Beam Transformation Research Articles

Study of the electro-optical transformation of linearly polarized Bessel beams propagating along the optic axis of an anisotropic DKDP crystal

This paper presents a numerical and experimental study of the electrically controllable transformation of linearly polarized Bessel laser beams propagating along the optic axis of an anisotropic DKDP (deuterated potassium dihydrophosphate) crystal. Based on numerical modeling and experiment, it is shown to be possible to vary the intensity distribution at the output of an anisotropic crystal by varying the wavelength of light at a fixed length of the crystal. The propagation of a plane-polarized zeroth-order Bessel beam is numerically modeled along the axis of a DKDP crystal in the presence of an applied electric field, which causes the appearance of induced biaxiality of the electro-optical crystal. The dynamic transformation of Bessel beams when an electric field is applied along the optic axis of an anisotropic crystal is experimentally studied.

The transformation of Hermite-Gauss beams with embedded optical vortex by lens system

In this paper the transformation of Hermite-Gauss beams with embedded vortex phase by lens system is investigated theoretically and numerically. A particular attention is devoted to the formation of vortex phase singularities in focal area. It is shown, that under appointed relations between HG mode indices and the number of embedded optical vortex the vortex phase singularity in a focal plane centre may disappear.

Formation and focusing of converging sheet electron beam based on field emission

The development of compact amplifiers with an average power of the frequency range 0.2–0.3 THz is related to the design of electron-optical systems using converging sheet beams that allow obtaining sufficiently high current densities with a lower current load on the cathode and with a lower value of the magnetic field. Based on the theory of synthesis the numerical simulation results for electron-optical systems for the formation of a converging sheet electron beam are presented. Reduction of the current load on the cathode allows the principle of transformation of a cylindrical electron beam into a sheet by employing electrostatic compression of the beam in one plane. A sheet beam electron-optical system with a field emission cathode with convergence of 10, and with the beam of 0.1 × 1.1 mm2 and current density of 45 A/cm2 has been performed. The electron gun employing the cathode–gate structure with diameter of 1 mm has an emitting current up to 10 mA in experiment. The modulation coefficient of the cathode current for a gun with a sheet electron beam has 0.3% of the anode potential.

Linear Transformation of Electromagnetic Wave Beams of the Electron-Cyclotron Range in Toroidal Magnetic Configurations

The field structure of quasi-optical wave beams tunneled through the evanescence region in the vicinity of the plasma cutoff in a nonuniform magnetoactive plasma is analyzed. This problem is traditionally associated with the process of linear transformation of ordinary and extraordinary waves. An approximate analytical solution is constructed for a rather general magnetic configuration applicable to spherical tokamaks, optimized stellarators, and other magnetic confinement systems with a constant plasma density on magnetic surfaces. A general technique for calculating the transformation coefficient of a finite-aperture wave beam is proposed, and the physical conditions required for the most efficient transformation are analyzed.

Spin-orbit transformation of Bessel light beams by electrically controlled liquid-crystal elements

The features of the transformation of linearly polarized Bessel light beams during their propagation through an electrically controlled liquid-crystal cell are studied theoretically and experimentally. Conditions were determined for realizing the spin–orbit transformation of Bessel light beams, which manifests itself through changes in polarization, phase, and spatial structure of the Bessel beam with the possibility of obtaining an azimuthally modulated light field intensity distribution.

Birefringence detection of a gradient-index lens based on astigmatic transformation of a Bessel beam

A method is proposed for detecting birefringence of mechanically free parabolic gradient-index lenses based on the astigmatic transformation of the zero-order Bessel beam. Numerical simulation shows a clearly visible distortion of the intensity structure in the propagation of scalable astigmatic Bessel beams. The degree of astigmatism can be determined from the intensity distribution of the distorted beam. Similar patterns are also obtained in an experimental study of the passage of a Bessel beam through a quarter-pitch gradient-index lens, which indicates the presence of birefringence of the lens material. Comparison of experimental data and numerical simulation shows the possibility of measuring the optical path difference of no worse than 0.05λ0 between ordinary and extraordinary beams.

Holographic Formation of Diffraction Elements for Transformation of Light Beams in Liquid Crystal – Photopolymer Compositions

A theoretical model of holographic formation of diffractive optical elements for transformation of light beam field into Bessel-like fields in liquid crystal – photopolymer (LC–PPM) composite materials with a dyesensitizer is developed. Results of numerical modeling of kinetics ofvariation of the refractive index of a material in the process of formation with different relationships between the photopolymerization rates and diffusion processes are presented. Based on the results of numerical simulation, it is demonstrated that when the photopolarization process dominates, the diffractive element being formed is distorted. This leads to a change in the light field distribution at its output and consequently, to ineffective transformation of the reading beam. Thus, the necessity of optimizing of the recording conditions and of the prepolymeric composition to increase the transformation efficiency of light beam fields is demonstrated.

Aberration laser beams with autofocusing properties.

We investigate theoretically, numerically, and experimentally a novel type of laser beam-an aberration laser beam (ALB). To generate the ALB, a diffractive optical element with a phase transmission function having an arbitrary radial dependence of power q and a periodic angular dependence of sin(mϕ) or cos(mϕ) form can be used. Such a light distribution is more general than classic aberrations including Zernike polynomials. We demonstrate that such radial nonuniformity results in autofocusing properties of ALBs. The autofocusing feature of ALBs is analogous to that of circular Airy beams, but the ALBs' autofocusing feature has more flexibility. The presence of the periodic angular dependence in the phase results in a diffraction pattern with mth-order symmetry. Transformation of ALBs during propagation in free space is analogous to transformation of the three-Airy beams; however, the generated light distributions have an arbitrary integer order of symmetry. The presence of an additional focusing lens leads to formation of an optical field in its focal plane with symmetry that depends on the parity of m: for even m, the generated light distribution has 2mth-order symmetry, and, for odd m, it has mth-order symmetry.

Strong Polarization Transformation of Bloch Surface Waves.

Polarization is an intrinsic attribute of optical waves, so manipulating the polarization state of optical surface waves can be of a fundamental importance for the next-generation information and bio-photonics technology. Here, we show theoretically that the polarization of the Bloch surface wave (BSW) on a dielectric multilayer can be transformed between a transverse-electric (TE) state and a transverse-magnetic (TM) state by using the laterally continuous grooves inscribed on this multilayer. This polarization transformation can be enhanced or inhibited by the interference between the reflected BSW beams, which can be tuned by the periodicity and depth of the grooves. The maximum polarization transformation efficiency can be achieved as high as 43% when the number of grooves is increased to 10. A generalized Fresnel formula is proposed to describe the polarization transformation of the BSW beams. Due to this polarization transformation, an anomalous reflection of BSW beams can be realized, which is the inequality between the incident angle and the reflection angle.

Beam-Doppler Unitary ESPRIT for Multitarget DOA Estimation

High-resolution direction of arrival (DOA) estimation is a critical issue for mainbeam multitarget tracking in ground-based or airborne early warning radar system. A beam-Doppler unitary ESPRIT (BD-UESPRIT) algorithm is proposed to deal with this problem. Firstly, multiple snapshots without spatial aperture loss are obtained by using the technique of time-smoothing. Then the conjugate centrosymmetric discrete Fourier transform (DFT) matrix is used to transform the extracted data into beam-Doppler domain. Finally, the rotational invariance property of the space-time beam is exploited to estimate DOA of the target. The DOA estimation accuracy is improved greatly because the proposed algorithm takes full advantage of temporal information of the signal. Furthermore, the computational complexity of the presented algorithm is reduced dramatically, because the degree of freedom after beam transformation is very small and most of the operations are implemented in real-number domain. Numerical examples are given to verify the effectiveness of the proposed algorithm.

Propagation of a Vector Cosine-Gaussian Correlated Beam Through an Active GRIN Medium

This paper presents a convenient approach that uses the tensor method to study the propagation of a nonuniformly correlated electromagnetic Cosine-Gaussian Schell-model (ECGSM) beam through an active gradient-index (GRIN) medium. It is shown that the initial correlation structure has a significant influence on the intensity gain; an ECGSM beam ( n = 1) experiences more gain than a conventional electromagnetic Gaussian Schell-model (EGSM) beam ( n = 0). The inhomogeneous gain induced by the medium leads to a nonlinear modulation of beam parameters such as the spectral intensity, coherence, and polarization. Although the gain leads to a broadening of the beam width, the coherence gradually decreases, which yields a useful guideline for manipulating active GRIN materials to generate numerous partially coherent beams. It is found that the polarization ellipse in the center of a conventional EGSM beam gradually evolves into circular polarization. However, the state of polarization of a nonuniformly correlated ECGSM beam gradually changes into linear polarization. The ability to manipulate light beams using active GRIN materials opens an alternative avenue for the generation of complex vector beams, which promises important supports in the fields of waveguide amplifiers, beam shaping, optical sensors, and beam transformer devices.

Fractional Airy beams.

Airy beams possess a number of properties that ensure their multifunction and high relevance in many applications. This fact stimulates scientists to search for new modifications and generalizations of classical Airy beams. Several generalizations of the Airy functions are known, on the basis of both the modification of the differential equation and the variations in the integral representation. In this paper we propose and investigate a new type of Airy beams-fractional Airy beams (FrAiB). They are based on the generalization of the integral representation and are close to the Olver functions, but we are considering a wider range of the power-law dependence of the argument, including non-integer (fractional) values of the power. A theoretical and numerical analysis of the FrAiBs, as well as their symmetrized variants, was performed. The properties of FrAiBs, such as being non-diffracting and autofocusing, were numerically investigated by means of the fractional Fourier transform, describing the beam transformations by paraxial optical systems. We believe that new beams can be useful for laser manipulation techniques and lensless laser patterning.

Topological charge transformation of beams with embedded fractional phase step in the process of second harmonic generation

We demonstrate collinear second harmonic generation performed with a beam with an embedded initial phase singularity of strength . We examine the law of topological charge conservation during this process. Despite the instability of the initial singularity, we observe a counterintuitive topological charge doubling. In the second harmonic, we observe an optical vortex of strength (topological charge) . The conservation of topological charge is confirmed by both numerical simulations and the experiment. We also provide a qualitative explanation of the process.

Propagation characteristics of Bessel-like beams through ABCD optical system

Based on the Collins diffraction integral formula, this work focus to the study of the propagation properties of a Bessel-like beam through an ABCD optical system. As it is not easy to develop an analytical expression describing the transformation of the Bessel-like beams by an ABCD optical system, numerical integration method was indispensable to conduct this research. The characteristics of the transformation of Bessel-like beams by three optical systems: free space, Fourier transform, Fractional Fourier transform system and quadratic graded-index system are numerically examined and treated as examples of optical systems in this investigation. Some numerical results are carried-out to show how the superposition of multiple Airy beams propagates and transforms by an ABCD optical system.

The review of liquid crystal wavefront corrector with fast response property

Liquid crystal wavefront corrector (LCWFC) is an optical device that can modulate wavefront of incident light, and shows advantages of high density pixels, high reliability, and high precision accuracy, and can be used in the field of optical beam shaping, optical information processing and beam transforming. All these application model show broad application prospect of LCWFC. When LCWFC is used in the optics systems, a fast response speed is always required, such as 1 ms. In optical application, specific modulation depth is always required. If the modulation depth is 1 λ , the response time of the commercial LCWFC is slow, such as, 10 ms, which block the application of LCWFC. The response speed of LCWFC always depends on two elements, the properties of LC material and the parameters of LC device. Firstly, fast response liquid crystal material with high birefringence and low viscosity was studied and reviewed in our research group. Secondly, the optimization of LC device parameters and driving method was reviewed. By the research in LC material and device, the response time of LCWFC can be fast to sub-millisecond, which will highly enhance the application region and depth of LCWFC.

Non-diffractive beam in random media

Beam propagation has been given important attention in a variety of applications in medicine, remote sensing and information science. Especially, the beam propagation in highly scattering media, which is called random media, is important. In general, the multiple scattering gets rid of beam characteristics, e.g., intensity distribution, phase front, and polarization. In this study, self-converging effect of annular beam was applied in random media. Diluted milk was used as random media, and the transmitted light was detected with a narrow view angle of 5.5mrad. The collimated annular beam of a few tens millimeters takes a few hundred meters to transform its beam shape into the non-diffractive beam in free space, while this transformation was shorten only to 20cm in random media, that is, the collimated annular beam caused its transformation at only 20cm in random media. The transformed beam kept its optical characteristics of “non-diffractive beam”. Such transformation of the annular beam needs the appropriate condition of random media. Media concentration and propagation distance control the generation of the center peak intensity of the transformed beam. This study indicates the generation of the non-diffractive beam in random media and reveals its appropriate condition.

Conversion of circular beams by a spiral phase plate: Generation of Generalized Humbert beams

Generalized Humbert beams (GHBs) are a novel donut beams family which created by converting of circular beams (CiBs) passing through a paraxial ABCD optical system with a spiral phase plate (SPP). The amplitude field of CiBs can be described by either the Whittaker or the confluent hypergeometric functions. The transformation and propagation of CiBs by the use of a SPP after propagating the considered optical system is presented and derived in detail. Some special cases of GHBs as standard, elegant and generalized Laguerre-Gaussian beams; Hypergeometric-Gaussian beams; Fractional order elegant Laguerre-Gaussian beams; Bessel-Gauss beams; quadratic Bessel–Gauss beams; and Whittaker-Gaussian beams are deduced in this paper. Numerical simulations are performed to study the transformation of the Whittaker-Gaussian beam by a SPP in free space as a particular example in this work.

Conservation of extremal ellipticity and analytical expressions for astigmatism and asymmetry in Gaussian beam transformations.

A Gaussian beam with initial astigmatism, waist, and M2 asymmetry propagates through a simple optical system consisting of a single thin, aberration-free lens. We derive simple analytical expressions for the asymmetry, astigmatism, and ellipticity of the beam after the lens, and show that the maximal ellipticity of the beam is a conserved quantity that is solely dependent on these input parameters. This appears to still hold for general astigmatic Gaussian beams. Our simple, analytical results conveniently determine the trade-off between astigmatism and asymmetry of a laser for a given output maximum ellipticity requirement pre- or post-lenses.

Transformation of Laguerre-Gaussian beam by a ring-lens

The propagation property of Laguerre-Gaussian (LG) beams passing through a diffractive ring-lens (RL) was studied, where the RL was generated by a liquid crystal spatial light modulator (LC-SLM). It was found that the LG beam was transformed into a sharp ring at the focal plane first, and then a Bessel-similar beam was formed behind the focal plane but the beam size was enlarged with the increase of propagation distance. With the help of a group of lenses, the beam was further collimated into a Bessel beam. Finally, the “non-diffractive” and selfreconstruction properties of the generated Bessel beams were experimentally verified.

Application of Waveguide/Free-Space Optics Hybrid to ROADM Device

As optical networks have evolved from point-to-point systems to ring or mesh networks, the optical devices that are needed to construct optical nodes have become more important and need to be more scalable. Hybridization of waveguide and free-space optics, or spatial and planar optical circuits (SPOCs), may provide the solutions for such needs. An SPOC platform is attractive because it can take advantage of both waveguide technology and free-space optics. Waveguide technology provides a high degree of integration of optical functionality for devices such as splitters and non-wavelength selective switches while free-space optics supplies a high degree of parallelism with two-dimensional spatial light modulators such as a liquid crystal on silicon (LCOS) devices. In this paper, we summarize the basics of SPOC technology and review its application to reconfigurable optical add-drop multiplexing (ROADM) devices. The key elements of a waveguide on an SPOC platform are an arrayed-waveguide grating and a spatial beam transformer. The latter functions as a microlens array and provides attractive features such as dense integration of switches. An LCOS device has numerous phase modulating pixels, enabling flexible manipulation of lightwaves. Using an SPOC platform, we constructed and demonstrated devices for ROADM applications including a wavelength filter, tunable optical dispersion compensators, and wavelength selective switches (WSSs). The WSSs range from an ultrahigh port count WSS to a single module wavelength cross connect.