Laguerre-Gaussian Beams Research Articles

Photothermal vortex interferometer with azimuthal complex spectra analysis for the measurement of laser-induced nanoscale thermal lens dynamics

A photothermal vortex interferometer (PTVI) is proposed to fill the gap of full-field measurement of the laser-induced nanoscale thermal lens dynamics of optical elements. The PTVI produces a multi-ring petal-like interferogram by the coaxial coherent superposition of the high-order conjugated Laguerre–Gaussian beams. The non-uniform optical path change (OPC) profile resulting from the thermal lens causes the petals of the interferogram at the different radii to shift by the different azimuths. To demodulate such an interferogram, an azimuthal complex spectra analysis is presented by using a camera with a pixelated multi-ring pattern written on its sensor to extract multiple azimuthal intensity profiles synchronously from the interferogram. Therefore, the OPC profile can be determined dynamically from the complex spectra of the azimuthal intensity profiles at the main frequency components. An analytical thermophysical model of the thermal lens is given, and the basic principle of the azimuthal complex spectra analysis is revealed. A proof-of-concept experiment is demonstrated using a N-BK7 glass sample heated by a pump laser. The results verified that the PTVI achieves the measurement accuracy of 47 pm with a standard deviation of 358 pm (3σ) and can be used for full-field measurement of the nanoscale OPC profile caused by the thermal lens dynamics. Due to the picometer-scale accuracy of the PTVI, the absorption coefficient and thermal diffusivity of the glass sample were determined to be A0 = 0.126 m−1 and D = 5.63 × 10−7 m2 s−1, respectively, which agree with the nominal ones of A0 = 0.129 m−1 and D = 5.17 × 10−7 m2 s−1. Although the PTVI is only suitable for measuring the rotationally symmetric OPC, it shows less computation burden and hardware complexity, and it is proved to be a highly sensitive and effective tool in studying optical, thermo-physical, and mechanical properties of optical elements.

Paraxial Dirac equation

In this work, the paraxial approximation of the free Dirac equation is examined. The results are first obtained by constructing superpositions of exact solutions with suitable profiles, which are borrowed from paraxial optics. In this manner, the paraxial Dirac beams are obtained in four cases: as Gaussian, Bessel-Gaussian, modified Bessel-Gaussian and elegant Laguerre-Gaussian beams. In the second part of the work, the paraxial Dirac equation is derived, and then its solutions in the aforementioned cases are directly obtained. All the resulting wave functions conform to those derived formerly by virtue of superpositions, except for terms that are negligible upon the assumption that the paraxial functions along the propagation axis vary only slightly over a distance equal to the de Broglie wavelength, which is the standard paraxial requirement.

The vortex light induced electric dipole and electric quadru-pole transition in Ca atom

The Laguerre–Gaussian beam induced electric transition model is presented. The major mechanism of angular momentum exchange between the light and the atomic system is discussed. The influence of the topological charge on the transition probability and selection rules is obtained. Our results show that the Ca(4s2 1S0–4s3d 1D2) electric quadrupole transition selection rules are sensitive to the sign of l, and the center of mass transition selection rules are governed by the topological charge l of the light. The electric dipole transition is possible in a field with topological charge l > 0, and the quadrupole transition is no longer forbidden. The overall transition probability difference between dipole transition and quadrupole transition can be decreased by the joint action of the light angular momentum exchange with the external and the internal motion.

Exploring the evolution of circular polarized light backscattered from turbid tissue-like disperse medium utilizing generalized Monte Carlo modeling approach with a combined use of Jones and Stokes-Mueller formalisms.

Phase retardation of circularly polarized light (CPL), backscattered by biological tissue, is used extensively for quantitative evaluation of cervical intraepithelial neoplasia, presence of senile Alzheimer's plaques, and characterization of biotissues with optical anisotropy. The Stokes polarimetry and Mueller matrix approaches demonstrate high potential in definitive non-invasive cancer diagnosis and tissue characterization. The ultimate understanding of CPL interaction with tissues is essential for advancing medical diagnostics, optical imaging, therapeutic applications, and the development of optical instruments and devices. We investigate propagation of CPL within turbid tissue-like scattering medium utilizing a combination of Jones and Stokes-Mueller formalisms in a Monte Carlo (MC) modeling approach. We explore the fundamentals of CPL memory effect and depolarization formation. The generalized MC computational approach developed for polarization tracking within turbid tissue-like scattering medium is based on the iterative solution of the Bethe-Salpeter equation. The approach handles helicity response of CPL scattered in turbid medium and provides explicit expressions for assessment of its polarization state. Evolution of CPL backscattered by tissue-like medium at different conditions of observation in terms of source-detector configuration is assessed quantitatively. The depolarization of light is presented in terms of the coherence matrix and Stokes-Mueller formalism. The obtained results reveal the origins of the helicity flip of CPL depending on the source-detector configuration and the properties of the medium and are in a good agreement with the experiment. By integrating Jones and Stokes-Mueller formalisms, the combined MC approach allows for a more complete representation of polarization effects in complex optical systems. The developed model is suitable to imitate propagation of the light beams of different shape and profile, including Gaussian, Bessel, Hermite-Gaussian, and Laguerre-Gaussian beams, within tissue-like medium. Diverse configuration of the experimental conditions, coherent properties of light, and peculiarities of polarization can be also taken into account.

Spin Hall Effect of Two-Index Paraxial Vector Propagation-Invariant Beams

We investigate a simple paraxial vector beam, which is a coaxial superposition of two single-ringed Laguerre–Gaussian (LG) beams, linearly polarized along the horizontal axis, with topological charges (TC) n and −n, and of two LG beams, linearly polarized along the vertical axis, with the TCs m and −m. In the initial plane, such a vector beam has zero spin angular momentum (SAM). Upon propagation in free space, such a propagation-invariant beam has still zero SAM at several distances from the waist plane (initial plane). However, we show that at all other distances, the SAM becomes nonzero. The intensity distribution in the cross-section of such a beam has 2m (if m > n) lobes, the maxima of which reside on a circle of a certain radius. The SAM distribution has also several lobes, from 2m till 2(m + n), the centers of which reside on a circle with a radius smaller than that of the maximal-intensity circle. The SAM sign alternates differently: one lobe has a positive SAM, while two neighbor lobes on the circle have a negative SAM, or two neighbor pairs of lobes can have a positive and negative SAM. When passing through a plane with zero SAM, positive and negative SAM lobes are swapped. The maximal SAM value is achieved at a distance smaller than or equal to the Rayleigh distance.

Conical Emission Induced by the Filamentation of Femtosecond Vortex Beams in Water

Conical emission is a typical nonlinear phenomenon that occurs during the filamentation of femtosecond laser pulses in transparent media. In this work, the conical emission induced by two kinds of typical vortex beams (i.e., Laguerre–Gaussian (LG) and Bessel–Gaussian (BG) beams) in water is experimentally studied. By recording the light spots of different spectra components from the supercontinuum induced by the vortex beams, the characteristics of the conical emission induced by femtosecond vortex beams are studied. It is found that the spots of the supercontinuum induced by the two kinds of vortex beams differ greatly from each other. The spots of the supercontinuum induced by the BG beams are a set of concentric rings like a rainbow with a white center, while the white light spots in the case of the LG beams are circular white disks, which are different from the commonly observed white light spots. By measuring the maximum divergence angle, it is observed that the divergence angle increases with a decrease in the wavelength, while it is merely affected by the topological charge, which is explained by the formation mechanism of conical emission in terms of self-phase modulation. Based on the observed results, we discuss the transfer of optical angular momentum during the supercontinuum induced by the filamentation of femtosecond vortex beams. This work may help to better understand the transfer of optical angular momentum in non-optical parametric processes as well as the interaction of high-intensity pulses with matter.

Radial spectrum spread of Laguerre-Gaussian beam transmission in weak compressible turbulence

Turbulence effects can seriously affect the propagation of structured light, especially for orbital angular momentum (OAM) modes, causing spread and crosstalk. We derive an analytical solution to the mode spectrum of a Laguerre-Gaussian beam (LGB) propagating in weak compressible turbulence. The influence of the radial number and turbulence strength in the mode spectrum on the probability of LGB propagation is mainly considered. The results show that the weak compressible turbulence interferes strongly with the LGB, and this effect is mainly reflected in the sharp drop of the signal mode energy at short transmission distance. We find that the pure radial mode has a higher signal mode energy than the pure OAM mode, which means that the pure radial mode is more resilient to compressible turbulence than the pure OAM mode. In addition, the increase of radial number can improve the performance of the OAM dimension, but on the other hand, it reduces the probability of the radial dimension. Finally, we discussed the propagation properties of higher-order modes. Our research clarifies the interaction of OAM mode and radial mode in turbulence, and provides a theoretical basis for applications based on radial modes in the field of free-space communication.

Transmission of optical communication signals through ring core fiber using perfect vortex beams.

Orbital angular momentum can be used to implement high capacity data transmission systems that can be applied for classical and quantum communications. Here we experimentally study the generation and transmission properties of the so-called perfect vortex beams and the Laguerre-Gaussian beams in ring-core optical fibers. Our results show that when using a single preparation stage, the perfect vortex beams present less ring-radius variation that allows coupling of higher optical power into a ring core fiber. These results lead to lower power requirements to establish fiber-based communications links using orbital angular momentum and set the stage for future implementations of high-dimensional quantum communication over space division multiplexing fibers.

Analysis of rotational Doppler shift with multi-ring vortex beams.

Vortex beams (VBs) with orbital angular momentum have shown great potential in the detection of transverse rotational motion of spatial targets which is undetectable in the classical radar scheme. However, most of the reported rotational Doppler measurements based on VBs can only be realized under ideal experimental conditions. The long-range detection is still a challenge. The detection distance based on rotational Doppler effect (RDE) is mainly limited by the scattered signal's signal-to-noise ratio (SNR). In this work, we investigated the influence of multi-ring vortex beams (MVBs) on the rotational Doppler frequency spectrum of scattered light from an object based on RDE and proposed a method of SNR enhancement of RDE signal. Firstly, different types of MVBs composed of a set of single-ring VBs with the same topological charge and different radii are designed, including multi-ring Laguerre Gaussian beam (MLGB), multi-ring perfect vortex beams (MPVB), and high-order Laguerre Gaussian beam (HLGB). Then, the influence of the number of rings and radial radius interval on the intensity profiles of MVBs and rotational Doppler frequency spectra under aligned and misaligned conditions is studied in detail. And the reasons why different types of MVBs lead to different SNR enhancement effectiveness with the increase of rings are also analyzed theoretically. Finally, proof-of-concept experiments were conducted to verify the effectiveness of the SNR enhancement method for RDE signals. The results showed that the amplitudes of the Doppler spectra generated by the MLGB and MPVB are improved substantially with the increase of rings, but the enhancement effect caused by the former is superior to the latter. The gain of HLGB on the RDE signal is the lowest. This study provides a useful reference for the optimization of rotational Doppler detection systems and may be of great application value in telemetry, long-range communication and optical imaging.

Simulation of the Propagation of Rotating Laguerre–Gaussian Beams in an Imaging System with an Obstacle

Simulation of the Propagation of Rotating Laguerre–Gaussian Beams in an Imaging System with an Obstacle

Spherical Gauss-Laguerre beam propagation in 4D space-time.

In this paper, what we believe to be a novel class of beams, which are referred to as the spherical Gauss-Laguerre beams, are proposed. The beams propagate stably in the anomalous dispersive media, within which the second order derivative with respect to t could be combined with the two-dimensional (2D) Laplacian operator in the transverse direction and forms a three-dimensional (3D) Laplacian operator, which describes the beam propagation in the z direction within the four-dimensional (4D) x-y-z-t space-time. The wave equation is solved by the variable separation method and the analytical expression for the spherical Gauss-Laguerre beams is derived. The beams have a 3D Gaussian field distribution with a variable beam waist with respect to the propagation distance. Unlike any 2D spatial vortex beams, the 3D beams could possess either the spatial vortex or the spatiotemporal optical vortex (STOV) by choosing the vortex plane in the 3D x-y-t space-time. The derived spherical Gauss-Laguerre beam expression in the 4D space-time is verified by the numerical simulations with excellent agreement.

Optical dipole potential energy of a two-level atom interacting with a tightly focused truncated optical Bessel beam

Truncated optical Bessel (TOB) beams are an orthonormal set of optical vortex beams that possess orbital angular momentum (OAM). It is characterized by a significant longitudinal electric field component at the sub-wavelength scales. The photons of a circularly polarized TOB beam also carry spin angular momentum (SAM) and can interact with a two-level atom, in the far-off resonance regime, giving rise to an optical dipole potential energy that involves a spin–orbit term that stems from the inclusion of the longitudinal field component. When a two-level atom is simultaneously irradiated by two TOB beams, the optical dipole potential energy, in some special cases, is entirely dependent on the OAM–SAM coupling. We explore the cold-atom trapping options enabled by the use of TOB beams, either single ones or combinations thereof. We put emphasis on case in which the OAM–SAM coupling is the dominant contribution. The similarities and differences between the results obtained for the TOB beams and those for the Laguerre–Gaussian beams are also discussed.

Magneto- and thermo-optic manipulation of imbert-fedorov shift for Laguerre-Gaussian beam in a graphene-VO2 multilayer structure

Imbert-Fedorov (IF) shift of Gaussian beams has been widely studied, while the IF shift of singular beams carrying Orbital Angular Momentum (OAM) also shows unique properties when reflected or refracted at optical interfaces. Here, through theoretical deduction and analysis, the IF shift of Laguerre-Gaussian beams with varying OAM in a graphene-VO2 multilayers structure is explored. The results demonstrate that the IF shift increases with the increase of topological charge l. Under the configuration of transverse magneto-optical Kerr effect (TMOKE), the IF shift increases by a factor of 10 compared to the Gaussian beam when l = 3. Additionally, under the polar magneto-optical Kerr effect (PMOKE) conditions, graphene demonstrates the magneto-optical (MO) effect and cross-polarization effect in the terahertz frequency range, and can effectively control the IF shift through the magnetic field. Both left- and right-handed circular polarization (LHCP and PHCP) exhibit asymmetry and non-reciprocity. Moreover, temperature control is achieved through the unique phase transition characteristics of VO2. These results offer novel insights into precision measurements, sensing techniques and the development of terahertz devices.

Properties of focused Laguerre–Gaussian beam propagating in anisotropic ocean turbulence

We analyze the properties of a focused Laguerre–Gaussian (LG) beam propagating through anisotropic ocean turbulence based on the Huygens–Fresnel principle. Under the Rytov approximation theory, we derive the analytical formula of the channel capacity of the focused LG beam in the anisotropic ocean turbulence, and analyze the relationship between the capacity and the light source parameters as well as the turbulent ocean parameters. It is found that the focusing mirror can greatly enhance the channel capacity of the system at the geometric focal plane in oceanic turbulence. The results also demonstrate that the communication link can obtain high channel capacity by adopting longer beam wavelength, greater initial beam waist radius, and larger number of transmission channels. Further, the capacity of the system increases with the decrease of the mean squared temperature dissipation rate, temperature-salinity contribution ratio and turbulence outer scale factor, and with the increase of the kinetic energy dissipation rate per unit mass of fluid, turbulence inner scale factor and anisotropy factor. Compared to a Hankel–Bessel beam with diffraction-free characteristics and unfocused LG beam, the focused LG beam shows superior anti-turbulence interference properties, which provide a theoretical reference for research and development of underwater optical communication links using focused LG beams.

A comparative study of electromagnetically induced transparency (EIT) in Λ-, V-, and Ξ-type systems using Laguerre–Gaussian (LG) laser beams

In this paper, a theoretical investigation of electromagnetically induced transparency (EIT) using Laguerre–Gaussian (LG) beams has been carried out for the three canonical atom-laser coupled systems (e.g. [Formula: see text]-, V-, and [Formula: see text]-type) in [Formula: see text]Rb atom. The required optical Bloch equations (OBEs) are derived for each system. The OBEs are analytically solved in steady-state condition under the weak probe field approximation. We have used the iterative perturbative technique to obtain the probe coherence term. The probe response w.r.t. probe detuning for different orders of the orbital angular momentum (OAM) number of both the pump and probe LG beams has been studied. We have also studied the effect of the OAM number on probe response in both Doppler-free and Doppler-broadened mediums. It has been observed that the EIT signal is squeezed for nonzero OAM number of the pump beam with arbitrary OAM number of the probe beam. It is found that for higher-order OAM number, the EIT signal is further squeezed. The modification of the EIT signal is attributed because of the spatial-dependent Rabi frequency. Our study demonstrates that the dynamic of the probe field inside an atomic medium may be controlled by tuning the OAM number of the LG beam.

Tailoring OAM spectrum of high-order harmonic generation driven by two mixed Laguerre–Gaussian beams with nonzero radial nodes

The extreme ultraviolet (XUV) light beam carrying orbital angular momentum (OAM) can be produced via high-order harmonic generation (HHG) due to the interaction of an intense vortex infrared laser and a gas medium. Here we show that the OAM spectrum of vortex HHG can be readily tailored by varying the radial node (from 0 to 2) in the driving laser consisting of two mixed Laguerre–Gaussian (LG) beams. We find that due to the change in spatial profile of HHG, the distribution range of the OAM spectrum can be broadened and its shape can be modified by increasing the radial node. We also show that the OAM mode range becomes much wider and its distribution shape becomes more symmetric when the harmonic order is increased from the plateau to the cutoff when the driving laser has the nonzero radial nodes. Through the map of coherence length and the evolution of harmonic field in the medium, we reveal that the favorable off-axis phase-matching conditions are greatly modified due to the change of intensity and phase distributions of driving laser with the radial node. We anticipate this work to stimulate some interests in generating the XUV vortex beam with tunable OAM spectrum through the gaseous HHG process achieved by manipulating the mode properties of the driving laser beam.

Three-dimensional measurement of laser-induced thermal mirror dynamics using photothermal vortex interferometer with azimuthal phase spectra analysis

Measurement of the thermal mirror caused by laser heating provides direct access to the optical, thermophysical, and mechanical properties of solid materials. However, the nanoscale time-dependent three-dimensional (3D) thermal mirror hinders the existing photothermal techniques to obtain the thermal mirror dynamics without sacrificing the spatial profile of the thermal mirror. To fill the gap of 3D measurement of laser-induced thermal mirror dynamics, a photothermal vortex interferometer (PTVI) is proposed. The PTVI produces a multi-ring petal-like interferogram by the coaxial coherent superposition of the high-order conjugated Laguerre-Gaussian beams. The nanoscale 3D thermal mirror with a rotationally symmetric surface profile can be encoded into different azimuthal phase shifts at the different radii of the interferogram. An azimuthal phase spectra analysis is proposed to extract the azimuthal phase shifts from the continuously captured interferograms, enabling reconstruction of the 3D thermal mirror dynamics. The experimental results verified that the PTVI can measure the surface deformation due to the thermal mirror at an accuracy of picometer scale, and the optical and thermophysical properties of an optical glass sample can be determined with the assistance of the thermophysical model of the 3D thermal mirror dynamics. The approach can be an effective tool for characterization of solid materials.

A Novel Perspective of a Laguerre–Gaussian Beam's Phase Acceleration in Chiral Medium by Using Distinguishability Property

A Novel Perspective of a Laguerre–Gaussian Beam's Phase Acceleration in Chiral Medium by Using Distinguishability Property

High-power vortex beams generated from a Yb:YAG thin-disk laser with spot-defect mirrors

We report the generation of high-power and high-order vortex beams based on a Yb:YAG thin-disk laser oscillator with a spot-defect mirror. High-quality vortex beams were directly emitted by the oscillator with an output power of 80 W, which is the highest output power of any vortex laser oscillator. Tunable high-order Hermite-Gaussian modes from HG1,1 to HG5,1 were also generated, and subsequently converted to Laguerre-Gaussian beams by a cylindrical-lens mode converter. The vortex characteristics of the output were confirmed with a Mach-Zehnder interferometer. This work demonstrates an effective way to generate high-quality, high-power and high-order optical vortex beams.

Inverse method for tailoring optical beams

We present an inverse design method for local tailoring of the characteristic properties of optical beams, including the formation of subwavelength features in the transverse plane. Our proposed technique is based on the superposition of paraxial Laguerre–Gaussian beams, that generate the desirable optical fields. Additionally the effect of nonparaxiality is also considered. This versatile method enables the precise control over amplitude and phase profiles, providing thus new potential applications in wavefront shaping and imaging.