Standard Laguerre-Gaussian Beams Research Articles

Comparative Study of Spiral Spectrum of Elegant and Standard Laguerre–Gaussian Beams in Atmospheric Turbulence

We derive the analytical expression of the probability density of orbital angular momentum modes for elegant and standard Laguerre–Gaussian beams in turbulence. The results show that we can increase the initial topological charge of the beams to reduce the detrimental mode crosstalk induced by the turbulence. We also discuss the influence of the beam parameters on the probability of signal and the variances of crosstalk probability. The results obtained show that the beams with smaller beam width and longer wavelength have higher detection probabilities of signal and are less affected by turbulence. Comparing with the results of elegant and standard Laguerre–Gaussian beams, we find that elegant Laguerre–Gaussian beams display stronger turbulence resistance. Our results will be useful in free-space optical communications.

Performance analysis of the OAM based optical wireless communication systems with partially coherent elegant Laguerre–Gaussian beams in oceanic turbulence

The transmission model of partially coherent elegant Laguerre–Gaussian (ELG) beams in oceanic turbulence is established by employing the spatial power spectrum of the refractive index of sea-water and the optics approximation. The mathematical expressions of mode probability, energy content, and orbital angular momentum (OAM) state detection probability for partially coherent ELG beams are obtained. The influences of beam and turbulence parameters on the propagation properties of light beam are illustrated in detail with numerical simulations. Results indicate that partially coherent ELG beams with smaller azimuthal mode, smaller OAM state difference, longer blue–green incident wavelength, and appropriate beam waist are less affected by turbulent ocean. Moreover, the evolution characteristics of laser beam may be able to keep a better quality under the condition of lower rate of dissipation of mean-square temperature, higher rate of dissipation of turbulent kinetic energy per unit mass of fluid, and smaller ratio of temperature to salinity for maritime environment. In addition, the partially coherent ELG beams exhibit more robust resistance to turbulence than the partially coherent standard Laguerre–Gaussian beams. These results are expected to be potential helpful in understanding the optical transmission process in turbulent media and designing the optical vortex communication systems.

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 factors of standard and elegant Laguerre Gaussian beams in non-Kolmogorov turbulence

Analytical formulae are derived for the propagation factors (M2-factors) of standard Laguerre Gaussian (SLG) beam and elegant Laguerre Gaussian (ELG) beam in non-Kolmogorov turbulence based on the extended Huygens-Fresnel principle and second order moments of the Wigner distribution function. The M2-factors of SLG beam and ELG beam in non-Kolmogorov turbulence have been discussed numerically and comparatively. It is shown that the relative M2-factors of ELG beam are more affected by the turbulence and keep the better beam quality in comparison with that of SLG beam. Furthermore, the normalized M2-factors of SLG beam and ELG beam with higher orders, longer wavelength, larger waist width, larger inner scale of turbulence and the generalized exponent parameter, smaller outer scale of turbulence and smaller the generalized structure parameter are less affected by the non-Kolmogorov turbulence.

Comparative studies of properties of standard and elegant Laguerre–Gaussian beams

Abstract The properties of standard Laguerre–Gaussian beam (sLGB) and elegant Laguerre–Gaussian beam (eLGB) through the misaligned complex hard edge apertures (MCHEAs) are investigated. Analytical formulae for the far field distributions of sLGBs and eLGBs through the different hard edge apertures are derived based on the generalized Huygens–Fresnel diffraction integral equation. The propagation properties and beam qualities of sLGBs and eLGBs are studied comparatively. It is shown that the divergence angle of sLGBs with the low order modes is less than that of eLGBs. However, the energy distributions of eLGBs with the high order modes after through the multiple hard edged apertures are more convergent in comparison with sLGBs, and eLGBs have the better beam quality than sLGBs. The study results are useful for the propagations and applications of sLGBs and eLGBs through the complex optical systems.

Average intensity and spectral shifts of a partially coherent standard or elegant Laguerre-Gaussian beam beyond paraxial approximation

With the help of the Rayleigh-Sommerfeld diffraction integral, an analytical formula for the spectral density of a nonparaxial polychromatic partially coherent (NPPC) standard or elegant Laguerre-Gaussian (LG) beam propagating through free space is derived. The evolution properties of the intensity distribution of a NPPC standard or elegant LG beam are studied numerically. It is found that the behavior of the intensity distribution of the NPPC standard or elegant LG beam is determined by the initial beam parameters (i.e., beam waist size, spatial coherence width and beam orders). Furthermore, we also study the influence of the initial beam parameters on the spectral change of a NPPC standard or elegant LG beam upon propagation in free space. It is shown that the on-axis spectral shift of a NPPC standard LG beam is almost the same with that of a NPPC elegant LG beam when the initial beam parameters of two type beams are identical. However, the difference between the off-axis spectral shift between a NPPC standard LG beam and a NPPC elegant LG beam is enhanced with the decrease of beam waist size or with the increase of spatial coherence width and beam mode orders.

Elegant Laguerre–Gaussian beam in a turbulent atmosphere

Paraxial propagation of an elegant Laguerre–Gaussian beam (ELGB) in a turbulent atmosphere is investigated in detail. Analytical formulae for the average intensity and effective beam size of an ELGB in a turbulent atmosphere are derived based on the extended Huygens–Fresnel integral. The average intensity and spreading properties of an ELGB in a turbulent atmosphere are studied numerically and compared with those of a standard Laguerre–Gaussian beam (SLGB). Our results indicate that the propagation properties of an ELGB in a turbulent atmosphere are much different from its properties in free space, and are closely related to its beam parameters and the structure constant of the atmospheric turbulence. The ELGB with higher mode orders is less affected by the turbulence. The SLGB spreads more rapidly than the ELGB in a turbulent atmosphere under the same conditions. Our results will be useful in long-distance free-space optical communications. ©2010 Elsevier Science B.V. All rights reserved.

Partially coherent standard and elegant Laguerre-Gaussian beams of all orders

Partially coherent standard and elegant Laguerre-Gaussian (LG) beams of all orders are introduced as a natural extension of coherent standard and elegant LG beams to the stochastic domain. By expanding the LG modes into a finite sum of Hermite-Gaussian modes, the analytical formulae are obtained for the cross-spectral densities of partially coherent standard and elegant LG beams in the source plane and after passing through paraxial ABCD optical system, based on the generalized Collins integral formula. A comparative study of the propagation properties of the partially coherent standard and elegant LG beams in free space is carried out via a set of numerical examples. Our results indicate that the intensity and spreading properties of partially coherent standard and elegant LG beams are closely related to their initial coherence states, and are very different from the corresponding results for the coherent standard and elegant LG beams. In particular, an elegant LG beam spreads slower than a standard LG beam, while this advantage disappears when their initial coherences are very small. Our results may find applications in connection with laser beam shaping, singular optics and astrophysical measurements of angular momentum of radiation.