I need to have written theory more about optical coherent receivers and some about optical dynamic networks(burst based) about 12 pages with formulas, graphs and figures

1 Coherent Receivers
1.1 Basic Coherent System
Improved receiver sensitivity and wavelength selectivity can be obtained using the coherent
detection techniques (i.e. hoeterdyne and homodyne detection) for the optical signal. How
the coherent optical system works is described in this section.
The schematic of a generalized coherent optical fiber communication system is given in
Fig. 1
Figure 1: Basic Coherent Optical Fiber Communication System
The dashed lines show the main elements of the coherent detection system which sets it
apart from the Intensity Modulation with Direct Detection based system. At the trans-
mitter, a CW na
ow-linewidth semiconductor laser is shown which acts as an optical
frequency oscillator. An external optical modulator provides ASK, PSK or FSK of the
optical ca
ier by the information signal. The modulated ca
ier waveforms for these three
are shown in Fig. 2. ASK is also called as on-off keying. In FSK, binary 1 is transmitted at
a higher optical frequency than binary 0. In PSK, there is 180◦ phase shift betwwen binary
1 and 0 signals.
In the receiver, the incoming signal is mixed with the optical output from a semiconducto
laser local oscillator. This function can be provided by a single-mode fiber fused biconical
coupler or an integrated optical waveguide coupler. The combined signal is the fed to a
photodetector for direct detection in the conventional square law device. To provide good
optical coherent detection, the coupler must combine the polarized optical information-
ca
ying signal with the similarly polarized local oscillator signal field.
In homodyne mode, the optical frequencies of the incoming signal and the local oscillato
signal are identical. Here, the electrical signal is recovered directly in baseband. Fo
heterodyne detection, they are not identical but offset from each other. Hence, electrical
1
Figure 2: Modulated Ca
ier Waveforms using (a)Amplitude Shift Keying, (b)FrPhase
Shift Keyingequency Shift Keying (c)
spectrum from the output of the detector is centered in an Intermediate Frequency(IF)
which is dependent on the offset and is chosen according to the information transmission
ate and modulation characteristics. The IF contains the information signal and can be
demodulated using standard electrical techniques.
The electrical demodulator block shown is required mainly for an optical heterodyne de-
tection system which uses either synchronous or asynchronous electrical detection. Optical
homodyne detection is of course a synchronous demodulation scheme.
1.2 Optical Coherent Network Principles
The basic coherent receiver model for ASK is shown in Fig. 3 [1]
Figure 3: Basic Coherent Receiver Model
The low-level incoming signal field es is combined with the larger signal field eL got from
the local oscillator laser. The two signals can be represented as shown below [2]
es = Escos(wst+ φ) (1)
eL = ELcos(wLt) (2)
2
where Es = peak incoming signal field
ws = angular frequency
EL = peak local oscillator field
wL = angular frequency
φ(t) = φs−φL = phase relationship between incoming signal phase φs and local oscillato
signal phase φL
For ASK, φt is constant and hence refe
ed to as φ in 1. The actual information is contained
in Es.
For heterodyne detection, wL is offset from ws by an intermediate frequency wIF :
ws = wL + wIF (3)
where wIF = angular frequency of IF.
For both heterodyne and homodyne detection, the optical detector produces a signal pho-
tocu
ent Ip, which is proportional to the optical intensity (i.e. the square of the total field,
for square law detection)
Ip ∝ (es + eL)2 (4)
Combining 1, 2 and 4,
Ip ∝ [Escos(wst+ φ) + ELcos(wLt)]2 (5)
Ip ∝ [Es2cos2(wst+ φ) + EL2cos2(wLt) + 2EsELcos(wst+ φ)coswLt]
= [1
2
Es
2+1
2
Escos(2wst+φ)+
1
2
EL
2+1
2
cos2wLt+EsEL(coswst+φ−wLt)+EsELcos(wst+
φ+ wLt)
Removing the higher frequency terms which are beyond the response of the detector,
Ip ∝
1
2
Es
2 +
1
2
EL
2 + 2EsELcos(wst− wLt+ φ) (6)
Ip ∝ Ps + PL + 2
√
PsPLcos(wst− wLt+ φ) (7)
where Ps and PL are optical powers in incoming signal and local oscillator signal resp.
(Note: Optical power is proportional to the square of its electrical field strength)
As the local oscillator signal is much larger than the incoming signal, the DC terms are not
much useful and can be removed and the Ip can be replaced by the approximate Is [3].
Is ∝ [2
√
PsPLcos(wst− wLt+ φ] (8)
Using 8, both homodyne and heterodyne detection can be explained.
For heterodyne detection, ws 6= wL and using 3,
Is ∝
√
PsPLcos(wIF t+ φ) (9)
3
This shows that the output from the photodetector is centered on an IF.
For homodyne detection, ws = wL, so 8 becomes
Is ∝
√
PsPLcosφ (10)
Here, the output from the photodetector is in the baseband and the local oscillator laser has
to be phase locked to the incoming signal.
1.3 Basic Optical Coherent Receivers
Basic coherent receiver configurations for heterodyne and homodyne detection are shown
in Fig. 4 [1]
Figure 4: Basic coherent receiver configurations (a) Optical heterodyne Receiver (b) Opti-
cal Homodyne Receive
For heterodyne detection, a beat-note signal between the incoming optical signal and the
local oscillator signal produces the IF signal which is obtained using the square-law de-
tector. The IF signal is then demodulated into the baseband using either synchronous o
asynchronous detection. Also, as If frequency fluctuation degrades the heterodyne receive
performance, the signal is fed back from the demodulator through an automatic frequency
control (AFC) circuit to the local oscillator circuit to achieve frequency stabilization.
For homodyne detection, as discussed before, a synchronous detection technique is needed.
Also, because the local oscillator and incoming signals are phase locked, the...