Symmetry reduction in group<i>4mm</i>photonic crystals

Anderson, Cheryl M.; Giapis, Konstantinos P.

doi:10.1103/physrevb.56.7313

Cited by 72 publications

(35 citation statements)

References 26 publications

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“…14 The reduction of the first gap can be understood by using the following simple arguments without knowing ͉E nk (r)͉ explicitly. Since the first band is dielectric band, the state at the lower edge of the first gap will have an electric field concentrated near the center of the unit cell.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

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Enlarging a photonic band gap by using insertion

Zhang

et al. 2000

Phys. Rev. B

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We propose a simple, systematic, and efficient method to enlarge the gap of a photonic crystal. In this method, we add a small fraction of a third component into the existing photonic crystal. The dielectric property of the third component as well as its insertion position in a unit cell are chosen according to the field-energy distribution of two Bloch states at the band edges. The method is very general. It can be applied to any microstructure and is independent of the dimensionality of the original photonic crystal. Thus, it opens up a way to engineer photonic band gaps. Here, we demonstrate the validity of this method explicitly in two dimensions for both s and p waves. We show that, for certain microstructures, absolute gaps can be significantly enlarged. The method is also demonstrated in microwave experiments.

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Section: Numerical Results and Discussionmentioning

confidence: 99%

“…1- 14 The existence of gaps, which prohibit the propagation of electromagnetic ͑EM͒ waves in any direction, provides an opportunity to confine and control the propagation of EM waves. It can have profound implications for quantum optics, high-efficiency lasers, optoelectronic devices, and other areas of applications.…”

Section: Introductionmentioning

confidence: 99%

Enlarging a photonic band gap by using insertion

Zhang

et al. 2000

Phys. Rev. B

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“…It consists of two offset square lattices with rods of different size. The structure is able to exhibit larger absolute band-gaps (overlapping gap for both polarizations), compared to the normal square lattice [20]. This is because the reduction of symmetry can lead to the canceling of degeneracies at band edges.…”

Section: Diatomic Photonic Crystalmentioning

confidence: 87%

Nonlinear lattice model for spatially guided solitons in nonlinear photonic crystals

Sande¹,

Maes²,

Bienstman³

et al. 2005

Opt. Express

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Abstract:Numerical simulations have shown the existence of transversely localized guided modes in nonlinear two-dimensional photonic crystals. These soliton-like Bloch waves induce their own waveguide in a photonic crystal without the presence of a linear defect. By applying a Green's function method which is limited to within a strip perpendicular to the propagation direction, we are able to describe these Bloch modes by a nonlinear lattice model that includes the long-range site-to-site interaction between the scattered fields and the non-local nonlinear response of the photonic crystal. The advantages of this semi-analytical approach are discussed and a comparison with a rigorous numerical analysis is given in different configurations. Both monoatomic and diatomic nonlinear photonic crystals are considered.

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“…Wang et al 37 investigated the effects of shapes and orientations of scatterers and lattice symmetries on PtC bandgaps. Anderson et al 38 also discussed the lattice symmetry reduction on PtC bandgap structures. Malkova et al 39,40 presented the symmetrical perturbation analysis of PtCs and predicted the band spectrum evolution.…”

Section: Introductionmentioning

confidence: 99%

“…34 Halkjer et al 36 maximized the phononic band gaps for the infinite periodic beams and plates. Many papers about PtCs and PnCs have studied the effects of symmetry reduction of lattices [37][38][39][40] or unit-cells 41 on the bandgaps. Wang et al 37 investigated the effects of shapes and orientations of scatterers and lattice symmetries on PtC bandgaps.…”

Section: Introductionmentioning

confidence: 99%

Reducing symmetry in topology optimization of two-dimensional porous phononic crystals

2015

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In this paper we present a comprehensive study on the multi-objective optimization of twodimensional porous phononic crystals (PnCs) in both square and triangular lattices with the reduced topology symmetry of the unit-cell. The fast non-dominated sorting-based genetic algorithm II is used to perform the optimization, and the Pareto-optimal solutions are obtained.The results demonstrate that the symmetry reduction significantly influences the optimized structures. The physical mechanism of the optimized structures is analyzed. Topology optimization combined with the symmetry reduction can discover new structures and offer new degrees of freedom to design PnC-based devices. Especially, the rotationally symmetrical structures presented here can be utilized to explore and design new chiral metamaterials.

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Symmetry reduction in group4mmphotonic crystals

Cited by 72 publications

References 26 publications

Enlarging a photonic band gap by using insertion

Enlarging a photonic band gap by using insertion

Nonlinear lattice model for spatially guided solitons in nonlinear photonic crystals

Reducing symmetry in topology optimization of two-dimensional porous phononic crystals

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