By Avijit Lahiri
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Tiny differences between such individual microscopic events lead to statistical fluctuations in the radiation emitted by the source, the latter being a macroscopic system made up of innumerable microscopic constituents. The emission processes from the microscopic constituents of the source are quantum mechanical events and, in addition, the electromagnetic field is made up of photons resulting from these emission processes. These photons themselves are quantum mechanical objects. It is this essential quantum mechanical nature of the microscopic events associated with the electromagnetic field that lends a distinctive character to the fluctuations of the field variables.
It may be noted, however, that we are considering here harmonic solutions of Maxwell’s equations that may be more general than plane waves. Still, we will refer to k as the propagation constant corresponding to the angular frequency ω. 45), now decoupled in E and H, are referred to as the inhomogeneous Helmholtz equations for the field variables. 47) The inhomogeneous Helmholtz equations are of use in setting up a general formulation for solving diffraction problems. An alternative approach for describing the harmonically varying fields would be to make use of the electromagnetic potentials φ and A.
In eq. 36b) the reference to the point r is omitted for the sake of brevity. 2 Poynting’s theorem: the Poynting vector 52 Considering any region V in an electromagnetic field bounded by a closed surface S, one can express in mathematical form the principle of conservation of energy as applied to the field and the system of particles constituting the charges and currents within this volume. The rate of change of the field energy within this region is obtained by taking the time derivative of the integral of the energy density over the region V, while the rate of change of the energy of the system of particles constituting the charges and currents in this region is the same as the rate at which the field transfers energy to these charges and currents.
Basic Optics I-II by Avijit Lahiri