Efficient numerical schemes and nonlinear aspects beyond SVEA in optics (TWI.4813)

In this project we want to contribute with advanced numerical and mathematical methods to the insight in various optical effects that are important for applications in telecommunications, light switching, sensors and light sources. For such applications chips and fibres are used; chips with wave guides for switching or (de) multiplexing of light (separation or combination of light of different wave lengths) or for the generation of second harmonic waves with double frequency, and fibres for the propagation of light over loong distances.
For the actual design and fabrication of devices with such aims, the understanding and efficient calculation of wave propagation through materials of different properties is required. Therefore, part of the project is aimed to improve existing numerical codes for beam and pulse prpagation through (linear) wave guides; based on experience in a previous project, the variational structure of the underlying equations will be exploited to obtain numerical codes that can calculate for wave guides the stepwise changing index of refraction very accurately and efficiently. Effects of nonlinear materials are used abundantly: second harmonic generation to produce light of smaller wave length and third order nonlinearity for efficient propagation through long fibres. The study of such effects is commonly restricted to models in which an important simplification is assumed, namely that the amplitude of the envelope changes slowly ( in time, in space), the socalled SVEA-assumption. For some modern applications this assumption is not justified anumore, and a better desciption is desired. We aim to contributeby studying these effects for the complete nonlinear Maxwell equations; advanced mathematical methods, based on an extension of the variational structure that is used for the numerical codes, are required for such a study.

Een basis is gelegd voor het toepassen van Finite Element Methoden, via een variationele formulering, in de numerieke behandeling van optica problemen. Een veelbelovende holle, geïntegreerd-optische golfgeleider is ontworpen, met aanzienlijk betere eigenschappen dan tot nu toe bekende golfgeleiders van dit type. De kennis zou door zowel C2V BV als Phoenix BV kunnen worden ingezet in hun softwareproducten. Recent is een overeenkomst gesloten met het software bedrijf C2V waarin de property rights worden overgedragen van software ontwikkeld in een EU-project. Dit is mede mogelijk gemaakt door de infrastructuur van projecten als dit STW-project.

Er zijn drie bedrijven en twee andere universiteiten bij dit project betrokken.

Prof.dr.ir. E.W.C. van Groesen
Universiteit Twente
Fac. Toegepaste Wiskunde
Vakgroep Toegepaste Analyse
Postbus 217
7500 AE Enschede