Abstract
We present the first experimental evidence, supported by theory and simulation, of spatiotemporal optical vortices (STOVs). Quantized STOVs are a fundamental element of the nonlinear collapse and subsequent propagation of short optical pulses in material media. A STOV consists of a ring-shaped null in the electromagnetic field about which the phase is spiral, forming a dynamic torus which is concentric with and tracks the propagating pulse. Depending on the sign of the material dispersion, the local electromagnetic energy flow is saddle or spiral about the STOV. STOVs are born and evolve conserving topological charge; they can be simultaneously created in pairs with opposite windings, or generated from a point null. Our results, here obtained for optical pulse collapse and filamentation in air, are generalizable to broad class of nonlinearly propagating waves.
Highlights
Vortices—localized regions in which the flow of some quantity such as mass or electromagnetic energy circulates about a local axis—are a common and fundamental element of classical [1] and quantum fluids [2,3,4] as well as optics [5]
The circulating quantity is the spatial atomic probability density; in optics, it is the electromagnetic energy density. Both densities are expressed as the magnitude squared of a complex scalar field ψ 1⁄4 ueiΦ derivable from a SchrödingeHr-like equation (SE), where the vortex circulation is Γ 1⁄4 c ∇Φ · dl, u and Φ are real scalar fields, and the integral is on a closed contour about the local axis
We have introduced the concept of the spatiotemporal optical vortex to ultrafast optics and demonstrated its existence
Summary
Vortices—localized regions in which the flow of some quantity such as mass or electromagnetic energy circulates about a local axis—are a common and fundamental element of classical [1] and quantum fluids [2,3,4] as well as optics [5]. A well-known example of a vortex in linear optics is the linearly polarized Laguerre Gaussian (LG) mode Eplðr; φ; zÞ of integer radial index p ≥ 0 and nonzero integer azimuthal index l, with azimuthal dependence expðilφÞ. This mode has an on-axis field null, a topological charge l 1⁄4 Γ=2π, an orbital angular momentum (OAM) of Nlħ, where N is the number of photons in the beam, and a spiral energy density flux about the propagation axis [7]. Their existence in nonlinear ultrafast pulse propagation appears to be ubiquitous, and their creation, motion, and destruction is strongly linked to the complex spatiotemporal evolution of the pulse
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