Zeroth-order complex-amplitude modulation with dielectric Fourier-type dififractive elements

Abstract

Diffraction by a lamellar grating with slowly modulated groove width and depth is considered. By mathematical design of the diffractive microstructure the zeroth diffraction order of the carrier grating may be modulated in amplitude and phase and thereby split into some specified on-axis far-zone diffraction pattern. The noise, which in diffractive optics normally appears in the immediate neighbourhood of the signal, is shifted angularly into the surroundings of the higher diffraction orders of the carrier grating. Therefore a large frame of virtually zero intensity can be formed around the original signal without brute force optimization. This is of interest in, for example, several space-invariant optical interconnection and photonic switching schemes that employ diffractive beam-splitter elements.     

Generation and selection of laser beams represented by a superposition of two angular harmonics

Abstract

The properties of fields generated by diffractive phase-only optical elements that generate combinations of two angular harmonic fields with different harmonic indices in Fraunhofer and Fresnel regions are investigated theoretically and experimentally. Camomile shaped diffraction patterns are predicted and observed. It is shown that multi-order diffractive phase elements can be used to both generate these beams and to identify the weights of different angular harmonics in a given incident laser beam.     

Diffractive phase elements for beam shaping: a new design method

A design method based on the Yang-Gu algorithm [Appl. Opt. 33, 209 (1994)] is proposed for computing the phase distributions of an optical system composed of diffractive phase elements that achieve beam shaping with a high transfer efficiency in energy. Simulation computations are detailed for rotationally symmetric beam shaping in which a laser beam with a radially symmetric Gaussian intensity distribution is converted into a uniform beam with a circular region of support. To present a comparison of the efficiency and the performance of the designed diffractive phase elements by use of the geometrical transformation technique, the Gerchberg-Saxton algorithm and the Yang-Gu algorithm for beam shaping, we carry out in detail simulation calculations for a specific one-dimensional beam-shaping example.     

Superresolution laser beam shaping

The superresolution technique is well known for its ability to compress the central diffractive spot that is smaller than the Airy diffractive spot. In this paper, we extend the superresolution technique for different laser beam shaping. A complete set of superresolution diffractive elements is developed for the flat-top beam shaping, the single-circle beam shaping, and the novel circular Dammann grating. Five phase plates, corresponding to each of its applications, have been made by use of micro-optics technology. Experiments that are presented are in good agreement with the theoretical results. The superresolution technique presented in this paper should be highly interesting for the wide applications of laser beam shaping.     

Zone-boundary optimization for direct laser writing of continuous-relief diffractive optical elements

Enhancing the diffraction efficiency of continuous-relief diffractive optical elements fabricated by direct laser writing is discussed. A new method of zone-boundary optimization is proposed to correct exposure data only in narrow areas along the boundaries of diffractive zones. The optimization decreases the loss of diffraction efficiency related to convolution of a desired phase profile with a writing-beam intensity distribution. A simplified stepped transition function that describes optimized exposure data near zone boundaries can be made universal for a wide range of zone periods. The approach permits a similar increase in the diffraction efficiency as an individual-pixel optimization but with fewer computation efforts. Computer simulations demonstrated that the zone-boundary optimization for a 6 microm period grating increases the efficiency by 7% and 14.5% for 0.6 microm and 1.65 microm writing-spot diameters, respectively. The diffraction efficiency of as much as 65%-90% for 4-10 microm zone periods was obtained experimentally with this method.     

Analysis and optimization of fabrication of continuous-relief diffractive optical elements

The fabrication of continuous-relief diffractive optical elements by direct laser beam writing in photoresist is analyzed. The main limitation and tolerances are identified, and their influence on optical performance is quantified. Fabricated structures show rounded profile steps resulting from the convolution of the desired profile with the writing beam. This leads to a reduction in diffraction efficiency. Optimization techniques are presented to minimize this effect. Scaling the profile depth by a factor of mu > 1 increases the first-order diffraction efficiency for blazed elements. This method is also applied to suppress the zeroth diffraction order in computer-generated holograms. A nonlinear compensation of the exposure data for the Gaussian beam convolution results in an 18% increase of the diffraction efficiency for a blazed grating with a 10-mum period to a value of 79%.     

Free-space wavelength-multiplexed optical scanner demonstration

Experimental demonstration of a no-moving-parts free-space wavelength-multiplexed optical scanner (W-MOS) is presented. With fast tunable lasers or optical filters and planar wavelength dispersive elements such as diffraction gratings, this microsecond-speed scanner enables large several-centimeter apertures for subdegree angular scans. The proposed W-MOS design incorporates a unique optical amplifier and variable optical attenuator combination that enables the calibration and modulation of the scanner response, leading to any desired scanned laser beam power shaping. The experimental setup uses a tunable laser centered at 1560 nm and a 600-grooves/mm blazed reflection grating to accomplish an angular scan of 12.92 degrees as the source is tuned over an 80-nm bandwidth. The values for calculated maximum optical beam divergance, required wavelength resolution, beam-pointing accuracy, and measured scanner insertion loss are 1.076 mrad, 0.172 nm, 0.06 mrad, and 4.88 dB, respectively.     

Optimal suppression of quantization noise with pseudoperiodic multilevel phase gratings

A comprehensive two-step approach to design staircase-type multilevel diffractive phase elements (DPEs) that generate arbitrary desired diffraction patterns with the highest possible accuracy is presented. First a preliminary periodic grating with an unconstrained phase delay and an optimized nonuniform amplitude profile is designed by means of a customized iterative Fourier-transform algorithm. Then this preliminary grating is subjected to a phase quantization in which strict periodicity is forgone in favour of the best possible preservation of the shape of the power spectrum yielding a final phase only DPE with only rudimentary periodicity. An arbitrarily high similarity between the diffraction patterns of the final DPE and the preliminary grating can be achieved independently of the number D of discrete phase delay levels as long as D > or = 3. The signal-to-noise ratio of the final DPE is close to the theoretical upper limit. These properties are confirmed in computer simulations and demonstrated in optical experiments. Pseudoperiodic DPEs may have applications in optical computing, optical communication and networking, optical authentication, or coherent laser coupling.     

Compensation of beam ellipticity and astigmatism based on holographic diffractive elements recorded onto spherical substrates

Abstract

Edge emitting diode lasers with their divergent, highly elliptical and astigmatic beams in the visible spectrum are widely used in all branches of photonics. Usually the beams must be transformed into circular anastigmatic beams for the majority of applications. Holographic diffractive elements on spherical substrates are devised for transformation of beams to circular collimated beams. An off-axis holographic set-up is used to record diffractive elements into a thin photoresist layer as shallow surface-relief gratings working in reflection mode with curved and chirped grooves. The elements are destined for the diode lasers emitting at a suitable wavelength and with appropriate ellipticity and astigmatism. The performance of the elements is tested on the basis of intensity patterns and the elements produced at a focal plane on their illumination with a collimated expanded beam of a HeNe laser.     

Beam separator for high-order harmonic radiation in the 3-10 nm spectral region

We present the scheme of a beam separator for ultrashort high-order harmonic radiation below 10 nm. The system consists of a collimating mirror and two plane grazing-incidence gratings in compensated configuration. The first grating acts as the beam separator: it diffracts the extreme ultraviolet (XUV) light into the first order while reflecting the fundamental laser beam into the zero order. The diffracted light goes to a second grating that compensates both for the spectral dispersion and for the temporal broadening of the XUV ultrashort pulse caused by the diffraction at the first grating. The system can be designed for any wavelength in the 3-40 nm region. Since the gratings are operated at extreme grazing incidence, the area of the optical surface illuminated by the fundamental laser pulse is large, and therefore there is no risk of damage of the optical surfaces. The effects on the phase of the ultrashort pulse for narrowband applications are discussed.     

Design considerations of stacked multilayers of diffractive optical elements for optical network units in optical subscriber-network applications

The detailed design process and experimental results of stacked multilayer diffractive optical elements are reported for an optical network unit used in optical subscriber-network applications. The optical network unit accepts two incoming light beams of 1.3- and 1.55-mum wavelengths through a single-mode optical fiber. A laser diode is also placed for bidirectional communications. The optical network unit consists of five diffractive optical elements that perform the following functions: collimation of incoming beams, focusing of the outgoing 1.55-mum beam, 3-dB splitting of the 1.3-mum beam, focusing of the 1.3-mum beam onto the photodiode, and collimation of the light emitted from a laser diode. Possible cost reductions as a result of mass production and the ease of alignment of the stacked diffractive optical elements could be ideal for constructing low-cost optical network units.     

Iterative calculation of diffractive optical elements focusing into a three-dimensional domain and onto the surface of the body of rotation

Abstract

The present paper deals with algorithms for calculating phase diffractive elements aimed at focusing the laser light into three-dimensional domains or onto the surface of the body of rotation. The algorithms are based on the expansion of the desired transmission function of the optical element in terms of a suitable orthogonal basis. The moduli of the expansion coefficients are assumed to be pre-given, whereas the arguments are free parameters of the task. Calculational results of focusing onto the surface of a diverging and a converging cone and onto the surface of a circular cylinder are presented.     

Development of a diffraction-type optical triangulation sensor

We propose a diffraction-type optical triangulation sensor based on the diffraction theorem and the laser triangulation method. The advantage of the proposed sensor is that it obtains not only the linear displacement of a moving object but also its three angular motion errors. The developed sensor is composed mainly of a laser source, two quadrant detectors, and a reflective diffraction grating. The reflective diffraction grating can reflect the incident laser beam into several diffractive rays, and two quadrant detectors were set up for detecting the position of 0- and + 1-order diffraction rays. According to the optical triangulation relationship between the spatial incident angles of a laser beam and the output coordinates of two quadrant detectors, the displacement and the three angular motion errors of a moving object can be obtained simultaneously.     

Optical Measurement Accuracy in the Case of Non-classical Light

Abstract

The influence of optical elements on the statistical properties of the input radiation is analysed by quantum-theoretical means for a representative optical arrangement consisting of beam splitters as well as for various types of grating spectrometers. In particular non-classical light states are studied. Optimum conditions for the maintenance of the signal-to-noise ratio of sub-Poissonian input radiation are derived.     

Design of a Binary Grating with Subwavelength Features that Acts as a Polarizing Beam Splitter

A binary diffractive optical element, acting as a polarizing beam splitter, is proposed and analyzed. It behaves like a transmissive blazed grating, working on the first or the second diffraction order, depending on the polarization state of the incident radiation. The grating-phase profile required for both polarization states is obtained by means of suitably sized subwavelength groups etched in an isotropic dielectric medium. A rigorous electromagnetic analysis of the grating is presented, and numerical results concerning its performances in terms of diffraction efficiency as well as frequency and angular bandwidths are provided.     

Stray-light effects of diffractive beam-shaping elements in optical microsystems

The use of diffractive beam-shaping elements in hybrid or monolithic microsystems is investigated. Compact optical systems require diffractive structures with small grating periods for creating large deflection angles. Such elements are difficult to fabricate while a low stray-light level is maintained. In addition, because of the small geometrical dimensions and the short propagation lengths in an optomechanical microsystem, any stray light generated by the diffractive structure critically affects the overall optical performance. A model for the estimation of the interference effects between the designed and the unwanted diffraction orders is developed and applied to an example of a collimating diffractive optical element. On the basis of theoretical and experimental results, design rules for the application of diffractive beam-shaping elements in microsystems are derived.     

Two-dimensionally-periodic diffractive optical elements: limitations of scalar analysis

The range of validity of the scalar diffraction analysis is quantified for the case of two-dimensionally-periodic diffractive optical elements (crossed gratings). Three canonical classes of two-dimensionally-periodic grating structures are analyzed by using the rigorous coupled-wave analysis as well as the scalar diffraction analysis. In all cases the scalar-analysis diffraction efficiencies are compared with the exact diffraction efficiencies. The error in using the scalar analysis is then determined as a function of the grating-period(s)-to-wavelength ratio(s), the minimum feature size, the grating depth, the refractive index of the grating, the incident polarization, and the number of phase levels. The three classes of two-dimensional (2-D) unit cells are as follows: (1) a rectangular pillar, (2) an elliptical pillar, and (3) an arbitrarily pixellated multilevel 2-D unit cell that is representative of more complicated diffractive optical elements such as computer-generated holograms. In all cases a normally incident electromagnetic plane wave is considered. It is shown that the error of the scalar diffraction analysis in the case of two-dimensionally-periodic diffractive optical elements is greater than that for the corresponding one-dimensionally-periodic counterparts. In addition, the accuracy of the scalar diffraction analysis degrades with increasing refractive index, grating thickness, and asymmetry of the 2-D unit cell and with decreasing grating-period-to-wavelength ratio and feature size.     

Erratum

Abstract

Results of a photon scanning tunnelling microscopy study of the plane diffraction grating with nickel stripes on a quartz substrate are reported. The ripples in the optical images with period of 600 nm have been observed when the plane of incidence of laser beam was perpendicular to the grooves of the grating. The interference patterns for the propagating modes in far field have been detected. They are supposed to be the result of Mie scattering of evanescent wave by the elements of the diffraction grating.     

Robust design method for highly efficient beam-shaping diffractive optical elements using an iterative-Fourier-transform algorithm with soft operations

Abstract

Beam-shaping diffractive optical elements give a desired intensity distribution in the diffraction plane over areas much larger than the diffraction limited spot size. Such elements can be designed using geometrical optics methods or iterative-Fourier-transform algorithms (IFTAs). The usefulness of geometrical optics methods is considerably limited for two reasons: first the number of cases for which a solution exists is small and second the design solution, if it exists, often does not work in practice. Then IFTAs can be used. They are applicable for any desired intensity distribution in the diffraction plane with any intensity cross-section of the incident beam. The IFTA presented in this paper uses a novel set of operations that introduce a minimum disturbance of the fields while still leading to an improved performance. This makes the method robust, insensitive to stagnation and capable of iteratively distributing an increasing portion of the light in the diffraction plane into the desired areas thus leading to a high efficiency (～95%). Three design examples are given and one is also tested experimentally.     

Diffraction characteristics of optical elements designed as phase layers with cosine-profiled periodicity in the azimuthal direction

The article concerns an investigation of the Fresnel diffraction characteristics of two types of phase optical elements under Gaussian laser beam illumination. Both elements provide an azimuthal periodicity of the phase retardation. The first element possesses azimuthal cosine-profiled phase changes deposited on a plane base. The second element is a combination of the first element and a thin phase axicon. The cosine profile of the phase retardation of both diffractive elements produces an azimuthal cosine-profiled modulation on their diffractograms. It destroys the vortex characteristics of their diffraction fields.