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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

Iso-frequency contour plots.The left panel (a,c) displays the square lattice results and the right column displays the hyperuniform results (b,d). The top row (a,b) shows the iso-frequency contours reconstructed from measured data and the bottom row (c,d), the ones reconstructed from field transmission simulations.
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f6: Iso-frequency contour plots.The left panel (a,c) displays the square lattice results and the right column displays the hyperuniform results (b,d). The top row (a,b) shows the iso-frequency contours reconstructed from measured data and the bottom row (c,d), the ones reconstructed from field transmission simulations.

Mentions: Figure 6a,b show the iso-frequency contour plots based on our experimental data, while Fig. 6c,d present the simulated iso-frequency contour plots. Since the gradient of the frequency with respect to the wavevector represents the group velocity, iso-frequency contour plots provides direct information about the orientation of group velocity vectors in these samples. The four-fold rotational symmetry of the square lattice is clearly demonstrated by the measured and simulated iso-frequency plots. The iso-frequency contour curves deform and bend near the Brillouin zone boundaries, and the resulting angular dependent dispersion relation and group velocities provide a clear signature of the underlying structure symmetry. The first and second Brillouin zone boundaries are clearly visible due to the randomly noisy phase data inside the stop bands caused by Bragg scattering for photonic crystals at Brillouin zone boundaries. For the HUD sample, as expected, all the iso-frequency lines remain concentric circles, due to the intrinsic isotropy of the structure. The band gap (associated with the randomly noisy data) in the HUD structure is isotropic and highlights an almost circular effective “Brillouin zone”. From the above data, the group velocity vector (dispersion) as a function of incident angles and frequencies can also be found. The measured effective group velocity is obviously reduced at frequencies near stop bands (Brillouin zone boundaries) for both the square lattice sample and the HUD sample.


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)

Iso-frequency contour plots.The left panel (a,c) displays the square lattice results and the right column displays the hyperuniform results (b,d). The top row (a,b) shows the iso-frequency contours reconstructed from measured data and the bottom row (c,d), the ones reconstructed from field transmission simulations.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f6: Iso-frequency contour plots.The left panel (a,c) displays the square lattice results and the right column displays the hyperuniform results (b,d). The top row (a,b) shows the iso-frequency contours reconstructed from measured data and the bottom row (c,d), the ones reconstructed from field transmission simulations.
Mentions: Figure 6a,b show the iso-frequency contour plots based on our experimental data, while Fig. 6c,d present the simulated iso-frequency contour plots. Since the gradient of the frequency with respect to the wavevector represents the group velocity, iso-frequency contour plots provides direct information about the orientation of group velocity vectors in these samples. The four-fold rotational symmetry of the square lattice is clearly demonstrated by the measured and simulated iso-frequency plots. The iso-frequency contour curves deform and bend near the Brillouin zone boundaries, and the resulting angular dependent dispersion relation and group velocities provide a clear signature of the underlying structure symmetry. The first and second Brillouin zone boundaries are clearly visible due to the randomly noisy phase data inside the stop bands caused by Bragg scattering for photonic crystals at Brillouin zone boundaries. For the HUD sample, as expected, all the iso-frequency lines remain concentric circles, due to the intrinsic isotropy of the structure. The band gap (associated with the randomly noisy data) in the HUD structure is isotropic and highlights an almost circular effective “Brillouin zone”. From the above data, the group velocity vector (dispersion) as a function of incident angles and frequencies can also be found. The measured effective group velocity is obviously reduced at frequencies near stop bands (Brillouin zone boundaries) for both the square lattice sample and the HUD sample.

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