## Abstract

A scheme to realize all-optical Boolean logic functions AND, XOR and NOT using semiconductor optical amplifiers with quantum-dot active layers is studied. nonlinear dynamics including carrier heating and spectral hole-burning are taken into account together with the rate equations scheme. Results show with QD excited state and wetting layer serving as dual-reservoir of carriers, as well as the ultra fast carrier relaxation of the QD device, this scheme is suitable for high speed Boolean logic operations. Logic operation can be carried out up to speed of 250 Gb/s.

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### Equations (6)

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(1)
$$\frac{dw}{dt}=\frac{I}{eV{N}_{wm}}-\frac{w}{{\tau}_{wr}}-\frac{w}{{\tau}_{w-e}}(1-h)+\frac{{N}_{esm}}{{N}_{wm}}\frac{h}{{\tau}_{e-w}}(1-w)$$
(2)
$$\frac{dh}{dt}=-\frac{h}{{\tau}_{esr}}+\frac{{N}_{wm}}{{N}_{esm}}\frac{w}{{\tau}_{w-e}}(1-h)-\frac{h}{{\tau}_{e-w}}(1-w)+\frac{{N}_{gsm}}{{N}_{esm}}\frac{f}{{\tau}_{g-e}}(1-h)-\frac{h}{{\tau}_{e-g}}(1-f)$$
(3)
$$\frac{df}{dt}=-\frac{f}{{\tau}_{gsr}}-\frac{f}{{\tau}_{g-e}}(1-h)+\frac{{N}_{esm}}{{N}_{gsm}}\frac{h}{{\tau}_{e-g}}(1-f)-\frac{{\Gamma}_{d}}{{A}_{d}}a(2f-1)\frac{1}{{N}_{gsm}}\frac{S(t)}{\hslash \omega}$$
(4)
$$g(t)=\frac{a(N-{N}_{t})}{1+({\epsilon}_{CH}+{\epsilon}_{SHB})S(t)}$$
(5)
$$\varphi (t)=-\frac{1}{2}[\alpha {G}_{l}(t)+{\alpha}_{CH}\Delta {G}_{CH}(t)]$$
(6)
$${P}_{out}(t)=\frac{{P}_{cb}(t)}{4}[{G}_{1}(t)+{G}_{2}(t)-2\sqrt{{G}_{1}(t){G}_{2}(t)})\mathrm{cos}({\varphi}_{1}(t)-{\varphi}_{2}(t))]$$