title: Lower bound for the spatial extent of localized modes in photonic-crystal waveguides with small random imperfections.
abstract: Light localization due to random imperfections in periodic media is paramount in photonics research. The group index is known to be a key parameter for localization near photonic band edges, since small group velocities reinforce light interaction with imperfections. Here, we show that the size of the smallest localized mode that is formed at the band edge of a one-dimensional periodic medium is driven instead by the effective photon mass, i.e. the flatness of the dispersion curve. Our theoretical prediction is supported by numerical simulations, which reveal that photonic-crystal waveguides can exhibit surprisingly small localized modes, much smaller than those observed in Bragg stacks thanks to their larger effective photon mass. This possibility is demonstrated experimentally with a photonic-crystal waveguide fabricated without any intentional disorder, for which near-field measurements allow us to distinctly observe a wavelength-scale localized mode despite the smallness (~1/1000 of a wavelength) of the fabrication imperfections.
authors.affiliation: LP2N, UMR 5298, CNRS - IOGS - Univ. Bordeaux, 33400 Talence, France.
authors.forename: Rémi
authors.initials: R
authors.lastname: Faggiani
authors.affiliation: LCF, UMR 8501, CNRS - IOGS - Univ. Paris-Sud, 91127 Palaiseau, France.|CRPP, UPR 8641, CNRS - Univ. Bordeaux, 33600 Pessac, France.
authors.forename: Alexandre
authors.initials: A
authors.lastname: Baron
authors.affiliation: LP2N, UMR 5298, CNRS - IOGS - Univ. Bordeaux, 33400 Talence, France.
authors.forename: Xiaorun
authors.initials: X
authors.lastname: Zang
authors.affiliation: ICB, UMR 6303, CNRS - Univ. Bourgogne, 21078 Dijon, France.
authors.forename: Loïc
authors.initials: L
authors.lastname: Lalouat
authors.affiliation: SUPA, School of Physics &Astronomy, University of St Andrews, St Andrews, KY16 9SS, UK.|Department of Physics and Max-Planck Centre for Extreme and Quantum Photonics, University of Ottawa, Ottawa, K1N 6N5, Ontario, Canada.
authors.forename: Sebastian A
authors.initials: SA
authors.lastname: Schulz
authors.affiliation: SUPA, School of Physics &Astronomy, University of St Andrews, St Andrews, KY16 9SS, UK.|Department of Physics, University of York, York, YO10 5DD, UK.
authors.forename: Bryan
authors.initials: B
authors.lastname: O'Regan
authors.affiliation: LP2N, UMR 5298, CNRS - IOGS - Univ. Bordeaux, 33400 Talence, France.
authors.forename: Kevin
authors.initials: K
authors.lastname: Vynck
authors.affiliation: ICB, UMR 6303, CNRS - Univ. Bourgogne, 21078 Dijon, France.
authors.forename: Benoît
authors.initials: B
authors.lastname: Cluzel
authors.affiliation: ICB, UMR 6303, CNRS - Univ. Bourgogne, 21078 Dijon, France.
authors.forename: Frédérique
authors.initials: F
authors.lastname: de Fornel
authors.affiliation: SUPA, School of Physics &Astronomy, University of St Andrews, St Andrews, KY16 9SS, UK.|Department of Physics, University of York, York, YO10 5DD, UK.
authors.forename: Thomas F
authors.initials: TF
authors.lastname: Krauss
authors.affiliation: LP2N, UMR 5298, CNRS - IOGS - Univ. Bordeaux, 33400 Talence, France.|LCF, UMR 8501, CNRS - IOGS - Univ. Paris-Sud, 91127 Palaiseau, France.
authors.forename: Philippe
authors.initials: P
authors.lastname: Lalanne