Laguerre Gaussian Research Articles

Generation of tunable terahertz pulse carrying orbital angular momentum in non-uniform vortex plasma channel

An amplitude modulated Laguerre-Gaussian (LG) laser beam carrying orbital angular momentum (OAM) is considered for terahertz radiation using non-uniform plasma vortex channel under relativistic conditions. The suggested approach involves the exchange of angular momentum between a non-uniform vortex plasma and a laser beam. During the interaction of non-uniform vortex plasma with photons, the laser angular momentum changes and twisted terahertz radiation is generated. The resultant THz radiation is shown to be substantially dependent on the beam width parameter and non-uniformity in the plasma channel. The amplitude of THz increases with beam focusing and the orbital angular momentum parameter. Due to higher amplitude of THz this study is useful in THz applications like, detection of counterfeit drugs, explosive material, analyze and identify defects in materials, medical imaging and communication.

Optical patterning fullerene nanostructures with high purity and high surface quality

Nanoscale patterning of fullerene materials with peculiar intrinsic electronic and optical properties is of crucial importance for their widespread applications. However, it remains a daunting challenge for current methods that suffer from both complicated lithography procedures and additives of photopolymers or photochemicals detrimental to the pristine properties of fullerene. Here, we developed a contamination-free laser printing approach for in situ patterning of fullerene with nanoscale resolution and high purity. The optical trapping force within the tight focus provides a lithography-free means to form densely packed fullerene nanostructures with two-order-of-magnitude enhanced fluorescence emission and a surface roughness of 6 nm. In addition, versatile fullerene nano-patterns from dots to concentric rings can be realized by flexibly shaping the optical trapping force of higher-order Laguerre–Gaussian beams. These results open a new route to programmable and high-quality patterning of fullerene optoelectronic devices with complex nanostructures.

Normal and anomalous dispersion study on probe light propagation in the presence of structured coupling light using electromagnetically induced transparency protocol

Here, we present a study on the dispersion features obtained in an electromagnetically induced transparency (EIT) experiment using a three-level cascade configuration in an 87Rb atomic vapor medium in the presence of Laguerre–Gaussian (LG) light as a coupling. A doublet transmission structure was obtained experimentally, and dispersion spectra were extracted using transmission spectra to study the probe light behavior. Dispersive regions that exhibit normal and anomalous nature were studied considering the polarization of various orientations as a coupling light. We established that normal dispersive region shows steep positive slopes, and anomalous dispersive region shows negative slopes, which can be controlled by polarization orientations. Owing to the change in the slopes of dispersion, normal and anomalous dispersive region is observed, and spectrum shows the effects of subluminal and superluminal propagation of probe light. This work, to the best of our knowledge, is novel in the study of dispersive region arising out of double-resonance EIT transmission spectra in the presence of LG light with the l=10 and p=0 mode as a coupling light with various polarization orientations. In the discussion, we establish that single parameter θ is sufficient for identifying the orientation and ellipticity of the polarization ellipse and also determine that the polarization of coupling light acts as a tuning parameter for changing the behavior of normal and anomalous dispersive region. Slow and fast light or superluminal propagation of probe light arise as a consequence of positive or negative group index, and fast light does not violate the principle of causality. Slow and fast light have future applications in high-speed quantum information and quantum communication using EIT-based protocol.

Laguerre–Gaussian beam scattering by a marine aerosol

Laguerre–Gaussian beam scattering by a marine aerosol

Ultra‐High‐Order Laguerre–Gaussian Field Generated Directly From a Laser Cavity with Spherical Aberration

AbstractPursuing higher topological charge—larger angular indices m of high‐order Laguerre–Gaussian (LG) beams—is not only important for frontier applications like optical/quantum communication, optical tweezers, and super‐resolution imaging, but also involves a novel laser cavity and beam dynamics. Active methods to directly generate high‐order‐mode vortex beams from a laser cavity have excellent power handling and conversion efficiency, but struggle to achieve hundred‐level ultra‐high‐order LG modes. Here, the generation of ultra‐high‐order LG beams with m beyond 300 is demonstrated, utilizing the spherical aberration of a lens in the cavity of a simple end‐pumped Nd:YVO4 laser at 1064 nm. LG0,±m modes with m up to 317, selectable across a large range, are generated. With a simple model, how the mode selection relates to the cavity parameters is explained, and it is predicted that even higher order mode output can be expected by appropriate management of the elements’ aperture and laser gain. The approach provides a simple and flexible method to convert a wide range of lasers to generate ultra‐high‐order LG modes.

Measuring Topological Charge of Laguerre–Gaussian Beams With a Y-Shaped Aperture

We study the diffraction pattern of a Laguerre–Gaussian (LG) beam passing through a Y-shaped aperture (YA), which can be used to measure the topological charge (TC) of such a beam. This paper confirms that the magnitude and sign of the TC of the LG beam can be measured with a YA. We also study the effect of the YA with different sizes on the diffraction pattern. In addition, YA diffraction itself can be used to verify the measurement results of the sign of TC. The experimental results agree well with the simulation results. The method is simple and reliable.

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.

Fine Structure of Optical Vortices in Linearly Polarized Laguerre–Gaussian Beams in Oblique Beams Propagating a Uniaxial Crystal

Traditional ideas about linearly polarized paraxial beam propagation along the optical axis of a uniaxial crystal suggest that at the crystal exit face, after propagation through the polarizer, the beam will form an intensity distribution in the form of a conoscopic pattern. Any violation of axial propagation was considered as a perturbation of the conoscopic pattern and was not taken into account. Nevertheless, this process opens up a wide variety of transformations of polarization singularities caused by weak perturbations. In this article, the behavior of linearly polarized low-order Laguerre–Gauss beams in a uniaxial crystal is considered. The existence of a fine structure of radiation on the output face of a uniaxial crystal and the dependence of this fine structure on the parameters of the crystal and the beam are shown.

Investigation of the 2-D modal coupling of a Laguerre Gaussian beam through the dynamic air–water interface

When a Laguerre Gaussian (LG) beam propagates through the dynamic air–water interface, the aerosol above the water and the water surface curvature could induce various degradations, resulting in modal power coupling. Such degradations include (i) beam distortion, which affects the spatial amplitude and phase of the beam, and (ii) beam wandering, which induces misalignment between the receiver and the beam. Our results for a transmitted LG11 beam show that: (i) with the increase of the sine-shape water curvature frequency from 4 to 8 Hz, the modal coupling to adjacent modes increases from ∼−11 to ∼−7 dB; (ii) with the increase of aerosol attenuation from 1–2 to 3–5 dB, the modal coupling increases from ∼−12 to ∼−8 dB; (iii) the combination of curvature and aerosol effect could induce stronger modal coupling compared to the single-effect cases. Furthermore, we study the contributions of beam distortion and beam wandering to modal coupling. We find that: (i) there is ∼−8 dB modal coupling from LG11 to adjacent modes under the simulated beam-wandering-only case (the beam wandering corresponds to the one under 8 Hz curvature); (ii) the higher modal coupling for the experimental result under the 8 Hz curvature (∼−7 dB) might be due to beam distortion. Additionally, we demonstrate a 1-Gbit/s on-off-keying (OOK) link carried by a single LG11 beam under aerosol and curvature effects.

Direct observation of the Faraday rotation using radially-polarised doughnut modes

A novel experimental technique for the realisation of the optical Faraday effect using Laguerre–Gaussian (LG) light is described. The experiment employs a zero-order vortex half-wave retarder to generate a radially or azimuthally-polarised LG doughnut beam. The light emerging from the retarder then passes through a linear polariser, which gives rise to two intensity lobes, with the orientation of the intensity gap between the two lobes pointing parallel (perpendicular) to the polarisation direction of the radially (azimuthally) polarised beam. To complete the Faraday set up, the light traverses a material subject to a magnetic field, before passing through a final linear polariser, which results in a visible rotation of the lobes pattern. This technique exhibits the Faraday effect readily visually, without further elaborate steps to detect changes in the light intensity. The degree of rotation of the plane of polarisation is determined directly by the visibly clear change in the orientation of the intensity gap between the lobes.

Focusing pattern of the Laguerre-Gaussian beam with polarization mixing helical-conical phase modulation.

This paper focuses on the focusing pattern of the Laguerre-Gaussian (LG) beam with polarization mixing helical-conical phase modulation, which is based on the vector diffraction theory. The results show that the topological charge number l can sensitively control the intensity of the intensity peaks. The focal spot will split along the optical axis under different polarization parameters P. When l=1, the spot position and the peak intensity can be modulated by changing the polarization parameter P. The truncation parameter β makes the focusing spot form an optical trap. By adjusting the eccentricity parameter K, the opening direction of the optical trap can be well controlled. These results may be helpful in optical applications such as optical manipulation, optical focusing, and optical information transmission.

Transformation of Laguerre-Gaussian beams into 1D array of Hermite-Gaussian modes under the Talbot effect.

This work explains diffraction of Laguerre-Gaussian (LG) beams having non-zero radial indices from one dimensional (1D) periodic structures and their transformation into Hermite-Gaussian (HG) modes, theoretically, verifies using simulations and demonstrates the phenomenon experimentally. We first report a general theoretical formulation for such diffraction schemes, and then use it to investigate the near-field diffraction patterns from a binary grating having a small opening ratio (OR) by providing numerous examples. Results show that for OR≲ 0.1, at the Talbot planes, mainly at the first Talbot image, the images of individual lines of the grating obtain HG modes' intensity patterns. Therefore, the topological charge (TC) of the incident beam and its radial index can be determined from the observed HG mode. In this study, the effects of the OR of the grating and the number of Talbot plane on the quality of the generated 1D array of HG modes are also investigated. The optimum beam radius for a given grating is also determined. The theoretical predictions, are well confirmed by a number of simulations based on the free space transfer function and fast Fourier transform approach, and by experiments. The observed phenomenon, the transformation of LG beams into 1D array of HG modes under the Talbot effect, in addition of providing a way for characterization of LG beams with non-zero radial indices, itself is interesting and may be used in other fields of wave physics, especially for long-wavelength waves.

The propagation speed of optical speckle

That the speed of light in vacuum is constant is a cornerstone of modern physics. However, recent experiments have shown that when the light field is confined in the transverse plane, the observed propagation speed of the light is reduced. This effect is a consequence of the transverse structure which reduces the component of wavevector of the light in the direction of propagation, thereby modifying both the phase and group velocity. Here, we consider the case of optical speckle, which has a random transverse distribution and is ubiquitous with scales ranging from the microscopic to the astronomical. We numerically investigate the plane-to-plane propagation speed of the optical speckle by using the method of angular spectrum analysis. For a general diffuser with Gaussian scattering over an angular range of 5°, we calculate the slowing of the propagation speed of the optical speckle to be on the order of 1% of the free-space speed, resulting in a significantly higher temporal delay compared to the Bessel and Laguerre–Gaussian beams considered previously. Our results have implications for studying optical speckle in both laboratory and astronomical settings.

Huge spikes and dips of the orbital angular momentum in structured Laguerre-Gaussian beams resistant to simple astigmatism

The article investigated conditions for shaping astigmatic-invariant structured Laguerre-Gaussian (LG) beams in the case of simple astigmatism. We have theoretically and experimentally confirmed that the conditions of astigmatic invariance are that the q-phase parameter of the structured LG (sLG) beam is equal to the arctangent of the ratio of the Rayleigh length z0 to the focal length fcyl of a cylindrical lens for a single amplitude parameter of epsilon;=1. For the rest amplitude parameter values, epsilon;NotEqual;1, the astigmatic invariance condition is set by the equality of the orbital angular momenta (OAM) of structured sLG and astigmatic-invariant sLG (asLG) beams. We have also found sharp spikes and dips of the OAM in astigmatic asLG beams in the region where OAM turns into zero. The height and depth of these spikes and dips significantly exceed the maximum and minimum OAM values in the conventional structured sLG beams. It has been shown that the occurrence of spikes and dips of the OAM is caused by a radical restructuring of the LG mode spectra in the form of their strong ordering. Theoretical calculations, accompanied by a computer simulation, and an experiment agree well with each other.

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.

A Fourier-invariant squared Laguerre-Gaussian vortex beam

It is shown that a squared Laguerre-Gaussian (LG) vortex beam is Fourier-invariant and retains its structure at the focus of a spherical lens. In the Fresnel diffraction zone, such a beam is transformed into superposition of conventional LG beams, the number of which is equal to the number of rings in the squared LG beam. If there is only one ring, then the beam is structurally stable. A more general beam, which is a “product” of two LG beams, is also considered. Such a beam will be Fourier-invariant if the number of rings in two LG beams in the “product” is the same. The considered beams complement the well-known family of LG beams, which are intensively studied as they remain stable during their propagation in turbulent media.

Complete transport of intensity equation for phase retrieval of optical vortex beams

We derive the complete form of the transport of intensity equation (TIE) for an arbitrary wave field, in which additional terms describing the effect of optical vortices are included. The Poynting vector of optical vortices goes in a spiral around the vortex core through space. Consequently, the intensity variation is not observable in the manner of wave propagation, thereby precluding the possibility of phase retrieval via near-field intensity measurements. This difficulty is elegantly overcome by introducing a hard-edged aperture, as a common procedure to produce the required Neumann boundary signal, to break the azimuthal symmetry of the propagation, and visualize the rotation of the beam’s local Poynting vector around the aperture boundary. The basic principle, numerical solution, and practical implementation of how to use this new version of TIE for phase retrieval of arbitrary wave fields including optical vortices are developed. Based on the new approach, we present the first experimental demonstration of non-interferometric phase retrieval of Laguerre–Gaussian vortex beams of different orders using only two near-field intensity measurements. Our results consummate the basic theoretical framework of TIE and represent an important step towards phase retrieval of arbitrary wave fields carrying phase singularities.

Effects of primary aberrations on a dark-field microscopy imaging system with the sharper focusing lens

The effects of primary aberrations of the sharper focusing lens on the image quality is analyzed for a dark-field microscopy imaging system, which is illuminated by a left-circularly (LC) polarized Laguerre–Gaussian (LG) vortex beam. To confirm the aberration tolerance range of the sharper focusing lens for precise measurement, the analytical expression of the field distribution on the image plane is deduced. Then the dark-field image results corresponding to a defect with a scale of 6µm×6µm are simulated. The influence of the spherical error, coma, and astigmatism on the imaging quality is compared in detail. Then the verification test has been carried out to show the effects of different primary aberrations. Finally, both the simulation and experiment results help us to identify that the tolerance range of spherical aberration, astigmatism, and coma should be less than 1.5λ, 1λ, and 1.25λ, respectively.

Generalized Asymmetric Hermite–Gaussian and Laguerre–Gaussian Beams

We derive analytical formulae for the complex amplitudes of variants of generalized Hermite–Gaussian (HG) and Laguerre–Gaussian (LG) beams. We reveal that, at particular values of parameters of the exact solution of the paraxial propagation equation, these generalized beams are converted into conventional elegant HG and LG beams. We also deduce variants of asymmetric HG and LG beams that are described by complex amplitudes in the form of Hermite and Laguerre polynomials whose argument is shifted into the complex plane. The asymmetric HG and LG beams are, respectively, shown to present the finite superposition of the generalized HG and LG beams. We also derive an explicit relationship for the complex amplitude of a generalized vortex HG beam, which is built as the finite superposition of generalized HG beams with phase shifts. Newly introduced asymmetric HG and LG beams show promise for the study of the propagation of beams carrying an orbital angular momentum through the turbulent atmosphere. One may reasonably believe that the asymmetric laser beams are more stable against turbulence when compared with the radially symmetric ones.

Nano-shaping of chiral photons

Abstract Localized surface plasmon polaritons can confine the optical field to a single-nanometer-scale area, strongly enhancing the interaction between photons and molecules. Theoretically, the ultimate enhancement might be achieved by reducing the “photon size” to the molecular extinction cross-section. In addition, desired control of electronic transitions in molecules can be realized if the “photon shape” can be manipulated on a single-nanometer scale. By matching the photon shape with that of the molecular electron wavefunction, optically forbidden transitions can be induced efficiently and selectively, enabling various unconventional photoreactions. Here, we demonstrate the possibility of forming single-nanometer-scale, highly intense fields of optical vortices using designed plasmonic nanostructures. The orbital and spin angular momenta provided by a Laguerre–Gaussian beam are selectively transferred to the localized plasmons of a metal multimer structure and then confined into a nanogap. This plasmonic nano-vortex field is expected to fit the molecular electron orbital shape and spin with the corresponding angular momenta.