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 0:6 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. DOI: 10.1103/PhysRevLett.97.124301 PACS numbers: 43.35.+d, 63.20.ÿe, 73.20.ÿr, 78.67.Pt The behavior of waves in periodic structures has attracted the interest of scientists for many centuries We studied a 75 period GaAs-AlAs SL consisting of alternating layers of thicknesses d GaAs 59 A and d AlAs 23:5 A, grown by molecular beam epitaxy on a (001) GaAs substrate. A 70-nm-thick layer of AlAs was deposited between the SL and the substrate to act as an etch stop. Coherent acoustic modes were generated using 70 fs laser pulses provided by an optical parametric amplifier, tunable in the range 400-650 nm, at the repetition rate of 250 kHz. There are two main processes by which light couples to sound, namely, through the strain modulation of the optical constants, as described by the photoelastic tensor is proportional to L, the total thickness of the SL. Here @u=@z is the uniaxial strain associated with the LA displacement uz, P is the appropriate photoelastic constant, and k I (k S ) is the magnitude of the wave vector of the incident (scattered) light. It follows that R B is nonzero only for modes with q jk I k S 2p='j (' 82:5 A is the SL period and p is an integer). These wave vectors, corresponding to q BS 4n C = C and q FS =c 0 in the reduced-zone scheme, satisfy phasematching conditions (quasimomentum conservation) for PRL 97