Entao Zhang

Superimposed partially coherent beams propagating through atmospheric turbulence

Two types of superposition, i.e., the superposition of the intensity and the superposition of the cross-spectral density function of off-axis partially coherent beams propagating through atmospheric turbulence, are analytically and numerically studied. The Gaussian-Schell model beam is taken as a typical example of the partially coherent beam, and analytical propagation equations for the resulting beam in turbulence are derived. The mean-squared beam width, the power in the bucket, and the β parameter are taken as the characteristic parameters of beam quality to compare the results of the two types of superimposed partially coherent beams in turbulence. It is shown that for the two types of superposition the smaller the coherence parameter α is, the less the resulting beam is sensitive to the effects of turbulence. The resulting beam of off-axis partially coherent beams for the superposition of the intensity is less affected by the turbulence than that for the superposition of the cross-spectral density function. The results are physically interpreted.

Angular spread of partially coherent Hermite-cosh-Gaussian beams propagating through atmospheric turbulence

The propagation of partially coherent Hermite-cosh-Gaussian (H-ChG)beams through atmospheric turbulence is studied in detail. The analytical expression for the angular spread of partially coherent H-ChG beams in turbulence is derived. It is shown that the angular spread of partially coherent H-ChG beams with smaller spatial correlation length sigma0, smaller waist width w0, smaller beam parameter Omega0, and larger beam orders m, n is less affected by turbulence than that of partially coherent H-ChG beams with larger sigma0, w0, Omega0, and smaller m, n. Under a certain condition partially coherent H-ChG beams may generate the same angular spread as a fully coherent Gaussian beam in free space and also in atmospheric turbulence. The angular spread of partially coherent Hermite-Gaussian (H-G), cosh-Gaussian (ChG), Gaussian Schell-model (GSM) beams, and fully coherent H-ChG, H-G, ChG, Gaussian beams is studied and treated as special cases of partially coherent H-ChG beams. The results are interpreted physically.

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.

Propagation and far-field beam quality of M × N Hermite–Gaussian beams propagating through atmospheric turbulence

The analytical propagation equation of M×N Hermite–Gaussian (H–G) beams, which are combined incoherently and propagate through atmospheric turbulence, is derived, which enables us to study their propagation properties and far-field beam quality. The propagation of M×N Gaussian beams through atmospheric turbulence and M×N H–G beams in free space are treated as special cases of our general result. The power in the bucket (PIB), β-parameter and Strehl ratio are chosen as the parameters characterizing the beam quality in the far field. The dependence of PIB, β-parameter and Strehl ratio of M×N H–G beams through atmospheric turbulence on the refraction index structure constant C n ², beam numbers M, N, mode indices m, n and separate distances xd , yd is illustrated numerically and interpreted physically. It is found that M×N H–G beams are less sensitive to the effects of turbulence than M×N Gaussian beams.

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.