Self-reconstruction of a distorted nondiffracting beam

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Abstract

It is shown that a nondiffracting beam disturbed by an obstacle is able to reconstruct its initial amplitude profile under free propagation. Simple theoretical explanation, numerical simulation and experimental verification of the effect are presented.

Introduction

Optical beams of Bessel-type such as so-called “nondiffracting beams” were introduced by Durnin and co-workers 1, 2. Since that time, diffraction-free propagation received great attention because explanation of the effect is important not only for applications but also for better understanding of the nature of the electromagnetic field. Ideal stationary nondiffracting beams can be obtained as exact solutions of the scalar Helmholtz equation. Applying the vectorial electromagnetic theory, they can be generalized to the exact solutions of the Maxwell equations [3]. As has been verified, nondiffracting beams represent a very wide class of fields which can propagate with various intensity profiles and polarizations 3, 4, 5, 6, 7. The propagation properties of nondiffracting beams are useful for applications in optical imaging, metrology and nonlinear optics 8, 9, 10, 11.

A very interesting property of nondiffracting and pseudo-nondiffracting beams is their self-reconstruction ability. Though the self-regeneration of the beam can be very useful for applications, relatively little attention was given to that phenomenon. Applications associated with the Bessel beam shadowing have been discussed in Ref. [12]and the self-reconstruction of the Bessel beam in nonlinear medium has been examined in Ref. [13]. In this paper, we present a simple explanation of the self-regeneration ability of the general nondiffracting beam applying Babinet's principle. It is shown that an ideal nondiffracting beam disturbed by an obstacle is able to regenerate its initial profile under free propagation. The effect is simulated numerically for both the ideal Bessel beam and the realizable solution of the paraxial wave equation of the Bessel-Gauss type [14]. Self-reconstruction ability of the zero-order Bessel beam is demonstrated experimentally.

Section snippets

Nondiffracting beam

Ideal stationary nondiffracting beams represent exact solutions of the Helmholtz equation which can be written in the form [1]U(x,y,z)=u(x,y)exp(iβz),where β is the propagation constant. In free-space, the beams are nondiffracting in the sense that their intensity profile given by I=|U|2 remains unchanged under propagation. In this article, attention is focused on the evolution of the initially nondiffracting beam whose amplitude is disturbed by an obstacle. If the complex amplitude of the

Experimental results

The self-regeneration property of pseudo-nondiffracting beams was also verified experimentally. In our experiment, the examined field is obtained by the setup shown in Fig. 4. The used axicon illuminated by a He-Ne laser produces a very good approximation to the zero-order Bessel beam. The beam obtained is strongly disturbed by an obstacle of rectangular form as shown in Fig. 5(a). Regeneration of the intensity profile at various distances behind the obstacle is illustrated in Fig. 5(b), 5(c)

Conclusion

In this paper, the self-reconstruction property of the nondiffracting and pseudo-nondiffracting beams is discussed. It is shown that an ideal nondiffracting beam can exactly reconstruct its initial intensity profile behind an obstacle of arbitrary form and size. It is also verified that self-reconstruction of the realizable pseudo-nondiffracting beam is possible only under certain conditions concerning the transverse dimension of the obstacle. The effect is verified by a simple experiment.

Acknowledgements

This work was partially supported by Grant No VS 96028 of the Ministry of Education and by Grant No 202/96/0421 of the Grant Agency of Czech Republic.

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