Photonic bands: simple-cubic lattice

Sözüer, H. Sami; Haus, Joseph W.

doi:10.1364/josab.10.000296

Cited by 153 publications

(43 citation statements)

References 18 publications

(13 reference statements)

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confidence: 99%

“…Highly coordinated lattices with, e.g., face-centered cubic or hexagonal symmetries in three dimensions [7] and triangular symmetry in two dimensions [23] are commonly observed in the experimental assembly of monodisperse particles with short-range, isotropic interactions. A broader array of thermodynamically stable 3D structures-including low-coordinated diamond and simple cubic (Sc) lattices of interest for technological applications [24,25]-has also been demonstrated by computer simulations of monodisperse particles with softer, repulsive potentials [26][27][28][29][30], including those that model the interactions between elastic spheres [31] or star polymers [32]. Similar interactions favor open 2D structures as well, including honeycomb and square lattices [33][34][35][36][37][38][39] with, e.g., sterically stabilized magnetic particles in the presence of an external field [40] providing one novel experimental realization.…”

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confidence: 99%

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Dimensionality and Design of Isotropic Interactions that Stabilize Honeycomb, Square, Simple Cubic, and Diamond Lattices

2014

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We use inverse methods of statistical mechanics and computer simulations to investigate whether an isotropic interaction designed to stabilize a given two-dimensional lattice will also favor an analogous three-dimensional structure, and vice versa. Specifically, we determine the 3D-ordered lattices favored by isotropic potentials optimized to exhibit stable 2D honeycomb (or square) periodic structures, as well as the 2D-ordered structures favored by isotropic interactions designed to stabilize 3D diamond (or simple cubic) lattices. We find a remarkable "transferability" of isotropic potentials designed to stabilize analogous morphologies in 2D and 3D, irrespective of the exact interaction form, and we discuss the basis of this cross-dimensional behavior. Our results suggest that the discovery of interactions that drive assembly into certain 3D periodic structures of interest can be assisted by less computationally intensive optimizations targeting the analogous 2D lattices. Material properties are intimately linked to structural characteristics featured at various length scales. Thus, discovering new ways to create materials with prescribed morphologies is a key challenge in their design for specific applications. In addition to the development of top-down material fabrication strategies, there has been considerable progress in bottom-up approaches in which the primary components (molecules, nanoparticles, colloids, etc.) A critical part of any self-assembly design problem is understanding how tunable aspects of the interactions affect the thermodynamic stability of competing assembled states with different morphologies. For nanoscale to microscale particles, this understanding has been guided in part via exploratory experiments and simulations to characterize the structures that spontaneously form from systems with various particle chemistries [7,8], shapes [9][10][11][12][13][14][15], and surface properties [16][17][18][19], as well as different dispersing solvents [20] and mixtures of assembling particles [21,22]. Highly coordinated lattices with, e.g., face-centered cubic or hexagonal symmetries in three dimensions [7] and triangular symmetry in two dimensions [23] are commonly observed in the experimental assembly of monodisperse particles with short-range, isotropic interactions. A broader array of thermodynamically stable 3D structures-including low-coordinated diamond and simple cubic (Sc) lattices of interest for technological applications [24,25]

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Dimensionality and Design of Isotropic Interactions that Stabilize Honeycomb, Square, Simple Cubic, and Diamond Lattices

2014

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“…The band gaps shown here along ΓX do not extend to all other crystal directions, a fact which is typical of isolated dielectric spheres in a SC lattice [9]. Resonant effects appear as almost flat modes in the band structure combined with sharp features in transmittance.…”

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confidence: 69%

Mie resonances and bonding in photonic crystals

Antonoyiannakis¹,

Pendry²

1997

Europhys. Lett.

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Abstract. -Isolated dielectric spheres support resonant electromagnetic (EM) modes which are analogous to electronic orbitals and, like their electronic counterparts, can form bonding or anti-bonding interactions between neighbouring spheres. By irradiating the system with light at the bonding frequency an attractive interaction is induced between the spheres. We suggest that by judicious selection of bonding states we can drive a system towards a desired structure, rather than rely on the structure dictated by gravitational or Van der Waals forces, the latter deriving from the zero point energy population of a state.Introduction. -The driving force behind our work is the understanding of EM forces in matter at the nanometre and micron scales. The biologically important Van der Waals force in solids belongs to this category. Developments in photonic band gap materials and colloidal crystals (as for example in [1]) have made it necessary to study such systems from the point of view of stability and cohesion. Up to now efforts to fabricate photonic crystals with tailored optical properties in the visible range of the spectrum have stumbled on the experimental difficulty in assembling crystal layers into fully three-dimensional (3D) structures, although some promising methods have arisen [2]. We report here on an idea which may facilitate formation of such structures, as well as being of physical interest in its own right.In this Letter we study the resonant EM modes in photonic crystals and their implications for EM forces. The origin of such modes lies in the EM field oscillations of an isolated sphere under the influence of an external plane-polarised radiation field (Mie resonances). Modes of similar nature (but corresponding to elastic waves in periodic composite materials) were identified by Kafesaki et al [3]. In the case of light in photonic crystals such resonant modes were first demonstrated (to our knowledge) by Zhang and Satpathy [4], whereas Stefanou et al [5] commented on their excitability by incident light. Recently Ohtaka and Tanabe [6] studied them thoroughly, appropriately calling them heavy photons due to their low dispersion behaviour; we adopt their terminology. We show that such modes result in sharp features in the force spectrum, causing mutual attraction or repulsion between successive crystal layers.

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“…[19][20][21][22][23][24][25][26][27][28][29][30] Some of the most attractive systems for integrated optics are planar-layer structures: [25][26][27][28][29] these have piecewise-constant cross-sections, and can thus be fabricated in a layer-by-layer fashion using traditional micro-lithography. The fine control provided by lithography promises the ability to precisely place defects in the crystal in order to construct integrated optical devices.…”

Section: Three-dimensional Photonic Crystalsmentioning

confidence: 99%

<title>New photonic crystal system for integrated optics</title>

2001

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We describe a new photonic-crystal structure with a complete three-dimensional photonic band gap (PBG) and its potential application to integrated optics. The structure not only has a large band gap and is amenable to layer-by-layer litho-fabrication, but also introduces the feature of high-symmetry planar layers resembling two-dimensional photonic crystals. This feature enables integrated optical devices to be constructed by modification of only a single layer, and supports waveguide and resonant-cavity modes that strongly resemble the corresponding modes in the simpler and well-understood 2d systems. In contrast to previous attempts to realize 2d crystals in 3d via finite-height "slabs," however, the complete PBG of the new system eliminates the possibility of radiation losses. Thus, it provides a robust infrastructure within which to embed complex optical networks, combining elements such as compact filters, channel-drops, and waveguide bends/junctions that have previously been proposed in 2d photonic crystals.

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Photonic bands: simple-cubic lattice

Cited by 153 publications

References 18 publications

Dimensionality and Design of Isotropic Interactions that Stabilize Honeycomb, Square, Simple Cubic, and Diamond Lattices

Dimensionality and Design of Isotropic Interactions that Stabilize Honeycomb, Square, Simple Cubic, and Diamond Lattices

Mie resonances and bonding in photonic crystals

<title>New photonic crystal system for integrated optics</title>

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