Xiaoling Ji

Beam propagation factor of partially coherent Hermite–Gaussian array beams

The analytical expression for the beam propagation factor (M2-factor) of partially coherent Hermite–Gaussian (H–G) array beams is derived. It is shown that for the superposition of the intensity the M2-factor increases monotonically with increasing the beam order, the beam number and the relative beam separation distance, and decreasing the beam coherence parameter. However, for the superposition of the cross-spectral density function there may appear a minimum of the M2-factor as the beam number or the beam coherence parameter changes. On the other hand, a comparison of the M2-factor between the two types of superposition is also given. It is found that the M2-factor for the superposition of the cross-spectral density function may be smaller or larger than that for the superposition of the intensity depending on the beam order and the relative beam separation distance. However, the M2-factor for the superposition of the cross-spectral density function is always smaller than that for the superposition of the intensity when the beam order is equal to zero or the relative beam separation distance is small enough. In particular, the M2-factor is nearly the same for the two types of superposition when the beam coherence parameter is small enough or the relative beam separation distance is large enough.

Spatial correlation properties of Gaussian–Schell model beams propagating through atmospheric turbulence

The closed-form expressions for the spectral degree of coherence and the width of the spectral degree of coherence of Gaussian–Schell model (GSM) beams propagating through atmospheric turbulence are derived. The influence of atmospheric turbulence on the spectral correlation properties of GSM beams is studied both analytically and numerically. A comparison between the width of the spectral degree of coherence and that of the spectral intensity of GSM beams propagating through atmospheric turbulence is also given. Some interesting results are obtained, which are different from those obtained previously, and are explained physically.

Propagation of multi-Gaussian beams in incoherent combination through turbulent atmosphere and their beam quality

Based on the extended Huygens–Fresnel principle, the propagation of M × N multi-Gaussian beams in incoherent combination through turbulent atmosphere, and their beam quality are studied. The power in the bucket (PIB), β parameter and strehl ratio (SR ) are taken as the characteristic parameters of beam quality, and analytical expressions for PIB and SR are derived. It is shown that multi-Gaussian beams in turbulent atmosphere undergo three stages of evolution with increasing propagation distance z, and turbulence accelerates the evolution of the three stages which multi-Gaussian beams undergo. The turbulence results in a degradation of the beam quality, and multi-Gaussian beams with higher numbers M and N are less sensitive to the effects of turbulence than those with lower M and N.

The far-field directionality of partially coherent flat-topped beams propagating through atmospheric turbulence

The far-field directionality of partially coherent flat-topped beams propagating through atmospheric turbulence is studied. The closed-form expressions for the mean squared beam width and angular spread of partially coherent flat-topped beams propagating through atmospheric turbulence are derived. It is shown that two partially coherent flat-topped beams may generate the same angular spread, and there exist equivalent partially coherent flat-topped beams which may have the same far-field directionality as a fully coherent Gaussian beam in free space and also in atmospheric turbulence. The far-field directionality of Gaussian Schell-model (GSM) beams in atmospheric turbulence is treated as a special case of partially coherent flat-topped beams. The theoretical results are illustrated by numerical examples and interpreted physically.

Changes in the spectrum of diffracted pulsed cosh-Gaussian beams propagating through atmospheric turbulence

The spectral changes of diffracted pulsed cosh-Gaussian (ChG) beams propagating through atmospheric turbulence are studied both analytically and numerically. It is shown that the on-axis spectrum is blue-shifted, and the spectrum becomes red-shifted with increasing transverse distance. There exist spectral switches at off-axis points. The spectral shifts and the transition height decrease as the turbulence increases and the lower-order spectral switch may disappear. The critical position at which the spectral switch takes place becomes closer to the axis as the truncation parameter and the decentered parameter increase. The transition height decreases with increasing truncation parameter. The results are interpreted physically.

Spectral properties of chirped Gaussian pulsed beams propagating through the turbulent atmosphere

The spectral properties of chirped Gaussian pulsed beams propagating through the turbulent atmosphere are studied. The analytical expression for the spectrum, algebraic equation governing the position ω max of the maximum spectrum and algebraic equation governing the position r 0 without spectral shift are derived. It is shown that the spectrum at the observation point ( r, z ) depends on the structure constant of the refractive index , chirp parameter C and pulse duration T. The normalized on-axis spectrum S(ω) is blue-shifted, and the off-axis spectrum becomes red-shifted with increasing radial coordinate. The effect of turbulence on the spectral shift of chirped Gaussian pulsed beams becomes smaller with decreasing C and increasing T. The position r 0 without spectral shift is dependent on ω0, and z, but independent of T and C. In addition, there exists an off-axis spectral transition of a chirped Gaussian pulsed beam in the turbulent atmosphere. The physical explanations of the spectral shift and spectral transition of chirped Gaussian pulsed beams propagating through the turbulent atmosphere are given.

Spreading of partially coherent flattened Gaussian beams propagating through turbulent media

Based on the extended Huygens–Fresnel principle, the spreading of partially coherent flattened Gaussian beams propagating through turbulent media is studied by using the incoherent superposition of higher-order Hermite–Gaussian beams. The mean-squared width of partially coherent flattened Gaussian beams in turbulence is derived. It is shown that the spreading of partially coherent flattened Gaussian beams increases with increasing turbulent parameter and beam order N. However, the difference between the relative spreading of partially coherent flattened Gaussian beams in turbulent media and in free space reduces as N increases. Therefore, partially coherent flattened Gaussian beams with high N are less sensitive to the effects of turbulence than those with lower N.

Matrix formulation of higher-order moments of partially coherent beams propagating through atmospheric turbulence along a slanted path

Based on the extended Huygens–Fresnel principle, the matrix formulae of higher-order moments of partially coherent beams propagating through atmospheric turbulence along a slanted path are derived by using the Wigner distribution function (WDF). The same matrix formulae for propagation along a vertical path, a horizontal path and in free space are discussed as special cases of our general results. Analytical expressions for the important turbulence parameters contained in the matrix formulae of higher-order moments are also derived.