1. 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 generates one or more new channels (or harmonics). For instance, when three waves at frequencies f i, f j, and f k traverse a fiber they generate another signal located at The effects of FWM

2. Fiber 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.

3. In general the number of newly generated signals is given by

4. Where P i, P j, P k are the input power of the channels D is the degeneracy factor 3 and 6 for two-tone and 6 for three-tone product Where A eff is the effective cross-sectional area and L eff is the effective length of the fiber given by The power of of newly generated signals is given by And  is given by

5. The nonlinear susceptibility  1111 The efficiency η is given by Where  f mn =  f m - f n , (m,n = 1, 2, 3)

6. The efficiency curve versus the channel separation in (GHz)

7. The following figure demonestrate the effect of FWM when Four signals with equally power 3mw traverses a fiber with the following specifications Table 3.xxxxxx: Fiber parameters. DescriptionValues Attenuation factor (  ) 0.2 dB/km Effective fiber cross-sectional area ( A eff )6.4x10 -11 m 2 Third order nonlinear susceptibility (  1111 ) 6*10 -15 cm 3 /erg Chromatic dispersion (D c )1ps/nm.km Dispersion slope ( ).07ps/km.nm 2 Refractive-index (n)1.48 Length L75 km Wavelength ( ) 1550 nm

8. The Original input signals

9. The newly generated signals and their corresponding power in dBm

10. The newly generated signals and their corresponding power in dBm after filtration

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

12. Noise Contributions in Optical Systems and detection 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):

13. The Optical Signal- to- Noise Ratio (OSNR) is given by [Reference] Where  is given by The noise due to FWM phenomenon is given by [Reference]

14. The bit error rate (P e ) versus the quality factor Q

15. Now, the question coming at this juncture how to include the effect of FWM in the fiber metrics I.Based on the system design target, which is mainly the BER, Q (or OSNR) can be evaluated from the BER curve. II.The noise in the system can also be calculated (mainly N th, N sh, and N FWM ). III.From step I and II, the required received power (P rec ) thus can be calculated. IV.Using the Power budget equation, the maximum fiber length ( L max in km) can be calculated as follow