Characterization of 1D diffractive optical elements by phase inversion

Abstract

We consider the feature dimensions of selected 1D diffractive optical elements (DOE) such that the Fourier transform based Gerchberg-Saxton (GS) iterative scalar phase retrieval algorithm, as calibrated by the results of vector coupled-wave theory, may be used for phase reconstruction. We consider examples only of continuous surface relief and binary (two level, not multi-level) phase-only DOE. Experimental phase distribution for rectangular and blazed gratings with ～ 5λ period agree within experimental limits with scalar theory, and, for the rectangular grating, were shown to agree also with the vector theory. Phase distributions are considered for a continuously varying linear blazed grating with 10λ periodicity, its sampled binary equivalent with minimum feature sizes of 0.1λ and for continuous linear blazed gratings with period varied from ～ 16λ to ～ 2λ. The vector calculations show an average linear dependence of the phase on grating period, but the vector curves are displaced to lower values from the scalar results by an increasing amount as the grating period is reduced. Grating performance is more influenced by the size of the grating period than the subwavelength size of the features in a binary representation. Reasonable equivalence is found in the prediction of correct phase distributions between scalar and vector theory for grating periods > ～ 5λ.     

Design of transmission blazed binary gratings for optical limiting with the form-birefringence theory

The structure of transmission blazed binary gratings for optical limiting is designed with the form-birefringence theory. This kind of grating has subwavelength features, can imitate the transmission blazed grating effectively, and has higher efficiencies than a transmission blazed grating with a subwavelength structure. The diffraction efficiencies are calculated and analyzed. For the normal incident light with 10.6 microm wavelength, the transmissivities for the designed grating at 0 degrees deviation angle for TE and TM polarizations are 0.05% and 5.09%, respectively, which are basically identical to the results of the finite-difference time-domain method. The diffraction efficiencies of the first transmitted order for TE and TM polarizations are 93.95% and 83.88%, respectively.     

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.     

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.     

Compact double-grating coupler between vertically stacked silicon-on-insulator waveguides

We analyze a compact double-grating coupler that provides coupling through radiation modes between two vertically stacked silicon-on-insulator waveguides. The grating is sufficiently strong to be considered a one-dimensional photonic bandgap structure that facilitates a short coupling length. Simulations suggest that a 29% coupling efficiency is achievable in coupling light from one waveguide to another with 12.9 microm long binary gratings. We found that the coupling efficiency is enhanced by Fabry-Perot resonance between two gratings. The coupling efficiency can be increased by use of a blazed grating. We use the eigenmode expansion method to design and optimize the binary grating coupler, and the results are verified by use of the finite-difference time-domain method.     

Diffraction based phase compensation method for phase-only liquid crystal on silicon devices in operation

A method to measure the optical response across the surface of a phase-only liquid crystal on silicon device using binary phase gratings is described together with a procedure to compensate its spatial optical phase variation. As a result, the residual power between zero and the minima of the first diffraction order for a binary grating can be reduced by more than 10 dB, from -15.98 dB to -26.29 dB. This phase compensation method is also shown to be useful in nonbinary cases. A reduction in the worst crosstalk by 5.32 dB can be achieved when quantized blazed gratings are used.     

Achromatic quarter-wave plates using the dispersion of form birefringence

We propose achromatic quarter-wave plates of a subwavelength grating structure. When the period of the grating structure is smaller than the wavelengths of the incident light, the structure is considered to be an optically anisotropic medium. The effective refractive indices strongly depend on the wavelengths, especially when the period is close to the wavelength. Using this feature, we can design a grating quarter-wave plate whose phase retardation is maintained at pi/2 for a wide wavelength range. A design method using the effective medium theory is described, and the wave plates designed were evaluated by numerical calculation with a rigorous electromagnetic grating theory. The calculation results led to the possibility of an achromatic quarter-wave plate whose retardation errors are smaller than 3 degrees for a +/-10% change in wavelength.     

On-axis beam extinction through diffraction design and analysis

To optimize the functions of the surface-relief diffractive optical elements for optical limiters and other applications, we present a systematic design and analysis with numerical illustrations of the transmission properties of different surface-relief phase gratings and Fabry-Perot elements. The spectral response and the tolerance of fabrication errors have been included. An analysis shows that the blazed grating and the echelon grating, a multilevel element as a substitute of the blazed grating, can make the on-axis transmittance very low (less than 1% with one grating) over the broad visible band with a large tolerance of fabrication errors. The results are highly significant for the design of optical-limiting devices.     

Dual-layer blazed grating fabricated by the roll-to-roll microreplication process for chromostereoscopy

In this work we present the design and fabrication of a dual-layer blazed grating (DBG) to replace a single-layer blazed grating for chromostereoscopy. Based on the physiological and physical background, we first analyze the relationship between the performance of a grating pair and color-stereo effect. The DBG is composed of two materials of different indices and fabricated upon a polyethylene terephthalate film by two steps of a roll-to-roll microreplication process. With this dual-layer design, the fabrication tolerance in the blazed facets of the grating is three times looser and more achievable as compared with that of a grating composed of single material.     

Generation of high quality Airy beams with blazed micro-optical cubic phase plates

We design and fabricate a hybrid refractive-diffractive cubic phase plate (CPP) with a combined conventional blazed grating for generating high quality Airy beams. The grating enables elimination of direct incident illumination in the reconstructed beam. The CPP is fabricated in a negative photoresist on a substrate by laser direct writing lithography with precise exposure control of gray scales. Experimentally measured intensity distribution of the Airy beam is found in good agreement with the theoretical predictions. Furthermore, self-healing and nondiffraction properties of the Airy beam are verified experimentally. The proposed method gives rise to a simple, reliable, and low-cost micro-optical element solution for the generation of high quality Airy beams.     

Achromatic system for a twisted alignment liquid crystal wavefront corrector

A twisted nematic liquid crystal wavefront corrector (TN-LCWFC) partially modulates the incident polarized light. A blazed grating may be preapplied on the TN-LCWFC to filter the unmodulated light for the purpose of stable adaptive correction. However, for broadband light, the dispersion of the blazed grating affects the image resolution. An achromatic method is presented to eliminate the dispersion of the blazed grating. Based on a prism model, we analyze the achromatic principle. An achromatic system with a conjugated blazed grating and an achromatic lens is given to eliminate the dispersion. An experiment was done with two transmitted blazed gratings so as to validate our method. Finally, a liquid crystal spatial light modulator was used as a conjugated grating to eliminate the dispersion of the blazed grating in an adaptive optics system. The results showed that the dispersion was partially compensated, and a resolvable image was achieved with a 600-700 nm wave band.     

Near-field Fourier transform polarimetry by use of a discrete space-variant subwavelength grating

We present a unique method for real-time polarization measurement by use of a discrete space-variant subwavelength grating. The formation of the grating is done by discrete orientation of the local subwavelength grooves. The complete polarization analysis of the incident beam is determined by spatial Fourier transform of the near-field intensity distribution transmitted through the discrete subwavelength dielectric grating followed by a subwavelength metal polarizer. We discuss a theoretical analysis based on Stokes-Mueller formalism, as well as on Jones calculus, and experimentally demonstrate our approach with polarization measurements of infrared radiation at a wavelength of 10.6 microm.     

Design of a nonpolarizing beam splitter based on the form birefringence of a subwavelength grating inside a glass cube

We propose a design concept to design a nonpolarizing beam splitter with a compact sandwich structure that has a subwavelength grating. The design is based on effective-medium theory and rigorous coupled-wave analysis. The simulation shows that a subwavelength grating inside a glass cube can eliminate the polarization effect.     

Noninvasive characterization of continuous-profile blazed diffraction gratings

Smooth, continuous-profile diffractive optical elements and other regular microstructures demand advanced characterization methods. Here the problem of reconstructing the profiles with optical scatterometry is addressed for the first time to our knowledge. We represent the profile of a blazed grating with an analytic Chebyshev series. The coefficients of the series are inferred from the far-field diffraction pattern, when the grating profile is illuminated with coherent light. An advanced neural-network model is used as a nonlinear statistical estimator. The reconstruction error is found to be less than 4% as normalized to the depth of the profile, even with realistic measurement errors included in the simulations.     

基于双频光栅的微分干涉相衬方法

针对传统微分干涉相衬技术对双折射性物体成像会有伪像的问题,用双频闪耀光栅取代传统微分干涉相衬的分光元件诺曼斯基棱镜,设计了一种微分干涉相衬方法.对双频闪耀光栅设计,模拟入射平面波通过它之后的光强分布,结果表明它能产生两束剪切角很小的光.用双频光栅微分干涉相衬方法对纯相位样品模拟成像,仿真结果和物体的相位轮廓一致.分析了...     

Design of binary diffraction gratings of liquid crystals in a linearly graded phase model

We report on a linearly graded phase model for the design of binary diffraction gratings of liquid crystals (LCs) associated with the periodic interfacial effect. The binary nature of the LC grating is produced by use of periodic striped domains in an alternating homeotropic and hybrid geometry. In our graded phase model the diffraction patterns and the diffracted intensities of the LC binary grating is primarily governed by three length scales: the cell thickness and two distortion parameters scaled by the grating period at two domain boundaries. The experimental data agree well with theoretical predictions made in our linearly graded phase model as well as the elastic continuum theory.     

用于分频的闪耀光栅设计及衍射行为研究

详细地介绍了用于分频的闪耀光栅设计方法 ;推导了影响元件性能的衍射效率公式 ;并研究了纵横向工艺误差对其衍射行为的影响。模拟结果显示在 8%和 5%纵横向相对误差范围内 ,该闪耀光栅具有良好的分色效果。     

Scanning methods for production of blazed relief gratings

Abstract

New methods for the production of blazed relief grating profiles using grating masks with either binary or harmonic transmittance have been developed. These methods are based on the recording of a scanning wave, properly modulated by a mask, through a grating period into photoresist. The applicability of the gratings produced by this method would be especially in the infrared or near-infrared wavelength regions in the reflection mode. These methods have been theoretically analysed and the principal ideas of the methods were experimentally verified.     

基于MEMS闪耀光栅的波分复用器的研究

针对刻划光栅因周期误差和刻线的不平整所带来的鬼线和杂散光的不足和缺陷,提出了基于MEMS闪耀光栅的波分复用器的构成方法,介绍了基于MEMS闪耀光栅的波分复用器的基本组成,介绍了MEMS闪耀光栅的工艺实现以及提高其衍射效率的方案.在LabVIEW中对MEMS闪耀光栅进行了数值仿真分析,同时在ZEMAX中对波分复用器进行了光线追迹,其结果证明了MEMS闪耀光栅应用于波分复用器中的可行性.     

On the fringing-field effect in liquid-crystal beam-steering devices

A detailed simulation of the fringing-field effect in liquid-crystal (LC)-based blazed-grating structures has been carried out. These studies are aimed at clarifying the relationship between the width of the fringing-field-broadened phase profile of the blazed grating and the LC cell thickness. This fringing-field broadening of the blazed grating's phase profile is shown to affect mostly the 2pi phase-step zone (fly-back zone) of the blazed grating. The results of the simulations carried out on the blazed-grating structure indicate two main effects of the fringing field: (1) reduction in the attainable diffraction efficiency and (2) limitation of the maximum deflection angle of the device. Both effects are shown to be directly linked to the broadening of the fly-back zone, which is shown to be proportional to the LC cell thickness.