A note on the almost one half holomorphic pinching

Motivated by a previous work of Zheng and the second named author, we study pinching constants of compact K\"ahler manifolds with positive holomorphic sectional curvature. In particular we prove a gap theorem following the work of Petersen and Tao on Riemannian manifolds with almost quarter-pinched sectional curvature.Comment: 6 pages. This is the version which the authors submitted to a journal for consideration for publication in June 2017. The reference has not been updated since the

Anomalous optical coupling between two silicon wires of a slot waveguide in epsilon-near-zero metamaterials

Anomalous optical coupling properties between two silicon wires in a silicon slot waveguide embedded in epsilon-near-zero (ENZ) metamaterials are proposed and demonstrated. The dependences of optical field enhancement in the slot region and transverse optical force on the slot size and the permittivity of surrounding material are studied in details. It is demonstrated that the optical field in the slot region is significantly enhanced due to the giant index contrast at the slot interface between silicon wires and ENZ metamaterials, but the optical mode coupling between silicon wires is greatly reduced so that the transverse optical force is suppressed into almost zero. Moreover, metal-dielectric multilayer structures are designed to realize ENZ metamaterials in the slot region for achieving the electric field enhancement.Comment: 14 pages, 5 figure

Coupled-mode theory for stimulated Raman scattering in high-Q/Vm silicon photonic band gap defect cavity lasers

We demonstrate the dynamics of stimulated Raman scattering in designed high-Q/Vm silicon photonic band gap nanocavities through the coupled-mode theory framework towards optically-pumped silicon lasing. The interplay of other chi(3) effects such as two-photon absorption and optical Kerr, related free-carrier dynamics, thermal effects, as well as linear losses such as cavity radiation and linear material absorption are included and investigated numerically. Our results clarify the relative contributions and evolution of the mechanisms, and demonstrate the lasing and shutdown thresholds. Our studies illustrate the conditions for continuous-wave and pulsed highly-efficient Raman frequency conversion to be practically realized in monolithic silicon high-Q/Vm photonic band gap defect cavities.Comment: 40 pages, 11 figures, submitted to Physics Review

Modernization of Agriculture and Long-Term Growth

This paper develops a two-sector model that illuminates the role played by agricultural modernization in the transition from stagnation to growth. When agriculture relies on traditional technology, industrial development reduces the relative price of industrial products, but has a limited effect on per capita income because most labor has to remain in farming. Growth is not sustainable until this relative price drops below a certain threshold, thus inducing farmers to adopt modern technology that employs industry-supplied inputs. Once agricultural modernization begins, per capita income emerges from stasis and accelerates toward modern growth. Our calibrated model is largely consistent with the set of historical data we have compiled on the English economy, accounting well for the growth experience of England encompassing the Industrial Revolution.long-term growth, transition mechanisms, relative price, agricultural modernization, structural transformation, Industrial Revolution, England

Broadband Epsilon-Near-Zero Metamaterials with Step-Like Metal-Dielectric Multilayer Structures

The concept of the broadband epsilon-near-zero meta-atom consisting of layered stacks with specified metallic filling ratio and thickness is proposed based on the Bergman spectral representation of the effective permittivity. The step-like metal-dielectric multilayer structures are designed to achieve realistic broadband epsilon-near-zero meta-atoms in optical frequency range. These meta-atoms can be integrated as building blocks for unconventional optical components with exotic electromagnetic properties over a wide frequency range, such as the demonstrated broadband directional emission and phase front shaping.Comment: 18 pages, 7 figure

Realizing broadband electromagnetic transparency with a graded-permittivity sphere

Broadband electromagnetic transparency phenomenon is realized with a well-designed graded-permittivity sphere, which has an extremely low scattering cross section over a wide frequency range, based on the generalized Mie scattering theory and numerical simulation in full-wave condition. The dynamic polarization cancellation is revealed by studying the variation of the polarization with respect to the frequency. Furthermore, a properly-designed multi-shell sphere is also proposed and examined in order to reduce the rigorous conditions for realizing the broadband transparency in experiments.Comment: 15 pages, 4 figure

Integrated optical devices based on broadband epsilon-near-zero meta-atoms

We verify the feasibility of the proposed theoretical strategy for designing the broadband near-zero permittivity (ENZ) metamaterial at optical frequency range with numerical simulations. In addition, the designed broadband ENZ stack are used as meta-atoms to build functional nanophotonic devices with extraordinary properties, including an ultranarrow electromagnetic energy tunneling channel and an ENZ concave focusing lens.Comment: 3 pages, 3 figure