The Automorphism Group of the Free Algebra of Rank Two

The theorem of Czerniakiewicz and Makar-Limanov, that all the automorphisms of a free algebra of rank two are tame is proved here by showing that the group of these automorphisms is the free product of two groups (amalgamating their intersection), the group of all affine automorphisms and the group of all triangular automorphisms. The method consists in finding a bipolar structure. As a consequence every finite subgroup of automorphisms (in characteristic zero) is shown to be conjugate to a group of linear automorphisms.

Broadband tunable all-fiber polarization interference filter based on 45° tilted fiber gratings

We have theoretically and experimentally designed and demonstrated an all-fiber polarization interference filter (AFPIF), which is formed by a polarization-maintaining (PM) fiber cavity structure utilizing two 45° tilted fiber gratings (45°-TFGs) inscribed by UV laser on the PM fiber. Such a filter could generate modulated transmission of linear polarization status. It has been revealed that the modulation depth of the transmission depends on the coupling angle between the 45°-TFGs and the PM fiber cavity. When the two 45°-TFGs in PM fiber are oriented at 45° to the principal axis of the PM fiber cavity, the maximum modulation depth is achievable. Due to the thermal effect on birefringence of the PM fiber, the AFPIF can be tuned over a broad wavelength range just by simple thermal tuning of the cavity. The experiment results show that the temperature tuning sensitivity is proportional to the length ratio of the PM fiber cavity under heating. For 18 and 40 cm long cavities with 6 cm part under heating, the thermal tuning sensitivities are 0.616 and 0.31 nm/° C, respectively, which are almost two orders of magnitude higher than normal fiber Bragg gratings. © 1983-2012 IEEE.

All-fiber noninterferometric narrow-transmission-bandpass filter

In-fiber mode engineering based on the combination of Bragg and long-period gratings (LPGs) permits the implementation of noninterferometric transmission filters with narrow passbands using standard single-mode fiber. The design of the bandpass filter is based on the coupling between propagating and counterpropagating cladding modes in two fiber Bragg gratings. A LPG located between the Bragg gratings transfers power from the input fundamental mode to a specific cladding mode and recouples the filtered signal to the output fundamental mode. The filter produces a series of narrow passbands of about 30 pm linewidth with a maximum transmittance above 60%, 20 dB isolation, and passband separation of about 1 nm, each corresponding to the contribution of a different cladding mode. © 2012 Optical Society of America.

Highly sensitive temperature and strain sensors based on all-fiber 45°-TFG Lyot filter

We demonstrate highly sensitive temperature and strain sensors based on an all-fiber Lyot filter structure, which is formed by concatenating two 45°-TFGs (tilted fiber gratings) with a PM fiber cavity. The experiment results show the all-fiber 45°-TFG Lyot filter has very high sensitivity to strain and temperature. The 45°-TFG Lyot filters of two different cavity lengths (18cm and 40 cm) have been evaluated for temperature sensing by heating a section of the cavity from 10°C to 50°C. The experiment results have shown remarkably high temperature sensitivities of 0.616nm/°C for 18cm and 0.31nm/°C for 40cm long cavity filter, respectively. The 18cm long cavity filter has been subjected to strain variations up to around 550μ ε and the filter has exhibited strain sensitivities of 0.02499nm/μ ε and 0.012nm/μ ε for two straining situations, where its cavity middle section of 18cm and 9cm were stretched, respectively. © 2012 SPIE.

Simultaneous interrogation of fiber Bragg grating sensors using an acoustooptic tunable filter

In this letter, we describe a novel technique to provide demultimplexing of fiber Bragg grating sensors, interrogated using interferometric wavelength shift detection. Amplitude modulation of multiple radio frequency driving signals allows au acoustooptic tunable filter to provide wavelength demultiplexing. We demonstrated a noise limited strain resolution of 150 nanostrain/√Hz and a crosstalk better than -50 dB.

Analysis and improvement of performance in LCL filter-based PWM rectifier/inverter application using hybrid damping approach

A hybrid passive-active damping solution with improved system stability margin and enhanced dynamic performance is proposed for high power grid interactive converters. In grid connected active rectifier/inverter application, line side LCL filter improves the high frequency attenuation and makes the converter compatible with the stringent grid power quality regulations. Passive damping though offers a simple and reliable solution but it reduces overall converter efficiency. Active damping solutions do not increase the system losses but can guarantee the stable operation up to a certain speed of dynamic response which is limited by the maximum bandwidth of the current controller. This paper examines this limit and introduces a concept of hybrid passive-active damping solution with improved stability margin and high dynamic performance for line side LCL filter based active rectifier/inverter applications. A detailed design, analysis of the hybrid approach and trade-off between system losses and dynamic performance in grid connected applications are reported. Simulation and experimental results from a 10 kVA prototype demonstrate the effectiveness of the proposed solution. An analytical study on system stability and dynamic response with the variations of various controller and passive filter parameters is presented.

Remotely tuneable optical filter based on polymer fibre Bragg grating

We propose a remotely tuneable optical Bragg grating filter written in polymer optical fibre (POF). Fibre optical pumping in the fibre's absorption bands increases the fibre temperature, which causes a negative wavelength change of the POF Bragg grating. By choosing a proper pumping wavelength remote tuning of the optical filter can be readily realized without changing the gain of the optical signal.

Bidirectional nonreciprocal wavelength-interleaving coherent fiber transversal filter

A bidirectional nonreciprocal wavelength-interleaving filter based on an optically coherent high birefringence fiber transversal filter structure is demonstrated. Stable, low loss, low dispersion, and high isolation operation is demonstrated with reconfigurable transfer characteristics for interleaved channel spacing of 0.8 nm.

Optimally-designed single fiber Bragg grating filter scheme for RZ-OOK/DPSK/DQPSK to NRZ-OOK/DPSK/DQPSK format conversion

We investigate return-to-zero (RZ) to non-return-to-zero (NRZ) format conversion by means of the linear time-invariant system theory. It is shown that the problem of converting random RZ stream to NRZ stream can be reduced to constructing an appropriate transfer function for the linear filter. This approach is then used to propose novel optimally-designed single fiber Bragg grating (FBG) filter scheme for RZ-OOK/DPSK/DQPSK to NRZ-OOK/DPSK/DQPSK format conversion. The spectral response of the FBG is designed according to the optical spectra of the algebraic difference between isolated NRZ and RZ pulses, and the filter order is optimized for the maximum Q-factor of the output NRZ signals. Experimental results as well as simulations show that such an optimallydesigned FBG can successfully perform RZ-OOK/DPSK/DQPSK to NRZOOK/ DPSK/DQPSK format conversion.

Multifunctional, tunable and wideband all-fiber filter based on θ shaped microfiber resonator

A compact Θ shaped microfiber resonator for multifunctional, tunable and wideband filter is proposed. The filtering performance of reflection and transmission spectra depending on coupling coefficients and cavity length is theoretically investigated and experimentally demonstrated. © 2015 OSA.

High speed and high resolution demodulation system for hybrid WDM/FDM based fiber microstructure sensor network by using Fabry-Perot filter

Hybrid WDM/TDM enabled microstructure based optical fiber sensor network with large capacity is proposed. Assisted by Fabry-Perot filter, the demodulation system with high speed of 500Hz and high wavelength resolution less than 4.91pm is realized. © OSA 2015.

Factorizations of some Groups of Lie Type of Lie Rank 4

Еленка Генчева, Цанко Генчев В настоящата работа се разглеждат крайни прости групи G , които могат да се представят като произведение на две свои собствени неабелеви прости подгрупи A и B. Всяко такова представяне G = AB е прието да се нарича факторизация на G, а тъй като множителите A и B са избрани да бъдат прости подгрупи на G, то разглежданите факторизации са известни още като прости факторизации на G. Тук се предполага, че G е проста група от лиев тип и лиев ранг 4 над крайно поле GF (q). Ключови думи: крайни прости групи, групи от лиев тип, факторизации на групи.

Soliton mode locking fiber laser with an all-fiber polarization interference filter

An erbium doped fiber ring laser achieving soliton mode locking by the use of an intra-cavity all-fiber polarization interference filter (AFPIF) has been demonstrated. To incorporate an AFPIF with relative narrow transmission bandwidth, the laser has produced clean soliton pulses of 1.2 ps duration at a repetition rate of 14.98 MHz with a polarization extinction ratio up to 25.7 dB. Moreover, we have demonstrated that the operating wavelength of the mode locking laser can be tuned over 20 nm range from 1545 to 1565 nm by thermally tuning the AFPIF cavity. © 2012 Optical Society of America.

Spectrum-, pulsewidth-, and wavelengthswitchable all-fiber mode-locked Yb laser with fiber based birefringent filter

We examined methods of controlling the pulse duration, spectral width and wavelength of the output from an all-fiber Yb laser mode-locked by carbon nanotubes. It is shown that a segment of polarization maintaining (PM) fiber inserted into a standard single mode fiber based laser cavity can function as a spectral selective filter. Adjustment of the length of the PM fiber from 1 to 2 m led to a corresponding variation in the pulse duration from 2 to 3.8 ps, the spectral bandwidth of the laser output changes from 0.15 to 1.26 nm. Laser output wavelength detuning within up to 5 nm was demonstrated with a fixed length of the PM fiber by adjustment of the polarization controller. © 2012 Optical Society of America.

High resolution demodulation platform for large capacity hybrid WDM/FDM microstructures sensing system assisted by tunable FP filter

In this paper we proposed a demodulation scheme based on tunable FP filter for the WDM/FDM sensing system of the microstructure mentioned in the previous work. Simulation is done to prove the feasibility of demodulating the microstructure with the tunable FP filter. The experiments result showed high consistence with the simulation. And with the help of the high speed FPGA module and a high resolution AD/DA card, the system has achieved a very high resolution, up to 2.5 pm, and wavelength ranges 1520nm to 1590 nm.