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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

Photonic bands diagrams (dispersion relations) for (a) the square lattice sample reconstructed from experimentally measured phase data, (b) the HUD sample reconstructed based on the experimentally measured phase data, (c) the square lattice directly computed by solving the definite-frequency eigenstates (harmonic modes) of Maxwell’s equations14, (d) the HUD sample reconstructed from numerically simulated phase data.
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f5: Photonic bands diagrams (dispersion relations) for (a) the square lattice sample reconstructed from experimentally measured phase data, (b) the HUD sample reconstructed based on the experimentally measured phase data, (c) the square lattice directly computed by solving the definite-frequency eigenstates (harmonic modes) of Maxwell’s equations14, (d) the HUD sample reconstructed from numerically simulated phase data.

Mentions: In order to visualize the dispersion relations in all directions, we use the reconstructed wavenumbers as a function of incident angle and frequency to extract the frequency as a function of wave vector component kx and ky in two perpendicular directions in the incidence plane. Figure 5a,b show the band diagram constructed using the experimental phase data, while Fig. 5c shows the band diagram for the square lattice sample calculated theoretically. As previously discussed, direct band calculations lead to folded band diagrams and cannot be used to construct dispersion relations for non-periodic systems. Consequently, we use the phase information to reconstruct the effective dispersion relation for the disordered structures. Figure 5d shows the band diagram constructed using our numerically simulated phase data. To enhance the visualization of stop bands in these 3D surface plots, the random phase jumps detected inside those stop bands were eliminated in Fig. 5a,b,d. Again, the bands diagram of the square lattice constructed from the experimentally measured phase data (Fig. 5a) agrees very well with the theoretically calculated bands diagram (Fig. 5c), further validating our method of constructing effective band diagrams using phase analysis. In homogeneous dielectrics, the dispersion relations present an isotropic light cone, and frequency is proportional to wave-number. For photonic crystals, as shown in Fig. 5a,c, at long wavelengths, there is little departure from the conic dispersion relation of a homogeneous medium. Close to the Brillouin zone boundary, stop bands form at continuously changing frequencies and the band diagram distorts differently in all directions. For a crystal, the dispersion and group velocity (the slope of the frequency vs. wavenumber) have strong angular dependence. In contrast, the HUD sample shown in Fig. 5b,d presents a bandgap and a truly isotropic dispersion relation. Note that a small number of artifacts are present in simulated phase data caused by the simulation geometry and errors in tracking phase jumps of 2π at the lower and upper band edges, which create a small amount of artificial gap widening in 4 directions.


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)

Photonic bands diagrams (dispersion relations) for (a) the square lattice sample reconstructed from experimentally measured phase data, (b) the HUD sample reconstructed based on the experimentally measured phase data, (c) the square lattice directly computed by solving the definite-frequency eigenstates (harmonic modes) of Maxwell’s equations14, (d) the HUD sample reconstructed from numerically simulated phase data.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f5: Photonic bands diagrams (dispersion relations) for (a) the square lattice sample reconstructed from experimentally measured phase data, (b) the HUD sample reconstructed based on the experimentally measured phase data, (c) the square lattice directly computed by solving the definite-frequency eigenstates (harmonic modes) of Maxwell’s equations14, (d) the HUD sample reconstructed from numerically simulated phase data.
Mentions: In order to visualize the dispersion relations in all directions, we use the reconstructed wavenumbers as a function of incident angle and frequency to extract the frequency as a function of wave vector component kx and ky in two perpendicular directions in the incidence plane. Figure 5a,b show the band diagram constructed using the experimental phase data, while Fig. 5c shows the band diagram for the square lattice sample calculated theoretically. As previously discussed, direct band calculations lead to folded band diagrams and cannot be used to construct dispersion relations for non-periodic systems. Consequently, we use the phase information to reconstruct the effective dispersion relation for the disordered structures. Figure 5d shows the band diagram constructed using our numerically simulated phase data. To enhance the visualization of stop bands in these 3D surface plots, the random phase jumps detected inside those stop bands were eliminated in Fig. 5a,b,d. Again, the bands diagram of the square lattice constructed from the experimentally measured phase data (Fig. 5a) agrees very well with the theoretically calculated bands diagram (Fig. 5c), further validating our method of constructing effective band diagrams using phase analysis. In homogeneous dielectrics, the dispersion relations present an isotropic light cone, and frequency is proportional to wave-number. For photonic crystals, as shown in Fig. 5a,c, at long wavelengths, there is little departure from the conic dispersion relation of a homogeneous medium. Close to the Brillouin zone boundary, stop bands form at continuously changing frequencies and the band diagram distorts differently in all directions. For a crystal, the dispersion and group velocity (the slope of the frequency vs. wavenumber) have strong angular dependence. In contrast, the HUD sample shown in Fig. 5b,d presents a bandgap and a truly isotropic dispersion relation. Note that a small number of artifacts are present in simulated phase data caused by the simulation geometry and errors in tracking phase jumps of 2π at the lower and upper band edges, which create a small amount of artificial gap widening in 4 directions.

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