Lateral shifts of an optical beam in an anisotropic metamaterial slab

The lateral shift of a light beam at the surface of an anisotropic metamaterial slab is investigated. Analytical expressions of the lateral shifts are derived using the stationary-phase method, in the case that total reflection does and does not occur at the first interface. The sign of the lateral shift in two situations is discussed, and the necessary conditions for the lateral shift to be positive or negative are given. It is shown that the thickness and physical parameters of the anisotropic metamaterial slab, as well as the incident angle of the light beam, strongly affect the properties of the lateral shift, and numerical results validate these conclusions. The effect of a lossy metamaterial on the lateral shift is also investigated. A restriction on the thickness of the slab is obtained, which is necessary for the stationary-phase method to remain valid.     

Construct a polarizing beam splitter by an anisotropic metamaterial slab

We present a theoretical investigation of polarizing beam splitters based on an anisotropic metamaterial (AMM) slab. At the interface associated with a certain AMM, TE- and TM-polarized waves exhibit opposite amphoteric refraction characteristics, such that one polarized wave is positively refracted whereas the other is negatively refracted. The opposite amphoteric refractions result in a large birefringence in the AMM slab. By suitably using the large birefringence, we introduce a very simple and very efficient beam splitter to route the light. We show that the splitting angle and the splitting distance between TE- and TM-polarized beams is the function of anisotropic parameters, incident angle and slab thickness. PACS 41.20.Jb; 42.25.Gy; 78.20.Ci     

Photon tunneling in a frustrated total internal reflection structure with a lossy indefinite metamaterial barrier

We study the phenomenon of photon tunneling through a frustrated total internal reflection structure with a dispersive lossy indefinite metamaterial barrier. The tunneling coefficient, lateral shift, and tunneling time for different incident light waves through the barrier are obtained by employing the stationary-phase approximation. The properties of tunneling time and lateral shift are discussed for different metamaterial parameters. It is shown that negative lateral shift and tunneling time can appear in the cutoff and always cutoff metamaterials. The lateral shift can be enhanced by adjusting the light frequency, the barrier thickness, and the permittivity or permeability of the indefinite metamaterial. In addition, it is found that the lateral shift can be resonantly amplified due to the weak loss of the indefinite metamaterial slab. The Hartman effects of the lateral shift and tunneling time are also demonstrated. PACS 42.50.Ct; 42.25.Bs; 73.43.Jn; 73.40.Gk; 42.70.Qs     

FDTD Simulation on the Interaction Between Gaussian Beam and Biaxial Anisotropic Metamaterial Slabs

The interaction between Gaussian beam and indefinite anisotropic metamaterial (AMM) slabs are simulated with auxiliary differential equation method in finite-difference time-domain method (FDTD). The directions of wave vector and energy flow densities in three types of AMM slabs are investigated. The field intensity distributions and phases of TE-polarized wave for the interaction between Gaussian beam and AMM slabs are given. Numerical results show that the sign of x component of relative permeability tensor of AMM determines the refraction is regular or anomalous, whereas the sign of z component of relative permeability tensor of AMM determines the energy flow is positively refracted or negatively refracted. Positive or negative Goos-H?nchen shift associated with Total Cutoff media are also shown. This work was supported by National Key Laboratory of Electromagnetic Environment fund (51486030305HT0101) and (9140C08060507ZCZJ18).     

Polarization-sensitive propagation in an anisotropic metamaterial with double-sheeted hyperboloid dispersion relation

The polarization-sensitive propagation in the anisotropic metamaterial (AMM) with double-sheeted hyperboloid dispersion relation is investigated from a purely wave propagation point of view. We show that TE and TM polarized waves present significantly different characteristics which depend on the polarization. The omnidirectional total reflection and oblique total transmission can occur in the interface associated with the AMM. If appropriate conditions are satisfied, one polarized wave exhibits the total refraction, while the other presents the total reflection. We find that the opposite amphoteric refractions can be realized by rotating the principle axis of AMM, such that one polarized wave performs the negative refraction, while the other undergoes positive refraction. The polarization-sensitive characteristics allow us to construct two types of efficient polarizing beam splitters under certain achievable conditions.     

Goos-Hänchen shift from an anisotropic metamaterial slab

We have theoretically and numerically investigated the Goos-Hänchen shift (the lateral shift) from the anisotropic metamaterial slab. The sign and degree of the shift can be determined by the choices of the electromagnetic parameters and thicknesses of slab, which is different from the case of the isotropic media. We also find that the weak lossy may produce large positive or negative lateral shift.     

Giant and negative bistable shifts for one-dimensional photonic crystal containing a nonlinear metamaterial defect

In this Letter, we investigate giant and negative bistable lateral shifts for a light beam transmitted through a one-dimensional photonic crystal containing a nonlinear metamaterial defect. It is shown that there exists a typical S-shaped curve of the normalized input-output intensity. The hysteresis of lateral shift, resulting from the reshaping effect (constructive and destructive interferences of each plane wave components undergoing different phase shifts) is dependent on the nonlinear defect, the incident intensity and incidence angle. Numerical simulations are also made for the validity of stationary phase approach. All these phenomena lead to potential applications in integrated optics and optical switches.     

Giant positive and negative lateral shifts from the Kretschmann-Raether configuration with a weakly absorbing left-handed slab

The lateral shift of a TE-polarized beam reflected from the Kretschmann-Raether structure with a weakly absorbing left-handed slab is studied theoretically. It is shown that the lateral shift can be very large negative as well as positive near the resonant condition. These large negative and positive shifts can be one order of magnitude much larger than the shift from the corresponding nonabsorbing slab. As the absorption factor increases, the incident angle of producing largest lateral shift increases when the thickness is kept unchanged but the thickness of the slab of producing largest lateral shift decreases when the incident angle is kept unchanged.     

Opposite Goos-Hänchen Displacements for TE- and TM-Polarized Beams Transmitting through a Slab of Indefinite Metamaterial

The Goos-Hänchen displacement of a light beam transmitting through an indefinite metamaterial slab is studied. The results indicate that the displacement would be negative or positive for different parameters, and the necessary conditions for negative or positive displacements are summarized. Due to the special anisotropic properties, the directions of displacements for different polarization beams are opposite by proper design. In addition, the simultaneously enhanced positive and negative displacements will appear at different resonant angles under consideration of the active slab. These phenomena could have convenient applications in optical devices.     

Negative and positive Goos–Hänchen shifts of a light beam transmitted from an indefinite medium slab

We study the lateral shift of a light beam transmitted from an indefinite medium slab. The analytic expressions for the transmission coefficient and the lateral shift are obtained by using the stationary-phase method, and different conditions for the occurrence of a negative lateral shift are deduced. It is shown that the thickness of the indefinite medium strongly affects the properties of the lateral shift. For a larger thickness, the sign of the lateral shift depends only on the signs of the permittivity and permeability, while, for a smaller thickness, the sign of the lateral shift is determined by the combined effect of the incident angle of the light, the signs of the permittivity and permeability, and the thickness of the indefinite medium slab. In addition, the lateral shift at the transmitted resonance points is found to be enhanced greatly, and the sign of the lateral shift around the transmitted resonance points is strongly dependent on the permittivity and permeability of the indefinite medium. Some examples are given to validate the obtained theoretical results. PACS 41.20.Jb; 42.25.Gy; 42.25.Bs; 78.20.Ci; 78.68.+m     

Simultaneously Large and Opposite Lateral Beam Shifts for TE and TM Modes on a Double Metal-Cladding Slab

We report simultaneously large and opposite Goos-Hanchen shifts for TE and TM beams on a double metalcladding slab. Theoretical examination shows that both positive and negative lateral shifts are in two orders of the wavelength. It is also found that the magnitude of the lateral beam shift strongly depends on the thickness of the upper metal layer. The optimal thickness of the upper metal layer for zero reflection is found to be the critical thickness above which a negative beam shift occurs. Numerical calculations are in good agreement with the theoretical results.     

Large lateral shift in a multi-layer waveguide with indefinite media

We explore the basic properties of lateral shift in a multi-layer waveguide including isotropic metamaterial and indefinite media. Effective index method is used to calculate the refractive index of indefinite media and stationary-phase approach is applied to analysis the lateral shift of reflected light. The influences of thicknesses of isotropic metamaterial and indefinite media, off-diagonal parameters of indefinite media, the loss of metamaterial and the permeability of lateral shift on the lateral shift are discussed based on simulation results, which give us a guidance in designing multi-functional devices by use of the lateral shift in the proposed structure.     

Large lateral shift in a prism–waveguide system with uniaxially anisotropic metamaterial

We study the lateral shifts of reflected light beams in a prism–waveguide system with uniaxially anisotropic metamaterial including lossless and lossy system. The conditions for appearance of large lateral shift are deduced in a lossless system and the expression of lateral shift in a lossy system is derived. Simulation results illustrate the influence of imaginary part of every parameter in the prism–waveguide system on lateral shift. The anisotropy of metamaterial brings us more flexibility in designing new style photonic devices, such as sensors with high sensitivity based on accurate control of constructive parameters of metamaterial.     

Origin of large lateral shift in a prism⿿waveguide coupling system with metamaterial

We study the lateral shifts of reflected light beams in a prism?waveguide system with lossless or lossy metamaterial, four sufficient conditions for the appearance of large lateral shift is concluded when the metamaterial is lossless, and the influence of lossy metamaterial on the properties of lateral shift is also analyzed by simulation results.     

Negative lateral shift of a light beam transmitted through a dielectric slab and interaction of boundary effects

It is found that when a light beam travels through a slab of optically denser dielectric medium in air, the lateral shift of the transmitted beam can be negative. This is a novel phenomenon that is reversed in comparison with the geometrical optic prediction according to Snell's law of refraction. A Gaussian-shaped beam is analyzed in the paraxial approximation, and a comparison with numerical simulations is made. Finally, an explanation for the negativity of the lateral shift is suggested, in terms of the interaction of boundary effects of the slab's two interfaces with air.     

Experimental observation of negative lateral displacements of microwave beams transmitting through dielectric slabs

It was theoretically predicted that when a beam of light travels through a thin slab of optically denser medium in the air, the emerging beam from the slab will suffer a lateral displacement that is different from the prediction of geometrical optics, that is, the Snell’s law of refraction and can be zero and negative as well as positive. These phenomena have been directly observed in microwave experiments in which large angles of incidence are chosen for the purpose of obtaining negative lateral displacements.     

Negative Goos-Hanchen Effect in Thin-Film Fabry-Perot Filter

We investigate the Goos-Hgnchen effect of a Gaussian light beam reflected by the thin-film Fabry-Perot filter. It is shown that the Goos-Hanchen shift can be either negative or positive, The Gaussian-beam analysis and stationary phase method are introduced to calculate the lateral shift between the incident beam and the reflected beam at different wavelengths and to analyse the Goos-Hgnchen effect in the thin-film Fabry-Perot filter, The effect of the incident beam diameter is also discussed,     

Focusing and phase compensation of paraxial beams by a left-handed material slab

On the basis of angular spectrum representation, a formalism describing paraxial beams propagating through an isotropic left-handed material (LHM) slab is presented. The treatment allows us to introduce the ideas of beam focusing and phase compensation by LHM slab. Because of the negative refractive index of LHM slab, the inverse Gouy phase shift and the negative Rayleigh length of paraxial Gaussian beam are proposed. It is shown that the phase difference caused by the Gouy phase shift in right-handed material (RHM) can be compensated by that caused by the inverse Gouy phase shift in LHM. If certain matching conditions are satisfied, the intensity and phase distributions at object plane can be completely reconstructed at the image plane.     

Non-geometrical effects on Gaussian beams transmitting through a thin dielectric slab

It is shown that a Gaussian light beam transmitting through a planar thin dielectric slab in the air undergoes four different effects, i.e. lateral Goos-Hanchen-like （GHL） displacement, angular deflection, width modification and longitudinal focal shift as compared with the results predicted by geometrical optics. According to the Taylor expansion of the exponent of transmission coefficient when expressed as an exponential form, the lateral GHL displacement and the angular deflection are the first-order effects and can be negative or positive. The width modification and the longitudinal focal shift are the second-order effects and can also be positive or negative. Owing to the waist-width dependent term, the non-geometrical effects of transmitted beam are not identical with the non-specular effects of reflected beam. The conditions for the validity of those effects are suggested and numerical simulations are also given.     

各向异性超常材料的偏振分离特性

提出了一种利用含有负介电常量和磁导率张量的各向异性超常材料实现偏振分离的方法。通过分析电磁波在无损耗各向异性超常材料中的传输性质以及透射率与入射角度的关系,分类比较了由不同符号的介电常量和磁导率张量组合而成具有不同波矢面的各向异性超常材料的偏振分离特性,比较结果表明波矢面为单叶双曲面和椭球双叶双曲面的各向异性超常材料的偏振分离特性强。前者可以实现入射波中的s分量和p分量中某一分量正折射,另一分量负折射,且在一定条件下可以同时全透射,从而实现大角度偏振分离。后者在一定条件下可实现入射波中的s分量和p分量某一分量全反射,另一分量全透射,从而实现偏振分离。最后,对从各向同性介质入射到这两种各向异性超常材料中的高斯光波的传输进行了模拟计算,结果表明这两种各向异性超常材料可以实现很好的偏振分离功能,有潜力成为新型的偏振分离元件。