Formation and evolution of far-field diffraction patterns of divergent and convergent Gaussian beams passing through self-focusing and self-defocusing media

Deng, Luogen; He, K. X.; Zhou, Tiezhong; Li, Chengde

doi:10.1088/1464-4258/7/8/011

Cited by 106 publications

(54 citation statements)

References 16 publications

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“…Lately, a theoretical study on the generation and evolution of far-field patterns was performed, taking into account the nonlinear nature of a thin compound and the beam wave front curvature [38]. The light beam profile is described as Gaussian, the nonlinear interaction with the thin medium is simply approximated as an added phase shift and then the far-field diffraction pattern is obtained with the Fresnel-Kirchhoff diffraction integral.…”

Section: Resultsmentioning

confidence: 99%

Nonlinear optical responses of MoS4Cu4(PzMe3)6Cl2 under low power CW He-Ne laser excitation

Sadr

Mohammadi

Soltani

et al. 2016

Optik

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Section: Resultsmentioning

confidence: 99%

Nonlinear optical responses of MoS4Cu4(PzMe3)6Cl2 under low power CW He-Ne laser excitation

Sadr

Mohammadi

Soltani

et al. 2016

Optik

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“…5b and c). According to [11], these observations are associated to the non-linear refractive index of samples. Consequently, the obtained results from SSPM patterns show the increase in non-refractive index with the increase of Ag-NPs concentration.…”

Section: Resultsmentioning

confidence: 99%

Investigation of spatial self-phase modulation of silver nanoparticles in clay suspension

Zamiri

Zakaria

Ahmad

et al. 2011

Optik

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a b s t r a c tWe have investigated the spatial self-phase modulation (SSPM) phenomena in a clay suspension containing silver nanoparticles. Silver nanoparticles (Ag-NPs) were synthesized in the space of lamellar structure of montmorillonite (MMT) by using chemical reducing agent. The UV-vis spectra of the obtained Ag-NPs showed that the intensity surface plasmon resonance (SPR) peaks increase with increasing in concentration of AgNO 3 . The results from Ag-NPs UV-vis spectra were in good agreement with the structure studies performed by TEM. The SSPM phenomena manifestation of the non-linear optical property appeared only when MMT suspension filled with Ag-NPs as shown in the existence of far-field pattern. This property increased with the increase of Ag-NPs concentration and limited to small range.

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“…Contributions to the phase shift can also originate from an input beam that is convergent (i.e., has a negative wavefront curvature R < 0) or divergent (i.e., with a positive wavefront curvature R > 0) [23] can be expressed through…”

Section: Introductionmentioning

confidence: 99%

“…The total transverse phase shift induced by the beam at a distance d from the input plane of the medium [23] therefore becomes…”

Section: Introductionmentioning

confidence: 99%

“…The optical field with this phase profile at the exit face of the sample can be freely propagated in space through the Fraunhofer approximation of the Fresnel-Kirchhoff diffraction formula to predict the pattern of diffraction rings in the far field [23]. Numerical simulations show that for a self-focusing, short pathlength medium, selfphase modulation under R < 0 conditions elicits a pattern of diffraction rings that bear a central dark spot whereas R > 0 conditions result in diffraction rings with a central bright spot.…”

Section: Introductionmentioning

confidence: 99%

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Diversity and slow dynamics of diffraction rings: a comprehensive study of spatial self-phase modulation in a photopolymer

Villafranca

Saravanamuttu

2012

J. Opt. Soc. Am. B

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Spatial self-phase modulation of a Gaussian beam in a photopolymer generated diffraction rings that propagated over unusually long distances (≫Rayleigh length) in the medium. Self-phase modulation was examined under negative, positive, and infinite wavefront curvatures (R) over different pathlengths. Resulting diffraction rings exhibited previously unobserved, slow dynamics, which could be directly monitored at the sample exit face. This study complements but differs fundamentally from previous ones that were predominantly carried out in thin films (≤Rayleigh length) and generated static diffraction rings, which were propagated through air and imaged in the far-field. In the photopolymer, an input beam with R < 0 generated diffraction rings with a dark center, which propagated through the medium while increasing in number, underwent filamentation, and finally transformed into a stable self-trapped beam. Diffraction rings generated under R > 0 bore a bright center and cyclically exchanged intensity with proximal diffraction rings. Statistical analyses of self-phase modulation at R ∞ identified diffraction rings, which (i) were superimposed with high order modes of a co-propagating self-trapped beam, (ii) resembled fingerprint-like rings, (iii) emerged sequentially, and (iv) possessed a bright center. Results were rationalized by combining self-phase modulation theory with the evolution of refractive index changes in the photopolymer. The findings expose a new facet of spatial self-phase modulation and the complex dynamics of diffraction rings that propagate over long distances.

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Formation and evolution of far-field diffraction patterns of divergent and convergent Gaussian beams passing through self-focusing and self-defocusing media

Cited by 106 publications

References 16 publications

Nonlinear optical responses of MoS4Cu4(PzMe3)6Cl2 under low power CW He-Ne laser excitation

Nonlinear optical responses of MoS4Cu4(PzMe3)6Cl2 under low power CW He-Ne laser excitation

Investigation of spatial self-phase modulation of silver nanoparticles in clay suspension

Diversity and slow dynamics of diffraction rings: a comprehensive study of spatial self-phase modulation in a photopolymer

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