Reverse engineering approach to focus shaping

Spatio-temporal structuring control of a vectorial focal field

Focal field modulation has attracted a lot of interest due to its potential in many applications such as optical tweezers or laser processing, and it has recently been facilitated by spatial light modulators (SLMs) owing to their dynamic modulation abilities. However, capabilities for manipulating focal fields are limited by the space-bandwidth product of SLMs. This difficulty can be alleviated by taking advantage of the high-speed modulation ability of digital micromirror devices (DMDs), i.e., trading time for space to achieve fine focus shaping. In this paper, we propose a new, to the best of our knowledge, technique for achieving four-dimensional focal field modulation, which allows for independent manipulation of the focal field's parameters (including amplitude, phase, and polarization) in both the space and time domains. This technique combines a DMD and a vector field synthesis system based on a 4-f system. The high-speed modulation ability of DMDs enables versatile focus patterns to be fast switchable during the exposure time of the detector, forming multiple patterns in a single recording frame. By generating different kinds of focal spots and lines at different moments during the exposure time of the detector, we can finally get complete multifocal spots and lines. Our proposed method is effective at improving the flexibility and speed of the focal field modulation, which is beneficial to applications.

Focus shaping of high numerical aperture lens using physics-assisted artificial neural networks

We present a physics-assisted artificial neural network (PhyANN) scheme to efficiently achieve focus shaping of high numerical aperture lens using a diffractive optical element (DOE) divided into a series of annular regions with fixed widths. Unlike the conventional ANN, the PhyANN does not require the training using labeled data, and instead output the transmission coefficients of each annular region of the DOE by fitting weights of networks to minimize the delicately designed loss function in term of focus profiles. Several focus shapes including sub-diffraction spot, flattop spot, optical needle, and multi-focus region are successfully obtained. For instance, we achieve an optical needle with 10λ depth of focus, 0.41λ lateral resolution beyond diffraction limit and high flatness of almost the same intensity distribution. Compared to typical particle swarm optimization algorithm, the PhyANN has an advantage in DOE design that generates three-dimensional focus profile. Further, the hyperparameters of the proposed PhyANN scheme are also discussed. It is expected that the obtained results benefit various applications including super-resolution imaging, optical trapping, optical lithography and so on.

Shaping the focal intensity distribution using a partially coherent radially polarized beam with multiple off-axis vortices

A new kind of partially coherent vector vortex beam, namely, the partially coherent radially polarized (PCRP) beam with multiple off-axis vortices, is introduced, and the average intensity distributions of such vortex beam focused by a thin lens are investigated theoretically. It is novelty that the off-axis vortices will induce the focal intensity redistribution and reconstruction, while this remarkable characteristic will be vanished in the case of a very low coherence. In view of this distinctive feature, a new method has been put forward to shape or modulate the focal intensity distribution by elaborately tailoring the multiple off-axis vortices as well as the coherence length. More importantly, some peculiar focal fields with novel structures, such as bar-shaped, triangle-shaped, square-shaped, and pentagon-shaped hollow profiles or flat-top foci, are obtained. Our results indicate that modulating the multiple off-axis vortices provides an additional degree of freedom for focus shaping.

Fast calculation of tightly focused random electromagnetic beams: controlling the focal field by spatial coherence

Focusing of a vectorial (electromagnetic) optical beam through a high numerical aperture can be investigated by means of the Richards-Wolf diffraction integral. However, such an integral extends from two-dimensional to four-dimensional, greatly increasing the computation time and therefore limiting the applicability, when light with decreased spatial coherence is considered. Here, we advance an effective protocol for the fast calculation of the statistical properties of a tightly focused field produced by a random electromagnetic beam with arbitrary state of spatial coherence and polarization. The novel method relies on a vectorial pseudo-mode representation and a fast algorithm of the wave-vector space Fourier transform. The procedure is demonstrated for several types of radially (fully) polarized but spatially partially coherent Schell-model beams. The simulations show that the computation time for obtaining the focal spectral density distribution with 512 × 512 spatial points for a low coherence beam is less than 100 seconds, while with the conventional quadruple Richards-Wolf integral more than 100 hours is required. The results further indicate that spatial coherence can be viewed as an effective degree of freedom to govern both the transverse and longitudinal components of a tightly focused field with potential applications in reverse shaping of focal fields and optical trapping control.

Analytical inversion of the focusing of high-numerical-aperture aplanatic systems

We propose a method for an analytical inversion of the electric and magnetic fields at the focus of a high-NA aplanatic system to obtain incident light beam distribution. Our approach is based on an inverse Fourier transform of the Richards-Wolf formalism for targeted longitudinal fields along the radial or axial directions at the non-paraxial focus. Analytical solutions are discussed for both axial and radial focal fields for a radially polarized incident light beam, and a criterion is defined to access a physically valid solution. We also validate the method according to results found in the literature. Finally, we show how the method can be generalized to other incident field distributions.

Focus shaping of partially coherent radially polarized vortex beam with tunable topological charge

In this paper, we have introduced a new class of partially coherent vector vortex beams, named radially polarized multi-Gaussian Schell-model (MGSM) vortex beam, carrying the vortex phase with tunable topological charges (i.e., both integral and fractional values) as a natural extension of the radially polarized MGSM beam. The tight focusing properties of the radially polarized MGSM vortex beam passing through a high numerical aperture (NA) objective lens are investigated numerically based on the vectorial diffraction theory. Numerical results show that the focal intensity distributions of the radially polarized MGSM vortex beam can be shaped by regulating the structure of the correlation functions and the topological charge of vortex phase. In contrast with the integral vortex beam, the most intriguing property of the fractional vortex beam is that the focal intensity distribution at the focal plane can be nonuniformity and asymmetry, while such unique characteristics will vanish when the spatial coherence length is sufficiently small. Furthermore, some focal fields with novel structure, such as a focal spot with nonuniform asymmetric or an anomalous asymmetric hollow focal field, can be formed by choosing suitable fractional values of topological charge and spatial coherence length. Our results will be useful for optical trapping, especially for trapping of irregular particles or manipulation of absorbing particles.

Inverse method to engineer uniform-intensity focal fields with arbitrary shape

We present an inverse method to engineer uniform-intensity focal fields with arbitrary shape. Amplitude, phase, and polarization states, as adjustable parameters, are used to seek the desired focal fields in the non-iterative computational procedure. Our method can be applied to the cases with low and moderate numerical aperture (NA), in which case the feasibility and validity of our approach have been demonstrated in theory, simulation and experiment, respectively. For the case of higher NA, simulated results based on the Richards-Wolf diffraction integral are shown. We also made some discussions on the experiments with the higher NA. Our method should have wide applications in optical micro machining, optical trapping and so on.

Spatially-distributed orbital angular momentum beam array generation based on greedy algorithms and coherent combining technology

A novel approach to generate a spatially-distributed orbital angular momentum (OAM) beam array based on coherent combining technology is presented. The arrangement of the multiple fundamental Gaussian beams at the initial plane, as well as the intensity weights and the phase distributions of the array beams, is determined by the reversal of Huygens Fresnel diffraction and the greedy algorithm. This method ensures that a vortex beam array is formed at a specified distance, and the distance can be adjusted by phase modulation. The evolution properties of the synthesized beam array near the receiver plane are studied as well to estimate the robustness of the method. The experimental limitations of this technique are discussed, including the maximum number of beams, the relative separation of each beam and the maximum topological charges. The results illustrate that a spatially-distributed OAM beam array can be effectively generated within a finite distance interval, and the distance is adjustable. This new method enables further applications of a structured optical field, such as optical communication and spatial light structuring.

Vector polymorphic beam

A scalar polymorphic beam is designed with independent control of its intensity and phase along a strongly focused laser curve of arbitrary shape. This kind of beam has been found crucial in the creation of freestyle laser traps able to confine and drive the motion of micro/nano-particles along reconfigurable 3D trajectories in real time. Here, we present and experimentally prove the concept of vector polymorphic beam adding the benefit of independent design of the light polarization along arbitrary curves. In particular, we consider polarization shaped tangential and orthogonal to the curve that are of high interest in optical manipulation and laser micromachining. The vector polymorphic beam is described by a surprisingly simple closed-form expression and can be easily generated by using a computer generated hologram.

Vectorial optical fields: recent advances and future prospects

Driven by their potential applications, vectorial optical fields with spatially inhomogeneous states of polarization within the cross section have drawn significant attention recently. This work intends to review some of the latest development of this rapidly growing field of optics and offer a general overview of the current status of this field in a few areas. Mathematical descriptions of generalized vectorial optical fields are provided along with several special examples. A time-reversal methodology for the creation of a wide variety of exotic optical focal fields with prescribed characteristics within the focal volume is presented. Recently developed methods for the generation of vectorial optical fields that utilize fiber lasers, digital lasers, vectorial optical field generator, metasurfaces or photoalignment liquid crystals are summarized. The interactions of these vectorial optical fields with various micro- and nano-structures are presented and the prospects of their potential applications are discussed. The connection of vectorial optical fields with higher dimensionality in quantum information is summarized.

Shaping of optical vector beams in three dimensions

We present a method of shaping three-dimensional (3D) vector beams with prescribed intensity distribution and controllable polarization state variation along arbitrary curves in three dimensions. By employing a non-iterative 3D beam-shaping method developed for the scalar field, we use two curved laser beams with mutually orthogonal polarization serving as base vector components with a high-intensity gradient and controllable phase variation, so that they are collinearly superposed to produce a 3D vector beam. We experimentally demonstrate the generation of 3D vector beams that have a polarization gradient (spatially continuous variant polarization state) along 3D curves, which may find applications in polarization-mediated processes, such as to drive the motion of micro-particles.

Efficient generation of vector beams by calibrating the phase response of a spatial light modulator

The spatial light modulator (SLM) is considered as an effective device to create beams with inhomogeneous phases and polarizations, such as vortex beams and vector beams. However, the nonlinear responses of SLM severely reduce the generation efficiency of these beams. In this paper, by calibrating the SLM to present a linear phase response in the scope of 0-2π, we propose a convenient and efficient method of creating vector beams with arbitrary polarizations based on phase encoding. Compared with the common methods of generating vector beams, our approach can distinctly enhance the generation efficiency.

Manipulating spin-dependent splitting of vector abruptly autofocusing beam by encoding cosine-azimuthal variant phases

We report the realization of spin-dependent splitting of vector abruptly autofocusing beam (AAB) by encoding cosine-azimuthal variant phases. By employing the local spatial frequency (LSF), we reveal an approximation mapping relationship between focal field intensity of the two spin components and the pertinent phase distribution of input field. As well as theoretical analysis, we present experimental demonstrations of this guidance. Special focal field intensity, polarization and phase are realized by consciously managing the cosine-azimuthal variant phase. This distinctive focal field of vector AAB may have a broad range of applications in harnessing the spin-orbit coupling, optical trapping and laser machining.

Synthesis of focused beam with controllable arbitrary homogeneous polarization using engineered vectorial optical fields

The propagation and focusing properties of light beams continue to remain a research interest owning to their promising applications in physics, chemistry and biological sciences. One of the main challenges to these applications is the control of polarization distribution within the focal volume. In this work, we propose and experimentally demonstrate a method for generating a focused beam with arbitrary homogeneous polarization at any transverse plane. The required input field at the pupil plane of a high numerical aperture objective lens can be found analytically by solving an inverse problem with the Richard-Wolf vectorial diffraction method, and can be experimentally created with a vectorial optical field generator. Focused fields with various polarizations are successfully generated and verified using a Stokes parameter measurement to demonstrate the capability and versatility of proposed technique.