Design Of Diffractive Optical Elements Research Articles

An improved Fourier modal method for design of metasurface diffractive optical elements

An improved Fourier modal method (FMM) is developed for the design of metasurface diffractive optical elements (DOEs), which combines the iterative Fourier transform algorithm (IFTA) with FMM. In which, the IFTA is executed for a coarse solution; then, FMM is for a precise solution. We take a 5 × 5 metasurface DOE with nanorods as an example to explore the improved FMM (IFTA + FMM). By varying the diameter of the nanorods on the metasurface DOE, a 5 × 5 spot array DOE has been created with a diffraction angle of 48°× 48° in the far field. The analysis results show that the improved FMM (IFTA + FMM) requires fewer iterations, about 17 times, while direct FMM requires about 70 times. The DOE designed with an improved FMM achieves a diffraction efficiency of 79.6% with a uniformity of 24.2%, while the DOE designed with a direct FMM shows a diffraction efficiency of 76.9% with a uniformity of 27.7%. The improved FMM (IFTA + FMM) shows a similar accuracy, but is more timesaving, simple, and intuitive.

Optical Force Effects of Rayleigh Particles by Cylindrical Vector Beams.

High-order cylindrical vector beams possess flexible spatial polarization and exhibit new effects and phenomena that can expand the functionality and enhance the capability of optical systems. However, building a general analytical model for highly focused beams with different polarization orders remains a challenge. Here, we elaborately develop the vector theory of high-order cylindrical vector beams in a high numerical aperture focusing system and achieve the vectorial diffraction integrals for describing the tight focusing field with the space-variant distribution of polarization orders within the framework of Richards-Wolf diffraction theory. The analytical formulae include the exact three Cartesian components of electric and magnetic distributions in the tightly focused region. Additionally, utilizing the analytical formulae, we can achieve the gradient force, scattering force, and curl-spin force exerted on Rayleigh particles trapped by high-order cylindrical vector beams. These results are crucial for improving the design and engineering of the tightly focused field by modulating the polarization orders of high-order cylindrical vector beams, particularly for applications such as optical tweezers and optical manipulation. This theoretical analysis also extends to the calculation of complicated optical vortex vector fields and the design of diffractive optical elements with high diffraction efficiency and resolution.

Generation of needle-shaped beam with super-resolution spot and large depth of focus using diffractive optics

The finite depth of focus (DOF) of a focusing lens gives rise to the degradation of lateral resolution at defocused positions. Consequently, the generation of a needle-shaped beam with sub-diffraction size and extended DOF can break through this limitation, but few studies have effectively balanced these two characteristics. In this paper, we propose a method based on the stochastic parallel gradient descent (SPGD) algorithm for designing multi-ring diffractive optical elements (DOEs) to produce the needle-shaped beam, which maintains a super-resolution and uniform spot within a large extended DOF range. Numerical simulations and experimental results have validated that our method can extend the DOF by 14 times longitudinally and reduce the lateral resolution to 73% of Airy spot, while maintaining up to 92% uniformity of the beam diameter. Furthermore, we demonstrate that the DOF of the needle-shaped beam extends with the increase of the number of rings and phase levels within the DOE. Our work provides an effective strategy for the design of DOF-extended DOE and it is anticipated to find potential applications in microscopy and three-dimensional imaging, photolithography, and optical manipulation.

A fireworks algorithm based Gerchberg–Saxton algorithm for the design of diffractive optical element for beam shaping

In this paper, a fireworks algorithm based Gerchberg–Saxton (GS) algorithm for the design of diffractive optical element is developed, named FW-GS algorithm, in which, the explosion mechanism of the fireworks algorithm is introduced to efficiently find the initial phase, thereby ensuring a superior phase solution for the subsequent GS algorithm. By employing this approach to shape a Gaussian beam into a square beam, the results illustrated the notable improvement of 16.10 % in RMSE and 3.29 % in diffractive efficiency when compared to the traditional GS algorithm, while exhibiting stable optimization performance. Furthermore, the proposed algorithm demonstrated adaptability to various shaping targets, with RMSE improved by about 16 % and diffractive efficiency improved by more than 3 % for shaping to circular, annular, and rectangular beams.

Hexagonal diffractive optical elements.

Diffractive optical elements (DOEs) have widespread applications in optics, ranging from point spread function engineering to holographic display. Conventionally, DOE design relies on Cartesian simulation grids, resulting in square features in the final design. Unfortunately, Cartesian grids provide an anisotropic sampling of the plane, and the resulting square features can be challenging to fabricate with high fidelity using methods such as photolithography. To address these limitations, we explore the use of hexagonal grids as a new grid structure for DOE design and fabrication. In this study, we demonstrate wave propagation simulation using an efficient hexagonal coordinate system and compare simulation accuracy with the standard Cartesian sampling scheme. Additionally, we have implemented algorithms for the inverse DOE design. The resulting hexagonal DOEs, encoded with wavefront information for holograms, are fabricated and experimentally compared to their Cartesian counterparts. Our findings indicate that employing hexagonal grids enhances holographic imaging quality. The exploration of new grid structures holds significant potential for advancing optical technology across various domains, including imaging, microscopy, photography, lighting, and virtual reality.

Design of freeform phase diffractive optical elements based on the quadratic assignment problem.

The design of freeform phase diffractive optical elements is a challenging task, typically necessitating the use of complex differential equations or a large number of iterative calculations. This paper proposes what we believe to be a novel approach to address this problem. In this strategy, we introduce overall comparison optimization (OCO) to ensure the fast convergence of the cost function. The quadratic assignment problem (QAP) is used as the mathematical framework for designing freeform phase diffraction optics. Specifically, the ray mapping calculation problem in geometric optics is simplified as a QAP. To solve this problem, we apply the OCO method, which ensures that the cost function rapidly progresses in the "non-negative" direction, thereby facilitating fast convergence in each optimization iteration. In this manner, the proposed approach alleviates the computational burden associated with repeated evaluations of the cost function and accelerates convergence in the design process. We construct holographic masks using the OCO method and perform simulations to demonstrate the potential of the proposed method in swiftly realizing complex illumination patterns. The results show that the design model has good performance when dealing with complex illumination tasks. The conclusions obtained in this paper can be extended to the realization of phase-only holography and the solution of freeform surfaces illumination design.

Simple Method of Light Field Calculation for Shaping of 3D Light Curves

We propose a method for generating three-dimensional light fields with given intensity and phase distributions using purely phase transmission functions. The method is based on a generalization of the well-known approach to the design of diffractive optical elements that focus an incident laser beam into an array of light spots in space. To calculate purely phase transmission functions, we use amplitude encoding, which made it possible to implement the designed elements using a single spatial light modulator. The generation of light beams in the form of rings, spirals, Lissajous figures, and multi-petal “rose” distributions uniformly elongated along the optical axis in the required segment is demonstrated. It is also possible to control the three-dimensional structure of the intensity and phase of the shaped light fields along the propagation axis. The experimentally generated intensity distributions are in good agreement with the numerically obtained results and show high potential for the application of the proposed method in laser manipulation with nano- and microparticles, as well as in laser material processing.

Design of adjustable multifocal diffractive optical elements with an improved smooth phase profile by continuous variable curve with multi-subperiods method.

Multifocal diffractive optical elements (MDOEs), which produce arbitrary light distribution, are widely used in lightweight and compact optical systems. MDOEs that are combined with multiple functions tend to have complex step structures, limiting their applications. We propose a facile method named continuous variable curve with multi-subperiods (CVCMS) to design adjustable multifocal single-layer diffractive optical elements. Through the analysis, the model achieved arbitrary diffraction efficiency distribution with an improved smooth continuous phase profile in each diffractive ring while retaining the periodicity. To display the high design freedom of the method, we utilized this method to design and discuss a broadband multifocal intraocular lens (MIOL) focused on the optimization of far focal point. Finally, the method was compared with other multifocal design methods. The results show that the CVCMS method achieved adjustable multifocal design with better performance and smoother profile than other MDOE design techniques. The proposed model can be applied to multifocal ophthalmic lens designs.

Designing diffractive optical elements for shaping partially coherent beams by proximity correction.

We propose a new method to design diffractive optical elements (DOE) for shaping partially coherent beams. The diffraction patterns of a DOE under a certain partially coherent beam can be modeled by the convolution of the coherent diffraction pattern and the inherent degree of coherent function. Two basic types of diffraction anomalies induced by partially coherent beams are discussed, including line-end shortening and corner rounding. A proximity correction (PC) method similar to the optical proximity correction (OPC) technique in lithography is used to compensate for these anomalies. The designed DOE exhibits good performance in partially coherent beam shaping and noise suppression.

Unfolding-Aided Bootstrapped Phase Retrieval in Optical Imaging: Explainable AI reveals new imaging frontiers

Phase retrieval in optical imaging refers to the recovery of a complex signal from phaseless data acquired in the form of its diffraction patterns. These patterns are acquired through a system with a coherent light source that employs a diffractive optical element (DOE) to modulate the scene, resulting in coded diffraction patterns (CDPs) at the sensor. Recently, the hybrid approach of a model-driven network or deep unfolding has emerged as an effective alternative to conventional model- and learning-based phase-retrieval techniques because it allows for bounding the complexity of algorithms while also retaining their efficacy. Additionally, such hybrid approaches have shown promise in improving the design of DOEs that follow theoretical uniqueness conditions. There are opportunities to exploit novel experimental setups and resolve even more complex DOE phase-retrieval applications. This article presents an overview of algorithms and applications of deep unfolding for bootstrapped—regardless whether near, middle, or far zones—phase retrieval.

The design of multi-wavelength confocal diffractive optical element based on set operation

A method suitable for the design of large aperture multi-wavelength confocal diffractive optical element (DOE) was proposed. The method is based on set operation for microstructures. As examples, different multi-wavelength confocal DOEs with aperture of 20 mm were designed. The results of the numerical simulations show that the confocal DOEs achieved diffraction-limited focusing performance at all design wavelengths, but the diffraction efficiencies were lower than the ideal DOEs. For experimental verification, one three-wavelength confocal DOE with focal length of 200 mm was fabricated and tested. The optimum full width at half maximum (FWHM) is preferably 1.067 times of the diffraction limit and the highest optical imaging solution reaches 94.6% of the diffraction limit. Both the simulation results and the experimental results verify the validity of this method for designing multi-wavelength confocal DOE. The presented work may find applications in large-aperture multi-wavelength laser communication, wide-spectrum diffractive telescopes, and high-precision multi-wavelength Computer generated holography (CGH).

Diffractive optical element design based on vector diffraction theory and improved PSO-SA algorithm

The existence of the beam vector effect requires rigorous electromagnetic computational methods for the optimization of subwavelength diffractive optical elements (DOEs). To design DOEs with high performance, we proposed an optimization strategy combining a global optimization algorithm with the finite difference time domain (FDTD) method. First, scalar initial solutions are obtained by the Gerchberg–Saxton algorithm. Then, regarding the diffraction efficiency, the uniformity error and figure of merit are calculated by FDTD as evaluation functions, and the optimization of the initial solutions is implemented by improved particle swarm optimization and continues with the simulated annealing algorithm. After several numerical simulations, the analysis results confirm the robustness of the algorithm and the reduction of the computational cost. The experimental data demonstrate that the correlation of diffraction energy orders between the simulated design and fabricated sample are above 85%. This method efficiently improves the DOEs design.

Theoretical model and optimization of diffractive optical elements with aspheric substrates inophthalmology.

Diffractive optical elements (DOEs), which can produce arbitrary light distribution, are widely applied in ophthalmic lens design with spheric substrates. However, diffraction substrates tend to be designed as aspheric surfaces to eliminate aberrations. In this case, the diffraction theory of plane substrates is no longer accurate, which affects the diffraction performance. Therefore, a diffraction theory of aspheric diffraction substrates is proposed in this paper. Using the range of common parameters for aspheric substrates in ophthalmology, the influence of the substrate diopter and the aspheric surface parameters on the period radius and phase delay is analyzed. Then, through a design example of a diffraction intraocular lens (IOL), an optimization equation is proposed and discussed. The results show that the diffraction theory of aspheric substrates and the optimization equation model can analyze and reduce the effect of aspheric diffraction substrates. This research can be used in DOE design with aspheric substrates in ophthalmology.

Design of Diffractive Optical Elements with Continuous Phase Distribution Based on Machine Learning

Design of Diffractive Optical Elements with Continuous Phase Distribution Based on Machine Learning

Optimal Design and Application of Double-Layer Diffractive Optical Element over Wide Temperature Range

Optimal Design and Application of Double-Layer Diffractive Optical Element over Wide Temperature Range

Three-dimensional tracking using a single-spot rotating point spread function created by a multiring spiral phase plate.

Three-dimensional (3D) imaging and object tracking is critical for medical and biological research and can be achieved by multifocal imaging with diffractive optical elements (DOEs) converting depth ( ) information into a modification of the two-dimensional image. Physical insight into DOE designs will spur this expanding field. To precisely track microscopic fluorescent objects in biological systems in 3D with a simple low-cost DOE system. We designed a multiring spiral phase plate (SPP) generating a single-spot rotating point spread function (SS-RPSF) in a microscope. Our simple, analytically transparent design process uses Bessel beams to avoid rotational ambiguities and achieve a significant depth range. The SPP was inserted into the Nomarski prism slider of a standard microscope. Performance was evaluated using fluorescent beads and in live cells expressing a fluorescent chromatin marker. Bead localization precision was in the transverse dimensions and along the axial dimension over an axial range of . Higher axial precision ( ) was achieved over a shallower focal depth of . 3D diffusion constants of chromatin matched expected values. Precise 3D localization and tracking can be achieved with a SS-RPSF SPP in a standard microscope with minor modifications.

Design and Application of Phase-Only Diffractive Optical Element Based on Non-Iterative Method

In this study, we devised a method for the design of continuous phase-only holographic masks that map laser light to arbitrary target illumination patterns, which have a wide range of applications. In this method, the discrete gradient of a holographic mask is obtained by combining geometric optics and the linear assignment problem (LAP) methods, and then the entire problem is transformed into an integral problem with a discrete gradient. Finally, the least squares method is used to solve the gradient integral to complete the construction of a phase holographic mask. Due to its good continuity, this mask design method can also be applied to the production of diffractive optical elements. We discussed the effectiveness of this method by constructing two holographic masks with uniform illumination. At the same time, we successfully constructed an Einstein face holographic mask with non-uniform illumination using the LAP method for the first time. It is believed that this method can be widely used in illumination mode, ion capture and other directions.

Compact structured illumination microscopy with high spatial frequency diffractive lattice patterns.

Structured illumination microscopy (SIM) enables live-cell super-resolution imaging with wide field of view (FOV) and high imaging speed, but the illumination system is usually bulky. With the advantages of small structure and high efficiency, lattice patterns assisted by diffractive optical elements (DOEs) have been used for structured illumination in SIM. But it is still challenging to raise the spatial frequency of diffractive lattice patterns when using traditional DOE design method, and thus the super-resolution imaging performance is restricted. In this paper, we propose a novel design method for DOE to generate lattice patterns with spatial frequency close to the cut-off frequency. It is the first time to obtain a lattice pattern with such high spatial frequency by diffractive optics. Finally, the proposed SIM achieves a lateral resolution of 131 nm at 519 nm fluorescent light while maintaining an original size as a standard inverted fluorescence microscope by only inserting a single well-designed DOE in the illumination optical path, which may promote this compact SIM applied in super-resolution imaging field.

Fast method for designing broadband achromatic diffractive optical elements.

Diffractive optical elements play a crucial role in the miniaturization of the optical systems, especially in correcting achromatic aberration. Considering the rapidity and validity of the design method, we propose a fast method for designing broadband achromatic diffractive optical elements. Based on the direct binary search algorithm, some improvements have been made including the selection of the initial height map to mitigate the uncertainty, the reduction of the variations to accelerate the optimization and the increase of sampling rate to deal with the large operation bandwidth. The initial height map is calculated instead of random initial value. Due to different regions of the height map contributing to point spread functions differently, the variations are reduced to speed up the optimization. The large operation bandwidth is solved by increasing the sampling rate at unfitted wavelengths instead of setting weighting coefficients. We demonstrate via simulations that our method is effective through several examples. The design of broadband achromatic diffractive optical elements can be quickly achieved by our method.

Method for calculating the eikonal function and its application to design of diffractive optical elements for optical beam shaping

We develop a method for calculating the eikonal function (or the phase function) of the light field, ensuring the formation of a prescribed irradiance distribution in the geometrical optics approximation. In the proposed method, the problem being solved is formulated in a semi-discrete form as a problem of the maximization of a concave function. For finding the solution to the latter problem, a gradient method is used, with analytical expressions obtained for the gradient. Using the developed method, we calculate an eikonal function that provides the formation of a “discontinuous” hexagram-shaped irradiance distribution. We demonstrate that the use of the solution obtained in the framework of the geometrical optics as an initial approximation in iterative Fourier transform algorithms allows one to calculate diffractive optical elements having a quasi-regular microrelief.