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Optical Sources, Detectors, and Systems by Robert H. Kingston

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6.5 Optical Amplification with Direct Detection
137
with unity quantum and mixing efficiency. If the if. frequency is
comparable to the optical bandwidth or if the local oscillator frequency is
set near the edge of the laser gain spectrum, then the image noise can be
eliminated and the ideal heterodyne performance attained. In general,
unless available detector quantum efficiencies are extremely low, optical
preamplification is not an attractive choice.
6.5 Optical Amplification with Direct Detection
We now consider the detection system as shown in Figure 6.5, which
shows a laser preamplifier of gain G, followed by an optical filter of
spectral bandwidth Av, which is less than or equal to the laser amplifier
bandwidth. The output radiation is focused at a field stop, which
determines the field of view at the entrance to the amplifier as seen by
the detector. A field stop of area Ap^ makes the solid-angle
field-of-
view of the receiver equal
A^^f-,
and the number of modes N seen by
the detector is given by
Q^QyAjX^
where A is the area of the amplified
beam. For N=l, the diameter of the field stop would be approximately
(//#)A. In the case of a single-mode optical fiber amplifier, N is auto-
matically unity.
Optical filter - Av
dx
Laser medium
(n^, n )
¥1
Field stop
jJ:JHEh-
Figure 6.5 EHrect detection with laser preamplification. The field stop limits the nimiber
of modes entering the detector.
138 Chapter 6 Heterodyne or Coherent Detection and Optical Amplification
Av/2^B
Figure 6.6 Spectral densities of signal and noise powers at optical and radio frequencies
for direct detection.
As shown in Figure 6.6, we assume that the signal bandwidth is
small compared with the net amplifier bandwidth, Av, and note that the
required signal bandwidth at optical frequencies is twice that at the de-
tector output because of the upper and lower sidebands at optical fre-
quencies. Since we are interested in the (S/N)y for a direct detection
system, we first write the output signal current as
is
=
^ (6.29)
hv
and then consider the several sources of noise similar to those discussed
for the heterodyne case. For convenience and by practice these are sep-
arated into two classes, N xN, noise "cross'' noise, and S xN, signal
"cross"
noise, as sketched in Figure 6.6. We first consider the N xN
term, which is the dominant mean-square noise current produced in the
absence
of signal. From Eqs. (6.25) and (6.27), the total consists of the
current-induced shot noise produced by the total mean noise power plus
the amplified spontaneous emission (ASE) noise in the N modes strik-
ing the detector. The result is
i^
= 2r]q^N(G
-
D/nAvB
+
iTiYin^mG
-1)^
AvB
^^ ^^^
=»
2rj2(/V^ WG - if AvB; G»l
with only the latter term, the N xN spectrum in Figure 6.6, important.
il-
= 2isin
Jri'q
-i
hv
^]
%Av
''n<lPn(out)^
; G»l
.
2riVPs
(hvf
6.5 Optical Amplification with Direct Detection 139
The S xN term is the result of mixing of the optical signal and noise
fields and can be derived using heterodyne theory as in Eq. (6.24). The
total mean square noise current is
(6.31)
where we have only used the noise power in the single mode which
matches the signal mode because we are performing a heterodyne
operation. The spectrum of this converted noise is a convolution of the
optical signal and noise spectra and is sketched in Figure 6.6. For small
signal bandwidths this results in a reduction of Eq. (6.31) by a factor of
B/(Av/2),
yielding the final result,
hv
Finally, there is the signal-power-induced shot noise term,
tl =
IqisB =
^^ ^ (6.33)
which for high gain is negligible compared with
Eq.
(6.32).
The resultant (S/N)y for optical amplification with direct detection
becomes, from
Eqs.
(6.29), (6.30), and (6.32),
S) nqGPs/hv
V hv
^ (6.34)
•^ln^Nihv)^
AvB+4nPshvB
Ps
^ i 2B fjhvB

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