Beam Waist Research Articles

The effective beam width of a partially coherent rectangular mul-ti-Gaussian Schell-model vortex beam propagating in a turbulent plasma

Based on the derived analytical formulae for the optical intensity and effective beam width of a partially coherent rectangular multi-Gaussian Schell-model (RMGSM) vortex beam, we analyzed the evolution of the effective beam width of a partially coherent RMGSM vortex beam propagating in an anisotropic turbulent plasma using numerical examples. The numerical results demonstrated that the effective beam widths in the x and y directions were similar. In studies on the influences of the source parameters, one can see that an RMGSM vortex beam with a larger topological charge and beam waist or a smaller correlation coefficient σ evolves into a beam with a larger effective beam width. However, the influence of beam order was not evident. In addition, numerical examples proved that the effective beam width increases with increasing propagation distance and refractive index fluctuation variance or decreasing anisotropy parameter , outer scale , and inner scale . This study's results will be beneficial for applications in free-space optical communications.

Effect of oceanic turbulence on the propagation behavior of a radially polarized Laguerre-Gaussian Schell-model vortex beam.

Optical wireless communications applications are restricted by oceanic media-induced beam quality degradation. However, modulating the coherence and polarization structures of the laser beams can effectively diminish the negative influence of oceanic turbulence on the beams. The average intensity of a radially polarized Laguerre-Gaussian Schell-model vortex (RPLGSMV) beam propagating through oceanic turbulence is explored by employing the extended Huygens-Fresnel principle. We found that the average intensity of an RPLGSMV beam is greatly affected by oceanic turbulence with a large rate of dissipation of the mean-square temperature and a large relative strength of the temperature and salinity fluctuations as well as the small rate of dissipation of the turbulent kinetic energy per unit mass of fluid and small Kolmogorov microscale. It was also found that a RPLGSMV beam with a larger radial index, topological charge, initial coherent length, and beam waist has a stronger anti-turbulence ability. Our numerical findings may be of great significance for the detection and imaging of oceanic optical telecommunications links.

Spatial and temporal characteristics of spontaneous parametric down-conversion with varying focal planes of interacting beams

Spontaneous parametric down-conversion (SPDC) is a widely used process to prepare entangled photon pairs. In SPDC, a second-order nonlinear crystal is pumped by a coherent laser beam to generate photon pairs. The photon pairs are usually detected by single-mode fibers (SMF), where only photons in a Gaussian mode can be collected. The collection modes possess typical Gaussian parameters, namely a beam waist and a focal plane position. The collection efficiency of photons highly depends on the choice of both parameters. The exact focal plane position of the pump beam relative to those of the detection modes is difficult to determine in a real experiment. Usually, theoretical and experimental studies assume that the focal plane positions of the pump and the generated beams are positioned in the center of the crystal. The displacement of beam focal planes can lead to deviations from expected results and the coupling efficiency into SMF can decrease. In this study, we theoretically examine variable positions of focal planes in the Laguerre–Gaussian basis, a popular experimental modal decomposition of the spatial biphoton state. We explore how the choice of focal plane positions affects the spatial and temporal properties and the purity of the photon pairs. We present SPDC setups where precise knowledge of the focal plane position is essential and scenarios where focal plane displacements have negligible impact on experimental outcomes.Graphical

Influence of off-focus and off-axis distances on trapping of a Rayleigh particle

The influence of the off-focus and off-axis distances on trapping of a metallic particle is investigated theoretically using vector diffraction and dipole approximation. Numerical results show that when the off-focus and off-axis distances of a metallic Rayleigh particle are smaller, typically smaller than 0.5[Formula: see text], the particle can be three-dimensionally trapped to the focus by a highly focused real radially polarized beam. However, when the off-focus and off-axis distances are large, the particle can not be three-dimensionally trapped to the focus but it may be trapped to an annular region. The dependence of the trapping stability and trapping stiffness on the off-focus and off-axis distances are calculated. The effect of the beam parameter (the ratio of the radius of the lens to the beam waist) of the radially polarized light on optical trap is discussed.

High accuracy Gouy rotation measurement for the composition vortex beams using imaging technology

The rotation characteristics of the composition Laguerre–Gaussian (LG) beams during the propagation are numerically analyzed. A simple rotation angle measure method based on imaging technology is proposed and demonstrated. First, the global feature points of the composite vortex pattern is extracted by the 8-connected boundary tracking algorithm. Then, the position coordinates of each feature point are calculated by using the weighting method. The rotation angle of each feature point relative to the center point is calculated under the coordinate system. Finally, the relative rotation angles of the composite vortex pattern at different positions relative to the original position are obtained. The results show that the measurement error reaches 10[Formula: see text] for composite beams with different sizes and beam waist, which is comparable to that of the theoretical value. The proposed method can be used to effectively and accurately measure the Gouy phase of the composite LG beams. We expect the proposed method will be benefit of the further research and application of Gouy phase.

Simulation analyses and configuration optimizations of an LD pumped 3.1 µm Co/Er:PbF2 MIR laser

The demand for mid-infrared physics technology is increasing, and it is still a difficult process from growing excellent laser crystals to performing laser experiments. In this paper, we consider the energy transfer process between Co2+ and Er3+, and present the theoretical simulation results of the output power of the 3.1 µm Co/Er:PbF2 MIR laser. Based on the setup of a LD pulse pumped laser system, the effects of beam waist radius, resonator parameters and crystal length on the output are discussed in detail. The calculation results show that under good cavity mirror conditions, we can obtain a 3.1 µm laser with an output slope efficiency of 43.4%, whose output energy reaches 2.19 mJ at an input of 5 mJ. This provides guidance include the cavity mirror parameters and crystal parameters for laser experiments.

Scaled-Model Radar Cross-Section Measurement: The Influence of the Scattered Field under Gaussian Beam Illumination-A Theoretical Analysis.

At microwave frequencies, radar cross-section (RCS) measurements are usually performed by placing the target in the far-field region of the antenna. The wavefront of the radiating field from the antenna can be approximated as planar, ensuring that the incident field and the power interact with the target independently of the antenna. However, for electrically large targets, the required distance becomes significant, posing challenges for implementation. Scaled-model RCS measurements offer an alternative solution. RCS measurements at terahertz and optical frequencies typically require a collimated beam as the source, where the intercepted power and RCS become dependent on the excitation. To address this dependency, researchers have proposed modifying the RCS definition to account for the intercepted power and to analytically formulate the scattering problem. However, such modifications require prior knowledge of the target's geometry and material properties, which are often not readily available in practice. This also limits the study to only canonical targets. In this paper, we propose an alternative approach for modelling the intercepted power. The Gaussian beam is decomposed into a number of plane waves travelling to different directions using the theory of plane wave spectrum. The scattering problem is solved using the full-wave method of moment. Through theoretical proofs and numerical examples involving spheres and a non-canonical target, with a scaled-model aircraft, we demonstrate that the original RCS definition can serve as a good approximation for scaled measurements, provided that the beam waist is approximately four times the target's dimensions. These findings provide valuable guidelines for radar engineers when performing scaled measurements using collimated beams. The results, which match those obtained from full-model measurements, enable us to predict the RCS of full-scale targets. This capability facilitates various target-related applications, such as target characterization, classification, detection, and even recognition.

Propagation behavior of orbital angular momentum in vector anomalous vortex beams under maritime atmospheric turbulence

This study explores the propagation properties of orbital angular momentum (OAM) carried by a vector anomalous vortex beam (VAVB) in maritime atmospheric turbulence, utilizing the Rytov approximation. A comparative analysis is conducted between the VAVB and Laguerre-Gaussian beam, revealing that the VAVB exhibits a higher detection probability under specific circumstances. This suggests that the VAVB is more suitable for scenarios where maximizing detection probability is critical. The detection probability of the signal OAM mode is affected by the characteristics of maritime atmospheric turbulence and propagation distance, but can be significantly improved by manipulating beam parameters such as wavelength, beam order, beam waist, and quantum number, while considering the characteristics of maritime atmospheric turbulence. Hence, the use of VAVB has the potential to facilitate reliable optical communication in challenging maritime environments.

Analysis on the performance of reconfigurable intelligent surface-aided free-space optical link under atmospheric turbulence and pointing errors

<span lang="EN-US">Free-space optical (FSO) communication can provide the cost-efficient, secure, high data-rate communication links required for applications. For example, it provides broadband internet access and backhauling for the fifth-generation (5G) and the sixth-generation (6G) communication networks. However, previous solutions to deal with signal loss caused by obstructions and atmospheric turbulence. In these solutions, reconfigurable intelligent surfaces (RISs) are considered hardware technology to improve the performance of optical wireless communication systems. This study investigates the pointing error effects for RIS-aided FSO links under atmospheric turbulence channels. We analyze the performance of RIS-aided FSO links influenced by pointing errors, atmospheric attenuation, and turbulence for the subcarrier quadrature amplitude modulation (SC-QAM) technique. Atmospheric turbulence is modeled using log-normal distribution for weak atmospheric turbulence. Several numerical outcomes obtained for different transmitter beam waist radius and pointing error displacement standard deviation are shown to quantitatively illustrate the average symbol error rate (ASER).</span>

Analysis on the performance of pointing error effects for RIS-aided FSO link over gamma-gamma channels

In this study, we analysis on the performance of pointing error effects for reconfigurable intelligent surfeces (RISs) aided free-space optical (FSO) communication link over moderate to strong atmospheric turbulence channels. Among these solutions, RISs are considered as hardware technology to improve performance of optical wireless communication systems. Performance evaluation of systems is affected by atmospheric attenuation, pointing errors and moderate to strong atmospheric turbulence channels for quadrature amplitude modulation (QAM) technique. Atmospheric turbulence channel from moderate to strong is modeled using gamma-gamma distribution. Several numerical results obtained the average symbol error rate (ASER) performance versus beam waist radius and signal to noise ratio for three value of pointing error displacement standard deviation. From the results, it is show that with RIS assisted can effectively improve the performance and link distance of the wireless communication systems.

Development of Super Fine Strand Nb3Al Cable for SuperKEKB Superconducting Sextupole Magnet System

Along the beam lines of the SuperKEKB main rings, 218 conventional sextupole magnets are installed, and they are used for tuning the chromaticity of the accelerator rings. Especially, 16 sextupole magnets in the beam straight lines in the Tsukuba area are quite essential for the Crab Waist beam colliding. To make the beam tuning process finer, we are studying the superconducting sextupole magnet system with three types of the corrector magnets. From the operation temperature of the system, A15 compound superconductor is chosen as the cable material, and the development of the react and wind coil production has been tried with the Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Al cable. The Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Al super fine strand superconducting cable for the corrector magnets was manufactured, and its superconducting characteristics are being studied. In this paper, as the first test result of the development, the critical current characteristics of the straight cable as variables of temperature and magnetic field are reported. As the results, the critical current of the Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Al cable was higher than the design values for the corrector magnets, and this level of cable performance also indicates the potential for the cable being used for the main sextupole magnet.

Second-Harmonic Generation of the Vortex Beams with Integer and Fractional Topological Charges

The single-pass second-harmonic generation (SHG) of a vortex beam under low fundamental wave depletion is systematically studied. Vortex modes at 1064 nm with integer topological charges from ±1 to ±9 and fractional ones at ±0.75 are generated by modulating the fundamental Gaussian beam with different spiral phase plates. The frequency doubling of these fundamental vortex modes is realized via single-pass SHG through the KTP. A detailed theoretical model is set up in the single-pass SHG of the vortex beams. Theoretical analysis indicates that the higher the order of the vortex beams, the lower the SHG efficiency, when the beam waists and fundamental power are given. The experimentally measured SHG output characteristics verify those obtained via theoretical analysis. Conservation of the orbital angular momentum during the SHG process is also verified, regardless of the fractional or integer vortex beams. SH LG0,2l vortex beams with high mode purity are obtained. The beam waists of fundamental/SH in KTP measured using a 4f system demonstrate that the Rayleigh ranges of the fundamental wave and SH wave are the same. The paper comprehensively presents some basic laws in the single-pass SHG of a vortex beam. In addition, it also indicates that SHG is an effective method to improve the mode purity of vortex beam.

Non-linear optical studies of CuPc

Thin films of Copper Phthalocyanine CuPc of various thicknesses (150, 300 and 450) nm have been deposited using pulsed laser deposition technique using Q – Switched Nd:YAG laser pulse at 1.64 μm wavelength, 6 Hz frequency, 9 ns width, and 240 mJ energy at room temperature. The study showed that the spectra of the optical absorption of the thin films of the CuPc are two bands of absorption one in the visible region at about 635 nm, referred to as Q-band, and the second in ultra-violet region where B-band is located at 330 nm. CuPc thin films were found to have direct band gap with values around (1.81 and 3.14) eV respectively. The vibrational studies were carried out using Fourier transform infrared spectroscopy (FT-IR). Finally, from open and closed aperture Z-scan data non-linear absorption coefficient and non-linear refractive index have been calculated respectively using He-Ne laser which have beam waist of (24.2 μm), wave-length of (632.8 nm) and Rayleigh thickness was 2.9 mm.

Fourier Ptychography-Based Measurement of Beam Divergence Angle for Vertical Cavity Surface-Emitting Laser

The Vertical Cavity Surface-Emitting Laser (VCSEL) has led to the rapid development of advanced fields such as communication, optical sensing, smart cars, and more. The accurate testing of VCSEL beam quality is an important prerequisite for its effective application. In this paper, a method for measuring the divergence angle of the VCSEL far field spot based on transmissive Fourier ptychography is proposed. First, a single CCD multi-angle VCSEL far-field spot acquisition system is designed. Second, based on the proposed Fourier ptychographic algorithm with synchronous optimization of embedded optical transfer function, a resolution-enhanced phase image of the spot is reconstructed and the boundary extracted by the Sobel operator of the phase image is defined as the boundary position of the beam waist. In this way, the beam waist radius of the laser beam is calculated. Finally, the divergence angle of the laser beam is measured via the radius of the beam waist. Compared with the traditional Gaussian beam definition method, the method proposed in this paper has higher accuracy in divergence angle measurement. The experimental results show that this method can improve the divergence angle measurement accuracy by up to 9.7%.

Development of mixed pitch grating for the optical addressing of trapped Sr+ ion with data analysis techniques.

Mixed pitch gratings are developed for the optical addressing of trapped 88Sr+ ion by means of simulation and experimental measurement approaches. Meanwhile, Python-based data analysis techniques were developed to analyze simulated and measured beam profiles. A fixed pitch grating with a pitch of 1.2 µm was used as a reference, and a mixed pitch grating with pitches of 1.1/1.2 µm of various ratios are investigated. The Python-based data analysis codes demonstrates highly automated capability in processing both simulated and measured beam profile data to compute key parameters, including beam waist and Gaussian fitting. Mixed pitch grating delivers light beam with smaller beam waist (17.4 µm) compared to the fixed pitch grating (26.4 µm), exhibiting ∼34% beam waist reduction.

Properties of Scattering Fields from Gaussian Beam Incident on Rough Cylinders

At present, most researchers focus on plane wave incident on targets, but in practical applications, most of the beams are Gaussian beam. We study the scattering fields of Gaussian beam incident on rough cylinders. Coherent and incoherent scattering coefficients are obtained based on the angular spectrum expansion and physical optics approximation, and the effects of cylinder roughness, beam radius, cylinder radius and angle of incidence on scattering coefficients are analyzed. The results show that, for a constant wavelength, when the root mean square height is greater than or equal to 1/5 of the wavelength, the coherent scattering coefficient curve undergoes a change in its distribution, with the peak transforming into a trough. Furthermore, when the root mean square height is greater than or equal to 1/3 of the wavelength, the incoherent scattering coefficient experiences a decline as the root mean square height increases. The correlation length only affects the incoherent scattering coefficient. Both the coherent and incoherent scattering coefficients decrease with the increase in the incident angle. Finally, when the roughness and incident angle are constant, with the increase in the ratio of the cylinder radius to the beam waist radius, the scattered light field is more concentrated. Our results provide the theoretical basis for the measurement of the cylindrical scattering field.

Microwave ion source with dual helical antenna for diagnostics neutral beam of ALBORZ tokamak

An efficient ion source of the diagnostic neutral beam injection (DNBI) is designed and simulated for Alborz Tokamak, based on the microwave plasma source. The diagnostic neutral beam is designed for use in some diagnostics system such as charge-exchange recombination spectroscopy (CXRS), Rutherford Scattering (RS), and Motional Stark Effect (MSE) of Alborz Tokamak. In this work, a new helical antenna is designed and simulated for a microwave plasma source, to reach a plasma density of order8.23×1017m−3. The microwave plasma source is employed by the high-efficient ion beam accelerator. In this simulation, three-electrodes in different potentials of 20 kV, −2 kV, and grounded respectively, are used as extraction system of the ion beam source. According to our design, nine apertures grids are considered for the accelerator system. The simulation results show that, the system can extract an ion beam with energy and current of 20 keV and 60 mA respectively. The extracted ion beam consists of nine beamlets, where the beam waist and the current of each of them are calculated about 3 mm and 6.5 mA, respectively. The results of this work indicate that the ion beam with minimum divergence angle of 32 mrad can be generated by the proposed ion beam source.

Scattering of Laguerre–Gaussian Beam by a Topological Insulator Cylinder Coated with Metamaterials

A theoretical investigation is presented to study the orbital angular momentum (OAM) beam scattering from a topological insulator (TI) cylinder coated with metamaterials. To calculate the electromagnetic (EM) response of the scattered field, the field equations are modified using Laguerre–Gaussian (LG) potential and plane wave scattering. The response of the metamaterial coated geometry has been reported for Double positive (DPS), Double negative (DNG), Epsilon negative (ENG), and Mu negative (MNG) coating layers, respectively. The normalized bistatic echo widths for the TI cylinder also change by changing the topological charge ( $$l$$ ), the radius of the metamaterial coated layer $$(b)$$ , source frequency $$(f)$$ , and beam waist radius $$({w}_{0})$$ . Our result for $${LG}_{00}$$ beam exactly tones with plane wave scattering as a reference. Numerical results in the form of bistatic echo widths have been calculated. Besides, the prementioned parameters, the influence of OAM mode index on the bistatic echo width is also analyzed. It can be seen that OAM mode number plays major role in controlling the scattering amplitude and intensity.

Self-focusing effect analysis of a perfect optical vortex beam in atmospheric turbulence.

The correlation function and the detection probability of orbital angular momentum (OAM) of a perfect optical vortex beam (POVB) were obtained under atmospheric turbulence conditions and then used to estimate the POVB propagation model through atmospheric turbulence. The POVB propagation in a turbulence-free channel can be divided into anti-diffraction and self-focusing stages. The beam profile size can be well preserved in the anti-diffraction stage as the transmission distance increases. After shrinking and focusing the POVB in the self-focusing region, the beam profile size expands in the self-focusing stage. The influence of topological charge on the beam intensity and profile size differs depending on the propagation stage. The POVB degenerates into a Bessel-Gaussian beam (BGB)-like when the ratio of the ring radius to the Gaussian beam waist approaches 1. The unique self-focusing effect of the POVB enables higher received probability compared to the BGB when propagating over long distances in atmospheric turbulence. However, the property of the POVB that its initial beam profile size is not affected by topological charge does not contribute to the POVB achieving a higher received probability than the BGB in short-range transmission application scenarios. The BGB anti-diffraction is stronger than that of the POVB, assuming a similar initial beam profile size at short-range transmission.

Effect of orbital angular momentum on dust-ion-acoustic waves in a superthermal plasma

Laser or electromagnetic radiation, in general, interacts with plasma in very interesting ways. In most cases, they induce orbital angular momentum (OAM) in such plasmas due to their polarization effects. Dust-ion-acoustic waves (DIAWs) with immovable dust particles are studied with the effect of rotation produced due to laser or electromagnetic interaction. The electrons are considered in the non-Maxwellian limit, with inertial ions and static dust grains possessing negative charges. Fluid theory is employed for obtaining the linear paraxial equation with regard to ion density perturbations. The fundamental Gaussian and Laguerre Gaussian (LG) beam solutions are talked over with the later being proved to be the source for OAM. By calculating the electrostatic potential for such linear waves, the components of the electric field with respect to the LG potential are shown. Finally, the energy density equation is used to calculate the OAM associated with DIAWs. The Laguerre Gauss mode is numerically shown to have greatly changed by varying the values of relevant plasma parameters, such as the electron superthermality parameter, radial and angular mode numbers, beam waist, and azimuthal angle. The present results may be useful in apprehending dust-ion-acoustic wave excitation due to Brillouin backscattering phenomenon of laser light interacting with plasma.