Phase-only Diffractive Optical Elements Research Articles

Generating phase-only diffractive optical elements using adaptive constraints in the Fourier domain

In this work, a modified iterative design method of generating pure phase diffractive optical elements is reported. The adaptive constraint on Fourier domain was derived as a result of minimizing a criterion-functional. Considering the design for manufacturing, the soft quantization method is introduced into the iteration process. The performance of the proposed algorithm was verified by comparing with the standard iterative design method using a binary as well as gray-scale image. The simulation results demonstrate that the proposed method is superior to the conventional iterative Fourier transform algorithm in terms of reconstruction accuracy. The results from proof-of-concept experiments confirmed the conclusions, suggesting that our design method provides a new alternative for the diffractive optics community.

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.

Dexterous holographic trapping of dark-seeking particles with Zernike holograms.

The intensity distribution of a holographically-projected optical trap can be tailored to the physical properties of the particles it is intended to trap. Dynamic optimization is especially desirable for manipulating dark-seeking particles that are repelled by conventional optical tweezers, and even more so when dark-seeking particles coexist in the same system as light-seeking particles. We address the need for dexterous manipulation of dark-seeking particles by introducing a class of "dark" traps created from the superposition of two out-of-phase Gaussian modes with different waist diameters. Interference in the difference-of-Gaussians (DoG) trap creates a dark central core that is completely surrounded by light and therefore can trap dark-seeking particles rigidly in three dimensions. DoG traps can be combined with conventional optical tweezers and other types of traps for use in heterogeneous samples. The ideal hologram for a DoG trap being purely real-valued, we introduce a general method based on the Zernike phase-contrast principle to project real-valued holograms with the phase-only diffractive optical elements used in standard holographic optical trapping systems. We demonstrate the capabilities of DoG traps (and Zernike holograms) through experimental studies on high-index, low-index and absorbing colloidal particles dispersed in fluid media.

Adjustable super-resolution microscopy with diffractive spot array illumination

Diffractive super-resolution spot arrays offer the possibility of adjustable super-resolution microscopic imaging. By inserting a phase-only diffractive optical element (DOE) into the illumination system of a standard microscope, super-resolution information of the sample can be obtained by spots. Here, we report an adjustable super-resolution microscopy (ASM) that the imaging resolution and the number of spot arrays can be adjusted by DOEs. The results of 3 × 3 and 5 × 5 spot arrays with 50% and 70% of the Airy spot size are, respectively, realized to support the flexibility of the ASM. The resolution test target was used as a sample to show the ASM can achieve about double-resolution experimentally, illuminated by a uniform 3 × 3 spot array with 50% of the Airy spot size under a small numerical aperture objective. Moreover, imaging of cellular mitochondria was performed, substantially realized resolution beyond the diffraction limit. The ability to adjust the super-resolution of microscopy using DOEs is of great importance for further nanoscale imaging.

Effective bandwidth approach for the spectral splitting of solar spectrum using diffractive optical elements.

Spectral splitting of the sunlight using diffractive optical elements (DOEs) is an effective method to increase the efficiency of solar panels. Here, we design phase-only DOEs by using an iterative optimization algorithm to spectrally split and simultaneously concentrate solar spectrum. In our calculations, we take material dispersion into account as well as the normalized blackbody spectrum of the sunlight. The algorithm consists of the local search optimization and is strengthened with an outperforming logic operation called MEAN optimization. Using the MEAN optimization algorithm, we demonstrate spectral splitting of a dichromatic light source at 700 nm and 1100 nm with spectral splitting efficiencies of 92% and 94%, respectively. In this manuscript, we introduce an effective bandwidth approach, which reduces the computational time of DOEs from 89 days to 8 days, while preserving the spectral splitting efficiency. Using our effective bandwidth method, we manage to spectrally split light into two separate bands between 400 nm - 700 nm and 701 nm - 1100 nm, with splitting efficiencies of 56% and 63%, respectively. Our outperforming and effective bandwidth design approach can be applied to DOE designs in color holography, spectroscopy, and imaging applications.

Binary square axicon with chiral focusing properties for optical trapping

We introduce a novel phase-only diffractive optical element called chiral binary square axicon (CBSA). The CBSA is designed by linearly rotating the square half-period zones of the binary square axicon with respect to one another. A quadratic phase mask (QPM) is combined with the CBSA using modulo-2{\pi} phase addition technique to bring the far-field intensity pattern of CBSA at the focal plane of the QPM and to introduce quasi-achromatic effects. The periodically rotated zones of CBSA produces a whirlpool phase profile and twisted intensity patterns at the focal plane of QPM. The degree of twisting seen in the intensity patterns is dependent upon the angular step size of rotation of the zones. The intensity pattern was found to rotate around the optical axis along the direction of propagation. The phase patterns of CBSA with different angles of zone rotation are displayed on a phase-only spatial light modulator and the experimental results were found to match with the simulation results. To evaluate the optical trapping capabilities of CBSA, an optical trapping experiment was carried out and the optical fields generated by CBSA were used for trapping and rotating yeast cells.

Detour phase Talbot array illuminator

In this Letter, we propose a simple and effective approach for transforming a conventional Talbot array illuminator (TAI) with multilevel phase steps into a binary-phase TAI (BP-TAI) through detour phase encoding. The BP-TAI is a binary (0 π) phase-only diffractive optical element, which can be utilized to generate a large-scale focal spots array with a high compression ratio. As an example, we design a square BP-TAI with the fraction parameter β = 15 for achieving a square multifocal lattice with a high compression ratio β2. Theoretical analysis and experimental results demonstrate that the detour phase encoding is efficient for designing the BP-TAI, especially with the high compression ratio. Such results may be exploited in practical large-scale optical trapping and X-ray imaging.

Projecting non-diffracting waves with intermediate-plane holography.

We introduce intermediate-plane holography, which substantially improves the ability of holographic trapping systems to project propagation-invariant modes of light using phase-only diffractive optical elements. Translating the mode-forming hologram to an intermediate plane in the optical train can reduce the need to encode amplitude variations in the field, and therefore complements well-established techniques for encoding complex-valued transfer functions into phase-only holograms. Compared to standard holographic trapping implementations, intermediate-plane holograms greatly improve diffraction efficiency and mode purity of propagation-invariant modes, and so increase their useful non-diffracting range. We demonstrate this technique through experimental realizations of accelerating modes and long-range tractor beams.

Design, fabrication and characterization of Computer Generated Holograms for anti-counterfeiting applications using OAM beams as light decoders

In this paper, we present the design, fabrication and optical characterization of computer-generated holograms (CGH) encoding information for light beams carrying orbital angular momentum (OAM). Through the use of a numerical code, based on an iterative Fourier transform algorithm, a phase-only diffractive optical element (PO-DOE) specifically designed for OAM illumination has been computed, fabricated and tested. In order to shape the incident beam into a helicoidal phase profile and generate light carrying phase singularities, a method based on transmission through high-order spiral phase plates (SPPs) has been used. The phase pattern of the designed holographic DOEs has been fabricated using high-resolution Electron-Beam Lithography (EBL) over glass substrates coated with a positive photoresist layer (polymethylmethacrylate). To the best of our knowledge, the present study is the first attempt, in a comprehensive work, to design, fabricate and characterize computer-generated holograms encoding information for structured light carrying OAM and phase singularities. These optical devices appear promising as high-security optical elements for anti-counterfeiting applications.

A highly efficient element for generating elliptic perfect optical vortices

We generalize the concept of perfect optical vortices, studying the elliptic perfect optical vortices (EPOVs), which also have diameters independent of the topological charge. A phase-only diffractive optical element is proposed for the efficient generation of such EPOV. The intensity of the EPOV generated by this element is higher than that of the EPOV generated approximately by an elliptical axicon. We obtain exact analytical expressions for the orbital angular momentum (OAM) density and for the total OAM of the EPOV. These expressions show that the normalized OAM of the EPOV is fractional and it exceeds the OAM of the conventional circular perfect optical vortex, which equals the topological charge. It allows continuous controlling of the OAM by changing the ellipticity. We show analytically that the OAM density is maximal on the smaller side of the EPOV. The ratio of the maximal to the minimal OAM density equals the squared ratio of the ellipse dimensions. Using the proposed element, EPOVs that carry different topological charges are generated experimentally with the aid of a spatial light modulator. We experimentally confirm the independence of their size from the topological charge, which is determined interferometrically. Such EPOVs can be used for moving microscopic particles along an ellipse with acceleration, as well as for the generation of OAM-entangled photons.

Diffractive optics for combined spatial- and mode- division demultiplexing of optical vortices: design, fabrication and optical characterization.

During the last decade, the orbital angular momentum (OAM) of light has attracted growing interest as a new degree of freedom for signal channel multiplexing in order to increase the information transmission capacity in today’s optical networks. Here we present the design, fabrication and characterization of phase-only diffractive optical elements (DOE) performing mode-division (de)multiplexing (MDM) and spatial-division (de)multiplexing (SDM) at the same time. Samples have been fabricated with high-resolution electron-beam lithography patterning a polymethylmethacrylate (PMMA) resist layer spun over a glass substrate. Different DOE designs are presented for the sorting of optical vortices differing in either OAM content or beam size in the optical regime, with different steering geometries in far-field. These novel DOE designs appear promising for telecom applications both in free-space and in multi-core fibers propagation.

Spiral phase plates with radial discontinuities for the generation of multiring orbital angular momentum beams: fabrication, characterization, and application

A design of spiral phase plates for the generation of multiring beams carrying orbital angular momentum (OAM) is presented. Besides the usual helical profile, these phase plates present radial π-discontinuities in correspondence of the zeros of the associated Laguerre polynomials. Samples were fabricated by electron beam lithography over glass substrates coated with a polymethylmethacrylate resist layer. The optical response was analyzed and the purity of the generated beams was investigated in terms of Laguerre-Gaussian modes contributions. The far-field intensity pattern was compared with theoretical models and numerical simulations, while the expected phase features were confirmed by interferometric analysis with a Mach-Zehnder setup. The high quality of the output beams confirms the applicability of these phase plates for the generation of high-order OAM beams with nonzero radial index. An application consisting of the design of computer-generated holograms encoding information for light beams carrying phase singularities is presented and described. A numerical code based on an iterative Fourier transform algorithm has been developed for the computation of phase-only diffractive optical element for illumination under OAM beams. Numerical analysis and preliminary experimental results confirm the applicability of these devices as high-security optical elements for anticounterfeiting applications.

Trade-off between diffraction efficiency and uniformity for design of binary diffractive laser beam shaper

The trade-off between diffraction efficiency and uniformity is studied when a binary phase-only diffractive optical element (DOE) is designed for transforming a Gaussian beam to an expanded squared uniform intensity distribution. The simulated annealing (SA) algorithm and Fresnel diffraction theory are applied in our design. Two types of cost functions are utilized in the SA algorithm, and the cases of different incident Gaussian diameters and bright-area sizes of the target patterns are studied. The mechanisms of reducing nonuniformity by the two cost functions are essentially different, and the mechanism combining nonuniformity and the intensity difference between the reconstructed and target patterns has better results. Satisfactory performance can be obtained under the trade-off between them.

Cascaded diffractive optical elements for improved multiplane image reconstruction

Computer-generated phase-only diffractive optical elements in a cascaded setup are designed by one deterministic and one stochastic algorithm for multiplane image formation. It is hypothesized that increasing the number of elements as wavefront modulators in the longitudinal dimension would enlarge the available solution space, thus enabling enhanced image reconstruction. Numerical results show that increasing the number of holograms improves quality at the output. Design principles, computational methods, and specific conditions are discussed.

Second order diffractive optical elements in a spatial light modulator with large phase dynamic range

A study of the diffraction efficiency of a spatial light modulator with a large dynamic phase range is reported. We use a phase-only device that reaches 4π phase modulation depth for the wavelength of 454nm. This allows operating phase-only diffractive optical elements in the second harmonic diffraction order, instead of in the usual first diffraction order. This type of implementation shows advantages in terms of resolution and diffraction efficiency. Experimental results are reported for blazed diffractive gratings and diffractive lenses.

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.

Speckle suppression in holographic projection displays using temporal integration of speckle images from diffractive optical elements

Speckles on images in holographic projection displays (HPDs) were efficiently suppressed by the temporal sum of two diffractive images generated from diffractive optical elements (DOEs). Using a modified iterative Fourier transform algorithm, we obtained pairs of phase-only DOEs that generated the diffractive images with high negative correlation coefficients of -0.827 and -0.490 in the one-dimensional and the two-dimensional simulations, respectively. The suppression ratios of the speckles in the two simulations were 0.301 and 0.457, which were 61% and 35% lower, respectively, than the sum of the two uncorrelated images. We have successfully demonstrated that the sum of two negatively correlated images from DOEs can effectively reduce the image speckles and improve the image quality in HPD systems.

Implementation of phase-shift patterns using a holographic projection system with phase-only diffractive optical elements

We proposed a method to implement spatial phase-shift patterns with subdiffraction limited features through a holographic projection system. The input device of the system displayed phase-only diffractive optical elements that were calculated using the iterative Fourier-transform algorithm with the dummy-area method. By carefully designing the target patterns to the algorithm, the diffractive optical elements generated the Fourier-transformed images containing the phase-shift patterns in which the widths of dark lines were smaller than the diffraction limit. With these demonstrations, we have successfully shown that the near-field phase-shift lithographic technique can be realized through an inexpensive maskless lithographic system and can still achieve subdiffraction limited images.

Intensity control of the focal spot by vectorial beam shaping

A vectorial beam shaping algorithm is presented for the design of a phase-only diffractive optical element to achieve a given target intensity profile in the focal plane under tight focusing conditions. The underlying iterative optimization scheme is based on the Richards–Wolf vectorial diffraction theory and the Gerchberg–Saxton method, and is suitable for an arbitrary incoming polarization distribution, since only the magnitudes of the field vectors in the focal plane are reshaped. The efficiency of the method is numerically demonstrated for flat-top beam shaping examples of linear and circular incoming beam polarizations and square and circular flat-top region shape. A diffraction efficiency of 97.1 % and a uniformity error of 4.8 % were achieved in the case of focusing a Gaussian input beam onto a 50 λ × 50 λ square flat-top region with a 1.4-NA lens.

Natural quasy-periodic binary structure with focusing property in near field diffraction pattern

A naturally-inspired phase-only diffractive optical element with a circular symmetry given by a quasi-periodic structure of the phyllotaxis type is presented in this paper. It is generated starting with the characteristic parametric equations which are optimal for the golden angle interval. For some ideal geometrical parameters, the diffracted intensity distribution in near-field has a central closed ring with almost zero intensity inside. Its radius and intensity values depend on the geometry or non-binary phase distribution superposed onto the phyllotaxis geometry. Along propagation axis, the transverse diffraction patterns from the binary-phase diffractive structure exhibit a self-focusing behavior and a rotational motion.