Three kinds of compact thin subwavelength cavity resonators containing lefthanded mediarectangular.pdf
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1、arXiv:cond-mat/0402164v1 cond-mat.mtrl-sci 5 Feb 2004 Three kinds of compact thin subwavelength cavity resonators containing left-handed media: rectangular, cylindrical, spherical Jian-Qi Shen 1,2 1 Centre for Optical and Electromagnetic Research, State Key Laboratory of Modern Optical Instrumentati
2、on, Zhejiang University, Hangzhou Yuquan 310027, P.R. China 2 Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027, P.R. China (February 2, 2008) In the present paper we investigate the restriction conditions for three kinds of cavity resonators (i.e.,
3、 the rectangular, cylindrical, spherical resonators).It is shown that the layer of materials with negative optical refractive indices can act as a phase compensator/conjugator, and thus by combining such a layer with another layer made of the regular medium one can obtain a so-called compact thin su
4、bwavelength cavity resonator. Keywords: subwavelength cavity resonators, left-handed medium I. INTRODUCTION More recently, a kind of artifi cial composite metamaterials (the so-called left-handed media) having a frequency band where the eff ective permittivity and the eff ective permeability are sim
5、ultaneously negative attracts considerable attention of many authors both experimentally and theoretically 15. In 19671 , Veselago fi rst considered this peculiar medium and showed from Maxwellian equations that such media having negative simultaneously negative and exhibit a negative index of refra
6、ction, i.e., n = 6. It follows from the Maxwells curl equations that the phase velocity of light wave propagating inside this medium is pointed opposite to the direction of energy fl ow, that is, the Poynting vector and wave vector of electromagnetic wave would be antiparallel, i.e., the vector k, t
7、he electric fi eld E and the magnetic fi eld H form a left-handed system; thus Veselago referred to such materials as “left-handed” media, and correspondingly, the ordinary medium in which k, E and H form a right-handed system may be termed the “right-handed” one. Other authors call this class of ma
8、terials “negative-index media (NIM)” 8, “backward media (BWM)” 7, “double negative media (DNM)” and Veselagos media. There exist a number of peculiar electromagnetic and optical properties, for instance, many dramatically diff erent propagation characteristics stem from the sign change of the optica
9、l refractive index and phase velocity, including reversal of both the Doppler shift and Cerenkov radiation, anomalous refraction, amplifi cation of evanescent waves 9, unusual photon tunneling 10, modifi ed spontaneous emission rates and even reversals of radiation pressure to radiation tension 1. I
10、n experiments, this artifi cial negative electric permittivity media may be obtained by using the array of long metallic wires (ALMWs) 11, which simulates the plasma behavior at microwave frequencies, and the artifi cial negative magnetic permeability media may be built up by using small resonant me
11、tallic particles, e.g., the split ring resonators (SRRs), with very high magnetic polarizability 12. A combination of the two structures yields a left-handed medium. Recently, Shelby et al. reported their fi rst experimental realization of this artifi cial composite medium, the permittivity and perm
12、eability of which have negative real parts 1. One of the potential applications of negative refractive index materials is to fabricate the so-called “superlenses” (perfect lenses): specifi cally, a slab of such materials may has the power to focus all Fourier components of a 2D image, even those tha
13、t do not propagate in a radiative manner 9,13. Engheta suggested that a slab of metamaterial with negative electric permittivity and magnetic permeability (and hence negative optical refractive index) can act as a phase compensator/conjugator and, therefore, by combining such a slab with another sla
14、b fabricated from a conventional (ordinary) dielectric material one can, in principle, have a 1-D E-mail address: 1Note that, in the literature, some authors mentioned the wrong year when Veselago suggested the left-handed media. They claimed that Veselago proposed or introduced the concept of left-
15、handed media in 1968 or 1964. On the contrary, the true history is as follows: Veselagos excellent paper was fi rst published in Russian in July, 1967 Usp. Fiz. Nauk 92, 517-526 (1967). This original paper was translated into English by W.H. Furry and published again in 1968 in the journal of Sov. P
16、hys. Usp. 6. Unfortunately, Furry stated erroneously in his English translation that the original version of Veselago work was fi rst published in 1964. 1 cavity resonator whose dispersion relation may not depend on the sum of thicknesses of the interior materials fi lling this cavity, but instead i
17、t depends on the ratio of these thicknesses. Namely, one can, in principle, conceptualize a 1-D compact, subwavelength, thin cavity resonator with the total thickness far less than the conventional 2 14. Enghetas idea for the 1-D compact, subwavelength, thin cavity resonator is the two-layer rectang
18、ular structure (the left layer of which is assumed to be a conventional lossless dielectric material with permittivity and permeability being positive numbers, and the right layer is taken to be a lossless metamaterial with negative permittivity and permeability) sandwiched between the two refl ecto
19、rs (e.g., two perfectly conducting plates) 14. For the pattern of the 1-D subwavelength cavity resonator readers may be referred to the fi gures of reference 14. Engheta showed that with the appropriate choice of the ratio of the thicknesses d1to d2, the phase acquired by the incident wave at the le
20、ft (entrance) interface to be the same as the phase at the right (exit) interface, essentially with no constraint on the total thickness of the structure. The mechanism of this eff ect may be understood as follows: as the planar electromagnetic wave exits the fi rst slab, it enters the rectangular s
21、lab of metamaterial and fi nally it leaves this second slab. In the fi rst slab, the direction of the Poynting vector is parallel to that of phase velocity, and in the second slab, however, these two vectors are antiparallel with each other. Thus the wave vector k2is therefore in the opposite direct
22、ion of the wave vector k1 . So the total phase diff erence between the front and back faces of this two-layer rectangular structure is k1d1|k2|d2 14. Therefore, whatever phase diff erence is developed by traversing the fi rst rectangular slab, it can be decreased and even cancelled by traversing the
23、 second slab. If the ratio of d1and d2is chosen to be d1 d2 = |k2| k1 , then the total phase diff erence between the front and back faces of this two-layer structure becomes zero (i.e., the total phase diff erence is not 2n, but instead of zero) 14. As far as the properties and phenomena in the subw
24、avelength cavity resonators is concerned, Tretyakov et al. investigated the evanescent modes stored in cavity resonators with backward-wave slabs 15. II. A RECTANGULAR SLAB 1-D THIN SUBWAVELENGTH CAVITY RESONATOR To consider the 1-D wave propagation in a compact, subwavelength, thin cavity resonator
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