Generalized Radially Self-Accelerating Helicon Beams

We report, in theory and experiment, on a new class of optical beams that are radially self-accelerating and nondiffracting. These beams continuously evolve on spiraling trajectories while maintaining their amplitude and phase distribution in their rotating rest frame. We provide a detailed insight into the theoretical origin and characteristics of radial self-acceleration and prove our findings experimentally. As radially self-accelerating beams are nonparaxial and a solution to the full scalar Helmholtz equation, they can be implemented in many linear wave systems beyond optics, from acoustic and elastic waves to surface waves in fluids and soft matter. Our work generalized the study of classical helicon beams to a complete set of solutions for rotating complex fields.

Figure 1

Illustration showing the accelerative behavior of (a) Airy and (b) radially self-accelerating beams.

Figure 2

Exemplary illustration of a radially self-accelerating field distribution with ${\tilde{C}}_n=1$ for $1\le n\le 4$ and ${\tilde{C}}_n=0$ for $n>4$. The figure consists of one-dimensional representation of the superimposed Bessel functions (main plot), resulting intensity distribution (upper inset row), and resulting phase pattern (lower inset row).

Figure 3

Exemplary illustration of a radially self-accelerating intensity distribution with ${\tilde{C}}_n=1$ for $-1\le n\le +1$ and ${\tilde{C}}_n=0$ for $|n|>1$. The figure consists of one-dimensional representation of the superimposed Bessel functions (main plot), resulting intensity distribution (upper inset row), and resulting phase pattern (lower inset row).

Figure 4

Experimental setup containing a telescope for beam expansion, SLM (Holoeye Pluto VIS) for amplitude and phase modulation, lens for Fourier transformation ($f=300\mathrm{mm}$), aperture and $4f$ arrangement ($f_1=f_2=200\mathrm{mm}$) for signal cleaning, and a movable CCD unit for data acquisition.

Figure 5

Propagation dynamics of a radially self-accelerating beam identical to the one in Fig. 3. Radii on the SLM were $R_1=2.328$, $R_2=1.958$, and $R_3=1.501\mathrm{mm}$.