2-fold and 3-fold mixing: why 3-dot-type counterexamples are impossible in one dimension

V.A. Rohlin asked in 1949 whether 2-fold mixing implies 3-fold mixing for a stationary process (ξ_i )_i2ℤ, and the question remains open today. In 1978, F. Ledrappier exhibited a counterexample to the 2-fold mixing implies 3-fold mixing problem, the socalled 3-dot system, but in the context of stationary random fields indexed by ℤ². In this work, we first present an attempt to adapt Ledrappier's construction to the onedimensional case, which finally leads to a stationary process which is 2-fold but not 3-fold mixing conditionally to the σ-algebra generated by some factor process. Then, using arguments coming from the theory of joinings, we will give some strong obstacles proving that Ledrappier's counterexample can not be fully adapted to one-dimensional stationary processes.     

Planar photonic crystal polarization splitter

The differential dispersion relation for the E and H modes (TM-like and TE-like, respectively) in planar photonic crystals is used to control the polarization-dependent propagation of light. E- and H-polarized beams were separated by 10 degrees after propagating through a 20-microm-long planar photonic crystal in the wavelength range from 1250 to 1300 nm. The plane-wave expansion calculation matches well with the experimental results. This result represents the first demonstration, to our knowledge, of a polarization splitter realized in a planar photonic crystal configuration in the near-infrared wavelength range operating solely in transmission mode.     

State‐of‐the‐art all‐silicon sub‐bandgap photodetectors at telecom and datacom wavelengths

Silicon‐based technologies provide an ideal platform for the monolithic integration of photonics and microelectronics. In this context, a variety of passive and active silicon photonic devices have been developed to operate at telecom and datacom wavelengths, at which silicon has minimal optical absorption ‐ due to its bandgap of 1.12 eV. Although in principle this transparency window limits the use of silicon for optical detection at wavelengths above 1.1 μm, in recent years tremendous advances have been made in the field of all‐silicon sub‐bandgap photodetectors at telecom and datacom wavelengths. By taking advantage of emerging materials and novel structures, these devices are becoming competitive with the more well‐established technologies, and are opening new and intriguing perspectives. In this paper, a review of the state‐of‐the‐art is presented. Devices based on defect‐mediated absorption, two‐photon absorption and the internal photoemission effect are reported, their working principles are elucidated and their performance discussed and compared.

     

Finite-sample properties of estimators for first and second order autoregressive processes

Statistical Inference for Stochastic Processes - The class of autoregressive (AR) processes is extensively used to model temporal dependence in observed time series. Such models are easily...     

Fabrication of multipassband moiré resonators in fibers by the dual-phase-mask exposure method

We report on the fabrication of in-fiber moiré filters by dual exposure of a nondedicated chirped phase mask. This simple technique produces broadband filters whose structure depends only on an intermediate stretch between two identical UV exposures. We demonstrate moiré filters with as many as four narrow passbands within a 2-nm stopband.     

Ion mobility studies of electronically excited states of atomic transition metal cations: Development of an ion mobility source for guided ion beam experiments

The design of an ion mobility source developed to couple to a guided ion beam tandem mass spectrometer is presented. In these exploratory studies, metal ions are created continuously by electron ionization of the volatile hexacarbonyls of the three group 6 transition metals. These ions are focused into a linear hexapole ion trap, which collects the ions and then creates high intensity pulses of ions, avoiding excessive ion losses resulting from the low duty cycle of pulsed operation. The ion pulses are injected into a six-ring drift cell filled with helium where ions having different electronic configurations can separate because they have different ion mobilities. Such separation is observed for chromium ions and compares favorably with the pioneering work of Kemper and Bowers (J. Phys. Chem.1991, 95, 5134). The results are then extended to Mo(+) and W(+), which also show efficient configuration separation. The source conditions needed for high intensities and good configuration separation are discussed in detail and suggestions for further improvements are also provided.     

On covering an independent set in a grid with a second independent set

We show that for every independent set O in an n × m grid, n, m > 1, there is a second independent set X with the property that every member of O is adjacent to at least one member of X . The proof gives a construction for X . Equivalently, we show that for every maximal independent set in a grid, there is a second, disjoint, maximal independent set. © 1996 John Wiley & Sons, Inc.     

Graphene-based Q-switched pulsed fiber laser in a linear configuration

A pulsed laser system is realized with graphene employed as a Q-switch.The graphene is exfoliated from its solution using an optical deposition and the optical tweezer effect.A fiber ferrule that already has the graphene deposited on it is inserted into an erbium-ytterbium laser(EYL)system with linear cavity configuration.We successfully demonstrate a pulsed EYL with a pulse duration of approximately 5.9μs and a repetition rate of 20.0 kHz.     

Spectral features associated with nonlinear pulse compression in Bragg gratings

We report, for the first time to our knowledge, direct spectral measurements of nonlinear spectral broadening caused by nonlinear propagation through Bragg gratings written on integrated AlGaAs waveguides. The spectral broadening is associated with pulse compression from 400 to 80 ps. The high nonlinearity of AlGaAs enables high-repetition-rate, low-peak-power sources to be used, facilitating easy spectral measurements.