Four Wave Mixing in Silicon Photonics

Part of the SpringerBriefs in Materials book series (BRIEFSMATERIALS)


In this chapter, Four Wave Mixing (FWM) and its types are elaborated in detail. It also describes the mathematical equations which provide basis for mathematical modeling and subsequent realization on various platforms. In order to achieve optical frequency shifting by FWM in silicon-on-insulator (SOI) waveguide, a nonlinear phenomenon has been presented. The FWM process in SOI waveguides is also discussed with an emphasis on the effects of two-photon absorption and the consequent free-carrier effects.


Four wave mixing Phase matching for four wave mixing 



Four wave mixing


Wavelength division multiplexing


Continuous wave


Self phase modulation


Cross phase modulation

List of Symbols

\( c \)

Speed of light

\( Tb/s \)

Terabits per second

\( Gb/s \)

Giga bits per second

\( n \)

Refractive Index



\( E \)

Electric field

\( \varepsilon_{0} \)

Vacuum permittivity

\( P_{T} \)

Transmitted power







\( P_{0} \)

Output power

\( \mu m \)

Micro meter

\( \Updelta \)

Index contrast

\( 1D \)

One dimentional

\( 2D \)

Two dimentional

\( 3D \)

Three dimentional



\( A_{\text{eff}} \)

Effective area






Nano meter

\( P_{\text{NL}} \)

Nonlinear polarization

\( \Upomega_{s} \)

Frequency shift

\( K \)

Propagation constant


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Copyright information

© The Author(s) 2013

Authors and Affiliations

  1. 1.HITEC UniversityTaxilaPakistan
  2. 2.School of Electrical and Electronic EngineeringNanyang Technological UniversitySingaporeSingapore
  3. 3.HITEC UniversityTaxilaPakistan

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