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Unfolding the band structure of non-crystalline photonic band gap materials.

Tsitrin S, Williamson EP, Amoah T, Nahal G, Chan HL, Florescu M, Man W - Sci Rep (2015)

Bottom Line: Our results demonstrate the existence of sizeable PBGs in these disordered structures and provide detailed information of the effective band diagrams, dispersion relation, iso-frequency contours, and their angular dependence.Slow light phenomena are also observed in these structures near gap frequencies.This study introduces a powerful tool to investigate photonic properties of non-crystalline structures and provides important effective dispersion information, otherwise difficult to obtain.

View Article: PubMed Central - PubMed

Affiliation: San Francisco State University, San Francisco, CA, 94132 USA.

ABSTRACT
Non-crystalline photonic band gap (PBG) materials have received increasing attention, and sizeable PBGs have been reported in quasi-crystalline structures and, more recently, in disordered structures. Band structure calculations for periodic structures produce accurate dispersion relations, which determine group velocities, dispersion, density of states and iso-frequency surfaces, and are used to predict a wide-range of optical phenomena including light propagation, excited-state decay rates, temporal broadening or compression of ultrashort pulses and complex refraction phenomena. However, band calculations for non-periodic structures employ large super-cells of hundreds to thousands building blocks, and provide little useful information other than the PBG central frequency and width. Using stereolithography, we construct cm-scale disordered PBG materials and perform microwave transmission measurements, as well as finite-difference time-domain (FDTD) simulations. The photonic dispersion relations are reconstructed from the measured and simulated phase data. Our results demonstrate the existence of sizeable PBGs in these disordered structures and provide detailed information of the effective band diagrams, dispersion relation, iso-frequency contours, and their angular dependence. Slow light phenomena are also observed in these structures near gap frequencies. This study introduces a powerful tool to investigate photonic properties of non-crystalline structures and provides important effective dispersion information, otherwise difficult to obtain.

No MeSH data available.


Related in: MedlinePlus

(a) Simulated band structure (blue) of a HUD dielectric wall-network strucutre with refractive-index contrast 1.6 vs.1. (b) Photo of the square lattice crystal (with lattice spacing a = 6.60 mm) (c) Photo of the HUD structure (average inter-vertex spacing a = 5.72 mm). The volume-filling fraction is 40.5% and the height is 100 mm for both samples.
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f1: (a) Simulated band structure (blue) of a HUD dielectric wall-network strucutre with refractive-index contrast 1.6 vs.1. (b) Photo of the square lattice crystal (with lattice spacing a = 6.60 mm) (c) Photo of the HUD structure (average inter-vertex spacing a = 5.72 mm). The volume-filling fraction is 40.5% and the height is 100 mm for both samples.

Mentions: For periodic structures, i.e. photonic crystals, band structure calculations produce accurate dispersion relations1415. The photonic dispersion and the associated mode structure are then employed to determine the fundamental properties of light in periodically structured media: the local density of states (LDOS), which determines the rates of spontaneous emission16; the group velocities, which govern the radiation transport properties; the group velocity dispersion (GVD), which is highly relevant for evaluating the effect of nonlinearities in photonic-crystal fibers17; the iso-frequency surfaces, which determine the behavior of the radiation at photonic-crystal interfaces18; and the curvature of the dispersion relation which determines the directional properties of the propagating radiation19. However, band calculations for non-periodic (quasiperiodic, disordered or random) structures employ super-cells with various sizes678. To achieve convergence, such simulations require large supercells containing hundreds to thousands of building blocks. For a supercell encompassing N building blocks, the corresponding first Brillouin zone shrinks its size N-times, and each band is “folded” into N effective bands. The super-cell’s first Brillouin zone has very small spatial extent in the wave-vector space, and the resulting band structure contains a very large number of almost horizontal bands that seem to have no resemblance to the band structure of related periodic structures9. The only useful information in the folded band structure is the position and width of eventual band gaps and the “density” of the horizontal bands in the frequency space, which provides a visual measure of the density of states (DOS). All information regarding group velocity, group velocity dispersion, and iso-frequency contours are hidden in the flat-appearing bands and the corresponding optical mode distributions. For example, as shown in Fig. 1a (similar to Fig. 4c in Ref. 9), the large number of calculated bands near the bandgap appear to be perfectly flat and occupy a large continuous frequency range. Moreover, various isotropy metrics introduced previously are misleading, since for the folded band structure associated with a supercell they account only for changes taking place on extremely small wave-vector ranges46 and provide little information about the true isotropy of the dispersion relation (an artificial supercell of perfectly anisotropic periodic photonic structure will produce a similar degree of flatness in the folded band structure). A different method is needed to reveal the dispersion relations inside non-crystalline photonic structures. Experimentally measuring the phase delay of microwave radiation through cm-scale periodic photonic structures can permit the structure’s band diagrams (dispersion relations) to be reconstructed20. In this study we apply similar phase analysis method to our disordered system to reconstruct its “unfolded” effective band structure.


Unfolding the band structure of non-crystalline photonic band gap materials.

Tsitrin S, Williamson EP, Amoah T, Nahal G, Chan HL, Florescu M, Man W - Sci Rep (2015)

(a) Simulated band structure (blue) of a HUD dielectric wall-network strucutre with refractive-index contrast 1.6 vs.1. (b) Photo of the square lattice crystal (with lattice spacing a = 6.60 mm) (c) Photo of the HUD structure (average inter-vertex spacing a = 5.72 mm). The volume-filling fraction is 40.5% and the height is 100 mm for both samples.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4542607&req=5

f1: (a) Simulated band structure (blue) of a HUD dielectric wall-network strucutre with refractive-index contrast 1.6 vs.1. (b) Photo of the square lattice crystal (with lattice spacing a = 6.60 mm) (c) Photo of the HUD structure (average inter-vertex spacing a = 5.72 mm). The volume-filling fraction is 40.5% and the height is 100 mm for both samples.
Mentions: For periodic structures, i.e. photonic crystals, band structure calculations produce accurate dispersion relations1415. The photonic dispersion and the associated mode structure are then employed to determine the fundamental properties of light in periodically structured media: the local density of states (LDOS), which determines the rates of spontaneous emission16; the group velocities, which govern the radiation transport properties; the group velocity dispersion (GVD), which is highly relevant for evaluating the effect of nonlinearities in photonic-crystal fibers17; the iso-frequency surfaces, which determine the behavior of the radiation at photonic-crystal interfaces18; and the curvature of the dispersion relation which determines the directional properties of the propagating radiation19. However, band calculations for non-periodic (quasiperiodic, disordered or random) structures employ super-cells with various sizes678. To achieve convergence, such simulations require large supercells containing hundreds to thousands of building blocks. For a supercell encompassing N building blocks, the corresponding first Brillouin zone shrinks its size N-times, and each band is “folded” into N effective bands. The super-cell’s first Brillouin zone has very small spatial extent in the wave-vector space, and the resulting band structure contains a very large number of almost horizontal bands that seem to have no resemblance to the band structure of related periodic structures9. The only useful information in the folded band structure is the position and width of eventual band gaps and the “density” of the horizontal bands in the frequency space, which provides a visual measure of the density of states (DOS). All information regarding group velocity, group velocity dispersion, and iso-frequency contours are hidden in the flat-appearing bands and the corresponding optical mode distributions. For example, as shown in Fig. 1a (similar to Fig. 4c in Ref. 9), the large number of calculated bands near the bandgap appear to be perfectly flat and occupy a large continuous frequency range. Moreover, various isotropy metrics introduced previously are misleading, since for the folded band structure associated with a supercell they account only for changes taking place on extremely small wave-vector ranges46 and provide little information about the true isotropy of the dispersion relation (an artificial supercell of perfectly anisotropic periodic photonic structure will produce a similar degree of flatness in the folded band structure). A different method is needed to reveal the dispersion relations inside non-crystalline photonic structures. Experimentally measuring the phase delay of microwave radiation through cm-scale periodic photonic structures can permit the structure’s band diagrams (dispersion relations) to be reconstructed20. In this study we apply similar phase analysis method to our disordered system to reconstruct its “unfolded” effective band structure.

Bottom Line: Our results demonstrate the existence of sizeable PBGs in these disordered structures and provide detailed information of the effective band diagrams, dispersion relation, iso-frequency contours, and their angular dependence.Slow light phenomena are also observed in these structures near gap frequencies.This study introduces a powerful tool to investigate photonic properties of non-crystalline structures and provides important effective dispersion information, otherwise difficult to obtain.

View Article: PubMed Central - PubMed

Affiliation: San Francisco State University, San Francisco, CA, 94132 USA.

ABSTRACT
Non-crystalline photonic band gap (PBG) materials have received increasing attention, and sizeable PBGs have been reported in quasi-crystalline structures and, more recently, in disordered structures. Band structure calculations for periodic structures produce accurate dispersion relations, which determine group velocities, dispersion, density of states and iso-frequency surfaces, and are used to predict a wide-range of optical phenomena including light propagation, excited-state decay rates, temporal broadening or compression of ultrashort pulses and complex refraction phenomena. However, band calculations for non-periodic structures employ large super-cells of hundreds to thousands building blocks, and provide little useful information other than the PBG central frequency and width. Using stereolithography, we construct cm-scale disordered PBG materials and perform microwave transmission measurements, as well as finite-difference time-domain (FDTD) simulations. The photonic dispersion relations are reconstructed from the measured and simulated phase data. Our results demonstrate the existence of sizeable PBGs in these disordered structures and provide detailed information of the effective band diagrams, dispersion relation, iso-frequency contours, and their angular dependence. Slow light phenomena are also observed in these structures near gap frequencies. This study introduces a powerful tool to investigate photonic properties of non-crystalline structures and provides important effective dispersion information, otherwise difficult to obtain.

No MeSH data available.


Related in: MedlinePlus