Observation of Interaction of Spin and Intrinsic Orbital Angular Momentum of Light

The interaction of spin and intrinsic orbital angular momentum of light is observed, as evidenced by length-dependent rotations of both spatial patterns and optical polarization in a cylindrically symmetric isotropic optical fiber. Such rotations occur in a straight few-mode fiber when superpositions of two modes with parallel and antiparallel orientation of spin and intrinsic orbital angular momentum ($\mathrm{IOAM}=2\hslash$) are excited, resulting from a degeneracy splitting of the propagation constants of the modes.

Figure 1

Superpositions of modes for observing the change of propagation constant $\delta \beta$. Color in the legend shows the phase. (a) The same IOAM $\ell$ and opposite circular polarizations ($+$ and $-$) combine to make (b) rotating linear polarization in orbit-controlled spin rotation. (c) The same circular polarizations but opposite IOAM combine to make (d) a rotating four-lobed spatial pattern in spin-controlled orbital rotation.

Figure 2

Experimental apparatus. The Ti:sapphire laser is configured for continuous-wave operation. BS, nonpolarizing beam splitter. QWP, quarter-wave plate. The spatial light modulator converts a Gaussian beam to the desired profile. The inset profiles are simulated. In measuring the fiber output beam, the reference arm is blocked to measure the profile and unblocked to measure the interferogram.

Figure 3

Input profiles. We use a total of five input settings. We probe spin-IOAM interaction with four inputs in the experimental group: two circularly polarized ($\sigma$) clover profiles and two horizontally polarized (arrowed lines) $\ell =\pm 2$ profiles. The control group consists of a horizontally polarized Gaussian profile, which lacks IOAM and is hypothesized to propagate unchanged through the fiber. Right: Intensity color legend.

Figure 4

Representative output profile pictures. Top row profiles are at $L=43.5\mathrm{cm}$. Bottom row profiles are at $L=38.4\mathrm{cm}$. Columns labeled with $\ell$ have IOAM input profiles, while LCP and RCP label the circular polarization of clover input profiles. Red cross hairs on clover profiles indicate the orientation of nodal lines for $\xi$ measurement, and white arrows indicate the major axis orientation $\varphi$ for linearly polarized modes. Width differences are due to the slight difference in the output objective distance from the fiber output at different lengths. Right: Intensity color legend.

Figure 5

Measured output parameters $\xi$ (spatial orientation of the clover profiles) and $\varphi$ (linear polarization orientations for all non-clover inputs). Vertical error bars are smaller than the data symbols. Both $\xi$ and $\varphi$ are in configuration space degrees. Best linear fits shown as colored lines with slopes given in degrees/cm. For ease of comparison, these lines are offset from the lines of total accumulated rotation by integer multiples of 360° and cross near 30.8 cm.