3,010 research outputs found
Taylor coefficients and series involving harmonic numbers
During 2022--2023 Z.-W. Sun posed many conjectures on infinite series with
summands involving generalized harmonic numbers. Motivated by this, we deduce
series identities involving harmonic numbers, three of which were
previously conjectured by the second author. For example, we obtain that
and where denotes .Comment: add some new serie
Broadband optical nonreciprocity via nonreciprocal band structure
As a promising approach for optical nonreciprocity without magnetic
materials, optomechanically induced nonreciprocity has great potential for
all-optical controllable isolators and circulators on chips. However, as a very
important issue in practical applications, the bandwidth for nonreciprocal
transmission with high isolation has not been fully investigated yet. In this
study we review the nonreciprocity in a Brillouin optomechanical system with
single cavity and point out the challenge in achieving broad bandwidth with
high isolation. To overcome this challenge, we propose a one dimensional
optomechanical array to realize broadband optical nonreciprocity via
nonreciprocal band structure. We exploit nonreciprocal band structure by the
stimulated Brillouin scattering induced transparency with directional optical
pumping, and show that it is possible to demonstrate optical nonreciprocity
with both broad bandwidth and high isolation. Such Brillouin optomechanical
lattices with nonreciprocal band structure, offer an avenue to explore
nonreciprocal collective effects in different electromagnetic and mechanical
frequency regimes, such as nonreciprocal topological photonic and phononic
phases.Comment: 10 pages, 6 figure
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