Tunable Orbital Angular Momentum Radiation from Angular-Momentum-Biased Microcavities

Lasers and light emitters do not typically radiate fields with orbital angular momentum (OAM). Here we show that a suitable scheme of spatiotemporal modulation of a microring cavity laser can impart a synthetic angular momentum, resulting in beams with well-defined OAM. The phenomenon relies on a traveling wave modulation of the refractive index of the microring, which breaks the degeneracy of oppositely oriented whispering gallery modes. In parallel, a static structural grating on the periphery of the microring enables efficient vertical radiation. The proposed structure is inherently tunable and can also emit fields with zero net OAM while retaining toroidal energy distributions similar to the effect of an axicon lens.

Figure 1

(a) Schematic diagram depicting a microring resonator and the directionality of two degenerate whispering gallery modes. (b) Dependence of the characteristic frequencies on modulation frequency ${\omega }_m$ of the four components resulting from spatiotemporal modulation. (c) Top view of the OAM laser cavity showing a static structural grating on the periphery of the microring. (d) Three-dimensional depiction of the vertical emission of OAM radiation. (e) Detailed view of resonance spectrum in the vicinity of $h/{\lambda }_0=0.2137$ where $h$ is the cavity height. Spectrum was obtained by taking the discrete Fourier transform of a time sequence calculated by the three-dimensional finite-difference time-domain method and fitted using Padé approximants [24].

Figure 2

(a) Field distributions $E_r(x,y,z=40h)$ calculated using a far-field transformation of the field obtained from FDTD just above the cavity. The width of the view shown is $305h$. (b) Distribution of power in the components of the Fourier-Bessel decomposition Eq. (7). (c) Field distribution $E_r(x,y,z=40h)$ of a radiation field with OAM $l=0$ calculated using a far-field transformation of the field obtained from FDTD just above the cavity. The width of the view shown is $305h$.

Figure 3

(a) Schematic depiction of a cavity with 17 discrete modulation contact points. The associated signal applied to the ring is shown for the first three sections. ${\phi }_n=(n+1/2)(2\pi /17)$ for $n=0\dots 16$. (b) Field distribution $E_r(x,y,z=40h)$ for the ${\omega }_{l\alpha ,-1}$ mode in the cavity shown in (a) calculated using a far-field transformation of the field obtained from FDTD just above the cavity. The width of the view shown is $305h$. (c) Strategy for dynamically changing the scattering grating period. Rather than applying a different signal to each individual section, adjacent sections can be grouped together, so that the cavity modes are scattered from gratings with larger periods. Five groups of six sections are shown. (d) Same as (c) but with six groups of five sections (modulation signals not shown). (e) Same as (d) but with ten groups of three sections.