Polarization-dependent Talbot effect

The term "polarization-dependent Talbot effect" means that the Talbot self-imaging intensity of a high-density grating is different for TE and TM polarization modes. Numerical simulations with the finite-difference time-domain method show that the polarization dependence of the Talbot images is obvious for gratings with period d between 2 lambda and 3 lambda. Such a polarization-dependent difference for TE and TM polarization of a high-density grating of 630 lines/mm (corresponding to d/lambda=2.5) is verified through experiments with the scanning near-field optical microscopy technique, in which a He-Ne laser is used as its polarization is changed from the TE mode to the TM mode. The polarization-dependent Talbot effect should help us to understand more clearly the diffraction behavior of a high-density grating in nano-optics and contribute to wide application of the Talbot effect.     

Talbot effect and Cornu's spiral

Cornu's spiral is used in the testing and extension of a recent explanation of the Talbot effect, which occurs in the Fresnel domain. The results confirm all parts tested. They also indicate that each band of a Talbot plane is controlled primarily by light from only a few slits of the grating, contrary to earlier assumptions. Increases in slit width are found to limit the number of Talbot planes that can be observed.     

Adaptive optoelectronic signal processor with metal-semiconductor-metal photodetector arrays

Optoelectronic structures utilizing switched fiber delays and switched metal-semiconductor-metal photodetectors for signal processing over a 1.25-GHz bandwidth are presented. Fully tunable finite-impulse-response and infinite-impulse-response structures were synthesized with internal compensation for bias dependency of photodetectors. The application of such filter structures to the equalization of modal dispersion in a multimode fiber is also described.     

Talbot effect with rough reflection gratings

The Talbot effect is analyzed when steel tape gratings are used. These gratings are made on a steel substrate, and, because of the manufacture process, both levels of the grating are rough with different roughness parameters. A theoretical analysis based on Fresnel regime, which considers the statistical properties of roughness, is developed. Analytical formulas that show a decreasing exponential dependence on the intensity in terms of the distance between the grating and the observation plane are obtained, and an experimental verification is also performed.     

Two-wavelength Talbot effect and its application for three-dimensional step-height measurement

The phenomenon of Talbot self-image shift by changing the wavelength of the illuminating light is described and demonstrated experimentally. A periodic grating is illuminated by light with wavelengths lambda1 and lambda2 generated by two lasers, and the Talbot self-images are recorded along the longitudinal direction at individual wavelengths. The Talbot self-image shift due to the change in the wavelength of light is implemented for the measurement of the three-dimensional step height of a large discontinuous object without any phase ambiguity problem. Fourier-transform fringe analysis was used to determine the maximum contrast of the high-visibility bands for the measurement of the step height of the object. The main advantages of the proposed system are nonmechanical scanning, high stability because of its common path geometry, compactness, and a wide range of measurement as compared to interferometric three- dimensional profilers.     

Talbot effect interpreted by number theory.

An interpretation of the Talbot effect in a tapered gradient-index medium by number theory as the output/input relationship between the integer and the noninteger difference of position and the slope of rays is presented. Unit cell and transverse magnification for Talbot images are evaluated, and two criteria for angular magnification are defined. The study is particularized to a finite set of diffracted rays.     

Theory of image formation using the Talbot effect

The information inside each subcell of a two-dimensional periodic object is replicated throughout all the subcells of the unit cell at certain planes. An explicit expression describing the relative phase relationship among the replicated information is derived. From this expression, the wave amplitude at all the subcells caused by the interaction among the information coming from different subcells in the original object is obtained. A computer simulation of gray-level image synthesis using binary substructures and image differentiation is also given.     

Analysis of wavefront propagation using the Talbot effect

Talbot imaging is a well-known effect that causes sinusoidal patterns to be reimaged by diffraction with characteristic period that varies inversely with both wavelength and the square of the spatial frequency. This effect is treated using the Fresnel diffraction integral for fields with sinusoidal ripples in amplitude or phase. The periodic nature is demonstrated and explained, and a sinusoidal approximation is made for the case where the phase or amplitude ripples are small, which allows direct determination of the field for arbitrary propagation distance. Coupled with a straightforward method for calculating the effect in a diverging or converging beam, the Talbot method provides a useful approximation for a class of diffraction problems.     

Talbot effect by a photorefractive volume phase grating

In our proposal a light intensity distribution generated by an incoherently illuminated planar amplitude grating is projected into a photorefractive crystal. This 3D distribution is mapped as an index refractive perturbation via the photorefractive effect thereby generating a volume phase grating. The self-imaging phenomenon in the Fresnel field of this volume phase grating coherently illuminated is theoretically and experimentally analyzed. A model to simulate this volume grating that considers the 3D light intensity distribution formed in the crystal combined with the photorefractive grating formation theory is proposed. A path-integral approach to calculate the self-image patterns which account for the inhomogeneous propagation through the photorefractive grating is employed. The experimental and theoretical results show that the self-images location coincides with that of the self-images generated by planar phase grating of the same period. Moreover, the self-images visibility depends on three parameters: the exit pupil diameter of the incoherent recording optical system, the external electric field applied on the crystal, and the crystal thickness. To study the visibility behavior, a phase parameter which includes the three mentioned parameters is proposed. The self-images visibility shows the typical sinusoidal dependence found in planar phase grating. A good agreement between theoretical and experimental results is observed.     

Temporal Talbot effect in fiber gratings and its applications

We show that a temporal effect equivalent to the spatial Talbot effect (self-imaging) applies to the reflection of periodic pulse trains from linearly chirped fiber gratings (LCFG's). For specific input repetition periods the reflected signal is an exact replica of the input signal. Input repetition period values that give rise to this effect depend on the dispersion coefficient of the grating. We propose to use this effect as an alternative for dispersion measurement in LCFG's. Furthermore, by using the properties of the temporal Talbot effect, we can design linear passive devices (LCFG's) for use as frequency multipliers, able to multiply the repetition rate of a given pulse train.     

Talbot effect of a grating with different kinds of flaws

The Talbot effect of a grating with different kinds of flaws is analyzed with the finite-difference time-domain (FDTD) method. The FDTD method can show the exact near-field distribution of different flaws in a high-density grating, which is impossible to obtain with the conventional Fourier transform method. The numerical results indicate that if a grating is perfect, its Talbot imaging should also be perfect; if the grating is distorted, its Talbot imaging will also be distorted. Furthermore, we evaluate high-density gratings by detecting the near-field distribution with the scanning near-field optical microscopy technique. Experimental results are also given.     

Single-shot color digital holography based on the fractional Talbot effect

We present a method for recording on-axis color digital holograms in a single shot. Our system performs parallel phase-shifting interferometry by using the fractional Talbot effect for every chromatic channel simultaneously. A two-dimensional binary amplitude grating is used to generate Talbot periodic phase distributions in the reference beam. The interference patterns corresponding to the three chromatic channels are captured at once at different axial distances. In this scheme, one-shot recording and digital reconstruction allow for real-time measurement. Computer simulations and experimental results confirm the validity of our method.     

Position-sensitive photodetector for rotation-angle transducers

A new position-sensitive photodetector (PSPD) for photoelectric transducers of rotation angle is described, which is based on a three-layer ring sector structure. The output voltage of the PSPD is a linear function of the angle of rotation of a light-emitting diode relative to the PSPD contacts. The proposed device is highly reliable and ensures angle determination to within 7 min of arc. Rotation-angle transducers based on this PSPD are compatible with any measuring, matching, and processing equipment.

     

Talbot effect of selective reflection from a homogeneous atomic vapour

In the present work, the Talbot effect of selective reflection (SR) modified by the coupling fields is examined. It is shown that SR Talbot (SRT) patterns can be dramatically modified by the detuning, the strength and the incident angles of the coupling fields. SRT patterns at the integer and the half integer planes are similar to conventional Talbot images. However, the manifest change in fractional SRT patterns can be observed at several planes, e.g. at the quarter and the three quarters planes, the spatial frequency of those patterns is doubled comparing to that of the original output plane, and the carpets become blurring with an increasing asymmetry as the coupling fields are detuned away from the resonant transition of atoms, or as its strength increases. These peculiar Talbot patterns are mainly from a combined contribution of real and imaginary parts of source SR field modified by the coupling light. The SRT images may have potential applications in the detection of atom–surface interactionsand the processing of optical information.     

Talbot conditions,Talbot resonators,and first-order systems

A study of first-order Talbot resonators is presented. The general conditions for Talbot effect in ABCD systems are determined. These conditions are applied to the computation of the diffraction overlapping coefficients between array Gaussian emitters in a general first-order Talbot resonator. Relations on the ray-transfer matrix to generate the symmetric and the totally antisymmetric supermodes of the array are derived. These relations generalize the free-space, round-trip lengths of 1/2 and 1/4 of the Talbot distance. A new type of resonator based on a plano-convex gradient-index rod is proposed.     

Uniform theory of the Talbot effect with partially coherent light illumination

A uniform formulation for the self-imaging of gratings with any kind of partially coherent illumination is developed in terms of the cross mutual spectral density of the partial coherence theory. The formulation includes the time diffractive intensity distribution and the averaged diffractive intensity distribution at self-imaging distances and can be applied to both continuous and temporal illuminations with any kind of spectra. It is found that the averaged intensity distribution is related only to the intensity spectrum of illumination. The continuous polychromatic illumination and the ultrashort laser pulses with or without frequency chirp are then studied by a numerical stimulation. It is shown that the ultrashort laser pulse and the continuous polychromatic illuminations have similar averaged self-image distributions. Thus the Talbot effect may help in the study of the temporal and spectral characteristics of ultrashort laser pulses. An experiment with an LED is given, as well.     

Fractional Talbot effect in a tapered gradient-index medium: unit cell

A generalization of the fractional Talbot effect to the case of a tapered gradient-index medium for uniform illumination is considered. A unit cell of the fractional Talbot image contains the superposition of unit cell images of the periodic object.     

Talbot and Amici

Abstract

In an effort to make his invention of negative-positive paper photography known in Europe, William Henry Fox Talbot (1800–1877) sent photogenic drawings to several Italian scientists in 1839 and 1840. Among the recipients of specimens of Talbot's new art were Antonio Bertoloni (1775–1869), Professor of botany at the University of Bologna; Michele Tenore (1780–1861), Director of the Botanic Garden in Naples; and the renowned optician, microscopic biologist, and astronomer Giovanni Battista Amici (1786–1868) (figure 1), who was Director of the astronomical observatory of the Royal Museum of Physics and Natural History in Florence.¹