Polarization beam splitter based on 2D transmissive grating.

This paper introduces a two-dimensional transmissive grating polarization beam splitter (PBS) exhibiting exceptional polarization-sensitive properties with high diffraction efficiency. The optimized grating structure can concentrate the energy of TE-polarized light at the (0, ±1) orders and the energy of TM-polarized light at the (±1, 0) orders under normal incidence with a wavelength of 550nm. The polarization splitting diffraction efficiency (DE) of the grating can reach 40.17%, and the extinction ratio (ER) exceeds 18dB. This proposal marks the pioneering use of two-dimensional transmissive grating to achieve a polarization beam splitter in two perpendicular diffraction planes, presenting an innovative approach to the development of such devices. The proposed grating structure is simple, high-performing, tolerant, and applicable in a wide range of applications such as polarization imaging and high-precision two-dimensional displacement measurement.

Dammann gratings-based truly parallel optical matrix multiplication accelerator.

Matrix multiplication (MM) is a fundamental operation in various scientific and engineering computations, as well as in artificial intelligence algorithms. Efficient implementation of MM is crucial for speeding up numerous applications. Photonics presents an opportunity for efficient acceleration of dense matrix computation, owing to its intrinsic advantages, such as huge parallelism, low latency, and low power consumption. However, most optical matrix computing architectures have been limited to realizing single-channel vector-matrix multiplication or using complex configurations to expand the number of channels, which does not fully exploit the parallelism of optics. In this study, we propose a novel, to the best of our knowledge, scheme for the implementation of large-scale two-dimensional optical MM with truly massive parallelism based on a specially designed Dammann grating. We demonstrate a sequence of MMs of 50 pairs of randomly generated 4 × 8 and 8 × 4 matrices in our proof-of-principle experiment. The results indicate that the mean relative error is approximately 0.048, thereby demonstrating optical robustness and high accuracy.

Polarization-independent 2×2 high diffraction efficiency beam splitter based on two-dimensional grating.

Better performances of two-dimensional (2D) grating are required recently, such as polarization independence, high efficiency, wide bandwidth and so forth. In this paper, we propose a 2×2 2D silver cylindrical array grating with excellent polarization-independent high diffraction efficiency (DE) over communication band for beam splitting. The grating was calculated by rigorous coupled wave analysis (RCWA) and can achieve over 24% DE of four first diffraction orders at 1550 nm with nonuniformity of 1.43% in both transverse electric (TE) and transverse magnetic (TM) polarizations, which is a significant improvement over previous reports. The holographic exposure technology, wet chemical development process and electron beam evaporation were used to fabricate the 2D grating. The correctness and accuracy of the calculation are fully verified with the measurement result of fabricated grating. Excellent performances of the 2D splitter we proposed will have great potential for applications in optical communication, semiconductor manufacturing and displacement measurement.

Polarization-independent high diffraction efficiency two-dimensional grating based on cylindrical hole nano arrays.

In this paper, we propose a reflective two-dimensional (2D) metal-dielectric grating based on cylindrical hole nano arrays with excellent polarization-independent high diffraction efficiency. The effects of the geometrical parameters on the polarization characteristic and diffraction efficiency are studied. Optimized results show that the (-1, 0) order diffraction efficiency of transverse electric (TE) and transverse magnetic (TM) polarizations under Littrow mounting is 98.31% and 98.05% at 780 nm incident wavelength, and the diffraction efficiency equilibrium is 99.74%, which is a significant improvement over the previously reported 2D gratings. The high efficiency in both TE and TM polarizations makes it a potential candidate as planar grating rulers for high precision multi-axis displacement measurement. Moreover, the cylindrical hole-based structure performs well in manufacturing tolerances, which provides the possibility for practical applications.

Two-dimensional picometer comb for three-dimensional reconstruction.

A two-dimensional (2D) picometer comb, a novel optical element made by picometer-differential four times exposed in two perpendicular directions, is proposed to generate the dot array projection pattern for three-dimensional (3D) shape reconstruction and other applications. Not only does a 2D picometer comb generate a stable light field distribution with extremely long depth of field and small divergence angle as a one-dimensional picometer comb, it also has new properties, such as periodicity of diffraction field in two perpendicular directions and high concentration of energy of points, which is particularly suitable for providing dot array structured light. We demonstrate that the diffraction field of a 2D picometer comb provides a solution for non-defocusing 3D reconstruction with a dot array. In fabrication of a 2D picometer comb, we can modulate the holography by changing the angle of two beams slightly, so its period can be measured at picometer accuracy. A 2D picometer comb can be made to any scale, then it can be integrated to mobile devices, such as a mobile phone, for 3D shape reconstruction. Furthermore, the concept of a 2D picometer comb would be applied to generate a picometer light field for opening the door of pico-optics in the future.

Picometer-differential twice-exposed element for three-dimensional measurement with extremely long depth of field.

The accuracy of optical three-dimensional (3D) shape measurement is always influenced by the defocusing of a projection or imaging system. In this paper, a novel optical element made by picometer-differential twice-exposed holography, called a picometer comb, is proposed to generate the projection pattern for 3D shape measurement. Two interference fields with picometer-scale period difference are recorded on a substrate to fabricate the picometer comb by twice-exposed laser holography; this element reconstructs the diffraction field, which is essentially the interference between the holograms of two object waves with a slight angle. This picometer comb has the advantage of the generation of a stable light field distribution with extremely long depth of field and small divergence angle. We demonstrate that this diffraction field provides a solution for non-defocusing 3D shape measurement.

Rapid optical µ-printing of polymer top-lensed microlens array.

Microlenses have wide applications for light beam focusing or shaping in micro-optical systems. However, it remains challenging for conventional microfabrication methods to rapidly fabricate arrays of microlenses with complex profiles like lens-on-lens structures. In this paper, we present the rapid fabrication of polymer microlenses with lens-on-lens structures by using a digital optical µ-printing technology. An improved dynamic optical exposure method is developed to directly and precisely fabricate polymer top-lensed microlenses (TLMLs). Arrays of TLMLs with either elongated focal depth or two separate foci have been numerically investigated and experimentally demonstrated.

Binocular vision profilometry for large-sized rough optical elements using binarized band-limited pseudo-random patterns.

In this paper, a non-contact binocular vision profilometry method is proposed to measure a rough lens with aperture of around 300mm. A series of binarized band-limited pseudo-random patterns (BBPPs) are projected onto the rough lens, we utilize the temporal encoding method so that each pixel in the captured images has its specific code word. Homologous points could be matched via stereo matching procedure, then the surface of the rough lens will be reconstructed based on triangulation method according to the previous calibration data. Compared with the three coordinate measuring machine (CMM), this method achieves a fast and cheap measurement of the large-sized rough lens, which might be highly interesting for fast and overall measurement of metre-sized rough elements in the future.

Scan angle error measurement based on phase-stepping algorithms in scanning beam interference lithography.

In this paper, a doubled-period grating (DPG) method is proposed to measure the scan angle error in scanning beam interference lithography (SBIL), together with a high-resolution two-dimensional stage and phase-stepping algorithms. A reference grating, which was the doubled period of the interference field, is adapted to diffract the incident left and right beams to form an interferogram captured by a CCD camera. The phase-stepping algorithm was applied to calculate the phase of the interferogram. First, by translating the stage, the reference grating lines were adjusted parallel to the scan direction by comparing the phase of the interferogram between the starting point and the ending point. Next, by rotating the stage step by step, the phase of the interferogram was obtained at each step as well as the phase slope. The scan angle error was considered to be least when the slope was minimum. Finally, a grating mask with a size of 100×100 mm2 was fabricated to verify the feasibility of the method. The scan angle error was measured with a precision of less than 12.65 µrad, which indicates the effectiveness of the proposed method to fabricate high-quality gratings in the future.

Long-range in situ picometer measurement of the period of an interference field.

A scanning reference grating (SRG) method is proposed for high-precision in situ measuring and controlling the period of a long-range interference field. The reference grating is produced with the in situ interference field; then it is used to obtain phase shift signal when scanning in the interference field. With the phase shift signal collected by the SRG system, before the exposure process of the holographic grating fabrication, the period and the period uniformity of the holographic grating can be evaluated directly from the interference field; then optical adjustment can be applied until the grating period is tuned to any certain desired value. Experiments of measurement and adjustment are conducted, and an interference field with period value of 833.335 nm±10 pm in 60 mm range is reached. The proposed method gives an efficient way to fabricate large gratings of an accurate period; furthermore, it provides a reliable tool that may lead us to picometer-level optical metrology and fabrication for the most advanced lithographic equipment and in other scientific fields.

Two-dimensional gold matrix method for encoding two-dimensional optical arbitrary positions.

In this study, a novel two-dimensional spatial coding pattern called two-dimensional Gold matrix method is proposed for general two-dimensional positioning. Considering the difficulty in representing a two-dimensional position in a single binary matrix, constructing a matrix while each submatrix refers to its location is a challenging mathematical problem. The general two-dimensional signal can be labeled by the two-dimensional Gold matrix, which results from a preferred pair of two m-sequences. For a pseudorandom m-sequence, the span-n property of the two-dimensional Gold matrix states that every n×n submatrix is unique and the decoding is fast and convenient. Numerical simulation and a proof-of-principle experiment are performed, and experimental results verified that the two-dimensional Gold matrix method is effective for high resolution and large range two-dimensional measurements.

Precision fringe period metrology using an LSQ sine fit algorithm.

High-precision grating fabrication is a precondition of grating-based displacement measurement techniques. Likewise, the value of high-precision fringe period is an essential parameter in the grating fabrication process, especially in scanning beam interference lithography. In this paper, a procedure for measuring the fringe periods of interference beams is introduced. The procedure includes signal acquisition and signal processing. The precisions of both the configuration for acquisition and the algorithm for processing are discussed. Experiments for fringe period measurement are also conducted, and an average value of 564.374 nm with a standard deviation of 1.5 pm is obtained, reaching a repeatability of 2.6 ppm. The value of precision period lays a solid foundation for the fabrication of high-precision gratings.

Eightfold optical encoder with high-density grating.

A novel grating interferometer configuration with eightfold optical subdivision to achieve ultrahigh resolution using a special symmetrical prism is proposed. The optical subdivision is enhanced by four times compared to traditional linear optical encoders. In this work, we take advantage of a high linear density grating of 1780 lines/mm, which is combined with an eightfold optical subdivision configuration. As a result, a high resolution of 68.6 pm is achieved. The apparatus adopts a symmetrical measurement configuration to reduce the error arising from environmental fluctuations. The verification experiments involve high optical subdivision, long- and short-range displacement measurement, and stability, with all results compared to those obtained with a commercial interferometer. The excellent agreement of the results demonstrates the effectiveness of our proposed system.

2016 Joint Applied Optics and Chinese Optics Letters digital holography and 3D imaging feature: introduction.

This digital holography and three-dimensional imaging feature issue is the second joint effort from Applied Optics (AO) and Chinese Optics Letters (COL).

Highly efficient reflective Dammann grating with a triangular structure.

A highly efficient reflective Dammann grating with a triangular structure operating at 1064 nm wavelength under normal incidence for TE polarization is designed and fabricated. Rigorous coupled wave analysis and particle swarm optimization algorithms are adopted to design and analyze the properties. The triangular reflective grating could cancel the 0th order, and the mechanism is clarified by the simplified modal method. The gratings are fabricated by direct laser writing lithography. The diffraction efficiency of fabricated grating is more than 86% at 1064 nm wavelength (97.6% in theory). This reflective grating should be a useful optical element in the field of high-power lasers as well as other reflective applications.

Polarization-independent Talbot effect.

We report the first observation of polarization-independent Talbot effect with a high-density grating for TE and TM polarizations, which is attributed to the identical phases and diffraction efficiencies of the diffraction orders for both polarizations. We introduce the simplified modal method that provides an insightful physical description for explanation of the diffraction efficiency and phase of the polarization-independent Talbot effect. Only two even grating modes can be excited, which determines the diffraction properties of the near-field image. We expect that this theoretical work will be helpful for the tremendous potential applications of the Talbot effect.

Square lattices of quasi-perfect optical vortices generated by two-dimensional encoding continuous-phase gratings.

We propose a type of two-dimensional (2D) encoding continuous-phase gratings capable of simultaneously generating a square lattice of multiple quasi-perfect vortices. As an example, a symmetrical and an asymmetrical 5×5 lattice of quasi-perfect vortices are experimentally demonstrated. It is shown that multiple quasi-perfect vortices with different topological charges are generated at different diffraction orders. The ring-width of these vortices is nearly constant, while there is a shift in the average ring-diameter when the carried charges are large enough, or when the ring-diameter is small. Additional axicon phase has been embedded into these 2D encoding gratings for the compensation of such shift in the average ring-diameter, and experimental results show that the shift can be greatly minimized after this compensation.

Unified beam splitter of fused silica grating under the second Bragg incidence.

A unified design for a 1×2 beam splitter of dielectric rectangular transmission gratings under the second Bragg incidence is theoretically investigated for TE- and TM-polarized light. The empirical equations of the relative grating parameters (ratio of the absolute one to incidence wavelength) for this design are also obtained with the simplified modal method (SMM). The influences of polarization of incident light and relative grating parameters on the performance of the beam splitter are thoroughly studied based on the SMM and rigorous coupled-wave analysis. Two specific gratings are demonstrated with an even split and high diffraction efficiency (>94% for TE polarization and >97% for the TM counterpart). The unified profiles of the 1×2 beam splitter are independent from the incidence wavelength since the refractive index of fused silica is roughly a constant over a wide range of wavelengths, which should be promising for future applications.

Binocular vision measurement using Dammann grating.

In this paper, we propose a novel three-dimensional (3D) profilometry using a binocular camera and a 64 × 64 Dammann grating for generation of a regular square laser array. A new constraint called a "ray constraint," taking advantage of the splitting characteristic of Dammann grating, is proposed for binocular matching. Binocular matching is realized by using ray constraint and precalibration of a laser array. Point clouds without outliers are obtained with binocular matching results according to triangulation. The experimental apparatus weighs less than 170 g with a width of less than 14 cm. We used this apparatus to scan a statue of Apollo under indoor illumination (at 450 lux). Its 3D model with complex profile was reconstructed by more than 150,000 points. This 3D profilometry has advantages of low cost, low power, and small size and should be useful for practical applications.

Feature issue of digital holography and 3D imaging (DH) introduction.

The OSA Topical Meeting "Digital Holography and 3D Imaging (DH)," was held in Seattle, Washington, July 13-17, 2014. Feature issues based on the DH meeting series have been released by Applied Optics (AO) since 2007. This year Optics Express (OE) and AO jointly decided to have one such feature issue in each journal. The DH meeting will continue in the future, as expected, and the next meeting is scheduled to be held on 24 - 28 May 2015, in Shanghai Institute of Optics and Fine Mechanics, Shanghai, China.