Microwave propagation in two-dimensional dielectric lattices

McCall, S. L.; Platzman, P. M.; Dalichaouch, R.; Smith, David R.; Schultz, S.

doi:10.1103/physrevlett.67.2017

Cited by 309 publications

(137 citation statements)

References 19 publications

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“…These results are insensitive to the precise values of w and l. For the cases with defects and randomness, we also found good agreements between theory and experiments. 2,7 To discuss the scattering and radiation behaviors, we chose a sample of 5 rows ͑in the x direction͒ and 25 columns arranged in a square array. Here, we consider only the case of S waves.…”

Section: ͑9͒mentioning

confidence: 99%

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Multiple-scattering approach to finite-sized photonic band-gap materials

1998

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Multiple-scattering theory is used to study the transmission, scattering, and radiation properties of finitesized photonic band-gap materials in two dimensions. By adopting a source with a finite beam width to simulate realistic experimental conditions, we are able to obtain transmission results that are in excellent quantitative agreements with the measured data. Also, we find that the apparent gaps seen by an antenna can be much larger than the full gaps of the system. Inside an apparent gap, analytic results have been obtained for the radiation patterns and the total radiation power. ͓S0163-1829͑98͒00139-8͔Materials with a photonic band gap ͑PBG͒ have been under intensive studies both theoretically and experimentally over the past few years. 1-9 The existence of gaps, which prohibit the propagation of electromagnetic waves, can have important impacts both in science and technology. Among other important issues, the study of transmittance, the most measured quantity, and the radiation patterns of an antenna on a PBG substrate are also the foci of much studies. In these studies, the finite-difference method is commonly used. 1,4 However, this method requires large storage and heavy CPU time. Also, various boundary conditions have to be imposed by hand. Very recently, the multiple-scattering theory has been used to study the transmission and defect properties of finite PBG samples. 9 The multiple-scattering method treats finite PBG samples as scattering objects in open geometry. The radiation boundary condition is naturally imposed. We have independently adopted this method to study the transmission, scattering, and radiation properties of finite PBG samples. In the case of transmission, we used a source with a finite beam width to simulate the realistic experimental situations. In this case, a generalized transmission coefficient can be defined in terms of the far-field total scattering amplitude. We demonstrate explicitly that this method can produce transmission results that are in excellent quantitative agreements with the available experimental data for both S and P waves. From the total scattering amplitude we can retrieve the dispersion relations and the decay length inside a gap. The dependence of total scattering amplitude on the beam width is also discussed. Our calculation of transmission coefficient is different from that of Ref. 9 where plane waves were used as the incident beam and the near-field flux was used to calculate the transmittance. In the case of radiation, we find that the apparent gaps seen by an antenna can be much larger than the full gaps of the system. Inside an apparent gap, analytic expressions have been obtained for the radiation pattern and total radiation power.Below we give a brief derivation of the multiplescattering method in a form that applies to both S and P waves. Consider a system of N identical cylinders of radius R and dielectric constant ⑀ under an external source u inc ( ជ ) at a fixed frequency ϭ2 f . Here ជ ϵ( , ) specifies the position in a two-dimensional plane....

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Section: ͑9͒mentioning

confidence: 99%

“…[1][2][3][4][5][6][7][8][9] The existence of gaps, which prohibit the propagation of electromagnetic waves, can have important impacts both in science and technology. Among other important issues, the study of transmittance, the most measured quantity, and the radiation patterns of an antenna on a PBG substrate are also the foci of much studies.…”

mentioning

confidence: 99%

Multiple-scattering approach to finite-sized photonic band-gap materials

1998

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“…It shows that after removing the spreading factor, the data can be fitted by e −r/ξ . From the slop of the solid line, the localization length ξ is estimated as around 2.02d, which is in the vicinity of the localization length 1.6d estimated experimentally for microwave localization in 2D dielectric lattices 13 .…”

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confidence: 99%

“…It is now well-known that the multiple scattering of waves is responsible for many fascinating phenomena, ranging from phenomena of macroscopic scales such as twinkling lights in the evening sky, modulation of ambient noise in the oceans, and electromagnetic scintillation of turbulence in the atmosphere, to phenomena of microscopic or mesoscopic scales including random lasers 2 and electronic resistivity in disordered solids 3 . It has also been proposed that under certain conditions, the multiple scattering can lead to the unusual phenomenon of wave localization, a concept originally introduced to describe disorder induced metal-insulator transitions in electronic systems 4 .Over the past two decades, localization of classical waves has been under intensive investigations, leading to a very large body of literature(e. g. 5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21 ). Such a localization phenomenon has been characterized by two levels.…”

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Localization of electromagnetic waves in a two-dimensional random medium

2002

Phys. Rev. E

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Motivated by previous investigations on the radiative effects of the electric dipoles embedded in structured cavities, localization of electromagnetic waves in two dimensions is studied ab initio for a system consisting of many randomly distributed two dimensional dipoles. A set of self-consistent equations, incorporating all orders of multiple scattering of the electromagnetic waves, is derived from first principles and then solved numerically for the total electromagnetic field. The results show that spatially localized electromagnetic waves are possible in such a simple but realistic disordered system. When localization occurs, a coherent behavior appears and is revealed as a unique property differentiating localization from either the residual absorption or the attenuation effects.PACS numbers: 42.25. Hz, 41.90.+e When propagating through a medium consisting of many scatterers, waves will be scattered by each scatterer. The scattered waves will be again scattered by other scatterers. Such a process will be repeated to establish an infinite recursive pattern of multiple scattering. As a result, the wave propagation may be significantly altered 1 . It is now well-known that the multiple scattering of waves is responsible for many fascinating phenomena, ranging from phenomena of macroscopic scales such as twinkling lights in the evening sky, modulation of ambient noise in the oceans, and electromagnetic scintillation of turbulence in the atmosphere, to phenomena of microscopic or mesoscopic scales including random lasers 2 and electronic resistivity in disordered solids 3 . It has also been proposed that under certain conditions, the multiple scattering can lead to the unusual phenomenon of wave localization, a concept originally introduced to describe disorder induced metal-insulator transitions in electronic systems 4 .Over the past two decades, localization of classical waves has been under intensive investigations, leading to a very large body of literature(e. g. 5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21 ). Such a localization phenomenon has been characterized by two levels. One is the weak localization associated with the enhanced backscattering. That is, waves which propagate in the two opposite directions along a loop will obtain the same phase and interfere constructively at the emission site, thus enhancing the backscattering. The second is the strong localization, without confusion often just termed as localization, in which a significant inhibition of transmission appears and the energy is mostly confined spatially in the vicinity of the emission site.While the weak localization, regarded as a precursor to the strong localization, has been well studied both theoretically (e. g. the monograph 3,18 ) and experimentally (e. g. 19 ), observation of strong localization of classical waves for higher than one dimension remains a subject of debate 20,21,22 , primarily because a suitable system is hard to find and the observation is often obscured by such effects as the residual absorption 22 and scatt...

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