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Optical phase-change materials have enabled nonvolatile programmability in integrated photonic circuits by leveraging a reversible phase transition between amorphous and crystalline states. To control these materials in a scalable manner on-chip, heating the waveguide itself via electrical currents is an attractive option which has been recently explored using various approaches. Here, we compare the heating efficiency, fabrication variability, and endurance of two promising heater designs which can be easily integrated into silicon waveguides—a resistive microheater using n-doped silicon and one using a silicon p-type/intrinsic/n-type (PIN) junction. Raman thermometry is used to characterize the heating efficiencies of these microheaters, showing that both devices can achieve similar peak temperatures but revealing damage in the PIN devices. Subsequent endurance testing and characterization of both device types provide further insights into the reliability and potential damage mechanisms that can arise in electrically programmable phase-change photonic devices.

 

Graph compression or sparsification is a basic information-theoretic and computational question. A major open problem in this research area is whether $(1+\epsilon)$-approximate cut-preserving vertex sparsifiers with size close to the number of terminals exist. As a step towards this goal, we initiate the study of a thresholded version of the problem: for a given parameter $c$, find a smaller graph, which we call \emph{connectivity-$c$ mimicking network}, which preserves connectivity among $k$ terminals exactly up to the value of $c$. We show that connectivity-$c$ mimicking networks of size $O(kc^4)$ exist and can be found in time $m(c\log n)^{O(c)}$. We also give a separate algorithm that constructs such graphs of size $k \cdot O(c)^{2c}$ in time $mc^{O(c)}\log^{O(1)}n$. These results lead to the first offline data structures for answering fully dynamic $c$-edge-connectivity queries for $c \ge 4$ in polylogarithmic time per query as well as more efficient algorithms for survivable network design on bounded treewidth graphs.