Decomposing the sales promotion bump accounting for cross-category effects

Extant research on the decomposition of unit sales bumps due to price promotions considers these effects only within a single product category. This article introduces a framework that accommodates specific cross-category effects. Empirical results based on daily data measured at the item/SKU level show that the effects of promotions on sales in other categories are modest. Between-category complementary effects (20%) are, on average, substantially larger than between-category substitution effects (11%). Hence, a promotion of an item has an average net spin-off effect of (20 - 11 =) 9% of its own effect. The number of significant cross-category effects is low, which means that we expect that, most of the time, it is sufficient to look at within-category effects only. We also find within-category complementary effects, which implies that competitive items within the category may benefit from a promotion. We find small stockpiling effects (6%), modest cross-item effects (22%), and substantial category-expansion effects (72%). The cross-item effects are the result of cross-item substitution effects within the category (26%) and within-category complementary effects (4%). Approximately 15% (= 11% / 72%) of the category-expansion effect is due to between-category substitution effects of dependent categories.

Microscopic optical buffering in a harmonic potential

In the early days of quantum mechanics, Schrödinger noticed that oscillations of a wave packet in a one-dimensional harmonic potential well are periodic and, in contrast to those in anharmonic potential wells, do not experience distortion over time. This original idea did not find applications up to now since an exact one-dimensional harmonic resonator does not exist in nature and has not been created artificially. However, an optical pulse propagating in a bottle microresonator (a dielectric cylinder with a nanoscale-high bump of the effective radius) can exactly imitate a quantum wave packet in the harmonic potential. Here, we propose a tuneable microresonator that can trap an optical pulse completely, hold it as long as the material losses permit, and release it without distortion. This result suggests the solution of the long standing problem of creating a microscopic optical buffer, the key element of the future optical signal processing devices.

Nanobump microresonators at the fiber surface

It is shown that an asymmetric nanometer-high bump at the fiber surface causes strong localization of whispering gallery modes. Our theory explains and describes the experimentally observed nanobump microresonators in Surface Nanoscale Axial Photonics. © OSA 2015.