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.     

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.     

Automatic symmetrical iterative Fourier-transform algorithm for the design of diffractive optical elements for highly precise laser beam shaping

A symmetrical iterative Fourier-transform algorithm (IFTA) using a combination of phase and amplitude freedom for the design of diffractive optical elements for highly precise laser beam shaping is presented. We compare this method with the basic IFTA and the symmetrical IFTA exclusively using phase freedom, and the basic IFTA using both phase and amplitude freedom, by employing these methods for super-Gaussian beam shaping. While the latter three methods fail to produce satisfactory solutions, the first method results in a beam non-uniformity error of 0.44% and a theoretical efficiency of 97.2%. Moreover, the new approach avoids the use of the trial-and-error method for finding the appropriate modified Fourier-domain constraints during the iteration, which can be difficult for some beam-shaping problems.     

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.     

Beam shaping for multicolour light-emitting diodes with diffractive optical elements

An improved particle swarm optimization method is proposed for the design of ultra-thin diffractive optical elements (DOEs) enabling multicolour beam shaping functionality. We employ pre-optimized initial structures and adaptive weight strategy in the algorithm to achieve better and identical shaping performance for multiple colours. Accordingly, a DOE for shaping light from green and blue LEDs has been designed and fabricated. Both experiment and numerical simulations have been conducted and the results agree well with each other. 15.66% average root mean square error (RMSE) and 0.22% RMSE difference are achieved. In addition, the parameters closely related to the performance of the optimization are analysed, which can provide insights for future application designs.     

Design concept for diffractive elements shaping partially coherent laser beams.

A new two-step design algorithm for the calculation of a diffractive phase element (DPE) for use with partially coherent laser beams is presented. The optical reconstruction of the DPE is modeled by the convolution of a coherent diffraction pattern and the far-field intensity distribution of a partially coherent laser beam. Numerical deconvolution is applied to derive a suitable amplitude pattern as signal input to a standard iterative Fourier transform algorithm (IFTA). Theory and numerical results are presented. Compared with a single-step IFTA design, this new approach yields nearly equal diffraction efficiencies and a relative improvement of 15% in signal reconstruction error.     

Wavelength-multiplexing diffractive phase elements: design, fabrication, and performance evaluation

We report on the wavelength-multiplexing diffractive phase element (WMDPE) capable of generating independent spot patterns for different wavelengths. The iterative method proposed by Bengtsson [Appl. Opt. 37, 1998] for designing a kinoform that produces different patterns for two wavelengths is extended to the WMDPE for multiple wavelengths (more than two wavelengths). Effectiveness of the design algorithm is verified by design and computer simulations on the WMDPE's for four and nine wavelengths. The WMDPE for three wavelengths (441.6, 543.5, and 633 nm) is designed with five phase levels and is fabricated by electron-beam lithography. We observed that the individual spot patterns are reconstructed for the design wavelengths correctly. Performance of the WMDPE is evaluated by computer simulations on the uniformity error, the light efficiency, and the contrast. On the basis of the results, the characteristics of the WMDPE's are discussed in terms of various conditions of fabrication and usage.     

Laser beam relaying with phase-conjugate diffractive optical elements

A diffractive optical element is used to relay complex laser beam profiles by phase conjugation. It has the advantage over a conventional afocal system of avoiding light concentration at the intermediate focal point. Theoretical and experimental results show that the image quality is a function of alignment errors and mode-size changes. When the optical system is within the calculated tolerances, the diffractive optic reproduces images of high quality.     

Astigmatic gradient-index elements for laser-diode collimation and beam shaping

For the conversion of light from edge-emitting laser diodes into symmetric laser beams two main tasks have to be performed: collimation and beam shaping. Generally these two jobs are performed separately. Because of the inherently different divergence angles of the emitted light, collimation with astigmatic lenses generally results in a beam with an elliptically shaped amplitude distribution. This asymmetry has to be compensated for by an anamorphic imaging step to obtain the desired spherical beam profile. It can be advantageous to combine both jobs in one element. We demonstrate the design, the fabrication, and the application of refractive gradient-index elements, which allow one to perform both jobs with a single element. Our astigmatic lenses were fabricated by silver-sodium ion exchange in glass.     

Crossed phase gratings with diffractive optical elements

Orienting two identical or complementary diffractive gratings with a small angle between the grating grooves allows a new crossed-grating device to be constructed. This device has an effective profile that varies locally. For understanding the effects of this variation and the diffraction efficiency of the gratings, the local profiles were correlated with the moiré period of the crossed-grating system by use of various techniques. Asymmetric intensity behavior in the first order of the crossed gratings was seen. Effectively, the diffraction efficiency of the crossed gratings yielded a response equivalent to that of a grating with variable blaze that could be useful in optical computing as a passive optical switching device. One of several models is described that creates greater asymmetric behavior.     

Rational design of a diffractive homogenizer for a laser beam

The problem of designing a diffractive optical element (DOE) that produces a uniform-intensity beam from a spatially variable source is considered. Under the thin-lens approximation, the DOE is fully characterized by a phase function. Fresnel approximation is used to simplify the relationship between the input amplitude, the phase function, and the image intensity. The case where the light source has partial coherence is considered. A simple design procedure based on a lenslet array is proposed. It is shown that under certain physical assumptions, this `engineering' solution leads to an effective design capable of producing a uniform intensity from a time-varying, non-uniform source.     

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。     

Asymptotic analysis and design of diffractive optical elements

The problem of light diffraction by a micro-optical diffractive element is investigated. The method of stationary phase is applied to obtain approximate values of the integrals in the Kirchhoff approximation. The accuracy of the asymptotic approximation is studied in detail. As an application, the obtained approximate formulas are used to solve a design problem of constructing a diffractive optical element with a desired intensity distribution.     

Analytic design and solutions for resonance domain diffractive optical elements

A model for designing and analyzing complicated surface relief diffractive elements in the resonance domain is developed. It is based on subdividing the complicated diffractive element into many highly efficient local diffraction gratings whose surface relief modulations can be effectively characterized as slanted volume gratings for which closed form analytic solutions exist. The model is illustrated by finding in the resonance domain the local period, effective slant angle, and groove depth at each location on an off-axis cylindrical diffractive lens.     

Diffractive optical elements for beam shaping of monochromatic spatially incoherent light

Fresnel-type diffractive optical elements (DOEs) for general beam shaping of monochromatic, spatially incoherent light are demonstrated. Direct and indirect methods, i.e., adding a lens' phase to the designed Fraunhofer-type DOEs, are used for the design. The indirect method can reduce the calculation time by approximately half without loss of design accuracy. Two different design examples are shown. For one design the direct method gives a maximum sidelobe intensity of 5.0% of the maximum intensity in the signal window. For the second design the indirect method gives 23.0% of this value. The generated patterns can maintain their basic shapes over a long distance. The elements have been fabricated by directly using gray-scale commercial slides as masks. Experimental results are in close agreement with numerical predictions.     

Efficient detour-phase encoding of one-dimensional multilevel phase diffractive elements

We show that detour-phase encoding with a multilevel blaze structure as a carrier grating is especially suited to the implementation of diffractive elements with relatively high complexity in one axis. For our proposal the carrier grating is aligned perpendicularly to this axis. In this way the element can be encoded with a high space-bandwidth product and a high phase resolution by use of a moderate carrier frequency. Moreover, this frequency can be adjusted to isolate the reconstructed field from the noise resulting from high diffraction orders of the carrier grating or caused by etching errors during fabrication.     

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.     

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.