Programmable pixel-mode linear interferometers using multi-plane light conversion

Abstract

Programmable linear optical interferometers are a core primitive in optical signal processing, quantum information processing, and photonic computing. Existing photonic-integrated implementations realize arbitrary $M$-mode unitaries using Mach--Zehnder-interferometer meshes whose footprint and accumulated loss scale with $O(M^2)$ optical components. Here we analyze and experimentally demonstrate a programmable architecture for implementing linear optical transformations directly on spatially tiled free-space pixel modes using multi-plane light conversion (MPLC). In this architecture, $M$ spatial modes arranged on a transverse lattice undergo a unitary transformation and are mapped to $M$ output modes of identical geometry through a sequence of programmable phase masks separated by free-space propagation segments. Numerical simulations show that arbitrary $M$-mode unitaries can be compiled to a desired high fidelity using a number of phase planes that scales approximately linearly with $M$. Using a spatial-light-modulator-based MPLC, we experimentally demonstrate programmable interferometers acting on up to $16$ spatial pixel modes, including tunable beamsplitters, Hadamard unitaries, spatial permutations, boosted-Bell-measurement unitaries, and partial unitaries on select subsets of modes. These results establish MPLC-based pixel-mode interferometers as a promising architecture for programmable linear optics with applications in classical and quantum optical interconnects, photonic switching, and quantum information processing.

Figures (22)

• Figure 1: Simulated beam propagation through a $5$-layer MPLC when implementing a $4 \times 4$ Hadamard unitary, shown to transform the input $|\alpha\rangle|\alpha\rangle|\alpha\rangle|\alpha\rangle$ into an output $|2\alpha\rangle|0\rangle|0\rangle|0\rangle$. The field envelope's $x$ and $y$ dimensional extents ${H}_x = {H}_y \equiv H$, defined as the transverse square-region with $99\%$ total-power confinement, is roughly $6\sigma$ to $6.5\,\sigma$ throughout the $K$ planes.
• Figure 2: (a) Mean transmissivity $\bar{\eta}$ and (b) mean crosstalk ${\bar{\epsilon}}$, plotted as a function of MFD-normalized inter-pixel-mode spacing $b/\sigma$, for the 50-50 beamsplitter unitary in Eq. \ref{['eq:beamsplitter']}.
• Figure 3: (a) Mean transmissivity $\bar{\eta}$ and (b) average crosstalk $\bar{\epsilon}$ versus pixel dimension $\Delta$, for the $2$-pixel-mode $50$-$50$ beamsplitter, with $K$$= 10$ to $13$.
• Figure 4: Left panel: (a) Required plane count $K$ versus mode count $M$ to realize an $M$-mode complex-Hadamard unitary at fixed $\bar{\eta}=0.95$ and $\bar{\epsilon}=0.005$, shown for different plane spacings $w/\sigma$. (b) Linear fit $K=cM$ to the numerically computed $K$, with proportionality constant $c$ plotted as a function of $w/\sigma$. Right panel: (c) Same as (a) but for an $M$-mode random-permutation unitary. (d) Corresponding proportionality constant $c$ versus $w/\sigma$.
• Figure 5: (a) The $4$-mode Hadamard unitary $H_4$; (b) The Green Machine architecture for realizing the Hadamard unitary using 4 50-50 beamsplitters; (c) A direct MPLC realization of $H_4$ via $K$ phase masks; (d) A stacked realization of $H_4$ where two 50-50 beamsplitters are realized in parallel using a $K/2$-plane MPLC, followed by a parallel realization of another pair of 50-50 beamsplitters using another $K/2$-plane MPLC.