By Paul Urquhart
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Additional resources for Advances in Optical Amplifiers
In order to describe adequately XGM and XPM in QD SOA we should take into account the interaction of QDs with optical signals. The optical signal propagation in a QD SOA is described by the following truncated equations for the slowly varying CW and pulse signals photon densities and phases SCW,P = PCW,P / h¯ ω CW,P v g CW,P Ae f f and θ CW,P Agrawal (1989). ∂SCW,P (z, τ ) = ( gCW,P − αint ) SCW,P (z, τ ) (43) ∂z ∂θ CW,P α = − gCW,P (44) ∂z 2 Here PCW,P are the CW and pulse signal optical powers, respectively, Ae f f is the QD SOA effective cross-section, ω CW,P , v g CW,P are the CW and pulse signal group angular frequencies and velocities, respectively, gCW,P are the active medium (SOA) gains at the corresponding optical frequencies, and αint is the absorption coefﬁcient of the SOA material.
F. (1999). The Physics of Semiconductors with applications to optoelectronic devices. C. (2005). Principles of Lasers and Optics. J. L. (2006). Slow and fast light in semiconductor quantum-well and quantum-dot devices. Journal of Lightwave Technology, Vol. 24, No. B. K. (2002). All-optical logic XOR using differential scheme and Mach-Zender interferometer. Electronic Letters, Vol. 38, No. , Öhman, F. & Mørk, J. (2008). Theory of optical-ﬁltering enhanced slow and fast light effects in semiconductor optical waveguides.
The modal gain g p,s (ω ) is given by Uskov (2004) g p,s (ω ) = 2ΓNQ a dωF (ω ) σ (ω 0 ) (2 f − 1) (41) where the number l of QD layers is assumed to be l = 1, the conﬁnement factor Γ is assumed to be the same for both the signal and the pump waves, a is the mean size of QDs, σ (ω 0 ) is the cross section of interaction of photons of frequency ω 0 with carriers in QD at the transition frequency ω including the homogeneous broadening factor, F (ω ) is the distribution of the transition frequency in the QD ensemble which is assumed to be Gaussian Qasaimeh (2004), Uskov (2004).