Tailoring dispersion properties of photonic crystal waveguides by topology optimization

The paper describes a systematic method for the tailoring of dispersion properties of slab-based photonic crystal waveguides. The method is based on the topology optimization method which consists in repeated finite element frequency domain analyzes, analytical sensitivity analyzes and gradient based design updates. The goal of the optimization process is to come up with slow light, zero group velocity dispersion photonic waveguides or photonic waveguides with tailored dispersion properties for dispersion compensation purposes. Two examples concerning reproduction of a specific dispersion curve and design of a wide bandwidth, constant low group velocity waveguide demonstrate the efficiency of the method.

[1]  R. Cook,et al.  Concepts and Applications of Finite Element Analysis , 1974 .

[2]  K. Svanberg.  The method of moving asymptotes—a new method for structural optimization , 1987 .

[3]  M. Bendsøe,et al.  Generating optimal topologies in structural design using a homogenization method , 1988 .

[4]  J. Petersson,et al.  Numerical instabilities in topology optimization: A survey on procedures dealing with checkerboards, mesh-dependencies and local minima , 1998 .

[5]  Steven J. Cox,et al.  Maximizing Band Gaps in Two-Dimensional Photonic Crystals , 1999, SIAM J. Appl. Math..

[6]  Steven G. Johnson,et al.  Linear waveguides in photonic-crystal slabs , 2000 .

[7]  M. Notomi,et al.  Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs. , 2001, Physical review letters.

[8]  Steven G. Johnson,et al.  Photonic-crystal slow-light enhancement of nonlinear phase sensitivity , 2002 .

[9]  S Guenneau,et al.  Sonic band gaps in PCF preforms: enhancing the interaction of sound and light. , 2003, Optics express.

[10]  Ole Sigmund,et al.  Systematic design of phononic band–gap materials and structures by topology optimization , 2003, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[11]  Jakob S. Jensen,et al.  Topology optimization and fabrication of photonic crystal structures. , 2004, Optics express.

[12]  Manfred Eich,et al.  Zero dispersion at small group velocities in photonic crystal waveguides , 2004 .

[13]  Jakob S. Jensen,et al.  Systematic design of photonic crystal structures using topology optimization: Low-loss waveguide bends , 2004 .

[14]  Toshihiko Baba,et al.  Dispersion-controlled optical group delay device by chirped photonic crystal waveguides , 2004 .

[15]  Jakob S. Jensen,et al.  Topology optimization of photonic crystal structures: a high-bandwidth low-loss T-junction waveguide , 2005 .

[16]  P. I. Borel,et al.  Topology optimised broadband photonic crystal Y-splitter , 2005 .

[17]  C. Martijn de Sterke,et al.  Dispersionless slow light using gap solitons , 2006 .

[18]  Jacob Fage-Pedersen,et al.  Photonic crystal waveguides with semi-slow light and tailored dispersion properties. , 2006, Optics express.

[19]  T. Krauss,et al.  Flatband slow light in photonic crystals featuring spatial pulse compression and terahertz bandwidth. , 2007, Optics express.

[20]  O. Sigmund.  Morphology-based black and white filters for topology optimization , 2007 .

[21]  F. Xia,et al.  Ultracompact optical buffers on a silicon chip , 2007 .

[22]  Masaya Notomi,et al.  Trapping and delaying photons for one nanosecond in an ultrasmall high-Q photonic-crystal nanocavity , 2007 .