Talbot Phenomenon Research Articles

Talbot phenomenon in binary optical gratings under Gaussian illumination

Binary optical gratings are used in applications such as optical metrology. Due to the fact, that self-imaging phenomenon depends on the grating fill factor, in present work the effect of fill factor on Talbot image formation has been analyzed when the grating is illuminated with a Gaussian beam. A model based on Fresnel regime is used to determine the intensity distribution in the near field. Self-images are obtained under different initial beam conditions and it is found several regimes of the effect of Gaussian beam intensity distribution on the self-images are found: (I) decreasing intensity of grating slit at the beam border when Gaussian waist radius is 10 times greater than grating period, (II) transforming binary-like self-image to the cosine-like one in case when Gaussian waist radius ranges from 2 to 5 grating periods, and (III) disappearing regular grating structure when Gaussian waist radius is less than grating period. Additionally it is analyzed transform from Fresnel to Fraunhofer regime in case of Gaussian beam and effect of wavefront curvature radius value on the distance where different regimes appear.

Deep learning self-image update procedure in a wavefront sensor based on the Talbot phenomenon under Gaussian illumination

A feature-based image update procedure using machine learning is proposed to use in preprocessing of self-images in a Talbot wavefront sensor. A variant of the recurrent neural network with backpropagation, which is one of most widely applied machine learning tools, is utilized to stabilize intensity distribution in self-images in the case of an optical beam with a Gaussian profile. Once well trained, the neural network can decrease pit image shifts caused by beam intensity distribution in the case of a cosine-like grating. It is shown that based on the proposed recurrent neural network, it is possible to decrease the shift error caused by the Gaussian beam up to nine times depending on the aberration order and value. Despite the decreasing shift error, the value of the error of the restored aberration coefficient does not decrease significantly because of the feature-vector extraction method. It is shown additionally that due to the spatial spectrum wideness, the proposed self-image procedure is not applicable to binary gratings on the example of binary gratings with square pits. Adequate simulations are implemented to demonstrate the effectiveness and accuracy of the proposed approach.

Wavefront curvature restoration by a sensor based on the Talbot phenomenon under Gaussian illumination.

The present paper deals with the accuracy of wavefront curvature restoration based on pit displacement measurements in a Talbot wavefront sensor under Gaussian illumination conditions. The measurement possibilities of the Talbot wavefront sensor are theoretically investigated. A theoretical model based on the Fresnel regime is used to determine the intensity distribution in the near field, and the effect of the Gaussian field is described in terms of the spatial spectrum of the grating image. The effect of wavefront curvature on the measurement error of the Talbot sensor is discussed-particularly, the measurement of wavefront curvature is investigated.

Talbot effect with a grating of period 1 μm

Under coherent plane wave illumination, the classical Talbot effect yields exact replica of the periodic input pattern in planes periodically distributed in the free propagation direction (paraxial regime). But when the period of the object is comparable with the wavelength, the Talbot phenomenon is considered to enter its non-paraxial regime(non-paraxial Talbot effect). In this contribution an experimental and theoretical report of this phenomenon is presented at non-paraxial regime with a amplitude grating of period 1μm, using a plane wave with wavelength of 616nm. The experimental self-images are registered by a confocal microscope and these self-images are contrasted with those obtained by the theory of diffraction in representation of plane waves. Contrary to what was expected, the remarkable results obtained is that it does not present quasi-self-images phenomenon and a detailed discussion of this behavior is included.

Perfect phase-coded pulse trains generated by Talbot effect

Abstract A perfect phase sequence is a finite and ordered set of constant-amplitude complex numbers whose periodic autocorrelation vanishes at any non-zero time shift. They find multiple applications in science an engineering as phase-coded waveforms, where the sequence defines the relative phases within a burst of electromagnetic or acoustic pulses. We show how a physical propagation effect, the so-called fractional Talbot phenomenon, can be used to generate pulse trains coded according to these sequences. The mathematical description of this effect is first reviewed and extended, showing its close relationship with Gauss perfect phase sequences. It is subsequently shown how it leads to a construction of Popović’s Generalized Chirp-Like (GCL) sequences. Essentially, a set of seed pulses with prescribed amplitude and phase levels, cyclically feeds a linear and dispersive medium. At particular values of the propagation length, multiple pulse-to-pulse interference induced by dispersion passively creates the sought-for pulse trains composed of GCL sequences, with the additional property that its repetition rate has been increased with respect to the seed pulses. This observation constitutes a novel representation of GCL sequences as the result of dispersive propagation of a seed sequence, and a new route for the practical implementation of perfect phase-coded pulse waveforms using Talbot effect.

Modulation Fading in Temporal Talbot Effect

Temporal Talbot phenomenon is the time-domain counterpart of the well-known spatial Talbot (self-imaging) phenomenon, which can be used to compress or expand input pulses or multiply the pulse repetition rate. It is of great interest to study the temporal Talbot effect with modulation due to its potential applications in information transmission, in which the envelope of the input pulse sequence is modulated by a signal. In this letter, we report the modulation fading phenomenon in the temporal Talbot effect, i.e., the phenomenon that the modulation depth degrades with the increase of the Talbot order, for the first time to our knowledge. A fully analytical expression of the modulation transfer function is presented to explain this phenomenon, which shows that the modulation fading relates to the pulse width, the repetition period of the pulse sequence, and the frequency of the modulating signal as well as the Talbot order. The theoretical results are then verified by simulations. Discussion on the method to mitigate the modulation fading is also presented.

Comments on the paper “Computer simulation of Talbot phenomenon using the Fresnel integrals approach”

The program code in the paper “Computer simulation of Talbot phenomenon using the Fresnel integrals approach” (http://dx.doi.org/10.1016/j.ijleo.2016.01.175) is incompatible with MATLAB 7 and MATLAB 8. According to MATLAB documentation mfun function will be removed in a future release, besides str2double function is used.

Edge spread function of Talbot phenomenon

The paper presents and analyses the edge spread function of Talbot phenomenon—self-imaging of a periodical structure in given distances behind a template, if the template is illuminated by a plane wave. This phenomenon has many applications in optical metrology and in industry. Detailed mathematical analysis with an amplitude grating illuminated by a monochromatic plane wave is performed, and a simple relation for the calculation of the edge spread function width of Talbot imaging of Ronchi grating is shown which allows a simple analysis of the edge spread function for different grating sizes without any difficult calculations. The results bring a complete insight to the problematics and it can serve as a great theoretical background in many applications which utilize Talbot phenomenon.

Adaptive wavefront sensor based on the Talbot phenomenon.

A new adaptive method of wavefront sensing is proposed and demonstrated. The method is based on the Talbot self-imaging effect, which is observed in an illuminating light beam with strong second-order aberration. Compensation of defocus and astigmatism is achieved with an appropriate choice of size of the rectangular unit cell of the diffraction grating, which is performed iteratively. A liquid-crystal spatial light modulator is used for this purpose. Self-imaging of rectangular grating in the astigmatic light beam is demonstrated experimentally. High-order aberrations are detected with respect to the compensated second-order aberration. The comparative results of wavefront sensing with a Shack-Hartmann sensor and the proposed sensor are adduced.

Computer simulation of Talbot phenomenon using the Fresnel integrals approach

Talbot phenomenon of the finiteness grating is studied both theoretically and experimentally. The simulations can be performed in any PC using a MATLAB program developed by the author. The diffractions of finiteness periodic square aperture arrays in Fresnel fields are analyzed according to the scalar diffraction theory. The additional intensity maxima in Talbot images of the finiteness gratings are theoretically predicted to appear. The square aperture arrays are produced and the self-images of the gratings are measured successfully in the experiment. A comparative analysis of theoretical results with experimental ones is illustrated.

Femtosecond ultrashort pulse generation by addition of positive material dispersion

We demonstrate femtosecond ultrashort pulse generation by adding further positive group velocity dispersion (GVD) to compensate for the presence of positive GVD. The idea is based on the integer temporal Talbot phenomenon. The broad Raman sidebands with a frequency spacing of 10.6 THz are compressed to form a train of Fourier-transform-limited pulses by passing the sidebands through a device made of dispersive material of variable thickness.

Tunable Talbot imaging distance using an array of beam-steered metamaterial leaky-wave antennas

A tunable spatio-temporal Talbot imaging phenomenon is presented. This phenomenon is based on the radiation properties of an array of beam-steered metamaterial composite right-/left-handed leaky-wave antennas, which is excited by a modulated pulse. The scanning law property of these antennas is exploited to achieve off-axis radiation, which leads to a tunable Talbot distance, as a function of the input pulse modulation frequency. The proposed Talbot phenomenon is analyzed theoretically, taking into account the aberrations produced by higher-order terms present in the free-space transfer function. Numerical simulations confirm the self-imaging and pulse multiplication effects and their tunability capabilities as a function of frequency. Finally, the experimental results are included to confirm the phenomenon predicted.

Spatio-temporal Talbot phenomenon using metamaterial composite right/left-handed leaky-wave antennas

A spatial-temporal Talbot phenomenon, based on metamaterial composite right/left-handed (CRLH) leaky-wave antennas (LWAs), is presented. This phenomenon, reported in the microwave domain, is based on the combination of the conventional spatial monochromatic Talbot effect and the transient (polychromatic) character of the pulse radiation phenomenon in the LWA structure. When the elements of a periodic CRLH LWA array are fed simultaneously by an input pulse, the spatial beams corresponding to different temporal frequencies constructively interfere in space so as to form a self-imaged pattern constituted by narrow Talbot zones. This Talbot effect is spatial-temporal since the Talbot zones are localized both in space and time. The phenomenon is analyzed theoretically and validated numerically for the case of narrow-band pulses.

Millimeter-Wave Talbot Array Illuminators

The Talbot effect has been thoroughly examined in the optical spectrum, and has found applications, most notably, in devices such as array illuminators. This letter presents an experimental investigation of the free-space Talbot phenomenon in the millimeter-wave band. Measured results for a one- (1-D) and two-dimensional (2-D) phase grating are presented. Also, a novel cascaded grating configuration, that is promising for future applications such as spatial power combining, is investigated.

Temporal self-imaging effects: theory and application for multiplying pulse repetition rates

A time-domain equivalent of the spatial Talbot or self-imaging phenomenon appears when a periodic temporal signal propagates through a dispersive medium under first-order dispersion conditions. The effect is of great interest because it can be applied for multiplying the repetition rate of an arbitrary periodic pulse train without distorting the individual pulse features and essentially without loss of energy. In this way, pulse sequences in the terahertz regime can be generated from typical mode-locked pulse streams (with a few gigahertz repetition rates). The Talbot-based repetition-rate-multiplication technique can be implemented by using a linearly chirped fiber grating (LCFG) as the dispersive medium. As compared with other alternatives, an LCFG can be designed to provide the required bandwidth and dispersion characteristics in significantly more compact forms. Here, by using a signal-theory-based approach, we carry out a general theoretical analysis of the temporal self-imaging phenomenon and derive analytical expressions for all cases of interest (integer and fractional self-imaging effects). We also show how to design a LCFG for implementing the repetition-rate-multiplication technique and discuss the impact of nonidealities in the grating's response on the multiplication process. Results of our study are relevant from both a physical and a practical perspective.

Precision small angle measurements with a digital moiré technique

A method to measure the rotation angle of structures is presented. The method is based on the projection digital moiré technique, but instead of using a projection system we make use of the Talbot (self-imaging) phenomenon in order to produce the grating on the surface.