Propagation of a partially coherent higher-order cosh-Gaussian beam through a paraxial ABCD optical system

Based on the generalized Huygens–Fresnel integral, analytical expressions for the mutual coherence function, the spatial complex degree of coherence, and the effective size of a partially coherent higher-order cosh-Gaussian beam through a paraxial ABCD optical system have been derived. As a numerical example, the propagation of a partially coherent higher-order cosh-Gaussian beam through an optical Fourier-transforming system with a limiting aperture is illustrated. The normalized intensity distribution, the spatial complex degree of coherence, and the effective beam size for the partially coherent higher-order cosh-Gaussian beam are numerically demonstrated in the observation plane. The influences of the spatial coherence length and the limiting aperture on the normalized intensity distribution, the spatial complex degree of coherence, and the effective beam size are also examined in detail.     

Propagation characteristics of partially coherent anomalous elliptical hollow Gaussian beam propagating through atmospheric turbulence along a slant path

Based on the extended Huygens–Fresnel principal and the Wigner distribution function, the root mean square (rms) angular width and propagation factor (M²-factor) of partially coherent anomalous elliptical hollow Gaussian (PCAEHG) beam propagating through atmospheric turbulence along a slant path are studied in detail. Analytical formulae of the rms angular width and M²-factor of PCAEHG beam are derived. Our results show that the rms angular width increases with increasing of wavelength and zenith angle and with decreasing of transverse coherence length, beam waist sizes and inner scale. The M²-factor increases with increasing of zenith angle and with decreasing of wavelength, transverse coherence length, beam waist sizes and inner scale. The saturation propagation distances (SPDs) increase as zenith angle increases. The numerical calculations also indicate that the SPDs of rms angular width and M²-factor for uplink slant paths with zenith angle of π/12 are about 0.2 and 20 km, respectively.     

Effects of atmosphere on spectrum of modified partially coherent flat-topped beams

The analytical formulas for the spectrum of modified partially coherent flat-topped (MPCFT) beams propagating in a turbulent atmosphere have been derived under strong fluctuation condition of turbulence. The spectral properties of MPCFT beams propagating in a strong turbulence have been investigated, and the changes of on-axis and off-axis spectral distributions have been analyzed quantitatively. The results show that the on-axis relative spectral shift of the modified partially coherent flat-topped beam exhibits spectral switch for the beam order M > 1, and with the increasing propagation distance the blue-shift gradually decreases in atmospheric turbulence. A rapid transition for the off-axis spectrum appears at one critical position in turbulence, and the position decreases with the increasing beam order for the lower beam order and the nearer propagation distance. The spectral properties and the spectral shifts of MPCFT beams also depend on the inner scale, the spatial coherence parameter.     

Composite coherence vortices in coherent and incoherent superpositions of two off-axis partially coherent vortex beams

The composite coherence vortices by coherently and incoherently superimposing two parallel, off-axis partially coherent vortex beams and their evolution in free space are studied. It is shown that the superposition scheme, off-axis distance, coherence parameter and propagation distance affect the position and number of composite coherence vortices. The motion, creation and annihilation of composite coherence vortices appear by varying the off-axis distance, coherence parameter and propagation distance. The coherent and incoherent superpositions result in the different position and number of composite coherence vortices and their different evolution behavior in the coherent limit.     

Channel correlation of transmit diversity FSO systems with partially coherent optical beams

Spatial diversity, including transmit diversity, has been proven to be a promising technique to mitigate turbulence-induced signal fading. However, due to the limitation of size in compact FSO (free-space optical) terminals, the transmit antennas cannot always be separated far enough from each other, resulting in increased channel correlation and deteriorated diversity performance. In this paper, we focus on the channel correlation statistics of transmit diversity FSO systems with two transmit beams. Specifically, we consider partially coherent optical beams, which reduce scintillation over fully coherent optical beams. We perform theoretical analysis and obtain some interesting numerical results, such as the degree of channel correlation which changed mainly with source correlation radius from 0.001 to 0.1 m. These results can be helpful for designing transmit diversity FSO systems with partially coherent beams.     

Focal shift of a focused partially coherent Laguerre-Gaussian beam of all orders

Abstract

We explore the focusing properties of a partially coherent Laguerre–Gaussian (LG) beam of all orders, particularly the focal shift (i.e. the shift of the actual focal plane away from the geometrical focal plane). We derive the analytical expressions for the average intensity and the effective beam width of a focused partially coherent LG beam, and we adopt the minimum effective beam width instead of the conventional maximum on-axis intensity to determine the actual focal plane. It is found that the focused beam shape, minimum effective beam width and the focal shift of a focused partially coherent LG beam are determined by its initial coherence width, radial mode order and azimuthal mode order (i.e. topological charge) together. Our results may be useful for optical trapping and micro-fabrication, where precise focal position and prescribed beam shape are required.     

多束部分相干光通过强湍流对光强闪烁的影响

在Rytov方差的基础上,利用Andrews的唯像闪烁模型,推导出部分相干光通过强大气湍流后其对数光强起伏方差的公式,并用此公式对部分相干光通过强湍流后给光强闪烁造成的影响进行了仿真。其结果表明,当光源的相干性变差,即变为部分相干光后,对数光强起伏方差变小;当采用多束部分相干光时,接收面上光强起伏方差得到明显改善,而且光束越多,改善越明显。     

Evolution of decentred laser beams propagating through atmospheric turbulence

The changes of the average intensity, the centre of beam gravity and the position of intensity maximum of decentred laser beams propagating through atmospheric turbulence are examined in detail. It is shown that the decentred intensity distribution is amended gradually with increasing the propagation distance and the strength of turbulence, and it becomes an off-axis Gaussian-like beam when the propagation distance and the strength of turbulence become large enough. The centre of beam gravity is independent of both the propagation distance and the strength of turbulence. On the other hand, there are two intensity maxima, and their positions are symmetrical around the propagation z-axis when the propagation distance z is small. With increasing z, there is only one intensity maximum. As z further increases, position of the intensity maximum is further shifted towards the z-axis. When z is large enough, the position of the intensity maximum is unchanged. The unchanged position of the intensity maximum moves further away from the z-axis with an increase in the refraction index structure constant, the decentred parameter and the waist width.     

Theoretical study on the spectral shifts of partially coherent array beams passing through ABCD optical systems

According to the extended Huygens–Fresnel integral, the expressions for the on-axis spectrum of partially coherent Gaussian Schell-model (GSM) rectangular array beams passing through ABCD optical systems have been derived. The generalized Fresnel number of the system, the spatial coherent parameter of array beamlets and the array beam parameters including the number of beamlets and the separation distance between beamlets have been taken as the characteristic parameters to compare the spectral shifts of GSM array beams for the two types of the superposition, i.e. the correlated superposition and the uncorrelated superposition. In particular, the effect of characteristic parameters on the on-axis relative spectral shifts has been discussed in detail. The results show that the spectral intensity of GSM array beams for the two types of the superposition passing through ABCD systems depends on the source spectral density S ⁰(ω), the spatial coherent parameter of array beamlets β, the generalized Fresnel number of the system F and the array beam parameters. Furthermore, for the uncorrelated superposition, the spectrum of GSM array beams only exhibit the blue-shift, whereas for the correlated superposition, GSM array beams exhibit the spectral switch and the number of spectral switches increases with the increase of array beam parameters in the near field due to the interference between beamlets. In particular, the effect of the array beam parameters on the on-axis relative spectral shift is more obvious.     

Effects of optical radiation on the Mössbauer spectrum of 151Eu3+: CaF2

We study the changes in the shape of the Mössbauer spectrum for the 21.5?keV transition of ¹⁵¹Eu³⁺ nuclei in a CaF₂ lattice, assuming that a population of the excited electronic state ⁵ D ₀ is maintained by optical pumping. For a population of the excited state ⁵ D ₀ of 10%, we determine the magnitude of the changes in the Mössbauer spectrum as 1.9% of the area of the unperturbed spectrum.     

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.     

Changes in the spectrum of radial array beams through turbulent atmosphere

According to the extended Huygens–Fresnel principle, the propagation formulas of the spectrum for correlated superposition radial array Gaussian Schell-model (RAGSM) beams in a turbulent atmosphere have been derived. The spectral properties of correlated superposition RAGSM beams in free space and in turbulence have also been compared and analyzed. The results show that there exist two identical spectral maxima for the normalized on-axis spectrum of RAGSM beams at one critical position against propagation distance. When the propagation distance is large enough, the on-axis relative spectral shifts in free space and those in turbulence tend to a steady nonzero and zero value, respectively. The off-axis relative spectral shift in free space exhibits a blue-shift alternating with red-shift against off-axis distance, and it depends on the array radius and the beamlet number; whereas the spectral shift has a rapid transition in turbulence. In addition, the on-axis and off-axis relative spectral shifts also depend on the characteristic parameters of turbulence, the beam parameters, and the array parameters.