Coherent Nonlinearities

Theoretical calculations within Htickel or Hartree-Fock formalism have been used primarily in order to get a better evaluation of second order hyperpolarizabilities T (Rustagi (197 )) They allowed to explain the observed increase of y with increasing molecule length L(T L ). 

For an infinite polymer chain one expects a satuation of y/L ratio for a sufficiently large length L. A finite y/L value was obtained within a band model formalism parametrized in function of overlap integrals of electrons in the case of polydiacetylene (Agrawal et al. (1978)). Moreover this method does not take account of electron-electron correlations strong in these systems and which affect strongly the y/L limit value. 

Second order hyperpolarlzablllty of centrosynmetrlc and non centro-symnetric molecules. Influence of polymer length. 

In the case of centrosymmetrlc molecules the quantum mechanical formulas 

Remark in several one-dimensional conjugated polymers the two-photon state (2) is located slightly below the one-photon state (1). 

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Laubereau A and Kaiser W 1978 Coherent picosecond interactions Coherent Nonlinear Optics ed M S Feld and V S Letokov (Berlin Springer) pp 271-92... 

Recently, there has been much interest in the development and application of multidimensional coherent nonlinear femtosecond techniques for the study of electronic and vibrational dynamics of molecules [1], In such experiments more than two laser pulses have been used [2-4] and the combination of laser pulses in the sample creates a nonlinear polarization, which in turn radiates an electric field. The multiple laser pulses create wave packets of molecular states and establish a definite phase relationship (or coherence) between the different states. The laser pulses can create, manipulate and probe this coherence, which is strongly dependent on the molecular structure, coupling mechanisms and the molecular environment, making the technique a potentially powerful method for studies of large molecules. 

In this section we first give a survey on the most common nonlinear Raman processes, i. e. the (incoherent) hyper Raman scattering and several forms of coherent nonlinear Raman scattering. We then describe the instrumentation needed to perform several practical kinds of these nonlinear laser spectroscopies. Applications of nonlinear Raman spectroscopy will be found in Sec. 6.1. 

In this section we first discuss the principles of resonance Raman and surface-enhanced Raman scattering and give some specific examples. Since the hyper Raman effect and the coherent nonlinear Raman effects have been described in Sec. 3.6, we only add some typical applications of the methods. 

The methods of nonlinear Raman spectroscopy, i. e. spontaneous hyper Raman scattering (based on the hyperpolarizability) and coherent nonlinear Raman scattering (based on the third-order-nonlinear susceptibilities) are discussed in detail in Sec. 3.6.1. In Sec. 3.6.2 the instrumentation needed for these types of nonlinear spectroscopy is described. In this section we present some selected, typical examples of hyper Raman scattering (Sec. 6.1.4.1), coherent anti-Stokes Raman. scattering (Sec. 6.1.4.2), stimulated Raman gain and inverse Raman spectroscopy (Sec. 6.1.4.3), photoacoustic Raman spectroscopy (Sec. 6.1.4.4) and ionization detected stimulated Raman spectroscopy (Sec. 6.1.4.5). 

In the present paper, we investigate the role of local fields in the coherent nonlinear interaction between light and a QD interacting with phonons. In particular, we show that step-like transitions are appeared in ROs at relatively long pulse duration and signatures of oscillations are suppressed for weak pulse intensities. 

Comprehensive reviews of coherent nonlinear Raman spectroscopy can be found in references [4 - 6]. 

G. Grynberg, B. Cagnbac, F. Biraben, Multiphoton resonant processes in atoms, in Coherent Nonlinear Optics, ed. by M.S. Feld, V.S. Letokhov. Topics Curt Rhys., vol. 21 (Springer, Berlin, 1980)... 

On the other hand, many possible applications of this type of spectroscopy have remained elusive because of a lack of spectral intensity, monochromaticity, tunability and of spatial coherence of the thermal light sources. This situation changed drastically with the advent of the laser that not only brought along a renaissance of classical double resonance spectroscopy, but also the development of new coherent, nonlinear spectroscopic techniques. 

Coherent nonlinear effects involve interactions that occur before the wave functions that describe the excitations of the medium have time to relax or dephase. They occur primarily when the nonlinear interaction involves one- or two-photon resonances, and the duration of the laser pulse is shorter than the dephasing time of the excited state wave functions, a time that is equivalent to the inverse of the linewidth of the appropriate transition. Coherent nonlinear optical interactions generally involve significant population transfer between the states of the medium involved in the resonance. As a result, the nonlinear polarization cannot be described by the simple perturbation expansion given in Eq. (2), which assumed that the population was in the ground state. Rather, it must be solved for as a dynamic variable along with the optical fields. 

Such coherent nonlinear effects may also induce gain losses by the self-focusing effect, destroying the desired mode properties of the optical cavity. A power threshold has been estimated by Yariv (1967)... 

Phase-dependent coherence and interference can be induced in a multi-level atomic system coupled by multiple laser fields. Two simple examples are presented here, a three-level A-type system coupled by four laser fields and a four-level double A-type system coupled also by four laser fields. The four laser fields induce the coherent nonlinear optical processes and open multiple transitions channels. The quantum interference among the multiple channels depends on the relative phase difference of the laser fields. Simple experiments show that constructive or destructive interference associated with multiple two-photon Raman channels in the two coherently coupled systems can be controlled by the relative phase of the laser fields. Rich spectral features exhibiting multiple transparency windows and absorption peaks are observed. The multicolor EIT-type system may be useful for a variety of application in coherent nonlinear optics and quantum optics such as manipulation of group velocities of multicolor, multiple light pulses, for optical switching at ultra-low light intensities, for precision spectroscopic measurements, and for phase control of the quantum state manipulation and quantum memory. 

NI Koroteev. Coherent nonlinear Raman and hyper-Raman spectroscopy of free atoms and ions. In W Kiefer, M Cardona, G Schaack, FW Schneider, HW Schrotter, eds. Proceedings of the Xlllth International Conference on Raman Spectroscopy. Chichester Wiley, 1992, pp 5-8. 

Cantrell, C. D., Letokhov, V. S., and Makarov, A. A. (1980). Coherent excitation of multilevel quantum system by laser light. In Coherent nonlinear optics (ed. M. S. Feld and V. S. Letokhov), Topics in Current Physics, vol. 21, pp. 165-269. Springer, Berlin. 

To optimize the intensity of a coherent nonlinear optical effect, there must be conservation of photon momentum. For sum frequency generation this requirement is expressed as... 

Spontaneous nonlinear as well as coherent nonlinear Raman methods are considered here. These are based on the contributions of the nonlinear part of the induced dipole moment (spontaneous effects) or the induced polarization (coherent effects) to the intensity of the frequency shifted light. In the first case, the Raman signal is generated in a spontaneous, incoherent but nonlinear optical process, whereas in the second case the Raman information is contained in a coherent laser beam whereby the nonlinear polarization acts as a coherent light source. 

Dantus, M. (2001). Coherent nonlinear spectroscopy from femtosecond dynamics to control. Ann. Rev. Phys. Chem. 52, 639. 

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