Standing Wave Solutions for the Discrete Coupled Nonlinear Schrödinger Equations with Unbounded Potentials

We demonstrate the existence of standing wave solutions of the discrete coupled nonlinear Schrödinger equations with unbounded potentials by using the Nehari manifold approach and the compact embedding theorem. Sufficient conditions are established to show that the standing wave solutions have both of the components not identically zero

All-optical processing systems based on semiconductor optical amplifiers

Doutoramento em Engenharia ElectrotécnicaNesta tese investigam-se e desenvolvem-se dispositivos para processamento integralmente óptico em redes com multiplexagem densa por divisão no comprimento de onda (DWDM). O principal objectivo das redes DWDM é transportar e distribuir um espectro óptico densamente multiplexado com sinais de débito binário ultra elevado, ao longo de centenas ou milhares de quilómetros de fibra óptica. Estes sinais devem ser transportados e encaminhados no domínio óptico de forma transparente, sem conversões óptico-eléctrico-ópticas (OEO), evitando as suas limitações e custos. A tecnologia baseada em amplificadores ópticos de semicondutor (SOA) é promissora graças aos seus efeitos não-lineares ultra-rápidos e eficientes, ao potencial para integração, reduzido consumo de potência e custos. Conversores de comprimento de onda são o elemento óptico básico para aumentar a capacidade da rede e evitar o bloqueio de comprimentos de onda. Neste trabalho, são estudados e analisados experimentalmente métodos para aumentar a largura de banda operacional de conversores de modulação cruzada de ganho (XGM), a fim de permitir a operação do SOA para além das suas limitações físicas. Conversão de um comprimento de onda, e conversão simultânea de múltiplos comprimentos de onda são testadas, usando interferómetros de Mach-Zehnder com SOA. As redes DWDM de alto débito binário requerem formatos de modulação optimizados, com elevada tolerância aos efeitos nefastos da fibra, e reduzida ocupação espectral. Para esse efeito, é vital desenvolver conversores integramente ópticos de formatos de modulação, a fim de permitir a interligação entre as redes já instaladas, que operam com modulação de intensidade, e as redes modernas, que utilizam formatos de modulação avançados. No âmbito deste trabalho é proposto um conversor integralmente óptico de formato entre modulação óptica de banda lateral dupla e modulação óptica de banda lateral residual; este é caracterizado através de simulação e experimentalmente. Adicionalmente, é proposto um conversor para formato de portadora suprimida, através de XGM e modulação cruzada de fase. A interligação entre as redes de transporte com débito binário ultra-elevado e as redes de acesso com débito binário reduzido requer conversão óptica de formato de impulso entre retorno-a-zero (RZ) e não-RZ. São aqui propostas e investigadas duas estruturas distintas: uma baseada em filtragem desalinhada do sinal convertido por XGM; uma segunda utiliza as dinâmicas do laser interno de um SOA com ganho limitado (GC-SOA). Regeneração integralmente óptica é essencial para reduzir os custos das redes. Dois esquemas distintos são utilizados para regeneração: uma estrutura baseada em MZI-SOA, e um método no qual o laser interno de um GC-SOA é modulado com o sinal distorcido a regenerar. A maioria dos esquemas referidos é testada experimentalmente a 40 Gb/s, com potencial para aplicação a débitos binários superiores, demonstrado que os SOA são uma tecnologia basilar para as redes ópticas do futuro.This thesis investigates and develops all-optical processing devices for wavelength division multiplexing networks (DWM) of the future. The ultimate goal of optical networks is to transport and deliver a densely multiplexed spectrum, populated by ultra-high bit rate signals over hundreds or thousands of kilometers of optical fiber. Such signals should be transported and routed transparently in the optical domain, without recurring to optic-electro-optic (OEO) conversions, avoiding its limitations and costs. Semiconductor optical amplifier (SOA) based technology is a promising building block due to its inherent ultra-fast and efficient non-linear effects, potential for integration, low power consumption and cost. Wavelength converters are the basic optical functionality to increase the network throughput and avoid wavelength blocking. Methods to increase the operation bandwidth of cross-gain modulation (XGM) converters are studied and experimentally assessed to enable operation beyond the physical constraints of SOA. Single and multi-wavelength conversion exploiting crossphase modulation (XPM) in Mach-Zehnder interferometer with semiconductor optical amplifiers (MZI-SOA) is tested. High bit rate DWDM networks require optimized modulation formats with enhanced tolerance to fiber impairments and reduced spectral tolerance. As a consequence, it is crucial to develop all-optical modulation formats between legacy on-off-keying networks and networks employing advanced modulation formats. An all-optical format converter between optical double sideband (ODSB) and optical vestigial sideband (OVSB) based on SOA self-phase modulation is proposed and thoroughly characterized by simulations and experimental tests. A converter, which uses a mix of XGM and XPM to allow simultaneous pulse and modulation format conversion to the carrier suppressed format, is proposed. The interface between ultra-high bit rate transport networks and lower bit rate access networks requires optical pulse format conversions between return-tozero (RZ) and non-return-to-zero (NRZ). Two different structures are proposed and investigated. The first is based on detuned filtering of XPM converted signal; while the second uses the dynamics of the internal laser of a gainclamped SOA. All-optical regeneration is one of the most sought functionalities to reduce network costs. Regeneration is achieved in this work through two simple setups: a MZI-SOA based structure, and a method in which the internal laser from a GC-SOA is modulated with the input distorted signal. Most applications are experimentally validated at 40 Gb/s, with potential for even higher bit rates, demonstrating that SOA can be one of the key elements for the next generation of optical networks

Mutually coupled lasers on a photonic integrated circuit

The number of internet users and the internet traffic are growing exponentially year-on-year, leading to an ever-increasing demand for data. This demand risks saturating the current network and is, therefore, driving research into technologies to increase the total data throughput of a single optical fibre. To further increase the data rate through a fibre and keep ahead of demand, the channel spectral density must be increased. One solution is to use super-channels to increase the spectral density and hence the number of channels. Many of the proposed methods for creating super-channels use optical combs. These combs must be demultiplexed so that each channel can be modulated separately. Demultiplexing can be achieved by injection locking a laser to each of the comb lines. It has been shown that for any cost-effective implementation of Tbps super-channels, photonic integration of the source of the super-channel, i.e. the optical comb, and the demultiplexer is necessary. Consequently, the optical comb must then be generated, and a laser injection locked to each of the comb lines, on a photonic integrated circuit (PIC). However, it has long been assumed that different lasers cannot coexist on a PIC without using an optical isolator, but this has never been investigated or proven. The work in this thesis aims to disprove this theory. This work experimentally investigates mutual injection locking between different lasers on a PIC. For this study, two tuneable slotted Fabry-Pérot lasers were integrated together through a variable optical attenuator/amplifier (VOA). The bias and length of the VOA controlled the coupling and time delay between the lasers, respectively. These, along with the detuning between the lasers, were the variable parameters investigated. The mutual and injection locking characteristics of the integrated lasers were compared, both off and on-chip, which established a baseline for more complex behavioural studies. This also led to the development of a measurement technique, using an optical spectrum analyser, an electrical spectrum analyser and a high speed oscilloscope, for examining the different operational regimes arising from optically locking a semiconductor diode laser. It was found that the coupling between the lasers is critical in obtaining stable mutual injection locking: if the coupling is too low, the lasers do not interact sufficiently to obtain mutual locking and if the coupling is too high, the full device from facet-to-facet behaves as a compound laser and mutual locking is not achieved. Additionally, it was shown that if the detuning between the lasers is small, the wavelength of both lasers can be fixed, and mutual locking can be attained by varying the coupling between the lasers. Various types of dynamical behaviour were also observed as a function of the coupling and detuning between the lasers. These include: symmetric and asymmetric beating, non-linear interactions, period doubling, pulsing and aperiodic behaviour. The coupling between the lasers was also measured as a function of the VOA bias and compared for different VOA lengths. This work experimentally verifies that two lasers can indeed coexist on a PIC without an optical isolator and stable mutual injection locking between the lasers can be obtained. In the short term, this work provides a baseline to support further theoretical studies and in the long term, contributes to enabling the development of integrated high data-rate transmitters that will support the internet traffic growth

Kondratieff Waves: Juglar – Kuznets – Kondratieff; Yearbook

In the period from the 1920s to 1930s the theory of economic cycles underwent dramatic changes. Due to the research of such famous economists as Nikolay Kondratieff, Joseph Kitchin, Wesley Mitchell, Simon Kuznets, and Joseph Schumpeter the idea of a whole system of economic cycles (with characteristic periods between two and sixty years) was developed. The idea of a system of intertwined economic cycles is nowadays paramount to the school of evolutionary economics and its development promises rather interesting future outcomes. That is why this issue of our ‘Kondratieff Waves’ Yearbook is devoted to the interconnections between various economic cycles. As to the subtitle of this volume, one should note that many of the contributors refer to the system of cycles and the fact that real economic cycles make up a system, whereas among different types of cycles, the Juglar, Kuznets, and Kondratieff cycles are the most important ones for the present-day economic dynamics. Although Kondratieff himself considered long waves as above all an economic phenomenon, the theory of the long waves became, however, very actively developed in connection with their political and geopolitical aspects. In this Yearbook, the political aspect of Kondratieff waves is the subject of several articles in the second section. The last section of this Yearbook is devoted to the heritage of Kondratieff and other prominent economists. The year 2015 marks the 150th anniversary of the outstanding Russian economist, one of the most prominent researchers of medium-term economic cycles, Mikhail Tugan-Baranovsky, and the volume is concluded with Kondratieff's article about him. Concerning 2015, we should mention another anniversary, namely, 30 years since the death of Simon Kuznets (1901–1985). This edition will be useful for economists, social scientists, as well as for a wide range of those interested in the problems of the past, present, and future of global economy and globalization