Novel complex gratings with third-order group-delay variations for tunable pure dispersion slope compensation

We present a novel tunable dispersion compensator that can provide pure slope compensation. The approach uses two specially designed complex fiber Bragg gratings (FBGs) with reversely varied third-order group delay curves to generate the dispersion slope. The slope can be changed by adjusting the relative wavelength positions of the two FBGs. Several design examples of such complex gratings are presented and discussed. Experimentally, we achieve a dispersion slope tuning range of +/-650ps/nm2 with >0.9nm usable bandwidth.

Approximating differentiable relationships between delay embedded dynamical systems with radical basis functions

This thesis is about the study of relationships between experimental dynamical systems. The basic approach is to fit radial basis function maps between time delay embeddings of manifolds. We have shown that under certain conditions these maps are generically diffeomorphisms, and can be analysed to determine whether or not the manifolds in question are diffeomorphically related to each other. If not, a study of the distribution of errors may provide information about the lack of equivalence between the two. The method has applications wherever two or more sensors are used to measure a single system, or where a single sensor can respond on more than one time scale: their respective time series can be tested to determine whether or not they are coupled, and to what degree. One application which we have explored is the determination of a minimum embedding dimension for dynamical system reconstruction. In this special case the diffeomorphism in question is closely related to the predictor for the time series itself. Linear transformations of delay embedded manifolds can also be shown to have nonlinear inverses under the right conditions, and we have used radial basis functions to approximate these inverse maps in a variety of contexts. This method is particularly useful when the linear transformation corresponds to the delay embedding of a finite impulse response filtered time series. One application of fitting an inverse to this linear map is the detection of periodic orbits in chaotic attractors, using suitably tuned filters. This method has also been used to separate signals with known bandwidths from deterministic noise, by tuning a filter to stop the signal and then recovering the chaos with the nonlinear inverse. The method may have applications to the cancellation of noise generated by mechanical or electrical systems. In the course of this research a sophisticated piece of software has been developed. The program allows the construction of a hierarchy of delay embeddings from scalar and multi-valued time series. The embedded objects can be analysed graphically, and radial basis function maps can be fitted between them asynchronously, in parallel, on a multi-processor machine. In addition to a graphical user interface, the program can be driven by a batch mode command language, incorporating the concept of parallel and sequential instruction groups and enabling complex sequences of experiments to be performed in parallel in a resource-efficient manner.

The application of fibre Bragg grating networks as strain sensors and as phased array antenna true time delay elements

The fabrication of in-fibre Bragg gratings, and the application of arrays of such gratings as strain sensors and as true time delay elements for the control of phased array antennas is reported. Chirped period Bragg gratings were produced using the fibre deformation fabrication technique, with chirps of between 2.9nm and 17.3nm achieved. Arrays of 5mm and 2mm long uniform period Bragg gratings were fabricated using the inscription method, for use as true time delay elements,dissimilar wavefronts and their spectral characteristics recorded. The uniform period grating arrays were used to create minimum time delays of 9.09ps, 19.02ps and 31ps; making them suitable for controlling phased array antennas operating at RF frequencies of up to 3GHz, with 10° phase resolution. Four 4mm long chirped gratings were produced using the dissimilar wavefronts fabrication method, having chirps of 7nm, 12nm, 20nm and 30nm, and were used to create time delays of between 0.3ps and 59ps. Hence they are suitable for controlling phased array antennas at RF frequencies of up to 48GHz. The application of in fibre Bragg gratings as strain sensors within smart structure materials was investigated, with their sensitivity to applied strain and compression measured for both embedded and surface mounted uniform period and fibre Fabry-Perot filter gratings. A fibre Bragg grating sensor demultiplexing scheme based on a liquid crystal filled Fabry-Perot etalon tuneable transmission filter was proposed, successfully constructed and fully characterised. Three characteristics of the LCFP etalon were found to pose operational limitations to its application in a Bragg grating sensor system; most significantly, the resonance peak wavelength was highly (-2,77nm/°C) temperature dependent. Several methods for minimising this temperature sensitivity were investigated, but enjoyed only limited success. It was therefore concluded that this type (E7 filled) of LCFP etalon is unsuitable for use as a Bragg grating sensor demultiplexing element.

Synthesis of arbitrary group delay responses with all-pass optical cavities structures

We propose a systematic method for the synthesis of arbitrary group delay responses by using all-pass structures of coupled optical cavities. Optimum structure parameters design, in terms of filter order and accuracy, are obtained.

Unified model for performance analysis of IEEE 802.11 ad hoc networks in unsaturated conditions

IEEE 802.11 standard has achieved huge success in the past decade and is still under development to provide higher physical data rate and better quality of service (QoS). An important problem for the development and optimization of IEEE 802.11 networks is the modeling of the MAC layer channel access protocol. Although there are already many theoretic analysis for the 802.11 MAC protocol in the literature, most of the models focus on the saturated traffic and assume infinite buffer at the MAC layer. In this paper we develop a unified analytical model for IEEE 802.11 MAC protocol in ad hoc networks. The impacts of channel access parameters, traffic rate and buffer size at the MAC layer are modeled with the assistance of a generalized Markov chain and an M/G/1/K queue model. The performance of throughput, packet delivery delay and dropping probability can be achieved. Extensive simulations show the analytical model is highly accurate. From the analytical model it is shown that for practical buffer configuration (e.g. buffer size larger than one), we can maximize the total throughput and reduce the packet blocking probability (due to limited buffer size) and the average queuing delay to zero by effectively controlling the offered load. The average MAC layer service delay as well as its standard deviation, is also much lower than that in saturated conditions and has an upper bound. It is also observed that the optimal load is very close to the maximum achievable throughput regardless of the number of stations or buffer size. Moreover, the model is scalable for performance analysis of 802.11e in unsaturated conditions and 802.11 ad hoc networks with heterogenous traffic flows. © 2012 KSI.

Reduction of XPM penalty by sub-bit delay demodulation of DQPSK

We show that using a shortened delay in the demodulator for DQPSK channels can significantly reduce the XPM penalties caused by transmitting 40Gb/s DQPSK channels alongside 10Gb/s OOK channels. © 2010 Optical Society of America.

Enhanced slotted aloha protocols for underwater sensor networks with large propagation delay

Recently underwater sensor networks (UWSN) attracted large research interests. Medium access control (MAC) is one of the major challenges faced by UWSN due to the large propagation delay and narrow channel bandwidth of acoustic communications used for UWSN. Widely used slotted aloha (S-Aloha) protocol suffers large performance loss in UWSNs, which can only achieve performance close to pure aloha (P-Aloha). In this paper we theoretically model the performances of S-Aloha and P-Aloha protocols and analyze the adverse impact of propagation delay. According to the observation on the performances of S-Aloha protocol we propose two enhanced S-Aloha protocols in order to minimize the adverse impact of propagation delay on S-Aloha protocol. The first enhancement is a synchronized arrival S-Aloha (SA-Aloha) protocol, in which frames are transmitted at carefully calculated time to align the frame arrival time with the start of time slots. Propagation delay is taken into consideration in the calculation of transmit time. As estimation error on propagation delay may exist and can affect network performance, an improved SA-Aloha (denoted by ISA-Aloha) is proposed, which adjusts the slot size according to the range of delay estimation errors. Simulation results show that both SA-Aloha and ISA-Aloha perform remarkably better than S-Aloha and P-Aloha for UWSN, and ISA-Aloha is more robust even when the propagation delay estimation error is large. © 2011 IEEE.

An alternating boundary integral based method for a Cauchy problem for the Laplace equation in semi-infinite regions

We consider a Cauchy problem for the Laplace equation in a two-dimensional semi-infinite region with a bounded inclusion, i.e. the region is the intersection between a half-plane and the exterior of a bounded closed curve contained in the half-plane. The Cauchy data are given on the unbounded part of the boundary of the region and the aim is to construct the solution on the boundary of the inclusion. In 1989, Kozlov and Maz'ya [10] proposed an alternating iterative method for solving Cauchy problems for general strongly elliptic and formally self-adjoint systems in bounded domains. We extend their approach to our setting and in each iteration step mixed boundary value problems for the Laplace equation in the semi-infinite region are solved. Well-posedness of these mixed problems are investigated and convergence of the alternating procedure is examined. For the numerical implementation an efficient boundary integral equation method is proposed, based on the indirect variant of the boundary integral equation approach. The mixed problems are reduced to integral equations over the (bounded) boundary of the inclusion. Numerical examples are included showing the feasibility of the proposed method.

On an indirect integral equation approach for stationary heat transfer in semi-infinite layered domains in R3 with cavities

Regions containing internal boundaries such as composite materials arise in many applications.We consider a situation of a layered domain in IR3 containing a nite number of bounded cavities. The model is stationary heat transfer given by the Laplace equation with piecewise constant conductivity. The heat ux (a Neumann condition) is imposed on the bottom of the layered region and various boundary conditions are imposed on the cavities. The usual transmission (interface) conditions are satised at the interface layer, that is continuity of the solution and its normal derivative. To eciently calculate the stationary temperature eld in the semi-innite region, we employ a Green's matrix technique and reduce the problem to boundary integral equations (weakly singular) over the bounded surfaces of the cavities. For the numerical solution of these integral equations, we use Wienert's approach [20]. Assuming that each cavity is homeomorphic with the unit sphere, a fully discrete projection method with super-algebraic convergence order is proposed. A proof of an error estimate for the approximation is given as well. Numerical examples are presented that further highlights the eciency and accuracy of the proposed method.

An iterative method based on boundary integrals for elliptic Cauchy problems in semi-infinite domains

In this study, we investigate the problem of reconstruction of a stationary temperature field from given temperature and heat flux on a part of the boundary of a semi-infinite region containing an inclusion. This situation can be modelled as a Cauchy problem for the Laplace operator and it is an ill-posed problem in the sense of Hadamard. We propose and investigate a Landweber-Fridman type iterative method, which preserve the (stationary) heat operator, for the stable reconstruction of the temperature field on the boundary of the inclusion. In each iteration step, mixed boundary value problems for the Laplace operator are solved in the semi-infinite region. Well-posedness of these problems is investigated and convergence of the procedures is discussed. For the numerical implementation of these mixed problems an efficient boundary integral method is proposed which is based on the indirect variant of the boundary integral approach. Using this approach the mixed problems are reduced to integral equations over the (bounded) boundary of the inclusion. Numerical examples are included showing that stable and accurate reconstructions of the temperature field on the boundary of the inclusion can be obtained also in the case of noisy data. These results are compared with those obtained with the alternating iterative method.

Transition of planar Couette flow at infinite Reynolds numbers

An outline of the state space of planar Couette flow at high Reynolds numbers (Re<105) is investigated via a variety of efficient numerical techniques. It is verified from nonlinear analysis that the lower branch of the hairpin vortex state (HVS) asymptotically approaches the primary (laminar) state with increasing Re. It is also predicted that the lower branch of the HVS at high Re belongs to the stability boundary that initiates a transition to turbulence, and that one of the unstable manifolds of the lower branch of HVS lies on the boundary. These facts suggest HVS may provide a criterion to estimate a minimum perturbation arising transition to turbulent states at the infinite Re limit. © 2013 American Physical Society.

Delay of light in an optical bottle resonator with nanoscale radius variation : dispersionless, broadband, and low-loss

It is shown theoretically that an optical bottle resonator with a nanoscale radius variation can perform a multinanosecond long dispersionless delay of light in a nanometer-order bandwidth with minimal losses. Experimentally, a 3 mm long resonator with a 2.8 nm deep semiparabolic radius variation is fabricated from a 19??µm radius silica fiber with a subangstrom precision. In excellent agreement with theory, the resonator exhibits the impedance-matched 2.58 ns (3 bytes) delay of 100 ps pulses with 0.44??dB/ns intrinsic loss. This is a miniature slow light delay line with the record large delay time, record small transmission loss, dispersion, and effective speed of light.

Synthesis of arbitrary group delay responses with all-pass optical cavities structures

We propose a systematic method for the synthesis of arbitrary group delay responses by using allpass structures of coupled optical cavities. Optimum structure parameters design, in terms of filter order and accuracy, are obtained. © 2012 OSA.

Delay of light in an optical bottle resonator with nanoscale radius variation:dispersionless, broadband, and low-loss

It is shown theoretically that an optical bottle resonator with a nanoscale radius variation can perform a multinanosecond long dispersionless delay of light in a nanometer-order bandwidth with minimal losses. Experimentally, a 3 mm long resonator with a 2.8 nm deep semiparabolic radius variation is fabricated from a 19??µm radius silica fiber with a subangstrom precision. In excellent agreement with theory, the resonator exhibits the impedance-matched 2.58 ns (3 bytes) delay of 100 ps pulses with 0.44??dB/ns intrinsic loss. This is a miniature slow light delay line with the record large delay time, record small transmission loss, dispersion, and effective speed of light.