Measurement of the orbital-angular-momentum spectrum of fields with partial angular coherence using double-angular-slit interference

We implement an interferometric method using two angular slits to measure the orbital-angular-momentum (OAM) mode spectrum of a field with partial angular coherence. As the angular separation of the slits changes, an interference pattern for a particular OAM mode is obtained. The visibility of this interference pattern as a function of angular separation is equivalent to the angular correlation function of the field. By Fourier transforming the angular correlation function obtained from the double-angular-slit interference, we are able to calculate the OAM spectrum of the partially coherent field. This method has potential application for characterizing the OAM spectrum in high-dimensional quantum information protocols.

Figure 1

Partially coherent field propagating through double angular slits with an angular separation of $\Delta \varphi$.

Figure 2

Simulation results for angular interference patterns for OAM mode projections from $\ell =0$ to $\ell =24$ for three values of coherence angle (a) ${\varphi }_{\mathrm{coh}}\approx 2\pi$ rad, (b) ${\varphi }_{\mathrm{coh}}=0.5$ rad, and (c) ${\varphi }_{\mathrm{coh}}$ $=$ 0.25 rad. The red rectangular boxes indicate the value of $\ell$ used in our experiment. The $z$ axis shows normalized intensity from 0 to 1, indicated by grayscale values.

Figure 3

(a) Schematic of the experimental setup. (b) Example of a phase hologram impressed on the SLM.

Figure 4

Normalized intensity for OAM mode projection $\ell =12$, of partially coherent light transmitted through two angular apertures, as a function of the angular separation $\Delta \varphi$ for three OAM mode distributions with different degrees of angular coherence, characterized by a coherence angle (a) ${\varphi }_{\mathrm{coh}}\approx 2\pi$ rads (b) ${\varphi }_{\mathrm{coh}}=0.71$ rad and (c) ${\varphi }_{\mathrm{coh}}$ $=$ 0.29 rad. The measured interference patterns as a function of angular slit separation $\Delta \varphi$ (dashed black line) are plotted alongside a fit (solid red line) obtained from theory. A fit to the visibility envelope is also plotted in (b) and (c) (long-dashed green line).

Figure 5

Calculated OAM mode spectrum for the two measured distribution widths of (a) ${\sigma }_m=1.4$ and (b) ${\sigma }_m=3.4$. The normalized amplitude is plotted as a function of OAM mode number $\ell$.