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.     

Far field of gratings with rough strips

In this work, we analyze the far-field pattern produced by a grating made of strips with two different random roughness levels. The efficiency and shape of the diffraction orders is obtained, which are shown to depend on the statistical properties of roughness. We assume for the calculations that the grating can be used in a mobile mechanical system. A preliminary experimental approach which partially corroborates the theoretical results is also performed.     

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.     

Amplitude checker grating from one-dimensional Ronchi grating and its application to array generation

The Ronchi grating is well known for its many applications in areas such as spectroscopy, grating interferometry, and Talbot interferometry. On the other hand, the checker grating has attracted very little attention. A checker grating also self-images at equidistant planes; the separation between these planes is a quarter of the Talbot distance of a Ronchi grating of the same period. To understand this and several other features, a transition from Ronchi grating (a one-dimensional grating) to checker grating (a two-dimensional grating) has been both theoretically and experimentally studied and results are presented. Because the checker grating self-images closer to the grating and its transmittance is higher than that of a Ronchi grating, the use of its self-image planes for array generation is also emphasized.     

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.     

Influence of surface roughness on the polarimetric characteristics of a wire-grid grating polarizer

The influence of surface roughness on the polarimetric performance of a wire-grid polarizer (WGP) is numerically investigated using rigorous coupled-wave analysis over 100 random surface realizations. Surface roughness is modeled with a Gaussian surface, represented by two independent parameters: surface height deviation and correlation length of a profile. The results show that WGP performance can suffer from significant degradation as well as increased deviation with surface roughness, although the extent varies with specific parameters. The influence of roughness was also examined with respect to grating period as a WGP parameter and incident light properties, such as wavelength and angle.     

Collimation testing by use of the Lau effect coupled with moiré readout

We present an easy, simple, and inexpensive technique for checking the quality of the collimation of optical beams using the Lau effect combined with moiré readout. The experimental arrangement consists of a modified Lau-based interferometer in which a white-light incoherent source illuminates a set of two gratings. A collimating lens is placed between the two gratings such that the self-images of the second grating are formed. The third grating is positioned at one of the self-imaging planes forming moiré fringes. The type of the moiré fringe demonstrates the quality of collimation of the optical beam. The necessary theoretical background is presented and the results of our experimental investigation are reported. The technique can also be used for accurate determination of the focal length of a collimating lens using low-cost components.     

Perturbed Talbot patterns for the measurement of low particle concentrations in fluids

Behind periodic amplitude or phase objects, the object transmittance is repeated at the so-called Talbot distances. In these planes perpendicular to the propagation direction, Talbot self-images are formed. In the case of plane wave illumination, the distances between the self-images are equally spaced. A periodic pattern called optical carpet or Talbot carpet is formed along the propagation direction. We show theoretically how the presence of spherical particles (10 to 100 μm in diameter) behind gratings of 20 and 50 μm period affects the formation of Talbot carpets and Talbot self-images at 633 nm illumination wavelength. The scattering of the particles is modeled by the Fresnel diffraction of its geometrical shadow. We analytically calculate the interference of the diffraction orders of rectangular and sinusoidal amplitude gratings disturbed by the presence of particles. To verify our model, we present measurements of Talbot carpets perturbed with both opaque disks and transparent spheres, and discuss the effects for various size parameters. We present an approach to simulate the movement of particles within the Talbot pattern in real time. We simulate and measure axial and lateral particle movements within a probe volume and evaluate the effect on the signal formation in a Talbot interferometric setup. We evaluate the best system parameters in terms of grating period and particle-detector-distance for a prospective measuring setup to determine characteristics of flowing suspensions, such as particle volume concentration or particle size distribution.     

Random phase mask as a model of rough surface. Part I. Theory

There have been numerous attempts to correlate light scattering measurements with the characteristics of surface roughness. Another but considerably more difficult approach is to solve the inverse scattering problem. A number of different empirical models of surface roughness have been used to characterize surfaces including the sine grating, triangle grating (echelette), and rectangle grating. In this paper, we use, for the first time, the random phase mask model, which is a two-dimension orthogonal grating with a stochastic distribution of square “defects” with size a. We describe our calculations of the polarizing characteristics of the random phase mask and discuss the influence of each of the parameters of defects on polarizing angles. The analysis was carried out for multiple-angles-of-incidence ellipsometric measurements.     

Polarizationally Non-sensitive Pseudo-holographic Computer Reconstruction of Random Rough Surface

Abstract

The function, describing a profile of a random rough surface (RRS) is expanded in a Fourier series, i.e. the surface is considered as a composition of sinusoidal gratings. The total diffracted optical field from this RRS is a sum of the fields due to all harmonic gratings, since Kirchhoff's condition for ‘locally flat surface’ is realized for each harmonic grating at a given light wavelength and at an appropriate choice of the basic grating period. The registered s and p components of the diffracted (+1 diffraction orders of each harmonic gratings), incident and mixed optic fields are separated with an optical analyser. These fields are experimentally measured and from these values the phase and the amplitude of each grating are determined. The profile of the surface is reconstructed for s and p polarization of the light scattered field, when the electric vector of the incident light concludes an arbitrary angle with the incidence plane. The mean roughness is determined in both cases. It is shown, that both reconstructions of the profile and the determination of the mean roughness are not dependent on the polarization of the incident light. The separation of the s and p components is of great importance at the two-dimensional reconstruction, when independent of incident light polarization (s or p), the scattered optical field is always depolarized. In this case the profile of the two-dimensional surface can be easily reconstructed with s or p component of the mixing and diffracted fields.     

Modal analysis of the self-imaging phenomenon in optical fibers with an annular core

We investigate the occurrence of self-images, or Talbot images, in a spatially multimode field that propagates along an optical fiber whose core has an annular-shaped cross section. By use of full-vectorial modal analysis, we study the effect of the transverse fiber dimensions on the self-imaging properties. According to our analysis, good self-images can be expected when the fiber core is thin and the modes are far from their cutoffs. However, as the core diameter is made larger to increase the number of modes available in the imaging, the general self-imaging properties tend to deteriorate.     

Broadband extraordinary optical transmission of sub-wavelength metallic grating with parabolic wall

We present a novel periodic sub-wavelength metallic grating with parabolic walls fabricated on the silica substrate. With finite difference time domain (FDTD) simulation, we find that the grating not only can realize broadband transmission in the visible range with TM-polarized incidence, but also can achieve higher transmission efficiency with TE-polarized light incidence. The transmission properties of the proposed grating strongly depend on the geometric parameters including the period, the thickness, the entrance width, and the exit width. The transmission spectra can be manipulated by tuning the parameters of the parabolic-wall grating. Transmission line theorem and the interaction between the surface plasmon waves on the slit walls are introduced to explain broadband extraordinary optical transmission of the grating proposed in this paper.     

Light Scattering by Composite Rough Surfaces

Abstract

Light scattering from a dielectric surface with composite roughness is considered, where the surface irregularities are modelled as a superposition of two roughness types of different length scales. Geometrical optics and the Rayleigh-Rice expansion, respectively, are employed in describing the scattering from the two roughness structures. Contrary to previous work, we concentrate on bistatic cross-sections, which are calculated analytically for scattering in the plane of incidence, and resulting plots for various parameter values are shown, especially for small-scale correlation lengths of the order of the wavelength of the incident light. The main effects of the small-scale roughness are an overall decrease of the coherent reflectance and a depolarization of the scattered light, which in the plane of incidence is not present for scattering from a surface with a single scale of roughness. It is, however, concluded that scattering at the surface and volume scattering have to be taken into account in order to explain the experimentally found degrees of depolarization.     

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.     

Ultrasensitive guided-mode resonance biosensors superimposed with vertical-sidewall roughness

In this paper, we present our investigations of the effects of vertical-sidewall roughness (VSR) on guided-mode resonance (GMR) filters made of subwavelength grating for applications to ultrasensitive biosensors operated under IR illumination. We designed the spectral FWHM of the grating filter to be as narrow as possible in order to emphasize the sensitivity and VSR effects. Three types of VSR morphologies on the grating-in terms of the correlation length ξ and the rms of the maximum roughness deviation σ-were considered and evaluated. Rigorous coupled-wave analysis was then implemented to quantify the shifts in the reflective resonance peak wavelength value (PWV) of the grating filter. Our simulations show that for specific ξ values, the PWVs remain constant even if σ becomes as large as 10?nm; this indicates dramatic bandgaplike stripes, which are similar to the bandgaps observed in the band diagrams of photonic crystals in the ξ-σ diagram that we have proposed in this study. In other words, the effects of VSR on the GMR biosensor performance are insignificant when ξ is located at certain bands; therefore, this type of roughness is highly tolerable even if the linewidth of the filter is decreased to only a few tens of nanometers.     

Polychromatic Self-imaging

Abstract

The necessary condition for self-imaging in incoherent polychromatic light is derived from the McCutchen and central-slice theorems. Two types of self-imaging pupils are analysed: a pupil produced by a diffracting mask which gives self-images at positions depending on the wavelength, and an interferential pupil using a Fabry-Perot etalon which produces achromatic self-images. Experimental verifications are presented.     

Relaxation of the Talbot condition in generalized grating imaging

We can form a grating image with two gratings having different pitches with an extended light source. It is called generalized grating imaging or the Talbot-Lau effect. When we want to obtain high contrast image with pure absorption gratings or pure phase gratings, the separation between the two gratings is restricted. This corresponds to the Talbot condition. In this paper, we propose to use a combination of absorption grating and phase grating to relax the separation restriction. The theory of generalized grating imaging is applied to the system with this kind of grating. Simulations are performed for calculating contrast variation and show that the proposed system practically relaxes the Talbot condition. An experiment verifies the result of the simulation.     

Fiber Bragg grating temperature sensor with controllable sensitivity

We demonstrate a fiber Bragg grating (FBG) sensor with controllable sensitivity by connecting two metal strips that have different temperature-expansion coefficients. By changing the lengths of the metal strips we successfully controlled and improved the temperature sensitivity to 3.3 times of that of bare FBG.     

Replication of a holographic ion-etched spherical blazed grating for use at extreme-ultraviolet wavelengths: topography

We have measured the topography of a holographic ion-etched spherical blazed grating and three of its replicas using an atomic force microscope. The master grating had a roughness of less than 5 angstroms rms, a blaze angle of 2.5 degrees, and an antiblaze angle of 3.3 degrees. Thus the groove profile was more triangular than sawtooth. We find that the replication process did not significantly change the master grating. Moreover, we find no significant difference in roughness, blaze angle, or antiblaze angle between the master and its replicas before or after multilayer coating. However, bumps were observed on the gratings after coating, the cause of which is not understood. Although widespread, they occupy a relatively small fraction of the total area.     

Mueller-matrix Ellipsometry on Electroformed Rough Surfaces

Abstract

Automated Mueller-matrix ellipsometry was used to investigate the optical properties of electroformed standard rough surfaces as a function of r.m.s. surface roughness heights and angle of incidence. The r.m.s. roughness of the specimens examined varied from 50 to 12 500 nm. Six different surface finishes and 22 different specimens were examined and Mueller matrices were obtained at angles of incidence that varied from 30 to 80°. Measurements were conducted at a wavelength of 633 nm with the use of a division-of-amplitude photopolarimeter capable of simultaneously measuring all four Stokes parameters of arbitrarily polarized light. Values of ψ and Δ, the ellipsometric parameters, were derived from the measured Mueller matrices. The results demonstrate firstly the monotonic variations in the derived values of Δ with surface roughness for fixed angles of incidence, which include a ‘resonance’ effect for specimens with r.m.s. roughness heights close to the wavelength of light, secondly a systematic variation of ψ with the angle of incidence for different specimen roughness values and a reversal in these trends beyond the pseudo-Brewster angle, thirdly a monotonic variation in Δ values with the angle of incidence for different roughness values, fourthly relatively large variations in ψ values for roughness values close to the wavelength of light and fifthly relatively little change in ψ and Δ values for roughness values that greatly exceeded the wavelength of light.