive optical Goos-Hänchen shift in photonic crystals.

Low-loss photonic crystal (PC) mirrors exhibit positive and negative Goos-Hänchen shift (GHS) due to the strong angular and wavelength dependencies of their reflected phase. This Letter demonstrates the existence of large positive and negative GHS in PC mirrors through theoretical, numerical, and experimental approaches. A simple algebraic relation shows that positive effective thickness yields positive (negative) GHS for resonances that blue (red) shift with angle, while the opposite is true for interfaces with negative effective thickness. Spatiotemporal coupled-mode theory demonstrates the above relation for simple systems with one or two resonance modes, and it also shows the existence of both positive and negative GHS. These effects are numerically and experimentally verified in complex PCs with several resonance modes.

Transitional-turbulent spots and turbulent-turbulent spots in boundary layers.

Two observations drawn from a thoroughly validated direct numerical simulation of the canonical spatially developing, zero-pressure gradient, smooth, flat-plate boundary layer are presented here. The first is that, for bypass transition in the narrow sense defined herein, we found that the transitional-turbulent spot inception mechanism is analogous to the secondary instability of boundary-layer natural transition, namely a spanwise vortex filament becomes a [Formula: see text] vortex and then, a hairpin packet. Long streak meandering does occur but usually when a streak is infected by a nearby existing transitional-turbulent spot. Streak waviness and breakdown are, therefore, not the mechanisms for the inception of transitional-turbulent spots found here. Rather, they only facilitate the growth and spreading of existing transitional-turbulent spots. The second observation is the discovery, in the inner layer of the developed turbulent boundary layer, of what we call turbulent-turbulent spots. These turbulent-turbulent spots are dense concentrations of small-scale vortices with high swirling strength originating from hairpin packets. Although structurally quite similar to the transitional-turbulent spots, these turbulent-turbulent spots are generated locally in the fully turbulent environment, and they are persistent with a systematic variation of detection threshold level. They exert indentation, segmentation, and termination on the viscous sublayer streaks, and they coincide with local concentrations of high levels of Reynolds shear stress, enstrophy, and temperature fluctuations. The sublayer streaks seem to be passive and are often simply the rims of the indentation pockets arising from the turbulent-turbulent spots.