Kinetic features of ethylene polymerization over supported catalysts [2,6‐bis(imino)pyridyl iron dichloride/magnesium dichloride] with AlR3 as an activator

The effects of polymerization temperature, polymerization time, ethylene and hydrogen concentration, and effect of comonomers (hexene‐1, propylene) on the activity of supported catalyst of composition LFeCl₂/MgCl₂‐Al(i‐Bu)₃ (L = 2,6‐bis[1‐(2,6‐dimethylphenylimino)ethyl] pyridyl) and polymer characteristics (molecular weight (MW), molecular‐weight distribution (MWD), molecular structure) have been studied. Effective activation energy of ethylene polymerization over LFeCl₂/MgCl₂‐Al(i‐Bu)₃ has a value typical of supported Ziegler–Natta catalysts (11.9 kcal/mol). The polymerization reaction is of the first order with respect to monomer at the ethylene concentration >0.2 mol/L. Addition of small amounts of hydrogen (9–17%) significantly increases the activity; however, further increase in hydrogen concentration decreases the activity. The IRS and DSC analysis of PE indicates that catalyst LFeCl₂/MgCl₂‐Al(i‐Bu)₃ has a very low copolymerizing ability toward propylene and hexene‐1. MW and MWD of PE produced over these catalysts depend on the polymerization time, ethylene and hexene‐1 concentration. The activation effect of hydrogen and other kinetic features of ethylene polymerization over supported catalysts based on the Fe (II) complexes are discussed. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 5057–5066, 2007     

Four-wave mixing of optical and microwave fields

We demonstrate degenerate four-wave mixing involving both optical and microwave fields. This four-wave mixing process, with fields that differ in frequency by 5 orders of magnitude, results from stimulated Raman scattering of the optical field from an atomic ground-state Zeeman coherence in warm rubidium vapor, which is induced and maintained by the microwave field.     

Vertically coupled whispering-gallery-mode resonator waveguide

We theoretically describe a novel configuration of a vertically coupled whispering-gallery-mode resonator waveguide. The waveguide is formed as a chain of doughnut-shaped low-contrast ripples on the surface of a vertical cylinder made from an optically transparent material. One can manipulate the properties of the waveguide by changing the shape of the resonators and the separation distance between them. Application of the structure as an optical delay line is discussed.     

Enhancement of Kerr nonlinearity by multiphoton coherence

We propose a new method of resonant enhancement of optical Kerr nonlinearity that uses multilevel atomic coherence. The enhancement is accompanied by suppression of the other linear and nonlinear susceptibility terms of the medium. We show that the effect results in a modification of the nonlinear Faraday rotation of light propagating in an 87Rb vapor cell by changing the ellipticity of the light.     

Radiation trapping in coherent media

We show that the effective decay rate of Zeeman coherence, generated in a (87)Rb vapor by linearly polarized laser light, increases significantly with the atomic density. We explain this phenomenon as the result of radiation trapping. Our study shows that radiation trapping must be taken into account to fully understand many electromagnetically induced transparency experiments with optically thick media.     

Ac-Stark shifts in the nonlinear Faraday effect

The frequency of the dark resonance in coherent population trapping experiments has been measured as a function of the degree of ellipticity and the intensity of the probe light. The results have been used to find the quantum limit of sensitivity of an optical magnetometer based on the nonlinear Faraday effect.     

Generation of near-infrared frequency combs from a MgF₂ whispering gallery mode resonator

We report on generation of a 20 nm wide, 35 GHz repetition rate optical frequency comb in a magnesium fluoride whispering gallery mode resonator pumped with 2 mW of 1543 nm light. The high efficiency of comb generation is associated with the small anomalous group velocity dispersion of the resonator. Growth dynamics of the comb is studied and compared with earlier theoretical predictions.     

A ponderomotive scheme for QND measurement of quadrature component

We propose a scheme for quantum nondemolition (QND) measurement of the quadrature component of a traveling wave, which uses the nonlinear ponderomotive interaction of electromagnetic waves reflected from a movable mirror. The influence of mechanical and optical losses and of imbalance in the interferometer arms is analyzed. Received: 27 March 1996 / Revised version: 25 September 1996     

Parametric oscillations in a whispering gallery resonator

We demonstrate strongly nondegenerate optical continuous-wave parametric oscillations in crystalline whispering gallery mode resonators fabricated from LiNbO3. The required phase matching is achieved by geometrical confinement of the modes in the resonator.     

Enabling arbitrary wavelength frequency combs on chip

A necessary condition for generation of bright soliton Kerr frequency combs in microresonators is to achieve anomalous group velocity dispersion (GVD) for the resonator modes. This condition is hard to implement in the visible as well as ultraviolet since the majority of optical materials are characterized with large normal GVD in these wavelength regions. We overcome this challenge by borrowing ideas from strongly dispersive coupled systems in solid state physics and optics. We show that photonic compound ring resonators can possess large anomalous GVD at any desirable wavelength, even if each individual resonator is characterized with normal GVD. Based on this concept, we design a mode‐locked frequency comb with thin‐film silicon nitride compound ring resonators in the vicinity of the rubidium D₁ line (794.6 nm) and propose to use this optical comb as a flywheel for chip‐scale optical clocks.