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# The effects of FWM - PowerPoint PPT Presentation

Four-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.

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## PowerPoint Slideshow about ' The effects of FWM' - randall-rosario

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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

Example : 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 .

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

The efficiency η is given by

Where

fmn = fm - fn, (m,n = 1, 2, 3)

The following figure demonestrate the effect of FWM when Four signals with equally power 3mw traverses a fiber with the following specifications

Description

Values

Attenuation factor ()

0.2 dB/km

Effective fiber cross-sectional area ( Aeff )

6.4x10-11m2

Third order nonlinear susceptibility (1111)

6*10-15 cm3/erg

Chromatic dispersion (Dc)

1ps/nm.km

Dispersion slope ( )

.07ps/km.nm2

Refractive-index (n)

1.48

Length L

75 km

Wavelength (  )

1550 nm

The original and the newly generated signals after filtration as well as their corresponding power in dBm

Noise Contributions in Optical Systems and detection filtration as well as their corresponding power in dBm

I. Thermal Noise:

K is Boltzmann’s 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):

Where  is given by

The noise due to FWM phenomenon is given by [Reference]

The bit error rate (P [Reference]e) versus the quality factor Q

Now, 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