10.1. BASIC CONCEPTS 481
in the microwave region (νIF∼1 GHz). Using Eq. (10.1.3) together withI=RP, the
photocurrent is now given by
I(t)=R(Ps+PLO)+ 2 R√
PsPLOcos(ωIFt+φs−φLO). (10.1.7)SincePLOPsin practice, the direct-current (dc) term is nearly constant and can
be removed easily using bandpass filters. The heterodyne signal is then given by the
alternating-current (ac) term in Eq. (10.1.7) or by
Iac(t)= 2 R√
PsPLOcos(ωIFt+φs−φLO). (10.1.8)Similar to the case of homodyne detection, information can be transmitted through
amplitude, phase, or frequency modulation of the optical carrier. More importantly, the
local oscillator still amplifies the received signal by a large factor, thereby improving
the SNR. However, the SNR improvement is lower by a factor of 2 (or by 3 dB)
compared with the homodyne case. This reduction is referred to as the heterodyne-
detection penalty. The origin of the 3-dB penalty can be seen by considering the signal
power (proportional to the square of the current). Because of the ac nature ofIac, the
average signal power is reduced by a factor of 2 whenIac^2 is averaged over a full cycle
at the intermediate frequency (recall that the average of cos^2 θoverθis^12 ).
The advantage gained at the expense of the 3-dB penalty is that the receiver design
is considerably simplified because an optical phase-locked loop is no longer needed.
Fluctuations in bothφsandφLOstill need to be controlled using narrow-linewidth semi-
conductor lasers for both optical sources. However, as discussed in Section 10.5.1,
the linewidth requirements are quite moderate when an asynchronous demodulation
scheme is used. This feature makes the heterodyne-detection scheme quite suitable for
practical implementation in coherent lightwave systems.
10.1.4 Signal-to-Noise Ratio
The advantage of coherent detection for lightwave systems can be made more quanti-
tative by considering the SNR of the receiver current. For this purpose, it is necessary
to extend the analysis of Section 4.4 to the case of heterodyne detection. The receiver
current fluctuates because of shot noise and thermal noise. The varianceσ^2 of current
fluctuations is obtained by adding the two contributions so that
σ^2 =σs^2 +σT^2 , (10.1.9)where
σs^2 = 2 q(I+Id)∆f, σT^2 =( 4 kBT/RL)Fn∆f. (10.1.10)
The notation used here is the same as in Section 4.4. The main difference from the
analysis of Section 4.4 occurs in the shot-noise contribution. The currentIin Eq.
(10.1.10) is the total photocurrent generated at the detector and is given by Eq. (10.1.5)
or Eq. (10.1.7), depending on whether homodyne or heterodyne detection is employed.
In practice,PLOPs, andIin Eq. (10.1.10) can be replaced by the dominant term
RPLOfor both cases.