Brno University of Technology Institute of Physical Engineering

Brno University of Technology, Institute of Physical Engineering Simple numerical scheme for modelling of nonlinear pulse propagation in coupled microring resonators Anna Sterkhova, Jiří Petráček, Jaroslav Luksch ICTON 2009, Ponta Delgada

CONTENTS 1. Introduction 2. Formulation 3. Numerical examples 4. Conclusion

INTRODUCTION nonlinear resonant structures • TMM [Y. Dumeige, P. Féron: Dispersive tristability in microring resonators, Physical Review E, vol. 72, pp. 066609 -1 - 066609 -8, 2005] - numerical solution of nonlinear equation; - solution is in frequency domain only;

INTRODUCTION • FD-TD - high spatial resolution required => time-consuming calculation => advanced algorithms [A. Christ, J. Fröhlich, N. Kuster. : Correction of numerical phase velocity errors in nonuniform FDTD meshes, IEICE Trans. Commun. , vol. E 85 -B, pp. 2904 -2915, 2002] • …

CONTENTS 1. Introduction 2. Formulation 3. Numerical examples 4. Conclusion

FORMULATION input output A racetrack microring resonator side-coupled to a waveguide.

FORMULATION input output Propagation of optical pulses outside of the coupling region inside of the coupling region

FORMULATION input output Boundary conditions

FORMULATION Using explicit finite-difference scheme where , , ,

FORMULATION Von Neumann stability analysis applied: • Courant condition • Additional criterion , ,

FORMULATION 1) In typical calculations: 2) 2) , ,

CONTENTS 1. Introduction 2. Formulation 3. Numerical examples 4. Conclusion

NUMERICAL EXAMPLES input output

NUMERICAL EXAMPLES input output

CONTENTS 1. Introduction 2. Formulation 3. Numerical examples 4. Conclusion

CONCLUSIONS • a simple finite-difference scheme for solution of nonlinear coupled equations has been developed; • the technique has been applied to Kerr-nonlinear structure; • stability criterions have been presented; • comparison with the TMM has been presented; • easy inclusion of nonlinear effects.

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