Title: Definition: Nonlinear effect that occurs in nonlinear optical materials such as photonic switch, optical fiber cable, etc. This interaction between waves leads to interaction between channels
1Four-Wave Mixing (FWM)
Definition Nonlinear effect that occurs in
nonlinear optical materials such as
photonic switch, optical fiber cable,
etc. This interaction between waves leads to
interaction between channels
The effects of FWM
generates one or more new channels (or
harmonics). For instance, when three waves at
frequencies fi, fj, and fk traverse a fiber they
generate another signal located at
2Example The input is two signals located at ? 1
and ? 2 traverse a fiber of length (L) and the
output is four different signals located at ?1, ?
2, 2?1 - ?2, and 2?2 - ?1 .
3In general the number of newly generated signals
is given by
4The power of of newly generated signals is given
by
Where Pi , Pj , Pk are the input power of the
channels
D is the degeneracy factor 3 and 6 for two-tone
and 6 for three-tone product
And ? is given by
Where Aeff is the effective cross-sectional area
and Leff is the effective length of the fiber
given by
5The nonlinear susceptibility ?1111
The efficiency ? is given by
Where ?fmn ?fm - fn?, (m,n 1, 2, 3)
6The efficiency curve versus the channel
separation in (GHz)
7Table 3.xxxxxx Fiber parameters.
The following figure demonestrate the effect of
FWM when Four signals with equally power 3mw
traverses a fiber with the following
specifications
8The Original input signals
9The newly generated signals and their
corresponding power in dBm
10The newly generated signals and their
corresponding power in dBm after filtration
11The original and the newly generated signals
after filtration as well as their corresponding
power in dBm
12Noise Contributions in Optical Systems and
detection
I. Thermal Noise
K is Boltzmanns constant, T is the absolute
temperature in Kelven, B is the receiver
electrical bandwidth and R is the load resistance
value.
II. Shot Noise
Where q is the electronic charge, I is the mean
optically generated current and Id is the photo
detector dark current
III. Relative Intensity Noise (RIN)
13The Optical Signal- to- Noise Ratio (OSNR) is
given by Reference
Where ? is given by
The noise due to FWM phenomenon is given by
Reference
14The bit error rate (Pe) versus the quality factor
Q
15Now, the question coming at this juncture how to
include the effect of FWM in the fiber metrics
- Based on the system design target, which is
mainly the BER, Q (or OSNR) can be evaluated
from the BER curve. - The noise in the system can also be calculated
(mainly Nth , Nsh , and NFWM). - From step I and II, the required received power
(Prec) thus can be calculated. - Using the Power budget equation, the maximum
fiber length ( Lmax in km) can be calculated as
follow