Coherent phase relationship

Laser Particle Size Analysis. The precise and constant wavelength and coherent phase relationships in LASER (q.v.) beams are valuable in particle-size anaylsis. Techniques include those based on diffraction, and on laser Doppler effect measurement of the velocities of falling particles, in which a system of beats is established between the unreflected beam and the beam reflected from the falling particles, to measure the frequency difference and hence the SEDIMENTATION (q.v.) Velocity. 

Coherence A condition in which nuclei precess with a given phase relationship and can exchange spin states via transitions between two eigenstates. Coherence may be zero-quantum, single-quantum, double-quantum, etc., depending on the AM of the transition corresponding to the coherence. Only single-quantum coherence can be detected directly. 

From the point of view of the study of dynamics, the laser has three enormously important characteristics. Firstly, because of its potentially great time resolution, it can act as both the effector and the detector for dynamical processes on timescales as short as 10 - s. Secondly, due to its spectral resolution and brightness, the laser can be used to prepare large amounts of a selected quantum state of a molecule so that the chemical reactivity or other dynamical properties of that state may be studied. Finally, because of its coherence as a light source the laser may be used to create in an ensemble of molecules a coherent superposition of states wherein the phase relationships of the molecular and electronic motions are specified. The dynamics of the dephasing of the molecular ensemble may subsequently be determined. 

As shown in Fig. 21a, the simulated broadband inversion profile by the three PIPs resembles the profile by the composite pulse 90°180°90° except for a different excitation region. The inversion profile is severely distorted (Fig. 21b) if the three initial phases, phase relationship in the rotating frame is the wrong one in the Eigenframe. The phase coherence in PIPs needs to be considered even for PIPs with the same frequency shift, A/ = 50 kHz in this case. 

Spatially coherent light is light that has a specific phase relationship between each photon on wave fronts emitted from the source. 

Ultrafast laser excitation gives excited systems prepared coherently, as a coherent superposition of states. The state wave function (aprobabihty wave) is a coherent sum of matter wave functions for each molecule excited. The exponential terms in the relevant time-dependent equation, the phase factors, define phase relationships between constituent wave functions in the summation. 

The matter wave function is formed as a coherent superposition of states or a state ensemble, a wave packet. As the phase relationships change the wave packet moves, and spreads, not necessarily in only one direction the localized launch configuration disperses or propagates with the wave packet. The initially localized wave packets evolve like single-molecule trajectories. 

Before we state this mathematically, let us consider the implication of perfectly monochromatic illumination. We shall assume that the slit elements are illuminated by light of exactly the same wavelength and frequency. Each given pair of points in the entrance slit will then have its own fixed phase relationship. Neither point can gain or lose phase relative to the other because the fields have exactly the same frequency. The fields at these two points are perfectly coherent. Because this is true for any given pair of points in the slit, all the points have a fixed phase relationship. We call this the case of coherent irradiation. 

Now let us assume that a monochromatic source of flux is placed in the plane of the entrance slit so that there is no constant phase relationship between the fields at any two given points in the slit. This, in itself, is a contradiction, because a perfect source monochromaticity implies both spatial and temporal coherence. By definition of coherence, a constant phase relationship would result. To eliminate the possibility of such a relationship, we must require the source spectrum to have finite breadth. Let us modify the assumption accordingly but specify the source spectrum breadth narrow enough so that its spatial extent when dispersed is negligible compared with the breadth of the slits, diffraction pattern, and so on. Whenever time integrals are required to obtain observable signals from superimposed fields, we evaluate them over time periods that are long compared with the reciprocal of the frequency difference between the fields. We shall call the assumed source a quasi-monochromatic source. 

The photon thus induced to be emitted has the same phase relationship as the inducing photon. Further amplification of this coherent emission is brought about in a resonant optical cavity containing two highly reflecting mirrors, one of which allows the amplified beam to come out, either through a pin-hole or by a little transmission (Section 10.4). 

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. 

Thus, the fact that there is a well-defined phase relationship between the eigenstates of the Hamiltonian, contained in the wave function, is manifest in the existence of off-diagonal elements in the energy representation. The absence of off-diagonal matrix elements for the thermally eqiulibrated case makes clear that collisions have destroyed matter coherence manifest as quantum correlations between energy eigenstates. 

The interference between different vibrations (including those of different molecules) resulting from the coherent nature of the experiment makes the analysis of VSFS spectra considerably more complicated than that of spectra recorded with linear spectroscopic techniques. However, this complexity can be exploited to provide orientational information if a complete analysis of the VSF spectrum is employed taking into account the phase relationships of the contributing vibrational modes to the sum-frequency response [15,16]. In the analysis it is possible to constrain the average orientation of the molecules at the surface by relating the macroscopic second-order susceptibility, Xs g of the system to the molecular hyperpolaiizabilities, of the individual... 

If the two beams have a well-defined phase relationship, they will interfere to produce regions of darkness as well as regions of bright illumination. It is this coherent interference that has been used for over half a century to produce holograms in thick photographic emulsions such as silver halides. 

It is worth noting that coherency of the electromagnetic wave elastically scattered by the electron establishes specific phase relationships between the incident and the scattered wave their phases are different by n (i.e. scatterred wave is shifted with respect to the incident wave exactly by 7J2). 

SH generation from aqueous suspensions of particles is not a coherent process because of random arrangement of the particles. No phase relationships occurs between the SH waves produced by each single particle. However the best agreement is obtained with theoretical models because for a liquid suspension of particles, the environment is rather homogeneous. The liquid medium can be described with... 

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