# Wavelength Conversion by Degenerate Four Wave Mixing in Silicon Waveguide

**Topics:**Nonlinear optics, Optics, Four-wave mixing

**Pages:**7 (1852 words)

**Published:**November 24, 2012

Abstract - Four-wave mixing (FWM) is one of the interesting nonlinearities in optical systems. It is mainly used for wavelength conversion. To investigate the factors that affect the wavelength conversion efficiency, the evolution of Four-wave mixing (FWM) in silicon waveguide is modeled using matlab. The method of modeling is described. The effects of input pump power and waveguide length on the conversion efficiency are investigated. Results show that when propagating along a 0.048m silicon waveguide, both the input pump power and stroke power decreases, while anti-stroke power increases first and then decreases along the waveguide. It is also shown that for a 0.048 silicon waveguide, output anti-stroke power is the maximum when the input pump power is 3W. Also, when the input pump power is kept constant, there is a most effective waveguide length for wavelength conversion. Keywords -FWM; model; conversion efficiency;

input pump power; waveguide length

1 Introduction

Four-wave mixing (FWM) is an inter modulation phenomenon in optical systems, whereby interaction between three waves (two pump waves and a signal wave) produce a fourth wave (idler wave) [1]. This phenomenon can be used for all optical wavelength conversion (AOWC) and entangled photon generation [2, 3]. As extremely small core of si wires produce the nonlinear optical effect even under low optical power, Silicon is used as waveguide in our project for practical wavelength conversion by FWM process with longer waveguide lengths and smaller propagation loss[4].Factors that affect optical wavelength conversion are being studied to enhance the conversion efficiency. It has therefore become important to study FWM in silicon waveguide theoretically to increase the conversion efficiency for further experiment. In our project, FWM matlab to study the factors that affect the conversion efficiency. This paper discusses the factors that affect FWM’s conversion efficiency in silicon waveguide. Theoretical treatment is presented in section 2, where FWM in silicon waveguide is described. The method to model FWM in silicon waveguide using matlab is described in section 3. Results are shown in section 4. Results show that both the input pump power and the waveguide length play an important part in the FWM’s conversion efficiency.

2 THEORY

The FWM process involves the interaction of four waves (two Pump waves, one signal and one idler wave) as they propagates along a medium. In our project, silicon waveguide is used as the medium. The schematic diagram of FWM in silicon waveguide is shown in figure 1. Here, E represents the electric field of the respective waves and normalized such that power P=|E|^2. Subscripts ‘p’, ‘s’ and ‘a’ represent pump, signal and idler respectively. The superscript ‘f’ represents forward propagating waves.

[pic] Figure 1 Schematic diagram of FWM in silicon waveguide

.

3 METHODOLOGY

The evolution of the three waves along the silicon waveguide can be modeled by the following differential equations [1].

[pic][pic][pic][pic]

where Aeff is the waveguide effective core area, λ is the wavelength, α is the linear propagation loss and β is the TPA coefficient, σ is the FCA cross section and τeff is the effective carrier lifetime. h and c follow their usual physical meaning of Plank’s constant and free-space speed of light respectively. Δk denotes the linear phase mismatch and can be expressed as[pic]. γ is the nonlinear parameter assumed to be the same for three wavelengths and defined as

[pic]

where n2 is the nonlinear refractive index.

To simulate the evolution of the three waves along the silicon waveguide, the above four differential equation are solved simultaneously using Runge-Kutta-Fehlberg (RKF) method [2]. |Parameters |Input-Output simulation values | |α |100/4.34 m-1...

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