Coherent Flat-topped Beam Research Articles

Analyzing the propagation behavior of coherence and polarization degrees of a phase-locked partially coherent radial flat-topped array laser beam in underwater turbulence

In this research, based on an analytical expression for cross-spectral density (CSD) matrix elements, coherence and polarization properties of phase-locked partially coherent flat-topped (PCFT) radial array laser beams propagating through weak oceanic turbulence are analyzed. Spectral degrees of coherence and polarization are analytically calculated using CSD matrix elements. Also, the effective width of spatial degree of coherence (EWSDC) is calculated numerically. The simulation is done by considering the effects of source parameters (such as radius of the array setup's circle, effective width of the spectral degree of coherence, and wavelength) and turbulent ocean factors (such as the rate of dissipation of the turbulent kinetic energy per unit mass of fluid and relative strength of temperature and salinity fluctuations, Kolmogorov micro-scale, and rate of dissipation of the mean squared temperature) in detail. Results indicate that any change in the amount of turbulence factors that increase the turbulence power reduces the EWSDC significantly and causes the reduction in the degree of polarization, and occurs at shorter propagation distances but with smaller magnitudes. In addition, being valid for all conditions, the degradation rate of the EWSDC of Gaussian array beams are more in comparison with the PCFT ones. The simulation and calculation results are shown by graphs.

Stokes parameters of phase-locked partially coherent flat-topped array laser beams propagating through turbulent atmosphere

In this study, generalized Stokes parameters of a phase-locked partially coherent flat-topped array beam based on the extended Huygens–Fresnel principle and the unified theory of coherence and polarization have been reported. Analytical formulas for 2 × 2 cross-spectral density matrix elements, and consequently Stokes parameters of a phase-locked partially coherent flat-topped array beam propagating through the turbulent atmosphere have been formulated. Effects of many physical attributes such as wavelength, turbulence strength, flatness order and other source parameters on the Stokes parameters, and therefore spectral degree of polarization upon propagation have been studied thoroughly. The behaviour of the spectral degree of coherence of a delineated beam for different source conditions has been investigated. It can be shown that four generalized Stokes parameters increase by raising the flatness order at the same propagation distance. Increasing the number of beams leads to a decrease in the Stokes parameters to zero slowly. The results are of utmost importance for optical communications.

Propagation Properties of a Partially Coherent Flat-Topped Vortex Hollow Beam in Turbulent Atmosphere

Using coherence theory, the partially coherent flat-topped vortex hollow beam is introduced. The analytical equation for propagation of a partially coherent flat-topped vortex hollow beam in turbulent atmosphere is derived, using the extended Huygens-Fresnel diffraction integral formula. The influence of coherence length, beam order N, topological charge M, and structure constant of the turbulent atmosphere on the average intensity of this beam propagating in turbulent atmosphere are analyzed using numerical examples.

部分相干平顶激光组束投射腔壁光强的分布特性

部分相干平顶激光组束投射腔壁光强的分布特性

斜程湍流大气中部分相干平顶光束的偏振度研究

斜程湍流大气中部分相干平顶光束的偏振度研究

Evolution properties of partially coherent flat-topped vortex hollow beam in oceanic turbulence.

Employing the theory of coherence, the partially coherent flat-topped vortex hollow beam is first introduced. The analytical propagation equation for a partially coherent flat-topped vortex hollow beam in oceanic turbulence is derived by using the extended Huygens-Fresnel diffraction integral and the spectrum of oceanic turbulence. The influences of coherence length, beam order N, the topological charge M, and the parameters of oceanic turbulence on evolution properties of partially coherent flat-topped vortex hollow beams propagating in oceanic turbulence are obtained by using the numerical examples.

Analyzing the propagation behavior of scintillation index and bit error rate of a partially coherent flat-topped laser beam in oceanic turbulence.

In this paper, on the basis of the extended Huygens-Fresnel principle, a semianalytical expression for describing on-axis scintillation index of a partially coherent flat-topped (PCFT) laser beam of weak to moderate oceanic turbulence is derived; consequently, by using the log-normal intensity probability density function, the bit error rate (BER) is evaluated. The effects of source factors (such as wavelength, order of flatness, and beam width) and turbulent ocean parameters (such as Kolmogorov microscale, relative strengths of temperature and salinity fluctuations, rate of dissipation of the mean squared temperature, and rate of dissipation of the turbulent kinetic energy per unit mass of fluid) on propagation behavior of scintillation index, and, hence, on BER, are studied in detail. Results indicate that, in comparison with a Gaussian beam, a PCFT laser beam with a higher order of flatness is found to have lower scintillations. In addition, the scintillation index and BER are most affected when salinity fluctuations in the ocean dominate temperature fluctuations.

Theoretical and experimental studies of the spectral changes of a focused polychromatic partially coherent flat-topped beam

An analytical propagation formula for a focused polychromatic partially coherent flat-topped beam with circular symmetry is derived in a tensor form that is based on the alternative flat-top beams model proposed by Li (Opt Lett 27:1007, 2002). The dependence of the relative spectral shift on the flat-top order N is investigated numerically in detail. It is shown that the on-axis maximum relative spectral shift occurs at the back focal plane, while the no spectral shift observes at the image plane. Furthermore, we report the experimental generation of a polychromatic partially coherent FT beam. The on-axis and off-axis spectral measurement verifies the theoretical study.

部分相干平顶光束在非Kolmogorov湍流中的湍流距离

部分相干平顶光束在非Kolmogorov湍流中的湍流距离

部分相干平顶光束在非Kolmogorov大气湍流中湍流距离的变化

部分相干平顶光束在非Kolmogorov大气湍流中湍流距离的变化

Beam wander of electromagnetic partially coherent flat-topped beam propagating in turbulent atmosphere

Beam wander of an electromagnetic partially coherent flat-topped (EPCFT) beam propagating through turbulent atmosphere is studied. The analytical expression of beam wander effect is obtained. The influence of source size, source spatially coherent lengths, degree of polarization, and beam flatness order are studied in detail. It has been shown that by adjusting these parameters appropriately, the beam wander effects could be greatly reduced. Compared with increasing the degree of polarization, the beam wander could be reduced much more effectively by increasing the beam flatness order. The EPCFT beam can greatly reduce the beam wander effect and the parameters should be chosen very carefully for different applications.

Propagation characteristics of tilted partially coherent rectangular flat-topped beam in turbulent atmosphere

In this paper, the effects of atmospheric turbulence on the intensity distribution of a tilted Rectangular Partially Coherent Flat-Topped (RPCFT) beam were studied. An analytical formula for the intensity distribution was derived. POWER In Bucket (PIB) value is calculated numerically. The effects of source parameters – such as correlation length, order of flatness and tilt coefficient – on the intensity were analyzed. Detailed analysis demonstrates that these parameters have an influence on beam propagation properties. The analyses are illustrated by numerical examples and graphs.

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.

Effect of spatial coherence on the scintillation properties of a dark hollow beam in turbulent atmosphere

With the help of a tensor method, we derive an explicit expression for the on-axis scintillation index of a circular partially coherent dark hollow (DH) beam in weakly turbulent atmosphere. The derived formula can be applied to study the scintillation properties of a partially coherent Gaussian beam and a partially coherent flat-topped (FT) beam. The effect of spatial coherence on the scintillation properties of DH beam, FT beam and Gaussian beam is studied numerically and comparatively. Our results show that the advantage of a DH beam over a FT beam and a Gaussian beam for reducing turbulence-induced scintillation increases particularly at long propagation distances with the decrease of spatial coherence or the increase of the atmospheric turbulence, which will be useful for long-distance free-space optical communications.

The influence of phase aperture on Beam propagation factor of partially coherent flat-topped beams in a turbulent atmosphere

Analytical formula has been derived for the M2-factor of a partially coherent flat-topped (PCFT) beam truncated by a phase aperture in turbulent atmosphere based on the extended Huygens–Fresnel principle and the second-order moments of the Wigner distribution function. The M2-factor of the mentioned beams in atmospheric turbulence have been discussed precisely with numerical analysis. It can be shown that the M2-factor of a PCFT beam truncated by a phase aperture in turbulent atmosphere increases with propagation distance, and is mainly determined by the parameters of the beam, phase aperture and turbulent atmosphere. The presented results are expected to be useful in long-distance free-space optical communications.

Spectral properties of a random electromagnetic partially coherent flat-topped vortex beam in turbulent atmosphere

Based on the extended Huygens–Fresnel principle, we introduced the analytic expression of a random electromagnetic partially coherent flat-topped (PCFT) vortex beam propagating in Kolmogorov atmospheric turbulence. The spectral properties of the random electromagnetic PCFT vortex beam are explored by using the unified theory of coherence and polarization. It is demonstrated by numerical results and found that after propagating through turbulent atmosphere, the spectral density, the spectral degree of polarization as well as the spectral degree of coherence of the random electromagnetic PCFT vortex beam vary. The variations of the spectral properties depend closely on the strength of atmospheric turbulence and the properties of the source beam, i.e. the topological charges, the order of flatness, the waist width as well as the initial spatial coherence. In addition, the distributions of the spectral density and the spectral degree of polarization undergo several stages of evolution and finally tend to Gaussian profile at the receiver plane. Some possible explanations have also been given for these interesting physical phenomena.

Spectrum changes of phase-locked partially coherent flat topped laser beam array propagating in turbulent atmosphere

Propagation of the phase-locked partially coherent flat topped laser beam array trough turbulent media is studied in details. Concentrating on critical radius as an important designing factor, effects of coherence length, beamlet distance and flat topped degree on this parameter are discussed. Also geometrical shape of the array is shown to be important by comparing circular and rectangular shapes.

Focal shift and focal switch of phase-lock partially coherent flat-topped array beams passing through an aligned and misaligned lens system with aperture

The focal shift and focal switch of phase-lock partially coherent flat-topped (PCFT) array beams passing through a lens system with aperture is studied in detail. It is shown that there is a focal shift for mention beam propagating through aligned optical system and the amount of the focal shift depend on optical system and beam characteristics. In addition, a new phenomenon called focal switch occurs for misaligned optical system, i.e. the focal shift experiences a sudden transition as the aligned optical system turns to misalign one. It is shown that, the necessary conditions for the focal switch to take place are also investigated.

Changes in the width of the coherence for partially coherent flat topped beams with a circular aperture in turbulent atmosphere

We study the change in the degree of coherence of partially coherent flat topped (PCFT) beam limited by a circular aperture propagating through atmospheric turbulence. It is shown analytically that the degree of coherence for mentioned beam reaches its maximum value after the beam propagates a specific distance. In this paper we define the width of the coherence and it is shown analytically that the effective width of the degree of coherence also has a maximum value at the specific distance. This phenomenon is dependent on the used aperture radius size. The results are illustrated by numerical curves.

Coherence vortex properties of partially coherent flat-topped vortex beams

The analytical propagation expression of partially coherent flat-topped vortex beams through a paraxial optical ABCD system is derived, and it then is used to investigate the coherence vortex properties of partially coherent flat-topped vortex beams in the Fourier transform and fractional Fourier transform systems. It is shown that in the Fourier transform system the coherence vortex depends on the flat-topped beam order N, spatial coherence parameter α and position (x1,y1) of the reference point, whereas in the fractional Fourier transform system the flat-topped beam order N does not affect the spectral degree of coherence. Furthermore, in both transform systems, depending on the choice of the reference point, the zero value point of the spectral degree of coherence may be present or absent. In particular, if x1=y1=0 is selected, the phase at the zero value point of the spectral degree of coherence may be determinate; thus the coherence vortex does not exist.