Dipole radiation modes

Finally, we make a few additional remarks. First, note that a pure number state is a3j= state whose phase 0k is evenly distributed between 0 and 2n. This is a consequence of the commutation relation [3] between Nk and e,0 <. Nevertheless, dipole mafKi w elements calculated between number states are (as all quantum mechanical amplitudes) well-defined complex numbers, and as such they have well-defined phajje j S Thus, the phases of the dipole matrix elements in conjunction with the mode ph f i f/)k [Eq. (12.15)] yield well-defined matter + radiation phases that determine the outcome of the photodissociation process. As in the weak-field domain, if only gJ one incident radiation mode exists then the phase cancels out in the rate expres4<3 [Eq. (12.35)], provided that the RWA [Eqs. (12.44) and (12.45)] is adoptedf However, in complete analogy with the treatment of weak-field control, if we irradh ate the material system with two or more radiation modes then the relative pb between them may have a pronounced effect on the fully interacting state, phase control is possible. 

Infrared spectroscopy is based on the conversion of IR radiation into molecular vibrations. For a vibration to be IR-active, it must involve a changing molecular dipole (asymmetric mode). For example, vibration of a dipolar carbonyl group is detectable by IR spectroscopy. Whereas IR has been traditionally used as an aid in structure elucidation, vibrational changes also serve as probes of intermolecular interactions in solid materials. 

A schematic representation of the valence k, n, n and 7t molecular orbitals is given in Fig. 3. The selection rules for electric dipole radiation do not permit the X Aj and A Aj states to combine. As a result, the 0° transition is formally electric dipole forbidden. (M denotes a vibronic transition involving a quanta in the upper state and b quanta in the lower state, while a level is designated M. In the case of the 0—0 origin transition, the mode is labelled 0 and the transition Oq.)... 

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. 

We determine the correction to the radiation from the current dipole of Section 25-12, when located on the axis of a weakly guiding, step-profile fiber. If the z-axis of Fig. 25-1 (a) coincides with the axis of the fiber, we can repeat the analysis of Section 25-12 using the weakly guiding radiation modes instead of the Tree-space modes. The on-axis fields and nd consequently the modal amplitudes of Eq. (25-30) are multiplied... 

The last five chapters have shown how the radiation fields of an optical waveguide can be represented in different ways. In Chapter 24, we introduced the notion of leaky modes to describe the bulk of the radiation field close to the waveguide axis at distances sufficiently far from the source of exdtatioa The remaining portion of the radiation field corresponds to a space wave, as defined in Eq. (24-1). The same radiation field can also be represented either by an expansion over radiation modes, as we showed in Chapter 25, or by a superposition of the fields of point dipole sources, using the Green s function techniques for waveguides described in Chapters 21 and 34. In this chapter, we show how to find the space-wave component of the radiation field by formally decomposing either representation into leaky modes and a space wave. 

For a vibrating molecule to absorb radiation from an incident IR beam at the frequency of a particular normal mode it must be situated at a position of finite intensity and with an orientation such that there is a finite component of the dipole derivative du /dQ in the direction of the electric vector of the radiation field, where duj is the change of dipole for the change of normal mode coordinate dQ. At a... 

While s-polarized radiation approaches a phase change near 180° on reflection, the change in phase of the p-polarized light depends strongly on the angle of incidence [20]. Therefore, near the metal surface (in the order of the wavelength of IR) the s-polarized radiation is greatly diminished in intensity and the p-polarized is not [9]. This surface selection rule of metal surfaces results in an IR activity of adsorbed species only if Sfi/Sq 0 (/i = dipole moment, q = normal coordinate) for the vibrational mode perpendicular to the surface. 

As the isoquinoline molecule reorients in the order listed above, the absorption of infrared radiation by the in-plane vibrational modes would be expected to increase, while that of the out-of-plane modes would be predicted to decrease (in accordance with the surface selection rule as described above). In the flat orientation there is no component of the dipole moment perpendicular to the surface for the in-plane modes, and under the surface selection rule these modes will not be able to absorb any of the incident radiation. However, as mentioned above, infrared active modes (and in some cases infrared forbidden transitions) can still be observed due to field-induced vibronic coupled infrared absorption (16-20). We have determined that this type of interaction is present in this particular system. 

Some polyatomic molecules like C02 CS2 or SnCl4 which do not possess a permanent dipole, but develop a fluctuating dipole due to certain modes of vibrations also respond to infrared region of electro magnetic radiation. 

An ordered monolayer of molecules having a large dynamical dipole moment must not be regarded as an ensemble of individual oscillators but a strongly coupled system, the vibrational excitations being collective modes (phonons) for which the wavevector q is a good quantum number. The dispersion of the mode for CO/Cu(100) in the c(2 x 2) structure has been measured by off-specular EELS, while the infrared radiation of course only excites the q = 0 mode. 

In order for the electrical component in electromagnetic radiation to interact with a bond, the bond must have a dipole. Thus symmetrical bonds such as those in O2 or Nj do not absorb infrared radiation. However, the majority of organic molecules have plenty of asymmetry. In even small organic molecules the modes of vibration are complex. This is illustrated by the vibrational modes which can occur in a... 

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