Time-resolved observation of coherent phonons by the Franz-Keldysh effect

Abstract

We report on the time-resolved observation of coherent optical phonons in GaAs by the Franz-Keldysh effect. This effect leads to a modulation of the optical interband transitions with a nonlinear dependence on the macroscopic electric field associated with the coherent phonons. We find that the nonlinear electro-optic effect forms a far more efficient detection mechanism for coherent phonons than the linear electro-optic effect near the band gap.In recent years, the study of coherent phenomena with ultrashort laser pulses has become a matter of growing interest. The use of subpicosecond laser pulses allows a direct observation of coherent vibrations in molecules, 1 phonons in solid-state materials, 2-4 and electronic wave-packet oscillations in quantum-well structures in the time domain. 5 In previous studies the excitation mechanisms and the dephasing of coherent oscillations have been addressed.Recent investigations of coherent phonons in solid-state materials have shown that the excitation results from the impulsive interaction of the material with laser pulses whose durations are shorter than the period of the oscillation. In molecules, coherent vibrations can be excited by impulsivestimulated Raman scattering processes. 1 In narrow-band-gap semiconductors, the strong interband excitation of carriers leads to the excitation of coherent phonons by the impulsive elongation of the bonds. 3 It was found that in these materials the breathing mode of the coherent lattice vibrations modifies the band gap via the deformation potential. 6 In III-V semiconductors, the femtosecond excitation of free carriers results in the impulsive screening of the surface depletion field due to an ultrafast charge separation. This mechanism generates coherent longitudinal optical ͑LO͒ phonons, which are associated with an oscillating macroscopic electric field. 2,7 These field changes have been observed in timeresolved reflectivity measurements via the linear electrooptic effect. 2 In principle, the reflectivity changes induced by coherent phonons in III-V semiconductors arise from the modulation of the optical susceptibility at the phonon frequency, which is expressed by the coupling of the Raman tensor with the coherent motion of the atomic displacement. In a first-order approximation the phonon-induced reflectivity changes ⌬R can be described bywhere is the real part of the optical susceptibility, Q the atomic displacement, and F the macroscopic electric field. The first and second terms at the right-hand side in Eq. ͑1͒ are the deformation potential and the electro-optic contribution, respectively. This first-order Raman tensor determines the usual allowed Raman scattering with its specific polarization selection rules. 8,9 However, in the vicinity of critical points in the electronic band structure, nonlinear effects such as forbidden Raman scattering and electric-field-induced Raman scattering by LO phonons become strongly enhanced. 8,9 The polarization selection rule for these types of Raman tensors is different from that of a...

Allowed and forbidden Raman scattering mechanisms for detection of coherent LO phonon and plasmon-coupled modes in GaAs

“…By contrast, for the LO phonon of n-GaAs we find a minor but indubitable isotropic contribution (C = 0). Furthermore, the L− and L+ modes exhibit larger isotropic amplitudes than the anisotropic ones, i.e., C > D for both i-GaAs and n-GaAs samples, which is consistent with the previous report for n-type GaAs with 1.47 eV pump-probe photon energy 14 . We attribute the isotropic amplitude C to the reflectivity modulation via the dipole-forbidden Raman scattering, whose Raman tensor is diagonal [eq.…”

“…The time-dependent surface field, which was proposed in Ref. 14 , cannot be the origin either, because the FK effect is negligible for the bulk LOPC mode. According to the electronic Raman scattering theory based on the Lindhard dielectric function, the Raman line shape (frequency and linewidth) detected in the allowed and forbidden geometries can be different, because the former is determined by the interference between the DP and EO scattering, and the latter by the interference between the CDF and F scattering 27,28,53 .…”

“…On one hand, they found the reflectivity modulation amplitude due to the coherent LO phonon of undoped GaAs to be probe-polarization-angle dependent, which they attributed to the linear electro-optic (LEO) effect 6 . By contrast, for heavily n-doped GaAs, in which the LO phonon couples with doped carriers to form LO phonon-plasmon coupled (LOPC) mode, the amplitude of the coherent LOPC mode was nearly independent of the probe polarization 14 . The observation was interpreted in terms of the nonlinear electro-optic (NEO), i.e., Franz-Keldysh effect.…”

“…In transient reflectivity measurements, a nuclear displacement Q associated with the LO phonon oscillation induces a change in reflectivity R through the refractive index n and the susceptibility χ. In a first-order approximation the change ∆R is given by 1,14 :…”

“…While the behavior of the dielectric constant under laser-induced phase transition has been extensively studied 13 , the mechanism of the reflectivity modulation by the small nuclear motion in the vicinity of the equilibrium remains largely unexplored in spite of its extensive application. Among the few experimental studies Kurz and coworkers measured the transient reflectivity response of GaAs and Ge for a few probe polarization angles 6,14,15 . On one hand, they found the reflectivity modulation amplitude due to the coherent LO phonon of undoped GaAs to be probe-polarization-angle dependent, which they attributed to the linear electro-optic (LEO) effect 6 .…”