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

Abstract

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 978-1-4666-4687-2.ch003.m01 at temperature 978-1-4666-4687-2.ch003.m02. Assume that the walls of the cavity absorb and emit electromagnetic radiation, and at thermal equilibrium, the absorbed power 978-1-4666-4687-2.ch003.m03 has to be equal to the emitted power 978-1-4666-4687-2.ch003.m04 for all frequencies. Inside the cavity, there is a stationary field 978-1-4666-4687-2.ch003.m05 that is described by a superposition of plane waves with the amplitude978-1-4666-4687-2.ch003.m06, the wave vectors 978-1-4666-4687-2.ch003.m07, and the angular frequency 978-1-4666-4687-2.ch003.m08 as follows (Born & Wolf 1999):

978-1-4666-4687-2.ch003.m09
(3.1)

The waves are reflected at the walls of the cavity, and for each wave vector 978-1-4666-4687-2.ch003.m10 there are 23=8 possible combinations 978-1-4666-4687-2.ch003.m11 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:

978-1-4666-4687-2.ch003.m12
(3.2) where 978-1-4666-4687-2.ch003.m13 are positive integers. The magnitudes of the wave vectors and associated information allowed by the boundary conditions are
978-1-4666-4687-2.ch003.m14
and
978-1-4666-4687-2.ch003.m15
978-1-4666-4687-2.ch003.m16
(3.3) from where these relationships follow:
978-1-4666-4687-2.ch003.m17
or

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