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We demonstrate that the top twenty distinguishable photonic crystal structures are all based on the diamond morphology

Diamond-structured photonic crystals.

NATURE MATERIALS, no. 9 (2004): 593-600

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摘要

Certain periodic dielectric structures can prohibit the propagation of light for all directions within a frequency range. These 'photonic crystals' allow researchers to modify the interaction between electromagnetic fields and dielectric media from radio to optical wavelengths. Their technological potential, such as the inhibition of spon...更多

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简介
  • The story of three-dimensional (3D) photonicbandgap structures begins with Yablonovitch at Bellcore, who first proposed the idea of “creating a periodic three-dimensional dielectric structure in which there exist an electromagnetic bandgap”[3].
  • The inverse structure made of air rods in a dielectric background shows a large 28% gap at f = 0.80 air volume fraction. the rodconnected diamond structures present the ‘champion’ photonic bandgap, their fabrication is seemingly complex.
重点内容
  • The story of three-dimensional (3D) photonicbandgap structures begins with Yablonovitch at Bellcore, who first proposed the idea of “creating a periodic three-dimensional dielectric structure in which there exist an electromagnetic bandgap”[3]
  • The existence of this pseudo-gap was demonstrated independently[5,6]. These theoretical calculations indicated that neither dielectric spheres nor air spheres arranged in a f.c.c. lattice possessed a complete photonic gap between the 2nd and 3rd bands
  • The first experimental structure with a photonic bandgap consisted of air spheres on the sites of a f.c.c. lattice in a dielectric background
  • Complete gaps were found in both types of structures; for dielectric spheres with refractive index n = 3.6 in an air matrix, a maximum 15% gap was obtained at a dielectric volume fraction f = 0.37, whereas for air spheres in a dielectric matrix a maximum 29% gap was found at air volume fraction f = 0.81
  • Spherical structures based on the diamond lattice demonstrated the first existence of a 3D complete photonic gap for periodic dielectric structures.An experimental technique to fabricate the close-packed diamond sphere structure was proposed[10], in which the use of a nanorobot was reported to assemble a body-centred cubic (b.c.c.) lattice of mixed silica and latex spheres of equal diameter
  • The transformation of the diamond into one of these structures[27] is shown in Fig. 3b. This structure shows an 18% diamond gap for refractive index n = 3.46.We proposed a layered structure obtained by the separation of the layers in the original woodpile structure[28]. This diamond-like woodpile structure (Fig. 3c) shows an increased diamond gap (23%) with respect to the standard woodpile (18%), but it requires additional layers to be assembled
  • Following the success of the spheres on diamond lattice sites photonic crystal — a structure made of cylindrical rods connecting nearest-neighbour sites in the diamond lattice (Fig. 1b) — was proposed[11,12]
结果
  • Fabrication of this structure was proposed to be by planar lithographic techniques[24].Considered as a three-layer structure,the disadvantage of the <111> diamond is the need to control the appropriate etching depth for each overlapping layer in order to replicate the set of rods that are along the [111] direction.The fabrication of this structure has been published[25]; the <111> threelayer diamond structure retains a 21% diamond photonic bandgap for a refractive index n = 3.46.
  • The proposed level-set diamond D structure (Fig. 5a) is given by the formula f(x,y,z) = sin(–x + y + z) + sin(x – y + z) + sin(x + y – z) + sin(x + y + z) obtained through a symmetry-based approach[32].
  • The main advantage of this level-set diamond D structure is that it has opened the possibility of fabrication of photonic crystals by 3D interference lithography first proposed by Turberfield et al 34.
  • This transformation does not close the diamond gap as shown in the corresponding plot of Fig. 6a.Again, it is the basic periodicity of the structure that determines the existence of the gap and not the crystal lattice[38].
  • The shortest wave-vector set in the 3D simple cubic lattice is the <100> family.A photonic crystal can be created by modulating the dielectric material along the x, y, z directions through f(x,y,z) = sin(x) + sin(y) + sin(z).
  • Layer-by-layer lithography the <110> directions create a three-connected b.c.c. gyroid structure.The authors introduced the first analytical description for this gyroid photonic crystal[31] given by f(x,y,z) = sin(x + y) + sin(x – y) + sin(y – z) + sin(y + z) + sin(x + z) + sin(z – x) and found a maximum 26% diamond gap for a refractive index n = 3.6.
  • All the known 3D complete, large-gap photonic crystal structures involve dielectric modulations along sets of principal directions.
结论
  • The change in translational symmetry from f.c.c.to b.c.c. does not close the gap,as shown in the plot of the upper and lower normalized frequencies ωa/2πc as a function of dielectric volume fraction (a).The basic periodicity of the structure is more important for the existence of the gap rather than the crystal lattice.
  • The more recent 3D interference lithography technique creates a promising method to fabricate certain diamond dielectric network structures defined by level sets.
总结
  • The story of three-dimensional (3D) photonicbandgap structures begins with Yablonovitch at Bellcore, who first proposed the idea of “creating a periodic three-dimensional dielectric structure in which there exist an electromagnetic bandgap”[3].
  • The inverse structure made of air rods in a dielectric background shows a large 28% gap at f = 0.80 air volume fraction. the rodconnected diamond structures present the ‘champion’ photonic bandgap, their fabrication is seemingly complex.
  • Fabrication of this structure was proposed to be by planar lithographic techniques[24].Considered as a three-layer structure,the disadvantage of the <111> diamond is the need to control the appropriate etching depth for each overlapping layer in order to replicate the set of rods that are along the [111] direction.The fabrication of this structure has been published[25]; the <111> threelayer diamond structure retains a 21% diamond photonic bandgap for a refractive index n = 3.46.
  • The proposed level-set diamond D structure (Fig. 5a) is given by the formula f(x,y,z) = sin(–x + y + z) + sin(x – y + z) + sin(x + y – z) + sin(x + y + z) obtained through a symmetry-based approach[32].
  • The main advantage of this level-set diamond D structure is that it has opened the possibility of fabrication of photonic crystals by 3D interference lithography first proposed by Turberfield et al 34.
  • This transformation does not close the diamond gap as shown in the corresponding plot of Fig. 6a.Again, it is the basic periodicity of the structure that determines the existence of the gap and not the crystal lattice[38].
  • The shortest wave-vector set in the 3D simple cubic lattice is the <100> family.A photonic crystal can be created by modulating the dielectric material along the x, y, z directions through f(x,y,z) = sin(x) + sin(y) + sin(z).
  • Layer-by-layer lithography the <110> directions create a three-connected b.c.c. gyroid structure.The authors introduced the first analytical description for this gyroid photonic crystal[31] given by f(x,y,z) = sin(x + y) + sin(x – y) + sin(y – z) + sin(y + z) + sin(x + z) + sin(z – x) and found a maximum 26% diamond gap for a refractive index n = 3.6.
  • All the known 3D complete, large-gap photonic crystal structures involve dielectric modulations along sets of principal directions.
  • The change in translational symmetry from f.c.c.to b.c.c. does not close the gap,as shown in the plot of the upper and lower normalized frequencies ωa/2πc as a function of dielectric volume fraction (a).The basic periodicity of the structure is more important for the existence of the gap rather than the crystal lattice.
  • The more recent 3D interference lithography technique creates a promising method to fabricate certain diamond dielectric network structures defined by level sets.
表格
  • Table1: Diamond-structured photonic crystals
Download tables as Excel
基金
  • This research was funded by the Institute for Soldier Nanotechnologies of the US Army Research Office under contract DAAD-19-02-0002. Competing financial interests The authors declare that they have no competing financial interests nature materials | VOL 3 | SEPTEMBER 2004 | www.nature.com/naturematerials
研究对象与分析
data: 3
The glancing-angle deposition technique is a possible method to make the square spiral diamond30. For dielectric rods (n = 3.45) in air, the structure shows a maximum 15% diamond gap at dielectric volume fraction f = 0.30, whereas for air rods in a dielectric background it shows a maximum 24% gap at air volume fraction f = 0.79. THE LEVEL-SET DIAMONDS AND 3D INTERFERENCE

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