Optical pulling forces and their applications

Hang Li, Yongyin Cao, Lei-Ming Zhou, Xiaohao Xu, Tongtong Zhu, Yuzhi Shi, Cheng-Wei Qiu, and Weiqiang Ding

Optical manipulations utilizing the mechanical effect of light have been indispensable in various disciplines. Among those various manipulations, optical pulling has emerged recently as an attractive notion and captivated the popular imagination, not only because it constitutes a rich family of counterintuitive phenomena compared with traditional manipulations but also due to the profound physics underneath and potential applications. Beginning with a general introduction to optical forces, related theories, and methods, we review the progresses achieved in optical pulling forces using different mechanisms and configurations. Similar pulling forces in other forms of waves, including acoustic, water, and quantum matter waves, are also integrated. More importantly, we also include the progresses in counterintuitive left-handed optical torque and lateral optical force as the extensions of the pulling force. As a new manipulation degree of freedom, optical pulling force and related effects have potential applications in remote mass transportation, optical rotating, and optical sorting. They may also stimulate the investigations of counterintuitive phenomena in other forms of waves.

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Mathematics of vectorial Gaussian beams

Uri Levy, Yaron Silberberg, and Nir Davidson

Since the development of laser light sources in the early 1960s, laser beams are everywhere. Laser beams are central in many industrial applications and are essential in ample scientific research fields. Prime scientific examples are optical trapping of ultracold atoms, optical levitation of particles, and laser-based detection of gravitational waves. Mathematically, laser beams are well described by Gaussian beam expressions. Rather well covered in the literature to date are basic expressions for scalar Gaussian beams. In the past, however, higher accuracy mathematics of scalar Gaussian beams and certainly high-accuracy mathematics of vectorial Gaussian beams were far less studied. The objective of the present review then is to summarize and advance the mathematics of vectorial Gaussian beams. When a weakly diverging Gaussian beam, approximated as a linearly polarized two-component plane wave, say (𝐸𝑥,𝐵𝑦), is tightly focused by a high-numerical-aperture lens, the wave is “depolarized.” Namely, the prelens (practically) missing electric field 𝐸𝑦,𝐸𝑧 components suddenly appear. This is similar for the prelens missing 𝐵𝑥,𝐵𝑧 components. In fact, for any divergence angle (𝜃𝑑<1), the ratio of maximum electric field amplitudes of a Gaussian beam 𝐸𝑥:𝐸𝑧:𝐸𝑦 is roughly 1:𝜃2𝑑:𝜃4𝑑. It follows that if a research case involves a tightly focused laser beam, then the case analysis calls for the mathematics of vectorial Gaussian beams. Gaussian-beam-like distributions of the six electric–magnetic vector field components that nearly exactly satisfy Maxwell’s equations are presented. We show that the near-field distributions with and without evanescent waves are markedly different from each other. The here-presented nearly exact six electric–magnetic Gaussian-beam-like field components are symmetric, meaning that the cross-sectional amplitude distribution of 𝐸𝑥(𝑥,𝑦) at any distance (𝑧) is similar to the 𝐵𝑦(𝑥,𝑦) distribution, 𝐸𝑦(𝑥,𝑦) is similar to 𝐵𝑥(𝑥,𝑦), and a 90° rotated 𝐸𝑧(𝑥,𝑦) is similar to 𝐵𝑧(𝑥,𝑦). Components’ symmetry was achieved by executing the steps of an outlined symmetrization procedure. Regardless of how tightly a Gaussian beam is focused, its divergence angle is limited. We show that the full-cone angle to full width at half-maximum intensity of the dominant vector field component does not exceed 60°. The highest accuracy field distributions to date of the less familiar higher-order Hermite–Gaussian vector components are also presented. Hermite–Gaussian 𝔼-𝔹 vectors only approximately satisfy Maxwell’s equations. We have defined a Maxwell’s-residual power measure to quantify the approximation quality of different vector sets, and each set approximately (or exactly) satisfies Maxwell’s equations. Several vectorial “applications,” i.e., research fields that involve vector laser beams, are briefly discussed. The mathematics of vectorial Gaussian beams is particularly applicable to the analysis of the physical systems associated with such applications. Two user-friendly “Mathematica” programs, one for computing six high-accuracy vector components of a Hermite–Gaussian beam, and the other for computing the six practically Maxwell’s-equations-satisfying components of a focused laser beam, supplement this review.

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Perspective on light-induced transport of particles: from optical forces to phoretic motion

Pavel Zemánek, Giorgio Volpe, Alexandr Jonáš, and Oto Brzobohatý

Propulsive effects of light, which often remain unnoticed in our daily-life experience, manifest themselves on spatial scales ranging from subatomic to astronomical. Light-mediated forces can indeed confine individual atoms, cooling their effective temperature very close to absolute zero, as well as contribute to cosmological phenomena such as the formation of stellar planetary systems. In this review, we focus on the transport processes that light can initiate on small spatial scales. In particular, we discuss in depth various light-induced mechanisms for the controlled transport of microscopic particles; these mechanisms rely on the direct transfer of momentum between the particles and the incident light waves, on the combination of optical forces with external forces of other nature, and on light-triggered phoretic motion. After a concise theoretical overview of the physical origins of optical forces, we describe how these forces can be harnessed to guide particles either in continuous bulk media or in the proximity of a constraining interface under various configurations of the illuminating light beams (radiative, evanescent, or plasmonic fields). Subsequently, we introduce particle transport techniques that complement optical forces with counteracting forces of non-optical nature. We finally discuss particle actuation schemes where light acts as a fine knob to trigger and/or modulate phoretic motion in spatial gradients of non-optical (e.g., electric, chemical, or temperature) fields. We conclude by outlining possible future fundamental and applied directions for research in light-induced particle transport. We believe that this comprehensive review can inspire diverse, interdisciplinary scientific communities to devise novel, unorthodox ways of assembling and manipulating materials with light.

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Recent advances in holographic 3D particle tracking

Pasquale Memmolo, Lisa Miccio, Melania Paturzo, Giuseppe Di Caprio, Giuseppe Coppola, Paolo A. Netti, and Pietro Ferraro

Particle tracking is a fundamental technique for investigating a variety of biophysical processes, from intracellular dynamics to the characterization of cell motility and migration. However, observing three-dimensional (3D) trajectories of particles is in general a challenging task in classical microscopy owing to the limited imaging depth of field of commercial optical microscopes, which represents a serious drawback for the analysis of time-lapse microscopy image data. Therefore, numerous automated particle-tracking approaches have been developed by many research groups around the world. Recently, digital holography (DH) in microscopy has rapidly gained credit as one of the elective techniques for these applications, mainly due to the uniqueness of the DH to provide a posteriori quantitative multiple refocusing capability and phase-contrast imaging. Starting from this paradigm, a huge amount of 3D holographic tracking approaches have been conceived and investigated for applications in various branches of science, including optofluids, microfluidics, biomedical microscopy, cell mechano-trasduction, and cell migration. Since a wider community of readers could be interested in such a review, i.e., not only scientists working in the fields of optics and photonics but also users of particle-tracking tools, it should be very beneficial to provide a complete review of state-of-the-art holographic 3D particle-tracking methods and their applications in bio-microfluidics.

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Momentum of Light in a Dielectric Medium

Peter W. Milonni and Robert W. Boyd

We review different expressions that have been proposed for the stress tensor and for the linear momentum of light in dielectric media, focusing on the Abraham and Minkowski forms. Analyses of simple models and consideration of available experimental results support the interpretation of the Abraham momentum as the kinetic momentum of the field, while the Minkowski momentum is the recoil momentum of absorbing or emitting guest atoms in a host dielectric. Momentum conservation requires consideration not only of the momentum of the field and of recoiling guest atoms, but also of the momentum the field imparts to the medium. Different model assumptions with respect to electrostriction and the dipole force lead to different expressions for this momentum. We summarize recent work on the definition of the canonical momentum for the field in a dielectric medium.

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