Coherent-mode representation and orbital angular momentum spectrum of partially coherent beam

Orbital angular momentum of the coherent beam has been intensively studied and promises potential applications in free space optical communication. But the orbital angular momentum of partially coherent beam is not well known. In this communication the coherent-mode representation method is adopted to describe the partially coherent beam and the orbital angular momentum spectrum is introduced for the partially coherent beam. The characteristics of the orbital angular momentum spectrum of partially coherent beam are discussed. To study the influence of the partial coherence on the optical link, the channel capacity is studied, with two kinds of available mode separators included.     

Conservation laws and angular transverse shifts of the reflected and transmitted light beams

The relation between the angular transverse shifts of the beams reflected and transmitted at a plane interface of two isotropic transparent media is established. The derivation of this relation is based on the conservation law of the transverse component of the total Minkowski linear momentum, which takes place in the processes of the reflection and transmission of wave packets.     

Smoothing effect in the broadband laser through a dispersive wedge

The propagation expression of a broadband laser passing through a dispersive wedge is derived on the basis of the Huygens-Fresnel diffraction integral. Smoothing effects caused by the phase perturbation of the dispersive wedge on the intensity profiles are investigated in detail. The phase perturbation of the dispersive wedge induces a relative transverse position shift between the diffraction patterns of different frequency components. The relative transverse position shift is of great benefit to the fill of the intensity peaks of some patterns in the valleys of others when these patterns are overlapped and thus the smoothing effect is achieved.     

Generation of bottle beam by focusing a super-Gaussian beam using a lens and an axicon

This study explores the characteristics of the bottle beams that are formed by super-Gaussian beams that impinge through an axicon and a positive lens. Analytical solutions for the on-axial intensity of Gaussian and apertured-plane beams were obtained. The barrier around the dark region has a larger variation of intensity for higher-order super-Gaussian profiles. Flattening the tops of the profiles increases the bottle lengths for a fixed second-order moment width or distance between the axicon and the lens.     

Different field distributions obtained with an axicon and an amplitude mask

A combination of an axicon and an amplitude mask is used to obtain an intensity distribution that differs from the typical Bessel one. Experimental and numerical characterization of the field is made for different propagation distances and types of amplitude masks.     

A Novel Method for Enhancing Goos-Hänchen Shift in Total Internal Reflection

Due to the tiny shift in order of optical wavelength for Goos-Hǎnchen （GH） shift, it is very difficult to directly measure and apply the GH shift. We develop a new method for enhancing GH shift of both TE and TM polarized waves. The method is based on a total reflection prism made of BK9 glass combined with a precise measurement of the resulting spatial displacement with a one-dimensional charge coupled device （CCD）. Measurements are performed to examine the validity of the method. Experimental and theoretical results indicate the feasibility of the method with an enhancement in optical wavelenghth shift at millimetre scale. The method is advantageous to application the GH shift in the optical domain, and is also meaningful for measuring even smaller changes in the refractive index of a liquid.     

A neat semi-Gaussian laser beam with no diffraction fringes: Theoretical analysis

We propose a simple optical device to convert a Gaussian laser beam into a neat semi-Gaussian laser beam without any diffraction fringe by using a spatial light modulator and a thin, sharp blade, and numerically calculate the diffracted, relative intensity distributions of both the semi-Gaussian laser field and the semi-Gaussian, pseudo-thermal light. We also study the dependence of the border width of the semi-Gaussian beam on the waist of the Gaussian beam. Our study shows that the proposed scheme can be used to cancel all diffraction fringes from both the straight edge of the blade and a finite lens aperture in all the planes vertical to the z axis and obtain a neat semi-Gaussian beam without any diffraction fringe, and find that the border width w_B of the generated semi-Gaussian beam is not dependent on the waist of the incident Gaussian beam.     

Generation of a radially polarized doughnut mode of high quality

We present an experimental set-up to generate laser beams with locally varying polarization distribution. In a linear set-up, a radially polarized beam of high quality regarding intensity distribution, polarization and phase-front distortion is generated. This beam can be used for tight focusing. Further applications are discussed.     

Conversion of high-order Laguerre-Gaussian beams into Bessel beams of increased, reduced or zeroth order by use of a helical axicon

We propose a new method for transformation of a Laguerre-Gaussian beam of azimuthal index l and radial index n = 0 (LG_l,0) into a vortex, diverging or nondiverging Bessel beam, which can have increased or decreased phase singularity order, or into a zeroth order Bessel beam, by means of a helical axicon. The Bessel beam divergence or nondivergence depends upon the waist position of the input Laguerre-Gaussian beam, regarding the plane where the helical axicon is situated.The expressions for the amplitude and the intensity distribution of the diffracted wave field, in the process of Fresnel diffraction, are deduced using the stationary phase method. The theoretical analysis for the vortex radius and the maximum propagation distance of the Bessel beams obtained is presented.     

Up-conversion detection of mid-infrared light carrying orbital angular momentum

Frequency up-conversion is an effective method of mid-infrared (MIR) detection by converting long-wavelength photons to the visible domain, where efficient detectors are readily available. Here, we generate MIR light carrying orbital angular momentum (OAM) from a difference frequency generation process and perform up-conversion on it via sum frequency conversion in a bulk quasi-phase-matching crystal. The maximum quantum conversion efficiencies from MIR to visible are 34.0%, 10.4%, and 3.5% for light with topological charges of 0, 1, and 2, respectively, achieved by utilizing an optimized strong pump light. We also verify the OAM conservation with a specially designed interferometer, and the results agree well with the numerical simulations. Our study opens up the possibilities for generating, manipulating, and detecting MIR light that carries OAM, and will have great potential for optical communications and remote sensing in the MIR regime.     

Observation of the orbital angular momentum spectrum of a light beam

We demonstrate an experimental scheme that allows the elucidation of the orbital angular momentum discrete spectrum of an arbitrary light signal. The orbital angular momentum spectrum is represented in a Laguerre-Gaussian mode base, and the spectral components are resolved in the frequency domain by exploiting the Doppler frequency shift that is imparted to rotating light beams.     

A Simple Model for Measuring Refractive Index of a Liquid Based upon Fresnel Equations

Due to many experimental data required and a lot of calculations involved, it is very complex and cumbersome to model prism-based liquid-refractive-index-measuring methods. We develop a new method of mathematical modelling for measuring refractive index of a liquid based upon the Fresnel formula and prism internal reflection at an incident angle less than the critical angle. With this method, only two different concentrations measurements for a kind of solution can lead to the determination of computational model. Measurements are performed to examine the validity of the theoretical model. Experimental results indicate the feasibility of the theoretical model with an error of 1%. The method is also capable of measuring even smaller changes in the optical refractive index of the material on a metal surface by the surface plasma resonance sensing techniques.     

Spatial coherence of an optical turbulent beam in a biased photorefractive crystal due to the spatiotemporal modulation instability

We report the experimental observation of the dynamic pattern formation of a broad coherent light beam in a biased photorefractive crystal due to the spatiotemporal modulation instability. When the nonlinearity exceeds a specific threshold, the coherent light beam not only breaks up into light spots due to the modulation instability but also fast fluctuates both spatially and temporally, forming an optical turbulent beam, which behaves as a quasi-homogeneous speckled beam or a partially incoherent beam. We investigate the spatial coherence property of an optical turbulent beam from the visibility of the averaged double-slit interference fringe. We also numerically demonstrate the visibility variation of the instantaneous interference fringe of an optical turbulent beam.     

The symmetry properties of stable polynomial Gaussian beam profiles

We consider the symmetry properties of polynomial Gaussian beam profiles (intensity distributions) that remain stable during propagation, apart from being scaled and possibly rotated. These beams are expressed as special linear combinations of the Laguerre-Gaussian modes. Two kinds of symmetries are present: discreet rotational symmetries and mirror symmetries. The symmetry properties are shown to depend on the particular subset of Laguerre-Gaussian modes that is used to construct the stable beam. We demonstrate the symmetry properties of a few examples of stable beams through numerical simulations.     

Effects of the frequency chirp on the fields of a chirped Gaussian pulse passing through a hard-edged aperture

Based on the Huygens-Fresnel diffraction integral and Fourier transform, propagation expression of a chirped Gaussian pulse passing through a hard-edged aperture is derived. Intensity distributions of the pulse with different frequency chirp in the near-field and far-field are analyzed in detail by numerical calculations. In the near-field, amplitudes of the intensity peaks generated by the modulation of the hard-edged aperture decrease with increasing the frequency chirp, which results in the improving of the beam uniformity. A physical explanation for the smoothing effect brought by increasing the frequency chirp is given. The smoothing effect is achieved not only in the pulse with Gaussian transverse profile but also in the pulse with Hermite-Gaussian transverse profile when the frequency chirp increases.     

Rotation of laser beams with zero of the orbital angular momentum

We show that among the multitude of rotating light beams whose complex amplitude can be represented as a linear superposition of the Laguerre-Gaussian (LG) modes with definite numbers there are light beams with zero orbital angular momentum (OAM) and vice versa, multi-mode LG beams that show no rotation and are lacking the radially symmetric intensity distribution can possess the non-zero OAM. Also, we give examples of the rotating light beams with zero OAM, represented as a superposition of the Bessel and new hypergeometric modes. Using an SLM, we generate a rotating Bessel beam with zero OAM for the first time.     

Generation and interference collapse of distortion-less fs pulses in free space by Fresnel sources

A method of formation of the tightly confined, distortion-free, femtosecond pulses in two dimensions (2D) with the step-like decreasing of intensity after a finite length of propagation in free space is described. The pulses are formed by the Fresnel source of modes corresponding to a 2D hollow waveguide with perfectly reflecting walls (material waveguide). The source reproduces in free space a propagation-invariant pulse confined by the waveguide. Unlike the case of material waveguides, when the pulse goes out from the virtual waveguide formed by the Fresnel source its shape does not change, but the intensity immediately drops down to the near-zero level. It is also shown that there is a limit of the duration of pulse beyond which the step-like decay is not observed.     

Influence of laser wavelength on target irradiation uniformity

Target irradiation uniformity is very important in laser-produced plasmas experiments. The wavelength dependence of the irradiation uniformity is investigated in the joint scheme using a lens array (LA) and the technique of smoothing by spectral dispersion (SSD). It is proved that, for the long wavelength laser, lateral thermal conduction smoothing within the target is quite effective, while for the ultraviolet laser, SSD is the main smoothing mechanism. So SSD and other temporal smoothing methods are very necessary in producing uniform irradiation with laser beam of short wavelength.     

Large Positive and Negative Lateral Displacements from Total Internal Reflection Configuration with a Weakly Absorbing Dielectric Film

It is theoretically shown that the simultaneously large positive and negative lateral displacements will appear when the resonant condition is satisfied for a TE-polarized light beam reflected from the total internal reflection configuration with a weakly absorbing dielectric film. Appearance of the enhanced negative lateral displacement is relative to the incidence angle, absorption of the thin film and its thickness. If we select an appropriate weakly absorbing dielectric film and its thickness, the simultaneously enhanced positive and negative lateral displacements will appear at different resonant angles. These phenomena may lead to convenient measurements and interesting applications in optical devices.     

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.