Electric dipole radiation polarization

Thus, the electric dipole a polarized emissions departing from the Ai level (in which the electric field of the emitted light is parallel to x or y) are those defined by the direct product Ai x L. An inspection of Table 7.6 shows that Ai X E = E, so that only A E emissions are allowed for a emitted radiation (as shown in Figures 7.7 and 7.8). 

As can be seen from the equations (21)-(22) and (23)-(24), there is an essential difference between the representations of plane and multipole waves of photons. In particular, a monochromatic plane wave of photons is specihed by only two different quantum numbers a = x, y, describing the linear polarization in Cartesian coordinates. In turn, the monochromatic multipole photons are described by much more quantum numbers. Even in the simplest case of the electric dipole radiation when X = E and j = 1, we have three different states of multipole photons in (23) with m = 0, 1. Besides that, the plane waves of photons have the same polarization a everywhere, while the states of multipole photons have given m. It is seen from (24) that, in this case, the polarization described by the spin index p can have different values at different distances from the singular point. In Section V we discuss the polarization properties of the multipole radiation in greater detail. 

For the electric dipole radiation described by the Jaynes-Cummings Hamiltonian (34), the polarization of photons at kr > 0 is defined by the quantum number m = 0, 1, describing the excited atomic state. 

In previous sections, we considered the polarization as a formal property of either plane or spherical waves of photons described by the corresponding index in the expansion (13) and (17). In this Section, we examine the quantum properties of polarization in more details. In particular, we show that the radiation phase of electric dipole radiation formally coincides with the inherent quantum phase of polarization which is the 517(2) phase of spin of photons. 

The SU(2) quantum phase of spin (polarization) of photons described in a proper reference frame coincides with the radiation phase of electric dipole radiation discussed in Section IV. 

The dipole components have the reps Ai(z), Bi(x), and Bz y). The transition to the njT state is therefore spatially forbidden for electric dipole radiation. The other two transitions are allowed and polarized in thex(di — B ) and y(di — fij) directions of the molecule. At the risk of laboring an already simple point it is easy to convince oneself that these results are correct without using group theory e.xplicitly. For e.xample, the Ax— mr transition probability is proportional to the integral given below ... 

The intensity, lifetime of the excited state, and polarization of the fluorescence of organic molecules in solution point to electric dipole radiation. Direct proof of this was obtained for fluorescein by Selenyi (1911, 1939) using his wide angle interference method and has been recently confirmed by Freed and Weissman (1941). 

This, of course, means that the plane of polarization is different in the two cases. For electric dipole radiation the electric vector lies in the plane defined by r and p, while for magnetic dipole radiation it is perpendicular... 

Fig.5.1. Selection rules for magnetic quantum number m and polarization of electric dipole radiation observed in the direction 6=0.

State I ) m the electronic ground state. In principle, other possibilities may also be conceived for the preparation step, as discussed in section A3.13.1, section A3.13.2 and section A3.13.3. In order to detemiine superposition coefficients within a realistic experimental set-up using irradiation, the following questions need to be answered (1) Wliat are the eigenstates (2) What are the electric dipole transition matrix elements (3) What is the orientation of the molecule with respect to the laboratory fixed (Imearly or circularly) polarized electric field vector of the radiation The first question requires knowledge of the potential energy surface, or... 

The dipole moment p = emaE0e, 0 tex of an ideal dipole, located at z = 0 and illuminated by an x-polarized plane wave is0exp(/ kz — iut)ex, oscillates with the frequency of the applied field therefore, the dipole radiates (i.e., scatters) an electric field E, (Stratton, 1941, p. 453)... 

Our task here is to determine whether any of the three Cartesian components is nonzero. Since, in DAh the z vector transforms according to the AZu representation and a and y jointly according to the representation, we need to know whether either of the direct products, Blg x AZu x BZu or BiK x Eu x BZu contains the Aljt representation. It is a simple matter to show that the first one is equal to AlK while the second is equal to Eg. Thus, the <5— S transition is electric-dipole allowed with z polarization and forbidden for radiation with its electric vector in the xy plane. 

Thus, the Alg — Blu and both of the Alg Biu transitions are electric dipole allowed. In all cases (see Fig. 7.2) the transitions are in-plane polarized, the first one occurring by absorption of radiation with its electric vector vibrating along the y or short axis of the molecule, the other two having x or long-axis polarization. 

Optical response of a material is generally described in the approximation of electric-dipole interaction with the radiation ( 0. In this model, the oscillating electric field of radiation induces a polarization in the medium. When a material is subject to a strong optical pulse from a laser the electric field is intense and the... 

Only one of these (Elu) contains a representation to which the electric dipole moment operator belongs. Therefore only one of the three possible transitions is symmetry allowed, and for this one the radiation must be polarized in the (x, v) plane (see Table 5.2). 

The latter equation assumes a 100% linearly polarized ionizing radiation, a is the fine structure constant, Nni is the number of electrons in a nl subshell, Dni->ei l is a radial dipole photoionization amplitude, fini is the dipole photoelectron angular asymmetry parameter, and A i2 is the electric dipole-quadrupole interference term arising due to the correction term ikr in the above expression for Mab,... 

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