[{"type":"speech","title":"Integrated photonic crystal circuits: comparison of FDTD simulations and scattering matrix calculations based on Wannier functions","issued":{"date-parts":[["2006"]]},"author":[{"family":"Zarbakhsh","given":"J."},{"family":"Hermann","given":"D."},{"family":"Mingaleev","given":"S."},{"family":"Hingerl","given":"K."},{"family":"Busch","given":"K."}],"note":"Fr\u00fchjahrstagung des Arbeitskreises Atome, Molek\u00fcle, Quantenoptik und Plasmen (AMOP) der DPG, Frankfurt, 13.-17.M\u00e4rz 2006 Verhandlungen der Deutschen Physikalischen Gesellschaft, R.6, B.41(2006) Q 25.3","abstract":"\u00a8\nQ 25.1 Di 13:45 HI\nResonant modes and lasing in deterministically aperiodic\nnanopillar arrays \u2014 \u2022Sergei V. Zhukovsky, Dmitry N.\nChigrin, and Johann Kroha \u2014 Physikalisches Institut, Universit\u00a8t\nBonn, Nussallee 12, 53115 Bonn, Germany\nAs shown previously [1], periodic one-dimensional nanopillar arrays can\nfunction as waveguides. We consider an analogous system of nanopillars\narranged in a deterministically aperiodic (DA) fashion, namely, according\nto quasiperiodic Fibonacci and fractal Cantor sequences [2]. It has been\nshown that such a nanopillar structure can exhibit both waveguide-like\nand resonant properties. The resonant modes present in a fractal nanopillar structure are highly localized and possess a Q-factor comparable with\nthe resonant mode of a point defect embedded in a periodic waveguide. At\nthe same time, the modes in a DA waveguide show much better coupling\nwith a coaxially placed terminal allowing energy exchange of a resonator\nwith other optical components. The coupling is especially increased when\nthe symmetry of a DA structure is slightly broken, which does not diminish the Q-factor or mode localization. It can be shown that owing to\nincreased coupling, such a resonant system can be used as a microlaser\nwhen nanopillars contain an active medium.\n[1] D. N. Chigrin, A. V. Lavrinenko, C. M. Sotomayor-Torres, Opt. Express 12, 617 (2004).\n[2] A. V. Lavrinenko, S. V. Zhukovsky, K. S. Sandomirskii, S. V. Gaponenko, Phys. Rev. E 65, 036621 (2002).\nQ 25.2 Di 14:00 HI\nPhotonic crystal cavities with high quality factors on GaAs\nmembranes \u2014 \u2022Thomas S\u00a8nner, Rafael Herrmann, Andreas\nL\u00a8 ffler, Johann-Peter Reithmaier, Martin Kamp, and Alfred\nmany\nCavities in photonic crystals (PhCs) can con\ufb01ne light in mode volumes\nof less than one cubic wavelength with quality factors of several hundred\nthousand. These properties make PhC cavities very promising candidates\nfor studies of cavity QED and non-linear optics.\nWe have investigated PhC cavities in GaAs membranes. The layer\nstructure consists of a 250 nm thick GaAs layer on top of a 2\u00b5m thick\nAl0.6 Ga0.4 As sacri\ufb01cial layer. The geometry of the cavity is based on a\nPhC heterostructure [1]. This design uses a variation of the lattice period along a waveguide de\ufb01ned by one missing row of holes (W1) in a\nhexagonal PhC lattice. The light is con\ufb01ned in a short waveguide section\nwith 410 nm period, sandwiched between \u2019mirror\u2019 waveguides with 400\nnm lattice period. The \u2019mirror\u2019 waveguides have a stopgap at the wavelength of the cavity resonance and therefore act as re\ufb02ectors. An access\nguide connects the cavity to the facets of the sample. The PhC pattern\nis \ufb01rst etched into the GaAs layer, which is then undercut by selective\nwet etching of the sacri\ufb01cial layer.\nTransmission measurements were performed using a tunable laser\nsource at 1.5\u00b5m We have observed cavity resonances with quality factors in excess of 100000.\n[1] B.S. Song et al., Nature Materials 4, 207 (2005)\nQ 25.3 Di 14:15 HI\nWannier Functions \u2014 \u2022Javad Zarbakhsh1 , Daniel Hermann2,3 ,\n1\nf\u00a8r Halbleiter und Festk\u00a8rperphysik, Johannes-Kepler-Universit\u00a8t Linz\n\u2014 2 Institut f\u00a8r Theoretische Festk\u00a8rperphysik, Universit\u00a8t Karlsruhe\n(CFN), Universit\u00a8t Karlsruhe \u2014 4 Institut f\u00a8r Nanotechnologie,\nWe present a detailed comparison between Finite Di\ufb00erence Time Domain (FDTD) simulations and Scattering Matrix calculations based on\nWannier functions [1,2] for the characterization of large-scale photonic\ncrystal circuits. A complex photonic crystal circuit consisting of several\nwaveguides, splitters, and bends, which have individually been optimized,\nusing the S-matrix method based on Wannier functions, has been studied. Our results show that the Scattering Matrix formalism is much more\ne\ufb03cient than FDTD when dealing with large systems that are composed\nRaum: HI\nof several smaller functional elements embedded in an overall periodic environment. Complementary comparisons with local density of photonic\nstates and plain wave expansion methods are presented as well [3].\n[1] J. Phys.: Condens. Matter 15, R1233 (2003)\n[2] Opt. Lett. 28, 619 (2003)\n[3] Appl. Phys. Lett. 84, 4687 (2004)\nQ 25.4 Di 14:30 HI\nNonlinear-optical response of metamaterials: Experimental\ndemonstration of second-harmonic generation \u2014 \u2022Matthias\nF\u00a8 rstner2 , Jerome V. Moloney2 , Walter Hoyer3 , Tineke\nStroucken3 , Torsten Meier3 , Stephan W. Koch3 , and Stefan\nLinden4 \u2014 1 Institut f\u00a8r Angewandte Physik, Universit\u00a8t Karlsruhe\n(TH), 76131 Karlsruhe \u2014 2 Arizona Center for Mathematical Sciences,\nUniversity of Arizona, Tucson, AZ 85721, USA \u2014 3 Fachbereich\nUniversit\u00a8t Marburg, 35032 Marburg \u2014 4 Institut f\u00a8r Nanotechnologie,\nThe fabrication of metamaterials [1] has recently [2,3] reached resonance frequencies in the near-infrared or even visible regime. This development has triggered many experiments in linear optics, however, the\nnonlinear optics of metamaterials is mostly unexplored so far. We present\nexperiments on second-harmonic generation (SHG) by lithographically\nde\ufb01ned Split-Ring Resonators (SRRs) arranged in planar 2D arrays with\n\u201clattice constants\u201d between 300-630 nm. Using di\ufb00erent arrays of SRRs\nwith di\ufb00erent resonances tuned to the \ufb01xed laser wavelength of 1500 nm,\nwe show that the SHG e\ufb03ciency strongly depends on the nature of the\nexcited resonance. We \ufb01nd that by far the largest signal arises from exciting the magnetic-dipole resonance.\n[1] D. R. Smith et al., Science 305, 788 (2004)\n[2] S. Linden et al., Science 306, 1351 (2004)\nQ 25.5 Di 14:45 HI\nNonlinear-optical response of metamaterials: Theory \u2014\nStephan W. Koch1 , Jens F\u00a8 rstner2 , Jerome V. Moloney2 ,\nMarburg \u2014 2 Arizona Center for Mathematical Sciences, University\nof Arizona, Tucson, AZ 85721, USA \u2014 3 Institut f\u00a8r Angewandte\nPhysik, Universit\u00a8t Karlsruhe (TH), 76131 Karlsruhe \u2014 4 Institut f\u00a8r\nMetamaterials composed of sub-wavelength structures are known to\nresult in fascinating physical e\ufb00ects in the microwave regime[1]. Lately,\nsimilar materials have been fabricated also in the optical regime and\nmany of the linear properties are well understood[2]. Here, we present\na theoretical approach suitable for the study of nonlinear e\ufb00ects as\ne.g. second-harmonic generation. The theory is based on a microscopic\nVlasov-Maxwell approach which in its classical limit results in an equation for the current density coupled to Maxwell\u2019s equations. Numerical\nsolutions for the case of split-ring resonators are compared to our experiments.\n[1] R. A. Shelby, D. R. Smith, S. Schultz, Science 292, 77 (2001)\n[2] S. Linden et al., Science 306, 1351 (2004)\nQ 25.6 Di 15:00 HI\nFemtosecond Laser Fabricated Components for Guiding and\nFocussing of Surface Plasmon Polaritons \u2014 \u2022Sven Passinger,\nCarsten Reinhardt, and Boris N. Chichkov \u2014 Laser Zentrum\nHannover e.V., Hollerithallee 8, 30419 Hannover\nIn this contribution, we study applications of two-photon polymerization (2PP) technique for the fabrication of dielectric structures on\nmetal","kit-publication-id":"230063840"}]