Gaussian Beam Mode Research Articles

Utilizing an aspheric lens and compound ellipsoidal cavity for a laser uniform illumination system

To achieve uniform laser illumination of an active imaging system with a small aperture diameter and large field angle, we have developed what we believe to be a novel structure for achieving uniform beam shaping that integrates a laser source, an aspheric lens, and a composite ellipsoidal cavity to enable active laser illumination. Through an aspheric lens, the fundamental mode Gaussian beam is transformed into double Gaussian and flat-top radiation at the target plane. The double Gaussian radiation is further reflected by a complex ellipsoidal cavity, where it is evenly distributed into equal radiation flux. This flux combines with the flat-top radiation, resulting in a uniform distribution at the target plane. The parameters of the complex ellipsoidal cavity are determined using an equalization algorithm. After combining the transmission for flat-top shaping by the aspheric lens and secondary reflection shaping by the composite ellipsoidal cavity, we achieved an aperture measuring 29.7 mm with an aperture angle of 84.0°, at a distance of 2 m from the target plane, with a diameter of 3.6 m, resulting in uniformity reaching 92.7%. RMS and MT/R determine the effectiveness of the compound ellipsoidal cavity design, depending on the maximum reflection angle and transmission angle. MT/R is inversely proportional to the maximum reflection angle, while RMS is directly proportional to the transmission angle. By setting the maximum reflection angle to 32.0° and the transmission angle to 8.0°, we were able to achieve a minimum root-mean-square focusing radius of 108.6 µm along with a minimum effective MT/R ratio of 1.07. The overlap degree between transmission and reflection directly impacts the target plane’s uniformity, adjusted through a defined adjustment factor. Optimizing this factor to 0.9 maximizes the uniformity of the target plane.

Quantum mechanical approach to plasma waves with helical wavefront

Plasma waves with helical wavefront are studied theoretically from the quantum mechanical viewpoint and are shown to produce a spinning motion of a charged macroparticle in a complex plasma. The electrostatic helical perturbations are described by the wave function for a Laguerre–Gaussian beam mode with the radial/angular mode numbers n/l. The interaction and the transfer of angular momentum from the wave to a particle are analyzed by the method of second quantization with the help of the Feynman diagram. Laguerre function, instead of the Born approximation, is introduced to describe plasma waves with helical wavefront. A pair of dust particles in a complex plasma exchange a quasiparticle (virtual plasmon) resulting in the acquisition of angular momentum, which makes a dust particle spin in motion with rotational frequency Ωϕ. The resonance condition ω−kvz−lΩϕ=0 and the conservation of angular momentum IdΩϕ=lℏ determine the rotational frequency, where ω and k are frequency and axial wave number of the helical wave, and vz and Id are axial velocity and the moment of inertia of a dust particle.

Direct‐Laser‐Written Polymer Nanowire Waveguides for Broadband Single Photon Collection from Epitaxial Quantum Dots into a Gaussian‐like Mode

AbstractSingle epitaxial quantum dots (QDs) embedded in nanophotonic geometries are a leading technology for quantum light generation. However, efficiently coupling their emission into a single mode fiber or Gaussian beam often remains challenging. Here, direct laser writing (DLW) is used to address this challenge by fabricating 1 µm diameter polymer nanowires (PNWs) in‐contact‐with and perpendicular‐to a QD‐containing GaAs layer. QD emission is coupled to the PNW's waveguide mode, enhancing collection efficiency into a single‐mode fiber. PNW fabrication does not alter the QD device layer, making PNWs well‐suited for augmenting pre‐existing in‐plane geometries. Standalone PNWs and PNWs in conjunction with metallic nanoring devices that have been previously established for increasing extraction of QD emission are studied. Methods that mitigate standing wave reflections and heat, caused by GaAs's absorption/reflection of the lithography beam, and which otherwise prevent PNW fabrication, are also reported. A maximum improvement of ( in a nanoring system with a PNW compared to the same system without a PNW is observed, in line with numerical results, and highlighting the PNW's ability to waveguide QD emission and increase collection efficiency simultaneously. These results demonstrate new DLW functionality in service of quantum emitter photonics that maintains compatibility with existing top‐down fabrication approaches.

Simulation of high-frequency gravitational wave detection using modulated Gaussian beam* *Supported in part by the National Natural Science Foundation of China (12147102) and the Youth Science and Technology Innovation Research Team of Sichuan Province, China (21CXTD0038)

This paper investigates the feasibility of using a Li-Baker detector based on a modulated Gaussian beam to detect gravitational waves in the GHz band. The first-order perturbation photon fluxes (PPF, signal of the detector) and the background photon fluxes (BPF, main noise of the detector), which vary with time, and the transverse distance are calculated. The results show that their propagation directions and energy densities are much different in some areas. Apart from BPF, we also consider two other important noises: diffraction noise and shot noise. In the simulation, it is found that the diffraction noise and shot noise are both lower than the signal level. Meanwhile, the main noise (BPF) can be eliminated when the receiving screen is located in certain special transverse areas where the BPF direction is opposite to that of PPF. Thus, the signal to noise ratio (SNR) obtained using our detection method can reach up to in some transverse areas. These results are beneficial for the design of the Li-Baker detector.

Multiwavelength high-order optical vortex detection and demultiplexing coding using a metasurface

Orbital angular momentum (OAM) of an optical vortex has attracted great interest from the scientific community due to its significant values in high-capacity optical communications such as mode or wavelength division multiplexer/demultiplexer. Although several configurations have been developed to demultiplex an optical vortex, the multiwavelength high-order optical vortex (HOOV) demultiplexer remains elusive due to lack of effective control technologies. In this study, we present the design, fabrication, and test of metasurface optical elements for multiwavelength HOOV demultiplexing based on optical gyrator transformation transformations in the visible light range. Its realization in a metasurface form enables the combined measurement of OAM, the radial index p, and wavelength using a single optical component. Each wavelength channel HOOV can be independently converted to a high-order Hermitian–Gaussian beam mode, and each of the OAM beams is demultiplexed at the converter output. Furthermore, we extend the scheme to realize encoding of the three-digit gray code by controlling the wavelength or polarization state. Experimental results obtained at three wavelengths in the visible band exhibit good agreement with the numerical modeling. With the merits of ultracompact device size, simple optical configuration, and HOOV recognition ability, our approach may provide great potential applications in photonic integrated devices and systems for high-capacity and demultiplex-channel OAM communication.

Polarization Spectroscopy Applied to Electromagnetically Induced Transparency in Hot Rydberg Atoms Using a Laguerre–Gaussian Beam

In this work, we have applied polarization spectroscopy to study electromagnetically induced transparency involving hot Rb85 Rydberg state in a vapor cell using a Laguerre–Gaussian mode beam. Such spectroscopy technique generates a dispersive signal, which allows a direct measurement of the transition linewidth. Our results show that the measured transition linewidth for a Laguerre–Gaussian mode control beam is narrower than for a Gaussian mode. Besides, it can be well reproduced by a simplified Lindblad master equation model.

Laser Gaussian beam analysis of structure constant depends on Kolmogorov in turbulent atmosphere for a variable angle of wave propagation

Laser Gaussian beam propagation is important in optical communications; the challenges of the measured constant parameters are varied angle wave propagation, the receiver plan in the slant path of laser Gaussian beam (G) in Kolmogorov gauges, and the effect of the laser in a random medium. At this point, atmospheric turbulence is reputable based on laser Gaussian beam propagation. Moreover, the space propagation of Gaussian beam waves of higher-order Gaussian beam modes has been expanded from the effects of the scintillation index and with different zenith angles between the laser propagator and the detector (receiver) in the ramp path. Furthermore, in the Cartesian coordinate system, the scintillation index in the Kolmogorov standard is evaluated, and it employs two methods; first, Huygens–Fresnel fundamental and, second, random phase screen for work synchronization. Additionally, to analyze the contour parameters of constant construction, the intensity and receiver field is found to compute the high turbulent modes in the atmospheric deposition, which depends on propagation distances. These result in significant reserves in the matlab computation period and serve the imitation for enhancement of the link transmission; therefore, the zenith angle and scintillation index are pretentious by slant beam, and they enhance the performance that makes the comparisons found with fixed structure constant parameters C2n and the propagation distance against the scintillation index.

A Design Method of Three-Dimensional Multireflector Quasi-Optical Systems Based on Gaussian Beam Mode Analysis

Two-dimensional (2-D) quasi-optical systems have been widely applied. However, the analysis and design of 3-D systems still need to be further developed. In this letter, an approach to rapidly analyze the performance of 3-D multireflector systems based on Gaussian beam mode analysis is proposed. The influence of reflector parameters, such as input distance, incidence angle, and so on, on the co- and cross polarization is discussed. Furthermore, a novel design method of high-performance 3-D multireflector systems is proposed. High computational efficiency is one of the advantages of this method due to the application of particle swarm optimization algorithm. 3-D systems with low cross polarization or other electromagnetic properties can be designed rapidly by this novel method. The proposed methods greatly improve the calculation efficiency, while providing calculation accuracy similar to that of physical optics (PO) in GRASP10.

Accurate S-Parameter Modeling and Material Characterization in Quasi-Optical Systems

In the article, we present an analytical model of a beam interaction with a sample in a quasi-optical system suitable for high accuracy S-parameter prediction and material extraction. Instead of assuming a plane wave illumination of the sample, our model works with the fundamental Gaussian-beam mode (TEM <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_{00}$</tex-math></inline-formula> ) incident on a homogeneous parallel sided slab with unknown refractive index. Using the Gaussian-beam coupling theory the sample’s parameters can be determined from the level of decoupling (defocusing) in the optical system caused by the sample’s presence. The complex transmission and reflection coefficients can both be calculated using the model for normal as well as for oblique incidence. Moreover, the model also allows for the inclusion of imperfections in the quasi-optical system such as frequency-dependent properties of source and detector antennas and nominal beam misalignment. We successfully test the model by measuring a high quality reference sample (refractive index independently characterized with an open resonator technique) in the frequency band 110–170 GHz. A comparison in terms of S-parameters and extracted refractive indices between our Gaussian-beam coupling model and a standard plane wave model is also given showing the relevance of our work.

Measuring the orbital angular momentum mode of vortex beam based on phase matching sequence

Measuring the orbital angular momentum(OAM) mode of vortex beams is of great significance in applications based on vortex beams.we propose a method of phase matching characteristics of vortex beams to measure the OAM mode. The method first use a high-speed spatial light modulator(SLM) to sequentially load a set of helical phase sequence images, so that the vortex beam is modulated by this SLM. Then obtain the modulated optical field through pinhole filtering, and then the synchronized tilt phase modulation is performed by the 4f system and high-speed SLM. When the OAM mode of vortex beam is opposite to the topological charge of helical phase image, that is, the incident vortex beam degenerates to the fundamental Gaussian mode beam,and through our optical system, the output plane obtained a indicating spot with the position related to the OAM mode. The Simulation and experimental results show that the method obtains a clear OAM mode indicating spot on the final output plane, which verifies the theoretical derivation.

Conservation of extremal ellipticity for coherent single mode Gaussian beams propagating in rotationally invariant media

We demonstrate that the conservation of extremal ellipticity for an astigmatic Gaussian beam propagating in a rotationally invariant medium, for example, an arbitrary sequence of free space propagation and stigmatic lenses, initially identified by Lo et al. (2017), is a direct consequence of the conservation of orbital angular momentum (OAM) of the beam. We derive explicit analytical expressions for the first few non-zero moments of the beam OAM and show that, apart from fundamental constants, they depend only on the beam’s extremal ellipticity. This unexpected connection uncovers the actual origin of a new propagation invariant, namely extremal ellipticity, for a broad class of coherent, single-mode Gaussian beams. We expect this principle to find use in various applications where spot circularity along an extended region of the beam is essential; such as laser micromachining, imaging, optical trapping, and inertial confinement fusion.

Measurement of real phase distribution of a vortex beam propagating in free space based on an improved heterodyne interferometer

This paper proposes an improved heterodyne interferometer to measure the real phase distribution of vortex beams propagating in free space. The fundamental mode Gaussian beam passes through the vortex phase plate and has one or more phase transitions of 2π along the angular direction. Such vortex beams undergo phase distortion during transmission, and their complex phase distribution is difficult to measure. The improved heterodyne interferometer proposed in this study successfully measures the phase distortion, demonstrating high spatial resolution and phase measurement accuracy. Both the theoretical and the experimental results show that in the process of free space propagation, the phase jump intersection boundary transforms from a straight line into a twisted line and that the phase distribution gradually becomes a spiral phase distribution followed by a ring intensity distribution corresponding to further increase in the propagation distance. The proposed method is estimated to be capable of predicting the variation of the vortex beams based on the research conducted on the interaction between the vortex beams and the atmospheric turbulence.

A 2D Gaussian beam launcher applied in parallel plate waveguide field mapping systems

Abstract3D Gaussian beam generation techniques have been studied by many researchers, while the problem of 2D Gaussian beam generations have not been addressed fully. However, 2D Gaussian beams are still useful in research and applications. This article presents the mechanism, design, simulation, and measurement of a 2D Gaussian beam launcher, which allows the easy control of the width and the location of Gaussian beam waist. The proposed Gaussian beam launcher consists of a radiator array fed with the designable excitation phase and magnitude to each radiator, so as to generate the necessary boundary condition that the Gaussian beam can be excited and propagate. Both simulation and measurement results are nearly identical with the profile of the lowest order 2D Gaussian beam mode. The proposed 2D Gaussian beam launcher is suitable as the excitation source of parallel plate waveguide measurement systems. By integrating tunable components, it can be easily extended in the future to control Gaussian beam parameters dynamically.

A Gaussian Beam Mode Analysis Method for 3-D Multi-Reflector Quasi-Optical Systems

3-D quasi-optical systems have a more comprehensive range of application scenarios, and their analysis and design are more complicated than those of 2-D systems. In this work, we improve Gaussian beam mode analysis (GBMA) to analyze 3-D multi-reflector systems. The expressions of co- and cross-polarization and their derivations are given and discussed in detail. Furthermore, several 3-D dual-reflector systems with different rotation angles are chosen as simulation examples to assess the validity and precision of 3-D GBMA compared with physical optics (PO) in the commercial software GRASP10. Furthermore, a 3-D double ellipsoidal reflector system with a π/2 rotation angle operating at 183 GHz is designed, manufactured, and tested. Measured results of the system demonstrate that it is in good agreement with the simulated results of 3-D GBMA and PO for both the co- and cross-polarization. By comparing the computing time performance of 3-D GBMA and PO in GRASP10, the high efficiency of 3-D GBMA is clarified. With 3-D GBMA, the field in 3-D quasi-optical systems can be calculated preciously and rapidly.

Wavelength and chemical potential dependence of optical beam shifts in graphene

We predict the spatial and angular Goos-Hänchen (GH) and Imbert-Fedorov (IF) shifts in partial (PR) and total internal reflection (TIR) conditions for fundamental Gaussian mode beams of a wide range of wavelength (400–1300 nm) impinging upon a graphene-coated dielectric surface. The GH and IF shifts turn out to be extremely dependent upon the chemical potential of graphene along with the wavelength of the incident light, thus enabling one to appropriately choose the operating wavelength and tune the chemical potential in the desired region to obtain maximum beam shifts in graphene. We also show that the typical features of the optical beam shifts are potentially linked with the optical conductivity of single-layer graphene. We expect the current study to be of fundamental significance in the field of optoelectronics and device industry based on graphene and other 2D materials.

On quantum bit coding by Gaussian beam modes for the quantum key distribution

On quantum bit coding by Gaussian beam modes for the quantum key distribution

Theoretical and experimental verification of a fast two‐dimensional Gaussian beam mode analysis method

In quasi-optical systems, the beam distortion and the cross-polarisation caused by the offset reflectors get a lot of attention. Also, the distortion was thoroughly studied in previous works. In this study, the authors give the detailed derivations of exact and approximate expressions of cross-polarisation and some simple explanations about energy conversion between co- and cross-polarisations in two-dimensional multi-reflector systems based on Gaussian beam mode analysis (GBMA). In addition two dual-reflector systems with different structures are used to verify the correctness and accuracy of GBMA comparing with physical optics (PO) in commercial software GRASP10. Furthermore, the authors fabricate one of these two systems and give experimental results. Then, they propose a fast analysis algorithm based on the vector addition method to reduce the computation time by eliminating the redundant modes. The efficiency of the proposed fast algorithm is illustrated by the number of modes and the calculation time for each reflection in a tri-reflector system. In addition, the authors also present the computation time of PO in GRASP10 as a reference. With the application of the fast algorithm, the computational efficiency is improved and increases with the number of reflections.

A two‐dimensional quasi‐optical system design method with low cross‐polarization based on Gaussian beam mode analysis

AbstractIn the design of quasi‐optical systems, the cross‐polarization introduced by off‐axis mirrors is a major concern to us. By Gaussian beam mode analysis (GBMA), the electric field could be predicted precisely with this factor. In this study, we present some significant expressions and a method based on the energy of modes to analyze the influence of design parameters such as the distance between two objects and the incident angles of beams on the cross‐polarization level of a two‐dimensional (2D) multi‐reflector system with a feed containing cross‐polarization. Finally, combining these discussions, an innovative 2D quasi‐optical system design algorithm with low cross‐polarization based on the particle swarm optimization (PSO) algorithm is proposed considering various system variables. In order to verify the validity and accuracy of our method, we compare the results of our approach and physical optics (PO) in the commercial software package GRASP10 with the example of a double ellipsoidal mirror system.

Propagation characteristics of vortex beams in anisotropic atmospheric turbulence

The phase distortion of vortex beams caused by atmospheric turbulence is calculated by the power spectral inversion method. An analytical expression of the fundamental mode Gaussian vortex beam that propagates through anisotropic atmospheric turbulence has been deduced. The influences of altitude, anisotropic factor, and topological charge (TC) on the propagation characteristics of vortex beams are discussed in detail. The results show that when the altitude is in the region of 3–6 km, the change of altitude has little influence on the quality of vortex beams. When the altitude is in the region of 6–7.8 km, beam quality will become better along with the increase in altitude. Otherwise, beam quality will be better with the increase in anisotropic factor, and the ability to resist distortion will be stronger with the increase in TC.

Hermite Gaussian beam scintillations in weak atmospheric turbulence for aerial vehicle laser communications

Scintillation index of Hermite Gaussian beams used for air vehicle communication systems in vertical paths of weak atmospheric turbulent medium are investigated by employing the modified Rytov method. By evaluating the on-axis scintillation index, variations of the scintillation indices of these beams are examined against the changes in the Gaussian beam size of the Hermite Gaussian beam mode, propagation distances and the zenith angles at the realistic propagation distances involved in uplink and downlink configurations. In the atmospheric environment, for uplink, the Hermite Gaussian beam modes have no advantage over the Gaussian beams at short propagation distances like L=20km,as well as at long propagation distances like L=700km. However, for downlink, although Hermite Gaussian beam modes are disadvantageous over the Gaussian beams at short propagation distances like L=20km, they are found advantageous over the Gaussian beams at long propagation distances like L=700km. The results of this study may encourage to use Hermite Gaussian beams, especially in the air vehicle laser communication links, and can be used in the design of an optical wireless communication link utilizing the vertical atmospheric medium.