Phase and amplitude beam shaping with two deformable mirrors implementing input plane and Fourier plane phase modifications

Multilevel synergically controlling wavefront correction of a high-power slab laser system

We present a multilevel synergically controlling wavefront correction method that can apply in a slab laser system. To fully utilize the response frequency and the stroke of actuators of the single deformable mirror (DM), we design a set of multilevel wavefront correction devices to reduce the root-mean square of wavefront aberration before the DM. As the wavefront of slab geometry solid-state lasers mainly consists of fourth and longitudinally distributed aberration, such as 5th, 9th, and 14th orders of Legendre polynomials. We design a precompensating level of the aberration with a slow-drift mirror, fast-steer mirror, one-dimensional adjustable slab-aberration compensator, and beam-shaping system to reduce these orders of wavefront aberration with low spatial resolution and large stroke. As the controlling bandwidth of different devices is diverse, the coupling oscillation between the precompensating level and adaptive optics (AO) level occurs, then we develop the multilevel synergically control to address the coupling. With the precompensating level, the experimental result shows the residual wavefront aberration of the slab laser is compensated well by the AO level effectively within the compensating capability. We clean up a 9.8 kW slab laser system with the beam quality β of far-field focus spots improved from 17.71 to 2.24 times the diffraction limit.

Calculation of the modified control matrix for a selected unimorph deformable mirror to compensate the piezoelectric hysteresis effect using the inverse Bouc-Wen model

The hysteresis behavior of piezoelectric actuators degrades the positioning accuracy and bandwidth of nano-positioning systems. Therefore, considering the hysteresis of piezoelectric deformable mirrors is completely essential and also improves the modeling accuracy of adaptive optics layouts. Because of the unique adaptability and mathematical flexibility of the Bouc-Wen model it has gained popularity, and as a result, in many scientific applications, it is one of the most conventional models typically employed to describe nonlinear hysteretic systems. Among different deformable mirrors, a unimorph piezoelectric deformable mirror is a suitable choice to be used in adaptive optics systems because of its relative convenience and cost-effective production. This paper proposes a new, to the best of our knowledge, approach to determine the influence function and the voltage control matrix of a specific unimorph mirror by considering a simplified inverse Bouc-Wen hysteresis model as a frequency function. Then the results for two selected standard Zernike modes, defocus and astigmatism-x, have been simulated using Comsol Multiphysics and MATLAB at a range of 5 to 100 Hz. For a more comprehensive comparison, the root-mean-square error and the coefficients of the Zernike terms have been applied as two criteria. According to the simulation results, the hysteresis effect of piezoelectric actuators has been significantly compensated by applying the inverse Bouc-Wen model at different frequencies, especially for higher frequencies. The effectiveness of the inverse Bouc-Wen model to compensate the hysteresis has been observed in astigmatism-x mode slightly more than in the defocus mode.

Principles of electron wave front modulation with two miniature electron mirrors

We have analyzed the possibilities of wave front shaping with miniature patterned electron mirrors through the WKB approximation. Based on this, we propose a microscopy scheme that uses two miniature electron mirrors on an auxiliary optical axis that is in parallel with the microscope axis. A design for this microscopy scheme is presented for which the two axes can be spatially separated by as little as 1 mm. We first provide a mathematical relationship between the electric potential and the accumulated phase modulation of the reflected electron wave front using the WKB approximation. Next, we derive the electric field in front of the mirror, as a function of a topographic or pixel wise excited mirror pattern. With this, we can relate the effect of a mirror pattern onto the near-field phase, or far field intensity distribution and use this to provide a first optical insight into the functioning of the patterned mirror. The equations can only be applied numerically, for which we provide a description of the relevant numerical methods. Finally, these methods are applied to find mirror patterns for controlled beam diffraction efficiency, beam mode conversion, and an arbitrary phase and amplitude distribution. The successful realization of the proposed methods would enable arbitrary shaping of the wave front without electron-matter interaction, and hence we coin the term virtual phase plate for this design. The design may also enable the experimental realization of a Mach-Zehnder interferometer for electrons, as well as interaction-free measurements of radiation sensitive specimen.

Light field camera study of near-ground turbulence anisotropy and observation of small outer-scales

Understanding turbulence effects on laser beam propagation is critical to the emerging design, study, and test of many long-range free space optical (FSO) communication and directed energy systems. Conventional studies make the prevalent assumption of isotropic turbulence, while more recent results suggest anisotropic turbulence for atmospheric channels within a few meters elevation above the ground. As countless FSO systems have been and continue to be deployed in such channels, analysis of anisotropic modelings has become one of the fastest growing areas in FSO research. This in turn motivates new tools that can distinguish anisotropic characteristics to improve both modeling accuracy and physical interpretations. Wavefront sensors such as Shack-Hartmann sensors, interferometers, and plenoptic sensors have been devised and used in experiments; however, they all require rigid alignments that lack resilience against temperature gradient buildup and beam wander. We find that by using a light field camera (LFC) that extracts perturbation of individual light rays, the wave structure function of turbulence can be retrieved with high reliability. Furthermore, we find through experiments that the outer scales of near-ground turbulence tend to be a magnitude smaller than conventional theoretical assumptions, agreeing with new findings by others but being absent in current theoretical modelings. As a result, we believe that the LFC is an ideal candidate in the frontier of turbulence research; it is both commercially available and easy to adapt to turbulence experiments.

Digital Image Watermarking Techniques: A Review

Digital image authentication is an extremely significant concern for the digital revolution, as it is easy to tamper with any image. In the last few decades, it has been an urgent concern for researchers to ensure the authenticity of digital images. Based on the desired applications, several suitable watermarking techniques have been developed to mitigate this concern. However, it is tough to achieve a watermarking system that is simultaneously robust and secure. This paper gives details of standard watermarking system frameworks and lists some standard requirements that are used in designing watermarking techniques for several distinct applications. The current trends of digital image watermarking techniques are also reviewed in order to find the state-of-the-art methods and their limitations. Some conventional attacks are discussed, and future research directions are given.

Statistical properties of a controllable partially coherent radially and azimuthally polarized rotating elliptical Gaussian optical coherence lattice in anisotropic ocean turbulence

The optical coherent lattice (OCL) with periodic reciprocity has been previously proposed for free-space information transfer and optical communications. Here, a new class of partially coherent radially and azimuthally polarized rotating elliptical Gaussian optical coherent lattice (PCRPREGOCL and PCAPREGOCL) is introduced. Based on the extended Huygens-Fresnel principle and the spatial power spectrum of the anisotropic ocean turbulence, the analytical expressions of the average intensity of the PCRPREGOCL and the PCAPREGOCL through the anisotropic ocean turbulence are obtained. The effects of elliptical coefficients, lattice constants, the number of lattice lobes, wavelengths and anisotropic ocean turbulence parameters on the statistical properties of the PCRPREGOCL and the PCAPREGOCL are studied in detail. It is found that each sub-pattern in the PCRPREGOCL maintains a controllable rotation within a certain distance, which plays an important role in resisting the influence of turbulence. When the propagation distance increases, the PCRPREGOCL and the PCAPREGOCL gradually change from two elliptical Gaussian patterns into a coherent array with periodic reciprocity and eventually evolves into a Gaussian-like pattern. Our work provides new thoughts in applying OCL to overcome turbulence influence in underwater optical communication and underwater laser radar.

Received Probability of Vortex Modes Carried by Localized Wave of Bessel–Gaussian Amplitude Envelope in Turbulent Seawater

By using the two-frequency coherence function model of a beam in a turbulent medium and the localized wave theory of the polychromatic beam, we develop the spectrum average mutual coherence function of the localized wave of Bessel–Gaussian amplitude envelope and the spectrum average coherence length of spherical wave. By the spectrum average coherence length and the spectrum average mutual coherence function, we construct a received probability of vortex modes carried by localized wave of Bessel–Gaussian amplitude envelope in anisotropic turbulent seawater. Our results show that the received probability of signal vortex modes increases with the increase of half-modulated pulse width of the input pulse, turbulent inner scale, anisotropic factor of turbulence and rate of dissipation of kinetic energy per unit mass of fluid, but it increases with the decrease of the Bessel cone angle and the dissipation rate of the mean-squared temperature. We also find that there is a maximum effective beam waist for a given receiving aperture, and the vortex mode is more sensitive to salinity fluctuations than to temperature fluctuations in turbulence. Our conclusions show that localized wave of Bessel–Gaussian amplitude envelope is a more suitable beam for the vortex mode communication than conventional vortex waves.

A Review of Tunable Orbital Angular Momentum Modes in Fiber: Principle and Generation

Orbital angular momentum (OAM) beams, a new fundamental degree of freedom, have excited a great diversity of interest due to a variety of emerging applications. The scalability of OAM has always been a topic of discussion because it plays an important role in many applications, such as expanding to large capacity and adjusting the trapped particle rotation speed. Thus, the generation of arbitrary tunable OAM mode has been paid increasing attention. In this paper, the basic concepts of classical OAM modes are introduced firstly. Then, the tunable OAM modes are categorized into three types according to the orbital angular momentums and polarization states of mode carrying. In order to understand the OAM evolution of a mode intuitively, three kinds of Poincaré spheres (PSs) are introduced to represent the three kinds of tunable OAM modes. Numerous methods generating tunable OAM modes can be roughly divided into two types: spatial and fiber-based generation methods. The principles of fiber-based generation methods are interpreted by introducing two mode bases (linearly-polarized modes and vector modes) of the fiber. Finally, the strengths and weaknesses of each generation method are pointed out and the key challenges for tunable OAM modes are discussed.

Compound Metaoptics for Amplitude and Phase Control of Wave Fronts

Metasurfaces allow tailored control of electromagnetic wave fronts. However, due to local conservation of power flow, passive, lossless, and reflectionless metasurfaces have been limited to imparting phase discontinuities-and not power density discontinuities-onto a wave front. Here, we show how the phase and amplitude profiles of a wave front can be independently controlled using two closely spaced phase-discontinuous metasurfaces. The two metasurfaces, each designed to exhibit spatially varying refractive properties, are separated by a wavelength-scale distance and together form a compound metaoptic. A method of designing the compound metaoptic is presented, which enables transformation between arbitrary complex-valued field distributions without reflection, absorption, polarization loss, or active components. Such compound metaoptics may find applications in the optical trapping of particles, displaying three-dimensional holographic images, shrinking the size of optical systems, or producing custom (shaped and steered) far-field radiation patterns.