Investigation On All-optically Solving Differential Equations Based On Differentiator And Integrator

As one of the most important components of all-optical logical computing, all-opticallysolving differential equations has the potential applications in generating special waveformsand solving complex problems. Based on the available devices and platform in our lab,theoretical and experimental investigations are carried out with focus on all-optically solvingdifferential equations. Main contents are summarized as follows:At first, the research background and research significance of all-optically solvingdifferential equations are introduced along with the conclusion of existing schemes. Then asthe key devices in solving differential equation, all-optical differentiators and integrators,which are also utilized in the following schemes in this thesis, are introduced in details,including their definition, classification, operational principles, existing schemes andimportant applications.Secondly, a scheme of using optical feedback loop that is based on all-optical intensitydifferentiator to solve differential equations is proposed. Detailed operational principle ofthis structure is analyzed mathematically and physically, while the threshold condition of thecoefficient in the equation is also given. Then experimentally, a feedback loop that is basedon the an intensity differentiator composed of a semiconductor optical amplifier (SOA) andan optical filter is demonstrated, realizing solving constant-coefficient first-order lineardifferential equations with different coefficients when the constants meet the thresholdcondition.Finally, according to integral principle, another scheme directly employing microringresonators as optical filters to solve differential equations is proposed. Theoretical derivationof the transfer function of a single microring resonator is offerd, proving the feasibility ofusing the drop port of an add-drop microring resonator to solve constant-coefficientfirst-order linear differential equation. The constant in the equation is determined by thequality factor of the microring resonators. Based on this, the second-order linear differentialequations can be simply solved by cascading two microring resonators when the output ofthe first microring resonator serves as the input of the second microring resonator. In theexperiment, two microring resonators with different radii are fabricated. Based on vernier effect, perfectly matched spectral peaks are obtained. When using different ports of thecascaded microring resonators, first-or second-order differential equations can be solved.