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Modeling Kerr non-linear devices

Main Researcher: Bjorn Maes

Non-linear materials are actively researched for designing all-optical devices. The Kerr effect is a promising nonlinearity as it means a near-instantaneous intensity dependent refractive index change. Because of the weakness of this effect strong field confinements are necessary, which are now possible in advanced structures such as photonic crystals or photonic wires. To simulate these devices efficient and accurate new methods are needed.
We developed an extension to the linear mode expansion method. In this way we inherit many of the benefits of the original method, such as advanced boundary conditions, rigorousness, small computational domain, etc.
Our method consists of an iteration of linear calculations, using CAMFR. The non-linear material is divided in a grid and each small rectangle is assigned its refractive index during iteration.

Example of a spatial grid.
Example of a spatial grid.

Starting from the linear index distribution, a guess or a previously calculated solution, we perform a linear eigenmode simulation. This gives us the intensities in the rectangles with which we can update the indexes using the Kerr constitutive relation of the material. If the new index distribution is approximately equal to the old one, we have converged to a solution of the full non-linear problem.
We have implemented this algorithm for finite and periodic infinite structures. Calculations are especially fast for structures with small non-linear sections, as the linear parts only have to be simulated once.

A nonlinear photonic crystal switch (Soljacic et al, 2002).
A nonlinear photonic crystal switch (Soljacic et al, 2002).

As mode expansion is a frequency domain technique we immediately obtain steady-state solutions. For this purpose time domain methods such as Finite-Difference Time-Domain (FDTD) require the simulation of long pulses.
We employ modes propagating in both directions, thus reflection and interference effects can be observed. This feedback in combination with nonlinearity can give rise to bistability, which means two possible outputs for one input. Our algorithm is able to track both branches of such bistable solution curves. FDTD needs a strong input excitation pulse before the main pulse to scan the upper branch, which complicates matters.

Bistable solution of the photonic crystal switch.
Bistable solution of the photonic crystal switch.

Other people involved:

PhD thesises

Publications

    International Journals

  1. M. Fiers, T. Van Vaerenbergh, K. Caluwaerts, D. Vande Ginste, B. Schrauwen, J. Dambre, P. Bienstman, Time-domain and frequency-domain modeling of nonlinear optical components on circuit-level using a node-based approach, Journal of the Optical Society of America B, 29(5), p.896900 (2012)  Download this Publication (482KB).
  2. A. Omari, I. Moreels, F. Masia, W. Langbein, P. Borri, D. Van Thourhout, P. Kockaert, Z. Hens, Role of interband and photoinduced absorption in the nonlinear refraction and absorption of resonantly excited PbS quantum dots around 1550 nm, Physical Review B, 85(115318), (2012)  Download this Publication (770KB).
  3. Zhiyong Xu, B. Maes, Xunya Jiang, John D. Joannopoulos, Lluis Torner, Marin Soljacic, Nonlinear photonic crystals near the supercollimation point, Optics Letters, 33(15), p.1762 (2008)  Download this Publication (242KB).
  4. B. Maes, P. Bienstman, R. Baets, Bobo Hu, Phillip Sewell, Trevor Benson, Modeling comparison of second-harmonic generation, Optical and Quantum Electronics, 40(1), p.13-22 (2008)  Download this Publication (402KB).
  5. 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 (2006)  Download this Publication (154KB).
  6. G. Van der Sande, B. Maes, P. Bienstman, J. Danckaert, R. Baets, I. Veretennicoff, Nonlinear lattice model for spatially guided solitons in nonlinear photonic crystals, Optics Express, 13(5), p.1544-1554 (2005)  Download this Publication (125KB).
  7. B. Maes, P. Bienstman, R. Baets, Bloch modes and self-localized waveguides in nonlinear photonic crystals, J. Opt. Soc. Am. B, 22(3), p.613-619 (2005)  Download this Publication (538KB).
      International Conferences

    1. A. Omari, I. Moreels, F. Masia, W. Langbein, D. Van Thourhout, P. Kockaert, Z. Hens, Nonlinear optical properties due to inter and intraband transitions in PbS quantum dots, 7th International Conference on Quantum Dots, United States, (2012)  Download this Publication (254KB).
    2. B. Kuyken, S. Clemmen, S. Selvaraja, W. Bogaerts, S. Massar, R. Baets, G. Roelkens, Self phase modulation in highly nonlinear hydrogenated amorphous silicon, Photonics Society Annual Meeting, United States, (2010)  Download this Publication (124KB).
    3. B. Maes, K. Huybrechts, G. Morthier, P. Bienstman, R. Baets, Switching with Coupled Photonic Crystal Cavities, SIAM Conference on Nonlinear Waves and Coherent Structures (invited), Italy, (2008)  Download this Publication (599KB).
    4. 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, (2006)  Download this Publication (76KB).
    5. 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)  Download this Publication (395KB).
    6. 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 (2006)  Download this Publication (513KB).
    7. 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)  Download this Publication (370KB).
    8. G. Van der Sande, B. Maes, P. Bienstman, J. Danckaert, R. Baets, I. Veretennicoff, Nonlinear lattice model for self-localized waveguides in nonlinear photonic crystals, SPIE International Congress on Optics and Optoelectronics, Poland, p.5949-22 (2005).
    9. P. Bienstman, B. Maes, P. Vandersteegen, R. Baets, Modelling of non-linear nanophotonic devices, OWTNM (invited), Australia, p.32 (2005)  Download this Publication (498KB).
    10. B. Maes, G. Van der Sande, P. Bienstman, J. Danckaert, R. Baets, I. Veretennicoff, Self-localized Waveguides in Nonlinear Photonic Crystals, IPRA, United States, p.ITuB2 (2005)  Download this Publication (608KB).
    11. P. Vandersteegen, P. Bienstman, R. Baets, Extending the Complex Jacobi Iteration method to simulate Kerr non-linear effects, OWTNM 2005, France, (2005)  Download this Publication (131KB).
    12. B. Maes, P. Bienstman, R. Baets, Bloch modes and self-localized waveguides in nonlinear photonic crystals, IEEE/Leos Benelux Annual Symposium 2003, Netherlands, p.233-236 (2003).
    13. B. Maes, P. Bienstman, R. Baets, Rigorous modelling of non-linear photonic components with mode expansion and spatial index discretisation, IPR, United States, p.105-107 (2003).
    14. B. Maes, P. Bienstman, R. Baets, Rigorous modelling of non-linear wavelength-scale structures with mode expansion and spatial index discretisation, OWTNM 2003 (Optical Waveguide Theory and Numerical Modelling), 11, Czech Republic, p.98 (2003).
    15. B. Maes, Modelling of non-linear effects in a mode expansion context, Workshop 2D photonic crystals, Switzerland, p.I-05 (2002).

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