Change of the size of vector Bessel beam rings under reflection

We theoretically predict the change of the size of Bessel beam rings under reflection. Considered electromagnetic Bessel beam is the superposition of phase shifted TE and TM polarized Bessel beams. Reflection from a semi-infinite medium and from a slab are studied. The sets of parameters maximizing the effect are discussed.     

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.     

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.     

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.     

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.     

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.     

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.     

A Zone Plate as a Tunable Terahertz Filter

A broadband tunable terahertz filter based on a zone plate is demonstrated in our terahertz time domain spec- trometer. The central bandpass frequency covers the whole spectral range of the terahertz wave emitted from a ZnTe emitter, from 0.5 THz to 2.5 THz, and can be tuned continuously by simply moving the zone plate along the terahertz beam path. The peak transmission is about 40% and the bandwidth varies from 0.16 THz to 0.25 THz at different bandpass frequencies when the aperture size is kept constant.     

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.     

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].     

Focal Shift of Paraxial Gaussian Beams in a Left-Handed Material Slab Lens

Focal shift is inevitable in conventional lens systems due to the Fresnel number and angular aperture. In this Letter, we demonstrate that there is no focal shift when a paraxial Gaussian beam passes through a left-handed material slab lens without absorption or gain. However, the effect is exhibited in the presence of absorption or gain, and becomes larger as the absorption or gain increases. When the absorption is equal to the gain, the phenomenon of the focal shift caused by the gain is more obvious. In addition, the field distribution is not affected by the absorption or gain and always remains Gaussian both in internal and external focus planes.     

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.     

ABCD matrix formalism for propagation of Gaussian beam through left-handed material slab system

We apply a simple ABCD matrix formalism to investigate beam propagation in left-handed material (LHM) slab systems. Firstly, we derive the expressions for the matrix elements for a single LHM slab. Based on the ABCD matrix, we obtain the field distributions both inside and outside the LHM slab, and the conditions for focusing and phase compensation of the Gaussian beam. Secondly, the derived ABCD law is applied to analyze the propagation properties of Gaussian beams through various cascaded LHM slab systems. The corresponding focusing and phase compensation conditions of the Gaussian beam are also obtained. Our theoretic formalism may be applied as a compact and effective tool for the research of light beam propagation in complex LHM slab systems, since it avoids the complicated integral operation.     

Observation of total omnidirectional reflection from a one-dimensional dielectric lattice

3 AlF₆/ZnSe multilayer structure developed by means of standard optical technology. The structure was found to have a reflection coefficient of more then 99% in the range of incident angles 0°-86°at the wavelength of 632.8 nm for s-polarization. The results are likely to stimulate new experiments on photonic crystals and controlled spontaneous emission. Received: 30 October 1998/Accepted: 2 November 1998     

Reflection and refraction of the electromagnetic field in a semi-infinite plasma

We compute the reflected and refracted electromagnetic fields for an ideal semi-infinite (half-space) plasma, as well as the reflection coefficient, by using a general procedure based on equations of motion and electromagnetic potentials. The approach consists of representing the charge disturbances by a displacement field in the positions of the moving particles (electrons). The propagation of an electromagnetic wave in plasma is treated by means of the retarded electromagnetic potentials, and the resulting integral equations are solved. Generalized Fresnel’s relations are thereby obtained for any incidence angle and polarization and the angles of total polarization and total reflection are derived. Bulk and surface plasmon-polariton modes are identified. As it is well known, the field inside the plasma is either damped (evanescent) or propagating (transparency regime), and the reflection coefficient exhibits an abrupt enhancement on passing from the propagating regime to the damped one (total reflection).     

Theory of frustrated total internal reflection: Superluminal singularities of optical waveguides

Classical approach to frustrated total internal reflection (FTIR) does not describe its temporal properties, that are additionally considered and their superluminal singularity is shown. The transition to quantum electrodynamics shows that momenta of photons are reduced at FTIR relative to energy, i.e. it is the tunnel process, the nonlocal manifestation of near field. The tunneling consists in the instantaneous jump of excitations (virtual photons) onto definite distance, and can be described by equation having certain instanton features. Thus, the possibility of signal transfer with superluminal group velocity via optical fibers is substantiated that conforms to certain supervisions. Such properties of FTIR near field may explain, in principle, some other observed phenomena.     

Highly collimated emission from a left-handed photonic crystal with a quasi-cavity

We study the collimated emission characteristics from a dipole source inside a negative-effective-refractive-index photonic crystal with a quasi-cavity constructed by a concave photonic crystal reflector. The emissions along the ±X and −Y directions are forbidden by the quasi-cavity, so that most emissions propagate along the +Y direction. Simulation results show that a narrow collimated beam is achieved due to the near-zero negative effective refractive index. Moreover, the half-power beam width of such a collimated beam can be reduced to 3.48° by optimizing the size of the source area. Such a compact structure would have potential applications in micro-optical devices.     

Numerical test of the theory of pseudo-diffusive transmission at the Dirac point of a photonic band structure

It has recently been predicted that a conical singularity (=Dirac point) in the band structure of a photonic crystal produces an unusual 1/L scaling of the photon flux transmitted through a slab of thickness L. This inverse-linear scaling is unusual, because it is characteristic of radiative transport via diffusion modes through a disordered medium - while here it appears for propagation of Bloch modes in an ideal crystal without any disorder. We present a quantitative numerical test of the predicted scaling, by calculating the scattering of transverse-electric (TE) modes by a two-dimensional triangular lattice of dielectric rods in air. We verify the 1/L scaling and show that the slope differs by less than 10% from the value predicted for maximal coupling of the Bloch modes in the photonic crystal to the plane waves in free space.     

Generation of thin and hollow beams by the axicon with a large open angle

We propose a method to produce diffraction-free thin and hollow beams. The method is based on Laguerre-Gaussian (LG) beams incident on a large open-angle axicon. We use the vector diffraction integrals and stationary phase method to deduce a simple and analytical formula of the propagating field of the linearly polarized LG beams through an axicon. The numerical results show that the hollow beams of whose diameter is in the order of the wavelength can be obtained by using the axicon with the refractive index n = 2 and the open angle α = 25°. These diffraction-free thin and hollow beams may be very useful to accurately trap and manipulate atoms. However, when the open angle is over large, the conversion efficiency from the LG beam to the diffraction-free hollow beam will decrease obviously.     

Arrangement of a 4Pi microscope for reducing the confocal detection volume with two-photon excitation

The main advantage of two-photon fluorescence confocal microscopy is the low absorption obtained with live tissues at the wavelengths of operation. However, the resolution of two-photon fluorescence confocal microscopes is lower than in the case of one-photon excitation. The 4Pi microscope type C working in two-photon regime, in which the excitation beams are coherently superimposed and, simultaneously, the emitted beams are also coherently added, has shown to be a good solution for increasing the resolution along the optical axis and for reducing the amplitude of the side lobes of the point spread function. However, the resolution in the transverse plane is poorer than in the case of one-photon excitation due to the larger wavelength involved in the two-photon fluorescence process. In this paper we show that a particular arrangement of the 4Pi microscope, referenced as 4Pi′ microscope, is a solution for obtaining a lateral resolution in the two-photon regime similar or even better to that obtained with 4Pi microscopes working in the one-photon excitation regime.