Electric dipole radiation angular momentum

In turn, the monochromatic multipole photons are described by the scalar wavenumber k (energy), parity (type of radiation either electric or magnetic), angular momentum j 1,2,..., and projection m = —j,..., / [2,26,27]. This means that even in the simplest case of monochromatic dipole (j = 1) photons of either type, there are three independent creation or annihilation operators labeled by the index m = 0, 1. Thus, the representation of multipole photons has much physical properties in comparison with the plane waves of photons. For example, the third spin state is allowed in this case and therefore the quantum multipole radiation is specified by three different polarizations, two transversal and one longitudinal (with respect to the radial direction from the source) [27,28], In contrast to the plane waves of photons, the projection of spin is not a quantum number in the case of multipole photons. Therefore, the polarization is not a global characteristic of the multipole radiation but changes with distance from the source [22],... 

In most of the examples described in this book, the rotational angular momentum is coupled to other angular momenta within the molecule, and the selection rules for transitions are more complicated than for the simplest example described above. Spherical tensor methods, however, offer a powerftd way of determining selection rules and transition intensities. Let us consider, as an example, rotational transitions in a good case (a) molecule. The perturbation due to the oscillating electric component of the electromagnetic radiation, interacting with the permanent electric dipole moment of the molecule, is represented by the operator... 

In Section III.B, we introduced the atomic quantum phase states through the use of the representation of the SU(2) algebra (37) and dual representation (48), corresponding to the angular momentum of the excited atomic state. The multipole radiation emitted by atoms carries the angular momentum of the excited atomic state and can also be specified by the angular momentum [2,26,27], The bare operators of the angular momentum of the electric dipole... 

A J = 0 this means that, in the absence of nuclear spin and external perturbations (electric or magnetic fields, electromagnetic radiation fields, or collisions with other molecules), the total angular momentum of the molecule remains well defined. Even if the perturbation operator includes J+ or J-, this operator cannot change the value of J. Even in case (b), J (as well as N) remains well defined. Perturbations (denoted by ) correspond to an interaction between two levels, as opposed to an electric dipole transition (denoted by —) between two levels. 

The electric and magnetic dipole, quadrupole, octupole, etc., transitions are denoted by El, E2, E3,. .. and Ml, M2, M3,. .., respectively. The selection rules deduced from angular momentum and parity conservation laws for electric and magnetic multipole radiations are summarized in Table 2.6. 

It has been shown experimentally that a beam o circularly-polarized light exerts a torque on any optical component, such as a quarter- or half-wave plate, which changes the state of polarization of the light. This corresponds to a transfer of angular momentum from the radiation fields to the material system. To calculate the rate at which angular momentum is radiated by an electric dipole... 

---