Lau Effect Research Articles

Talbot-Lau devices: a reappraisal

The Talbot effect and the Lau effect have been usefully applied in optical interferometry, and for designing novel X-ray devices, as well as for implementing useful instruments for matter waves. In temporal optics, the above phenomena play a significant role for reconstructing modulated, optical short pulses that travel along a dispersive medium. We note that the Talbot-Lau devices can be spatial frequency tuned if one employs varifocal lenses as a nonmechanical technique. Thus, we identify a pertinent link between the Talbot-Lau sensors and the development of artificial muscle materials, for generating tunable lenses. Our discussion unifies seemly unrelated topics, for providing a global scope on the applications of the Talbot-Lau effect.

Investigations of Talbot and Talbot–Lau effects with various light sources

Investigations of Talbot and Talbot–Lau effects with various light sources

Tunable Lau effect: Optical frequency sweeping

For controlling the visibility of the Lau patterns, we disclose the use of a zoom system that implements a zero-throw, tunable magnification of the source grating. The zoom system implements a nonmechanical technique, for controlling the in-register condition of the Lau patterns. We show that one can increase the sharpness the Lau fringes, by exploiting the noncyclic autocorrelation of the Fourier coefficients, associated to the grating acting as spatial filter. The described technique can be thought of as a frequency sweeping technique, which tunes the visibility and the shape of the Lau fringes.

Fractional Lau effect with binary gratings: A frequency analysis

A theoretical study of the fractional Lau effect is performed for a Lau set-up equipped with binary gratings. The separations between the two gratings are chosen equal to an elementary distance divided by a positive integer. Fourier components of the observed pattern function are calculated for these distances. Also, this study shows that it is sufficient to study the Lau patterns in a restricted interval of the gratings separation. Experimental and simulation results are consistent with the theoretical predictions.

Lau Effect Using LED Array for Lithography

Illumination with LEDs is of increasing interest in imaging and lithography. In particular, compared to lasers, LEDs are temporally and spatially incoherent, so that speckle effects can be avoided by the application of LEDs. Besides, LED arrays are qualified due to their high optical output power. However, LED arrays have not been widely used for investigating optical effects, e.g., the Lau effect. In this paper, we propose the application of an LED array for realizing the Lau effect by taking into account the influence of the coherence properties of illumination on the Lau effect. Using spatially incoherent illumination with the LED array or a single LED, triangular distributed Lau fringes can be obtained. We apply the obtained Lau fringes in the optical lithography to produce analog structures. Compared to a single LED, the Lau fringes using the LED array have significantly higher intensities. Hence, the exposure time in the lithography process is largely reduced.

Coherent-mode representation of self-imaging optical fields

The coherent-mode representation is a fundamental tool that helps us understand the processes of producing and propagating optical fields. In this work, such representation for self-imaging phenomena under partially coherent illumination is presented within the frame of partial coherence theory in the space-frequency domain. Additionally, it is shown that the well-known Talbot and Lau effects are particular cases included in this new formalism. When complete coherence of the field is considered, the general expression for coherent self-imaging of optical fields is obtained (Talbot effect for both linear and circular gratings are presented); on the other hand, when an incoherent superposition of an infinite number of modes are considered, the expression to describe the Lau effect is obtained.

Full-description of integer Lau effect with arbitrary amplitude diffracting grating

A complete theoretical explanation of the integer Lau effect is presented for arbitrary transmission function of diffracting grating based on Fresnel diffraction theory and Fourier series representation of the grating function. It is shown that, in the case of amplitude diffracting grating, for some gratings separation distances which are equal to an even multiple of an elementary distance the intensity distribution function at output plane in Lau setup are similar to the squared modulus of the diffracting grating. For the gratings separation distances equal to an odd multiple of the elementary distance the output intensity functions are also similar to the squared modulus of the diffracting grating but with only its even frequencies. Binary gratings are treated as an important case. Performed simulations and experiments verify correctness of this theoretical analysis.

Specification of multiple image characteristics viewed through a grating

When a person observes an object, illuminated incoherently by a quasi-monochromatic source, through a grating, he will see more than one image. Angular positions of these images are derived in terms of wavelength, period of the grating, separation between the object and the grating, and position of the object relative to the observer. In a special case, when the object is another grating, the condition of coincidence of its multiple images is investigated. The relation derived is, to some extent, similar to that seen in the Lau effect. As a secondary outcome, it is shown that the sum of the squared modulus of the odd Fourier series coefficients for a binary grating function is equal to that of the even coefficients.

Electromagnetically induced classical and quantum Lau effect

We present two schemes of Lau effect for an object, an electromagnetically induced grating generated based on the electromagnetically induced effect. The Lau interference pattern is detected either directly in the way of the traditional Lau effect measurement with a classical thermal light being the imaging light, or indirectly and nonlocally in the way of two-photon coincidence measurement with a pair of entangled photons being the imaging light.

两个不同光栅的Lau效应

两个不同光栅的Lau效应

Second-order Lau effect with pseudo-thermal light

Lau effect is a self-imaging formed in the far field of a pair of gratings illuminated by spatially incoherent light. We report the experimental demonstration of the second-order Lau effect with incoherently pseudo-thermal light. Spatially periodic structures were nonlocally superposed giving rise to interference patterns in intensity correlation measurement. The experimental results are in agreement with the theoretical analysis. The second-order Lau effect can be well understood by the unfolded version of the experimental setup where the bucket detection can be thought as the incoherent illumination in classical Lau effect.

Two-photon Lau effect

The Lau effect is an interference phenomenon in which two transmission gratings are located in tandem and illuminated incoherently. Here we report the experimental observation of the quantum Lau effect using a two-photon entangled source. Two experimental schemes are proposed and performed. In one scheme, two gratings are nonlocally set in two different paths of two field modes. However, in the other scheme, only one grating is employed to receive the two-mode photons. In both schemes, the Lau interference patterns can be reproduced in a two-photon coincidence measurement where one photon is collected by a bucket detector.

Axial resonance of periodic patterns by using a Fresnel biprism

This paper proposes a method for the generation of high-contrast localized sinusoidal fringes with spatially noncoherent illumination and relatively high light throughput. The method, somehow similar to the classical Lau effect, is based on the use of a Fresnel biprism. It has some advantages over previous methods for the noncoherent production of interference fringes. One is the flexibility of the method, which allows the control of the fringe period by means of a simple axial shift of the biprism. Second is the rapid axial fall-off in visibility around the high-contrast fringe planes. And third is the possibility of creating fringes with increasing or with constant period as the light beam propagates. Experimental verifications of the theoretical statements are also provided.

Temporal Lau effect: a multiwavelength self-imaging phenomenon

We provide experimental evidence of the temporal analog of the spatial Lau phenomenon. This effect can be interpreted as an incoherent superposition of multiple temporal self-images. Using an array of continuous-wave lasers modulated by a single external electro-optic modulator driven by a repetitive pattern, and dispersing the light in a medium satisfying the integer Talbot self-imaging condition, each monochromatic carrier generates a temporally shifted self-image. We show experimentally that, if the wavelength separation satisfies the temporal Lau condition, the self-images appear superimposed in intensity. The requirements for this incoherent regime are analyzed. This work paves the way to achieve multiwavelength pulse trains with the ability to control the time interleaving between pulses, with potential applications for pulse shaping and high-speed sampling.

Ambiguity function analysis of pulse train propagation: applications to temporal Lau filtering

We use the periodic-signal ambiguity function for visualizing the intensity-spectrum evolution through propagation in a first-order dispersive medium. We show that the degree of temporal coherence of the optical source plays the role of a low-pass filter on the signal's ambiguity function. Based on this, we present a condition on the temporal Lau effect for filtering harmonics at fractions of the Talbot length. This result allows one to increase the repetition rate of a pulse train obtained from a sinusoidally phase-modulated CW signal.

Dynamic noise elimination on 2-D periodic structures using a liquid crystal display as an incoherent reconfigurable spatial source

Dynamic noise elimination in 2-D periodic structures is achieved with a liquid crystal display used as a 2-D incoherent reconfigurable source. The method, which is based on the Lau effect, shows that under certain conditions it can be used for correcting, in real time, defects dues to noise in 2-D periodic structures. Experimental verification of the noise elimination is presented.

Mirror-based double diffraction grating system for coherence generation: additional study of periodicity error

The Lau effect consists of generating spatial coherence by using an extended light source that illuminates a double diffraction grating system. The price of this coherence generation is a huge energy loss caused by the successive amplitude gratings, which are blocking elements. To significantly reduce the energy loss, our approach consists in using a longitudinal mirror system to collect the light rays initially blocked by the gratings of the Lau set-up. This technique offers high power efficiency and can be straightforwardly extended to provide Talbot array illuminators. The impact of periodicity error is studied and illustrations are given at the end.

Peculiarities of archimedes lau effect in saturated soils

Peculiarities of archimedes lau effect in saturated soils

Temporal Lau effect: Noncoherent regeneration of periodic pulse trains

We present an optical method for implementing the temporal Talbot effect with a spectrally incoherent optical source and a linear dispersive medium, at the first-order dispersion regime. We state the condition for achieving this effect, here denoted as the temporal Lau effect.

A low cost technique for automated measurement of focal length using Lau effect combined with Moiré readout

A low cost, accurate and relatively simple technique based on the Lau effect coupled with Moiré readout for measuring the focal length of collimating lenses is demonstrated. The method is based on defocusing the collimating lens and measuring the corresponding variation in the inclination angle of the Moiré fringes. Details of theoretical background, experimental arrangement and error analysis are presented. Experimental results of the measurements are in close agreement with the true values.