National Cheng Kung University, Taiwan. The optical carrier before modulation is in the form of a continuous wave (CW) and its electric field can be written as ...
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where Re denotes the real part, E is the electric field vector, ê is a unit vector representing the state of the polarization of the optical field, A0 is its amplitude, w0 is its carrier frequency, and f0 is its phase. The spatial dependence of E is suppressed for simplicity of notation.
of the modulated optical carrier for the three
modulation formats using a specific bit pattern.
Figure 2.1: Modulated optical carrier in the case of the ASK, PSK, and FSK formats for a specific bit pattern shown on the top.
where A0(t)changes with time in the same fashion as the electrical bit stream.
where P0is the peak power, fp(t)represents the optical pulse shape, Tb = 1/B is thebit slot at the bit rate B, and the random variable b, takes values 0 and 1, dependingon whether the n-th bit in the optical signal corresponds to a 0 or 1.
Figure 2.3: Two kinds of external modulators: (a) a LiNbO3 modulator in the Mach-Zehnder configuration; (b) an electro-absorption modulator with multi-quantum-well (MQW) absorbing layers.
where the phase f0 changes with time in the same fashion as the electrical bit stream.
commonly chosen to be 0 and p, andit can be
written in the form
where fp(t)represents the temporal profile and
the random variable bntakes values0and 1,
depending on whether the n-th bit in the optical
signal corresponds to a 0 or 1.
w0-Dwandw0+Dw, depending on whether a “0” or “1” bit is being transmitted. The shift Df = Dw/2pis called the frequency deviation.
where GA(t) = <A*(t)A(t+t)> is the autocorrelation function of A(t) and the angle brackets <.> denote ensemble averaging.
where the power spectral density Sb(w)is defined
where the correlation coefficient rm is defined as
the power spectral density can be written as
Figure 2.5: Power spectral density of (a) NRZ bit stream and (b) RZ bit stream with 50% duty cycle. Frequencies are normalized to the bit rate and the discrete part of the spectrum is shown by vertical arrows.
Which ones survive depends on the duty factor.
-Vp/4to +Vp/4 between “0” and “1” bits.
Figure 2.8: RZ pulses (a) created by a pulse carver driven by a sinusoidal clock (b) at the bit rate.
Figure 2.10: (a) Amplitude of CSRZ pulses for a 40-Gb/s bit stream and the (b) sinusoidal clock at half the bit rate used to generate it. Two pulses created during a single clock cycle are shifted in phase by p.
Figure 2.12: (a) The NRZ data; (b) its differentially encoded version; (c)original (solid) and delayed (dashed) phase profiles at the output coupler; (d) final RZ bit stream; and (e) phase variations across it.
more robust to the dispersive and nonlinear effects
for WDM systems transmitting multiple channels
shifting the phase of alternating pulses by p,in
addition to the phase and amplitude changes
associated with the transmitted data.
be used to create an optical bit stream in the RZ-
using a phase modulator driven by the differentially
encoded NRZ signal.
intensity since information is hidden in the phase of
the optical carrier as shown in the inset (a).
Figure 2.13: Schematic of an RZ-DPSK transmitter together with the receiver design. The insets (a) and (b) show how the electric field varies across two bits after first and second modulators, respectively.
whereDf(t) = f(t) -f(t - Tb)is the phase difference between the two neighboring bits.
Figure 2.21: Schematic view of a wavelength-selective transmitter designed with a WSL chip (left inset) in which the output of multiple DFB lasers is coupled into a single SOA through a MMI coupler. The right inset shows photograph of the butterfly package housing the transmitter.