Broad line excitation

We wish to add that there exists a wide variety of literature that considers the opposite case of monochromatic excitation by an infinitely narrow line causing velocity selection, such as [261, 268, 269, 320, 362] and the sources quoted therein. This description has been developed basically in connection with laser theory it refers most often to stabilized single-mode excitation. The intermediate case between monochromatic and broad line excitation is the most complex one, requiring integration over the modal structure of the laser inside the bounds of the absorption contour [28, 231, 243]. 

This system in many cases can be simplified further. For example, if we have a broad spectral line excitation with a not very intense laser radiation, we have a situation for an open transition when 7 Ti, H. In practical cases this condition is often fulfilled at excitation with cw lasers operating in a multimode regime. If the homogeneous width of spectral transition usually is in the range of 10 MHz, then the laser radiation spectral width broader than 100 MHz usually can be considered as a broad line excitation. In this case we can use a procedure known as adiabatic elimination. It means that we are assuming that optical coherence pi2 decays much faster than the populations of the levels puJ = 1,2. Then we can find stationary solution for off-diagonal elements for the density matrix and afterwards find a rate equations for populations in this limit. For the two level system we will have... 

In the linear approximation there is a direct Fourier relationship between the FID and the spectrum and, in the great majority of experunents, the spectrum is produced by Fourier transfonnation of the FID. It is a tacit assumption that everything behaves in a linear fashion with, for example, imifonn excitation (or effective RF field) across the spectrum. For many cases this situation is closely approximated but distortions may occur for some of the broad lines that may be encountered in solids. The power spectrum P(v) of a pulse applied at Vq is given by a smc fiinction 18]... 

The sinc fiinction describes the best possible case, with often a much stronger frequency dependence of power output delivered at the probe-head. (It should be noted here that other excitation schemes are possible such as adiabatic passage [9] and stochastic excitation [fO] but these are only infrequently applied.) The excitation/recording of the NMR signal is further complicated as the pulse is then fed into the probe circuit which itself has a frequency response. As a result, a broad line will not only experience non-unifonn irradiation but also the intensity detected per spin at different frequency offsets will depend on this probe response, which depends on the quality factor (0. The quality factor is a measure of the sharpness of the resonance of the probe circuit and one definition is the resonance frequency/haltwidth of the resonance response of the circuit (also = a L/R where L is the inductance and R is the probe resistance). Flence, the width of the frequency response decreases as Q increases so that, typically, for a 2 of 100, the haltwidth of the frequency response at 100 MFIz is about 1 MFIz. Flence, direct FT-piilse observation of broad spectral lines becomes impractical with pulse teclmiques for linewidths greater than 200 kFIz. For a great majority of... 

Germanium crystals that contain the substitutional triple acceptor copper (Hall and Racette, 1964), as well as hydrogen, exhibit in PTIS a series of broad lines that belong to an acceptor with a ground state at 17.81 meV above the top of the valence band (Haller et al., 1977a). PTIS studies over a range of temperatures have shown that this acceptor has a ls-state that is split into a large number of components that are closely spaced (Kahn et al., 1987). When thermally populated, each of the components of the ls-state manifold acts as an initial state for optical trasitions of the bound hole to one of the effective mass-like excited states. This in turn explains why the lines of this center appear broad. 

Single crystals of cubic boron nitride, with excess boron, have been studied20 by X-band and W-band EPR. Two types of defect were detected called D1 and D2. The D1 centre exhibits local axial < 111 > symmetry and ground spin state S = 1/2, with g = 2.0033 and gL = 2.0094 at T = 10 K. A broad line from D2 was observed only at X-band at high temperature with g = 2.0084. It was attributed to transitions inside the excited levels of another boron related defect. 

Broad-line NMR, 359 6-type transition, 219 Butadiene excited states, 312-313... 

In practice this condition may be fulfilled not only in excitation, e.g. by means of a pulsed laser or a continuous dye laser with insufficient frequency selectivity, but also by means of fines from a continuous gas laser working in simultaneous axial mode u>i (multimode) generation regime see Fig. 3.10(a). Let Au>i = u>i+1 — uii = itc/L denote the mode separation in a laser, L being the resonator length. Then, as pointed out in [110, 127, 231], broad line approximation works if Awj is smaller than the width of the Bennet holes r en [268, 320] in the absorption contour see Fig. 3.10(6). The positions of the Bennet holes are determined by the condition ujq — w/ + kv = 0, where luq is the central transition frequency, k is the wave vector and v is the velocity of the absorbing particle. The broad fine approximation is valid if the following conditions are fulfilled (see Fig. 3.10) ... 

The system of equations obtained, (5.22) and (5.23), in broad line approximation in many cases allows us to carry out the analysis of non-linear optical pumping of both atoms and molecules in an external magnetic field. Some examples will be considered in Section 5.5, among them the comparatively unexplored problem of transition from alignment to orientation under the influence of the dynamic Stark effect. But before that we will return to the weak excitation and present, as examples, some cases of the simultaneous application of density matrix equations (5.7) and expansion over state multipoles (5.20). 

Mason et al supported the two step process based on the decrease in relative intensity with below bandgap excitation [19]. Partially based cm their PL lifetime studies, Hofmann and co-workers have argued that the spin-dependent process is a radiative transition from a shallow donor to a much deeper single donor [20,21], The basic argument that there is a level in the lower half of the bandgap with a broad line having a g value a little less than two has been supported by Reinacher et al based cm their LESR results [13],... 

Neutron [102] and electron [70,103] irradiated TCNQ salts were investigated by IR spectroscopy. The spectra of irradiated samples gradually become weaker when the dose is increased the broad lines change shape and decrease in intensity some even vanish (Fig. 18). It was shown [103] that the vibrational features connected with the totally symmetric modes of the TCNQ are particularly sensitive to structural disorder. In some cases, for example, in MTPP(TCNQ)2 irradiated by electrons, the disappearance of distinct doublets of activated ag modes was noticed. Different mechanisms of the excitation of both the narrow and wide components explain their different dose and temperature dependences [70]. The changes of band intensity in the UV-VIS region imitate the electrical conductivity as a function of dose. 

Figure 2. Characterization of intermolecular exci-plexes by hole-burning spectroscopy. Adapted from Ref. [22a] (a) Fluorescence excitation ( emission set at 375 nm) and (b) hole-burning spectra of the R-isomer of the anthracene-dimethylaniline (An-DMA) adduct in a supersonic jet. The probe laser was tuned on the most intense line of the adduct. Lines marked with asterisks are due to bare anthracene, (c) Fluorescence excitation ( emission set at 450 nm) and (d) hole-burning spectra of the E-isomer of the An- DMA adduct in a supersonic jet. The probe laser was tuned to the maximum of the broad exciplex excitation band.

In these equations that are valid for broad spectral line excitation (large q) and arbitrary t ues for all other parameters, one can easily see a simple rate equations if we assume that absorption rate is expressed as... 

In practice, hard rf-pulses are used for uniform excitation of broad lines. Our own work has tended to use an echo sequence with the phase cycling first proposed by Kun-war. Turner and Oldfield (1986) which combines quadrature phase cycling with further cycling designed to cancel direct magnetisation (the remaining FID) and ringing effects ... 

Figure 8. Top, optical absorption and the corresponding prompt fluorescence spectra of diacetylene polymer molecules middle, excitation and the corresponding delayed emission spectra and bottom, transient absorption for a partially polymerized (broad line) and fully polymerized (narrow line) diacetylene crystal.

Fig. 14. Schematic of selective excitation and ID exchange spectroscopy, (a) Typical pulse sequence with a soft selective pulse centered at pulsation a>s with a frequency dispersion AcoP <3C Aoj much smaller than the typical linewidth. After an evolution time te smaller or of the order of the spin-lattice relaxation time, a reading sequence of hard pulses that covers uniformly the whole broad line is applied, (b) Effect of a selective excitation on a homogeneously broaden line, (c) Selective frequency labeling of an inhomogeneously broaden line at the irradiation pulsation cos of the first soft pulse. For a soft n pulse, the magnetizations of all the spins that can exchange energy at this pulsation are reversed. By following the difference spectra between the spectra acquired at different evolution times te and the fully relaxed spectrum AS(te) — S(t -> oo) — S(te), limits or evaluation of the correlation time tc of the motion can be achieved.

A characteristic feature of many quadmpolar nuclei is the broad lines they produce, due to rapid quadmpolar relaxation (Section 2.5.5). The rapid recovery of the spins following excitation means they can often be acquired under conditions of very fast pulsing with full excitation by a 90° pulse, which is clearly beneficial for signal averaging purposes. However, the corresponding rapid decay of an FID can make the direct observation of nuclei with linewidths... 

With these assumptions we have the following rate cejuations for populations in an assumption of broad spectral line excitation... 

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