Abstract:In this work we formulate the main properties of the gyrator operation which produces a rotation in the twisting (position -spatial frequency) phase planes. This transform can be easily performed in paraxial optics that underlines its possible application for image processing, holography, beam characterization, mode conversion and quantum information. As an example, it is demonstrated the application of gyrator transform for the generation of a variety of stable modes.

We present a method for efficient and versatile generation of beams whose intensity and phase are prescribed along arbitrary 3D curves. It comprises a non-iterative beam shaping technique that does not require solving inversion problems of light propagation. The generated beams have diffraction-limited focusing with high intensity and controlled phase gradients useful for applications such as laser micro-machining and optical trapping. Its performance and feasibility are experimentally demonstrated on several examples including multiple trapping of micron-sized particles.

Crucial benefits provided by partially coherent light microscopy such as improved spatial resolution, optical sectioning and speckle-noise suppression are exploited here to achieve 3D quantitative imaging: reconstruction of the object refractive index (RI). We present a partially coherent optical diffraction tomography technique (PC-ODT) that can be easily implemented in commercially available bright-field microscopes. We show that the high numerical apertures of the objective and condenser lenses, together with optical refocusing, are main issues for achieving fast and successful 3D RI reconstruction of weak objects. In particular, the optical refocusing is performed by a high-speed focus tunable lens mounted in front of the digital camera enabling compatibility with commercial microscopes. The technique is experimentally demonstrated on different examples: diatom cells (biosilica shells), polystyrene micro-spheres and blood cells. The results confirm the straightforward 3D-RI reconstruction of the samples providing valuable quantitative information for their analysis. Thus, the PC-ODT can be considered as an efficient and affordable alternative to coherent ODT which requires specially designed holographic microscopes.

The gyrator transform (GT) promises to be a useful tool in image processing, holography, beam characterization, mode transformation, and quantum information. We introduce what we believe to be the first flexible optical experimental setup that performs the GT for a wide range of transformation parameters. The feasibility of the proposed scheme is demonstrated on the gyrator transformation of Hermite-Gaussian modes. For certain parameters the output mode corresponds to the Laguerre-Gaussian one. © 2007 Optical Society of America OCIS codes: 070.2590, 120.4820, 200.4740, 140.3300. where r i,o = ͑x i,o , y i,o ͒ are the input and output coordinates, respectively. This transform is additive and periodic with respect to ␣. For ␣ = 0 it corresponds to the identity transform, for ␣ = / 2 it reduces to the direct/inverse Fourier transform with rotation of the coordinates at / 2, and for ␣ = the reverse transform described by the kernel ␦͑r o + r i ͒ is obtained. The applications of the GT for spacevariant filtering, hyperbolic noise reduction, and encryption have been proposed in [5]. Moreover the GT corresponds to the movement on the main meridian of the orbital Poincaré spheres [6,7] introduced by the analogy to the polarization Poincaré sphere. The GT can be considered a universal mode converter, since it allows the generation of all essentially different structurally stable Gaussian modes, which can be obtained from the Hermite-Gaussian (HG) modes by the integral canonical transforms [7]. To use the GT for optical information processing we need an optical setup performing this operation for different parameters ␣. The design for such a system has been proposed in [9]. Based on the ABCD matrix formalism for the first-order lossless optical systems, it has been shown that the coherent optical system, which contains three generalized lenses with fixed distances between them [ Fig. 1(a)] is able to perform the GT for the large range of angles ␣. The transformation angle ␣ is changed by rotation of the cylindrical lenses, which forms the generalized lenses.In this paper the first experimental implementation of the flexible optical scheme for the GT is reported. The action of this system is demonstrated on the example of the transformation of the HG modes into the helicoidal Laguerre-Gaussian (LG) ones for ␣ = ͑2k +1͒ /4 (k is an integer) passing through intermediate modes [7,8] for other values ␣.We start from a detailed description of the symmetric optical setup constructed with three generalized lenses performing the GT [ Fig. 1(a)]. Every generalized lens is a combination of two convergent thin cylindrical lenses of the same power. The action of the generalized lens leads to the quadratic phase modulation written aswhere is the wavelength, f is the focal distance of a cylindrical lens, and angle indicates the position of the axis of symmetry of the cylindrical lenses. Thus the axis of the cylindrical lenses forms angle 1 =− and 2 = − / 2 with the vertical axis OY, respectively [10,11] [see Fig. 1(b)]. The first and t...

No abstract