Polarization waves, coherent electric

Finally, in this section, possible frequencies for the excitation of coherent vibrations should be considered. Originally special reference was made to membrane oscillations as their high polarization will then yield coherent electric oscillations (cf. Ref. 7, with earlier literature). Since the thickness of a membrane is about 10" cm and its elastic constant is equivalent to a velocity of sound of about lO cm/s, a frequency of the order of 10 Hz was expected, corresponding to electromagnetic waves in the millimeter region. When based on proteins or DNA, however, both higher and lower frequencies may be expected. 

ABSTRACT We present a dynamical scheme for biological systems. We use methods and techniques of quantum field theory since our analysis is at a microscopic molecular level. Davydov solitons on biomolecular chains and coherent electric dipole waves are described as collective dynamical modes. Electric polarization waves predicted by Frohlich are identified with the Goldstone massless modes of the theory with spontaneous breakdown of the dipole-rotational symmetry. Self-organization, dissipativity, and stability of biological systems appear as observable manifestations of the microscopic quantum dynamics. 

H. Frohlich has introduced, in a framework of far-from-equilibrium processes, coherent electric polarization waves as the physical agent able to control the working of distant and separate parts of the system, making them cooperative. On the other hand, it has been shown that biomolecules are able to host on their own chains, in a conservative framework, highly nonlinear subdynamics which give rise to deep structural and conformational changes. 

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. 

To illustrate the exchange of the phase information between the atomic transition and the multipole field, consider the electric dipole Jaynes-Cummings model (34). Assume that the field consists of two circularly polarized components in a coherent state each. The atom is supposed to be initially in the ground state. Then, the time-dependent wave function of the system has the form [53]... 

Let us show now that the vacuum electric polarization is induced by a coherent homogeneous condensation of the massless dipole-wave quanta / (x) in the vacuum 0>, which is controlled in turn by the field translation (3.53) and (3.54). We get indeed, by using Eq. (3.56),... 

Much more important for gas phase spectroscopy than the hyper-Raman effect are the various coherent Raman effects, so we shall develop the theory of coherent Raman scattering in rather more detail. The usual starting point is the bulk polarization of the medium expressed as a function of the electric field vectors of the various light waves present simultaneously in the medium (SI)... 

If we specifically consider the mixing of two single-mode, amplitude-stabilized, first-order coherent waves, both of which are well collimated, parallel, plane polarized along a common unit vector, and normally incident onto a photosensitive material, we may write the positive portion of the electric field operator as the superposition of two scalar fields... 

The mixer consists of a photodetector and a local oscillator. We are interested in determining the signal-to-noise ratio at the output of the photodetector. The input electric field consists of three plane, parallel, coincident electromagnetic waves, which are assumed to be polarized and to impinge normally on the photodetector. Spatial first-order coherence is assumed over the detector aperture. The total incident electric field , may therefore be written as... 

We consider interference of mutually coherent polarized light in uniaxial anisotropic media. As illustrated in Fig. 1, the xz -plane is the incident plane and the z -axis is taken normal to the film plane. Assuming that the two recording beams are plane waves and that the amplitude of their incident angles is small, the electric field of interference light is described using the Jones vector as... 

The electronic absorption spectra of nanocrystals of metals is dominated by the surface plasmon band which arises due to the collective coherent excitation of the free electrons within the conduction band [66-69]. A schematic illustration of the electric field component of an incoming light wave inducing a polarization of the free or itinerant electrons is shown in Fig. 1.15. It corresponds to the dipolar excitation mode which is the most relevant for particles whose diameters are much less than the wavelength of light. However, higher order excitations are possible and come into play for nanocrystals with diameters in the range of tens of nanometers. 

Tables 1 and 2 and Figure 1 summarize a number of distinct nonlinear optical effects, in particular including those of third order arising from the combined influence of three frequencies, CO2, (Oy These effects are collectively called four-wave mixing, as three incident waves combine coherently to give a fourth resulting one of frequency o)i 0)2 o)y The radiation-induced polarization depends to third order on the electric field strength of the incident radiation, namely, on the triple product E(o)i) 2 ( (O2) E( ( 3). In the particular case where co = a)2 = o)y we may have third-harmonic generation, proportional to E (o)). Correspondingly, the intensity of the third harmonic radiation I(3oo) depends on P((jo),...

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