ECE 455: Optical Electronics
Homework 6
Due: Oct. 20, 2010
1
Derivations
Derive the following equations. Writing down the final expressions without derivation or explanation
will not receive credit.
(a) Derive the relationship between intensity and energy density for a plane wave. Hint: Consider
a box with sides
dx
,
dy
and
dz
=
cdt
. Consider the flux of energy through the dxdy surface.
(b) Derive an expression for
dI
dz
including the effect of saturation in terms of
γ
0
and
I
. Hint: Consider
the effect of an optical field on the steady state populations.
Write two rate equations, one
including stimulated emission and one without.
(c) Integrate the expression in part (b) to find the gain of a plane was as it passes through a gaim
medium length
L
. Obtain an equation containing
I
out
/I
in
.
(d)
(Optional)
What does this equation become in the limit that
I
out
I
sat
?
(e)
(Optional)
What does this equation become in the limit that
I
out
I
sat
?
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 Fall '08
 Eden,J
 Atom, Photon, Stimulated emission, absorption coefficient, Rate Equations, IOUT

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