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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

Contour plots of the experimentally measured transmission (a,b) and phase delay (c,d) as a function of frequency and incident angle for the square-lattice crystal (a,c) and HUD structure (b,d).In the square lattice, Bragg scattering is responsible for forming stop bands (blocking regions), and their center frequency and width vary rapidly with the incident angle. In the HUD sample, a truly isotropic PBG is observed around 23.5 GHz despite the low index-contrast of 1.6:1 and the lack of Bragg scattering. The measured phase delay varies with frequency continuously for propagating modes outside of stop bands and appears to be random inside the stop bands where transmission is extremely low.
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f2: Contour plots of the experimentally measured transmission (a,b) and phase delay (c,d) as a function of frequency and incident angle for the square-lattice crystal (a,c) and HUD structure (b,d).In the square lattice, Bragg scattering is responsible for forming stop bands (blocking regions), and their center frequency and width vary rapidly with the incident angle. In the HUD sample, a truly isotropic PBG is observed around 23.5 GHz despite the low index-contrast of 1.6:1 and the lack of Bragg scattering. The measured phase delay varies with frequency continuously for propagating modes outside of stop bands and appears to be random inside the stop bands where transmission is extremely low.

Mentions: In Fig. 2a,b, we use 3D color contour plots to present the measured transmission for the square lattice and the HUD sample as a function of frequency and incident angle9. The green-to-blue regions correspond to the stop bands. For the square lattice, the variation of the frequency range of the stop bands with incident angle prevents the formation of a PBG (blocking propagation in all directions). The HUD structure forms a truly isotropic PBG indicated by two-order-of-magnitude transmission drop around 23 GHz9. In Fig. 2c,d, we use 3D color contour plots to present the measured phase for the square lattice and the HUD sample as a function of frequency and incident angle. At frequencies outside of the stop bands, the measured phase varies continuously as a function of frequencies at each angle, while inside the stop bands, the measured phase acquires a random noise characteristic when the transmitted intensity is close to zero. The square lattice phase data plot shows the angular dependence in perfect agreement with the transmission intensity data. The angular-dependent dispersion relation in the square lattice can be reconstructed from the measured phase data. At frequencies close to the stop bands, the measured phase varies more quickly as a function of the frequencies, indicating a slower group velocity than that at frequencies far from the stop bands. For the HUD sample, the measured phase data is isotropic, varies continuously as a function of frequency outside of the band gap, and also presents random noise inside the stop bands.


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)

Contour plots of the experimentally measured transmission (a,b) and phase delay (c,d) as a function of frequency and incident angle for the square-lattice crystal (a,c) and HUD structure (b,d).In the square lattice, Bragg scattering is responsible for forming stop bands (blocking regions), and their center frequency and width vary rapidly with the incident angle. In the HUD sample, a truly isotropic PBG is observed around 23.5 GHz despite the low index-contrast of 1.6:1 and the lack of Bragg scattering. The measured phase delay varies with frequency continuously for propagating modes outside of stop bands and appears to be random inside the stop bands where transmission is extremely low.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f2: Contour plots of the experimentally measured transmission (a,b) and phase delay (c,d) as a function of frequency and incident angle for the square-lattice crystal (a,c) and HUD structure (b,d).In the square lattice, Bragg scattering is responsible for forming stop bands (blocking regions), and their center frequency and width vary rapidly with the incident angle. In the HUD sample, a truly isotropic PBG is observed around 23.5 GHz despite the low index-contrast of 1.6:1 and the lack of Bragg scattering. The measured phase delay varies with frequency continuously for propagating modes outside of stop bands and appears to be random inside the stop bands where transmission is extremely low.
Mentions: In Fig. 2a,b, we use 3D color contour plots to present the measured transmission for the square lattice and the HUD sample as a function of frequency and incident angle9. The green-to-blue regions correspond to the stop bands. For the square lattice, the variation of the frequency range of the stop bands with incident angle prevents the formation of a PBG (blocking propagation in all directions). The HUD structure forms a truly isotropic PBG indicated by two-order-of-magnitude transmission drop around 23 GHz9. In Fig. 2c,d, we use 3D color contour plots to present the measured phase for the square lattice and the HUD sample as a function of frequency and incident angle. At frequencies outside of the stop bands, the measured phase varies continuously as a function of frequencies at each angle, while inside the stop bands, the measured phase acquires a random noise characteristic when the transmitted intensity is close to zero. The square lattice phase data plot shows the angular dependence in perfect agreement with the transmission intensity data. The angular-dependent dispersion relation in the square lattice can be reconstructed from the measured phase data. At frequencies close to the stop bands, the measured phase varies more quickly as a function of the frequencies, indicating a slower group velocity than that at frequencies far from the stop bands. For the HUD sample, the measured phase data is isotropic, varies continuously as a function of frequency outside of the band gap, and also presents random noise inside the stop bands.

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