2nd order Bragg rasonance generated in a 45° tilted fiber grating and its application in a fiber laser

We report the generation of a 13dB 2nd order Bragg resonance in a conventionally UV inscribed 45° tilted fiber grating, showing strong polarization dependency and its application for singe polarization output of a fiber laser. © 2010 Optical Society of America.

All fibre femtosecond pulse generation using an intracavity 45°-tilted fibre grating

We demonstrate an all-fibre erbium doped fibre laser mode-locked by using an intracavity 45°-Tilted Fibre Grating as a polarization element. The laser produces soliton-like pulses with ~600fs pulse duration and ~1nJ output energy at a repetition rate of 10.34MHz. © 2010 Optical Society of America.

Single polarisation output of erbium-doped fibre ring laser utilising a small tilted fibre grating structure

Single polarisation operation of a fibre ring laser was realised by employing an intra-cavity 9.3°-tilted fibre Bragg grating as an in-fibre polariser. The laser showed a polarisationextinction-ratio of ~ 31dB with a good stability. © 2010 Optical Society of America.

Optically pumped chirped grating for tunable chromatic dispersion compensation

We demonstrate a novel optically tunable dispersion compensator based on pumping a chirped grating made in Er/Yb co-doped fiber. The dispersion was tuned from 900 to 1900ps/nm and also from-600 to-950ps/nm in the experiment. © 2010 Optical Society of America.

Refractometer probe based on a reflective carbon nanotube-modified microfiber Bragg grating

A carbon nanotube (CNT)-modified microfiber Bragg grating (MFBG) is proposed to measure the refractive index with a strong enhancement of the sensitivity in the low refractive index region. The introduction of the CNT layer influences the evanescent field of the MFBG and causes modification of the reflection spectrum. With the increase of the surrounding refractive index (SRI), we observe significant attenuation to the peak of the Bragg resonance, while its wavelength remains almost unchanged. Our detailed experimental results disclose that the CNT-MFBG demonstrates strong sensitivity in the low refractive index range of 1.333-1.435, with peak intensity up to -53.4 dBm/refractive index unit, which is 15-folds higher than that of the uncoated MFBG. Therefore, taking advantage of the CNT-induced evanescent field enhancement, the reflective MFBG probe presents strong sensing capability in biochemical fields.

High spatial and temporal resolution interrogation of fully distributed chirped fiber Bragg grating sensors

A novel interrogation technique for fully distributed linearly chirped fiber Bragg grating (LCFBG) strain sensors with simultaneous high temporal and spatial resolution based on optical time-stretch frequency-domain reflectometry (OTS-FDR) is proposed and experimentally demonstrated. LCFBGs is a promising candidate for fully distributed sensors thanks to its longer grating length and broader reflection bandwidth compared to normal uniform FBGs. In the proposed system, two identical LCFBGs are employed in a Michelson interferometer setup with one grating serving as the reference grating whereas the other serving as the sensing element. Broadband spectral interferogram is formed and the strain information is encoded into the wavelength-dependent free spectral range (FSR). Ultrafast interrogation is achieved based on dispersion-induced time stretch such that the target spectral interferogram is mapped to a temporal interference waveform that can be captured in real-Time using a single-pixel photodector. The distributed strain along the sensing grating can be reconstructed from the instantaneous RF frequency of the captured waveform. High-spatial resolution is also obtained due to high-speed data acquisition. In a proof-of-concept experiment, ultrafast real-Time interrogation of fully-distributed grating sensors with various strain distributions is experimentally demonstrated. An ultrarapid measurement speed of 50 MHz with a high spatial resolution of 31.5 μm over a gauge length of 25 mm and a strain resolution of 9.1 μϵ have been achieved.

Design, fabrication and characterization of resonant waveguide grating based optical biosensors

The absence of rapid, low cost and highly sensitive biodetection platform has hindered the implementation of next generation cheap and early stage clinical or home based point-of-care diagnostics. Label-free optical biosensing with high sensitivity, throughput, compactness, and low cost, plays an important role to resolve these diagnostic challenges and pushes the detection limit down to single molecule. Optical nanostructures, specifically the resonant waveguide grating (RWG) and nano-ribbon cavity based biodetection are promising in this context. The main element of this dissertation is design, fabrication and characterization of RWG sensors for different spectral regions (e.g. visible, near infrared) for use in label-free optical biosensing and also to explore different RWG parameters to maximize sensitivity and increase detection accuracy. Design and fabrication of the waveguide embedded resonant nano-cavity are also studied. Multi-parametric analyses were done using customized optical simulator to understand the operational principle of these sensors and more important the relationship between the physical design parameters and sensor sensitivities. Silicon nitride (SixNy) is a useful waveguide material because of its wide transparency across the whole infrared, visible and part of UV spectrum, and comparatively higher refractive index than glass substrate. SixNy based RWGs on glass substrate are designed and fabricated applying both electron beam lithography and low cost nano-imprint lithography techniques. A Chromium hard mask aided nano-fabrication technique is developed for making very high aspect ratio optical nano-structure on glass substrate. An aspect ratio of 10 for very narrow (~60 nm wide) grating lines is achieved which is the highest presented so far. The fabricated RWG sensors are characterized for both bulk (183.3 nm/RIU) and surface sensitivity (0.21nm/nm-layer), and then used for successful detection of Immunoglobulin-G (IgG) antibodies and antigen (~1μg/ml) both in buffer and serum. Widely used optical biosensors like surface plasmon resonance and optical microcavities are limited in the separation of bulk response from the surface binding events which is crucial for ultralow biosensing application with thermal or other perturbations. A RWG based dual resonance approach is proposed and verified by controlled experiments for separating the response of bulk and surface sensitivity. The dual resonance approach gives sensitivity ratio of 9.4 whereas the competitive polarization based approach can offer only 2.5. The improved performance of the dual resonance approach would help reducing probability of false reading in precise bio-assay experiments where thermal variations are probable like portable diagnostics.

Chemical Sensor Based on a Long-Period Fibre Grating Modified by a Functionalized Polydimethylsiloxane Coating

A chemical sensor based on a coated long-period grating has been prepared and characterized. Designer coatings based on polydimethylsiloxane were prepared by the incorporation of diphenylsiloxane and titanium cross-linker in order to provide enhanced sensitivity for a variety of key environmental pollutants and optimal refractive index of the coating. Upon microextraction of the analyte into the polymer matrix, an increase in the refractive index of the coating resulted in a change in the attenuation spectrum of the long-period grating. The grating was interrogated using ring-down detection as a means to amplify the optical loss and to gain stability against misalignment and power fluctuations. Chemical differentiation of cyclohexane and xylene was achieved and a detection limit of 300 ppm of xylene vapour was realized.

Optimal 5-step nilpotent quadratic algebras

By the Golod–Shafarevich theorem, an associative algebra $R$ given by $n$ generators and $<n^2/3$ homogeneous quadratic relations is not 5-step nilpotent. We prove that this estimate is optimal. Namely, we show that for every positive integer $n$, there is an algebra $R$ given by $n$ generators and $\lceil n^2/3\rceil$ homogeneous quadratic relations such that $R$ is 5-step nilpotent.

Two problems from the Polishchuk and Positselski book on Quadratic algebras

In the book ’Quadratic algebras’ by Polishchuk and Positselski [23] algebras with a small number of generators (n = 2, 3) are considered. For some number r of relations possible Hilbert series are listed, and those appearing as series of Koszul algebras are specified. The first case, where it was not possible to do, namely the case of three generators n = 3 and six relations r = 6 is formulated as an open problem. We give here a complete answer to this question, namely for quadratic algebras with dimA_1 = dimA_2 = 3, we list all possible Hilbert series, and find out which of them can come from Koszul algebras, and which can not. As a consequence of this classification, we found an algebra, which serves as a counterexample to another problem from the same book [23] (Chapter 7, Sec. 1, Conjecture 2), saying that Koszul algebra of finite global homological dimension d has dimA_1 > d. Namely, the 3-generated algebra A given by relations xx + yx = xz = zy = 0 is Koszul and its Koszul dual algebra A^! has Hilbert series of degree 4: HA! (t) = 1 + 3t + 3t^2 + 2t^3 + t^4, hence A has global homological dimension 4.

The Helmholtzian Equation: Stabilizing Mechanisms for Quadratic Nonlinear Fields

Hexagonal Resonant Triad patterns are shown to exist as stable solutions of a particular type of nonlinear field where no cubic field nonlinearity is present. The zero ‘dc’ Fourier mode is shown to stabilize these patterns produced by a pure quadratic field nonlinearity. Closed form solutions and stability results are obtained near the critical point, complimented by numerical studies far from the critical point. These results are obtained using a neural field based on the Helmholtzian operator. Constraints on structure and parameters for a general pure quadratic neural field which supports hexagonal patterns are obtained.

Evaluation and FMEA of Fabrication Techniques for Metallic Grating Couplers on Polymer Substrates with Low Glass Transition Temperatures

The main task is to analyze the state of the art of grating couplers production and low-cost polymer substrates. Then to provide a recommendation of a new or adapted process for the production of metallic gratings on polymer sheets, based on a Failure Mode and Effect Analysis (FMEA). In order to achieve that, this thesis is divided into four chapters. After the first introductory chapter, the second section provides details about the state-of-the-art in optical technology platforms with focus on polymers and their main features for the aimed application, such as flexibility, low cost and roll to roll compatibility. It defines then the diffraction gratings and their specifications and closes with the explanation of adhesion mechanisms of inorganic materials on polymer substrates. The third chapter discusses processing of grating couplers. It introduces the basic fabrication methods and details a selection of current fabrication schemes found in literature with an assessment of their potential use for the desired application. The last chapter is a FMEA analysis of the retained fabrication process, called Flip and Fuse, in order to check its capability to realize the grating structure.

Iterated responsive threshold search for the quadratic multiple knapsack problem

International audience

Robust solutions of bi-blend recipe optimization with quadratic constraints

Production companies use raw materials to compose end-products. They often make different products with the same raw materials. In this research, the focus lies on the production of two end-products consisting of (partly) the same raw materials as cheap as possible. Each of the products has its own demand and quality requirements consisting of quadratic constraints. The minimization of the costs, given the quadratic constraints is a global optimization problem, which can be difficult because of possible local optima. Therefore, the multi modal character of the (bi-) blend problem is investigated. Standard optimization packages (solvers) in Matlab and GAMS were tested on their ability to solve the problem. In total 20 test cases were generated and taken from literature to test solvers on their effectiveness and efficiency to solve the problem. The research also gives insight in adjusting the quadratic constraints of the problem in order to make a robust problem formulation of the bi-blend problem.