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Wide-angle beam propagation methods using complex Jacobi iteration

Main Researcher: Khai Quang Le

The development of three-dimensional (3D) waveguide structures for chip scale planar lightwave circuits (PLCs) is hampered by the lack of efficient 3D wide-angle beam propagation methods (WA-BPMs). To overcome this problem, we propose to use the recently introduced complex Jacobi iterative (CJI) method for dealing with 3D propagation equation. This method numerically integrates the laws of Maxwell in the frequency domain. It accomplishes this with an iterative process. Each iteration the calculated fields are further refined until a desired relative error is achieved. The contour of Gaussian beam propagating in loss media calculated by CJI method is depicted in Fig. 1.

Intensity contour of Gaussian beam propagating in loss media.

At each propagation step, the beam propagation equation is recast in terms of Helmholtz equation with source term, which is solved quickly and accurately by CJI method.

TE fundamental mode propagating in slab waveguide

Through a performance comparison of the traditional direct matrix inversion (DMI) and this new iterative method for WA-BPMs it is convincingly demonstrated that the CJI method is very competitive for demanding problems.

Other people involved:

Khai Quang Le

PhD thesises

Peter Vandersteegen, Modellering van het optische gedrag in organische LEDs voor verlichting, Modeling of the Optical Behavior of Organic LEDs for illumination, (11/2008)
Khai Quang Le, Naar efficiente driedimensionale wijdhoek-bundelpropagatiemethodes en theoretische studie van nanostructuren voor verbeterde prestaties van fotonische componenten, Towards Efficient Three-Dimensional Wide-Angle Beam Propagation Methods and Theoretical Study of Nanostructures for Enhanced Performance of Photonic Devices, (6/2011)
Publications
International Journals

A. Hossain Khan, V. Pinchetti, I. Tanghe, Z. Dang, B. Martin-Garcia, Z. Hens, D. Van Thourhout, P. Geiregat, S. Brovelli, I. Moreels, Tunable and Efficient Red to Near-Infrared Photoluminescence by Synergistic Exploitation of Core and Surface Silver Doping of CdSe Nanoplatelets, Chemistry of Materials, 31(4), Belgium, p.1450-1459 doi:10.1021/acs.chemmater.8b05334 (2019)  .
K. Quang Le, P. Bienstman, Padé Approximate Solution for Wave Propagation in Graded-Index Metamaterials, Journal of Optics, 13, p.024015 doi:10.1088/2040-8978/13/2/024015 (2010)  .
K. Quang Le, P. Bienstman, The complex Jacobi iterative method for non-paraxial beam propagation in nonlinear optical waveguides, Optical and Quantum Electronics, 41(9), p.705-709 doi:10.1007/s11082-010-9382-2 (2010)  .
K. Quang Le, P. Bienstman, Three-dimensional higher-order Padé approximant-based wide-angle beam propagation method using complex Jacobi iteration, Electronics Letters, 46(3), p.231-233 doi:10.1049/el.2010.3204 (2010)  .
K. Quang Le, P. Bienstman, A stable complex Jacobi iterative solution of 3D semivectorial wide-angle beam propagation using the iterated Crank-Nicholson method, Optical and Quantum Electronics, 41(215-221), doi:10.1007/s11082-009-9346-6 (2009)  .
K. Quang Le, T. Benson, P. Bienstman, Application of modified Padé approximant operators to time-domain beam propagation methods, Journal of Optical Society of America B, 26(12), p.2285-2289 doi:10.1364/josab.26.002285 (2009)  .
K. Quang Le, P. Bienstman, Fast three-dimensional generalized rectangular wide-angle BPM using complex Jacobi iteration, Journal of Optical Society of America B, 26(7), p.1469-1472 doi:10.1364/josab.26.001469 (2009)  .
K. Quang Le, Complex Padé approximant operators for wide-angle beam propagation, Optics Communications, 282(7), p.1252-1254 doi:10.1016/j.optcom.2008.12.014 (2009)  .
K. Quang Le, P. Bienstman, Wide-angle beam propagation method without using slowly varying envelope approximation, Journal of Optical Society of America B, 26(2), p.353-356 doi:10.1364/josab.26.000353 (2009)  .
K. Quang Le, R. Godoy-Rubio, P. Bienstman, G. R. Hadley, The complex Jacobi iterative method for three-dimensional wide-angle beam propagation: erratum, Optics Express, 16(26), p.21942-21942 doi:10.1364/oe.16.021942 (2008)  .
K. Quang Le, R. Godoy-Rubio, P. Bienstman, G. Ronald Hadley, The complex Jacobi iterative method for three-dimensional wide-angle beam propagation, Optics Express, 16(21), p.17021-17030 doi:10.1364/oe.16.017021 (2008)  .
P. Vandersteegen, B. Maes, P. Bienstman, R. Baets, Using the complex Jacobi method to simulate Kerr non-linear photonic components, Optical and Quantum Electronics, 38(1-3), p.35--44 doi:10.1007/s11082-006-0021-x (2006)  .

International Conferences

K. Quang Le, T. Benson, P. Bienstman, Modified Padé Approximant Operators for Efficient Time-Domain Beam Propagators, 19th International Workshop on Optical Waveguide Theory and Numerical Modelling, United Kingdom, (2010)  .
K. Quang Le, H.G. Dantanarayana, E.A. Romanova, T. Benson, P. Bienstman, Comparative Assessment of Time-Domain Models of Nonlinear Optical Propagation, 3rd ICTON-MW, France, doi:10.1109/ictonmw.2009.5385628 (2009)  .
K. Quang Le, P. Bienstman, Non-paraxial beam propagation in nonlinear optical waveguides using complex Jacobi iteration, 9th International Conference on Numerical Simulation of Optoelectronic Devices, South Korea, doi:10.1109/nusod.2009.5297205 (2009)  .
K. Quang Le, P. Bienstman, G. Ronald Hadley, Fast wide-angle BPMs using complex Jacobi iteration, XVIII th International Workshop on Optical Waveguide Theory and Numerical Modelling, Germany, (2009)  .
K. Quang Le, R. Godoy-Rubio, P. Bienstman, G. R. Hadley, A three-dimensional non-paraxial beam propagation method using complex Jacobi iteration, 13th Annual Symposium of the IEEE/LEOS Benelux Chapter, Netherlands, p.221-224 (2008)  .
K. Quang Le, R. Godoy-Rubio, P. Bienstman, G. Ronald Hadley, A Three-Dimensional Non-Paraxial Beam Propagation Method using Complex Jacobi Iteration, International workshop on photonics and applications, Vietnam, (2008)  .
P. Bienstman, P. Vandersteegen, B. Maes, R. Baets, Modeling methods for high-index contrast linear and non-linear nanophotonics, NUSOD 2006 (Numerical Simulation of Optoelectronics Devices) (invited), Singapore, doi:10.1109/nusod.2006.306763 (2006)  .
P. Vandersteegen, P. Bienstman, R. Baets, Extensions of the Complex Jacobi Iteration to simulate Photonic Wavelength Scale Components, European Conference on Computational Fluid Dynamics (ECCOMAS CFD 2006), Netherlands, (2006)  .
P. Vandersteegen, P. Bienstman, R. Baets, A. Dewandre, M. Haelterman, Simulations of Kerr based non linear optical components with the Complex Jacobi iteration, ICTON (COSTP11 training school), p.We.P.14 doi:10.1109/icton.2006.248459 (2006)  .
P. Vandersteegen, B. Maes, P. Bienstman, R. Baets, Simulating non-linear third order effects with the adapted complex Jacobi iteration method, 2005 IEEE/LEOS Symposium Benelux Chapter Proceedings, Belgium, p.193-196 (2005)  .
P. Bienstman, B. Maes, P. Vandersteegen, R. Baets, Modelling of non-linear nanophotonic devices, OWTNM (invited), Australia, p.32 (2005)  .
P. Vandersteegen, P. Bienstman, R. Baets, Extending the Complex Jacobi Iteration method to simulate Kerr non-linear effects, OWTNM 2005, France, (2005)  .
National Conferences

K. Quang Le, P. Bienstman, Modified Padé-Approximant-Based Wide-Angle Beam Propagators, 10th FirW PhD Symposium, Belgium, (2009)  .
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