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Emission and Transport of Light in Photonic Crystals

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Emission and Transport of Light in Photonic Crystals Emission and Transport of Light in Photonic Crystals Femius Koenderink Emission and Transport of Light in Photonic Crystals Emission and Transport of Light in Photonic Crystals ACADEMISCH PROEFSCHRIFT ter verkrijging van de graad van doctor aan de Universiteit van Amsterdam op gezag van de Rector Magnificus prof. mr. P. F. van der Heijden ten overstaan van een door het college voor promoties ingestelde commissie, in het openbaar te verdedigen in de Aula der Universiteit op vrijdag 27 juni 2003, te 10.00 uur door Albert Femius Koenderink geboren te Utrecht Promotiecommissie: Promotores Prof. Dr. W. L. Vos Prof. Dr. A. Lagendijk Overige leden Prof. Dr. M. S. Golden Prof. Dr. L. Kuipers Prof. Dr. H. De Raedt Prof. Dr. P. St. J. Russell Dr. R. Sprik Prof. Dr. D. A. M. Vanmaekelbergh Faculteit der Natuurwetenschappen, Wiskunde en Informatica The work described in this thesis is part of the research program of the “Stichting Fundamenteel Onderzoek der Materie (FOM)”, which is financially supported by the “Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO)”. It was carried out at the Van der Waals-Zeeman Instituut, Universiteit van Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam, The Netherlands, and in the group Complex Photonic Systems, Faculty of Science & Technology and MESA+ Research Institute, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands, where a limited number of copies of this thesis is available. Druk: PrintPartners Ipskamp, Enschede, The Netherlands. Omslag: face centered cubic marbles 180-49a. ISBN: 90-9016903-2 Contents 1 Photonic Crystals as a Cage for Light 9 1.1 Complexphotonicsystems........................ 9 1.2 PhotoniccrystalsandBraggdiffraction................. 11 1.3 Fabricationofthree-dimensionalphotoniccrystals.......... 14 1.4 Externalopticalprobesofphotoniccrystals............... 16 1.5 Probinginsidephotoniccrystals..................... 17 1.6 Disorderinphotoniccrystals....................... 18 1.7 Thisthesis................................. 19 References.................................... 21 2 Dispersion, Density of States and Refraction 27 2.1 Introduction................................ 27 2.2 Blochmodes,dispersionandtheplane-wavemethod......... 29 2.3 Photonicdispersionandphotonicstrength............... 32 2.4 Spontaneousemission.......................... 37 2.5 CalculationoftheDOS.......................... 39 2.6 Transmission,reflectionandrefraction................. 42 2.7 Dispersionsurfaces............................ 45 2.8 Refractionprobleminthreedimensions................ 46 2.9 Conclusions................................ 48 References.................................... 49 3 Angular Redistribution of Spontaneous Emission 53 3.1 Introduction................................ 53 3.2 Experiment................................ 54 3.3 Emissionspectraandstopbands..................... 57 3.4 Diffusetransportandthestopbandattenuation............ 60 3.5 StopbandsbeyondsimpleBraggdiffraction.............. 62 3.6 GeometryoftheavoidedcrossingintheBrillouinzone........ 64 3.7 Bandstructure............................... 65 3.8 Conclusion................................. 66 References.................................... 66 4 Broadband Fivefold Reduction of Vacuum Fluctuations Probed by Dyes 69 4.1 Introduction................................ 69 4.2 Fermi’sGoldenRuleandquantumefficiency.............. 70 4.3 Nonphotonicreferencehost....................... 72 4.4 Experiment................................ 73 7 Contents 4.5 InhibitionofemissionandtheDOS................... 76 4.6 Conclusion................................. 82 References.................................... 82 5 Ultra-fast Switching of the Density of States and of Photonic Band Gaps 87 5.1 Introduction................................ 87 5.2 Switchingmechanismsforphotoniccrystals.............. 88 5.3 EffectonDOS:possibleexperiments.................. 91 5.4 Absorption,extinctionandfinitesizeeffect............... 93 5.5 Switchingtimescalesandmagnitudes.................. 95 5.6 Outlook.................................. 96 References.................................... 98 6 Enhanced Backscattering from Opals and Inverse Opals 101 6.1 Introduction................................ 101 6.2 Multiplescatteringanddiffusion..................... 102 6.3 Enhancedbackscattering......................... 105 6.4 Experiment................................ 109 6.5 Backscatteringconesfromphotoniccrystals.............. 111 6.6 Photoniceffectontheconewidth.................... 114 6.7 Scatteringbypolydispersityanddisplacements............. 119 6.8 Conclusion................................. 122 References.................................... 123 7 Angular Redistribution of Diffuse Light 127 7.1 Introduction................................ 127 7.2 Diffusiontheoryofangle-resolvedtransmission............ 128 7.3 Experiment................................ 133 7.4 Escapefunctions.............................. 134 7.5 Diffuseinternal-reflectionmodel.................... 139 7.6 Diffusionincaseofabandgap:beyondKossellines.......... 142 7.7 Extrapolationlengthandtotaltransmission.............. 145 7.8 Conclusion................................. 148 References.................................... 149 Index 153 Summary 157 Samenvatting voor iedereen 161 Dankwoord 169 8 Chapter 1 Photonic Crystals as a Cage for Light 1.1 Complex photonic systems Complex photonic systems are composite optical materials in which the refractive index varies on length scales comparable to the wavelength of light. The adjective ‘complex’ indicates that propagation of light is most difficult to understand in such composites; the propagation strongly deviates from the rectilinear plane wave prop- agation in homogeneous media. The complexity resides in the fact that the optical properties of the composite are vastly dissimilar to those of the separate constituents. As two possible realizations of complex photonic systems, one may consider random media on the one hand, and ordered dielectric composites on the other hand. Wave propagation in random media is a research area with a rich history [1–3]. In contrast, ordered complex photonic systems, or photonic crystals,haveonlybecomesubjectof intense research since the last decade [4, 5]. The propagation of light in ordered complex photonic systems bears a strong similarity to the wave propagation of a conduction electron in a crystalline solid [6, 7]. Interference of waves diffracted by different lattice planes determines the optical modes and dispersion. The periodicity gives rise to Bragg diffractions, that are as- sociated with frequency windows that are forbidden for propagation in a certain di- rection. Such stop gaps have long been known to arise for light in one-dimensionally periodic structures, known as dielectric mirrors [8]. A stop gap is associated with propagation along a specific direction. In three-dimensionally periodic dielectrics a stop gap for all directions simultaneously can be achieved, a so-called photonic band gap. The total absence of optical modes for frequencies in a photonic band gap has im- plications beyond classical optics. Photonic crystals are expected to play an important role in cavity quantum electrodynamics, as first put forward in 1987 by Yablonovitch and John [9, 10]. Probably the most eagerly awaited phenomenon is complete inhi- bition of spontaneous emission: excited atoms inside a crystal with their transition frequencies tuned to the band gap cannot emit photons. The inhibition of sponta- neous emission in periodic structures was first predicted by Bykov in 1972 [11]. Any 9 Photonic Crystals as a Cage for Light interaction mediated by vacuum fluctuations is affected by their suppression in the band gap [4, 5, 12]. In addition to spontaneous emission processes, a photonic band gap also modifies van der Waals and Casimir forces, the spectrum of black body radi- ation, as well as, e.g., resonant dipole-dipole interactions [4, 12, 13]. Contrary to the localized suppression of spontaneous emission that can be achie- ved in microcavities, photonic crystals provide inhibition anywhere, in a volume only limited by the extent of the crystal. Such suppression of electromagnetic modes in the band gap is unique to photonic crystals, and can not be found in other optical materials that appear to exclude all light in a given frequency range. A photonic crystal reflects all light in the band gap not because light can’t couple through the surface, as would be the case for, e.g., a metal box. In a metal box a light source can still emit light, though it cannot be seen from outside the box. In a photonic band gap there are simply no electromagnetic states available and a light source can’t emit at all. Once a band gap is created, the physics can be further enriched by creating isolated defects. Such defects are predicted to introduce single electromagnetic modes with frequency in the band gap, localized to within a wavelength [14–16]. Such ‘cages for light’ provide a route to solid state cavity quantum electrodynamics [12]. In addition, it is expected that such cavities combined with optical gain promise thresholdless lasers [9]. The threshold of a laser is reached when the gain overcomes the losses. As only one mode exists for a point defect in a band gap material, there is no loss into modes other than the lasing mode. Thefieldofphotonicbandgapcrystalsisintimatelylinkedtothatofrandom media by the role of interference in modifying the transport of light. In everyday life disordered dielectric media, such as paint,
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