Gaussian-Schell-model beams propagating through rough gratings

In this work we analyze the near-field intensity distribution produced by a rough grating illuminated with a Gaussian-Schell-model beam. This kind of grating is formed by rough and smooth slits. Statistical techniques are used to describe the grating, and the Fresnel approach is used to perform the propagation of light. Two kinds of coherence affect the light propagation. One of them comes from the light beam, since it is not totally coherent. The other one comes from the rough topography of the grating surface. We have found that the Talbot effect is not present just after the grating, but it gradually increases. In addition, the contrast of the self-images decreases from a certain distance due to the coherence properties of the illumination beam. Then, the self-imaging process is only present between two specific distances from the grating. To corroborate the analytical results, we have performed numerical simulations for the mean intensity distribution based on the Sommerfeld-Rayleigh approach, showing their validity.     

Radio-frequency spectrum analysis of a jittery train after a second-order dispersive Talbot line

The power spectral density of the intensity of coherent Gaussian pulse trains suffering timing jitter after a dispersive line with arbitrary first- (beta(2)) and second-order (beta(3)) dispersion is computed in the small-signal approximation. Due to timing jitter noise, the initial radio-frequency spectrum shows noise bands whose bandwidth and position depend, respectively, on the jitter's standard deviation and on the jitter's pulse-to-pulse correlation. After setting the accumulated first-order dispersion to Talbot conditions, it is shown that the influence on the noise spectrum is a multiplicative factor with a multiple-bandpass structure. This factor depends on both the dispersive characteristics of the line and the pulse parameters, but not on the timing jitter's correlation properties, and represents the filtering mechanism responsible for Talbot repetition-rate multiplication. It is shown that the integer or fractional temporal Talbot effect does not worsen the timing properties of the initial train. In addition, and depending on the type of jitter correlation, the pulse width, and the total dispersion, it is shown that the temporal Talbot effect may lead to significant jitter reduction. The theory is exemplified by use of simulations. The applicability of the model to practical situations is also analyzed.     

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.     

An Entropy Approach to Light Propagation

Abstract

An entropy concept similar to that of thermodynamics and information theory is applied to locate coherent propagation planes which are interesting from an optical viewpoint. It is shown that for entropy to be stationary, intensity stationarity is a sufficient condition. Talbot self-images and Gaussian beam waists are found to satisfy entropy stationarity. Paraxial operator equations are found for other extreme entropy solutions which are not stationary in intensity.     

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.     

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.     

Theory of partial coherence for weakly periodic media

The second-order theory of partial coherence for scalar and TE or TM fields is developed for weakly periodic media, and the van Cittert-Zernike theorem of classical coherence theory is generalized for such media. The coherence properties of a wave field, generated by a quasi-homogeneous source distribution at the entrance plane of a finite weakly periodic medium, are calculated both inside such a structure and in the far field. The second-order theory of partial coherence for pulse propagation through weakly periodic media is also developed.     

Quasi-stationary plane-wave optical pulses and the van Cittert-Zernike theorem in time

We study the properties of quasi-stationary, partially coherent, plane-wave optical pulses in the space-time and space-frequency domains. A generalized van Cittert-Zernike theorem in time is derived to describe the propagation of the coherence function of quasi-stationary pulses. The theory is applied to rectangular pulses chopped from a stationary light source, and the evolution characteristics of such pulse trains with different states of coherence are discussed and illustrated with numerical examples.     

Temporal transformation of periodic incoherent ultrashort light pulses by chirped fiber gratings

The analogy between free-space propagation of optical beams and light-pulse reflection from linearly chirped fiber gratings is used to analyze the Lau effect in the temporal domain. The coherence conditions that are satisfied in the spatial domain for obtaining, at certain fixed locations, periodic fringes patterns are reformulated for guided light propagation. In this analogy, spatial periodic irradiance distributions are transformed in periodic sequences of light pulses. An optical setup is proposed to produce sharp pulse trains, with minimal distortion effects, that have repetition frequencies that are different from those associated with the input periodic optical signal. Some numerical results are given to illustrate this approach.     

Shannon entropy of partially polarized and partially coherent light with Gaussian fluctuations

We propose to analyze Shannon entropy properties of partially coherent and partially polarized light with Gaussian probability distributions. It is shown that the Shannon entropy is a sum of simple functions of the intensity, of the degrees of polarization, and of the intrinsic degrees of coherence that have been recently introduced. This analysis clearly demonstrates the contribution of partial polarization and of partial coherence to the characterization of disorder of the light provided by the Shannon entropy, which is a standard measure of randomness. We illustrate these results on two simple examples.     

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.     

Phase-space evolution of x-ray coherence in phase-sensitive imaging

X-ray coherence evolution in the imaging process plays a key role for x-ray phase-sensitive imaging. In this work we present a phase-space formulation for the phase-sensitive imaging. The theory is reformulated in terms of the cross-spectral density and associated Wigner distribution. The phase-space formulation enables an explicit and quantitative account of partial coherence effects on phase-sensitive imaging. The presented formulas for x-ray spectral density at the detector can be used for performing accurate phase retrieval and optimizing the phase-contrast visibility. The concept of phase-space shearing length derived from this phase-space formulation clarifies the spatial coherence requirement for phase-sensitive imaging with incoherent sources. The theory has been applied to x-ray Talbot interferometric imaging as well. The peak coherence condition derived reveals new insights into three-grating-based Talbot-interferometric imaging and gratings-based x-ray dark-field imaging.     

Interferometry Based on the Partially Coherent Effect Lying between the Talbot and Lau Effects

Abstract

Based on the partially coherent effect that lies between the Talbot effect and the Lau effect, a novel type of interferometry is proposed in this paper for a general configuration. The resultant interferogram is characterized by two different grating-like carriers. Such an interferometer becomes a Talbot or a Lau interferometer by adjusting the source slit to one or other of the two extremes of coherence. The partially coherent effect and the performance of the interferometer are analysed in detail in terms of the ambiguity function. Experimental results are shown to be in good agreement with the predicted intensity distributions.     

A computational study about the types of entropy generation in three different R134a ejector mixing chambers

The purpose of this investigation is to study the efficiency of a R134a ejector operating with three different mixing chambers by means of a CFD based entropy generation analysis. With the aid of the differential equation for entropy, the local entropy generation is pursued. Using this method, the areas where the irreversibilities occur are identified and geometry improvements suggested. The novelty of the numerical procedure presented herein is that the bulk entropy generation is analysed by means of four sources related with viscous dissipation and heat transfer, divided in mean and fluctuating terms. Entropy generation within the boundary layer has also been considered. The latter has proved to be small, as well as the heat transfer contribution. The fluctuating viscous dissipation accounts for more than 75% of the added entropy, being its main sources the shear layer after the nozzle exit and the shock wave trains, independently of their position.     

Numerical experiment of the Shannon entropy in partially coherent imaging by Koehler illumination to show the relationship to degree of coherence

This paper describes the Shannon entropy in a partially coherent imaging system with Koehler illumination. Numerical simulation shows that the entropy has a one-to-one relationship with the normalized mutual intensity given by the van Cittert-Zernike theorem. Analytical evaluation shows that the entropy is consistent with the definition of coherence and incoherence, which is also verified by numerical simulations. Additional numerical experiments confirm that the entropy depends on the source intensity distribution, polarization state of the source, object, and pupil. Therefore, the entropy quantitatively measures the degree of coherence of the partially coherent imaging system.     

Monte Carlo modeling of optical coherence tomography imaging through turbid media

We combine a Monte Carlo technique with Mie theory to develop a method for simulating optical coherence tomography (OCT) imaging through homogeneous turbid media. In our model the propagating light is represented by a plane wavelet; its line propagation direction and path length in the turbid medium are determined by the Monte Carlo technique, and the process of scattering by small particles is computed according to Mie theory. Incorporated into the model is the numerical phase function obtained with Mie theory. The effect of phase function on simulation is also illustrated. Based on this improved Monte Carlo technique, OCT imaging is directly simulated and phase information is recorded. Speckles, resolution, and coherence gating are discussed. The simulation results show that axial and transversal resolutions decrease as probing depth increases. Adapting a light source with a low coherence improves the resolution. The selection of an appropriate coherence length involves a trade-off between intensity and resolution.     

正火12CrlMoV钢的回火脆化及影响因素

采用示波冲击韧性试验研究了正火１２ＣｒｌＭｏＶ钢回火脆化的行为、机制及影响因素。结果表明，基体α相的时效析出行为是导致回火脆化的主要原因，峰时效阶段沉淀出细小碳化物质点对位错的强钉扎作用使基体塑性变形能力下降，质点与基体的共格、半共格关系使基体弹性畸变能较高，冲击断裂过程为理解纹萌生控制的脆性失稳断裂。     

Complex degree of coherence for partially coherent general beams in atmospheric turbulence

With the use of the general beam formulation, the modulus of the complex degree of coherence for partially coherent cosh-Gaussian, cos-Gaussian, Gaussian, annular and higher-order Gaussian optical beams is evaluated in atmospheric turbulence. For different propagation lengths in horizontal atmospheric links, the moduli of the complex degree of coherence at the source and receiver planes are examined when reference points are taken on the receiver axis and off-axis. In the on-axis case, it is observed that in propagation, the moduli of the complex degree of coherence are symmetrical and look like the intensity profile of the related coherent beam propagating in a turbulent atmosphere. For all the beams considered, the moduli of the complex degree of coherence profiles turn into Gaussian shapes beyond certain propagation lengths. In the off-axis case, the moduli of complex degree of coherence patterns become drifted at the earlier propagation lengths. Among the beams investigated, the cos-Gaussian beam is found to be almost independent of the changes in the source partial coherence parameter, and the annular beam seems to be affected the most against the variations of the source partial coherence parameter.     

Analysing the behaviour of partially coherent divergent Gaussian beams propagating through oceanic turbulence

Theoretical study of propagation behaviour of partially coherent divergent Gaussian beams through oceanic turbulence has been performed. Based on the previously developed knowledge of propagation of a partially coherent beam in atmosphere, the spatial power spectrum of the refractive index of ocean water, extended Huygens–Fresnel principle and the unified theory of coherence and polarization, analytical formulas for cross-spectral density matrix elements are derived. The analytical formulas for intensity distribution, beam width and spectral degree of coherence are determined by using cross-spectral density matrix elements. Then, the effects of some source factors and turbulent ocean parameters on statistical properties of divergent Gaussian beam propagating through turbulent water are analysed. It is found that beam’s statistical propagation behaviour is affected by both environmental and source parameters variations.     

Pulse-mode study of the quantum correlation of photons in an N-photon Dicke model

Abstract

We find the N-photon state emitted by an N-step Dicke model and provide a method to construct the field coherence functions based on it. Our effort is concentrated on the second order coherence, or the one-photon density matrix. When expressed in its canonical representation, this matrix gives the photon number occupying each ‘pulse eigenmode’. This number serves as an indicator of the correlation between photons. By studying the evolution of the one-photon density matrix we can trace the creation of such correlation during the emission. From the asymptotic solution we are able to find approximate scaling law relations between the photon degeneracy in the eigenmodes and the total number of photons involved.