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.     

A planar waveguide concave grating employing dielectric mirrors

Dielectric mirrors, which yield high-reflectances on grating facets, are proposed for the design of a planar waveguide concave grating. The transfer-matrix method is used to derive an expression for the reflectance of a series of air slots and high-index stacks. The FullWAVE software, a finite difference time-domain EM solver from R-Soft, is used to evaluate the loss of the resulting 2D waveguide grating. The simulation results show that the polarization-dependent loss (PDL) is below 0.25 dB when the proposed dielectric mirror is used. The influence of the width variation of the dielectric stack is also taken into account.     

Phase diffractive optical gratings on glass substrates by laser ablation

A novel and rapid laser ablation method for the fabrication of phase diffractive gratings in low-cost glass substrates is presented. The structures are characterized in terms of their shape and physical parameters by confocal microscopy and SEM microscopy. The first-order diffraction efficiency at normal incidence under 632.8 nm wavelength is shown. The influence of the overlap factor on the period grating is studied.     

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.     

Dynamic gratings in KDP induced by piezoelectric vibrations at optical frequencies

Optical interference fringes were observed in the beam spot of the He-Ne laser transmitted through KDP. The interference fringes originate from the dynamic gratings induced by the electromagnetic field of the incident light. Diffraction fringes appear only in certain propagation directions of light through KDP. This observation is different from that monitored in α-quartz.     

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.     

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.     

A Modified full-vectorial finite-difference beam propagation method based on H-fields for optical waveguides with step-index profiles

A modified full-vectorial finite-difference beam propagation method based on H-fields in solving the guided-modes for optical waveguides with step-index profiles is described. The propagation is split into two substeps. In the first substep, the field propagates in the absence of the cross-coupling terms, and then they are evaluated and double used in the second substep. An improved six-point finite-difference scheme is constructed to approximate the cross-coupling terms along the transverse directions. By using the imaginary-distance procedure, the field patterns and the normalized propagation constants of the fundamental modes for a buried rectangular waveguide and rib waveguide are presented, and the hybrid nature of the full-vectorial guided-modes is demonstrated. Solutions are in good agreement with the benchmark results from film mode matching method, which tests the validity and utility of the present method.     

Generation of optical vortices with tunable intensity modulation

We analyze vortex properties of the optical beams generated by a spiral phase plate (SPP) which cannot modulate the phase of the incident beam range from 0 to 2π nicely, and find that the vortices have intensity modulation (IM) with central bright speckle. We construct an improved SPP to produce high quality optical vortices with definite IM. Theoretical analysis and real experiments show that this improved SPP can be used to produce optical vortices with configurable intensity modulation degree and without central bright spot.     

Anomalous behaviour in a Bragg reflection waveguide

A novel asymmetric Bragg reflection waveguide (BRW) showing anomalous dispersion characteristic is presented. The abnormal behaviour of increase of modal effective index with wavelength is primarily caused by the changes taking place in the imaginary part of the Bloch wavevector, in the periodic stratified cladding. The phase velocity and the group velocity dispersion characteristics for the waveguide have also been analyzed. Such an anomalous behaviour can find applications in the design of integrated optical devices.     

Measurement of small chirp-parameter for Mach-Zehnder-type optical modulator

A new measurement method of chirp-parameters is proposed for electro-optic (EO) intensity modulators with the Mach-Zehnder (MZ) waveguide interferometer. This method is suitably applied for the measurement of the small chirp with operation at a specific RF-frequency. To determine the chirp-parameter, optical spectrum components of the modulated light are observed with varying the relative optical phase difference between the two arms of the MZ waveguide interferometer. The chirp-parameter of 0.17, which is a value small enough for EO intensity modulation, was successfully measured by the experiment.     

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%).     

Optimization of signal-to-noise ratio in integrated planar optical interconnects packages

The signal-to-noise ratio (SNR) of integrated planar optical (IPO) board-to-board interconnections system is analyzed. The SNR is derived as a function of separation between the boards, beam spot size, optical system efficiency, receiver thermal noise, thickness of the substrate, and the angle of propagation of the beam. Based on the analyses and the results obtained it is shown that the design of optical interconnects system can be optimized for maximum SNR using at least one parameter, namely, angle of propagation.     

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.     

Confinement of infrared radiation to nanometer scales through metallic slit arrays

One-dimensional metallic slit array has been intensively studied in the spectral range from ultraviolet to near-infrared due to its enhanced transmission for transverse magnetic waves. However, the transmission enhancement is sensitive to the wavelength of incident radiation because of resonance characteristics. In this paper, we theoretically demonstrate that confining mid-infrared radiation to nanometer scales with a large transmission enhancement can be achieved from an aluminum slit array in a wavelength-insensitive manner, for potential applications in localized heating and nanothermal patterning. The Poynting vector and energy density calculated from the rigorous coupled-wave analysis (RCWA) are used to explain the strong localization of electromagnetic energy in the near-field regime. Furthermore, the localization of energy is also studied when a dielectric substrate is used to support the slit array in practical applications.     

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.     

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     

Solutions of the full- and quasi-vector wave equations based on H-field for optical waveguides by using mapped Galerkin method

The mapped Galerkin method in solving the full-vector and quasi-vector wave equations in terms of transverse magnetic fields (H-formulation) for optical waveguides with step-index profiles is described. By transforming the whole x-y space onto a unit square and using two-dimensional Fourier series expansion, the modal distributions and propagation constants for optical waveguides are obtained in the absence of boundary truncation. Results for step-index circular fiber, buried rectangular waveguide, and optical rib waveguide are presented. Solutions are good agreed with exact solutions and numerical results by using vector nonlinear iterative method, Fourier operator transform method, and vector beam propagation method.     

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.     

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.