Entwurf und Optimierung von 1D-Photonischen Kristallen zur Dispersionskompensation (English shop)

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Today, most data transmission takes place over standard single-mode optical fibres (SMMF). Using modulated lasers, data can be transported at transmission rates of more than 160 Gbit/s in a single channel and of several Tbit/s in multichannel operation. Once the transmission speed exceeds the 10 Gbit/s limit, chromatic dispersion (CD) plays a major role, since it causes a temporal broadening of the short pulses. If pulses are sent at short time intervals, the broadened pulses at the output may overlap to such an extent that the individual pulses can no longer be correctly detected. If data are to be transmitted at high rates, the pulses must not arrive distorted at their destination. For this reason, dispersion compensation has developed into one of the most important research fields in recent years.

The present work deals with the design and optimisation of 1D photonic crystals (1D-PhCs) for the compensation of CD. To this end, the chromatic dispersion and the transmission of such structures are first calculated on the basis of the transfer function determined by means of the transfer matrix method. By introducing defect layers into the otherwise homogeneous 1D-PhC structure and subsequently optimising the overall structure, targeted passbands can be created within the original stopbands. In the vicinity of an optical stopband there is a strong frequency-dependent difference between phase and group velocity in the direction of propagation. This effect was demonstrated at the end of the 1970s and can be used for dispersion compensation.

The designed PhCs are intended to produce either desired profiles of the CD or of the transmission behaviour. In order to determine the best possible structures that permit this, a hybrid optimisation procedure was implemented that systematically varies the parameters of the structures, such as refractive index and thickness. This procedure consists of both a stochastic and a deterministic optimisation algorithm. The genetic algorithm was chosen as the stochastic algorithm. For the optimisation with the deterministic algorithm, a function based on the subspace trust-region method was used. Both algorithms were applied alternately. In this way, the probability of finding an optimal structure was drastically increased.

The 1D-PhC structures obtained using the hybrid algorithm show good agreement with the target values at the wavelengths considered in the optimisation. Thus, for example, structures could be found that exhibit a linear dispersion profile or that compensate the dispersion of a 10 km long SMMF. These structures are characterised by an overall length ranging from a few micrometres up to four millimetres. In order to compensate the dispersion of 100 km long SMMFs, not only 1D-PhCs provided with defect layers were optimised, but also 1D-PhC tapers and ring resonators with integrated 1D-PhCs were investigated. The integration of a 1D-PhC into a ring resonator allowed the generation of periodic CD profiles. Such structures can therefore be used for a selective compensation of the CD.

For demultiplexing in UDWDM networks, several extremely narrowband filters connected in series are used. With the algorithm implemented in this work, structures with corresponding transmission profiles as well as 1D-PhCs that can be used as mirrors can be optimised.