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Diffraction-free optical beams propagate freely without change in shape and scale. Monochromatic beams that avoid diffractive spreading require two-dimensional transverse profiles, and there are no corresponding solutions for profiles restricted to one transverse dimension. Here, we demonstrate that the temporal degree of freedom can be exploited to efficiently synthesize one-dimensional pulsed optical sheets that propagate self-similarly in free space. By introducing programmable conical (hyperbolic, parabolic, or elliptical) spectral correlations between the beams spatio-temporal degrees of freedom, a continuum of families of axially invariant pulsed localized beams is generated. The spectral loci of such beams are the reduced-dimensionality trajectories at the intersection of the light-cone with spatio-temporal spectral planes. Far from being exceptional, self-similar axial propagation is a generic feature of fields whose spatial and temporal degrees of freedom are tightly correlated. These one-dimensional `space-time beams can be useful in optical sheet microscopy, nonlinear spectroscopy, and non-contact measurements.
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We investigate the dynamics of spatiotemporal optical waves with one transverse dimension that are obtained as the intersections of the dispersion cone with a plane. We show that, by appropriate spectral excitations, the three different types of conic sections (elliptic, parabolic, and hyperbolic) can lead to optical waves of the Bessel, Airy, and modified Bessel type, respectively. We find closed form solutions that accurately describe the wave dynamics and unveil their fundamental properties.
It is observed that a constant unit vector denoted by $mathbf I$ is needed to characterize a complete orthonormal set of vector diffraction-free beams. The previously found diffraction-free beams are shown to be included as special cases. The $mathbf I$-dependence of the longitudinal component of diffraction-free beams is also discussed.
Free-space optical communication is a promising means to establish versatile, secure and high-bandwidth communication for many critical point-to-point applications. While the spatial modes of light offer an additional degree of freedom to increase the information capacity of an optical link, atmospheric turbulence can introduce severe distortion to the spatial modes and lead to data degradation. Here, we propose and demonstrate a vector-beam-based, turbulence-resilient communication protocol, namely spatial polarization differential phase shift keying (SPDPSK), that can encode a large number of information levels using orthogonal spatial polarization states of light. We show experimentally that the spatial polarization profiles of the vector modes are resilient to atmospheric turbulence, and therefore can reliably transmit high-dimensional information through a turbid channel without the need of any adaptive optics for beam compensation. We construct a proof-of-principle experiment with a controllable turbulence cell. Using 34 vector modes, we have measured a channel capacity of 4.84 bits per pulse (corresponding to a data error rate of 4.3%) through a turbulent channel with a scintillation index larger than 1. Our SPDPSK protocol can also effectively transmit 4.02 bits of information per pulse using 18 vector modes through even stronger turbulence with a scintillation index of 1.54. Our study provides direct experimental evidence on how the spatial polarization profiles of vector beams are resilient to atmospheric turbulence and paves the way towards practical, high-capacity, free-space communication solutions with robust performance under harsh turbulent environments.
We demonstrate that beams originating from Fresnel diffraction patterns are self-accelerating in free space. In addition to accelerating and self-healing, they also exhibit parabolic deceleration property, which is in stark contrast to other accelerating beams. We find that the trajectory of Fresnel paraxial accelerating beams is similar to that of nonparaxial Weber beams. Decelerating and accelerating regions are separated by a critical propagation distance, at which no acceleration is present. During deceleration, the Fresnel diffraction beams undergo self-smoothing, in which oscillations of the diffracted waves gradually focus and smooth out at the critical distance.
A unified description of the free-space cylindrical vector beams is presented, which is an integral transformation solution to the vector Helmholtz equation and the transversality condition. The amplitude 2-form of the angular spectrum involved in this solution can be arbitrarily chosen. When one of the two elements is zero, we arrive at either transverse-electric or transverse-magnetic beam mode. In the paraxial condition, this solution not only includes the known $J_1$ Bessel-Gaussian vector beam and the axisymmetric Laguerre-Gaussian vector beam that were obtained by solving the paraxial wave equations, but also predicts two new kinds of vector beam, called the modified-Bessel-Gaussian vector beam.
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