605 research outputs found
Spin-orbit interaction of light induced by transverse spin angular momentum engineering
We report the first demonstration of a direct interaction between the
extraordinary transverse spin angular momentum in evanescent waves and the
intrinsic orbital angular momentum in optical vortex beams. By tapping the
evanescent wave of whispering gallery modes in a micro-ring-based optical
vortex emitter and engineering the transverse spin state carried therein, a
transverse-spin-to-orbital conversion of angular momentum is predicted in the
emitted vortex beams. Numerical and experimental investigations are presented
for the proof-of-principle demonstration of this unconventional interplay
between the spin and orbital angular momenta, which could provide new
possibilities and restrictions on the optical angular momentum manipulation
techniques on the sub-wavelength scale. This phenomenon further gives rise to
an enhanced spin-direction coupling effect in which waveguide or surface modes
are unidirectional excited by incident optical vortex, with the directionality
jointly controlled by spin-orbit states. Our results enrich the spin-orbit
interaction phenomena by identifying a previously unknown pathway between the
polarization and spatial degrees of freedom of light, and can enable a variety
of functionalities employing spin and orbital angular momenta of light in
applications such as communications and quantum information processing
Efficient Gradient Approximation Method for Constrained Bilevel Optimization
Bilevel optimization has been developed for many machine learning tasks with
large-scale and high-dimensional data. This paper considers a constrained
bilevel optimization problem, where the lower-level optimization problem is
convex with equality and inequality constraints and the upper-level
optimization problem is non-convex. The overall objective function is
non-convex and non-differentiable. To solve the problem, we develop a
gradient-based approach, called gradient approximation method, which determines
the descent direction by computing several representative gradients of the
objective function inside a neighborhood of the current estimate. We show that
the algorithm asymptotically converges to the set of Clarke stationary points,
and demonstrate the efficacy of the algorithm by the experiments on
hyperparameter optimization and meta-learning
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