Developments and extensions of Roth's method of double Fourier series with applications to the solution of electromagnetic field problems

The first part of the thesis compares Roth's method with other methods, in particular the method of separation of variables and the finite cosine transform method, for solving certain elliptic partial differential equations arising in practice. In particular we consider the solution of steady state problems associated with insulated conductors in rectangular slots. Roth's method has two main disadvantages namely the slow rate of con­vergence of the double Fourier series and the restrictive form of the allowable boundary conditions. A combined Roth-separation of variables method is derived to remove the restrictions on the form of the boundary conditions and various Chebyshev approximations are used to try to improve the rate of convergence of the series. All the techniques are then applied to the Neumann problem arising from balanced rectangular windings in a transformer window. Roth's method is then extended to deal with problems other than those resulting from static fields. First we consider a rectangular insulated conductor in a rectangular slot when the current is varying sinusoidally with time. An approximate method is also developed and compared with the exact method.The approximation is then used to consider the problem of an insulated conductor in a slot facing an air gap. We also consider the exact method applied to the determination of the eddy-current loss produced in an isolated rectangular conductor by a transverse magnetic field varying sinusoidally with time. The results obtained using Roth's method are critically compared with those obtained by other authors using different methods. The final part of the thesis investigates further the application of Chebyshdev methods to the solution of elliptic partial differential equations; an area where Chebyshev approximations have rarely been used. A poisson equation with a polynomial term is treated first followed by a slot problem in cylindrical geometry.

Characterisation and performance of a Terfenol-D coated femtosecond laser inscribed optical fibre Bragg sensor with a laser ablated microslot for the detection of static magnetic fields

We present a novel device for the characterisation of static magnetic fields through monitoring wavelength shifts of femtosecond inscribed fibre Bragg grating and micromachined slot, coated with Terfenol-D. The device was sensitive to static magnetic fields and can be used as a vectoral sensor for the detection of magnetic fields as low as 0.046 mT with a resolution of ± 0.3mT in transmission and ± 0.7mT in reflection. The use of a femtosecond laser to both inscribe the FBGs and micromachine the slot in a single stage prior to coating the device significantly simplifies the fabrication.

Optical grooming switch with regenerative functionality for transparent interconnection of networks

We demonstrate a regenerative optical grooming switch for buffer-less interconnection of metro/access and metro/core ring networks with switching functionality in time, space and wavelength domain. Key functionalities of the router are the traffic aggregation with time-slot interchanging (TSI) functionality, the WDM-to-ODTM multiplexing and the OTDM-to-WDM demultiplexing of high-speed channel into lower bit-rate tributaries as well as multi-wavelength all-optical 2R regeneration of several higher-speed signals. BER and Q-factor measurements of different switching scenarios show excellent performance with no error floor and Q-factors above 21 dB.

Passive mode-locked lasing by injecting a carbon nanotube-solution in the core of an optical fiber

In this paper, we propose a saturable absorber (SA) device consisting on an in-fiber micro-slot inscribed by femtosecond laser micro fabrication, filled by a dispersion of Carbon Nanotubes (CNT). Due to the flexibility of the fabrication method, efficient and simple integration of the mode-locking device directly into the optical fiber is achieved. Furthermore, the fabrication process offers a high level of control over the dimensions and location of the micro-slots. We apply this fabrication flexibility to extend the interaction length between the CNT and the propagating optical field along the optical fiber, hence enhancing the nonlinearity of the device. Furthermore, the method allows the fabrication of devices that operate by either a direct field interaction (when the central peak of the propagating optical mode passes through the nonlinear media) or an evanescent field interaction (only a fraction of the optical mode interacts with the CNT). In this paper, several devices with different interaction lengths and interaction regimes are investigated. Self-starting passively modelocked laser operation with an enhanced nonlinear interaction is observed using CNT-based SAs in both interaction regimes. This method constitutes a simple and suitable approach to integrate the CNT into the optical system as well as enhancing the optical nonlinearity of CNT-based photonic devices.

An all-optical grooming switch for interconnecting access and metro ring networks

A regenerative all-optical grooming switch for interconnecting 130 Gbit/s on-off keying (OOK) metro/core ring and 43 Gbit/s-OOK metro/access ring networks with switching functionality in time, space, and wavelength domains is demonstrated. Key functionalities of the switch are traffic aggregation with time-slot interchanging functionality, optical time division multiplexing (OTDM) to wavelength division multiplexing (WDM) demultiplexing, and multi-wavelength 2R regeneration. Laboratory and field demonstrations show the excellent performance of the new concept with error-free signal transmission and Q-factors above 20 dB.

Field experiments with a grooming switch for OTDM meshed networking

Field experiments of 42.7/128.1 Gb/s wavelength-division multiplexed, optical time-division multiplexed (WDM-OTDM) transmultiplexing and all-optical dual-wavelength regeneration at the OTDM rate are presented in this paper. By using the asynchronous retiming scheme, we achieve error-free bufferless data grooming with time-slot interchange capability for OTDM meshed networking. We demonstrate excellent performance from the system, discuss scalability, applicability, and the potential reach of the asynchronous retiming scheme for transparent OTDM-domain interconnection.

Femtosecond laser inscribed Bragg sensor in Terfenol-D coated optical fibre with ablated microslot for the detection of static magnetic fields

A novel device for the detection and characterisation of static magnetic fields is presented. It consists of a femtosecond laser inscribed fibre Bragg grating (FBG) that is incorporated into an optical fibre with a femtosecond laser micromachined slot. The symmetry of the fibre is broken by the micro-slot, producing non-uniform strain across the fibre cross section. The sensing region is coated with Terfenol-D making the device sensitive to static magnetic fields, whereas the symmetry breaking results in a vectorial sensor for the detection of magnetic fields as low as 0.046 mT with a resolution of ±0.3mT in transmission and ±0.7mT in reflection. The sensor output is directly wavelength encoded from the FBG filtering, leading to simple demodulation through the monitoring of wavelength shifts that result as the fibre structure changes shape in response to the external magnetic field. The use of a femtosecond laser to both inscribe the FBG and micro-machine the slot in a single stage, prior to coating the device, significantly simplifies the sensor fabrication.

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.

Femtosecond laser inscribed Bragg sensor in Terfenol-D coated optical fibre with ablated microslot for the detection of static magnetic fields

A novel device for the detection and characterisation of static magnetic fields is presented. It consists of a femtosecond laser inscribed fibre Bragg grating (FBG) that is incorporated into an optical fibre with a femtosecond laser micromachined slot. The symmetry of the fibre is broken by the micro-slot, producing non-uniform strain across the fibre cross section. The sensing region is coated with Terfenol-D making the device sensitive to static magnetic fields, whereas the symmetry breaking results in a vectorial sensor for the detection of magnetic fields as low as 0.046 mT with a resolution of ±0.3mT in transmission and ±0.7mT in reflection. The sensor output is directly wavelength encoded from the FBG filtering, leading to simple demodulation through the monitoring of wavelength shifts that result as the fibre structure changes shape in response to the external magnetic field. The use of a femtosecond laser to both inscribe the FBG and micro-machine the slot in a single stage, prior to coating the device, significantly simplifies the sensor fabrication.

In-fiber polymer–glass hybrid waveguide Bragg grating

A 1.2 µm (height) × 125 µm (depth) × 500 µm (length) microslot along a fiber Bragg grating was engraved across the optical fiber by femtosecond laser patterning and chemical etching. By filling epoxy in the slot and subsequent UV curing, a hybrid waveguide grating structure with a polymer core and glass cladding was fabricated. The obtained device is highly thermally responsive with linear coefficient of 211 pm/°C.

Lattice approach to the dynamics of phase-coded soliton trains

We address the collective dynamics of a soliton train propagating in a medium described by the nonlinear Schrödinger equation. Our approach uses the reduction of train dynamics to the discrete complex Toda chain (CTC) model for the evolution of parameters for each train constituent: such a simplification allows one to carry out an approximate analysis of the dynamics of positions and phases of individual interacting pulses. Here, we employ the CTC model to the problem which has relevance to the field of fibre optics communications where each binary digit of transmitted information is encoded via the phase difference between the two adjacent solitons. Our goal is to elucidate different scenarios of the train distortions and the subsequent information garbling caused solely by the intersoliton interactions. First, we examine how the structure of a given phase pattern affects the initial stage of the train dynamics and explain the general mechanisms for the appearance of unstable collective soliton modes. Then we further discuss the nonlinear regime concentrating on the dependence of the Lax scattering matrix on the input phase distribution; this allows one to classify typical features of the train evolution and determine the distance where the soliton escapes from its slot. In both cases, we demonstrate deep mathematical analogies with the classical theory of crystal lattice dynamics.

Refractometer based on a liquid core FBG device

A 1.2X500µm slot was engraved across a fiber Bragg grating (FBG) using femtosecond laser patterning and chemical etching. liquid core FBGs were constructed and their sensitivity to refractive index of up to 10-6/pm was measured.

Highly thermally responsive hybrid in-fiber slab waveguide grating structure with a plastic core and a silica cladding

A 1.2(height)×125(depth)×500(length) micro-slot was engraved along a fiber Bragg grating by chemically assisted femtosecond laser processing. By filling epoxy and UV-curing, waveguide with plastic-core and silica-cladding was created, presenting high thermal responding coefficient of 211pm/°C.

Drop and insert multiplexing with simultaneous clock recovery using an electroabsorption modulator

A three-node optical time-division multiplexing (OTDM) network is demonstrated that utilizes electroabsorption (EA) modulators as the core elements. Each node is self contained and performs its own clock recovery and synchronization. "Drop and insert" functionality is demonstrated for the first time with an EA modulator by completely removing a 10-Gb/s channel from a 40-Gb/s OTDM data stream. A different 10-Gb/s channel was subsequently inserted into the vacant time slot. Clock recovery is achieved by using an EA modulator in a novel bidirectional configuration. Bit-error-rate (BER) measurements are presented for each of the 10-Gb/s OTDM channels.

Highly thermally responsive hybrid in-fiber sSlab waveguide grating structure with a plastic core and a silica cladding

A 1.2(height)×125(depth)×500(length) micro-slot was engraved along a fiber Bragg grating by chemically assisted femtosecond laser processing. By filling epoxy and UV-curing, waveguide with plastic-core and silica-cladding was created, presenting high thermal responding coefficient of 211pm/°C.