Optical Detection of Coherent Phonons

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, 

By using a nonlinear optical process such as SHG, one can probe surface phonons and adsorbate-related vibrations exclusively [14,15,32,34]. Time-resolved SHG (TRSHG) detects the second harmonic (SH) of the probe beam as a function of time delay between pump and probe. The SH electric field is driven by the nonlinear polarization Pi 2w) at the surface, which 

The SH intensity is proportional to P 2. Experimentally, the oscillatory part of the total SH is so small that one can ignore its second-order term. If coherent surface phonons are created by ISRS, the whole process including excitation and detection is the coherent time-domain analogue of stimulated hyper Raman scattering (y(4) process) [14]. The cross section of the SHG process is then proportional to the product of a Raman tensor in the pump transition and a hyper-Raman tensor dx k/dQn in the probe transition. 

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