Lower-depth programmable linear optical processors

TL;DR

The paper addresses the high phase-shifter depth of traditional MZI-based programmable LOPs by introducing a MPLC-based architecture that uses $N$ input/output ports from an $N'\times N'$ universal multiport interferometer with $N' \ge 2N$. The core idea embeds the standard $S = U\Sigma V$ decomposition into a larger unitary that can be realized with a reduced circuit depth, achieving $N+2$ phase shifter stages for dense matrices and $N+3$ for sparse ones in numerical tests. Experiments show comparable performance across MMI and MDC couplers and demonstrate robustness to phase quantization relative to conventional MZI meshes. Overall, this approach enables compact, low-loss, and energy-efficient programmable LOPs with potential impact on on-chip optical computing and information processing.

Abstract

Programmable linear optical processors (LOPs) can have widespread applications in computing and information processing due to their capabilities to implement reconfigurable on-chip linear transformations. A conventional LOP that uses a mesh of Mach-Zehnder interferometers (MZIs) requires $2N+3$ stages of phase shifters for $N \times N$ matrices. However, it is beneficial to reduce the number of phase shifter stages to realize a more compact and lower-loss LOP, especially when long and lossy electro-optic phase shifters are used. In this work, we propose a novel structure for LOPs that can implement arbitrary matrices as long as they can be realized by previous MZI-based schemes. Through numerical analysis, we further show that the number of phase shifter stages in the proposed structure can be reduced to $N+2$ and $N+3$ for a large number of random dense matrices and sparse matrices, respectively. This work contributes to the realization of compact, low-loss, and energy-efficient programmable LOPs.

Figures (7)

• Figure 1: (a) Conventional programmable LOPs based on singular value decomposition. The target matrix is first decomposed into the product of two unitary matrices and a diagonal matrix. (b) A compact universal multiport interferometer proposed by Bell et al. for implementing arbitrary unitary matrices bell2021further. $N+2$ stages of phase shifters are needed ($N=4$ in this figure). (c) The structure of a LOP using the Bell structure. The last phase shifter stage in the section for $\rm \bf V$ and the first phase shifter stage in the section for $\rm \bf U$ have been absorbed into the MZI array for $\rm \bf \Sigma$. $2N+3$ stages of phase shifters are needed ($N=4$ in this figure).
• Figure 2: The proposed LOP structure. While the whole device has $N'$ ports, only $N$ ports are used as input/output ports. For unused input and output ports, phase shifters are not needed and thus are omitted in the first and last stages. For the stages in between two $N' \times N'$ couplers, all $N'$ phase shifters are used. The couplers can be multimode interference (MMI) couplers or multiport directional couplers. $M$ is the number of phase shifter arrays.
• Figure 3: Average NSEs when the proposed LOPs are used to implement 100 random dense matrices with non-zero elements. The error bar represents the range between the maximum and minimum values among the 100 cases. The dash line indicates the NSE of $10^{-12}$. (a) LOPs using MMI couplers. (b) LOPs using MDCs.
• Figure 4: Average NSEs for random dense matrices with non-zero elements. The error band represents the range between the maximum and minimum values among the 100 cases. (a) LOPs using MMI couplers. (b) LOPs using MDCs.
• Figure 5: Average NSEs for random sparce matrices with one non-zero element. The error band represents the range between the maximum and minimum values among the 100 cases. (a) LOPs using MMI couplers. (b) LOPs using MDCs.