Observation of Surface-Avoiding Waves: A New Class of Extended States in Periodic Media

Coherent time-domain optical experiments on GaAs-AlAs superlattices reveal the existence of an unusually long-lived acoustic mode at $\sim 0.6\mathrm{THz}$ which couples weakly to the environment by evading the sample boundaries. Classical as well as quantum states that steer clear of surfaces are generally shown to occur in the spectrum of periodic structures, for most boundary conditions. These surface-avoiding waves are associated with frequencies outside forbidden gaps and wave vectors in the vicinity of the center and edge of the Brillouin zone. Possible consequences for surface science and resonant-cavity applications are discussed.

Figure 1

Calculated dispersion of LA modes propagating along [001] for the GaAs-AlAs SL investigated in this work. Panels on the right show a schematic diagram and four representative eigenmodes of the 619-nm-thick SL slab (striped area) attached to a $5\mathrm{\text{−}}\mu \mathrm{m}$-thick substrate. Vertical green bars denote the SL-substrate boundary. SAM is the surface-avoiding mode at $q\approx 0$. The wave vector associated with modes labeled FP, $q_{\mathrm{BS}}$ (see text), is sufficiently far removed from the zone center so that the FP waves reflect only weakly at the boundary. The mode with frequency in the minigap, GM, decays exponentially into the SL.

Figure 2

Differential reflectivity data at 300 K and $10\mathrm{ps}<t<250\mathrm{ps}$ showing coherent acoustic oscillations. The central wavelength of the laser pulses is ${\lambda }_C=546\mathrm{nm}$. A slowly varying background has been subtracted. The yellow rectangle indicates the range of the scan shown in the inset.

Figure 3

Fourier transform of the time-domain data for the intervals: (a) 10–125, (b) 250–350, and (c) 350–500 ps. SAM is the surface-avoiding wave at $q\approx 0$. The bottom panel shows the inverted dispersion relation (parameters are the same as in Fig. 1). The horizontal line represents the wave vector $q_{\mathrm{BS}}$ determined from phase-matched backscattering conditions.