Double-helix singularity and vortex-antivortex annihilation in space-time helical pulses

Abstract

Topological structures reveal the hidden secrets and beauty in nature, such as the double helix in DNA, whilst, the manipulation of which in physical fields, especially in ultrafast structured light, draw booming attention. Here we introduce a new family of spatiotemporal light fields, i.e. helical pulses, carrying sophisticated double-helix singularities in its electromagnetic topological structures. The helical pulses were solved from Maxwell's equation as chiral extensions of toroidal light pulses but with controlled angular momentum dependence. We unveil that the double helix singularities can maintain their topological invariance during propagation and the field exhibits paired generation and annihilation of vortices and antivortices in ultrafast space-time, so as to be potential information carriers beating previous conventional vortex structured light.

Keywords: helical pulses; optical vortices; singularities; spatiotemporal light fields; topology.

Figure 1:

Double-helix singularities in helical pulses. (a)–(c) Displays the cross-sectional and contour topological images of E _ρ , E _θ and $\left|E\right|$ at time points t = −7.5q ₁/c, 0, 7.5q ₁/c, with parameters set to q ₁ = 0.01 and q ₂ = 10q ₁. (a) The iso surface indicates the value of normalized intensity E _ρ = ±0.1. (a1/a2/a3) Section map of the E _ρ components on the y = 0/x = 0/z = 0 plane. (b) The iso surface indicates the value of normalized intensity E _θ = ±0.1. (b1/b2/b3) Section map of the component on the y = 0/x = 0/z = 0 plane. (c) The iso surface image of $\left|E\right|$ , the iso surface is set to normalized intensity $\left|E\right|=0.1$ . (c1/c2/c3) Section map of the $\left|E\right|$ component on the y = 0/x = 0/z = 0 plane. In figure (c), the green iso surface indicates the value of normalized intensity $\left|E\right|=0.1$ , and the red and blue curves are connected by the right-handed and left-handed vortex core, respectively. For clarity, we have only plotted the curve in the region where the wave packet is located, while the actual curve extends to infinity on both sides. All values in the graph have been normalized. (d) Schematic diagram of double-helix singularities. Red and blue represent the singularity lines, while yellow and green arrows indicate the direction of the electric field vectors. (e) The structure of DNA, adapted from Wikipedia.

Figure 2:

Electric field vector and singularity line at focus (t = 0). (a) Shows electric field vector and singularity at the focusing time (t = 0). (b)–(d) Shows the singularity lines and electric field vectors at the planes of z = 2q ₁, q ₁, 0, and the red and blue arrows indicate the direction of the electric field. In (a), the color matching of electric field vector is related to its azimuth ϕ in the x–y plane, and the polar angle binds with brightness intensity, as shown in the illustration. The red and blue curves are respectively connected by the right-handed vortex core and the left-handed vortex core.

Figure 3:

Electric field and singularity lines of helical pulses. (b) This figure presents the streamline plot of the electric field in the plane of the singular point and z = −70q ₁, −15q ₁, 30q ₁, 70q ₁ at the instant when t = −15q ₁/c. (a) And (c) are enlarged local images of the red and green dashed rectangles in (b), respectively. The spiral structure maintains topological invariance. (c1–c4) Displays the electric field vector and modulus contour lines on z = 25q ₁, z = 30q ₁, z = 35q ₁ and z = 40q ₁. In the image, the red curved arrow represents vortices, the blue curved arrow represents antivortices, the position of the green arrow indicates that vortices and antivortices are about to be generated or have already been annihilated, and the direction of the green arrow indicates the direction of the electric field vector. The orange dashed arrow indicates the direction of motion of the singularity. (c1–c4) Reveal the variation of the singular points with different planes.