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

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

3. INTRODUCTION 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; nonlinear resonant structures

4. 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. E85-B, pp. 2904-2915, 2002] …

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

6. FORMULATION inputoutput A racetrack microring resonator side-coupled to a waveguide.

7. FORMULATION outside of the coupling region inside of the coupling region Propagation of optical pulses inputoutput

8. FORMULATION Boundary conditions inputoutput

9. FORMULATION Using explicit finite-difference scheme where,,,

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

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

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

13. NUMERICAL EXAMPLES inputoutput

14. NUMERICAL EXAMPLES inputoutput

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

16. 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.

17. Thank you for your attention!