Influence of the generated power, measurement bandwidth, and noise level on intensity statistics of a quasi-CW Raman fiber laser

In the present paper we numerically study instrumental impact on statistical properties of quasi-CW Raman fiber laser using a simple model of multimode laser radiation. Effects, that have the most influence, are limited electrical bandwidth of measurement equipment and noise. To check this influence, we developed a simple model of the multimode quasi- CW generation with exponential statistics (i.e. uncorrelated modes). We found that the area near zero intensity in probability density function (PDF) is strongly affected by both factors, for example both lead to formation of a negative wing of intensity distribution. But far wing slope of PDF is not affected by noise and, for moderate mismatch between optical and electrical bandwidth, is only slightly affected by bandwidth limitation. The generation spectrum often becomes broader at higher power in experiments, so the spectral/electrical bandwidth mismatch factor increases over the power that can lead to artificial dependence of the PDF slope over the power. It was also found that both effects influence the ACF background level: noise impact decreases it, while limited bandwidth leads to its increase. © (2014) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.

High extinction ratio in-fibre polarisers based on 45° tilted fibre Bragg gratings

We report a near-ideal in-fiber polarizer implemented by use of 45° tilted fiber Bragg grating structures that are UV inscribed in hydrogenated Ge-doped fiber. We demonstrate a polarization-extinction ratio of 33 dB over a 100-nm operation range near 1550 nm. We further show an achievement of 99.5% degree of polarization for unpolarized light with these gratings. We also theoretically investigate tilted grating structures based on the Green's function calculation, therein revealing the unique polarization characteristics, which are in excellent agreement with experimental data.

Advanced tilted fiber gratings and their applications

This thesis presents a detailed numerical analysis, fabrication method and experimental investigation on 45º tilted fiber gratings (45º-TFGs) and excessively tilted fiber gratings (Ex-TFGs), and their applications in fiber laser and sensing systems. The one of the most significant contributions of the work reported in this thesis is that the 45º-TFGs with high polarization extinction ratio (PER) have been fabricated in single mode telecom and polarization maintaining (PM) fibers with spectral response covering three prominent optic communication and central wavelength ranges at 1060nm, 1310nm and 1550nm. The most achieved PERs for the 45º-TFGs are up to and greater than 35-50dB, which have reached and even exceeded many commercial in-fiber polarizers. It has been proposed that the 45º-TFGs of high PER can be used as ideal in-fiber polarizers for a wide range of fiber systems and applications. In addition, in-depth detailed theoretical models and analysis have been developed and systematic experimental evaluation has been conducted producing results in excellent agreement with theoretical modeling. Another important outcome of the research work is the proposal and demonstration of all fiber Lyot filters (AFLFs) implemented by utilizing two (for a single stage type) and more (for multi-stage) 45º-TFGs in PM fiber cavity structure. The detailed theoretical analysis and modelling of such AFLFs have also been carried out giving design guidance for the practical implementation. The unique function advantages of 45º-TFG based AFLFs have been revealed, showing high finesse multi-wavelength transmission of single polarization and wide range of tuneability. The temperature tuning results of AFLFs have shown that the AFLFs have 60 times higher thermal sensitivity than the normal FBGs, thus permitting thermal tuning rate of ~8nm/10ºC. By using an intra-cavity AFLF, an all fiber soliton mode locking laser with almost total suppression of siliton sidebands, single polarization output and single/multi-wavelength switchable operation has been demonstrated. The final significant contribution is the theoretical analysis and experimental verification on the design, fabrication and sensing application of Ex-TFGs. The Ex-TFG sensitivity model to the surrounding medium refractive index (SRI) has been developed for the first time, and the factors that affect the thermal and SRI sensitivity in relation to the wavelength range, tilt angle, and the size of cladding have been investigated. As a practical SRI sensor, an 81º-TFG UV-inscribed in the fiber with small (40μm) cladding radius has shown an SRI sensitivity up to 1180nm/RIU in the index of 1.345 range. Finally, to ensure single polarization detection in such an SRI sensor, a hybrid configuration by UV-inscribing a 45º-TFG and an 81º-TFG closely on the same piece of fiber has been demonstrated as a more advanced SRI sensing system.

A Computer Algebra Application to Determination of Lie Symmetries of Partial Differential Equations

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006

The General Differential Operators Generated by a Quasi-Differential Expressions with their Interior Singular Points

The general ordinary quasi-differential expression M of n-th order with complex coefficients and its formal adjoint M + are considered over a regoin (a, b) on the real line, −∞ ≤ a < b ≤ ∞, on which the operator may have a finite number of singular points. By considering M over various subintervals on which singularities occur only at the ends, restrictions of the maximal operator generated by M in L2|w (a, b) which are regularly solvable with respect to the minimal operators T0 (M ) and T0 (M + ). In addition to direct sums of regularly solvable operators defined on the separate subintervals, there are other regularly solvable restrications of the maximal operator which involve linking the various intervals together in interface like style.

All-fiber 250 MHz fundamental repetition rate pulsed laser with tilted fiber grating polarizer

We demonstrated a high fundamental repetition-rate pulsed erbium-doped fiber laser with all-fiber-integrated configuration. A novel scheme using a 45°-tilted fiber grating as the in-fiber polarizing element was employed to shorten the total cavity length and, thus, increase the fundamental repetition rate of the laser. Dissipative soliton pulses mode-locked with a fundamental repetition rate of 251.3 MHz and pulse duration of 96.7 fs have been achieved from the compact and all-fiber ring cavity laser. Additionally, passively Q-switched pulses were observed from this high fundamental repetition-rate fiber laser, which is the first report on Q-switched fiber laser using a tilted fiber grating.

On Parabolic Subgroups and Hecke Algebras of some Fractal Groups

* The authors thank the “Swiss National Science Foundation” for its support.

Partial Quasi-Bilateral Generating Function Involving some Special Functions

A group-theoretic method of obtaining more general class of generating functions from a given class of partial quasi-bilateral generating functions involving Hermite, Laguerre and Gegenbaur polynomials are discussed.

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.

A Note on Totally Bounded Quasi-Uniformities

We present the original proof, based on the Doitchinov completion, that a totally bounded quiet quasi-uniformity is a uniformity. The proof was obtained about ten years ago, but never published. In the mean-time several stronger results have been obtained by more direct arguments [8, 9, 10]. In particular it follows from Künzi’s [8] proofs that each totally bounded locally quiet quasi-uniform space is uniform, and recently Déak [10] observed that even each totally bounded Cauchy quasi-uniformity is a uniformity.

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.

Power tapping function in near infra-red region based on 45° tilted fiber gratings

We report an efficient power tapping device working in near infra-red (800 nm) wavelength region based on UV-in- scribed 45° tilted fiber grating (45°-TFG) structure. Five 45°-TFGs were UV-inscribed in hydrogenated PS750 fiber using a custom-designed phase mask with different grating lengths of 3 mm, 5 mm, 9 mm, 12 mm and 15 mm, showing polarization dependent losses (PDLs) of 1 dB, 3 dB, 7 dB, 10 dB and 13 dB, respectively. The power side-tapping efficiency is clearly depending on the grating strength. It has been identified that the power tapping efficiency increases with the grating strength and deceases along the grating length. The side-tapped power profile has also been examined in azimuthal direction, showing a near-Gaussian distribution. These experimental results clearly demonstrated that 45°- TFGs may be used as in-fiber power tapping devices for applications requiring in-line signal monitoring.

Sub-100 fs mode-locked erbium-doped fiber laser using a 45°-tilted fiber grating

We demonstrate generation of sub-100 fs pulses at 1.5 μm in a mode-locked erbium-doped fiber laser using a 45°-tilted fiber grating element. The laser features a genuine all-fiber configuration. Based on the unique polarization properties of the 45°-tilted fiber grating, we managed to produce sub-100 fs laser pulses through proper dispersion management. To the best of our knowledge, this is the shortest pulse generated from modelocked lasers with fiber gratings. The output pulse has an average power of 8 mW, with a repetition rate of 47.8 MHz and pulse energy of 1.68 nJ. The performance of laser also matches well the theoretical simulations. © 2013 Optical Society of America.

Some Comments on Q-Irresolute and Quasi-Irresolute Functions

The aim of this paper is to continue the study of θ-irresolute and quasi-irresolute functions as well as to give an example of a function which is θ-irresolute but neither quasi-irresolute nor an R-map and thus give an answer to a question posed by Ganster, Noiri and Reilly. We prove that RS-compactness is preserved under open, quasi-irresolute surjections.