Coherent Laguerre Gaussian Beams Research Articles

Propagation properties of a partially coherent Laguerre–Gaussian beam with multiple off-axis vortex phases

In this paper, a new theoretical model of a partially coherent Laguerre–Gaussian (LG) beam carrying multiple off-axis vortex phases was established. The evolution properties of the focused intensity of the beam after passing through a thin lens were theoretically studied, and then the modulation effect of multiple off-axis vortex phases on the beam with multiring structured intensity was explored. The results indicate that the multiple off-axis vortex phases can reconstruct the multiring structured intensity within the LG beam, thus generating a structured intensity with multilobe and multiring patterns. What is more, the intensity distribution of the lobes between two adjacent rings is complementary, and its number is related to the number and topological charge of off-axis vortex phases. However, with a decrease in the coherence, such a multilobe and multiring structured intensity distribution disappears, gradually evolves into a polygonal flat-topped distribution, and finally degenerates into a quasi-Gaussian distribution. This work demonstrates the effective regulation of multiple off-axis vortex phases on a beam with a multiring structured intensity and indicates that regulating the multiple off-axis vortices provides an additional degree of freedom for optical field modulation, which will have potential applications in the fields of optical micromanipulation and optical information storage.

Topological Charge of Multi-Color Optical Vortices

The topological charge of an optical vortex is a quantity rather stable against phase distortions, for example, turbulence. This makes the topological charge attractive for optical communications, but for many structured beams it is unknown. Here, we derive the topological charge (TC) of a coaxial superposition of spatially coherent Laguerre–Gaussian beams with different colors, each beam with its own wavelength and its own TC. It turns out that the TC of such a superposition equals the TC of the LG beam with a longer wavelength, regardless of the weight coefficient of this beam in the superposition and regardless of its TC. It is interesting that the instantaneous TC of such a superposition is conserved on propagation, whereas the time-averaged intensity distribution of the colored optical vortex changes its gamut; if, in the near field, the colors of the light rings arrange along the radius according to their TCs in the superposition from lower to greater, then, on space propagation, the colors of the light rings in the cross-section are arranged in reverse order from the greater TC to the lower TC. We also demonstrate that, by choosing appropriate wavelengths (blue, green, and red) in a three-color superposition of single-ringed LG beams, it is possible to generate, at some propagation distance, a time-averaged light ring of the white color. If all the beams in a three-color superposition of single-ringed LG beams have the same TC, then there is a single ring of nearly white light in the initial plane. Then, on propagation in space, light rings of different colors acquire different radii: a smaller ring radius for a shorter wavelength.

Designing laser beams carrying OAM for a high-performance underwater communication system.

We present a design methodology for creating a distinct laser beam set suitable for detection by using only the recorded intensity pattern. We consider four coherent Laguerre-Gaussian beams carrying orbital angular momentum (OAM) to form the basis for optical communication. The complex electric fields of the beams are superimposed to create 16 dissimilar intensity patterns. The presented beam set design method considers the beam generation hardware limitations and aims to minimize the correlation among the messages and maximize their intensity differences. After propagating the 16 messages through a water channel, we measured high correlation, intensity similarity, and R-squared values for the identical messages and low values for the different ones. Distinct clustering between the measurements for the matching messages and the rest allows us to set a threshold in the gap among the groupings and successfully classify the received images.

Propagation properties of OAM modes carried by partially coherent LG beams in turbulent ocean based on an oceanic power-law spectrum

On the basis of the power-law spectrum of the oceanic refractivity fluctuations recently proposed by Yi (2018), we study the propagation properties of partially coherent Laguerre Gaussian (LG) beams under weak turbulence conditions. Specifically, we analyze the mode probability density and the mode detection probability of the orbital angular momentum (OAM) modes carried by the LG beams. As compared with the previous results on Nikishov’s spectrum, our results present a lower mode detection probability, which corresponds to the stronger oceanic turbulence predicted by Yi’s spectrum.

Propagation of partially coherent Laguerre Gaussian beams through inhomogeneous turbulent atmosphere.

Analytical formulas for the root-mean-square (rms) spatial width, the rms angular width, and the M2-factor of partially coherent standard Laguerre Gaussian beams (PC-SLGBs) and partially coherent elegant Laguerre Gaussian beams (PC-ELGBs) in inhomogeneous turbulent atmosphere have been derived. The propagation properties of PC-SLGBs and PC-ELGBs in inhomogeneous atmospheric turbulence are studied numerically and comparatively. It can be found that the propagation of laser beams in inhomogeneous turbulence is different from that in homogeneous turbulence. It is also shown that relative rms spatial widths and M2-factors of PC-ELGBs are more affected by inhomogeneous turbulence than those of PC-SLGBs. Moreover, the relative rms spatial widths and M2-factors of PC-SLGBs and PC-ELGBs in inhomogeneous turbulent atmosphere are closely related with waist widths, coherence widths, zenith angles, inner scales, and beam orders. Furthermore, the saturation propagation distance of the relative M2-factor and rms angular width with zenith angles of π/6 are 20 km and 0.5 km, respectively.

Propagation of an optical vortex carried by a partially coherent Laguerre-Gaussian beam in turbulent ocean.

The analytical formulas for the orbital angular momentum (OAM) mode probability density, signal OAM mode detection probability, and spiral spectrum of partially coherent Laguerre-Gaussian (LG) beams with optical vortices propagation in weak horizontal oceanic turbulent channels were developed, based on the Rytov approximation theory. The effect of oceanic turbulence and beam source parameters on the propagation behavior of the optical vortices carried by partially coherent LG beams was investigated in detail. Our results indicated that optical turbulence in an ocean environment produced a much stronger effect on the optical vortex than that in an atmosphere environment; the effective range of the signal OAM mode of LG beams with a smaller ratio of the mode crosstalk was limited to only several tens of meters in turbulent ocean. The existence of oceanic turbulence evidently induced OAM mode crosstalk and spiral spectrum spread. The effects of oceanic turbulence on the OAM mode detection probability increased with the increase of radial and azimuthal mode orders, oceanic turbulent equivalent temperature structure parameter, and temperature-salinity balance parameter. The spatial partial coherence of the beam source would enhance the effect of turbulent aberrations on the signal OAM mode detection probability, and fully coherent vortex beams provided better performance than partially coherent ones. Increasing wavelength of the vortex beams would help improve the performance of this quantum optical communication system. These results might be of interest for the potential application of optical vortices in practical underwater quantum optical communication among divers, submarines, and sensors in the ocean environment.

Focal shift of a focused partially coherent Laguerre-Gaussian beam of all orders

We explore the focusing properties of a partially coherent Laguerre–Gaussian (LG) beam of all orders, particularly the focal shift (i.e. the shift of the actual focal plane away from the geometrical focal plane). We derive the analytical expressions for the average intensity and the effective beam width of a focused partially coherent LG beam, and we adopt the minimum effective beam width instead of the conventional maximum on-axis intensity to determine the actual focal plane. It is found that the focused beam shape, minimum effective beam width and the focal shift of a focused partially coherent LG beam are determined by its initial coherence width, radial mode order and azimuthal mode order (i.e. topological charge) together. Our results may be useful for optical trapping and micro-fabrication, where precise focal position and prescribed beam shape are required.

Propagation based on second-order moments for partially coherent Laguerre–Gaussian beams through atmospheric turbulence

The Wigner distribution function (WDF) has been used to study the propagation properties of partially coherent Laguerre Gaussian (PCLG) beams through atmospheric turbulence. Based on the extended Huygens–Fresnel principle, an analytical formula of the propagation matrixes in terms of the second-order moments of the WDF for PCLG Beams in the receiving plane is derived. And then the analytical formulae for the curvature radii of PCLG Beams propagating in turbulence are given by the second-order moments of the WDF. The numerical results indicate that the curvature radius of PCLG Beams changes more rapidly in turbulence than that in the free space. The influence of the transverse coherence width and the beam waist width on the curvature radius of PCLG Beams is obvious, while the laser wavelength and the inner scale of turbulence have a slight effect. The study results may be useful for remote sensing and free space optical communications.

Degree of paraxiality of cylindrical vector partially coherent Laguerre–Gaussian beams

We derive the analytical expression for the degree of paraxiality of cylindrical vector (CV) partially coherent Laguerre–Gaussian (LG) beams based on the definition of the degree of paraxiality. Numerical results show that the degree of paraxiality of the CV partially coherent LG beams does not always increase with the increase of the initial beam waist, but oscillates when the initial beam waist and wavelength are comparable. The degree of paraxiality also depends on the beam orders and the initial coherence length of the CV partially coherent LG beams. Our results are useful for determining whether the CV partially coherent LG beams are paraxial or nonparaxial. It may be useful in some applications such as atomic trapping, tight focusing and micro-lithography.

Quantum polarization fluctuations of a partially coherent Laguerre–Gaussian beam in a slant turbulent channel

The propagation of a partially coherent Laguerre–Gaussian beam in a slant turbulent channel is studied. The analytical formula for the quantum degree of polarization of a partially coherent Laguerre–Gaussian beam is derived based on the quantum Stokes operators and the extended Huygens–Fresnel principle. It is shown that the zenith angle slightly affects the polarization degree of partially coherent Laguerre–Gaussian beams, and the changes of polarization degree are affected by the detection photon-number. Furthermore, the numerical simulations show that a partially coherent Laguerre–Gaussian beam with higher photon-number level, lower beam orders, longer wavelength is less affected by the turbulence. These results indicate that one can choose the partially coherent Laguerre–Gaussian beam with lower beam orders, longer wavelength, higher detection photon-number to improve the performance of a polarization-encoded free-space quantum communication system.

Intensity and polarization properties of the partially coherent Laguerre–Gaussian vector beams with vortices propagating through turbulent atmosphere

Abstract By using the extended Huygens–Fresnel principle, the analytical expressions for the cross-spectral density matrix of the partially coherent Laguerre–Gaussian vector beams with vortices propagating through atmospheric turbulence are derived theoretically in detail, and used to study the intensity and polarization properties of partially coherent Laguerre–Gaussian beams in atmospheric turbulence. It is found that the variations of the intensity of the completely polarized part and the completely unpolarized part are closely related with the strength of atmospheric turbulence, the topological charge and the beam width in the source plane. The spectral degree of polarization of the partially coherent Laguerre–Gaussian vector beams with vortices tends to a certain value that is different from the source plane after a sufficiently long propagation distance in turbulent atmosphere. Furthermore, this value is dependent of the strength of turbulent atmosphere, the topological charge and the beam width in the source plane. The polarization property of the partially coherent Laguerre–Gaussian vector beams with vortices can be modulated by modulating the topological charge and the beam width in the source plane.

Experimental generation of a partially coherent Laguerre–Gaussian beam

We report experimental generation of a partially coherent Laguerre–Gaussian beam with mode orders 0 and l (i.e., LG0l beam) using a rotating ground-glass plate and a spatial light modulator. Focusing properties of the generated beam are studied both theoretically and experimentally. It is found that the focused intensity of the LG0l beam is shaped through varying the initial spatial coherence, and our experimental results agree well with the theoretical predictions. Our results will be useful in particle trapping and free-space optical communications.

Evolution properties of the complex degree of coherence of a partially coherent Laguerre–Gaussian beam in turbulent atmosphere

Evolution properties of the complex degree of coherence of a partially coherent Laguerre–Gaussian beam (LGB) on propagation in free space and turbulent atmosphere are studied comparatively with the help of the general propagation formula for such beam. It is found that the behavior of the complex degree of coherence of a partially coherent LGB on propagation in turbulent atmosphere is much different from that in free space and is closely related to the initial beam parameters and the structure constant of the turbulent atmosphere. The distribution of the modulus of the complex degree of coherence of the partially coherent LGB finally becomes of Gaussian distribution at long propagation distance in turbulent atmosphere, and it becomes of Gaussian distribution more slowly with the increase of the mode orders, beam width and wavelength. Our results will be useful in long-distance free-space optical communications.

Coherence vortices of partially coherent beams in the far field

Based on the propagation law of cross-spectral density function, studied in this paper are the coherence vortices of partially coherent, quasi-monochromatic singular beams with Gaussian envelope and Schell-model correlator in the far field, where our main attention is paid to the evolution of far-field coherence vortices into intensity vortices of fully coherent beams. The results show that, although there are usually no zeros of intensity in partially coherent beams with Gaussian envelope and Schell-model correlator, zeros of spectral degree of coherence exist. The coherence vortices of spectral degree of coherence depend on the relative coherence length, mode index and positions of pairs of points. If a point and mode index are kept fixed, the position of coherence vortices changes with the increase of the relative coherence length. For the low coherent case there is a circular phase dislocation. In the coherent limit coherence vortices become intensity vortices of fully coherent Laguerre–Gaussian beams.