Iterative algorithm for the design of free-space diffractive optical elements for fiber coupling

We present a design method based on the Gerchberg-Saxton algorithm for the design of high-performance diffractive optical elements. Results from this algorithm are compared with results from simulated annealing and the iterative Fourier-transform algorithm. The element performance is comparable with those designed by simulated annealing, whereas the design time is similar to the iterative Fourier-transform method. Finally, we present results for a demanding beam-shaping task that was beyond the capabilities of either of the traditional algorithms. The element performances demonstrate greater than 85% efficiency and less than 2% uniformity error.     

Laser beam shaping with polarization-selective diffractive phase elements

A new scheme for converting a Gaussian irradiance profile beam on the input plane into a uniform irradiance profile beam on the output plane is presented based on polarization-selective diffractive phase elements. The relevant elements were designed by use of the simulated annealing method. The simulation design shows that the shaping quality is substantially improved and is much better than that obtained with traditional diffractive phase elements.     

Effects of the spatial frequency composition of the target pattern and the number of quantization levels in diffractive beam shaper design

A mathematical model is derived, and numerical simulation is analyzed for laser beam shaping by using multilevel phase-only diffractive optical elements (DOEs). We used the simulated annealing algorithm to design the beam shapers. The result has an essential effect on the diffractive pattern quality caused by the spatial frequency composition of target patterns for the same incident gaussian beam size and target pattern area. The root mean square error between the diffractive and target patterns is smaller for the target patterns with lower spatial frequencies. Moreover, the effect of spatial frequency composition can be relaxed for the cases of larger incident gaussian beam size. In addition, finer quality control of a diffraction pattern can be obtained by increasing the number of quantization levels at the DOEs.     

Comparison of simulated quenching algorithms for design of diffractive optical elements

We compare the performance of very fast simulated quenching; generalized simulated quenching, which unifies classical Boltzmann simulated quenching and Cauchy fast simulated quenching; and variable step size simulated quenching. The comparison is carried out by applying these algorithms to the design of diffractive optical elements for beam shaping of monochromatic, spatially incoherent light to a tightly focused image spot, whose central lobe should be smaller than the geometrical-optics limit. For generalized simulated quenching we choose values of visiting and acceptance shape parameters recommended by other investigators and use both a one-dimensional and a multidimensional Tsallis random number generator. We find that, under our test conditions, variable step size simulated quenching, which generates each parameter's new states based on the acceptance ratio instead of a certain theoretical probability distribution, produces the best results. Finally, we demonstrate experimentally a tightly focused image spot, with a central lobe 0.22-0.68 times the geometrical-optics limit and a relative sidelobe intensity 55%-60% that of the central maximum intensity.     

Importance of Initial Distribution for Iterative Calculation of Quantized Diffractive Elements

Abstract

The significance of the initial distribution for three iterative calculation techniques of diffractive elements; simulated annealing, direct binary search, and Fourier transform algorithm, is investigated. Depending on the initial distributions, convergence problems may occur. Techniques to calculate special initial distributions for the three methods are described: these significantly improve the capabilities of the iterative techniques.     

Energy control by linking individual patterns to self-repeating diffractive optical elements

In general, as diffractive optical elements formed by use of self-repeating patterns possess beneficial characteristics such as scratch resistance, low design effort, ease of fabrication, and natural formation of large panels, an efficient design methodology that was developed with a modified preserving-the-best strategy of genetic algorithms is presented. Both genetic algorithms and simulated annealing are examined by the Markov-chain stochastic process to create the insight needed to use these two heuristic algorithms efficiently. It was found that adding the preserving-the-best strategy to traditional genetic algorithms guarantees the possibility of locating the global optimum. Combining this sufficient and necessary condition for locating a global optimum for genetic algorithms with the built-in chromosome crossover searching mechanism and its neighborhood identification makes this newly developed genetic algorithm an effective method for designing diffractive optical elements. In our study, a prototype was fabricated based on our case study with the modified genetic algorithm. The performance of this prototype was measured and analyzed. Experimental results are shown to agree well with theoretical predictions.     

Integrated diffractive andrefractive elements for spectrum shaping

Diffractive elements can be designed for spectrum shaping in the Fourier or Fresnel plane by iterative methods. It is necessary to use a Fourier lens and the wavelength for which the diffractive elements were designed to get the required spectrum shaping at the Fourier plane. Using a different wavelength will cause chromatic aberration. We deal with the combination of refractive and diffractive elements and two or more different diffractive elements on the same element to get appropriate beam shaping of light sources with a multiple spectral output. Simulations are preformed that transform the profile of a He-Ne laser with a Nd:YAG laser source, and shape the trapezoidal beam profile of an excimer laser into a Gaussian beam is also considered.     

Genetic local search algorithm for optimization design of diffractive optical elements

We propose a genetic local search algorithm (GLSA) for the optimization design of diffractive optical elements (DOE's). This hybrid algorithm incorporates advantages of both genetic algorithm (GA) and local search techniques. It appears better able to locate the global minimum compared with a canonical GA. Sample cases investigated here include the optimization design of binary-phase Dammann gratings, continuous surface-relief grating array generators, and a uniform top-hat focal plane intensity profile generator. Two GLSA's whose incorporated local search techniques are the hill-climbing method and the simulated annealing algorithm are investigated. Numerical experimental results demonstrate that the proposed algorithm is highly efficient and robust. DOE's that have high diffraction efficiency and excellent uniformity can be achieved by use of the algorithm we propose.     

Design methods for space-variant optical interconnections to achieve optimum power throughput

Optoelectronic systems based on space-variant optics give great freedom to the system designer in terms of interconnect topologies. One feature of space-variant systems is that they can achieve a high interconnect density. However, this density is achieved by having large arrays of diffractive elements with very small apertures relative to the propagation distances involved. Thus diffraction losses from the finite apertures can significantly affect power throughput for these types of systems, regardless of the diffractive efficiencies of the optical elements involved. Therefore it is desirable that this loss be minimized. We present several space-variant optical interconnect design methods (for both one-to-one and fan-out interconnects) and compare them in terms of power throughput for diffraction-limited interconnect distances. Both numerical simulations and experimental results are presented.     

遗传算法用于衍射光学元件的优化设计

提出了一种基于遗传算法的衍射光学元件优化设计方法;在衍射光学元件设计中遗传算法运行参数对遗传算法性能有一定的影响:采用较大的群体规模,遗传算法越容易获得最优解;交叉算子越大,遗传算法全局搜索能力越强;选择算子对遗传算法的影响不是太大;如果要进一步提高解的精度,可选取较大的终止代数。数值计算结果表明,用遗传算法优化设计的衍射光学元件,其误差小于 5.2%,衍射效率达到 91.2%。遗传算法很适合衍射光学元件的优化设计。     

Low-coherence interferometry with synthesis of coherence function

Synthesis of a coherence function by manipulation of the spectral phase of low-coherent light with a segmented liquid-crystal phase modulator and its application in a low-coherence interferometry are described. Effects of space-time coupling caused at diffractive gratings and second-order dispersion at the spatial light modulator on the coherence function synthesis are theoretically and experimentally verified. Various coherence functions can be shaped with phase-only masks designed by simulated annealing optimization algorithm. We utilized this technique for a novel optical low-coherence reflectometry without any mechanical movement for scanning optical delay.     

High-efficiency production of propagation-invariant spot arrays

Tailoring of the transverse intensity profiles of propagation-invariant optical fields is considered. The design of diffractive elements capable of realizing such fields by Fourier synthesis is discussed. High-efficiency realization of finite-aperture approximations of the constructed fields is demonstrated in a system consisting of two multilevel diffractive elements. The first element is a diffractive toroidal lens, which focuses the incident field into a ring pattern. The second diffractive element, located at the focal plane of the first element, introduces the phase modulation necessary to realize the desired transverse intensity profile behind a separate collimating lens. The influence of the fabrication errors of the diffractive elements on the fidelity of the propagation-invariant spot array is simulated, and system-integration aspects based on substrate-mode planar-integrated optics are considered.     

初始状态对形变及热处理后工业纯钛组织和力学性能的影响

利用Gleeble 3800热模拟试验机对退火态和淬火态的工业纯钛进行多道次平面应变压缩,研究不同初始状态经过压缩变形和热处理后的组织和性能的演变规律。通过流变曲线、组织观察和显微硬度分析表明:退火态相对于淬火态变形组织较为均匀且变形抗力低10~25MPa,显微硬度也较低。经过不同工艺热处理后,工业纯钛淬火态的组织不均匀性未得到消除且出现混晶现象,淬火态与退火态的显微硬度趋于一致。     

Algorithm based on rigorous coupled-wave analysis for diffractive optical element design

Diffractive optical element design is an important problem for many applications and is usually achieved by the Gerchberg-Saxton or the Yang-Gu algorithm. These algorithms are formulated on the basis of monochromatic wave propagation and the far-field assumption, because the Fourier transform is used to model the wave propagation. We propose an iterative algorithm (based on rigorous coupled-wave analysis) for the design of a diffractive optical element. Since rigorous coupled-wave analysis (instead of Fourier transformation) is used to calculate the light-field distribution behind the optical element, the diffractive optical element can thus be better designed. Simulation results are provided to verify the proposed algorithm for designing a converging lens. Compared with the well-known Gerchberg-Saxton and Yang-Gu algorithms, our method provides 7.8% and 10.8%, respectively, improvement in converging the light amplitude when a microlens is desired. In addition, the proposed algorithm provides a solution that is very close to the solution obtained by the simulated annealing method (within 1.89% error).     

衍射微透镜列阵掩模制作软件的设计

研究了衍射微透镜列阵的设计方法及ＣＩＦ格式掩模数据的数据结构与生成方法,设计了一套产用软件,采用图形切割、跟踪计算等方法,解决了生成子孔径为矩形、六 方形及圆环扇形的衍射微透镜列阵掩模的问题,满足了实际系统对衍射微透镜列阵子孔径形状的各种需求。     

Application of a new selection algorithm to the development of a wide-range equation of state for refrigerant R134a

Refrigerant R134a (1,1.1,2-tetrafuoroethane) is a leading substitute for refrigerant R12. As such, there has been worldwide activity to develop accurate wide-range equations of state for this fluid. In this study. we have developed a new selection algorithm for determining high-accuracy equations of state in the Helmholtz representation. This method combines least-squares regression analysis with simulated annealing optimization. Simulated annealing, unlike stepwise regression, allows for the controlled acceptance of random increases in the objective function. Thus, this procedure produces a computationally efficient selection algorithm which is not susceptible to the function-space local-minima problems present in a purely stepwise regression approach. Two equations are presented in this work and compared against experimental data and other high-accuracy equations of state for R134a. One equation was produced strictly by using stepwise a regression algorithm, while the other was produced using the simulated-annealing selection algorithm. In both cases the temperature dependence of the equations was restricted to have no terms whose exponents were greater than live.Paper presented at the Twelfth Symposium on Thermophysical Properties. June 19–24, 1994, Boulder, Colorado, U.S.A.     

FMS machine loading: A simulated annealing approach

In this paper the problem of FMS machine loading is considered with the objective of minimizing the system imbalance using a simulated annealing (SA) approach. New job sequences are generated with a proposed perturbation scheme named the 'modified insertion scheme' (MIS). These sequences are used in the proposed simulated annealing algorithm to arrive at a near global optimum solution. A new approach for temperature variation in the SA algorithm is also suggested in which temperature is assumed to be parabolic. The SA algorithm using the proposed MIS and the assumed temperature variation proved to be giving substantial improvement in system imbalance as against conventional sequences.     

Theoretical and experimental investigations of the effect of diffractive multifocal focusing of radiation

The new optical effect of diffractive multifocal focusing of radiation, predicted earlier by theory, on a bicomponent diffraction system with small Fresnel numbers that consists of two plane screens with circular apertures on given optical axes, is confirmed experimentally. It is shown that the diffraction picture in the focal planes of such a system represents the circular nonlocal bands of the Fresnel zones with a bright narrow peak at the center, whose intensity in the experiment can exceed by six to ten times the value of the incident plane-wave intensity. Experimentally it is established that the diffractive multifocal focusing of radiation on real screens with axial circular apertures, whose diameters exceed the radiation wavelength, is insensitive to the rough external conditions: thickness of the screens, irregularities of the edges and nonideal form of the apertures, heterogeneity of the initial distribution of the incident-wave intensity, and changes in the medium of the wave propagation.     

Metal contacts to n-type AlGaAs grown by molecular beam epitaxy

We report for the first time the barrier heights of Cu, Ni, Ag, Ti on etched n-type Al_0.33Ga_0.67As and their dependence on annealing temperature with I–V and C–V techniques. The barrier heights of Al and Au, measured for comparison, are 0.96 and 1.06 eV, respectively, in excellent agreement with the results reported previously. The barrier heights of the Cu, Ni, Ag and Ti/n---Al_0.33Ga_0.67As diodes are found to be 1.08, 0.90, 0.87 and 0.87 eV, respectively. It is observed that the barrier heights for Al, Au, Cu and Ti contacts monotonically decrease with annealing temperature. For the Ag and Ni contacts, however, they become higher after being annealed at 473 K for 10 min and become lower thereafter, accompanied by a change of their ideality factors in opposite direction. The barrier heights extrapolated from C–V measurements for all metals studied are higher than that deduced from I–V data, and become higher after annealing at high temperatures, indicating the existence of a thin oxide layer at interface and broadening of the oxide after annealing. Our results can be qualitatively explained by the quality of contact and defects created at the semiconductor surface due to interdiffusion.     

Local improvement of the signal-to-noise ratio for diffractive optical elements designed by unidirectional optimization methods

We present a straightforward method to design multilevel phase-only diffractive optical elements with a locally improved signal-to-noise ratio in the reconstruction. The method is generally applicable to all unidirectional design schemes, such as direct search, simulated annealing, or genetic optimization. As the shape and the location of the desired low noise areas are supplied by a bit map file the method allows for the design of basically any two-dimensional low noise area. The improvement in the signal-to-noise ratio that may be achieved is considerable but also entails reduced diffraction efficiency. The suggested method is applied to different beam-splitter design examples. All examples are calculated with the scalar diffraction approximation in the far field.