Dark Hollow Beam Research Articles

Size-variable dark-hollow beam generation using cross-phase modulation

We demonstrate dark-hollow beam (DHB) generation based on cross-phase modulation (XPM) in the hot Rb cell. It is found that a Gaussian beam (probe beam) can be converted into a DHB when the Rb cell is illuminated by a relatively intense counter-propagating Gaussian beam (pump beam). The size of the DHB can be adjusted by the pump power and sample temperature. In addition, a Bessel beam is obtained by focusing the DHB, which exhibits superior non-diffraction and self-healing abilities. The merits of tunable in size, simple setup, and low cost would make this method of significance in a variety of applications.

Propagation characteristics and optical forces exerted upon a Rayleigh dielectric sphere for a controllable dark-hollow beam

Propagation characteristics and optical forces exerted upon a Rayleigh dielectric sphere for a novel controllable dark-hollow beam (CDHB) are analyzed theoretically and illustrated numerically. In view of the unique focusing characteristics that a sharp, peak-centered, and adjustable configuration would be produced in the focal region, a tightly focused CDHB could be exploited to trap and manipulate particles with high-refractive index in the focal vicinity. Furthermore, it is significant that the CDHB tweezers’ trapping efficiency and optical trap stiffness could be finely controlled by adjusting either the targeted beam’s order or the central dark size controlling parameter. Finally, the trapping stability conditions are analyzed. The results obtained here are of interest and importance in optical manipulations and investigations for a CDHB.

Propagation properties of optical bottle beam in turbulence

We study the propagation properties of optical bottle beams in turbulent atmosphere. By allowing the mathematical expression of source plane to cover both the symmetric and asymmetric forms, the beam is propagated through turbulence using random phase screens. On the source plane, the intensity profile of the bottle beam resembles a dark hollow beam with an outside ring for symmetric cases, whereas it becomes divided into two or more separate lobes for the asymmetric cases. During propagation, both symmetric and asymmetric beams concentrate the intensity toward the center, eventually assuming a Gaussian shape, where this process seems to be more rapid for the former beam types. The rising trend of the kurtosis parameter of bottle beams changes to a falling trend when the refractive index structure constant is reduced from 10 − 14 to 10 − 13 m − 2/3.

Synthesis of ununiformly correlated radially polarized partially coherent beam

Since the unified theory of coherence and polarization for partially coherent vector beams was proposed by Gori and Wolf, the characterization, generation and propagation of partially coherent vector beams have been extensively studied. During the last decade, partially coherent vector beams with non-uniform polarization, also referred to as cylindrical vector partially coherent beams, have gained more and more attention. It was found that the intensity profile of focused azimuthally/radially polarized beam could be shaped by varying its initial spatial coherence. This characteristic may have potential applications in material thermal processing and particle trapping. Until now, there have been several reports concerning the generation of cylindrical vector partially coherent beams. However, in most of these reports a ground-glass diffuser was used, which generally restricts the generation of shell-model sources. In this paper, we theoretically and experimentally investigate the generation of radially polarized partially coherent beams with non-uniform correlation. According to the relation between phase correlation and optical coherence, we theoretically investigate the 2 × 2 cross-spectral density matrix and the coherence distribution of our generated non-uniformly correlated radially polarized partially coherent beams. In experiment, we generate dynamic random phase patterns with uniform distribution in time and inverse Gaussian distribution in space. A complete coherent radially polarized beam is divided into two parts by a polarizing beam splitter, i.e., the transmitted <i>x</i>-polarization component (HG<sub>10</sub> beam) and the reflected <i>y</i>-polarization component (HG<sub>01</sub> beam). The two orthogonally polarized components are respectively modulated with the two halves of a single phase-only liquid crystal spatial light modulator, thus generating a radially polarized partially coherent beam. We measure the correlation distribution of the generated beam in Young’s two-pinhole experiment. It is shown that the experimental observations are in agreement with our theoretical analyses. The generated partially coherent beam has an un-uniform correlation structure, and its coherence degree may be controlled by varying the Gaussian modulation half-width of the random phase. Our experimental results have also shown that the intensity profile of the radially polarized partially coherent beam can be modulated with the Gaussian modulation half-width. With the increase of Gaussian modulation half-widths and the gradual decrease of coherence degree, the intensity profile gradually transforms from a dark hollow beam profile into a flat-topped-like beam profile. The radially polarized partially coherent beams with non-uniform correlation may have some applications in optical manipulation and material thermal processing.

Spiral spectrum analysis and application ofcoherent synthetic vortex beams

The vortex beam is a ring-shaped beam whose center intensity or axial intensity is zero in the propagation direction and whose phase has a spiral rising or falling gradient distribution, which is also called a dark hollow beam. Vortex beams have important applications in free-space optical communication, optical micromanipulation, quantum information processing, optical measurement, super-resolution imaging, laser processing, and material processing. In recent years, with the in-depth research on vortex beams, the application requirements for high-power vortex beams also increase. High-power and high-quality vortex beam can be obtained by coherent combining technology. However, the spiral spectrum characteristics of the vortex beam generated by coherent combining technology need further exploring. In this paper, based on the theory of spectral analysis, we derive the position and magnitude of the spiral phase spectral component of the coherent synthetic vortex beam. The numerical results verify the correctness of the theoretical derivation. Based on the above spectral analysis theory, the mode purity of the target synthesis topology charge can be used as the evaluation function to evaluate quality and optimize the parameters for the coherent synthetic vortex beam, and then to quantitatively guide the coherent synthesis of the vortex beam. The results show that with the increase of the number of sub-beams and the radius of the beam waist of the source plane, the reduction of the radius of the bundle ring and the mode purity of the target synthesis topology charge can be improved, and then we can obtain the high-quality vortex beam. This is consistent with the conclusion obtained by using traditional evaluation functions such as power in the bucket. The spiral spectrum analysis of the coherent synthetic vortex beam not only makes up for the lack of evaluation of the spiral phase synthesis effect by the traditional evaluation function, but also has certain reference significance for understanding the nature of the coherent synthesis technique.

Generation of propagation-invariant and intensity-controlled dark hollow beams by a refractive beam shaping system.

Dark hollow beams (DHBs) have great potential in the applications of optical manipulation, and the generation of DHBs is still a challenging and rewarding issue. In this paper, we present a beam shaping system for generating DHBs. The proposed system is composed of a freeform lens array and a non-classical zoom system which has a constant focal length but various image locations. The DHBs with a well-controlled intensity profile generated by the proposed system is not sensitive to the change of the intensity distribution of the incident beam, which allows flexible choices of light sources. Moreover, the annular pattern produced by the DHB remains unchanged when the image plane is moved a long distance of 17mm, and the energy efficiency of the beam shaping system is greater than 90% when Fresnel loss is considered. The proposed beam shaping system endows the generated DHBs with new properties and may have great potential in the field of optical tweezers and atom guides.

M2 factor of controllable dark-hollow beams through a multi-apertured ABCD optical system.

Under an optical system with multiple hard-edged apertures in a cylindrical coordinate system, the recurrence propagation expression is derived for the controllable dark-hollow beams (CDHBs) by expanding the hard-aperture function into a finite sum of complex Gaussian functions. Given the recurrence propagation expression, we deduce the approximate analytical expressions of the beam propagation factor M2 in terms of the generalized truncated second-order moments. This provides a fast algorithm for the evaluation of the beam propagation quality for CDHBs through complicated optical trains with a series of apertures. The propagation of CDHBs through a two-aperture-lens ABCD optical system serves as the special case of multi-apertured ABCD optical systems. Our numerical results suggest that a one-aperture-lens optical system reduces the beam propagation quality of CDHBs, and a two-aperture-lens optical system improves the beam propagation quality of CDHBs by selecting appropriate beam parameters and aperture parameters.

Average intensity of anomalous hollow beam with orbital angular momentum in atmospheric turbulence

The propagation equation of average intensity of anomalous hollow beam (AHB) with optical angular momentum (OAM) in atmospheric turbulence has been derived, and the influences of constant of refraction index structure of atmospheric turbulence and the parameters of AHB with OAM on the average intensity and spreading properties are analyzed. It is found that AHB with OAM propagating in atmospheric turbulence can almost the dark hollow center as the propagation distance increases, and the AHB with OAM propagating in free space can keep its dark hollow center, and the beam propagating in stronger atmospheric turbulence will lose its initial dark hollow beam profiles more rapidly. This obtained results are useful to the practical application in free space optical communication using the AHB with OAM.

Second-order moments of a twisted Gaussian Schell-model beam in anisotropic turbulence

Analytical formulas for the Wigner distribution functions and the second-order moments (SOMs) of a twisted Gaussian Schell-model (TGSM) beam propagating through anisotropic turbulence have been derived by means of a tensor method. It is found that the propagation law for the SOMs of a TGSM beam spreading in turbulence can be described as a first-order optical systems propagation law with an additional turbulence-induced effect. Based on the SOMs, second-order statistics in terms of the effective beam width, the M2-factor, the orbital angular momentum flux, and the effective radius curvature are analyzed in detail. One finds that the anisotropic turbulence leads to an anisotropic spreading of light beams, and a TGSM beam is less affected by turbulence than a Gaussian Schell-model beam without the twist phase. For short distance propagation, the light beam is more sensitive to the initial beam parameters than turbulence parameters, while for sufficiently long transmission distance, the beam characteristics are determined at most by turbulence statistics. The method can be extended to study the propagation characteristics of various coherent and partially coherent complex Gaussian beams, such as flat-topped beams, dark hollow beams, and array beams in turbulence, and promotes important supports in free-space optical communications and remote sensing.

Propagation characteristics of radially shifted Gaussian beams and their radiation forces on Rayleigh particles

A new kind of strictly Gaussian-shaped dark hollow beam (DHB), called radially shifted Gaussian beam (RSGB), is proposed in this paper. Compared with previous approximately Gaussian-shaped DHB [i.e., Hollow Gaussian beam (HGB) and hollow sinh-Gaussian beam (HsGB)], it is much more convenient to design any special sized DHB by using RSGB. The propagation characteristics of RSGB, especially its autofocusing property, are investigated in detail and compared with that of HGB and HsGB under the same condition. It is found that the hollow region of RSGB can remain for a longer distance; and its autofocusing property is much stronger. An analytical expression for the focal position is also obtained for Gaussian-shaped DHB for the first time. Radiation forces of these beams exerted on two kinds of Rayleigh particle are analyzed. Numerical results show that RSGB also has advantages over previous Gaussian-shaped DHB in two-dimensional optical micromanipulation. For the low-index particle, RSGB can trap it for a longer distance; for the high-index particle, RSGB can produce a larger trapping force at the focal point.

Axicon aberration leading to short-range nondiverging optical array and elliptical dark hollow beam

We propose a unique method for producing nondiverging optical array and elliptical hollow beam in a controlled manner using aberration patterns generated from oblique illumination of axicon. The optical arrays with propagation invariance property are persisted for short ranges in the focal depth, whereas diverging array with a constant number of bright spots is produced beyond bottle beam. The measured variation in the geometrical parameters of obliquely illuminated axicon setup has facilitated precise control on the dimension of optical array and shape of the elliptical hollow beam, respectively. The theoretical analysis confirms the experimental results for the generation of short-range nondiverging optical array and elliptical dark hollow beam with fine control. To the best of our knowledge, this is the first experimental approach to extend the potential of axicon beyond generation of Bessel and circular hollow beams.

Propagation characteristics of controllable dark-hollow beams in a quadratic-index medium.

In this paper, the propagation of controllable dark-hollow beams (CDHBs) passing through a quadratic-index medium is studied. An analytical expression for the propagation of CDHBs in a quadratic-index medium is presented based on the ABCD matrix method, and the effect of the beam parameters on the evolution of a CDHB is investigated. It is found that the intensity distribution of CDHBs evolves periodically during propagation in the quadratic-index medium. The results indicate that the distance in which the dark-hollow center of a CDHB disappears can be increased by the beam parameters.

Fractional Fourier transform of double-half inverse Gaussian hollow beams

In this paper, we study an appropriate mathematical model of dark-hollow beam by concerning double-half inverse Gaussian hollow (DHIGH) beams passing through fractional Fourier transform (FRFT) optical systems. Based on Collins integral formula and using the expression of the hard-edged aperture function into a finite sum of complex Gaussian functions, analytical expressions for the propagation properties of DHIGH beams through the FRFT optical systems without and with apertures have been derived in detail. Some numerical simulations are given to illustrate the normalized intensity distribution of DHIGH beams in a FRFT system by studying the important factors of both incident beams order and the FRFT order. Our results obtained by using an approximate analytical formula, are in a good agreement with those obtained by using numerical integral method. The results show that the FRFT optical system is a convenient way for DHIGH beams shaping.

The influence of circular aperture on the focusing properties of partially coherent controllable dark-hollow beams

Based on the generalized Huygens-Fresnel integral, the focusing properties of partially coherent controllable dark-hollow beams(CDHBs) through a thin lens with circular aperture are studied in detail. Our main attention is focused on the influence of circular aperture on the focusing properties of partially coherent controllable dark-hollow beams. Numerical calculation results are shown that the circular aperture leads to the increase of the relative focal shift and the decrease of the effective beam width in the actual focal plane, and changes the dependences of the relative focal shift and the effective beam width on p (dark-size adjusting parameter), N(the order of the CDHBs), δg (initial transverse coherence width) and the effective Fresnel number Nw. Some physical explanations are also given.

A theoretical investigation on the propagation properties of Hollow Gaussian beams passing through turbulent biological tissues

Hollow Gaussian beam (HGB) is a new mathematical model to describe a dark hollow beam with circular and noncircular symmetry. By expanding the HGB as a superposition of a series of Hermite-Gaussian mode, the analytical formulae of the considered beam passing through turbulent biological tissues are investigated and developed, based on the extended Huygens-Fresnel integral. Our results indicate the effect of the turbulent biological tissues on the propagation properties of the HGB. The present study shows that the circular and the elliptical HGB propagating in biological tissues will evolve into Gaussian like beam in the far field, and the central irradiance of the HGB propagating in biological tissues rises more rapidly with lager constant of refraction index structure Cn2. We also calculate the formulae of the effective beam size of the HGB in turbulent biological tissues which provide a convenient way to learn the spreading properties of the considered beam.

Experimental study of wavefront distortion in the dark hollow beam generated using axicon

Axicons are the optical components widely used for the generation of dark hollow beam in a controlled manner. In certain circumstances, distortion in the transverse intensity profile (i.e. wavefront distortion) appears in DHB produced by axicon-lens assembly. In this paper, we performed the detailed experimental study for exploring the reasons for the appearance of wavefront distortion including its control and removal in partially coherent dark hollow beam produced from axicon-lens assembly. This experimental study find its crucial importance in the applications, where axicon is used for producing dark hollow beams, e.g. in eye surgery, atom trapping, laser machining and laser resonator. We also observed that the effect of chromatic aberration near the region of induced wavefront distortion in the depth of focus changes with propagation and can be controlled by varying spatial coherence of the beam. This control on the effect of chromatic aberration will be helpful in attaining achromatic dark hollow beam from axicon.

Propagation properties of nonuniform cosine-Gaussian correlated Bessel-Gaussian beam through paraxial ABCD system and generation of dark-hollow beam array

Partially coherent beams with nonconventional correlation functions have been extensively studied due to their wide and important applications in free-space optical communication, particle trapping, image transmission and optical encryption. Here, we study the propagation of nonuniform cosine-Gaussian correlated Bessel-Gaussian beam (cGBCB) in detail. Analytical expressions for the cross-spectral density function of cGBCBs through paraxial ABCD system are derived based on the extended Huygens-Fresnel integral. By use of the derived formulae, the intensity distribution properties of a nonuniform cGBCB on propagation in free space are analytically investigated. Some numerical calculation results are presented and discussed graphically. It is found that when the root-mean-square correlation width δ and the parameter controlling the degree of coherence profiles β are appropriately chosen, the intensity distribution of the nonuniform cGBCB displays self-splitting properties during propagation. We point out that rather than a simple duplication, the self-splitting behaviour consists of a complex process in which the dark hollow pattern for cGBCB is gradually filled in the centre at first, then starts to split with increasing the propagation distance, and most impressively, an evolution process from a single dark hollow beam in the source plane to quadruple dark hollow profiles in certain propagation ranges can be realized. The influence of correlation function on the evolution properties of the intensity distribution is investigated, demonstrating that the values of parameters δ and β of the correlation function play a critical role in inducing the self-splitting effect for nonuniform cGBCB on propagation in free space. Therefore, it is clearly shown that modulating the correlation function of a partially coherent beam can alter the coherence length and the degree of nonuniformity, and thus provides an effective way of manipulating its propagation properties. We also find the evolution speed of the intensity distribution can be greatly affected by the topological charge n of the beam function and the parameter R controlling the hollow size of cGBCB in source plane, e. g. the intensity distribution evolves into quadruple dark hollow profiles more slowly with larger n or smaller R. As is well known, the dark-hollow intensity configurations are useful in many applications and have been extensively studied both theoretically and experimentally. Therefore, the results drawn in the paper develop an alternative way to realize dark-hollow beam array, and further pave the way for dark hollow beam applications in long-distance free-space optical communications.

Singular behaviour of polychromatic dark hollow beams—Experimental observations based investigation

Polychromatic dark hollow beams (PDHBs) produced by axicon-lens system exhibit very interesting behaviour. Such type of polychromatic focused beams possesses so called generic singularities (Berry, 2002; Leach and Padgett, 2003 [2]) that influence the wave-filed and its characteristics (Yadav et al., 2014). The aim of this paper is to report the crux of some very interesting observations recorded during a comprehensive experiential study on PDHBs. This investigation may have potential applications to understand the anomalous behaviour of polychromatic light passes through an axicon-lens system.

Quantum polarization fluctuations of partially coherent dark hollow beams in non-Kolmogorov turbulence atmosphere**Project supported by the Major Research Plan of the National Natural Science Foundation of China (Grant No. 61405205).

Non-classical polarization properties of dark hollow beams propagating through non-Kolmogorov turbulence are studied. The analytic equation for the polarization degree of the quantization partially coherent dark hollow beams is obtained. It is found that the polarization fluctuations of the quantization partially coherent dark hollow beams are dependent on the turbulence factors and beam parameters with the detection photon numbers. Furthermore, an investigation of the changes in the on-axis propagation point and off-axis propagation point shows that the polarization degree of the quantization partially coherent dark hollow beams presents oscillation for a short propagation distance and gradually returns to zero for a sufficiently long distance.

The conversion of a Li’s flat-topped-Gaussian beam to a superposition of Kummer dark hollow beam by the illumination of a fractional radial Hilbert transform system

A new method of the generation of superposition of Kummer beam is introduced by the illumination of a fractional radial Hilbert transform (FRHT) system with an apertured spiral phase plate (SPP) instrument by a Li’s flattened Gaussian (LFTG) beam. To study the propagation properties of the produced beam, two main approximate analytical expressions are developed. The first one concerns the SPP integer topological charges and the second one is about the non-integer ones. From the both principle formulas devoted, some studies about the generation of the Kummer beam, with integer and non-integer topological charges, by the conversion of a fundamental Gaussian beam and the propagation of the LFTG beams through a FRHT system without apertured SPP are deduced in this work as special investigations of the main studies. For reason to determine the effects of the incident beam parameters and the optical system coefficients on the propagation characteristics of the created beam, several numerical calculations are carried out, analyzed and discussed in the work. Simples concluding remarks are outlined in the end of the paper.