Grating Lines Research Articles

Nano-Grating Fabrication Technique

In this paper, a novel nano-moiré grating fabrication technique was proposed for nanometer deformation measurement. The grating fabrication process was performed with the aid of Atomic Force Microscope (AFM) on the basis of micro-fabrication technique. On the analysis of some correlative factors of influencing grating line quality, some important experimental parameters were optimized. In this study, some parallel and cross nano-gratings with frequencies of from 10000lines/mm to 20000lines/mm were fabricated. The successful experimental results demonstrate that the nano-grating fabrication technique is feasible and also indicated that these nano-gratings with nano-moiré method can be applied to deformation measurement, which offers a nanometer sensitivity and spatial resolution.

Arrayed‐waveguide‐grating‐based correlator for optical header recognition

AbstractWe propose an incoherent optical correlator for header recognition in optical packet‐switched networks, employing two arrayed waveguide grating and waveguide delay lines. The operation is demonstrated experimentally for 4‐bit patterns at 2.5 Gb/s. Results show that the proposed optical correlator generates autocorrelation and cross‐correlation signals that can easily be recognized using a simple threshold detector. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 48: 1839–1843, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21782

Reversal of apparent rotation in the Enigma-figure with and without motion adaptation and the effect of T-junctions

We studied the time course of apparent rotation and directional reversal in Leviant’s Enigma figure. On average, periods of clockwise rotation lasted 5.0 s as opposed to 4.4 s for counter-clockwise rotation, resulting in an average reversal frequency of 6.4 within 30 s. At the beginning of a trial, clockwise rotation was perceived almost twice as often as counter-clockwise rotation. This bias could be shifted by previous adaptation to a black-and-white rotating sector disk, suggesting a neural interaction between real motion and illusory motion. We further studied Enigma-type motion on a chromatic bar superimposed onto a black-and-white linear grating. Illusory motion was strongest when the bar was oriented at 90 deg to the grating lines and became progressively weaker with a decrease in angle. This suggests that T-junctions formed by the radial rays impinging onto the colored rings of the Enigma figure are instrumental for eliciting the rotary motion and may rule out a low-level sensory origin of the illusion.

Design and Evaluation of Fundamental-Mode and Polarization-Stabilized VCSELs With a Subwavelength Surface Grating

We demonstrate 850-nm oxide-confined vertical-cavity surface-emitting lasers (VCSELs) with a locally etched subwavelength surface grating that are single-mode and polarization stable from threshold up to thermal roll-over, reaching /spl sim/4 mW of output power. The side-mode suppression ratio (SMSR) is >30 dB and the orthogonal polarization suppression ratio (OPSR) is /spl sim/20 dB. Moreover, no distortion of the far-field beam profile is observed as a result of the surface grating. Our numerical calculations show that a carefully designed VCSEL can have a high simultaneous mode and polarization selectivity without a significant increase in loss for the favored fundamental mode with polarization state perpendicular to the grating lines. This indicates characteristics such as threshold current and resonance frequency will not be notably degraded. The calculations also show a low sensitivity to variations in grating etch depth and duty cycle, which relaxes fabrication tolerances. In our experimental parametric study, where the oxide aperture diameter, surface grating diameter, and grating duty cycle were varied, the combined mode and polarization selection was investigated. For an optimum combination of oxide aperture and surface grating diameters of 4.5 and 2.5 /spl mu/m, respectively, the device is found to be single-mode and polarization stable for a broad range of grating duty cycles, from 55% to 75%, with only a small variation in other laser performances, which is in line with theory.

Neural mechanisms mediating responses to abutting gratings: Luminance edgesvs.illusory contours

The discontinuities of phase-shifted abutting line gratings give rise to perception of an "illusory contour" (IC) along the line terminations. Neuronal responses to such ICs have been interpreted as evidence for a specialized visual mechanism, since such responses cannot be predicted from conventional linear receptive fields. However, when the spatial scale of the component gratings (carriers) is large compared to the neuron's luminance passband, these IC responses might be evoked simply by the luminance edges at the line terminations. Thus by presenting abutting gratings at a series of carrier spatial scales to cat A18 neurons, we were able to distinguish genuine nonlinear responses from those due to luminance edges. Around half of the neurons (both simple and complex types) showed a bimodal response pattern to abutting gratings: one peak at a low carrier spatial frequency range that overlapped with the luminance passband, and a second distinct peak at much higher frequencies beyond the neuron's grating resolution. For those bimodally responding neurons, the low-frequency responses were sensitive to carrier phase, but the high-frequency responses were phase-invariant. Thus the responses at low carrier spatial frequencies could be understood via a linear model, while the higher frequency responses represented genuine nonlinear IC processing. IC responsive neurons also demonstrated somewhat lower spatial preference to the periodic contours (envelopes) compared to gratings, but the optimal orientation and motion direction for both were quite similar. The nonlinear responses to ICs could be explained by the same energy mechanism underlying responses to second-order stimuli such as contrast-modulated gratings. Similar neuronal preferences for ICs and for gratings may contribute to the form-cue invariant perception of moving contours.

Sequential Stretching Lithography

ABSTRACTWe developed an embossing/imprinting based nanofabrication technique, dubbed Sequential Stretching Lithography (SSL). In this process, a master pattern is imprinted into an elastomer containing a film of uncured elastomer. The elastomer is cured and then elongated to increase feature density and reduce feature size. Replication of this substrate yields a new master that can be used in further reduction steps. One-dimensional grating features with a pitch size below 200 nm were fabricated from 750 nm-pitch grating lines. This process gives us a faithful pattern miniaturization in all aspects and, as a result, a much effective control on density and dimension regulation.

Surface Relief Formation with Molecular Orientation in Photoreactive Liquid Crystalline Polymer Film

Surface relief gratings (SRG) with anisotropic gratings in photo-cross-linkable liquid crystalline (LC) polymethacrylate films comprising 4-(4-methoxycinnamoyloxy)-biphenyl (MCB) side groups were fabricated by irradiating with a linearly polarized ultraviolet (LPUV) light through a grating photomask and subsequent annealing at LC temperature range of the film. A reorientation of the mesogenic groups accompanied the molecular diffusion after the annealing, although the molecular diffusion and the reorientation direction depended on degree of the photoreaction of the mesogenic groups and the polarization (E) of LPUV light. When the degree of the photoreaction was around 7 mol%, molecules moved from illuminated area to non-illuminated area, and the molecular reorientation direction was parallel to the grating line regardless of E of LPUV light. In contrast, the diffusion direction was determined from the non-illuminated area to the illuminated region, and the molecular reorientation direction was always parallel to E of LPUV light when the degree of the photoreaction was around 20 mol%. All the fabricated SRGs showed characteristics of the polarization dependent gratings due to the surface relief formation and the molecular reorientation direction. The diffraction properties of the SRGs were good agreement with theoretical analyses.

Portable coordinate measuring tool

The ability to accurately measure the placement of features within a level is becoming increasingly critical in integrated circuit fabrication. In this article the level to be measured is patterned on a transparent wafer in poly(methylmethacrylate) (PMMA) resist to which a blue absorbing dye has been added. The dyed resist is on top of a thin partially transparent aluminum layer and is highly visible when viewed in reflected blue light in an oil immersion microscope. It is placed over a diffraction grating, which is not visible, both because the aluminum layer reflects most of the light and because the grating is far out of focus. In transmitted red laser light the grating can be seen, since various techniques may be used to increase the depth of focus of gratings in collimated monochromatic light. However, the resist pattern is not seen, because the resist is transparent to red light and the immersion oil matches its index of refraction. Measuring the separation between features reduces to measuring their location with respect to individual grating lines, and then counting the number of lines between them. The image placement accuracy of levels measured with two-dimensional gratings will be limited by the accuracy of the gratings—at present less than 2nm.

Measurement of the electro-optic coefficient of polymer thin films with better spatial resolution

A method for measuring the electro-optic coefficient of polymer films on the basis of an asymmetry Fabry–Perot cavity is introduced. The sample layer is located between two aluminium layers, which are deposited on glass substrates by thermal evaporation. This layer structure is objected to a laser beam, and a variable voltage is applied to the aluminium films resulting in a modulation of the transmitted laser power. The electro-optic coefficient γ 13 of the poled polymer film can be calculated by evaluating the Fabry–Perot equation. The spatial resolution is tested with a polymer film that was poled by a needle corona discharge in air through a metal grating with a period of 120 μm. By scanning the sample plate in the direction perpendicular to the grating lines, the spatial resolution is also demonstrated according to the spacing of the poled structure.

Electrodeposition of copper and cobalt nanostructures using self-assembled monolayer templates

Selective copper and cobalt deposition on e-beam patterned thiol self-assembled monolayers (SAMs) was studied. Gold electrodes were coated with 1-octadecanethiol (CH 3–(CH 2) 17–SH, ODT) and 1,1′-biphenyl-4-thiol (C 6H 5–C 6H 4–SH, BPT) and patterned by e-beam lithography and proximity printing using stencil masks and 300 eV electrons. Electron impact caused ODT-SAMs to lose molecular order and BPT SAMs to cross-link. In both cases the electron induced changes have a distinct influence on the electrochemical properties, which allows selective metal deposition. Selectivity is only achieved within a relatively narrow potential range which depends on the SAM type and the electrolyte. By optimizing the deposition parameters we obtained for copper and cobalt deposition a resolution of about 30 nm for single lines and 50 nm in the fabrication of line gratings. For highest resolution a small proximity effect has to be taken in account.

Smith-Purcell radiation from a charge moving above a finite-length grating

Smith-Purcell radiation (SPR), generated by an electron beam traveling above a grating, is characterized by a broad range of frequencies. The radiated wavelength depends on the angle of observation according to the SPR resonance relationship and the bandwidth is inversely proportional to the number of the grating grooves. A rigorous theoretical model of SPR from a three-dimensional bunch of relativistic electrons passing above a grating of finite length is presented by an electric-field integral equation method. The finite-length grating results are compared with the case of an infinitely long grating assumption in which periodic boundary conditions are rigorously applied and with a model based on the image-charge approximation. The SPR resonance relationship is the same in all three formalisms. Significant errors in the strength of the radiated energy are introduced by the two approximations. In particular, for gratings with less than $\ensuremath{\sim}20$ periods, the image-charge approximation and the infinitely long grating assumption result in an order of magnitude too high and too low radiated energy per groove, respectively, in the plane transverse to the grating groove lines. Numerical examples are calculated for an $\ensuremath{\sim}18\text{ }\text{ }\mathrm{MeV}$ bunch traveling above different finite-length gratings with a period of 2.5 mm.

Liquid Crystal Filled Polymer Structure SLM Devices

ABSTRACT Liquid Crystal Filled Polymer Structure (LiCFiPS) Devices consist of a polymer structure, which performs the desired spatial phase modulation of the incident light, filled with liquid crystal to permit modulation of this optical function. Fabrication of this type of device may be carried out at very low cost using established polymer embossing techniques. Devices with the liquid crystal aligned in the plane of the device and along the polymer faces have shown good quality optical switching. However regions with the liquid crystal aligned perpendicular to the grating lines show defects and inhomogeneities which give rise to spurious optical effects. To better understand the factors influencing the alignment of the liquid crystal computer modelling has been used to simulate the orientation of the liquid crystal director within such devices. The field within the device and orientation of the liquid crystal were calculated iteratively using the Landau-De Gennes form of the free-energy equation. The computational models of these devices show features that correspond well with the observed switching characteristics of actual devices. The features and changes that eradicate the defect provide insight into how the device configuration might be improved. While such devices might not offer the ultimate versatility of matrix addressed devices they do offer switchable optical devices of complex functions at very low cost.

Using the digital phase-shifting projection Moiré method and wavelet transformation to measure the deformation of a PMMA cantilever beam

In the present study, the digital projection Moiré method with wavelet transformation and phase-shifting technique has been applied to measure the out-of-plane deformation of a PMMA (polymethyl methacrylate) cantilever beam. In the digital projection Moiré method, the parallel grating lines are projected onto the specimen surface and captured by a CCD camera. The projection Moiré patterns are generated by the captured image and a virtual reference grating produced from the digital image process. Clear Moiré patterns can be obtained by the 2D Debauchies wavelet transformation. The phase-shifting method can also be realized by changing the phase of the virtual reference grating. Finally, the experimental results are compared with the calculations from the finite element method.

Geometrical aberrations of self-imaged line gratings

We analyze the properties of a self-imaging system from the point of view of aberration theory. We examine analytically and numerically the geometrical aberrations that are observed in the self-image of a parallel-line grating. We first derive the raytracing equations for determining the optical path of a self-imaging ray with the order of diffraction l . We then obtain the third- and fifth-order contributions to ray aberrations which arise from the difference between the optical paths of a self-imaging ray and of an actual ray. We show that the overall ray aberrations are entirely undercorrected. The ray aberrations approach zero as the ratio of the grating constant to the wavelength of light becomes large enough. In a case of unit magnification, no curvatures are observed in the self-imaged lines. If the magnification is bigger than unity, the light rays passing through the point in a positive or negative domain of the aperture variable contribute to the formation of the curved images. The image evaluation technique discussed here can be useful in the various applications related to the self-image formation of a parallel-line grating and it can also provide insight into the self-imaging of other periodic objects.

Subwavelength gratings fabricated on semiconductor substrates via E-beam lithography and lift-off method

We present results of the fabrication and measurements on reflective polarizers consisting of stacked bi-layer subwavelength metal gratings prepared on GaAs (100) substrates. These linear gratings were fabricated using electron-beam direct-writing lithography and the lift-off method with periods less than the wavelength of light used for measurements. At normal incidence, the polarizer reflects the light polarized perpendicular to the grating lines (transverse magnetic polarization, TM polarized) but absorbs parallel-polarized light (transverse electric polarization, TE polarized). By optimizing structural parameters, the polarization extinction ratio close to 20 has been experimentally achieved at wavelength of 650 nm.

Self-imaging pitch variation applied to focal length digital measurements

Several approaches were developed in the literature for focal length measurements. In our experimental arrangement, a collimated laser beam illuminates a test lens with a Ronchi grating placed against this lens. This procedure gives rise to a series of classical Talbot images, although magnified due to the non-parallel illumination. In this configuration, we propose to relate the self-images positions and pitches to obtain the focal length. We designed a software that helps first to precisely focus each self-image plane by a best-contrast algorithm and then to take an intensity histogram along a direction perpendicular to the grating lines. A theoretical explanation, experimental results and error analysis are presented.

Surface profiling using phase shifting Talbot interferometric technique

We implement a phase-shifting Talbot interferometric technique to measure step heights of a single-step and channel (dip) objects. Experimentally recorded interferograms include noise due to grating lines and speckles. To make the phase map, four interferograms are recorded with /2 phase shifts. To remove noise due to grating lines and speckle, interferogram data are first filtered using Fourier filtering. Height variations per profile of the objects is calculated from the phase map made using Fourier-filtered data. Results obtained from this technique are compared with the results acquired from a profile projector having a coordinate measurement facility with a resolution of 1 µm and an accuracy of ±1 µm. The results are in good agreement.

Multiscanning method for fabricating electron moiré grating

In this paper we present a multiscanning method for fabricating an electron moire grating. Many repeated scans are used, instead of a single scan. The resultant grating lines are the sum of these scans. Through this process, the grating error can be reduced from about 85% in the single-scanning method to below 5%. The experimental results show that a highly accurate grating can be fabricated in this way.

Nanostructures produced by ultraviolet laser irradiation of silicon. I. Rippled structures

One- and two-dimensional (1D and 2D) nanorippled structures produced in silicon by ultraviolet laser irradiation were investigated using atomic force and scanning electron microscopy. One- and two-beam illumination of the substrate was used to generate the nanostructures. Single-beam irradiation was done using p-polarized laser light, while the two-beam incidence was achieved employing a Lloyd’s mirror arrangement to reflect part of the beam onto the substrate. The structures were characterized by direct measurement of the ripple spacing or by measurements done on the fast Fourier transform of their atomic force microscopy (AFM) images. Under single-beam illumination, only 1D gratings were generated on the substrate surface. The grating lines were perpendicular to the projection of the electric field of the incident light on the substrate surface. For the two-beam illumination, it was very difficult to obtain the Lloyd’s mirror characteristic interference pattern due to the poor coherency of the laser employed. Nonetheless, the use of a Lloyd’s mirror not only enhanced the production of rippled structures strongly but also produced 2D gratings. The gratings generated with this arrangement are many millimeters long and cover the entire laser illuminated area. In contrast with one-beam illumination, linearly polarized light was not required to promote the rippled structures. Experimental evidence strongly suggests the following: (1) the p component of the laser light is responsible for ripple formation; (2) ripples can propagate with increasing number of pulses; and (3) the ripple structure is produced while the silicon is melted. The occurrence of melting is further supported by a computer simulation of the thermal field during the laser pulse. An estimate done using the lubrication approximation indicates that liquid is displaced from the hotter into the cooler regions by the gradient of surface tension. At angles of incidence equal or larger that 50°, the ripple spacing data indicate that incident laser light promotes the generation of plasma oscillation in the liquid silicon. These surface electromagnetic waves are responsible for the formation of ripples with lines that run parallel to the projection of the wave vector of the incident wave on the substrate surface. The simple irradiation procedure used to produce these nanostructures opens the possibility of using them as a template for ordering other nanostructures on a vast scale.

Improved outcoupling of light in organic light emitting devices, utilizing a holographic DFB-structure

In this work organic light emitting devices (OLEDs) were fabricated implementing gratings, in order to extract waveguided electroluminescence (EL). The gratings were recorded by exposing thin films of the molecular azo glass N, N′-bis (4-phenyl)-N, N′-bis [(4-phenylazo)-phenyl] benzidine (AZOPD) to holographic light patterns. The photopatterned AZOPD serves as hole transport material for devices with aluminum-tris(8-hydroxyquinoline) doped with 1% of 4-(dicyanomethylene)-2-methyl-6-(4-dimethylaminostyryl)-4H-pyran (Alq 3:DCM) as emissive/electron transport layer. The corrugated devices showed enhanced emission in the forward direction. The emitted light is polarized preferably parallel to the grating lines. In addition, we have found a doubling in the total luminance with respect to the unstructured device.