Fabrication and characterization of diffractive optical elements in InP for monolithic integration with surface-emitting components

We report on the fabrication and subsequent characterization of binary diffractive optical elements (DOE's) in InP for operation at 1.3 mum. Fresnel lenses of different focal lengths and a DOE that splits and focuses an incident beam into a 1 x 4 array of spots (optical fan-out) were fabricated. We realized the surface reliefs by patterning resist, using electron-beam lithography and etching with a chemically assisted ion beam, which produced well-defined patterns with smooth sidewalls and little if no surface roughness. The measured efficiency for the lenses was 36%. For the fan-out element the efficiency and the uniformity error were 26% and 30%, respectively. Spot sizes as small as 16 mum were measured.     

Fabrication of diffractive optical elements inside polymers by femtosecond laser irradiation

Bragg-type gratings were prepared by irradiation inside a series of optical polymers with femtosecond laser pulses and the preparation conditions of the grating were examined. Repeated scanning irradiation with femtosecond laser pulses formed gratings due to refractive index changes inside polymers. Among the polymers examined in the present study, polymethylpentene (PMP) showed the highest diffraction efficiency, which was an order of magnitude higher than those of other optical polymers. The density of PMP was the lowest among the polymers evaluated in the present study, and the large volume contraction based on its low density was responsible for the larger refractive index change of PMP. Furthermore, we fabricated large-area diffractive optical elements (DOEs) in PMP measuring 15 × 25 mm² by widening the scanning area.     

Optimal quantization by use of an amplitude-weighted probability-density function for diffractive optical elements

We present a method for determining the optimal quantitized phase levels for phase-only diffractive optical elements by taking into account a modified probability-density function (PDF). This modified PDF was obtained from the PDF of the phase distribution weighted by the incident amplitude distribution. We applied the proposed method to construct a multilevel Fresnel zone plate with a focal length of 8 m and a diameter of 6.2 mm upon which was incident a Gaussian beam with a 1/e width of 1.4 mm. The efficiency of a binary design was improved by 26.4% and the signal-to-noise ratio by was improved by 18.2% compared with those obtained by the uniform quantization method.     

Cost-effective mass fabrication of multilevel diffractive optical elements by use of a single optical exposure with a gray-scale mask on high-energy beam-sensitive glass

We present a method for reproducing diffractive optical elements in quantity. The method is compatible with VLSI microfabrication techniques and involves generating a gray-scale mask. The gray-scale mask is employed in an optical aligner to expose an analog photoresist on any environmentally durable substrate, e.g., glass, quartz, semiconductor, or metal, one exposure for each diffractive optical element. After copies of the mask on the photoresist are developed, many substrates can be processed in parallel in a chemically assisted ion-beam etcher to transfer the microstructures on the analog resists simultaneously onto the surfaces of the substrates.     

Design and fabrication of diffractive optical elements by use of gray-scale photolithography

Diffractive optical elements (DOEs) are key components in the miniaturization of optical systems because of their planarity and extreme thinness. We demonstrate the fabrication of DOEs by use of gray-scale photolithography with a high-energy-beam sensitive glass photomask. We obtained DOE lenses with continuous phase profiles as small as 800 microm in diameter and 5.9 microm in the outermost grating pitch by selecting a suitable optical density for each height level and optimizing the process variables. Microlenses patterned with eight levels and replicated by UV embossing with the polymer master mold showed a diffraction efficiency of 81.5%, which was sufficiently high for the devices to be used as optical pickups. The effects of deviations in diffraction efficiency between the DOE height and profile design were analyzed.     

Fabrication of a multichannel wavelength-division multiplexing-passive optical net demultiplexer with arrayed-waveguide gratings and diffractive optical elements

A novel, to our knowledge, integrated wavelength-division multiplexing-passive optical net demultiplexer that uses an arrayed-waveguide grating and diffractive optical elements is presented. The demultiplexer is used to distribute 1.3-mum wavelength signals and to multiplex an eight-channel wavelength-division multiplexer spectrum at a 1.55-mum wavelength. The device shows high functionality and good optical performance. The measured cross talk was less than -21 dB, and the 3-dB bandwidth was determined to be 97 GHz, which is close to the theoretical value of 93 GHz. Average losses of 4.5 and 8 dB were measured for the 1.3- and the 1.55-mum signals, respectively.     

Rigorous electromagnetic design of finite-aperture diffractive optical elements by use of an iterative optimization algorithm

We propose a rigorous electromagnetic design of two-dimensional and finite-aperture diffractive optical elements (DOEs) that employs an effective iterative optimization algorithm in conjunction with a rigorous electromagnetic computational model: the finite-difference time-domain method. The iterative optimization process, the finite-difference time-domain method, and the angular spectrum propagation method are discussed in detail. Without any approximation based on the scalar theory, the algorithm can produce rigorous design results, both numerical and graphical, with fast convergence, reasonable computational cost, and good design quality. Using our iterative algorithm, we designed a diffractive cylindrical lens and a 1-to-2-beam fanner for normal-incidence TE-mode illumination, thus showing that the optimization algorithm is valid and competent for rigorously designing diffractive optical elements. Concerning the problem of fabrication, we also evaluated the performance of the DOE when the DOE profile is discrete.     

Thermal embossing of mid-infrared diffractive optical elements by use of a self-processing photopolymer master

Surface-relief transmissive diffractive elements were fabricated by embossing. The master was made by lithography with a self-developing photopolymer. The highly cross-linked structure exhibited by the polymer has made possible the direct replication by thermal embossing of polyethylene substrates. Fabricated elements are meant to work with mid-infrared radiation. The influence of some process variables, related to the performance of the diffractive elements, is analyzed.     

Fabrication and simulation of diffractive optical elements with superimposed antireflection subwavelength gratings

With the aim of reducing surface reflections and increasing the diffraction efficiency we investigated the superposition of subwavelength phase gratings onto blazed phase gratings. With direct-write electron-beam lithography bare blazed gratings and blazed gratings carrying subwavelength gratings were fabricated and their optical performances compared. For TE polarization the subwavelength-carrying gratings showed a maximum diffraction efficiency of 90.6%, whereas the corresponding maximum value for the bare grating was 86.3%. The experiment was simulated with rigorous diffraction theory.     

Generating inhomogeneously polarized higher-order laser beams by use of diffractive optical elements

We propose an improved version of the earlier developed optical arrangement for generating inhomogeneously polarized laser light modes with the aid of a diffractive optical element (DOE) with carrier frequency. By eliminating lenses from the optical arrangement, we achieve the miniaturization, reduced light losses, a smaller number of parameters being matched, and a simpler system adjustment procedure. Note that all the capabilities of the previous version, namely, the universality and simple readjustment to different polarization types, are fully retained. The numerical modeling of the polarization mode combiner has made it possible to analyze its performance and capabilities. In the experiments, the quality of the resulting beams is shown to be improved. For generating higher-order cylindrical beams, a lower-order mode at the output of the polarization mode combiner is additionally transformed with a DOE that operates in the zero diffraction order, introducing radial phase changes.     

Rapid fabrication of diffractive optical elements by use of image-based excimer laser ablation

We describe a method of fabricating multilevel diffractive optics by excimer laser ablation. A portion of a chrome mask containing many patterns is illuminated by 193-nm laser light and imaged by an objective lens onto a poly(imide) substrate. Ablation of an entire single pattern is achieved in a single laser pulse. Multiple pulses are used to vary the ablation depth, and multiple patterns are used to create a variety of multilevel optics. We have successfully fabricated arrays of eight-level diffractive microlenses with varying focal lengths and decenters. The optics performed with diffraction-limited focusing and near-theoretical diffraction efficiency (92%).     

Optimal quantization method for uneven-phase diffractive optical elements by use of a modified iterative Fourier-transform algorithm

A method based on an iterative Fourier-transform algorithm (IFTA) with phase optimization for phase-only multilevel diffractive optical elements (DOEs) is presented. Phase optimization by minimizing the mean-squared error composed of an amplitude-weighted probability-density function is performed in the IFTA iterations to ensure that the wavefront difference is minimized and thus to improve the DOEs' performance. Using the proposed method, we obtained a small standard deviation of diffraction efficiency of 20 uneven-phase DOEs, showing that DOEs with high diffraction efficiency did not vary significantly with the initial conditions. The simulation results of even- and uneven-phase four-level DOEs designed by use of direct and stepwise quantization IFTA methods are compared.     

Fabrication of two-dimensional photonic crystals with controlled defects by use of multiple exposures and direct write

We have developed an approach for relatively rapid and easy fabrication of large-area two-dimensional (2-D) photonic crystal structures with controlled defects in the lattice. The technique is based on the combination of two lithographic steps in UV-sensitive SU-8 photoresist. First, multiple exposures of interference fringes are used in combination with precise rotation of the sample to define a 2-D lattice of holes. Second, a strongly focused UV laser beam is used to define line-defect waveguides by localized exposure in the recorded but not yet developed lattice from the first step. After development, the mask is transferred into a GaAs substrate with dry etching in chemically assisted ion-beam etching.     

Efficient encoding algorithms for computer-aided design of diffractive optical elements by the use of electron-beam fabrication

One of the general requirements of a computer-aided design system is the existence of efficient (in data size and running time) algorithms that are generally reliable for the broadest range of design instances. The restricted data formats of the electron-beam machines impose difficulties in developing algorithms for the design of diffractive optical elements (DOE's) and computer-generated holograms (CGH's). Issues that are related to the development of CGH algorithms for e-beam fabrication of DOE's and CGH's are discussed. We define the problems the CGH algorithms need to solve, then introduce general curve drawing algorithms for the e-beam data generation of diffractive optical components. An efficient algorithm for general aspherical DOE's is proposed. Actual design and fabrication examples are also presented.     

Directional narrowing of the diffractive pattern through a combination of spherical and spiral optical elements within a single aperture

The intensity pattern produced by the zero-order Bessel beam can be squeezed along certain directions if it interferes with the Bessel beam of a higher order. The concept of directional narrowing can be extended onto the zone plates by the division of the aperture into a set of concentric annuli; within some of the apertures the phase function of the spherical optical element is substituted or supplemented by the spiral optical element. The proposed approach is verified by the numerical simulation of the interference of Bessel beams, linear axicons, and spherical zone plates of zero order and second order.     

Iterative optimization of phase-only diffractive optical elements based on a lenslet array

We describe the design of Fourier-type phase-only array generators. The numerical optimization employs the Fienup algorithm, where the parageometric design of the phase retardation profile, with the form of a lenslet array, is used as the initial guess of the optimization process. This approach provides designs with high performance that can be obtained with comparatively low computing effort. This is particularly true for elements generating large spot arrays. For symmetric reconstruction fields, the optimized phase profile typically has the same symmetry as that for the reconstruction field and can be easily unwrapped.     

Implementation of ordinary and extraordinary beams interference by application of diffractive optical elements

Abstract

We apply diffractive optical elements in problems of transformation of Bessel beams in a birefringent crystal. Using plane waves expansion we show a significant interference between the ordinary and extraordinary beams due to the energy transfer in the orthogonal transverse components in the nonparaxial mode. A comparative analysis of the merits and lack of diffractive and refractive axicons in problems of formation non-paraxial Bessel beams has shown the preferability of diffractive optics application in crystal optics. The transformation of uniformly polarised Bessel beams in the crystal of Iceland spar in the nonparaxial mode by application of a diffractive axicon is investigated numerically and experimentally.     

Fabrication of microprisms for planar optical interconnections by use of analog gray-scale lithography with high-energy-beam-sensitive glass

For an integrated free-space optical interconnection system we suggest the use of microprisms to achieve large coupling angles at low loss. Prisms were fabricated in photoresist and quartz glass by analog lithography. High-energy-beam-sensitive glass was used as the gray-tone mask. Optical testing of the prisms shows acceptable surface quality and high efficiency (95%).     

Design and analysis of a diffractive optical filter for use in an optoelectronic error-diffusion neural network

The design, fabrication, experimental characterization, and system-performance analysis of a diffractive optical implementation of an error-diffusion filter for use in digital image halftoning is reported. A diffractive optical filter was fabricated as an eight-level phase element that diffuses the quantization error nonuniformly in both the weighting and the spatial dimensions, according to a prescribed algorithm. Ten identical diffractive elements were fabricated on ten different wafers and subsequently characterized experimentally. A detailed error analysis including both fabrication and instrumentation errors was carried out to quantify the performance of the fabrication process as well as the expected system performance of the filters. Halftone system performance was evaluated by use of the experimental filter's performance and both quantitative and qualitative performance metrics. The results of this analysis demonstrate that multiple identical copies of a diffractive optical filter can be produced with sufficient accuracy that no loss in the halftoning system performance results.