Brno University of Technology, Institute of Physical Engineering

1
Brno University of Technology, Institute of
Physical Engineering
Simple numerical scheme for modelling of
nonlinear pulse propagation in coupled microring
resonators
Anna Sterkhova, Jirí Petrácek, Jaroslav Luksch
ICTON 2009, Ponta Delgada
2
CONTENTS
1. Introduction
2. Formulation
3. Numerical examples
4. Conclusion
3
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

4
INTRODUCTION

• FD-TD
• - high spatial resolution required
• gt time-consuming calculation
• gt 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
input
output
A racetrack microring resonator side-coupled to a
waveguide.
7
FORMULATION
input
output
Propagation of optical pulses
outside of the coupling region
inside of the coupling region
8
FORMULATION
input
output
Boundary conditions
9
FORMULATION
Using explicit finite-difference scheme
where
,
,
,
10
FORMULATION

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

11
FORMULATION

• In typical calculations
  , ,
• 2)

12
CONTENTS
1. Introduction
2. Formulation
3. Numerical examples
4. Conclusion
13
NUMERICAL EXAMPLES
input
output
14
NUMERICAL EXAMPLES
input
output
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!