Study of group velocity in the negative refractive index region in three level closedΛsystem via spontaneously generated coherence

Abstract

A new approach is suggested to realize simultaneous negative permittivity and permeability in a three level closed system with incoherent pumping via spontaneously generated coherence (SGC). In this system the negativity of the real part of magnetic permeability can be achieved in the presence of SGC whereas in the absence of SGC it is positive. Thus the SGC makes the system a negative index medium (NIM) in a band of frequency range. The position and the band of the frequency region of negative refraction can be manipulated by controlling the incoherent pump rate. We achieve FOM ¼ 7.91165. We have studied the group index in the negative refractive index region and have shown that the group velocity switches from superluminal to subluminal mode in this region of negative refraction. We have shown that the negative refractive index can be realized in a heteronuclear molecule.Keywords: negative refractive index; spontaneously generated coherence IntroductionThe left-handed materials (LHMs), first introduced by Veselago [1], have recently attracted much attention because of their surprising and counterintuitive electromagnetic properties. Such materials possessing negative real parts of both dielectric permittivity ( r ) and magnetic permeability ( r ) over a certain frequency band characterize a negative value of the refraction denoted by real part of an index n ¼ À ( r r ) 1/2 [1][2][3][4][5][6][7][8][9][10][11]. These LHMs exhibit a number of peculiar electromagnetic and optical effects including the reversals of both Doppler shift and Cherenkov radiation [1], anomalous refraction [1], amplification of evanescent waves [3], subwavelength focusing [3,5], a negative Goos-Ha¨nchen shift [6], a reversed circular Bragg phenomenon [7], photon helicity inversion [8], some unusual photon tunnelling effects [9], reversed H field circulation patterns and inverted E field lines in propagating structures [10], and switched field intensity locations in anisotropic transmission structures [11].Although naturally occurring materials with simultaneous negative permittivity and permeability are not available, LHMs can be artificially realized. There are several ways to realize LHM, including artificial composite metamaterials [12][13][14][15], photonic crystal structures [16][17][18], transmission line simulation [19] and chiral material [20][21][22][23]. These methods based on

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