Research ArticleCONDENSED MATTER PHYSICS

Anderson localizations and photonic band-tail states observed in compositionally disordered platform

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Science Advances  05 Jan 2018:
Vol. 4, no. 1, e1602796
DOI: 10.1126/sciadv.1602796
  • Fig. 1 Compositionally disordered PhCs.

    (A) SEM image of a fabricated PhC alloy device. The device is composed of four kinds of photonic atoms with different air-hole sizes, distributed randomly at otherwise regular hexagonal lattice sites. Multiple hexagons are intentionally overlapped with the SEM image to illustrate that the hexagonal symmetry is strictly preserved. (B) Calculated photonic band structure of the reference PhC composed of homogenous air holes in a slab waveguide, arranged in the hexagonal lattice: r0 = 0.30a and h = 0.51a, where a = 450 nm is the lattice constant and h is the MQW slab thickness. (C) Schematic of photonic density of states (PDOS) versus photon energy with an illustration of band-tail states expected as a consequence of disorder.

  • Fig. 2 Band-tail states in lasing spectra.

    (A) Measured μPL spectra from the PhC alloy devices with different degrees of disorder (γ = 0.0, 0.2, 0.4, 0.6, and 0.8). Each spectrum is constructed by overlapping at least five individual spectra taken from different locations on the same device. The excitation power density was 6.2 kW/cm2 throughout the measurements. Each peak in the spectra corresponds to an individual laser line with a well-defined threshold. (B) Simulated |E|2 spectra for the model structures that correspond to those shown in (A). (C and D) Measured (C) and simulated (D) spectra, plotted as a function of the degree of disorder. Note that simulations are performed over an extended spectral range that includes the M2 BE as well. (E) Statistical summary of all the band-tail states identified from μPL measurements. For each degree of disorder, the average (▲,▼) and SD (I) are determined from an ensemble of 10 PhC alloy devices with different disorder configurations. The shaded areas are from simulations. (F) Energy range occupied by the K1 band-tail states, presented as a function of the degree of disorder. Results from μPL measurements and FDTD simulations are presented as red bars and white bars, respectively. The solid line is an exponential fitting to the simulation result.

  • Fig. 3 Mode patterns of the K1 band-tail states.

    (A) Representative SNOM images taken from devices with different degrees of disorder: γ = 0.0, 0.2, 0.4, and 0.6. For each degree of disorder, near-field images for the shallowest and deepest K1 band-tail states are shown in the left and right columns, respectively. All the SNOM images were taken at a fixed excitation power density (~7 kW/cm2) well above laser thresholds of the modes. (B) Simulated |E|2 mode patterns for the band-tail states that correspond to those shown in (A). (C) Measured (SNOM) and simulated (FDTD) images of various K1 band-tail states for a fixed degree of disorder (γ = 0.6) but at different band-tail state energies. The images are arranged in the order of state energy (from the shallowest at the top to the deepest at the bottom): ΔEEES = 0.0, 2.5, 4.9, 6.3, 9.5, and 13.0 meV. The inset is a schematic SNOM measurement configuration.

  • Fig. 4 Spatial extents of band-tail states.

    (A) Effective spatial widths of band-tail states, deduced from SNOM images for various degrees of disorder, band-tail state energies, and disorder configurations. (B) Simulated effective widths of various band-tail states. Simulations were performed over an extended spectral range to include the M2 band-tail states. (C) Effective width versus PhC pattern size, simulated for various degrees of disorder (0.0 ≤ γ ≤ 0.7). Throughout simulations, the disorder configuration is fixed so as to exclude configuration-specific fluctuations. (D) Modified Ioffe-Regel factors (k*l) estimated for the deepest band-tail states of γ ≥ 0.3. The results are plotted as a function of the envelope wave number k* such that the slope directly reflects the mean free path l.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/1/e1602796/DC1

    section S1. SEM images of fabricated devices

    section S2. Ordered and disordered components in compositional disorder

    section S3. Lasing properties of band-tail states

    section S4. Mode profiles in momentum space

    section S5. Gain overlap factors of band-tail states

    section S6. Eigenmode profiles of the M2 band-tail states

    section S7. Excitation strength dependence of modal properties

    section S8. Estimation of the K1 BE positions in disordered PhCs

    section S9. Localization length and mean free path

    section S10. The Bloch states in simulated spectra

    section S11. Effective width in momentum space

    section S12. Resolution dependence of effective widths

    fig. S1. Fabricated devices.

    fig. S2. Ordered versus disordered components.

    fig. S3. Lasing properties of band-tail states.

    fig. S4. Momentum space profiles of the band-tail states.

    fig. S5. Gain overlap factors of band-tail states.

    fig. S6. Mode profiles of the M2 band-tail states.

    fig. S7. Excitation power density dependence of modal properties.

    fig. S8. K1 band edges in disordered PhCs.

    fig. S9. Localization length and mean free path.

    fig. S10. Bloch states.

    fig. S11. Effective widths in momentum space.

    fig. S12. Resolution dependence of effective widths.

    References (4548)

  • Supplementary Materials

    This PDF file includes:

    • section S1. SEM images of fabricated devices
    • section S2. Ordered and disordered components in compositional disorder
    • section S3. Lasing properties of band-tail states
    • section S4. Mode profiles in momentum space
    • section S5. Gain overlap factors of band-tail states
    • section S6. Eigenmode profiles of the M2 band-tail states
    • section S7. Excitation strength dependence of modal properties
    • section S8. Estimation of the K1 BE positions in disordered PhCs
    • section S9. Localization length and mean free path
    • section S10. The Bloch states in simulated spectra
    • section S11. Effective width in momentum space
    • section S12. Resolution dependence of effective widths
    • fig. S1. Fabricated devices.
    • fig. S2. Ordered versus disordered components.
    • fig. S3. Lasing properties of band-tail states.
    • fig. S4. Momentum space profiles of the band-tail states.
    • fig. S5. Gain overlap factors of band-tail states.
    • fig. S6. Mode profiles of the M2 band-tail states.
    • fig. S7. Excitation power density dependence of modal properties.
    • fig. S8. K1 band edges in disordered PhCs.
    • fig. S9. Localization length and mean free path.
    • fig. S10. Bloch states.
    • fig. S11. Effective widths in momentum space.
    • fig. S12. Resolution dependence of effective widths.
    • References (45–48)

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