Partially Coherent Flat-topped Research Articles

Numerical research on partially coherent flat-topped beam propagation through atmospheric turbulence along a slant path.

In this paper, we investigate the propagation of partially coherent flat-topped (PCFT) beams through atmospheric turbulence along a slant path. Using wave optics simulation (WOS), we calculated the on-axis intensity of PCFT beams in both vacuum and turbulence links, finding that PCFT beams will self-focus during propagation and that the beam coherence length has a significant impact on this focusing phenomenon. The effects of the zenith angle and the source coherence length on the scintillation index and mean signal-to-noise ratio (SNR) are analyzed. Furthermore, taking into consideration the limitation of available devices, we examined the impacts of source coherence time and detector integration time on the performance of PCFT beams in slant links. WOS results indicate as much as an extra 2 dB SNR gain from PCFT beams in short links in comparison with Gaussian Schell-model beams.

Scintillation and bit error rate analysis of a phase-locked partially coherent flat-topped array laser beam in oceanic turbulence.

In this paper, the performance of underwater wireless optical communication (UWOC) links, which is made up of the partially coherent flat-topped (PCFT) array laser beam, has been investigated in detail. Providing high power, array laser beams are employed to increase the range of UWOC links. For characterization of the effects of oceanic turbulence on the propagation behavior of the considered beam, using the extended Huygens-Fresnel principle, an analytical expression for cross-spectral density matrix elements and a semi-analytical one for fourth-order statistical moment have been derived. Then, based on these expressions, the on-axis scintillation index of the mentioned beam propagating through weak oceanic turbulence has been calculated. Furthermore, in order to quantify the performance of the UWOC link, the average bit error rate (BER) has also been evaluated. The effects of some source factors and turbulent ocean parameters on the propagation behavior of the scintillation index and the BER have been studied in detail. The results of this investigation indicate that in comparison with the Gaussian array beam, when the source size of beamlets is larger than the first Fresnel zone, the PCFT array laser beam with the higher flatness order is found to have a lower scintillation index and hence lower BER. Specifically, in the sense of scintillation index reduction, using the PCFT array laser beams has a considerable benefit in comparison with the single PCFT or Gaussian laser beams and also Gaussian array beams. All the simulation results of this paper have been shown by graphs and they have been analyzed in detail.

Propagation characteristics of partially coherent flat-topped beams propagating through inhomogeneous atmospheric turbulence.

M2-factor and root-mean-square (rms) angular width of partially coherent flat-topped (PCFT) beams propagating through inhomogeneous atmospheric turbulence are studied based on the extended Huygens-Fresnel principle and the Wigner distribution function (WDF). It is shown that the effect of turbulence on the PCFT beams can be neglected as the vertical height increases, which is different from the homogeneous turbulence. Analytical formulae of the M2-factor and rms angular width of PCFT beams have been given. The saturation propagation distances (SPDs) increase with increasing zenith angle. It can be seen that the SPDs of the M2-factor and rms angular width of PCFT beams propagating through inhomogeneous atmospheric turbulence are about 30 km and 0.5 km, respectively, when the zenith angle is π/4. It can be found that the M2-factor increases with increasing beam order and zenith angle, and with decreasing waist width, inner scale, wavelength, and transverse coherence length. The rms angular width increases with increasing beam order, wavelength, and zenith angle, and decreasing waist width, inner scale, and transverse coherence length.

Analyzing the average intensity distribution and beam width evolution of phase-locked partially coherent radial flat-topped array laser beams in oceanic turbulence

In this research, an analytical expression for cross-spectral density matrix elements (and consequently, average intensity) of partially coherent flat-topped (PCFT) radial array laser beams in weak oceanic turbulence are derived based on the extended Huygens–Fresnel principle and the previously developed knowledge of the propagation of a partially coherent beam in atmosphere. Mean-squared beam width is calculated analytically using average intensity formula. The simulation is done by considering the effects of source parameters (such as the radius of the array setup’s circle and effective width of spectral degree of coherence) 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-salinity fluctuations, Kolmogorov micro-scale, and the rate of dissipation of the mean squared temperature) in detail. It is found that when salinity fluctuations in the ocean dominate temperature fluctuations, the average intensity of the PCFT array beam becomes more broad and the array beam profile conversion process to a single wider Gaussian beam profile will occur at a faster rate. For the same turbulent conditions and the same initial beam width, the divergence of a flat-topped array beam is less than the Gaussian array beam. The simulation and calculation results are shown by graphs.

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.

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.

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.

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.

Beam propagation analysis of a multi beam FSO system with partially flat-topped laser beams in turbulent atmosphere

In this paper, the propagation properties of partially coherent flat-topped (PCFT) laser beams in multi-beam FSO communication links are analyzed. Analytical expressions for the average intensity and beam width of PCFT multi beams are derived based on extended Huygens–Fresnel principle by considering the effects of turbulent atmosphere. Also power in bucket (PIB) is calculated numerically based on analytical expression of average intensity. It is revealed that PCFT multi beams can be converted into a Gaussian beam after sufficiently large propagation distance. It is found that correlation length, order of flatness and beams’ separation distances in the source plane have strong effects on minimum distance required for this conversion as well as beam width and PIB. Obtained results are confirmed and illustrated with numerical examples and resulted graphs.

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.

Changes in the state of polarization of partially coherent flat-topped beam in turbulent atmosphere for different source conditions

The polarization states, i.e. the size, the shape and the orientation of the polarization ellipse of partially coherent flat-topped (PCFT) beams passing through atmospheric turbulence are studied in detail. The effects are studied of different source conditions on the polarization states of a PCFT beam propagating through atmospheric turbulence. Based on the unified theory of the polarization states for random electromagnetic beams, we have established the detailed formula for calculating the change of the polarization states of such beams.

Focal shift and focal switch of partially coherent flat-topped beams passing through an alignment and misalignment lens system with aperture

The focal shift and focal switch of partially coherent flat-topped (PCFT) beams passing through a lens system with an aperture are studied in detail. We have shown that a focal shift is also present for beams propagating through an aligned optical system and the amount of the focal shift depends not only on the radius aperture of the focusing system, but also on the spatial coherence and order of the flat-topped beam of the incident partially coherent light. A new phenomenon called ‘focal switch’ occurs for misaligned optical systems, i.e. the focal shift experiences a sudden transition as the aligned optical system becomes misaligned, and the influence of the spatial coherence, order of flat-topped beam and aperture size reduction, on the focal switch is investigated in detail. Finally, the necessary conditions for the focal switch to take place are investigated.

Propagation properties of a non-circular partially coherent flat-topped beam in a turbulent atmosphere

The propagation of partially coherent flat-topped (PCFT) beams with non-circular symmetries in a turbulent atmosphere is investigated and an analytical formula for the average intensity is derived. Detailed analyses of PCFT beams in a turbulent media led to the derivation of analytical formulae. These formulae demonstrated that higher-order PCFT beams are less broadened in comparison with those with smaller orders and also demonstrated that PCFT beams with smaller correlation lengths are more broadened than the others. The Strehl ratio for PCFT beams is also calculated and the results show that PCFT beams with a higher order of flatness and smaller correlation length are less affected in turbulent media.

Beam propagation factor of partially coherent flat-topped beams in a turbulent atmosphere

The Wigner distribution function (WDF) has been used to study the beam propagation factor (M(2)-factor) for partially coherent flat-topped (PCFT) beams with circular symmetry in a turbulent atmosphere. Based on the extended Huygens-Fresnel principle and the definition of the WDF, an expression for the WDF of PCFT beams in turbulence has been given. By use of the second-order moments of the WDF, the analytical formulas for the root-mean-square (rms) spatial width, the rms angular width, and the M(2)-factor of PCFT beams in turbulence have been derived, which can be applied to cases of different spatial power spectra of the refractive index fluctuations. The rms angular width and the M(2)-factor of PCFT beams in turbulence have been discussed with numerical examples. It can be shown that the M(2)-factor of PCFT beams in turbulence depends on the beam order, degree of global coherence of the source, waist width, wavelength, spatial power spectrum of the refractive index fluctuations, and propagation distance.

Propagation of partially coherent flat-topped beams through a turbulent atmosphere

Based on the modified beam model for flat-topped beams and the Schell model for partially coherent light, an expression for partially coherent flat-topped (PCFT) beams has been proposed. The propagation characteristics of PCFT beams with circular symmetry through a turbulent atmosphere have been studied. By using the generalized Huygens-Fresnel integral and Fourier transform method, the expressions for the cross-spectral density function and the average intensity have been given and the analytical expression for the root-mean-square width has been derived. The effects of the beam order, the spatial coherence, and the turbulent parameter on the intensity distributions and beam spreading have been discussed in detail. Our results show that the on-axis intensity of the beams decreases with increasing turbulence and decreasing coherence of the source, whereas the on-axis intensity of the beams in the far field decreases slightly with increasing beam order. The relative spreading of PCFT beams is smaller for beams with a higher order, a lower degree of global coherence of the source, a larger inner scale, and a smaller outer scale of the turbulence.

Spectral changes of partially coherent flat topped beam in turbulent atmosphere

Spectral characteristics of partially coherent flat-topped (PCFT) beams propagated in a turbulent atmosphere are investigated and an analytical formula for the spectrum S(ω) is derived. It is shown that, if the scaling law is valid, the normalized spectrum S(ω) of PCFT beams propagating through turbulent atmosphere is the same as the normalized source spectrum S(0)(ω), this similarity is valid for any arbitrary order of the circular flat-topped “N”. It is proved that if the scaling law is not valid, S(ω) of PCFT is different from S(0)(ω). Also spectral behavior of PCFT beams in free space and turbulence media is investigated in detail.