The Fundamentals of Quantum Optical Transitions

The Fundamentals of Quantum Optical Transitions

Copyright: © 2014 |Pages: 59
DOI: 10.4018/978-1-4666-4687-2.ch003


Elementary and advanced concepts of quantum optics and spectroscopy are formulated, exemplified, and applied, and they relate the quantum states of a substance under electromagnetic action: from black-body radiation, to a spectral line profile’s characterization by widths and intensities, to solving two-level spectral problems to understand the coherence and relaxation properties of light in matter.
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3.2. Cavity Modes Of Black-Body Radiation

Consider a cubic cavity with sides at temperature . Assume that the walls of the cavity absorb and emit electromagnetic radiation, and at thermal equilibrium, the absorbed power has to be equal to the emitted power for all frequencies. Inside the cavity, there is a stationary field that is described by a superposition of plane waves with the amplitude, the wave vectors , and the angular frequency as follows (Born & Wolf 1999):


The waves are reflected at the walls of the cavity, and for each wave vector there are 23=8 possible combinations that interfere with each other. When the superposition causes standing waves, the result is a stationary field configuration that includes boundary conditions for the wave vector:

(3.2) where are positive integers. The magnitudes of the wave vectors and associated information allowed by the boundary conditions are
(3.3) from where these relationships follow:

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