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Cylindrical vector beams are described by the representation formalism of finite electromagnetic beams in free space. This is achieved by factorizing the field vector into a mapping matrix and a Jones-like vector. The vectorial property of a finite beam can be described by a degree of freedom of the mapping matrix that can be determined by the azimuthal angle of a fixed unit vector with respect to the wave vector. In addition, it is a simple and flexible experimental device for converting linearly polarized light beams into cylindrical vector beams. The radially or azimuthally polarized beam is easily converted into either one of these by varying the applied voltage.

We study the bistable and negative lateral shifts of the reflected light beam from Kretschmann configuration containing left-handed metamaterials with self-focusing and self-defocusing Kerr-type nonlinearity. It is shown that the lateral shifts can be large and negative when the thickness of the middle metal film is smaller than the critical value. Taking the nonlinear effect into account, there exists a hysteretic response between the beam shift and the intensity of the incident light beam. These results suggest that the bistable and negative beam shifts can be modulated by nonlinear coefficients and intensity of incident beam, which might be used in integrated photonics and optical switches.

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.

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.

In this work, we systematically investigate the group delay time of an electron wave packet through a two-dimensional semiconductor heterostructure. It is shown that the lateral displacement, resulting from the angular spread of the electron wave packet, plays an important role in total delay time. In the propagating case, the group delay time can be negative due to the effect of lateral displacement, and is greatly enhanced by transmission resonances. In the evanescent case, the delay time saturates to a constant in the opaque limit, which is simply the Hartman effect observed for a two-dimensional situation.

The authors observed amplified spontaneous emission (ASE) action with an ultra-low threshold under optical excitation from an active polymeric distributed-feedback (DFB) resonator which consists of sub-micrometer fiber grating. A dendrimer was used to modify the laser dye and increased its concentration up to 4.95 wt. % in the photocured resin. The DFB resonator was fabricated by using two-photon induced polymerization (TPIP) technique. The ASE at 556 nm was observed with a threshold of 0.30 μJ/pulse due to fourth-order diffraction feedback of the optical gain. This DFB could be expected to open a way for the fabrication and application of microscale polymeric mirrorless laser.

Since the Goos-Hänchen (GH) effect is the displacement of the totally reflected beam at a dielectric interface from the position prediction by geometrical reflection, the concept of GH displacement is applicable only when the reflected beam retains the shape of the geometrically reflected or incident beam. The necessary and sufficient condition has been advanced for the totally reflected beam to retain the shape of the incident beam. Numerical simulations have been performed to confirm this condition. It has been shown that the GH displacement results from the mechanism of beam reshaping due to the linear dependence of the reflection phase shift upon the parallel component of the wave vector, in the interval in which the angular spectral distribution function of the incident beam is appreciable.

The optical holographic recording properties of the azo dye l-(2-Pyridylazo)-2-Naphthol in PMMA thin film were studied by using the three-dimensional forward degenerate four-wave mixing technique with a ps pulse laser at 532 nm. It demonstrated that the transient grating turned into a permanent grating with the increase of the pulse energy and the grating can be erased through a thermal treatment of the film. The mechanism of the fixed grating was attributed to the trans – cis isomerization of the azo molecules induced by singlet excited-state absorption and the subsequent orientation of the molecules.

An experimental technique is presented in this paper for the measurement of the crosslinking temperature ( T crosslinking ) of the polymer films by using the attenuated total reflection (ATR) spectrum. According to the change of the ATR spectrum, the changing value of the refractive index of the polymer film can be determined during the ascending temperature. Experimental results definitely show that the temperature dependence of the refractive index d n /d T changes discontinuously. By linear fits, the d n /d T curve exists two intersection points. The temperature range between two intersection points is regarded as T crosslinking . The crosslinking range of the polyurethane is determined as the range from 85 °C to 122 °C. It is examined and convinced by the measurement of electro-optic r 33 coefficient of the poled polyurethane film with several temperatures in the range of T crosslinking at which poling is started.

Using a omega-3 omega combination scenario, we investigate the absolute phase control of the spectra effects for ultrashort laser pulses propagating in a two-level medium. It is found that the higher spectral components can be controlled by the absolute phases. In particular, different absolute phase combinations can lead to the buildup or split of the even harmonics. (c) 2006 Elsevier B.V. All rights reserved.

We investigate the large negative lateral displacements of TE polarized light beams reflected from or transmitted through an active slab surrounded by transparent medium. The large negative displacements can be achieved when the incidence angle of the beam is less than but close to the critical angle for total reflection. It is also shown that both the reflectivity and transmissivity of the beam that correspond to the large negative displacements can be enhanced by active medium. These phenomena may lead to convenient measurements and interesting applications in optical devices.

Lateral displacement and its mechanism in asymmetric layered configuration are investigated. It is shown by the stationary-phase approach that displacements of both the transmitted and reflected beams can be positive as well as negative, and their magnitude can be greatly enhanced at transmission resonances. Numerical simulations show that for a well-collimated incident beam, if the norms of transmission and reflection coefficients are approximately constant within the peak of the angular-spectrum distribution of the beam, the transmitted and reflected beams can undergo lateral displacement without distortion, as long as the thickness of the layer satisfies a restriction. It is concluded that lateral displacement is not caused by beam distortion, but the result of reshaping the multiply transmitted (or reflected) beams.

The lateral displacement of electron beams transmitting through a two-dimensional semiconductor barrier is quite different from the prediction from Snell's law for electron waves. It is shown that the displacement can be greatly enhanced by transmission resonance when the incidence angle is less than but close to the critical angle for total reflection. The displacement depends not only on the barrier's thickness but also on the incidence angle and the incidence energy. The influence of electron's effective mass is also discussed. Theoretical results of the stationary-phase approach are confirmed by numerical simulations for a Gaussian-shaped incident beam. These phenomena may lead to novel applications in quantum electronic devices.

It is shown that transmission and reflection group delay times in an asymmetric single quantum barrier are greatly enhanced by the transmission resonance when the energy of incident particles is larger than the height of the barrier. The resonant transmission group delay is of the order of the quasibound state lifetime in the barrier region. The reflection group delay can be either positive or negative, depending on the relative height of the potential energies on the two sides of the barrier. Its magnitude is much larger than the quasibound state lifetime. These predictions have been observed in microwave experiments.

Photon tunnelling in a metamaterial photonic crystal composed by positive index material (PIM) and negative index material (NIM) layers is discussed. First, a single period of this photonic crystal is considered as the barrier in a frustrated total internal reflection (FTIR) structure, and the transmittance, the post-tunnelling position shift and the group delay time of different frequency incident waves through the barrier are calculated. In the case of a barrier of more periods of photonic crystal, the transmittance and the group delay time also vary with layer number, which are analysed in detail.

The propagation of a Gaussian-shaped beam through a slab of optically denser dielectric medium in the air, a two-dimensional optical counterpart of the quantum potential well, is investigated in order to elucidate the negative lateral shifts of transmitted and reflected beams. It is shown that the locus of the peak of the beam inside the slab consists of two parts. One propagates backwards and seems to be the geometric reflection of the other that propagates forwards. But they are not continuous with the loci of the peaks of the incident and reflected beams. A restriction to the thickness of the slab is obtained that is necessary for the shape of the beam to remain unchanged in the travelling.

It is observed that there exist two different classes of vector light beams that have the same first-order paraxial approximation. They are characterized by the axial and transverse orientations of a constant unit vector that comes from the constraint of transversality condition. Their vectorial structures in the nonparaxial regime and angular momentum properties are compared.

A new kind of traversal time for tunneling particles through a potential barrier that has no problem of superluminality is introduced. Its physical significance is investigated. Several limits are considered, which are physically meaningful. Comparisons with dwell time and phase time are also made.

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.

We investigate the lateral shift of a TM-polarized light beam reflected from Otto configuration under grazing incidence. It is found that the lateral shift is strongly dependent on the thickness of the air-gap layer. By employing the pole-null representation, we demonstrate that the lateral shift is closely related to the null of the reflection function. The numerical simulations for a Gaussian beam are performed to demonstrate the validity of our theoretical analysis.

Motivated by the realization of the Dirac point (DP) with a double-cone structure for optical field in the negative-zero-positive index metamaterial (NZPIM), the reflection, transmission, and Goos-H\"{a}nchen (GH) shifts inside the NZPIM slab are investigated. Due to the linear Dirac dispersion, the transmission as the function of the frequency has a gap, thus the correspond reflection has a frequency or wavelength window for the perfect reflection, which is similar to the Bragg reflection in the one-dimensional photonic crystals. Near the DP, the associated GH shifts in the transmission and reflection can be changed from positive to negative with increasing the wavelength. These negative and positive shifts can also be enhanced by transmission resonances, when the frequency is far from that at the DP. All these phenomena will lead to some potential applications in the integrated optics and optical devices., Comment: 5 pages, 5 figures

The experimental data reported in Science 319, 787 (2008) are shown to demonstrate the existence of a new characteristic vector of light beams advanced in a previous paper Physical Review A 78, 063831 (2008).

Thin annular sources, either Coherent or completely incoherent from the spatial standpoint, have played a significant role in the synthesis of diffraction-free and J(0)-correlated fields, respectively. Here, we consider thin annular sources with partial correlation. A scalar description is developed under the assumption that the correlation function between two points depends on their angular distance only. We show that for any such source the modal expansion can easily be found. Further, we examine how the correlation properties of the radiated fields change on free propagation. We also give a number of examples and present possible synthesis schemes. (C) 2008 Optical Society of America

We report that the transmitted evanescent light beam under total reflection will experience a lateral displacement similarly to that of the reflected beam, called Goos-Hanchen (GH) effect. By a dielectric thin film coated onto the dielectric surface, which is usually considered as the near-field enhanced configuration in atom optics, we indicate that the displacement of the transmitted evanescent beam can be greatly enhanced to several tens of wavelengths at transmission resonance under total internal reflection. Numerical simulations have been performed and it is shown that the transmitted evanescent beam maintains well the shape of the incident beam when the thickness of the thin film is required to be of the order of wavelength. Further, it is demonstrated that the stationary-phase approach is also applicable to transmitted evanescent beam and the GH displacement of the transmitted beam is just half the GH displacement of the reflected beam. The discussions presented here may arouse interest in atom optics and near-field microscope.

It is investigated that the Goos-Hanchen-like displacement of light beams transmitting through periodical multiple-layered structures can be negative as well as positive. The numerical simulations for Gaussian-shaped beam are made to demonstrate the validity of the stationary phase approach.

It is predicted that large and opposite generalized Goos-Hänchen (GGH) shifts may occur simultaneously for TE and TM light beams upon reflection from an asymmetric double-prism configuration when the angle of incidence is below but near the critical angle for total reflection, which may lead to interesting applications in optical devices and integrated optics. Numerical simulations show that the magnitude of the GGH shift can be of the order of beam's width.

It is reported that when a light beam travels through a slab of left-handed medium in the air, the lateral shift of the transmitted beam can be negative as well as positive. The necessary condition for the lateral shift to be positive is given. The validity of the stationary-phase approach is demonstrated by numerical simulations for a Gaussian-shaped beam. A restriction to the slab's thickness is provided that is necessary for the beam to retain its profile in the traveling. It is shown that the lateral shift of the reflected beam is equal to that of the transmitted beam in the symmetric configuration., Comment: 14 pages, 4 figures

Recent papers [1, 2] on the Goos-Hanchen (GH) shift [3] are still in the wake of the original effort to find new situations that allow for the occurrence of the GH shift. Previously found GH shifts are in general the order of the wavelength. Rare effort has been made to find the way of obtaining large GH shifts. Last year, Lai and Chan [4] and Broe and Keller [5] reported large GH shifts for TM beams in different configurations. In this paper, I report a new phenomenon that large and opposite GH shifts may occur simultaneously for TE and TM beams in an unsymmetrical double-prism configuration.

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.

An amendment is made to the nonparaxial beam solution advanced by Barnett and Allen for the purpose of exploring the problem of angular momentum.

Systems involving nonlinear media and their interaction with electromagnetic waves are potentially useful in various important practical applications. In the last decade or so, the availability of high-quality gyromagnetic crystal has led to a growing interest in nonlinear magnetic waves14. The interactions of gyromagnetic crystals with infrared waves or microwaves have drawn much attention. And many distinguishing features have been discovered in gyromagnetic waveguides. Recently. we have studied the frequency characteristics of magnetic spatial solitons on the surface of two-sublattice uniaxia! antiferrornagnetic crystal241. The striking feature of the soliton is the existence of the frequency passband(s) and stopband(s) that can be switched into each other by varying the power. In this article we studied the TE (transverse electric) surface waves, in the region of microwave frequency, on the interface between a linear ferromagnet and a two sublattice Un iaxial nonlinear antiferromagnet.

The three dimensional intensity distribution of focused spatial-variant polarized vector Bessel–Gauss beams is investigated in the vicinity of the focal plane by using the Richards–Wolf vectorial diffraction method. The local polarized states of the incident beams vary between linearity and ellipse, and can be easily controlled in real time by a new parameter, namely the phase delay angle, which is introduced by a liquid crystal variable retarder. Our analysis proves the existence of a focal shift toward the focusing objective for this type of beam. The dependence of the focal shift on the different parameters of the beams is discussed in detail. Numerical results indicate that the magnitude of the focal shift is associated with the mode number, the local polarization, the beam width and the wavelength of the incident beams. The controllability of the focal shift indirectly caused by the phase delay angle will have great potential applications in optical micro-manipulation.

This paper is concerned with an observable effect of an unusual quantal degree of freedom that is compatible with the constraint of the transversality condition. The dependence of the barycenter of a diffraction-free light beam on this degree of freedom is investigated.

It is observed that a constant unit vector denoted by $\mathbf I$ is needed to characterize a complete orthonormal set of vector diffraction-free beams. The previously found diffraction-free beams are shown to be included as special cases. The $\mathbf I$-dependence of the longitudinal component of diffraction-free beams is also discussed., 8 pages and 2 figures

We investigate guided modes in the asymmetric waveguide structure with a left-handed material (LHM) layer surrounded by air and metal. A graphical method is proposed to determine the guided modes. New properties of the oscillating and surface guided modes, such as absence of the fundamental mode, coexistence of the oscillating and surface guided modes, fast attenuation of the surface guided modes, and mode degeneracy, are analyzed in detail. We also investigate dispersive characteristics of the metal-LHM-air optical waveguide. The propagation constant increases with decreasing slab thickness for the first-order oscillating mode, which is different from that in traditional metal-cladding waveguides.

Beams of non-uniform elliptical polarization distribution have been obtained in real time from a radially or an azimuthally polarized beam by using a liquid crystal variable retarder (LCVR), which can be modulated by varying the applied voltage. The local polarization states analyzed by the Stokes parameters strongly depend on the spatial position and the phase retardation angle of the LCVR. The angular momentum of the beams varies in each quadrant, where the polarization rotated direction for the radially polarized beam through the LCVR is right-handed in the first quadrant and the third quadrant, while it is left-handed in the second quadrant and the fourth quadrant. However, the polarization rotated direction for the azimuthally polarized beam through the LCVR is the inverse of that for the radially polarized beam.

The origin of negative and positive lateral shifts of the light beams in a dielectric slab configuration is investigated from the viewpoint of the interference between multiple light beams, due to the multiple reflections and transmissions inside the slab. It is shown that the whole reflected and transmitted beams with negative shifts can be obtained from the successively reflected and transmitted constituents, respectively, with positive displacements predicted from geometrical optics. When the slab's thickness is much smaller in comparison with the width of the beam waist, the reshaping reflected and transmitted beams retain the profile of the incident beam. The physical mechanism presented here could also be applicable in investigating other counterintuitive phenomena, such as the superluminal traversal time in quantum tunneling and dispersive media.

We have investigated the tunable lateral shift and polarization beam splitting of the transmitted light beam through electro-optic crystals, based on the Pockels effect. The positive and negative lateral shifts could be easily controlled by adjusting the permittivity tensor, which is modulated by the external applied electric field. An alternative way to realize the polarization beam splitter was also proposed by the polarization-dependent lateral shifts. Numerical simulations for Gaussian-shaped incident beam have demonstrated the above theoretical results obtained by stationary phase method. All these phenomena have potential applications in optical devices.

The guided modes are investigated in a symmetric five-layer slab waveguide with a core of negative refractive index material surrounded by four normal dielectrics. The graphical method is applied to determine the guided optical modes. The left-handed material waveguide supports both oscillating and surface guided modes. For oscillating guided modes the fundamental mode can be supported. Mode double-degeneracy appears and some modes are absent in the five-layer waveguide. High-order surface guided modes exist due to the oscillating electric field in the inner claddings. Energy flux for the oscillating and surface guided modes is also discussed in detail.

We investigate the reflection of a TM-polarized light beam from a Kretschmann configuration with a Kerr nonlinear dielectric. It is found that there exists a hysteretic response between the lateral shift of the reflected beam and the intensity of the incident beam. In contrast to the lower switch threshold, the higher switch threshold of optical bistability is more sensitive to the variations of the angle of incidence and the thickness of metal film. It is also found that the peak value of the lateral shift is strongly dependent on the thickness of metal film.

It is predicted that the Goos-Hanchen displacement in the usual frustrated total internal reflection configuration can be resonantly enhanced greatly by coating a dielectric thin film onto the surface of the first prism when the angle of incidence is larger than the critical angle for total reflection at the prism-vacuum interface and is smaller than but close to the critical angle for total reflection at the prism-film interface. Theoretical analysis shows that the displacement of transmitted beam is about half the displacement of reflected beam in the thick limit of the vacuum gap between the two prisms. This is to be compared with the relation in the usual symmetric double-prism configuration that the displacement of transmitted beam is equal to the displacement of reflected beam. Numerical simulations for a Gaussian incident beam of waist width of 100 wavelengths reveal that when the dielectric thin film is of the order of wavelength in thickness, both the reflected and transmitted beams maintain well the shape of the incident beam in the thick limit of the vacuum gap. So largely enhanced displacements would lead to applications in optical devices and integrated optics.

The frequency properties of the nonlinear transverse electric (TE) waves on the interface between a dielectric and a nonlinear antiferromagnet are studied. The analyzed expressions of the field components of TE waves are derived in a large power case. We find that the peak magnetic field moves into the nonlinear antiferromagnet from the interface when the power of TE waves increases. Using the explicit dispersion equation obtained in this article we analyze in detail the frequency regions of the TE surface waves. The results show the nonlinear TE surface waves have frequency passband and stopband, which can be switched into each other by varying the power. It is also revealed that, under certain conditions, the nonlinear TE waves on the interface are backward surface waves with the group and phase velocities opposite in direction.