Ji Xiao-Ling

Turbulence-induced changes in degree of polarization, degree of coherence and spectrum of partially coherent electromagnetic beams

Based on a recently formulated unified theory of coherence and polarization, a method is described to study turbulence-induced changes in the polarization, the coherence and the spectrum of partially coherent electromagnetic beams on propagation. The electromagnetic Gaussian Schell-model beam is taken as a typical example of partially coherent electromagnetic beams, and the closed-form expressions for the degree of polarization, the degree of coherence and the spectrum of electromagnetic Gaussian Schell-model beams propagating through atmospheric turbulence are derived in the quadratic approximation of Rytov’s phase structure function. Some interesting results are obtained, which are illustrated by numerical examples and are explained in physics.

Propagation of the off-axis superposition of partially coherent beams through atmospheric turbulence

The propagation properties of the off-axis superposition of partially coherent beams through atmospheric turbulence and their beam quality in terms of the mean-squared beam width w(z) and the power in the bucket (PIB) are studied in detail, where the effects of partial coherence, off-axis beam superposition and atmospheric turbulence are considered. The analytical expressions for the intensity, the beam width and the PIB are derived, and illustrative examples are given numerically. It is shown that the maximum intensity I max and the PIB decrease and w(z) increases as the refraction index structure constant C 2 n increases. Therefore, the turbulence results in a degradation of the beam quality. However, the resulting partially coherent beam with a smaller value of spatial correlation parameter γ and larger values of separate distance x d and beam number M is less affected by the turbulence than that with a larger value of γ and smaller values of x d and M. The main results obtained in this paper are explained physically.

Rayleigh Range of Hermite-Gaussian Array Beams *

An analytical expression for the Rayleigh range of Hermite–Gaussian (H-G) array beams is derived. It is shown that under the non-phase-locked case the Rayleigh range zR increases monotonously with the increasing beam number M, the beam separation distance xd and the beam waist width w0, and with decreasing the beam order m. However, under the phase-locked case there exists oscillatory behavior of zR versus m and xd. For Gaussian array beams, under the phase-locked case, zR is always larger than that under the non-phase-locked case. However, it holds true only when xd is small enough or w0 is large enough for H-G array beams. In addition, zR of Gaussian array beams is always larger than that of H-G array beams.

A further study on the spreading and directionality of Gaussian array beams in non-Kolmogorov turbulence

It is found that in free space, the curves of the mean-squared beam width may each have a cross point at a certain propagation distance zc. For Gaussian array beams, the analytical expressions of zc are derived. For the coherent combination, zc is larger than that for the incoherent combination. However, in non-Kolmogorov turbulence, the cross point disappears, and the Gaussian array beams will have the same directionality in terms of the angular spread. Furthermore, a short propagation distance is needed to reach the same directionality when the generalized exponent is equal to 3.108. In particular, it is shown that the condition obtained in previous studies is not necessary for laser beams to have the same directionality in turbulence, which is explained physically. On the other hand, the relative average intensity distributions at the position where the Gaussian array beams have the same mean-squared beam width are also examined.

Consistency of the directionality of partially coherent beams in turbulence expressed in terms of the angular spread and the far-field average intensity

Under the quadratic approximation of the Rytovs phase structure function, this paper derives the general closed-form expressions for the mean-squared width and the angular spread of partially coherent beams in turbulence. It finds that under a certain condition different types of partially coherent beams may have the same directionality as a fully coherent Gaussian beam in free space and also in atmospheric turbulence if the angular spread is chosen as the characteristic parameter of beam directionality. On the other hand, it shows that generally, the directionality of partially coherent beams expressed in terms of the angular spread is not consistent with that in terms of the normalized far-field average intensity distribution in free space, but the consistency can be achieved due to turbulence.

Partially Coherent cosh-Gaussian Beams in Atmospheric Turbulence with the Same Directionality as a Laser

Directionality of a class of partially coherent cosh-Gaussian beams propagating in atmospheric turbulence is studied. It is shown that two partially coherent cosh-Gaussian beams may generate the same angular spread, and there exist equivalent partially coherent cosh-Gaussian beams which may have the same directionality as a fully coherent Gaussian laser beam in free space and also in atmospheric turbulence. The theoretical results are interpreted physically and illustrated numerically.