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Quantitative isolation of band-gap formation mechanisms by randomizing the lattice arrangement in photonic crystals
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10.1063/1.4797482
/content/aip/journal/jap/113/12/10.1063/1.4797482
http://aip.metastore.ingenta.com/content/aip/journal/jap/113/12/10.1063/1.4797482
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Modes created in an optical diatomic molecule: (a) mode positions on the frequency axis, where the shaded areas indicate the band gaps that will emerge when this basic unit is expanded to form a PC with the square lattice, (b) electric field distribution for mode in the vicinity of the molecule (two circles), where the white line shows the field profile along the molecular axis, and (c) electric field distribution for mode as well.

Image of FIG. 2.
FIG. 2.

Spectra of the total scattering cross-section in the vicinity of the estimated first band-gap for light scattered by (a) the metallic PC and (b) the dielectric PC. Here, the incident light is sent from the left of the PC ( ; the X-point in the k-space) or from the lower left of the PC ( ; the M-point in the k-space). The light frequency and the scattering cross-section are normalized to and , respectively. The primary peaks observed are written as LE (lower edge of the band gap) and UE (upper edge of the band gap).

Image of FIG. 3.
FIG. 3.

Variations of the upper and lower band edges as a function of R (randomness) for (a) the metallic system and (b) the dielectric system, for which the combination of seeds (3, 5) are used for the randomization. See Sec. III for the definition of R.

Image of FIG. 4.
FIG. 4.

Light field intensity distributions in the PCs ( ) together with the rod array: (a) the lower and (b) the upper edge modes in the metallic PC, and (c) the lower and (d) the upper edge modes in the dielectric PC. The field intensity increases in the order: blue, white, yellow, red, and black. The arrows indicate the incident directions of light.

Image of FIG. 5.
FIG. 5.

Light field intensity distributions in the system with the maximal randomization ( ) together with the rod positions: (a)the lower and (b) the upper edge modes in the metallic PC, and (c)the lower and (d) the upper edge modes in the dielectric PC.

Image of FIG. 6.
FIG. 6.

Relative band-gap variation as a function of the randomness R, where is the angular frequency for the band gap of the deformed PC with randomness R. Here, the blue and red symbols, respectively, show the results for the metallic and dielectric systems. The closed and open circles correspond to the results obtained by using the random numbers generated from the combinations of seeds for the x and y directions of and , respectively. The black circles show the values calculated using the band-gap shrinkage rate at randomness . Here, is the degree of the contribution of the Bragg process to the band-gap formation in the dielectric PC, where it is calculated using Eq. (1) .

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/content/aip/journal/jap/113/12/10.1063/1.4797482
2013-03-27
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Quantitative isolation of band-gap formation mechanisms by randomizing the lattice arrangement in photonic crystals
http://aip.metastore.ingenta.com/content/aip/journal/jap/113/12/10.1063/1.4797482
10.1063/1.4797482
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