Snake beam: a paraxial arbitrary focal line

Simple algorithm for the design of accelerating Bessel-like beams with adjustable features along their propagation

We present an extremely simple method for designing self-accelerating non-diffracting beams having arbitrary trajectories while their intensity, width and orbital angular momentum are modulated in a prescribed way along their propagation. Different beams constructed with this method are demonstrated experimentally in the paraxial regime and numerically in the non-paraxial regime.

Non-diffracting and self-accelerating Bessel beams with on-demand tailored intensity profiles along arbitrary trajectories

Owing to their robustness against diffraction, Bessel beams (BBs) offer special advantages in various applications. To enhance their applicability, we present a method to generate self-accelerating zeroth-order BBs along predefined trajectories with tunable z direction intensity profiles. The character of tunable z direction intensity profiles in non-diffracting self-accelerating BBs potentially can attract interest in the regimes of particle manipulation, microfabrication, and free-space optical interconnects.

Designing the phase and amplitude of scalar optical fields in three dimensions

The ability to generate any arbitrarily chosen optical field in a three-dimensional (3D) space, in the absence of any sources, without modifying the index of refraction, remains an elusive but much-desired capability with applications in various fields such as optical micromanipulation, imaging, and data communications, to name a few. In this work, we show analytically that it is possible to generate any desired scalar optical field with predefined amplitude and phase in 3D space, where the generated field is an exact duplicate of the desired field in case it is a solution of Helmholtz wave equation, or if the existence of such field is strictly forbidden, the generated field is the closest possible rendition of the desired field in amplitude and phase. The developed analytical approach is further supported via experimental demonstration of optical beams with exotic trajectories and can have a significant impact on the aforementioned application areas.

Tunable self-similar Bessel-like beams of arbitrary order

We predict that Bessel-like beams of arbitrary integer order can exhibit a tunable self-similar behavior (that take an invariant form under suitable stretching transformations). Specifically, by engineering the amplitude and the phase on the input plane in real space, we show that it is possible to generate higher-order vortex Bessel-like beams with fully controllable radius of the hollow core and maximum intensity during propagation. In addition, using a similar approach, we show that it is also possible to generate zeroth-order Bessel-like beams with controllable beam width and maximum intensity. Our numerical results are in excellent agreement with our theoretical predictions.

Wavefront shaping through emulated curved space in waveguide settings

The past decade has witnessed remarkable progress in wavefront shaping, including shaping of beams in free space, of plasmonic wavepackets and of electronic wavefunctions. In all of these, the wavefront shaping was achieved by external means such as masks, gratings and reflection from metasurfaces. Here, we propose wavefront shaping by exploiting general relativity (GR) effects in waveguide settings. We demonstrate beam shaping within dielectric slab samples with predesigned refractive index varying so as to create curved space environment for light. We use this technique to construct very narrow non-diffracting beams and shape-invariant beams accelerating on arbitrary trajectories. Importantly, the beam transformations occur within a mere distance of 40 wavelengths, suggesting that GR can inspire any wavefront shaping in highly tight waveguide settings. In such settings, we demonstrate Einstein's Rings: a phenomenon dating back to 1936.

Periodic self-accelerating beams by combined phase and amplitude modulation in the Fourier space

We propose and demonstrate the generation of periodic self-accelerating beams through both phase and amplitude modulation in the Fourier space. For small amplitude variations, an accelerating beam still follows a smooth convex trajectory, which can be traced by acting on the spectral phase only. However, large modulations such as those generated from the Heaviside function with a zero amplitude distribution partially modify the convex trajectory due to the appearance of straight-line paths. Furthermore, periodic self-accelerating beams along convex trajectories are realized by employing an array of "spectral wells" in both the paraxial and nonparaxial regimes.

Arbitrary accelerating micron-scale caustic beams in two and three dimensions

We generate arbitrary convex accelerating beams by direct application of an appropriate spatial phase profile on an incident Gaussian beam. The spatial phase calculation exploits the geometrical properties of optical caustics and the Legendre transform. Using this technique, accelerating sheet caustic beams with parabolic profiles (i.e. Airy beams), as well as quartic and logarithmic profiles are experimentally synthesized from an incident Gaussian beam, and we show compatibility with material processing applications using an imaging system to reduce the main intensity lobe at the caustic to sub-10 micron transverse dimension. By applying additional and rotational spatial phase, we generate caustic-bounded sheet and volume beams, which both show evidence of the recently predicted effect of abrupt autofocussing. In addition, an engineered accelerating profile with femtosecond pulses is applied to generate a curved zone of refractive index modification in glass. These latter results provide proof of principle demonstration of how this technique may yield new degrees of freedom in both nonlinear optics and femtosecond micromachining.

Accelerating light beams along arbitrary convex trajectories

We demonstrate, theoretically and experimentally, nonbroadening optical beams propagating along any arbitrarily chosen convex trajectory in space. We present a general method to construct such beams, and demonstrate it by generating beams following polynomial and exponential trajectories. We find that all such beams, accelerating along any convex trajectory, display the same universal intensity cross section, irrespective of their acceleration. The universal features of these beams are explored using catastrophe theory.

Linear focusing by a plane grating with curved grooves

We study the field diffracted by a plane grating with curved (parabolic) grooves. We will demonstrate that when a monochromatic plane wave is incident on a grating with parabolic grooves the diffracted field has a focal line whose position depends on the curvature radius of the parabolas and the incidence angle of the light onto the grating. The effect described has potential applications in grating-based devices for focusing light without requiring any additional optics.