Energy band of photons and low-energy photon diffraction

Ohtaka, K.

doi:10.1103/physrevb.19.5057

Cited by 329 publications

(148 citation statements)

References 40 publications

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“…These materials can strongly modulate light [1] and, with sufficient dielectric contrast and an appropriate geometry, may exhibit a photonic bandgap (PBG). This concept was first proposed in 1975 by Bykov [2] but remained relatively unknown until the seminal work of Yablonovitch [3] and John.…”

Section: Introductionmentioning

confidence: 99%

Introducing Defects in 3D Photonic Crystals: State of the Art

2006

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Public Reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comment regarding this burden estimates or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302, and to the Office of Management and Budget, Paperwork Reduction Project (0704-0188,) Washington, DC 20503. AGENCY USE ONLY ( Leave Blank)2. REPORT DATE Advanced Materials, 18, 2665-2678 (2006). 3D photonic crystals (PhCs) and photonic bandgap (PBG) materials have attracted considerable scientific and technological interest. In order to provide functionality to PhCs, the introduction of controlled defects is necessary; the importance of defects in PhCs is comparable to that of dopants in semiconductors. Over the past few years, significant advances have been achieved through a diverse set of fabrication techniques. While for some routes to 3D PhCs, such as conventional lithography, the incorporation of defects is relatively straightforward; other methods, for example, selfassembly of colloidal crystals (CCs) or holography, require new external methods for defect incorporation. In this review, we will cover the state of the art in the design and fabrication of defects within 3D PhCs. The figure displays a fluorescence laser scanning confocal microscopy image of a y-splitter defect formed through two-photon polymerization within a CC. SUBJECT TERMS 15. NUMBER OF PAGES 1416. PRICE CODE SECURITY CLASSIFICATION OR REPORT UNCLASSIFIED SECURITY CLASSIFICATION ON THIS PAGE UNCLASSIFIED SECURITY CLASSIFICATION OF ABSTRACT UNCLASSIFIED LIMITATION OF ABSTRACT UL IntroductionPhotonic crystals (PhCs) are materials that possess spatial periodicity in their dielectric constant on the order of the wavelength (k) of light. These materials can strongly modulate light [1] and, with sufficient dielectric contrast and an appropriate geometry, may exhibit a photonic bandgap (PBG). This concept was first proposed in 1975 by Bykov [2] but remained relatively unknown until the seminal work of Yablonovitch [3] and John. [4] In a rough analogy to semiconductors, which possess an electronic bandgap, a PBG material prohibits the existence of photons with energies in the PBG. PhCs are naturally classified by the dimensionality of their periodicity, and in order to rigorously prevent the propagation of PBG frequencies in all directions, a 3D PhC with an omnidirectional, or complete PBG (cPBG) is required. cPBG materials have been fabricated and well characterized for operation at microwave and radio frequencies, however, operation in the visible and IR requires the characteristic length scales of these structures to be scaled down by several orders of magnitude...

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Section: Introductionmentioning

confidence: 99%

Introducing Defects in 3D Photonic Crystals: State of the Art

2006

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“…The so-called on-shell methods developed in relation to photonic crystals can do exactly that, besides an accurate evaluation of the frequency band structure. [26][27][28] In these methods one determines for a given frequency ω and a given reduced wavevector, k , parallel to a given crystallographic plane of the crystal, the Bloch-wave solutions of the elastic field of the infinite crystal; these consist of propagating and evanescent waves. The propagating waves constitute the normal modes of the infinite phononic crystal.…”

Section: Introductionmentioning

confidence: 99%

Scattering of elastic waves by periodic arrays of spherical bodies

2000

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We develop a formalism for the calculation of the frequency band structure of a phononic crystal consisting of non-overlapping elastic spheres, characterized by Lamé coefficients which may be complex and frequency dependent, arranged periodically in a host medium with different mass density and Lamé coefficients. We view the crystal as a sequence of planes of spheres, parallel to and having the two dimensional periodicity of a given crystallographic plane, and obtain the complex band structure of the infinite crystal associated with this plane. The method allows one to calculate, also, the transmission, reflection, and absorption coefficients for an elastic wave (longitudinal or transverse) incident, at any angle, on a slab of the crystal of finite thickness. We demonstrate the efficiency of the method by applying it to a specific example.

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“…The equation set derived above can be further simplified after applying the addition theorem for the vector spherical harmonics to move the centre of coordinates to the same origin. The equation set governing the coefficients a finally takes the form [21,[26][27][28] (…”

Section: The Vector-wave Korringa-kohn-rostoker Methodsmentioning

confidence: 99%

“…This is the so-called Korringa-KohnRostoker (KKR) method [19,20], which was first put into practice in electronic band-structure calculations some decades ago. Recently, the vector-wave KKR method has been formulated for electromagnetic waves propagating in photonic crystals [21][22][23][24][25][26][27][28]; also we have written a very efficient program code based on the vector-wave KKR method and tested it on a variety of previous known results: fast convergence and high accuracy have been proved for all cases. The advantage of the vector-wave KKR method is most obvious for photonic crystals with metallic components; comparison of diamond structures made of ideal metal spheres embedded in dielectric media shows that the vector-wave KKR method needs much less CPU time and memory space than the finite-difference time-domain method [29].…”

Section: Introductionmentioning

confidence: 99%

The photonic band structures of body-centred-tetragonal crystals composed of ionic or metal spheres

Zhang

Wang

et al. 2000

J. Phys.: Condens. Matter

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Abstract. The photonic band structures of body-centred-tetragonal (BCT) crystals composed of ionic or metal spheres are computed using the highly efficient vector-wave Korringa-KohnRostoker (KKR) method; an absolute band gap is found for the photonic crystals with high filling ratio. The band gap is smaller in the crystals composed of ionic spheres than in those composed of metal spheres. The particular BCT structure was chosen since such structure can be easily realized in an electrorheological fluid in the presence of an electric field.

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Energy band of photons and low-energy photon diffraction

Cited by 329 publications

References 40 publications

Introducing Defects in 3D Photonic Crystals: State of the Art

Introducing Defects in 3D Photonic Crystals: State of the Art

Scattering of elastic waves by periodic arrays of spherical bodies

The photonic band structures of body-centred-tetragonal crystals composed of ionic or metal spheres

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