1. Nonlinear Mixing In Optical Signal Processing
Nourin Ahmed and Refat Kibria
Department of Computer Science and Engineering
Shahjalal University of Science & Technology, Sylhet,Bangladesh.
December, 2015
WIECON-ECE,Dhaka, Bangladesh.

2. WIECON-ECE,Dhaka, Bangladesh.
Overview
Why we need Photonic Signal Processing?
Nonlinear Mixing
Types of Nonlinear Mixing
Comparison
Future Work
December, 2015
WIECON-ECE,Dhaka, Bangladesh.

3. Need of Photonic Signal Processing[1]
Interaction between microwave and optical signals
Low-loss, wide bandwidth capability
Microwave techniques in optical transmitters and receivers
December, 2015
WIECON-ECE,Dhaka, Bangladesh.

4. WIECON-ECE,Dhaka, Bangladesh.
Nonlinear Mixing[2]
Intensity-dependent phenomena
Change in refractive index of the medium
Inelastic-scattering phenomenon
December, 2015
WIECON-ECE,Dhaka, Bangladesh.

5. WIECON-ECE,Dhaka, Bangladesh.
Types of Nonlinear Mixing[2][3]
Kerr effect
Self-Phase Modulation
Cross-Phase Modulation
Four Wave Mixing
Inelastic Scattering
Stimulated Raman scattering
Stimulated Brillouin scattering
December, 2015
WIECON-ECE,Dhaka, Bangladesh.

6. WIECON-ECE,Dhaka, Bangladesh.
Self Phase Modulation[4]
Light beam with high optical intensity changes its own phase by changing refractive index of the medium.
Figure 1: Instantaneous frequency of an initially unchanged pulse which has experienced SPM. The central part of the pulse exhibits an up-chirp.[5]
Up-chirp : instantaneous frequency rises with time.
December, 2015
WIECON-ECE,Dhaka, Bangladesh.

7. Self Phase Modulation Equation[6]
Phase change of an optical field is given by,
Φ = ͂nk0L
= (n+n2|E|2)k0L
k0 = 2π/λ,
L is the fiber length,
n = refractive index,
n2 = nonlinear refractive index,
|E|2 = Optical intensity inside the fiber,
The intensity-dependent nonlinear phase shift
ΦNL = n2k0L|E|2 is due to self-phase modulation.
December, 2015
WIECON-ECE,Dhaka, Bangladesh.

8. WIECON-ECE,Dhaka, Bangladesh.
Application of SPM
Amplitude Modulation[2]
All optical data regeneration technique utilizing spectral broadening characteristic[7]
Wavelength conversion[8]
December, 2015
WIECON-ECE,Dhaka, Bangladesh.

9. WIECON-ECE,Dhaka, Bangladesh.
Cross Phase Modulation[9]
Change in the optical phase of a light beam is caused by the interaction with another beam
Refractive index dependency on the intensity of all propagating light beams
Effect is twice as more effective than that of SPM
December, 2015
WIECON-ECE,Dhaka, Bangladesh.

10. Cross Phase Modulation Equation[2]
Nonlinear phase shift due to XPM effect,
Φ2NL = ω2zn2 / c (|E2|2 + 2|E1|2)
The factor 2 indicates that XPM effect is double in effectiveness compared to SPM.
December, 2015
WIECON-ECE,Dhaka, Bangladesh.

11. WIECON-ECE,Dhaka, Bangladesh.
Application of XPM
Amplitude Modulation[10]
Ultra-fast optical switching[11]
Wavelength conversion[12]
Pulse compression[13]
Pulse retiming[14]
December, 2015
WIECON-ECE,Dhaka, Bangladesh.

12. WIECON-ECE,Dhaka, Bangladesh.
Four Wave Mixing[3]
Three electromagnetic fields interacting to produce a fourth field.
At least two different frequency components propagate together in a nonlinear medium.
Figure 2 : FWM in Highly Nonlinear Fiber[15]
December, 2015
WIECON-ECE,Dhaka, Bangladesh.

13. Four Wave Mixing Equation[16]
Three waves with the frequencies ωp , ωq, and ωr generate a fourth wave at a frequency ωp ± ωq ± ωr

14. WIECON-ECE,Dhaka, Bangladesh.
Application of FWM
High speed wavelength conversion[17]
Convolution based photonic pattern recognition[18]
Remote transmitter correlation[19]
Optical subtraction[20]
Wavelength conversion in W-type soft glass fiber
Wavelength conversion in highly nonlinear crystal fiber
Wavelength conversion in HNLF
December, 2015
WIECON-ECE,Dhaka, Bangladesh.

15. WIECON-ECE,Dhaka, Bangladesh.
Comparison[21]
Single WDM channel – SPM
Multiple WDM channel – XPM & FWM
FWM more suitable
Table 1 : Performance Comparison of SPM,XPM and FWM
December, 2015
WIECON-ECE,Dhaka, Bangladesh.

16. WIECON-ECE,Dhaka, Bangladesh.
Future Work
Thorough comparison of the Kerr-Nonlinear effects
Graphical Representation
Signal Processing Application
December, 2015
WIECON-ECE,Dhaka, Bangladesh.

17. Thank You !

18. WIECON-ECE,Dhaka, Bangladesh.
References
[1] A. J. Seeds, "Microwave photonics," Microwave Theory and Techniques, IEEE Transactions vol. 50, pp
[2] R. Ramaswami and K. N. Sivarajan, "2 Chapter - Propagation of Signals in Optical Fiber," in Optical Networks (Second Edition), R. Ramaswami and K. N. Sivarajan, Eds., ed San Francisco: Morgan Kaufmann, 2002, pp
[3] K. Thyagarajan and A. Ghatak, "Nonlinear Effects in Optical Fibers," in Fiber Optic Essentials, ed: Wiley-IEEE Press, 2007, pp
[4] G. P. Agrawal, "Chapter 4 - Self-Phase Modulation," in Nonlinear Fiber Optics (Fourth Edition), G. P. Agrawal, Ed., ed San Diego: Academic Press, 2006, pp
[5] R. Paschotta, article on 'self-phase modulation' in the Encyclopedia of Laser Physics and Technology, accessed on
[6] S. P. Singh, "Nonlinear effects in optical fibers: origin, management and applications," Progress In Electromagnetics Research, vol. 23, pp , 2007.
[7] M. Matsumoto, "Analysis of optical regeneration utilizing self-phase modulation in a highly nonlinear fiber," Photonics Technology Letters, IEEE, vol. 14, pp , 2002.
December, 2015
WIECON-ECE,Dhaka, Bangladesh.

19. WIECON-ECE,Dhaka, Bangladesh.
References(Cont.)
[8] M. Chen, Tan Yan-lan, and Li Tian-song, "Wavelength conversion technique based on self phase modulation in highly nonlinear microstructure fiber," Optoelectronics Letters, vol. 6, pp , 2010/07/
[9] G. P. Agrawal, "Chapter 2 - Pulse Propagation in Fibers," in Nonlinear Fiber Optics (Fourth Edition), G. P. Agrawal, Ed., ed San Diego: Academic Press, 2006, pp
[10] S. Betti and M. Giaconi, "Analysis of the cross-phase modulation effect in WDM optical systems," Photonics Technology Letters, IEEE, vol. 13, pp , 2001.
[11] G. P. Agrawal, "Chapter 7 - Cross-Phase Modulation," in Nonlinear Fiber Optics (Fourth Edition), G. P. Agrawal, Ed., ed San Diego: Academic Press, 2006, pp
[12] M. Galili, L. K. Oxenlowe, H. C. Hansen Mulvad, A. T. Clausen, and P. Jeppesen, "Optical Wavelength Conversion by Cross-Phase Modulation of Data Signals up to 640 Gb/s," Selected Topics in Quantum Electronics, IEEE Journal of, vol. 14, pp , 2008.
[13] K.-t. Chan and W.-h. Cao, "Enhanced soliton-effect pulse compression by cross-phase modulation in optical fibers," Optics Communications, vol. 178, pp , 5/1/ 2000.
December, 2015
WIECON-ECE,Dhaka, Bangladesh.

20. WIECON-ECE,Dhaka, Bangladesh.
References(Cont.)
[14] K. S. Abedin, "Ultrafast pulse retiming by cross-phase modulation in an anomalous-dispersion polarization-maintaining fiber," Optics Letters, vol. 30, pp , 2005/11/15
2005.
[15] R. Kibria and M. Austin, "All Optical Signal-Processing Techniques Utilizing Four Wave Mixing," Photonics, vol. 2, p.200, 2015.
[16] Thiel, C.W. Four-Wave Mixing and Its Applications. Available online: (accessed on 25 October 2015).
[17] P. A. Andersen, T. Tokle, G. Yan, C. Peucheret, and P. Jeppesen,"Wavelength conversion of a 40-Gb/s RZ-DPSK signal using fourwave mixing in a dispersion-flattened highly nonlinear photonic crystal fiber," Photonics Technology Letters, IEEE, vol. 17, pp , 2005.
[18] R. Kibria, B. Lam Anh, and M. W. Austin, "Nonlinear mixing based photonic correlator," in Microwave Photonics (MWP), 2012 International Topical Meeting on, 2012, pp
[19] R. Kibria, B. Lam, A. Mitchell, and M. W. Austin, "HNLF-Based Photonic Pattern Recognition Using Remote Transmitter,"Photonics Technology Letters, IEEE, vol. 26, pp , 2014.
December, 2015
WIECON-ECE,Dhaka, Bangladesh.

21. WIECON-ECE,Dhaka, Bangladesh.
References(Cont.)
[20] R. Kibria, L. A. Bui, A. Mitchell, and M. W. Austin, "(IPC) A Photonic Correlation Scheme Using FWM With Phase Management to Achieve Optical Subtraction," Photonics Journal,IEEE, vol. 5, pp , 2013.
[21] L. J. B.K.Mishra, Karishma Mhatre, "Performance analysis of third order nonlinearities in optical communication system,"International Journal of Scientific & Engineering Research -
IJSER, vol. 4, Mar
December, 2015
WIECON-ECE,Dhaka, Bangladesh.