Influence of Transverse Cross‐Phases on Propagations of Optical Beams in Linear and Nonlinear Regimes

Abstract

It is predicted that an orbital angular momentum (OAM) carried by an elliptic Gaussian beam (EGB) with a cross‐phase can induce an effective anisotropic diffraction (AD). At the so‐called critical OAM, such an OAM‐induced AD makes the spiraling elliptic Gaussian mode, which expands owing to the diffraction while keeping its elliptic degree changeless, exist in linearly isotropic media, where only the circular Gaussian mode is supposed to exist for a beam without an OAM. In this study, such a phenomenon is experimentally demonstrated via the propagations of the EGBs with the OAM in linearly and both‐linearly‐and‐nonlinearly isotropic media. In the former case, the spiraling elliptic Gaussian mode is observed at the critical OAM in the free space. In the latter case, the spiraling elliptic soliton predicted by Desyatnikov et al. is observed for the first time in cylindrical lead glass. The physics behind the spiraling elliptic soliton is the OAM‐induced AD, which preserves the elliptic degree of the EGB, whereas the nonlinearity only balances the diffraction of the EGB. The OAM‐induced AD is just a linear effect and has nothing to do with nonlinearity.

Robust far-field imaging by spatial coherence engineering

“…The last term exp[iu(x 1 y 1 −x 2 y 2 )] is the CP, where u is a measure of the strength of the CP. The sign of the parameter u only determines the rotation direction of the beam 39 . It can be regarded as the extension of astigmatic phase, and it is a separable function with respect to (x 1 , y 1 ) and (x 2 , y 2 ).…”

“…The CP has been extensively explored 39−44 . The studies reveal that such a phase structure can make the beam rotate 39 , realize coherent modes conversion 41 , flexibly focus the ring Pearcey beam 42 , as well as manipulate the high-order optical vortices 43,44 . In order to investigate the effect of the CP on the evolution of the DOC, we first set μ 0 (∆r) as the cosine-Gaus- ) cos…”

“…In fact, the DOC in the focal plane rotates π/2 rad, but its shape is unchanged. The rotation of the DOC attributes to the particular orbital angular momentum (OAM) flux density induced by the CP 39 .…”

Spiraling elliptic hollow beams with cross phase

“…Then the elliptical Gaussian beam with the cross phase is also called the spiraling elliptical beam [21]. In the nonlinear media, the cross phase can make the elliptical Gaussian beams propagate stably as the elliptic solitons even though the saturable nonlinearity [22] or the nonlocal nonlinearity of media is isotropic [19,23].…”

“…The OAM of optical vortices is only determined by the topological charge. While, the OAM of the spiraling elliptical beam is proportional to Θ(b 2 − c 2 ) [21,23], where the cross phase coefficient Θ, the major semiaxis b and the minor semiaxis c can all be continuously tuned in experiments. In this paper, based on the spiraling elliptic beam with the cross phase, we can construct the hollow beams with faint intensities at the center.…”