Transient four-wave mixing

Fig. 1. Degenerate four-wave mixing transient of cyclopropane (left) and cyclobutane (right). The upper traces in the insets are simulations. The recurrences in cyclobutane are very weak compared to the coherence peak at time zero.

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,... 

Ogilvie, J. P, Plazanet, M., Dadusc, G., and Miller, R. J. D. 2002. Dynamics of ligand escape in myoglobin Q-band transient absorption and four-wave mixing studies. J. Phys. Chem. 109 10460-67. 

Photon Echo (PE) and Reverse Transient Grating (RTG) measurements of the loss of electronic coherence between the X( 2g+) and B(3FIou+) states of molecular iodine are measured by three pulse four wave mixing (FWM). Two cases are considered, relatively low pressure isolated iodine (1-2 Torr), and iodine at high pressure (>10torr) or in the presence of several hundred Torr of buffer gas. 

The description of pump-probe signals presented in the preceding section can be immediately generalized to heterodyne-detected transient grating spectroscopy as well as to other four-wave mixing techniques. Heterodyne detection involves mixing the scattered field with an additional heterodyne field 4(r). The signal in the ks direction can then be written in terms of the polarization Ts(t) as... 

The three-pulse experiments contain more information than two-pulse methods when the direction and timing of all three pulses is controlled. We have seen that this additional information cannot be interpreted within a Bloch picture. We will therefore outline in the following a more detailed theory, which includes spectral diffusion and which simultaneously explains the linear response (absorption spectrum) and the nonlinear response (four wave mixing, photon echo, transient grating, pump-probe) of vibrational transitions. 

There are several classes of optical effects induced by an internal perturbation, such as saturation of absorption, coherent Raman spectroscopy, multi-photon absorption processes, coherent transient spectroscopy (see Table 0.3). Section 5.1 of this chapter deals with saturation of absorption and multi-photon absorption processes. Section 5.2 outlines the principles of coherent anti-Stokes Raman spectroscopy (CARS), Raman-induced Kerr effect spectroscopy (RIKES), four-wave mixing (FWM), and photon echo. 

The evaluation of TPA activity of the materials can be made by various techniques such as up-converted fluorescence emission, nonlinear transmission, transient absorption, Z-scan, and four-wave mixing [122]. Among them, the up-converted fluorescence emission method is a simpler technique and the setup is shown in Fig. 49.10. In this method, the TPA cross-section value, 0-2 can be estimated according to the following equation [123] ... 

Fig. 2 Typical correlation traces of transient degenerate four-wave mixing calculated by analytical equations for idealized light sources t (A) coherent short pulses with zero pulse width (tp 0), and (B) incoherent long pulses with zero correlation time (Tq 0). Here, x is the delay time, and Tj and T2 denote the longitudinal (energy) and transverse (phase) relaxation times, respectively.

In actual materials, there exists more or less the cross relaxation effect within an inhomogeneous broadening, which has been neglected in the previous consideration. Its effect in the transient four-wave mixing will be examined next. The model and basic equations representing the cross... 

Fig. 7 Effect of cross relaxation time (T3) on the correlation traces of transient degenerate four-wave mixing with light sources of (a) transform-limited short pulse and (b) Gaussian incoherent light as given in Fig. 5. Broadly inhomogeneous transition and the conditions Ti >> T2 and T2/T(- = 5 have been assumed.

Fig. 8 Effect of time dulation (D) of incoherent incident light on the correlation traces of transient degenerate four-wave mixing (a) without (T2/T3 0) and (b) with (T2/T3 = 0.2) cross relaxation effect. Other conditions are the same as in Fig. 7. Curves 1, 2, 3 correspond to D/t = 19, 38, 76, respectively.

Incoherent light sources can effectively be used to determine ultrafast relaxation times, in particular T2, by means of transient four-wave mixing in relatively simple, inhomogeneously broadened two-level systems. The most important feature is that material nonlinear responses with incoherent light are dispersion-free, and are essentially suitable to achieve ultrahigh time-resolution in the extremely short time region. For optical transitions with very fast cross-relaxation or with complicated multi-level structure, incoherent sources are not so effective for the above purpose. 

Fig. S. (a) Phase matching in optical wavelength conversion using AT, and K2 to induce the grating and to generate K4 via four-wave mixing process, (b) Experimental setup for infrared-to-visible image conversion using the transient grating induced by infrared (1.06 fim) Nd YAG laser pulses in a dyed nematic liquid crystal film. The reconstructing beam is a CW He-Ne (0.63 / m) laser. The photo insert is a typical observed reconstructed image of the wire mesh object.

Morgan, G.P., S.Z. Chen and W.M. Yen, 1986b, Transient Grating Spectroscopy of LaP50 Nd in Dynamics Gratings and Four Wave Mixing, ed. H.J. Eichler, IEEE J. Quantum Electron. QE-22, 1360. 

Recently, the femtosecond time-resolved spectroscopy has been developed and many interesting publications can now be found in the literature. On the other hand, reports on time-resolved vibrational spectroscopy on semiconductor nanostructures, especially on quantum wires and quantum dots, are rather rare until now. This is mainly caused by the poor signal-to-noise ratio in these systems as well as by the fast decay rates of the optical phonons, which afford very fast and sensitive detection systems. Because of these difficulties, the direct detection of the temporal evolution of Raman signals by Raman spectroscopy or CARS (coherent anti-Stokes Raman scattering) [266,268,271-273] is often not used, but indirect methods, in which the vibrational dynamics can be observed as a decaying modulation of the differential transmission in pump/probe experiments or of the transient four-wave mixing (TFWM) signal are used. 

We have reviewed the EOM-PMA method for the calculation of two-pulse-induced (spontaneous emission, pump-probe, photon echo) and three-pulse-induced (transient grating, photon echo, coherent anti-Stokes-Raman scattering, four-wave-mixing) optical signals. In the EOM-PMA, the interactions of the system with the relevant laser pulses are incorporated into the system Hamiltonian and the driven system dynamics is simulated numerically exactly. 

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