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Structured light harnessing multiple degrees of freedom has become a powerful approach to use complex states of light in fundamental studies and applications. Here, we investigate the light field of an ultrafast laser beam with a wavelength-depended polarization state, a beam we term spectral vector beam. We demonstrate a simple technique to generate and tune such structured beams and demonstrate their spectroscopic capabilities. By only measuring the polarization state using fast photodetectors, it is possible to track pulse-to-pulse changes in the frequency spectrum caused by, e.g. narrowband transmission or absorption. In our experiments, we reach read-out rates of around 6 MHz, which is limited by our technical ability to modulate the spectrum and can in principle reach GHz read-out rates. In simulations we extend the spectral range to more than 1000 nm by using a supercontinuum light source, thereby paving the way to various applications requiring high-speed spectroscopic measurements.
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A representation theory of finite electromagnetic beams in free space is formulated by factorizing the field vector of the plane-wave component into a $3 times 2$ mapping matrix and a 2-component Jones-like vector. The mapping matrix has one degree of freedom that can be described by the azimuthal angle of a fixed unit vector with respect to the wave vector. This degree of freedom allows us to find out such a beam solution in which every plane-wave component is specified by the same fixed unit vector $mathbf{I}$ and has the same normalized Jones-like vector. The angle $theta_I$ between the fixed unit vector and the propagation axis acts as a parameter that describes the vectorial property of the beam. The impact of $theta_I$ is investigated on a beam of angular-spectrum field scalar that is independent of the azimuthal angle. The field vector in position space is calculated in the first-order approximation under the paraxial condition. A transverse effect is found that a beam of elliptically-polarized angular spectrum is displaced from the center in the direction that is perpendicular to the plane formed by the fixed unit vector and the propagation axis. The expression of the transverse displacement is obtained. Its paraxial approximation is also given.
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.
Harnessing the spontaneous emission of incoherent quantum emitters is one of the hallmarks of nano-optics. Yet, an enduring challenge remains-making them emit vector beams, which are complex forms of light associated with fruitful developments in fluorescence imaging, optical trapping and high-speed telecommunications. Vector beams are characterized by spatially varying polarization states whose construction requires coherence properties that are typically possessed by lasers-but not by photons produced by spontaneous emission. Here, we show a route to weave the spontaneous emission of an ensemble of colloidal quantum dots into vector beams. To this end, we use holographic nanostructures that impart the necessary spatial coherence, polarization and topological properties to the light originating from the emitters. We focus our demonstration on vector vortex beams, which are chiral vector beams carrying non-zero orbital angular momentum, and argue that our approach can be extended to other forms of vectorial light.
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.
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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