Haken H. Laser light dynamics, vol.2 (NH, 1985)(T)(354s).djvu: eKnigu

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Haken H. Laser light dynamics, vol.2 (NH, 1985)(T)(354s).djvu

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Date Aug 21, 2004

We
have to refer the reader for that case to the book Advanced Synergetics
(see references)...
We decompose
the parameters CU, B, C, which occur in G.122) into their real and imaginary
parts,
p G.123)
B = d+i<f>, G.124)
C = -f+iiff...
Because the amplitude b of the single mode interacts with the set of dipole
moments of the lasing atoms and with those of the absorber, eq...
In
order to cut down the complexity of the problem of solving these equations
Lorenz introduced a Fourier decomposition...
When numerical values are used in the condition (8.12)
it turns out that the Prandtl number must be so high that it cannot be
realized by realistic fluids...
Inserting (8.14) into (8.13) and
linearizing the resulting equations with respect to u we obtain equations of
§8.5...
,nM exp[i(n, <u, + n2oj2 + ¦ ¦ ¦+nMa)M)t] (8.18)
n
is bigger than the number of basic frequencies oju (o2,..., the endpoints
of the vector q(t) can be represented as trajectory lying on a torus...
Spectra corresponding to (a) and (e)
are also shown, observed -9 MHz from the main line center...
One sees instead a gradual reduction of the self-pulsing amplitude
which, eventually, vanishes at the injection threshold...
Therefore the
steady state solution becomes particularly simple in the case aL< 1, because
as one sees from eqs...
This is an important advantage,
also because the presence of a field too intense in the absorber might produce
undesirable effects, e.g...
A0.1)
Here and in the following we shall speak of Hamiltonians, though, more
precisely, we should speak of Hamiltonian operators...
The time dependence of
the operators is determined by the Heisenberg equations of motion which
can be obtained as follows...
We shall assume as usual that
each atom is coupled to its own heatbaths, so that the heatbath variables
are independent of each other...
Our subsequent discussions will show that such
a meaning can indeed be attached to that operator...
A0.119)
fj.fj.'fl"fi.'"
It contains only two types of contributions which do not vanish, namely
li = l*."\ /*' = /*", A0.120)
and
H = H", /x' = /x'"...
Quantum theory of the laser I
But now we wish to show that the statistical properties of laser light differ
from those of light from usual lamps fundamentally...
Below
threshold light consists of exponentially damped wave tracks whose phases
are entirely uncorrelated...
Another
approach consists in using the method of "quantum-classical correspon-
dence" through which we may transform the density matrix equation into
a "generalized Fokker-Planck equation"...
Here we
anticipate the result of the rigorous quantum theoretical treatment to be
presented in chapter 11...
A similarly good
agreement has been found for other quantities also, which can be expressed
by higher moments, such as M3 = (n3) and M4 = (n4)...
The remaining
terms in A1.1) describe the coupling of the field mode and the atoms to
their corresponding heatbaths...
It should be noted that both approaches imply the same kind of approxima-
tion, namely it is assumed that the interaction between the field mode and
the atoms is not so strong that the interaction of these individual systems
with their individual heatbath is appreciably disturbed...
We first note that according to
the basic principles of quantum theory classical observables, such as q(t),
are replaced by operators b in quantum mechanics...
As the reader may recall, in quantum mechanics we
read operators from the right to the left...