Gaussian Beams In Turbulent Atmosphere Research Articles

Propagation factors of Hermite–Gaussian beams in turbulent atmosphere

Based on the extended Huygens–Fresnel integral and the second-order moments of the Wigner distribution function, an analytical formulae for the propagation factors ( M 2-factors) of coherent and partially coherent one-dimensional Hermite–Gaussian beams in a turbulent atmosphere are derived. Evolution properties of the M 2-factor of the Hermite–Gaussian beam in a turbulent atmosphere are studied numerically in detail. Our results show that the M 2-factor of the Hermite–Gaussian beam increases upon propagation in a turbulent atmosphere. The M 2-factor of the Hermite–Gaussian beam with larger beam order (or lower coherence) increases slower that of the Hermite–Gaussian beam with smaller beam order (or higher coherence) in a turbulent atmosphere, which means that the Hermite–Gaussian beam with a larger beam order and lower coherence is less affected by a turbulent atmosphere. Our results will be useful in long-distance free-space optical communications.

Relay propagation of partially coherent flattened Gaussian beam in turbulent atmosphere

Relay propagation of partially coherent flattened Gaussian–Schell beam in turbulent atmosphere has been studied. The analytical expresses of average intensity distribution at target are derived. The effects of spatial correlation length of initial and relay beam on the average intensity are analyzed in details. Study shows that the effects of the variation of spatial correlation length of relay beam are much larger than that of initial beam. The effects of spatial correlation length on relay propagation become smaller and smaller with the increase of structure constant. When the spatial correlation length is large and turbulence is strong, the effects of the variation of spatial correlation length on relay propagation are so small that can be neglected.

Propagation analysis of flattened circular Gaussian beams with a misaligned circular aperture in turbulent atmosphere

The propagation properties of flattened Gaussian beam with a misaligned circular aperture in turbulent atmosphere have been studied by using the extended Huygens–Fresnel formula. From the study and numerical calculation, the effects of aperture parameters on the propagation properties of flattened Gaussian beams in turbulent atmosphere have been illuminated. The results show that angle misalignments and lateral displacements of aperture create unsymmetrical average intensity distribution at any cross section. The intensity distributions are much more sensitive to the lateral displacement than to the angle misalignments. And the propagation properties of different flattened Gaussian beams in turbulent atmosphere are also compared.

Average intensity and spreading of an elegant Hermite–Gaussian beam in turbulent atmosphere

The propagation of an elegant Hermite-Gaussian beam (EHGB) in turbulent atmosphere is investigated. Analytical propagation formulae for the average intensity and effective beam size of an EHGB in turbulent atmosphere are derived based on the extended Huygens-Fresnel integral. The corresponding results of a standard Hermite-Gaussian beam (SHGB) in turbulent atmosphere are also derived for the convenience of comparison. The intensity and spreading properties of EHGBs and SHGBs in turbulent atmosphere are studied numerically and comparatively. It is found that the propagation properties of EHGBs and SHGBs are much different from their properties in free space, and the EHGB and SHGB with higher orders are less affected by the turbulence. What's more, the SHGB spreads more rapidly than the EHGB in turbulent atmosphere under the same conditions. Our results will be useful in long-distance free-space optical communications.

A comparative study of the beam-width spreading and angular spread in atmospheric turbulence

Taking the HermitecoshGaussian（HChG） beam as a typical example, the beamwidth spreading and angular spread of HChG beams propagating through atmospheric turbulence are throughly studied. The relative beamwidth and relative angular spread instead of the beamwidth and angular spread have been used to study the sensitivity of a beam to the effect of turbulence. It is found that the smaller the refraction index structure constant C2n is, the less the beamwidth spreading and angular spread of HChG beams are. The angular spread of HChG beams with larger beam orders m, n, smaller parameter Ω0 and smaller waist width w0 is less affected by turbulence. This conclusion also holds true for the beamwidth spreading of HChG beams for the case of the propagation distance is sufficiently long. The variation of the relative beamwidth of HChG beams versus Ω0 and w0 is analyzed if the propagation distance being not so long. The results are illustrated by numerical examples and the validity of the results is explained physically. The spreading of HermiteGaussian, coshGaussian and Gaussian beams in atmospheric turbulence can be treated as special cases of HChG beams.

Propagation aspects of Mathieu–Gaussian beams in turbulence

Based on our recent source plane formulation, the propagation characteristics of Mathieu–Gaussian beams in turbulent atmosphere are investigated. In this connection, the average receiver plane intensity expression is deduced using the Huygens–Fresnel integral. Our results offered in the form of graphical illustrations reveal that, for some settings of source and propagation parameters, the center of the source beam is evacuated after propagation, while the initially smaller side lobes begin to grow. In a parallel development, the angular distribution of the beam also changes. At small Gaussian source sizes and transverse components of the wave vector, the source beam profile remains almost invariant throughout the propagation. The larger refractive index structure constant values cause the final Gaussian beam profile to be attained at earlier propagation distances. Smaller refractive index structure constants, on the other hand, do not change the beam profile substantially from that of free space.

Propagation of Four-Petal Gaussian Beams in Turbulent Atmosphere

An analytical expression for the average intensity of four-petal Gaussian beams in turbulent atmosphere is derived. Studies show that in turbulent atmosphere, the contour lines of four-petal Gaussian beams with lower order N evolve into a number of petals with the increase in propagation distance, the contour lines with higher order N can reserve four-petal distribution at longer propagation distance than that with lower order N. These properties are similar to those in free space. However, with further increases of the propagation distance, the contours lines in turbulent atmosphere are different from those in free space.

Propagation analysis of flattened circular Gaussian beams with a circular aperture in turbulent atmosphere

The propagation properties of flattened Gaussian beam with aperture in turbulent atmosphere have been studied by using the extended Huygens–Fresnel principle. From the study and numerical calculation, the effects of aperture on the propagation of flattened Gaussian beams in turbulent atmosphere have been illuminated. It shows that when the value of the truncation parameter δ is bigger, for example δ ⩾ 2 , the effects of aperture on the propagation properties are too small to be neglected. But when the truncation parameter δ is smaller, for example δ < 2 , the effects of aperture are complex. The peak value of the average intensity descends more rapidly and the beam spot spreads quicker with aperture than that without aperture when the propagation distance increases. Meanwhile, with the propagation distance increasing, the average intensity profiles of flattened Gaussian beams gradually convert into Gaussian average intensity profiles. In addition, some limiting cases are also discussed. It agrees with the existing results.

Propagation characteristics of higher-order annular Gaussian beams in atmospheric turbulence

The propagation characteristics of higher-order annular Gaussian (HOAG) beams in turbulence are investigated. From a HOAG source plane excitation, the average intensity of the receiver plane is developed analytically. This formulation is verified against the previously derived HOAG beam solution in free space. The graphical outputs indicate that, upon traveling in turbulent atmosphere, the HOAG beam will undergo different stages of evolution. At intermediate propagation distances, it will attempt to concentrate the energy near the origin. In this process, the appearance of the single higher-order primary beam will be encountered. Eventually HOAG originated beam will become a pure Gaussian beam after propagating an excessive distance in the turbulent medium.

Propagation properties of one-dimensional off-axis Gaussian beams through the turbulent atmosphere

The propagation properties of one-dimensional off-axis Gaussian beams through the turbulent atmosphere are studied in detail. The propagation equation of intensity is derived. It is shown that one-dimensional off-axis Gaussian beams in turbulent atmosphere undergo three stages of evolution with increasing propagation distance z, i.e., their saw-tooth beam profile is similar to the initial one in the near field, then becomes a flat-topped profile with increasing z, and at last turns into Gaussian-like profile in the far field. The turbulence accelerates the evolution of the stages which one-dimensional off-axis Gaussian beams undergo. Furthermore, the normalized intensity distributions of one-dimensional off-axis Gaussian beams with different beam numbers become close to each other due to turbulence. In addition, one-dimensional off-axis Gaussian beams with higher beam numbers are less sensitive to the effects of turbulence than those with lower beam numbers, and one-dimensional off-axis Gaussian beams are less sensitive to the effects of turbulence than Gaussian beams.

Beam wander in a turbulent medium: An application of Ehrenfest’s theorem

Beam wander of a finite optical beam propagating in a turbulent medium is investigated theoretically. Using the optical analog of Ehrenfest’s theorem, it is shown that the centroid of a finite beam propagates as a paraxial ray in a certain effective refractive index that depends on the irradiance profile of the beam. Ray statistics in the effective refractive index are studied for arbitrary irradiance profiles and new results are obtained for the variance of spot displacement and beam angle of arrival. These results are then applied to the particular cases of focused and collimated gaussian beams in atmospheric turbulence with a modified Von Karman power spectrum to yield the functional dependence of spot dancing and angle-of-arrival statistics on the inner and outer scales of turbulence and on the Fresnel number for focused gaussian beams.