The wavefront reconstruction of the preconditioned conjugate-gradient method and the Fourier transform method in the lateral shearing interferometry are discussed for their feasibility and accuracy in this paper. The numerical simulation study on the accuracy of both the wavefront reconstruction method under ideal situation and under the simulated noisy situation is also introduced. Simulation experiments show that the preconditioned conjugate-gradient method has better anti-noise performance, and provides higher precision for discontinuous phase wavefront reconstruction. The two-grating lateral shearing interference experiment is carried out to verify the simulated results based on both the preconditioned conjugate-gradient method and the Fourier transform method.
A chiral plasmonic lens (CPL) suitable for circular polarization analyzer is designed and numerically investigated. It consists of two arrays of rectangular nanoslits milled into a gold film along Archimedes spirals. We demonstrate both theoretically and numerically that the designed structure can convert an incident circularly polarized light beam with prescribed chirality into a Bessel-like distributed focus, but the circularly polarized one with the opposite chirality cannot be transmitted and focused by the same CPL due to the alternative chirality. Further, three-dimensional finite-difference time-domain (FDTD) simulations show that an ultrahigh extinction ratio up to ten thousands of the CPL is numerically achieved with a device less than 10 λ<sub>spp</sub>, which is two orders higher than that of a conventional plasmonic circularization analyzer with single Archimedes-spiral groove. The designed structure can be widely used in miniature polarimeter and detection of spin angular momentum.
The two-dimensional wavefront reconstruction method based on double-shearing and least squares fitting is proposed in this paper. Four one-dimensional phase estimates of the measured wavefront, which correspond to the two shears and the two orthogonal directions, could be calculated from the differential phase, which solves the problem of the missing spectrum, and then by using the least squares method the two-dimensional wavefront reconstruction could be done. The numerical simulations of the proposed algorithm are carried out to verify the feasibility of this method. The influence of noise generated from different shear amount and different intensity on the accuracy of the reconstruction is studied and compared with the results from the algorithm based on single-shearing and least squares fitting. Finally, a two-grating lateral shearing interference experiment is carried out to verify the wavefront reconstruction algorithm based on doubleshearing and least squares fitting.
This paper introduces a new way of two-dimensional wavefront reconstruction based on the Fourier modal method. Expending the target wavefront by using Fourier series, calculating the expansion coefficient based on the differential phase measured from the experiment, and fitting the coefficients at the missing points by averaging adjacent values, the target wavefront could be reconstructed eventually by using inverse Fourier transform on the expansion coefficients. The paper also introduces our numerical simulation study on the precisions of both the wavefront reconstruction under ideal situation and under the situation with simulated noise respectively. Corresponding verification experiment for the two-dimensional wavefront reconstruction based on the Fourier modal method is also done by using a two-grating lateral shearing interferometry system, with the 3D profile of the sample obtained.
Orbital angular momentum (OAM), as nature of optical field, has attracted considerable attention, due to its
academic interest and potential applications such as quantum information, atomic manipulation, micromanipulation
and the biosciences. The well-known OAM carried by an optical field originates from the azimuthal phase
gradient of an optical vortex field with a helical phase structure. Here we predict a novel optical OAM, which
is induced by curl of polarization. To demonstrate experimentally the above prediction, we present an idea for
creating a kind of radial-variant vector fields, which could have all local linear polarization and hybrid states of polarization (SoPs). By specifically arranging the SoPs of the vector fields, new effects and phenomena can be anticipated that can expand the functionality and enhance the capability of optical system. The generated vector fields with the radial-variant hybrid SoPs can carry such a novel OAM. Optical trapping experiments validate that the focused vector fields without any additional phase vortex, as the ring optical tweezers, exert torques to drive the orbital motion of the trapped isotropic microspheres.
We describe a convenient way to generate arbitrary vector beams by using a spatial light modulator, based on
interferometric superposition of two orthogonally polarized beams. In our constructed optical setup, the SLM is used to
produce a computer-generated holographic grating that diffracts a linearly polarized incident light into the +1st and -1st
diffraction orders with desired wavefronts. After the two diffraction beams pass through two quarter wave-plates, the
left- and right-handed circularly polarizations are yielded, respectively. Then a Rochi grating is utilized to recombine the
two beams into single one such that any desired polarization configuration is achieved. We demonstrate the versatility of
our method through optical experiment, in which a variety of polarization beams are realized. By making use of the
incident wave with helical phase, our technique can produce both cylindrically symmetric and asymmetric polarizations.
To the best of our knowledge, the experimental realization of cylindrically asymmetric polarization is reported for first
time. We also study the focal properties of vector beam through a high numerical aperture lens. Starting from
Richards-Wolf vectorial diffraction theory we calculate the focal field distribution and obtain some interesting focal
volume structures, such as flat-topped focus, doughnut focus with special dark volume structure.
A novel algorithm is proposed to reconstruct two-dimensional wave-front from differential wave-fronts measured in shearing interferometer. Two 1-dimensional estimates of object wave-front are computed using Fourier transform from differential wave-fronts, and then the 2-dimensional wave-front distribution is derived by use of least-square fitting. The algorithm is applicable to cases in which the shear amount is larger than one sampling interval, and thus alleviates the limitation on the shear amount imposed by conventional algorithms. Investigations into reconstruction accuracy and reliability are carried out by computer simulation. Optical experiments are made in a lateral shearing interferometer based on double-grating, and 3-dimensional surface profile of optical element under test are measured and presented. The analysis and discussion are also given in the final part of this article.
The kinoform is attractive because of the high diffraction efficiency and the manner of on-axial reconstruction. In this work, we use the Gerchberg-Saxton iterative algorithms to optimize phase distribution of the kinoform. The phase in each pixel is then quantized into a set of eight-level values. The surface of quartz glass plate is etched to a depth determined by the corresponding phase retard, forming a kinform with stair-like surface relief. The optical experiments are canied out. The on-axial reconstruction image with high fidelity and high efficiency is obtained.
A phase-compensated encoding method is proposed in this paper for the design of phase-only optical element (also called kinoform). The proposed elements are surface relief plates, i.e. , phase-only elements, which are based on the concept of computer-generated masks fabricated by common etching processes. The new encoding method can reduce the reconstructed errors such as quantization error through multi-level phase compensations. The number of subcells of every encoded cell is determined by the requirement of error reduction in actual implementation. Computer simulation confirms that the proposed encoding scheme can produce reconstruction with higher signal-to-noise ratio, higher diffractive efficiency and better uniformity than conventional encoding methods.
We have proposed a novel principle for design of the binary GZP that can produce the desired pattern in the focal plane. The modified GZP can be fabricated as easily as the FZP. The proposed GZP has great flexibility in terms of manipulating the focusing properties. Optical experiments have confirmed the reliability of the GZP in focusing light into the specified area. The low cost and easy production of the element show that it can serve an alternative to refractive lens in the short wavelength region where refractive optics is not applicable owing to possible strong absorption.
Optimal incoherent filters are proposed for distortion- invariant and noise-tolerance correlation. The optical transfer function (OTF) of the correlator is specified as a realizable phase-only term which is modified by a passband function. The phase-only term is optimized by the simulated annealing for producing a sharp and distortion-invariant correlation peak, and the passband function is selected by a direct iterative search algorithm to achieve the noise- tolerant image recognition. The designed OTF is generated by dual-filter synthesis. The correlation output is obtained from the subtraction between the correlation of two realizable filters with the input image. Optical experiments and computer simulations show that the proposed correlator can yield a sharp correlation peak with excellent distortion robustness and noise tolerance.
A method is proposed for designing a distortion-invariant correlation phase-only filter by iteratively optimizing the Homer efficiency. Comparisons with conventional filters show some attractive properties of the proposed filters, such as a high correlation peak and good discrimnation ability. An effective improvement for reducing the peak deviation of the phase-only filter is also proposed. The correlation performance of the constructed filters is confirmed by computer simulation.