![]() ![]() Characteristic of the phase fronts of zeroth-order Bessel beams are the \(\pi\)-phase shifts from one ring to the next and the planar phase front of the central peak as shown interferometrically in Ref. They also showed 6 that the depth-of-field of a Bessel beam can be made arbitrarily larger than that of a Gaussian beam having the same spot size. showed that one can generate its reasonable approximation 5. Mathematically, the Bessel beam has an infinite number of rings, and hence, it is carrying infinite power/energy and cannot be generated in the exact sense. It is very intriguing to follow the early history and discussion regarding the term “non-diffracting” beams 4-beams whose central maxima are remarkably resistant to diffractive spreading commonly associated with all wave propagation. In the review paper of Bouchal 3, the physical concept of the non-diffracting propagation is presented and the basic properties of the non-diffracting beams are reviewed. More generally, plane waves (in rectangular coordinates), Bessel beams (in circular cylindrical coordinates), Mathieu beams (in elliptic cylindrical coordinates), and parabolic beams (in parabolic cylindrical coordinates) are exact solutions of the Helmholtz equation (see 2 and the references therein). More than 30 years ago, the first non-singular solution of the scalar Helmholtz wave equation describing non-diffracting beams, namely the zeroth-order Bessel function of the first kind, was reported by Durnin 1. The presented method is flexible, easily realizable by using a spatial light modulator, does not require any special optical elements and, thus, is accessible in many laboratories. The developed analytical model reproduces the experimental data. Moreover, at large propagation distances the quality of the generated GBBs significantly surpasses this of GBBs created by low angle axicons. The method is much more efficient as compared to this using annular slits in the back focal plane of lenses. The influences of the charge state of the TCs, the propagation distance behind the focusing lens, and the GBB profiles on the relative intensities of the peak/rings are discussed. The generated long-range GBBs are proven to have negligible transverse evolution up to 2 m and can be regarded as non-diffracting. Both the ring-shaped beam and the required phase profile can be realized by creating highly charged optical vortices by a spatial light modulator and annihilating them by using a second modulator of the same type. The phase profile required for creating zeroth-order GBBs is flat and helical for first-order GBBs with unit topological charge (TC). ![]() Starting from a Gaussian beam, the key point is the creation of a bright ring-shaped beam with a large radius-to-width ratio, which is subsequently Fourier-transformed by a thin lens. We demonstrate an alternative approach for generating zeroth- and first-order long range non-diffracting Gauss–Bessel beams (GBBs).
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |