Luis Miguel Bernardo

Fast algorithms for free-space diffraction patterns calculation

Here we present a fast algorithm for Fresnel integral calculation. Some fast algorithms using the fast Fourier transform are analysed and their performance has been checked. These methods are of easy implementation, but are only valid for a specific range of distances. Fast algorithms based on the Fractional Fourier transform allow accurate evaluation of the Fresnel integral from object to Fraunhofer domain in a single step.

ABCD MATRIX FORMALISM OF FRACTIONAL FOURIER OPTICS

The use of the ABCD matrix formalism to study fractional Fourier transforms (FRFTs) opens new perspectives on the optical implementation of the FRFTs and on the analysis and synthesis of optical systems. ABCD matrices of basic geometries implementing perfect and imperfect FRFTs are presented. The ABCD matrix method is used to demonstrate the cascading performances of FRFT elementary units and to support the established cascading rules. The matrix formalism is used to show that real and complex optical systems realize FRFTs of complex order.

Fractional Fourier transforms and optical systems

Abstract Fractional Fourier transforms of an arbitrary degree can be implemented by refractive lenses. Perfect imaging systems and correlators may be implemented by cascading fractional Fourier transformer units of the same family and fractional degree.

Sub-two-cycle pulses by soliton self-compression in highly nonlinear photonic crystal fibers

We demonstrate the direct generation of sub-two-cycle pulses by soliton self-compression of femtosecond pulses from a Ti:sapphire laser at 85 MHz using a 4.85-mm-long highly nonlinear photonic crystal fiber. Sub-nanojoule, 41 fs input pulses were compressed down to 4.6 fs without additional phase compensation schemes. To our knowledge, these are the shortest pulses obtained by soliton-effect compression of a laser oscillator. Efficient, near-dispersionless collimation of the fiber output was achieved with a simple lens and an octave-spanning double-chirped mirror pair. The full electric field of the compressed pulses was retrieved with a genetic algorithm applied to spectral and interferometric autocorrelation measurements, and the results are well described by numerical simulations.

Evaluation of the focal distance of a lens by Talbot interferometry

A simple and precise technique, based on Talbot interferometry, of measuring the focal distance of a simple lens or a compound lens system is described. To establish the foundations of the technique, properties of selfimages in free space and of their images, when formed by a lens, are first examined and experimentally demonstrated.

Antireflection structures with use of multilevel subwavelength zero-order gratings

It is known that the zero-order two-phase-level gratings with a period much smaller and a thickness much larger than the wavelength may have antireflection properties the same as appropriate dielectric layers under normal incidence. On the basis of the rigorous coupled-wave analysis method formulation, it is shown that multilevel unidimensional phase gratings, for both TE and TM polarization, are functionally equivalent to antireflection structures of multilevel dielectric layers, even if the period is close to the wavelength.

Hole–electron competition with fast and slow gratings in Bi 12 SiO 20 crystals

Two samples of nominally pure Bi(12)SiO(20) show distinct behavior in experiments of diffraction efficiency kinetics, and two-beam coupling. The results can be understood by the presence of fast and slow gratings due to electrons and holes.

From Fresnel patterns to fractional Fourier transform through geometrical optics

A convenient relation between fractional Fourier transform patterns and diffraction patterns is obtained by applying the Gauss equa- tion of geometrical optics. Thus, Fresnel and fractional domains cannot be considered as independent domains, since one is just a geometrical image of the other, providing a physical and direct connection.

Talbot self-imaging in fractional Fourier planes of real and complex orders

Abstract A study of Talbot self-imaging associated with fractional Fourier transforms (FRFTs) of real and complex orders, as realised by bulk lenses, is presented. Self-images of a periodic object, corresponding to different orders, can be observed in different FRFT planes, herein called Talbot-FRFT planes. The spatial scaling factor of the self-images is shown to be a harmonic function of the FRFT order.

Detection of colon and rectum cancers by terahertz techniques

Based on experimental analyses of colon and rectal tissues by THz spectroscopy and THz imaging, we show it is possible to distinguish between healthy and cancerous zones. Plots of the absorption coefficient and the index of refraction of the healthy and cancer affected tissues as well as 2-D transmission THz images will be presented. The experimental results will be discussed and the conditions for the tissues discrimination will be established.