Two mechanisms of disorder-induced localization in photonic-crystal waveguides

Editors' Suggestion

Two mechanisms of disorder-induced localization in photonic-crystal waveguides

P. D. García, G. Kiršanskė, A. Javadi, S. Stobbe, and P. Lodahl

Phys. Rev. B 96, 144201 – Published 6 October 2017

Abstract

Unintentional but unavoidable fabrication imperfections in state-of-the-art photonic-crystal waveguides lead to the spontaneous formation of Anderson-localized modes thereby limiting slow-light propagation and its potential applications. On the other hand, disorder-induced cavities offer an approach to cavity-quantum electrodynamics and random lasing at the nanoscale. The key statistical parameter governing the disorder effects is the localization length, which together with the waveguide length determines the statistical transport of light through the waveguide. In a disordered photonic-crystal waveguide, the localization length is highly dispersive, and therefore, by controlling the underlying lattice parameters, it is possible to tune the localization of the mode. In the present work, we study the localization length in a disordered photonic-crystal waveguide using numerical simulations. We demonstrate two different localization regimes in the dispersion diagram where the localization length is linked to the density of states and the photon effective mass, respectively. The two different localization regimes are identified in experiments by recording the photoluminescence from quantum dots embedded in photonic-crystal waveguides.

Received 18 July 2017
Revised 22 September 2017

DOI:https://doi.org/10.1103/PhysRevB.96.144201

Physics Subject Headings (PhySH)

Anderson localization Photonic crystals

Disordered systems Quantum dots

Quantum Information, Science & TechnologyCondensed Matter, Materials & Applied Physics

Authors & Affiliations

P. D. García, G. Kiršanskė, A. Javadi, S. Stobbe, and P. Lodahl^*

Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK-2100 Copenhagen, Denmark

^*lodahl@nbi.ku.dk; http://www.quantum-photonics.dk/

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 96, Iss. 14 — 1 October 2017

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Localization length in disordered photonic-crystal waveguides. (a) Steady-state electromagnetic-field intensity (normalized) in a disordered photonic-crystal waveguide calculated near the cutoff frequency of the unperturbed waveguide mode. The parameters used for the calculation are given in the text. (b) Electromagnetic field intensity (normalized) emitted from a dipole source at $ω = 0.266 a / λ$ placed at the center of a waveguide perturbed by $σ = 0.04 a$ after averaging over ten different configurations. (c) Ensemble-averaged electromagnetic-field intensity profile along the waveguide direction. The localization length can be extracted from the slope of the exponential decay.
Reuse & Permissions
Figure 2
Two regimes of disorder-induced localization. (a) Localization length calculated in a photonic-crystal waveguide with a lattice constant $a = 260 nm$ and a hole radius $0.29 a$ perturbed by $σ = 0.01 a$ (black dots). The dashed line pinpoints the cutoff frequency of the propagating Bloch mode in the ideal structure. Two different scalings are observed. In the band region of a propagating waveguide mode, the red line shows $ξ \propto {DOS}^{- 2}$ , while the blue line is $ξ \propto m^{- 1 / 2}$ in the band gap region. (b) The black line plots the corresponding density of optical states (DOS) of a perfect photonic-crystal waveguide. (c) and (d) Plot the localization length vs disorder at $ω = 0.266 a / λ$ [(c) inside band] and at $ω = 0.261 a / λ$ [(d) inside band gap], respectively. The red line in (c) shows the scaling $ξ \propto 1 / ρ Σ$ . The inset shows the effective scattering (shaded) area when a hole is displaced from its ideal position. Finally, the inset in (d) shows the electric-field component perpendicular to the waveguide at $ω = 0.261 a / λ$ and for $σ = 0.05 a$ .
Reuse & Permissions
Figure 3
Effective mass of photons and localization length. (a) Dispersion relation of a photonic-crystal waveguide with $a = 260 nm$ , a hole radius $0.29 a$ , and a standard width of $\sqrt{3} a$ (black curve) and for a stretched photonic-crystal waveguide with a reduced width of $0.60815 a$ (red curve). By stretching the waveguide, the resulting guided mode maintains the same cutoff frequency but has an eight times larger curvature (second derivative of the dispersion curve) than in the standard case. (b) and (c) Calculated electric-field intensity emitted from a dipole source at $ω = 0.261 a / λ$ (dashed line) and placed at the center of the standard stretched photonic-crystal waveguide after ensemble average over ten different configurations, respectively.
Reuse & Permissions
Figure 4
Experimental extension of localized modes. (a) Scanning-electron micrograph of a photonic-crystal waveguide with a 5- $μ m$ -long slow light section (white-shaded region) and parameters $a = 252 nm$ and $r = 0.27 a$ . The sample contains InGaAs quantum dots which are excited in the slow-light section (blue circle) and their photoluminescence is collected either from the same spot or from the circular grating (red circle) after propagation through a fast-light section corresponding to $a = 270 nm$ and $r = 0.27 a$ (orange-shaded region). (b) The localization length calculated for the parameters of the fabricated slow-light section of the waveguide, where scattering is most pronounced. The dashed line marks the localization length corresponding to the length of the slow-light region of the sample. (c) High-power photoluminescence spectra probing light from the quantum dots that are coupled to the waveguide mode and subsequently coupled out through the grating (red-filled line) or localized in the slow-light section of the waveguide and coupled out through leaky modes (blue-filled line). (d) Normalized photoluminescence intensity of the localized modes measured while raster scanning the sample under high-excitation power.
Reuse & Permissions

Physical Review B

covering condensed matter and materials physics