Light beats the spread: “non‐diffracting” beams

Abstract

Non-diffracting" beams do not spread as they propagate. This property is useful in many areas. Here, the theory, generation, properties, and applications of various "non-diffracting" beams, including the Bessel beam, Mathieu beam, and Airy beam is reviewed. Applications include imaging, micromanipulation, nonlinear optics, and optical transfection."Non-diffracting" finite energy Airy beam clearing a chamber of micro-particles.

Engineering light-matter interaction for emerging optical manipulation applications

“…These propagation-invariant beams are interesting for a number of reasons. Certain parts of such beams, such as the central lobe of a Bessel beam, can seemingly have a diffraction-free character [23]: the light that diffracts out of the central lobe is replenished by diffraction from the other parts of the beam. This constant replenishment by diffraction from the other parts of the beam during propagation also leads to the seemingly self-healing or self-reconstructing behavior.…”

“…Such synthesized beams include phase gradient beams [17], vortex beams [21,22], non-diffracting beams [23], accelerating beams [24], self-healing beams [25], or more complex structured beams achieved by encoding holograms on spatial light modulators (SLM) [26,27]. Among these synthesized beams, a phase-gradient force can be generated, which provides a complementary force to the intensity-gradient force.…”

Propagation-invariant beams with quantum pendulum spectra: from Bessel beams to Gaussian beam-beams

“…The family is based on the set of special function solutions of a wellunderstood physical problem, namely the eigenstates of a quantum pendulum [12,13] for a matter wave confined to a circle of radius L subject to a constant gravitational field strength g, which acts as the interpolating parameter for 0 ≤ g ≤ ∞. Such pendulum eigenstates are complex distributions on the circle with angle θ (with radius the pendulum length L), which we consider as the spectral distribution of our beams in Fourier space.With a spectrum restricted to the circle (with L → k r , the radial wavenumber), the propagating beam in real space has an invariant amplitude profile upon propagation [1,8]. The eigenfunctions of the quantum pendulum, first studied by Condon [12] and subsequently re-discovered several times [13] are Mathieu functions [13,14], which determine the spectra of our 'pendulum beams'.…”

“…With a spectrum restricted to the circle (with L → k r , the radial wavenumber), the propagating beam in real space has an invariant amplitude profile upon propagation [1,8]. The eigenfunctions of the quantum pendulum, first studied by Condon [12] and subsequently re-discovered several times [13] are Mathieu functions [13,14], which determine the spectra of our 'pendulum beams'.…”

General quasi-nonspreading linear three-dimensional wave packets

“…Wavepackets that do not spread in time and/or space upon propagation in linear optical media are of paramount importance in diverse applications, such as medical imaging, microscopy, tomography, lithography, data storage, interconnects, optical tweezing and trapping, and optical lattices, to name a few [1,2]. The shapes of non-spreading field distributions depend on their dimensionality.…”