Synthesis of nondiffracting beams in free space

Axial field shaping under high-numerical-aperture focusing

Kant reported [J. Mod. Optics 47, 905 (2000)] a formulation for solving the inverse problem of vector diffraction, which accurately models high-NA focusing. Here, Kant's formulation is adapted to the method of generalized projections to obtain an algorithm for designing diffractive optical elements (DOEs) that reshape the axial point-spread function (PSF). The algorithm is applied to design a binary phase-only DOE that superresolves the axial PSF with controlled increase in axial sidelobes. An 11-zone DOE is identified that axially narrows the PSF central lobe by 29% while maintaining the sidelobe intensity at or below 52% of the peak intensity. This DOE could improve the resolution achievable in several applications without significantly complicating the optical system.

Optimal synthesis of three-dimensional complex amplitude distributions

The synthesis of three-dimensional (3-D) light distributions is important for many applications. For example, in scanning applications it is preferable that the scanning beam preserve its characteristics over a large distance to yield elongated scanning range. It is evident that any 3-D light distribution must satisfy the wave equation or, in second-order approximation, the Fresnel diffraction formula. Thus many desirable 3-D light distributions may not be realizable. We propose a single optical element (OE) that synthesizes a physical beam within a certain 3-D region. The OE provides the optimal physical beam in comparison with a desired one in the sense of minimal mean-square error.

Implementation of pseudo-nondiffracting beams by use of diffractive phase elements

We report the experimental implementation of pseudo-nondiffracting beams by use of diffractive phase elements (DPE's). Based on the conjugate-gradient method presented in J. Opt. Soc. Am. A 15, 144-151 (1998), these DPE's are designed and fabricated on a flat quartz substrate. The experimental results show that the performance of the fabricated DPE's is in good agreement with the theoretical prediction.

Diffractive phase elements that synthesize color pseudo-nondiffracting beams

The design of diffractive phase elements (DPE's) for generating color pseudo-nondiffracting beams (PNDB's) in a multiple-wave illuminating system by the conjugate-gradient method is described. The axial-intensity distributions for dual-color PNDB's generated by the DPE's are shown. The color PNDB's behave as segmented axial-intensity distributions; in each of segments only one color persists. The sequence of wavelength components in the color PNDB's can be arbitrarily preset. Three-dimensional plots of a dual-color PNDB indicate the characteristics of a beam with high transverse resolution.

Image restoration by a novel method of parallel projection onto constraint sets

Image restoration from degraded observations and from properties that the image is supposed to satisfy has been approached by the method of projections onto convex constraint sets. Previous attempts have incorporated only partially the knowledge that we possess about the image to be restored because of difficulties in the implementation of some of the projections. In the parallel-projection algorithm presented here the a priori knowledge can be fully exploited. Moreover, the algorithm operates well even if the constraints are nonconvex and/or if the constraints have an empty intersection, without a limitation on the (finite) number of constraint sets.

Pseudonondiffracting slitlike beam and its analogy to the pseudonondispersing pulse

A new nonspreading beam is proposed for the case in which diffraction occurs only in one transverse coordinate. The beam has the shape of a pulse in one dimension and is constant in the other (slitlike shape). The intensity of the pulse's peak remains almost constant along a finite interval on the propagation axis. The proposed beam is analyzed and demonstrated experimentally. The analogy between this beam and the temporal pulse in a dispersive medium is discussed.

Control of wave-front propagation with diffractive elements

In principle, diffractive elements can be designed to control a propagating wave in three dimensions, but no general procedure has been proposed. We present an iterative method that is suitable for the design of such diffractive elements. The resulting complex amplitude distribution will approach any arbitrary requirement, as much as is permitted by basic physical principles. The problem of "nondiffracting-beam" propagation is analyzed as a special case, and intensity peaks are generated that propagate as much as 4 m with a bounded width. The generality of the method, as compared with other techniques, is beams.

Synthesis of an arbitrary axial field profile by computer-generated holograms

Computer-generated holograms are employed to design any desired intensity distribution along the propagation axis for a finite specified distance.