Generation of Coherent Phonons

When metals have Raman active phonons, optical pump-probe techniques can be applied to study their coherent dynamics. Hase and coworkers observed a periodic oscillation in the reflectivity of Zn and Cd due to the coherent E2g phonons (Fig. 2.17) [56]. The amplitude of the coherent phonons of Zn decreased with raising temperature, in accordance with the photo-induced quasi-particle density n.p, which is proportional to the difference in the electronic temperature before and after the photoexcitation (Fig. 2.17). The result indicated the resonant nature of the ISRS generation of coherent phonons. Under intense (mJ/cm2) photoexcitation, the coherent Eg phonons of Zn exhibited a transient frequency shift similar to that of Bi (Fig. 2.9), which can be understood as the Fano interference [57], A transient frequency shift was aslo observed for the coherent transverse optical (TO) phonon in polycrystalline Zr film, in spite of much weaker photoexcitation [58],... 

Measurements and information. Signal processing allows both time- and frequency-domain information to be obtained depending on the type of specimen studied. In addition, the use of frequency-tunable laser to generate density variations within the sample results in thermal expansion by absorption of light. Compared to spontaneous Brillouin scattering, the SNR in this forced Brillouin spectrometry is substantially enhanced by the generation of coherent phonons within the sample. 

Kuett, W Albrecht, W. and Kurz, H. (1992) Generation of coherent phonons in condensed media. IEEE J. Quantum. Electron., 42, 2434-2444. 

FIGURE 8 (a) Time-resolved second-harmonic generation spectroscopy reveals the generation of coherent phonon modes in native oxide covered GaAs (100) crystal, (b) Left inset shows the oscillatory part of the time domain data, (c) Right inset shows the Fourier power spectrum of the oscillatory part. 

Summary. Coherent optical phonons are the lattice atoms vibrating in phase with each other over a macroscopic spatial region. With sub-10 fs laser pulses, one can impulsively excite the coherent phonons of a frequency up to 50THz, and detect them optically as a periodic modulation of electric susceptibility. The generation and relaxation processes depend critically on the coupling of the phonon mode to photoexcited electrons. Real-time observation of coherent phonons can thus offer crucial insight into the dynamic nature of the coupling, especially in extremely nonequilibrium conditions under intense photoexcitation. 

Fig. 2.2. Two generation models of coherent optical phonons, (a), (c), (e) impulsive stimulated Raman scattering (ISRS). (b), (d), (f) displacive excitation of coherent phonons (DECP). Graphs (e) and (f) display the time evolution of the driving force (grey areas) and that of the displacement (solid, curves) for ISRS and DECP, respectively...

The coherent oscillation of the A g mode was a cosine function of time (Fig. 2.8) [21,24-26]. Recent X-ray measurements demonstrated a clear shift in the equilibrium position at photoexcitation [35], as we will see in the next chapter. These results confirmed the displacive generation of coherent A g phonons, as discussed in Sect. 2.2.2. In contrast, the coherent oscillation of the Eg mode was a sine function of time, and its amplitude exhibited a cos 2ip dependence on the pump polarization angle ip. Both features indicated the ISRS generation of the coherent Eg phonons [21,25],... 

One of the most exciting prospects in the study of phonon dynamics is the use of nonlinear optical phenomena to generate monochromatic, coherent phonon distributions and to detect their subsequent evolution. 

Chang, Y. M., Xu, L. and Tom, H. W. K. (1997) Observation of coherent surface optical phonon oscillations by time-resolved surface second-harmonic generation. Phys. Rev. Lett., 78, 4649-4652. 

The key requirements for ISRS excitation are the existence of Raman active phonons in the crystal, and the pulse duration shorter than the phonon period loq1 [19]. The resulting nuclear oscillation follows a sine function of time (i.e., minimum amplitude at t=0), as shown in Fig. 2.2e. ISRS occurs both under nonresonant and resonant excitations. As the Raman scattering cross section is enhanced under resonant excitation, so is the amplitude of the ISRS-generated coherent phonons. 

Experimental verification of the ISRS generation can be primarily given by the pump polarization dependence. The coherent phonons driven by ISRS (second order process) should follow the symmetry of the Raman tensor, while those mediated by photoexcited carriers should obey the polarization dependence of the optical absorption (first order process). It is possible, however, that both ISRS and carrier-mediated generations contribute to the generation of a single phonon mode. The polarization dependence is then described by the sum of the first- and second-order processes [20-22], as shown in Fig. 2.3. 

For surface coherent phonons of ferromagnetic metals, a spin-driven generation mechanism was proposed, as will be described in Sect. 2.6. 

Optical detection offers the most conventional technique to time-resolve the coherent phonons. It includes four-wave mixing [8], transient reflectivity [9,10] and transmission [7] measurements, as well as second harmonic generation (SHG) [15,32]. Coherent nuclear displacement Q induces a change in the optical properties (e.g., reflectivity R) of the crystal through the refractive index n and the susceptibility y,... 

Systematic TRSHG studies on alkali-atom adsorbed metal surfaces by Matsumoto and coworkers provided a deep insight on how coherent motions are created under very different electronic configurations [15, 77, 78]. The results showed that the coherent phonon generation critically depends on the surface and bulk electronic structure of the substrate. 

The earliest control experiments were performed in double- (or multiple-) pump and probe scheme on optical phonons generated via ISRS in transparent materials by Nelson and coworkers [24,25], Shortly later, similar experiments were carried out on coherent phonons generated in semiconductors via TDFS by Dekorsy and coworkers [26], and on those generated in semimetals via DECP by Hase and coworkers [27] (Fig. 2.1 in the previous chapter). These experiments demonstrated that the amplitude of the coherent oscillation can be controlled by varying the temporal separation At between the two pump pulses. At = nT leads to the maximum enhancement of the amplitude with an integer n and the phonon period T, while At = (n + 1/2)T results in complete cancelation. 

Doublets of folded longitudinal acoustic (LA) phonons due to the superlattice periodicity [143] can also be seen in the Raman spectra of the SLs (indicated by arrows in Fig. 21.2). The positions of the doubled peaks agree well with the first doublet frequencies calculated within the elastic continuum model [144]. The observation of the LA phonon folding suggests that these superlattices possess the requisite structural quality for acoustic Bragg mirrors and cavities to be used for potential coherent phonon generation applications [145-147]. 

A real nanometric material is composed not only of electrons but also of a crystal lattice. In this case, after a dressed photon is generated on an illuminated nanometric particle, its energy can be exchanged with the crystal lattice, as shown by the Feynman diagram of Fig. 1.3a. By this exchange, the crystal lattice can excite the vibration mode coherently, creating a coherent phonon state. As a result, the dressed photon and the coherent phonon can form a coupled state, as is schematically explained by Fig. 1.3b. The creation operator a] of this novel form of elementary excitation is expressed as... 

Fig. 1.3 Feynman diagrams representing the coupling of a dressed photon with phonons, (a) Generation of a dressed photon and exchange with the crystal lattice, (b) A coupled state of a dressed photon and a coherent phonon...

Step 1 Under light illumination, an optical near-field is generated on the Ag surface. This optical near-field excites a coherent phonon at the />n-junction, resulting in generation of a DP-CP. By the two-step phonon-assisted process, electrons can be excited to create electron-hole pairs at the /injunction even though the photon energy of the incident light is lower than Eg. 

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). 

With development of ultrashort pulsed lasers, coherently generated lattice dynamics was found, first as the periodic modulation in the transient grating signal from perylene in 1985 by De Silvestri and coworkers [1], Shortly later, similar modulation was observed in the reflectivity of Bi and Sb [2] and of GaAs [3], as well as in the transmissivity of YBCO [4] by different groups. Since then, the coherent optical phonon spectroscopy has been a simple and powerful tool to probe femtosecond lattice dynamics in a wide range of solid... 

Silicon is a model for the fundamental electronic and mechanical properties of Group IV crystals and the basic material for electronic device technology. Coherent optical phonons in Si revealed the ultrafast formation of renormalized quasiparticles in time-frequency space [47]. The anisotropic transient reflectivity of n-doped Si(001) featured the coherent optical phonon oscillation with a frequency of 15.3 THz, when the [110] crystalline axis was parallel to the pump polarization (Fig. 2.11). Rotation of the sample by 45° led to disappearance of the coherent oscillation, which confirmed the ISRS generation,... 

One of the applications of TRXRD is to study complex systems where electric fields couple to multiple degrees of freedom. Though femtosecond laser pulses can generate THz radiation from ferroelectric LiTa03, the corresponding lattice motion remained undetected by optical measurements. Cavalleri and coworkers demonstrated the coherent modulation of the X-ray intensity at 1.5 THz [10], and assigned it as phonon-polariton mode of A symmetry (Fig. 3.3). Nakamura and coworkers detected the coherent LO phonon of CdTe... 

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