Nondiffracting beams and the self-imaging phenomenon

Szwaykowski, Piotr; Ojeda‐Castañeda, J.

doi:10.1016/0030-4018(91)90511-b

Cited by 33 publications

(9 citation statements)

References 9 publications

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“…Recent research has uncovered new invariance properties of scalar and vector waves that open new possibilities in applications related to this field. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] A notable manifestation of propagation invariance is the self imaging effect, which is characterized by a repetition of the transverse intensity distribution of the wave along the direction of propagation. General conditions for self-imaging, valid for coherent wave fields (WF's) that satisfy the Helmholtz equation, have been presented in Ref.…”

Section: Introductionmentioning

confidence: 99%

Propagation-invariant wave fields with finite energy

2000

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Propagation invariance is extended in the paraxial regime, leading to a generalized self-imaging effect. These wave fields are characterized by a finite number of transverse self-images that appear, in general, at different orientations and scales. They possess finite energy and thus can be accurately generated. Necessary and sufficient conditions are derived, and they are appropriately represented in the Gauss-Laguerre modal plane. Relations with the following phenomena are investigated: classical self-imaging, rotating beams, eigenFourier functions, and the recently introduced generalized propagation-invariant wave fields. In the paraxial regime they are all included within the generalized self-imaging effect that is presented. In this context we show an important relation between paraxial Bessel beams and Gauss-Laguerre beams. © 2000 Optical Society of America [S0740-3232(00)

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Section: Introductionmentioning

confidence: 99%

Propagation-invariant wave fields with finite energy

2000

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“…(3) and taking into account eqs. (4)(5), it follows that the complex amplitude distribution at distances Zq S a replica of the complex amplitude distribution at z = 0, as well known imaging condition H1 (Zq ) = 0 , for a GRIN medium is satisfied7.…”

Section: Self-imaging Phenomenon: Imaging Condition and Talbot Effectmentioning

confidence: 96%

“…Substituting eqs. (3)(4)(5) and (9) into eq. (8) and integrating we arrive at the following complex amplitude distribution…”

Section: Evaluation Of the Complex Amplitude Distribution In A Taperementioning

confidence: 98%

<title>GRIN optics and Talbot effect</title>

et al. 1999

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A generalization of Talbot effect to the case of a tapered GRIN medium for non-uniform illumination is considered and an analogy with the conventional lens-imaging formula is presented. Self-imaging positions are evaluated. Results on Talbot effect are applied to a particular case of a tapered GRIN medium with divergent linear taper function in order to show the dependence of self-image distances on taper function, illumination and periodic object as well as the variation of the transverse magnification with self-image number.

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“…Recently Talbot effect is also been studied in atom optics 2-3 and transverse quadratic index medium [4][5][6] In this work we study a generalization of Talbot effect to a tapered gradient index medium characterized by a transverse parabolic refractive index modulated by an axial index and whose refractive index profile is given by n2(x,z)=n[i_g2(z)x2] (1) where n0 is the index at the z optical axis and g(z) is the taper function which describes the evolution of the transverse index distribution along the z axis. Fundamental properties and many practical applications have been considered .…”

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confidence: 99%