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A new method to reliably simulate the PDE and jitter tail for realistic three-dimensional SPAD devices is presented. The simulation method is based on the use of electric field lines to mimic the carriers’ trajectories, and on one-dimensional models for avalanche breakdown probability and charges transport. This approach allows treating a three-dimensional problem as several one-dimensional problems along each field line. The original approach is applied to the McIntyre model for avalanche breakdown probability to calculate PDE, but also for jitter prediction using a dedicated advection-diffusion model. The results obtained numerically are compared with an extensive series of measurements and show a good agreement on a wide variety of device designs.

Relationships between debt and poor health are worrisome as access to expensive credit expands and population health worsens along certain metrics. We focus on payday lenders as one type of expensive credit and investigate the spatial relationships between lender storefronts and premature mortality rates. We combine causes of death data from the Centers for Disease Control and Prevention (CDC) and payday lender locations at the county-level in the United States between 2000 and 2017. After accounting for county socioeconomic and demographic characteristics, the local presence of payday lenders is associated with an increased incidence risk of all-cause and specific-cause premature mortality. State regulations may attenuate these relationships, which provides insights on policy strategies to mitigate health impacts.

Entanglement swapping in high dimensions requires large numbers of entangled photons and consequently suffers from low photon flux. Here the authors demonstrate entanglement swapping of multiple spatial modes of light simultaneously, without the need for increasing the photon numbers with dimension.