Propagation of a stochastic electromagnetic Gaussian Schell-model beam through an optical system in turbulent atmosphere

A generalized diffraction integral formula for stochastic electromagnetic beams propagating through an optical system in turbulent atmosphere is derived with the help of tensor method. Some analyses are illustrated by a numerical example relating to changes in the average intensity and the degree of polarization of an electromagnetic Gaussian Schell-model beam propagating through a double-lenses system. It is shown that the optical system has strong influence on the propagation properties of the beam. The method used in this paper can be widely applied to the propagation of astigmatic beams through an optical system in turbulent atmosphere.     

Propagation of random electromagnetic beams through axially nonsymmetrical optical systems

When random electromagnetic beams passing through axially nonsymmetrical ABCD optical systems, the analytical formula for the transformation of the elements of 2 × 2 cross-spectral density matrix is obtained with the help of vector integration. We derive analytical expressions of the spectral degree of polarization, the spectral degree of coherence, and the spectral density in any output plane z > 0. Some numerical calculations are illustrated relating to the electromagnetic Gaussian Schell-model beams propagating through such optical systems.     

Polarization Changes of Partially Coherent Electromagnetic Vortex Beams Propagating in Turbulent Atmosphere

We investigate the polarization change of partially coherent electromagnetic vortex beams propagating in turbulent atmosphere. It is shown that the polarization of the beams will experience changes, and the changes of the polarization are dependent on the spatial coherence, topological charges of the beams, and the degree of polarization of the source plane and the atmospheric turbulence. The results obtained may have applications in space optical communication.     

Changes in the coherence of quasi-monochromatic electromagnetic Gaussian Schell-model beams propagating through turbulent atmosphere

Based on the extended Huygens-Fresnel principle, the mutual coherence function of quasi-monochromatic electromagnetic Gaussian Schell-model (EGSM) beams propagating through turbulent atmosphere is derived analytically. By employing the lateral and the longitudinal coherence length of EGSM beams to characterize the spatial and the temporal coherence of the beams, the behavior of changes in the spatial and the temporal coherence of those beams is studied. The results show that with a fixed set of beam parameters and under particular atmospheric turbulence model, the lateral coherence of an EGSM beam reaches its maximum value as the beam propagates a certain distance in the turbulent atmosphere, then it begins degrading and keeps decreasing along with the further distance. However, the longitudinal coherence length of an EGSM beam keeps unchanging in this propagation. Lastly, a qualitative explanation is given to these results.     

Propagation properties of anomalous hollow beams in a turbulent atmosphere

Propagation of circular and elliptical anomalous hollow beams in a turbulent atmosphere is investigated in detail. Based on the extended Huygens–Fresnel integral, analytical formulae for the average irradiance of circular and elliptical anomalous hollow beams propagating in a turbulent atmosphere are derived. The irradiance and spreading properties of circular and elliptical anomalous hollow beams in a turbulent atmosphere and in free space are studied numerically. It is found that circular and elliptical anomalous hollow beams at short propagation distance in turbulent atmosphere have similar propagation properties to those of free space, while at long propagation distance, circular and elliptical anomalous hollow beams eventually become circular Gaussian beams in a turbulent atmosphere, which is much different from their propagation properties in free space. The conversion from an anomalous hollow beam to a circular Gaussian beam becomes quicker and the beam spot spreads more rapidly for a larger structure constant, a shorter wavelength and a smaller waist size of the initial beam.     

Spectral changes of aberrated stochastic electromagnetic flat-topped beams propagating in turbulent atmosphere

In this paper, taking the electromagnetic partially coherent flat-topped (PCFT) beam as an example, we investigate the spectral changes of stochastic electromagnetic beams with astigmatic aberration propagating through a turbulent atmosphere. The analytic expressions for the spectrum of the beams propagating through the turbulent atmosphere are derived. It is shown that the spectral changes of the electromagnetic PCFT beams in the turbulent atmosphere are closely related with the astigmatism aberration, the strength of atmospheric turbulence, the inner scale of turbulence, the correlation of source and the order of flatness of electromagnetic PCFT beams. It is important to note that the spectral changes of the aberrant electromagnetic PCFT beams are insensitive to the atmospheric turbulence. Some possible explanations have also been given for the interesting physical phenomena.     

Generation of thin and hollow beams by the axicon with a large open angle

We propose a method to produce diffraction-free thin and hollow beams. The method is based on Laguerre-Gaussian (LG) beams incident on a large open-angle axicon. We use the vector diffraction integrals and stationary phase method to deduce a simple and analytical formula of the propagating field of the linearly polarized LG beams through an axicon. The numerical results show that the hollow beams of whose diameter is in the order of the wavelength can be obtained by using the axicon with the refractive index n = 2 and the open angle α = 25°. These diffraction-free thin and hollow beams may be very useful to accurately trap and manipulate atoms. However, when the open angle is over large, the conversion efficiency from the LG beam to the diffraction-free hollow beam will decrease obviously.     

Statistical properties of correlated radial stochastic electromagnetic array beams on propagation

A kind of array beam named the correlated radial stochastic electromagnetic array beam that is generated by an electromagnetic Gaussian Schell-model source is introduced by use of tensor method. The analytical expression for the cross-spectral density matrix of this array beam propagating through the turbulent atmosphere and in free space is obtained after performing vector integration. Some typical numerical calculations are illustrated for the changes in the spectral density, spectral degree of polarization, and spectral degree of coherence of the beam on propagation. We find that the atmospheric turbulence can destroy the correlated effect among the beamlets.     

Analytical formula for a decentered elliptical Gaussian beam propagating in a turbulent atmosphere

Analytical formulas for the average intensity and decentered parameter of a decentered elliptical Gaussian beam (DEGB) propagating in a turbulent atmosphere are derived in a tensor form. The propagation properties of a DEGB in a turbulent atmosphere are investigated in detail, and found to be different from that in free space. Furthermore, as an application example, we investigate the propagation of a decentered elliptical flat-topped beam (DEFB) by expressing its electric field as a finite sum of DEGBs in a turbulent atmosphere. The properties of a DEGB or a DEFB in a turbulent atmosphere are closely related with the beam’s parameters and the structure constant of the turbulent atmosphere.     

Off-axis Gaussian Schell-model beam and partially coherent laser array beam in a turbulent atmosphere

The propagation of an off-axis Gaussian Schell-model (GSM) beam in a turbulent atmosphere is investigated based on the extended Huygens-Fresnel integral formula. Analytical formulae for the cross-spectral density and corresponding partially coherent complex curvature tensor of an off-axis GSM beam propagating in a turbulent atmosphere are derived. Based on these formulae, the propagation properties of such kind of beam in a turbulent atmosphere are investigated in detail. Furthermore, the methods are extended to investigate the propagation properties of a partially coherent laser array beam in a turbulent atmosphere. The properties of an off-axis GSM beam and a partially coherent laser array beam in a turbulent atmosphere are closely related with the beam parameters and the structure constant of the turbulent atmosphere.     

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 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 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.     

Changes in the spectrum of twist anisotropic Gaussian Schell-model beams propagating through turbulent atmosphere

Based on the extended Huygens-Fresnel principle, the spectrum of twist anisotropic Gaussian Schell-model (TAGSM) beams propagating through turbulent atmosphere is derived analytically by using the partially coherent complex curvature tensor. The relative spectral shift of TAGSM beams propagating through turbulent atmosphere is closely related with the strength of atmospheric turbulence, the beam’s parameter and the radial coordinate. The on-axis spectral shift of TAGSM beams propagating through turbulent atmosphere changes from blue shift to red shift with the increasing of the propagation distance z, and at a certain propagation distance z, there exists a rapid transition of the spectrum at the critical position r_c.     

Manipulation of Particles with Counter-Propagating Evanescent Waves

Two counter-propagating evanescent beams are used to align and manipulate polystyrene particles on a prism surface. Since the radiation pressure transferred laterally from the evanescent wave is negated on both sides, particles can be stably aligned. By projecting a circular and a linear beam spot onto the interface, both multiple and single arrays of particles are achieved. Arrays of particles trapped on the interface can be easily moved adjusting the intensity of incident beams on either side. We also simulate electromagnetic distribution of scattering light that is converted from the evanescent wave using the FDTD method. The results show that scattering light converts from an evanescent wave propagating through a particle array and has a distance longer than that propagating from a normal evanescent wave.     

Intensity distribution for the broadband aberrated partially coherent flat-topped beam propagating through turbulent atmosphere

In this paper, taking the partially coherent flat-topped (PCFT) beam as an example, we investigate the intensity distribution of broadband beams with astigmatic aberration propagating through a turbulent atmosphere. The analytic expressions for the intensity of the beams propagating through the turbulent atmosphere are derived. It is shown that the intensity distribution of the broadband aberrated PCFT beams in the turbulent atmosphere are closely related with the astigmatism aberration, the strength of atmospheric turbulence, the order of flatness, the correlation of source and the bandwidth of PCFT beams. It is important to note that the position of the focal plane of the broadband aberrated (or not) PCFT beams can be modulated by changing the aberration, the order of flatness, the correlation and the bandwidth of PCFT beams.     

Spectral shifts and spectral switches of elliptical Gaussian beam propagating through turbulent atmosphere

Based on the extended Huygens-Fresnel principle, the spectrum of elliptical Gaussian beam (EGB) propagating through turbulent atmosphere can be derived analytically by tensor method. It can avoid time-consuming numerical integral that was commonly used in the previous study of spectral changes. Analytical results show that the on-axis normalized spectrum S(ω) of EGB propagating through turbulent atmosphere is different from the original spectrum S₀(ω) and there exist spectral shifts and spectral switches for EGB propagating through turbulent atmosphere. Besides, spectral shifts and spectral switches of EGB are closely related with the structure constant of the turbulent atmosphere, the beam parameters and the coordinate of observation point. Compared with the Gaussian beam, there are two spectral switches for EGB propagating through turbulent atmosphere.     

Generalized tensor ABCD law for an elliptical Gaussian beam passing through an astigmatic optical system in turbulent atmosphere

The propagation of an elliptical Gaussian beam (EGB) through an astigmatic ABCD optical system in a turbulent atmosphere is investigated. An analytical formula for the average intensity of an EGB and a generalized tensor ABCD law for the generalized complex curvature tensor are derived. As an application example, we derived an analytical formula for the average intensity of an elliptical flat-topped beam propagating through an astigmatic ABCD optical system in a turbulent atmosphere. As a numerical example, the focusing properties of an EGB focused by a thin lens in a turbulent atmosphere are studied. It is found that the focused beam at the focal plane becomes a circular Gaussian beam when the atmospheric turbulence is strong enough, and the beam width of the circular Gaussian beam is determined by atmospheric turbulence strength, focal length of the thin lens, and wavelength of the initial beam but is independent of the initial beam widths (i.e., initial intensity distribution).     

Giant optical activity and circular dichroism in the terahertz region based on bi-layer Y-shaped chiral metamaterial

We present a bi-layer Y-shaped chiral metamaterial (CMM) that can realize a giant optical activity and circular dichroism (CD) effect to the incident linear polarization wave in the terahertz (THz) region. Numerical simulation results exhibit that the pronounced CD effect with a great difference between the transmission coefficients for the circularly polarized waves can be obtained at 5.06 THz, meanwhile the 90°-polarization rotation can be observed at 5.2 THz when a y-polarized wave is incident to this CMM propagating along the −z-axis. The mechanism of the optical activity and giant CD effect is illustrated by simulated surface current distributions. Further, the influences of the structural parameters of the proposed CMM to the optical activity and CD effect have been investigated numerically.     

Change in degree of coherence of partially coherent electromagnetic beams propagating through atmospheric turbulence

We study the change in the degree of coherence of partially coherent electromagnetic beam (so called electromagnetic Gaussian Schell-model beam). It is shown analytically that with a fixed set of source parameters and under a particular atmospheric turbulence model, an electromagnetic Gaussian Schell-model beam propagating through atmospheric turbulence reaches its maximum value of coherence after the beam propagates a particular distance, and the effective width of the spectral degree of coherence also has its maximum value. This phenomenon is independent of the used turbulence model. The results are illustrated by numerical curves.