Cascade arrangement of irregular optical phased arrays

We present the principle of cascade arrangement of irregular optical phased arrays. The optical phased-array beam deflector comprises arrayed optical waveguides that are spaced irregularly and arranged in a two-stage cascade. Relations between optical path differences and corresponding center-to-center spacings among elements in each stage are found, and phase matches between the two stages are achieved. Simulation shows a wide scanning angle with dramatically suppressed sidelobes.     

Infrared Femtosecond Laser Direct-Writing Digital Volume Gratings in Fused Silica

We demonstrate that digital volume gratings can be fabricated in fused silica glass conveniently by direct femtosecond laser writing. The diffraction efficieneies of volume gratings can be essentially modulated by simply stacking and offsetting the unit structure. A series of volume gratings, which have the pitches of 5 μm and the size of 1 mm × 1 mm, have been fabricated with the writing speed of 500μm/s, with which the processing period of each grating layer could be reduced to several minutes with a 1-kHz femtoseeond laser system. Results show that the power spectrum of the diffracted waves of the volume gratings are dependent on the layer gap and layer offsetting.     

Fabrication of blazed gratings by area-coded effective medium structures

Area-coded effective medium structures (ACES) are a recently presented novel type of diffractive structure. Because of their higher stability compared to 2D binary blazed gratings, they have the potential of a broader use in micro-optics applications. The first fabrication with electron-beam lithography validate the theoretical model of blazed ACES. The measured diffraction efficiencies are in very good agreement with the values obtained from rigorous electromagnetic analysis.     

Talbot effect in metallic gratings under Gaussian illumination

Metallic gratings can be found in applications such as optical metrology. Due to their fabrication process, the surface presents a certain roughness. In this work, the effect of roughness on Talbot effect has been analyzed when the grating is illuminated with a Gaussian beam. A model based on Fresnel regime is used in order to determine the intensity distribution in the near field. Contrast of the self-images is obtained and it is found that it decreases in terms of the distance between the grating and the observation plane. When the autocorrelation function of roughness presents a Gaussian behaviour, the diffracted beams are still Gaussian although some of their properties change. For example, the width of the diffracted beams increases with respect to the case of the standard chrome on glass gratings. On the other hand, the power of each diffracted beam is independent on the roughness properties of the surface.     

Optical substrate thickness measurement system using hybrid fiber-freespace optics and selective wavelength interferometry

Proposed and demonstrated is a simple few components non-contact thickness measurement system for optical quality semi-transparent samples such as Silicon (Si) and 6H Silicon Carbide (SiC) optical chips used for designing sensors. The instrument exploits a hybrid fiber-freespace optical design that enables self-calibrating measurements via the use of confocal imaging via single mode fiber-optics and a self-imaging type optical fiber collimating lens. Data acquisition for fault-tolerant measurements is accomplished via a sufficiently broadband optical source and a tunable laser and relevant wavelength discriminating optics. Accurate sample thickness processing is achieved using the known material dispersion data for the sample and the few (e.g., 5) accurately measured optical power null wavelengths produced via the sample etalon effect. Thicknesses of 281.1 μm and 296 μm are measured for given SiC and Si optical chips, respectively.     

Replicated data-matrix array generators

The fabrication and replication of binary spot array generators using 4 and 16 levels gratings is investigated. The elements are designed using iterative Fourier transform algorithm and fabricated by electron-beam lithography. Finally elements are copied by fabricating nickel shims and using hot embossing technique. In each step the optical signals are measured and signals are characterized using bit error rate as a measure of quality. The results show that although 16 level element gives theoretically superior performance, the bit error rate is much lower (∼0.2%) for replicated 4 level elements than for their 16 level counterparts (∼9%).     

Effects of the frequency chirp on the fields of a chirped Gaussian pulse passing through a hard-edged aperture

Based on the Huygens-Fresnel diffraction integral and Fourier transform, propagation expression of a chirped Gaussian pulse passing through a hard-edged aperture is derived. Intensity distributions of the pulse with different frequency chirp in the near-field and far-field are analyzed in detail by numerical calculations. In the near-field, amplitudes of the intensity peaks generated by the modulation of the hard-edged aperture decrease with increasing the frequency chirp, which results in the improving of the beam uniformity. A physical explanation for the smoothing effect brought by increasing the frequency chirp is given. The smoothing effect is achieved not only in the pulse with Gaussian transverse profile but also in the pulse with Hermite-Gaussian transverse profile when the frequency chirp increases.     

Photonic nanojet modulation by elliptical microcylinders

The detailed analysis of localized photonic nanojets generated at the shadow side surfaces of dielectric elliptical microcylinder illuminated by a plane wave is reported. We have studied the distribution of the electric energy density within and in the vicinity outside an elliptical microcylinder by using finite-difference time-domain calculation with high resolution. The location of photonic nanojet depends on the radius ratio of the microcylinder. We have further analyzed the effect of the rotation angle of elliptical microcylinder upon the focal length of photonic nanojets. The horizontal and vertical shifts of photonic nanojet can be changed by rotating the rotation angle of elliptical microcylinder. The mechanisms of elliptical microcylinder may supply a new ultra-lens approach to distinguish nanoscale targets such as nanoparticles, optical gratings, and nanoscale surface roughness.     

Group-theoretic approach to enhancing the Fourier modal method for crossed gratings with equilateral triangular symmetry

The Fourier modal method for crossed gratings is reformulated by use of a group-theoretic approach when the grating structures have the equilateral triangular symmetry. In the new formulation, a grating problem is first decomposed into four symmetrical basis problems whose field distributions are the symmetry modes (two are nondegenerate and the other two are doubly degenerate) of the grating. Then the symmetry relations of fields in the symmetry modes are used to reduce the number of unknowns in numerical computation. After the symmetrical basis problems are solved, their solutions are superposed to get the solution of the original problem. It is shown that when the grating is at some incident mountings, the memory occupation can be saved by 2/3 and the computation time can be reduced to 1/12 to 1/13.5 of the original one for different incident cases. Numerical examples are given to illustrate the effectiveness of the new formulation and verify the improved computation efficiency.     

Rigorous electromagnetic analysis of dual-closed-surface microlens arrays

In this paper, we investigated the focal performance of the dual-closed-surface microlens arrays (DCSMAs) based on rigorous electromagnetic theory and boundary element method (BEM) in the case of TE polarization. The DCSMAs are designed with different substrate thickness and different distance between microlenses. DCSMAs designed according to different wavelengths are surveyed. The DCSMAs with different incident angles are also studied. Several focusing performance measures, such as the focal spot size, the focal position on the preset focal plane, the diffraction efficiency and the normalized transmitted power, are presented. Numerical results indicate the DCSMAs with different parameters can implement focusing beams and the focal performance of DCSMAs is easily influenced by the substrate thickness and the incident wavelength. Furthermore, the optimal thickness for the maximal diffraction efficiency of the DCSMAs is given. It is expected that the DCSMAs may be used as a parallel processing device in micro-optics systems.     

Dual spectral filters with multi-layered grating waveguide structures

Promising configurations for dual spectral filters based upon grating-waveguide structures are presented. In these configurations, the parameters of the multimode waveguide and grating are carefully chosen to achieve dual resonances at two different pre-determined wavelengths. Specifically, the grating-waveguide structure resonates for each pre-selected wavelength with a different waveguide mode. Theoretical and experimental results reveal that the resonance wavelengths can be accurately selected and that the resonance spectral bandwidths can be less than 1 nm with high contrast ratios. Received: 14 December 2000 / Published online: 9 May 2001     

Energy emission from evanescent wave and interference of opposite wave streams

A basic formula for the coefficient of energy emission from an evanescent electromagnetic wave at scattering by a dielectric structure is derived. The derived formula is interpreted in terms of interference of an incident evanescent wave with its reflection by the structure and applied to evanescent wave scattering by a 3D random medium.     

Double grating systems with one steel tape grating

Steel tape gratings are used in different metrology applications. As the period of these gratings was large (around 100μm,), its analytical study has been performed, up to date, using a geometrical approach. Nowadays, steel tape gratings can be manufactured with lower periods, around 20-40 μm, and diffractive effects must be taken into account. Also, due to the roughness of the surface, statistical techniques need to be considered to analyze their behavior. In this work, an analysis of the pseudo-imaging formation in a double grating system including one steel tape grating is performed. In particular Moiré and Lau configurations are analyzed. We have found that roughness significantly affects to Moiré configuration. However, its effect is negligible in Lau configuration. Generalized grating imaging configuration is also studied in depth. It is shown that roughness does not affect to the contrast of pseudoimages, but it modifies their depth of focus.     

Pairs of opposite decaying evanescent waves in random media and tunneling radiative transfer

A tunneling mechanism of radiative transfer through a dielectric random medium is revealed applying technique of Dyson and Bethe-Salpeter equations for electromagnetic wave multiple scattering by medium inhomogeneities (scatterers) with near fields effects in scattered fields. The mechanism consists in existing inside of a random inhomogeneity a pair of virtually opposite decaying evanescent waves whose interference results in energy flux.     

Heterodyne polarimetry for mapping defects in lithography masks

A new optical technique based on the heterodyne polarimetry is developed for fast inspection of uniformity of lithography masks in semiconductor industry. Sub-wavelength periodical structure of a sample acts as a wire-grid polarizer, making both the amplitude and phase of the reflected laser beam dependent on geometrical dimensions and optical properties of the mask pattern. The heterodyne technology based on the cross-polarized two-frequency Zeeman laser is used to simultaneously measure the amplitude and the phase of the reflected laser beam. A two-dimensional map of spatial variations can be obtained via point-by-point scanning of the sample. The technique is applicable not only to exact periodical structures like diffraction gratings, but also to double-periodical patterns consisting of large number of periodically distributed small areas of sub-wavelength gratings. Theoretical background, simulation, and experimental results are presented.     

Astigmatic telescopic transformation of a high-order optical vortex

Properties of an optical vortex light beam formed after the astigmatic telescopic transformation of a circular Laguerre-Gaussian mode are considered both theoretically and experimentally. The beam evolution is found to be in conformity with the general notions on the high-order optical vortex symmetry breakdown. Upon propagation, the asymmetric beam shows a sort of rotation of its transverse profile in accord with the energy circulation in the original circular mode; this process is described on the base of the beam intensity moments and the vortex and asymmetry components of its orbital angular momentum. An l-charged optical vortex converts into |l| secondary first-order vortices positioned on a straight line crossing the beam axis. Orientation of this straight line in the beam cross section and spatial separation of the secondary vortex cores depend on the propagation distance. Morphology (orientation and anisotropy) of all the secondary vortices is the same and depends on the propagation distance; the anisotropy can be characterized by the vortex component of the beam angular momentum. At certain distance, relative separation of secondary vortices with respect to the beam transverse size reaches its maximum that corresponds to the minimum anisotropy of the vortices. The results can be useful in the context of current research of the optical vortex arrays.     

Surface relief diffraction gratings fabricated in ZnSe by frequency doubled Nd:YAG laser micromachining

A novel and rapid laser ablation method for the fabrication of diffractive optical elements (DOE) in ZnSe that takes advantage of the relatively low intensity damage threshold of the material is presented. The structures were characterized in terms of their shape and diffraction efficiency at normal incidence under 10.6 μm radiation for TE and TM polarizations. Sample surface polishing as well as the possible effect of the melted zone and structural modification of the material around the ablated region on the power transmission capability of the grating are also discussed.     

Polarization-Independent Guided-Mode Resonance Filters under Oblique Incidence

We present the dispersion relation of guided-mode resonances in planar periodic waveguides, both for s-polarized （TF, mode） and p-polarized （TM mode） incident waves. For a fixed homogeneous planar waveguide, dispersion curves of the TE eigenmode cannot cross that of the TM eigenmode at all. That is to say, at a certain wavelength, TE and TM modes cannot be excited with the same propagation constant. Due to Bragg reflection in the planar periodic waveguide, dispersion curves of the TE leaky mode may intersect with that of the TM leaky mode in the first Brillouin zone. We employ these intersections to achieve polarization-independent guided-mode resonance filters.     

Flat-topped spectrum obtained from partially coherent hollow Gaussian Schell-model beams passing through a slit

The anomalous spectral behaviors of partially coherent polychromatic hollow Gaussian Schell-model beams (HGSMBs) diffracted by a slit are investigated. Besides spectral switches, asymmetrical dual-peak spectral split and multi-peak spectral split are observed. In the vicinity of the positions where spectral switches occur, flat-topped spectrum can be obtained, the bandwidth of which is adjustable by changing the transverse coherence width and the observation position. The flat-topped spectrum has potential application for creating probe beams in optical metrology systems and generating broadband optical sources in fiber optic sensor interface systems.