Intensity transformation of vector Bessel beams using a multilayer system

We theoretically investigate the generation of vector Bessel beams of the order m using a phase shifted superposition of TE and TM electromagnetic Bessel beams. Such Bessel beams are characterized by the intensity profile described by the superposition of squared Bessel functions of the orders (m-1) and (m+1). We derive the conditions for creating the special distributions of the intensity, which are determined by only one Bessel function, or . We offer the approach of intensity transformation based on the Bessel beam transmission through a multilayer system. Finally, we reveal the perfect intensity transformation transferring the whole energy from - to -profile of intensity distribution.     

Total reflection of electromagnetic waves propagating from an isotropic medium to an indefinite metamaterial

The existence conditions for total reflection and the corresponding critical angle at the interface separating an isotropic medium and an indefinite metamaterial for TE- and TM-polarized electromagnetic waves are obtained. For different kinds of indefinite metamaterial, there appear different total reflection phenomena. Particularly, the anomalous total reflection in which the incident angle is smaller than the critical angle and the Brewster’s angle can be smaller than the critical angle can occur for anti-cutoff medium. Furthermore, the omnidirectional total reflection exists for the always cutoff medium and anti-cutoff medium. The total reflection depends on the thickness of indefinite metamaterial when the indefinite metamaterial is finite, and the photon tunneling phenomenon can occur when the thickness of indefinite metamaterial is smaller than wavelength.     

Effects of metal and “magnetic wall” on the dispersion characteristic of magnetostatic waves

The dispersion relation of magnetostatic waves tangentially magnetized to saturation ferrite film, with a “magnetic wall” condition (tangential component of microwave magnetic field is equal to zero) on one of the film surface and with a metal condition on the opposite surface is analyzed. The dispersion characteristics show that unidirectional magnetostatic waves appear in this structure: they can transfer energy in one direction only and fundamentally cannot transfer energy in the opposite direction. The dispersion-free propagation of magnetostatic waves also is possible in the structure in a wide frequency interval.     

Transverse displacement at total reflection near the grazing angle: a way to discriminate between theories

The transverse shift is observed and precisely measured at total internal reflection on a dielectric interface for a circularly polarized light beam when the incident angle is scanned from the critical angle up to the grazing angle close to 90°. The experimental results show with no doubt that the transverse displacement exists far away from the critical angle and only vanishes at grazing angle. A comparison with theories also allows a discrimination between the most different theoretical models traditionally used to interpret physically this effect.     

Electromagnetic Invisibility of Elliptic Cylinder Cloaks

Structures with unique electromagnetic properties are designed based on the approach of spatial coordinate transformations of Maxwell's equations. Thisapproach is applied to scheme out invisible elliptic cylinder cloaks, which provide more feasibility for cloaking arbitrarily shaped objects. The transformation expressions for the anisotropic material parameters and the field distribution are derived. The cloaking performances of ideal and lossy elliptic cylinder cloaks are investigated by finite element simulations. It is found that the cloaking performance will degrade in the forward direction withincreasing loss.     

The Imbert-Fedorov shift of paraxial light beams

We present a solution to the problem of reflection and transmission of a polarized paraxial light beam at an interface between two homogeneous media by using a two-form amplitude and an extension matrix to represent the vectorial angular spectrum of a three-dimensional (3D) light beam. We derive general formulas for the Imbert-Fedorov (IF) shift of the reflected and transmitted beams of a polarized paraxial light beam. The IF shift of two different types of polarized beams is calculated, and the influence of the polarization state and the polarization feature of the vectorial angular spectrum on the IF shift is discussed.     

Comment on “The Imbert-Fedorov shift of paraxial light beams”

Here I argue that Liu and Li [B.-Y. Liu, C.-F. Li, Opt. Commun. 281 (2008) 3427] reproduce calculations of the Imbert-Fedorov transverse shift previously made in a number of other works. However, it has recently been shown that these results are not valid for standard uniformly polarized beams. The corrected values of the Imbert-Fedorov shift were derived in papers [K.Y. Bliokh, Y.P. Bliokh, Phys. Rev. Lett. 96 (2006) 073903; Phys. Rev. E 75 (2007) 066609] and confirmed by recent measurements [O. Hosten, P. Kwiat, Science 319 (2008) 787] with a great accuracy.     

Reply to “Comment on ‘The Imbert-Fedorov shift of paraxial light beams’”

This is a reply to the Comment by Bliokh on our paper that appeared in Opt. Commun. 281 (2008) 3427. After a brief introduction of the representation theory of vector electromagnetic beams advanced in a recent paper, I point out that the Imbert-Fedorov effect is the evidence of the change of the beam parameter Θ and the polarization ellipticity σ caused by the reflection or transmission process in the linear approximation. Then I explain that it is because the linear approximation of the incident beam that we used in our paper had been assumed in previous works that we reproduced their results.     

Investigation of one-dimensional photonic crystals composed of dispersive materials

One-dimensional photonic crystals (1DPCs) composed of dispersive materials (including negative refractive index materials, negative μ materials, and negative ? materials) are proposed. The dependence of the band gaps on the angle of incidence and thickness scale are investigated by using the transfer matrix method. Simulation results show that the band gaps of these dispersive material 1DPC are insensitive to the thickness scale. The defect modes of these doped 1DPCs behave specially when the thickness of the defect layer, the angle of incidence and the thickness scale of PC change.     

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.     

Positive and Negative Lateral Shifts from an Anisotropic Metamaterial Slab Backed by a Metal

The lateral shift of a light beam at the surface of an anisotropic metamaterial (AMM) slab backed by a metal 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 AMM slab and the incident angle of the light beam strongly affect the properties of the lateral shift. Numerical results validate these conclusions. The lossy effect of the metamaterial on the lateral shift is also investigated.     

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.     

Anomalous wave propagation in quasiisotropic media

Based on boundary conditions and dispersion relations, the anomalous propagation of waves incident from regular isotropic media into quasiisotropic media is investigated. It is found that the anomalous negative refraction, anomalous total reflection and oblique total transmission can occur in the interface associated with quasiisotropic media. The Brewster angles of E- and H-polarized waves in quasiisotropic media are also discussed. It is shown that the propagation properties of waves in quasiisotropic media are significantly different from those in isotropic and anisotropic media.     

Chiral planar waveguide for guiding single-mode backward wave

Single-mode backward wave is shown to be guided in a planar dielectric waveguide with a strong chiral core. The significant difference of such a waveguide from the traditional one is the guidance of single-mode backward wave, without using negative permittivity and/or negative permeability. In the design, we generalize the idea of total internal reflection to the chiral medium and make a numerical analysis on the reflection with oblique incidence. We deduce rigorously a general solution of incident wave on the boundary of two arbitrary chiral magneto-electric media. We observe that the impedance matching can eliminate the coupling between two eigenwaves in chiral media. With strong chiral core and the matched impedance with cladding, one eigenwave becomes a backward wave and can be guided without transferring to the other eigenwave. If a single-mode propagation condition is satisfied, we will get single-mode backward guided wave. A special interface has been designed to prevent the forward wave entering the waveguide from the source.     

Two-Dimensional （2D） Polygonal Electromagnetic Cloaks

Transformation optics offers remarkable control over electromagnetic fields and opens an exciting gateway to design ＇invisible cloak devices＇ recently. We present an important class of two-dimensional （2D） cloaks with polygon geometries. Explicit expressions of transformed medium parameters are derived with their unique properties investigated. It is found that the elements of diagonalized permittivity tensors are always positive within an irregular polygon cloak besides one element diverges to plus infinity and the other two become zero at the inner boundary. At most positions, the principle axes of permittivity tensors do not align with position vectors. An irregular polygon cloak is designed and its invisibility to external electromagnetic waves is numerically verified. Since polygon cloaks can be tailored to resemble any objects, the transformation is finally generalized to the realization of 2D cloaks with arbitrary geometries.     

Analysis of closed-boundary cylindrical microlenses with long focal depth designed by the general focal length function

In this paper, the general focal length function is used to design two-dimensional closed-boundary cylindrical microlenses (CBCMs) with long focal depth. The focusing characteristics of the designed microlenses is investigated by rigorous electromagnetic theory and the boundary element method. A number of focusing performance measures of the designed microlenses, such as the real focal depth, the focal depth range, the focal spot size, and the diffraction efficiency, are presented in detailed. As comparison, the focusing performance of the conventional lenses with the same parameters are investigated simultaneously. Our analysis indicates that the general focal length function is valid in designing CBCMs with larger extended focal depth. Comparing with the open-boundary cylindrical microlenses (OBCMs) designed using the same focal length function, we also find that the designed CBCMs with low f-number exhibit superiority of long focal depth.     

Focusing performance of the closed-boundary cylindrical microlenses analyzed by the boundary element method

In this paper, we investigate the focusing performance of closed-boundary cylindrical microlenses (CBCMs) based on rigorous electromagnetic theory and the boundary element method. The CBCMs with different incident angles, different quantization-level numbers, different microlens diameters, different f-numbers, and different polarizations of incidence are studied. Several focusing performance measures, such as the focal spot size, the diffraction efficiency, the real focal position, and the normalized transmitted power, are presented. It provides very useful information in designing the CBCMs in micro-optical systems.     

A Time Domain Algorithm on the Reconstruction of Rough Surfaces

We consider the inverse scattering problem of a perfectly conducting one-dimensional rough surface in the case that the incident field is unnecessary to be time harmonic. Based on our previous investigation of the frequency domain algorithm, a new time domain algorithm is proposed, in which we approximate the incident pulse by a finite sum of time harmonic fields and then apply the frequency domain algorithm for time harmonic waves. Numerical experiments indicate that the time domain algorithm shows great accuracy of reconstruction of the surface profile and yields significant improvement than the frequency domain algorithm.     

The finite-thickness model applied to designs of closed-boundary cylindrical microlenses with small f-numbers

Instead of the existing zero-thickness model (ZTM), the finite-thickness model (FTM) is employed to designs of closed-boundary cylindrical microlenses (CBCMs) with small f-numbers based on the wave-front interference principle. To demonstrate the superiority of the FTM to the ZTM in the design of CBCMs, focal performance of all the designed microlenses is investigated by the rigorous boundary element method (BEM). For CBCMs with small f-numbers, numerical results by the BEM reveal that the designed CBCMs by using the FTM possess better focal performance than the designed CBCMs by using the ZTM, such as a more exact real focal position, a smaller focal spot size, and a higher diffraction efficiency.     

Erratum to: “Comment on: ‘Electromagnetic wave propagation in single-wall carbon nanotubes’ [Phys. Lett. A 333 (2004) 303]” [Phys. Lett. A 364 (2007) 515]

Here we plot the correct form of Fig. 2 in [H. Khosravi, A. Moradi, Phys. Lett. A 364 (2007) 515].