Coherent phonon packets

Of the various methods which fall under the category of nonlinear optical techniques (Demtroder 1981, Levenson and Song 1980, Laubereau and Kaiser 1978, von der Linde 1981), the one which so far appears to have the most potential is the generation of short duration (subnanosecond) coherent phonon packets through coherent excitation, and the detection of the packet by coherent antiStokes Raman scattering (CARS). 

The presence of the coherent phonon packet causes an oscillatory polarizability at frequency as indicated in Eq. (16), which can in turn interact with the third laser at frequency 0)3 to yield a nonlinear polarization, pNL, (see Eq. (19))... 

Coherent optical phonons can couple with localized excitations such as excitons and defect centers. For example, strong exciton-phonon coupling was demonstrated for lead phtalocyanine (PbPc) [79] and Cul [80] as an intense enhancement of the coherent phonon amplitude at the excitonic resonances. In alkali halides [81-83], nuclear wave-packets localized near F centers were observed as periodic modulations of the luminescence spectra. 

The interaction between light and matter can be viewed as the creation of a coherent quantum superposition of initial and final electron states that has an associated polarization [3], as shown in Figure 1. The coherence between states with different wave vector requires an intermediate virtual state and the presence of a coherent phonon. A transition between the initial and final states may occur when the coherence of the system is broken either due to the finite width of an optical wave packet or by scattering from the environment. The transition results in the absorption of a photon and the creation of a hot electron-hole pair. Otherwise, the photon is re-radiated with a different phase and, perhaps, polarisation. 

In these expressions Rg is the Raman tensor, and the coherent amplitude, Q, of the excited phonon packet is given by Eq. (29). 

The subsequent temporal variation of the coherent LO phonon packet is measured through the CARS technique. For this purpose a small part of the beam is extracted and delayed by an optical delay line, so that pulses from it appear at the focal point at any delayed time, At, of between 0 and 0.3 ns, with a resolution of fractions of picoseconds. As described above, the delayed beam scatters from the component of the packet which remains coherent after At and produces a coherent beam propagating along... 

Fig. 3.11. Left spectrum of the tailored pump beam for different spectral separations Aw CC2 — oji between two spectral packets (oJi and Lof). The bottom case is resonant to the E2 phonon frequency l o- Right transient transmittance of GaN excited with the tailored pump pulses, showing the enhancement of coherent oscillation of the E2 phonon for u) — u)2 — Oo- From [28]...

The magnitude of Eg classifies the materials on the basis of their ability to conduct electricity. For Eg kT the material is a good conductor and the Ev and Ec overlap. Insulators, on the other hand, have a large value of Eg, typically in excess of 5 eV. Packets of coherent acoustic energy called phonons move through the crystal lattice and cause dissociation of electrons from the valence band to the conduction band leaving behind holes. In an intrinsic semiconductor, the concentration of electrons n (or holes p) is given by... 

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