Sinusoidal Gaussian Beams Research Articles

Interaction of astigmatic hyperbolic sinusoidal Gaussian beams in strongly nonlocal nonlinear media

In this paper, we obtain analytical expressions for the co-propagation of two and four interacting astigmatic hyperbolic sinusoidal Gaussian beams in strongly nonlocal nonlinear media by using nonlocal nonlinear Schrödinger equation. Through numerical simulations, we characterize their interaction properties and differences between the interaction of two beams and four beams, primarily focusing on the transverse intensity distribution of beam clusters and the evolution of intensity along the axis. We find that in strongly nonlocal nonlinear media, the evolution of multiple interacting astigmatic hyperbolic sinusoidal Gaussian beams is periodic. Regardless of whether the beams are in-phase or out-of-phase, the interaction among multiple beams is always attractive. The difference lies in the fact that in the case of complete in-phase beams, there are two small intensity peaks at the center of the interaction region, whereas this is not the case for other scenarios. Furthermore, among the four beams, the evolution of the in-phase interaction between vertically adjacent beams is exactly opposite to the out-of-phase interaction between horizontally adjacent beams. This research provides valuable insights for interaction of multiple beams and optical wireless communication.

Minimization of the scintillation index of sinusoidal Gaussian beams in weak turbulence for aerial vehicle-satellite laser communications.

Minimization of the on-axis scintillation index of sinusoidal Gaussian beams is investigated by using the modified Rytov method in weak atmospheric turbulence for uplink/downlink of aerial vehicle-satellite laser communications. Among the focused cosh-Gaussian (cosh-G), cos-Gaussian (cos-G), annular, and Gaussian beams, a suitable displacement parameter for a cosh-G beam is determined that will minimize the scintillation index in uplink and downlink configurations. Then, for both uplink and downlink, the variations of the scintillation index against the propagation distance, source size, and zenith angle are examined and compared among themselves to show the optimum beam that possesses the minimum scintillation index. Sinusoidal Gaussian beams that are focused at the receiver and obtained by employing the appropriate displacement parameter, which we name the optimum beams, are recommended to obtain smaller intensity fluctuations in atmospheric wireless optical communication systems operating in vertical links in weak turbulence.

Propagation of hyperbolic sinusoidal Gaussian beams in uniaxial crystals orthogonal to the optical axis

In this paper, hyperbolic sinusoidal Gaussian(HSG) beam propagates in uniaxial crystal orthogonal to the propagation axis. Received field expression is evaluated analytically based upon Huygens-Fresnel integration. Numerical results are plotted in order to analyze the effect of variations in source beam parameters, crystal refractive index features, and propagation distance. We investigate that beam size and peak intensity of received beam can be managed by adjusting crystal structure. We anticipate that our results will be useful for optical tracking applications.

Propagation characteristics of astigmatic hyperbolic sinusoidal Gaussian beams in nonlocal nonlinear media

In this paper, the propagation characteristics of astigmatic hyperbolic sinusoidal Gaussian beams (AHSGB) in strongly nonlocal nonlinear media are discussed. The propagation expression of the AHSGB is theoretically derived and the evolution characteristics of the light intensity distribution, the beam width, and the phase curvature are analyzed by using mathematical and numerical methods. We find that the parameters of the hyperbolic sinusoidal function, the initial power and the initial position are important factors that influence the propagation behavior of the beam.

Scintillation and BER for optimum sinusoidal Gaussian beams in weak non-Kolmogorov turbulence

The scintillation index and the average bit error rate (BER) are evaluated for the optimum sinusoidal Gaussian beams in weak non-Kolmogorov turbulence. The beam parameters that minimize the scintillation index and the average BER are stated and such beams are denoted as the optimum beams. For the collimated Gaussian, cos- and cosh-Gaussian beams, the scintillations increase as the power law exponent, α increases. Cos- and cosh-Gaussian beams that have larger absolute displacement parameters are found to exhibit larger scintillations especially at small α. Larger focal length and larger source size of cos-Gaussian beams induce reduction in the scintillations. When the propagation distance is large, the power law exponent is small and the source size is large, the scintillations of the optimum beams tend to decrease. Small power law exponent and large source size reduce the average BER. The optimum beam is shown to exhibit the smallest average BER for any α.

Evolution of Intensity Distribution of Partially Coherent Sinusoidal-Gaussian Beams through Slant Atmospheric Turbulence

Based on the extended Huygens-Fresnel principle, the analytical expressions for the intensity of partially coherent sinusoidal-Gaussian beams with Schell-model correlator in atmospheric turbulence along a slant path are derived, and used to study the evolution of intensity distribution of partially coherent sinusoidal-Gaussian beams, including partially coherent sin-Gaussian (SiG), cos-Gaussian (CoG), sinh-Gaussian (ShG), cosh-Gaussian (ChG) beams. It is shown that the different intensity distribution at the source plane of the four beams evolve to the same Gaussian distribution in atmospheric turbulence along a slant path. The spreading of the partially coherent sinusoidal-Gaussian beams along a horizontal path is larger than that along a slant path in the long atmospheric propagation, and the slant path is more beneficial to the beam propagation through atmospheric turbulence in comparison with the horizontal propagation. The validity of our results is interpreted physically. Results in this paper may provide potential applications in free-space optical communications.

Sinusoidal Gaussian beam field correlations

Field correlations of sinusoidal Gaussian beams are formulated in turbulence, and specifically cos Gaussian (cG) and cosh Gaussian (chG) beam field correlations are evaluated versus the diagonal length at the receiver plane. The effects of the displacement parameters, the coordinates of the first receiver point and the source sizes on the field correlations of monochromatic light sources having cG and chG field distributions are investigated when such beams traverse turbulent media. Such parameters affect spatial heterodyne measurement. Field correlations found at the receiver plane reflect the combined variations of diffraction patterns and turbulence effects. To differentiate the diffraction patterns and the turbulence effects, field correlations of cG and chG beams in turbulence and in the absence of turbulence are compared. For cG beams, the oscillatory behaviour of the field correlations versus the diagonal length at the receiver plane in the absence of turbulence becomes smoother in the presence of turbulence. The received fields of cG and chG beams become decorrelated at shorter diagonal distances in turbulence.

Minimization effects on scintillations of sinusoidal Gaussian beams in strong turbulence

Minimization effects on the on-axis scintillation index of cos Gaussian (cG) and coshGaussian (chG) beams are studied in strong turbulence. In our formulation, the unifiedsolution of the Rytov method, which imposes spatial filtering to extend the solution to thestrong turbulence regime, is applied. Our solution correctly reduces to the weak turbulencesinusoidal beam scintillations and the strong turbulence Gaussian beam scintillations. Theconditions to minimize the scintillations are found to be focused chG beams. Small scalescintillations mainly determine the overall scintillations of cG and chG beams instrong turbulence. In strong turbulence, increase in the source size decreases thescintillations of collimated cG beams but does not change the scintillations of focused cGbeams. Collimated cG beams having larger displacement parameters and large focallengths show smaller scintillations in the strong regime. Change in the displacementparameters for collimated and focused chG beams and the focal length of focusedchG beams do not considerably vary their scintillations in strong turbulence.

An analysis on radius of curvature aspects of hyperbolic and sinusoidal Gaussian beams

The effective radius of curvature of hyperbolic and sinusoidal Gaussian beams in free space and turbulent atmosphere is studied analytically and numerically. It is shown that the radius of curvature rises with growing source size, and changes slowly with wavelength. In general, given the same source and propagation settings, the beams can be listed in descending order of radius of curvature magnitudes as sinh Gaussian, cosh Gaussian, sine Gaussian, pure Gaussian and cos Gaussian beams. However, the radius of curvature and the difference of the radius of curvature between the different beams reduce with growing strength of turbulence because the beam’s spatial phase distribution is destroyed by turbulence.

Beam propagation factor of decentred gaussian and cosine—gaussian beams

On the basis of the second moment method, the beam propagation factor (M 2−factor) of decentred Gaussian beam has been derived, and analysed physically. Then, the result is extended to novel sinusoidal-Gaussian beams, one type of which is the cosine—Gaussian beam, which can be regarded as a superposition of two decentred Gaussian beams.

Beam-propagation factor and mode-coherence coefficients of hyperbolic-cosine–Gaussian beams

Analytical expressions for the M(2) factor and the mode-coherence coefficients of hyperbolic-cosine- (cosh-) Gaussian beams have been derived, and a simple method of producing cosh-Gaussian beams in an experiment, superposition of two decentered Gaussian beams, has been proposed. Our results will be useful for studying more-general Hermite-sinusoidal-Gaussian beams.

Hermite–sinusoidal-Gaussian beams in complex optical systems

Sinusoidal-Gaussian beams have recently been obtained as exact solutions of the paraxial wave equation for propagation in complex optical systems. Another useful set of beam solutions for Cartesian coordinate systems is based on Hermite–Gaussian functions. A generalization of these solution sets is developed here. The new solutions are referred to as Hermite–sinusoidal-Gaussian beams, because they are in the form of a product of Hermite-polynomial functions of either complex or real argument, sinusoidal functions of complex argument, and Gaussian functions of complex argument. These beams are valid for propagation through systems that can be represented in terms of complex beam matrices, and the previous beam solution sets are special cases of these more general results. Propagation characteristics and applications of these beams are discussed, including their use as a basis set for propagation of arbitrary electromagnetic beams.

Sinusoidal-Gaussian beams in complex optical systems

Sinusoidal-Gaussian beam solutions are derived for the propagation of electromagnetic waves in free space and in media having at most quadratic transverse variations of the index of refraction and the gain or loss. The resulting expressions are also valid for propagation through other real and complex lens elements and systems that can be represented in terms of complex beam matrices. The solutions are in the form of sinusoidal functions of complex argument times a conventional Gaussian beam factor. In the limit of large Gaussian beam size, the sine and cosine factors of the beams are dominant and reduce to the conventional modes of a rectangular waveguide. In the opposite limit the beams reduce to the familiar fundamental Gaussian form. Alternate hyperbolic-sinusoidal-Gaussian beam solutions are also found.