Excitation bound modes

It is also possible to measure microwave spectra of some more strongly bound Van der Waals complexes in a gas cell ratlier tlian a molecular beam. Indeed, tire first microwave studies on molecular clusters were of this type, on carboxylic acid dimers [jd]. The resolution tliat can be achieved is not as high as in a molecular beam, but bulk gas studies have tire advantage tliat vibrational satellites, due to pure rotational transitions in complexes witli intennolecular bending and stretching modes excited, can often be identified. The frequencies of tire vibrational satellites contain infonnation on how the vibrationally averaged stmcture changes in tire excited states, while their intensities allow tire vibrational frequencies to be estimated. 

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]. 

Fig. 6.4. Ground- and excited-state potential energy curves illustrating possible dissociation pathways. For a diatomic molecule r is the internuclear distance in a polyatomic molecule r is a normal mode displacement. Vibrational separations are greatly exaggerated. The vertical arrows correspond to Franck-Condon allowed transitions. Where possible, molecular examples are indicated, (a) Repulsive excited state—immediate dissociation, (b) Crossing of bound and repulsive excited states—intersystem crossing leads to predissociation. (c) Metastable excited state—tunneling leads to dissociation, (d) Bound state— excitation energy greater than dissociation limit.

Under these conditions, maximum bound-ray power results when satisfies Eq. (4-33), i.e. 9 S rtcolf o) c> nd all the light emitted from the source falls on the core endface when f9 p, where 9 is the maximum angle of emission relative to the fiber axis. By combining these two relations, all source power excites bound modes provided (P/ d)( co/ o)9c- Thus the maximum bound-ray power increases by a factor of [rjpy- compared to placing the source directly against the end of the fiber. 

In the previous chapter we examined the excitation of modes of a fiber by illumination of the endface with beams and diffuse sources, i.e. by sources external to the fiber. Here we investigate the power of bound modes and the power radiated due to current sources distributed within the fiber, as shown in Fig. 21-1. Our interest in such problems is mainly motivated by the following chapter, where we show that fiber nonuniformities can be modelled by current sources radiating within the uniform fiber. Thus, isolated nonuniformities radiate like current dipoles and surface roughness, which occurs at the core-cladding interface, can be modelled by a tubular current source. 

Eq. (21-11) that the on-axis dipole excites zero power, while the dipole at = r excites maximum power. Furthermore, the power of the bound mode due to the z-directed... 

The tubular current source was described in Section 21-6, where we showed that it is ineffective in exciting bound modes unless either of the resonance conditions of Eq. (21-15) is satisfied. A similar conclusion holds for the radiation fields. If the tube length 2L is large compared to the spatial period 2n/Sl, where 2 is the frequency in Eq. (21-13), it is intuitive that power will be radiated essentially at a fixed angle to the fiber axis. This is also a consequence of Floquets theorem [7]. However, unlike the current dipole, radiation now depends on the orientation of the currents on the tube. 

When light propagates along a fiber and impinges on nonuniformities due to imperfections in the fiber, some of its power is scattered, as shown schematically in Fig. 22-1 (a). Part of the scattered power is distributed into forward-and backward-propagating modes, while the remainder is radiated. For multimode fibers, the distribution of scattered power is best treated by the ray methods of Chapter 5. Here we are primarily interested in fibers that propagate only one or a few modes. We treat the nonuniformities of the perturbed fiber as induced current sources within the unperturbed fiber. The results of the previous chapter can then be used to describe excitation of bound modes and the radiation field [1-3]. 

As we now have orthogonality relations and normalization expressions for leaky modes, results which were derived for bound modes in earlier chapters can simply be extended to apply to leaky modes. These include the perturbation expressions of Chapter 18, the modal amplitudes due to illumination in Chapter 20, and the excitation and scattering effects of current sources in Chapters 21 to 23. We give an example of leaky-mode excitation by a source in Section 24—23. 

Given a source of excitation, either at the waveguide endface or within the waveguide, the modal amplitudes aj Q) of radiation modes are found by analogy with the bound-mode amplitudes aj. 

Here we determine the amplitudes of bound and radiation modes excited by a prescribed distribution of currents J, which occupy a volume y between the planes z = Zi and z = Z2 of a waveguide, as shown in Fig. 31-1. The total fields everywhere in the waveguide are expanded in terms of the complete set of forward- and backward-propagating modes... 

Contents Introduction. - Volume Plasmons. - The Dielectric Function and the Loss Function of Bound Electrons. -Excitation of Volume Plasmons. - The Energy Loss Spectrum of Electrons and the Loss Function. - Experimental Results. - The Loss Width. - The Wave Vector Dependency of the Energy of the Volume Plasmon. - Core Excitations. -Application to Microanalysis. - Energy Losses by Excitation of Cerenkov Radiation and Guided Light Modes. - Surface Excitations. - Different Electron Energy Loss Spectrometers. - Notes Added in Proof - References. - Subject Index. 

The point q = p = 0 (or P = Q = 0) is a fixed point of the dynamics in the reactive mode. In the full-dimensional dynamics, it corresponds to all trajectories in which only the motion in the bath modes is excited. These trajectories are characterized by the property that they remain confined to the neighborhood of the saddle point for all time. They correspond to a bound state in the continuum, and thus to the transition state in the sense of Ref. 20. Because it is described by the two independent conditions q = 0 and p = 0, the set of all initial conditions that give rise to trajectories in the transition state forms a manifold of dimension 2/V — 2 in the full 2/V-dimensional phase space. It is called the central manifold of the saddle point. The central manifold is subdivided into level sets of the Hamiltonian in Eq. (5), each of which has dimension 2N — 1. These energy shells are normally hyperbolic invariant manifolds (NHIM) of the dynamical system [88]. Following Ref. 34, we use the term NHIM to refer to these objects. In the special case of the two-dimensional system, every NHIM has dimension one. It reduces to a periodic orbit and reproduces the well-known PODS [20-22]. 

---