With increasing bandwidth demand, DSL system continuously evolves to increase the maximum transmission frequency. However, the resulting cross-talk comes ever stronger and significantly degrades the system transmission performance. The cross-talk mainly comes from the DSLAM, modem, cable and splitter in a DSL system. This thesis proposes a signal cancellation method to overcome the cross-talk problem in a DSL splitter, which makes the DSL splitter no longer one of the cross-talk sources to affect the system transmission performance.

A polarization-independent electro-optically tunable add/drop filter utilizing non-polarizing novel relaxed beam splitters has been developed in LiNbO3 at the 1.55μm wavelength regime. The operation of this filter is based on passive directional coupler type beam splitters and strain-induced phase-matched TE↔TM polarization mode converters on an asymmetric Mach-Zehnder interferometer waveguide configuration. Fabrication parameters for channel waveguides, relaxed beam splitters and polarization mode converters were optimized individually then integrated to produce the final device. Single mode channel waveguides for both TE and TM polarizations were realized by the diffusion of 7μm wide Ti strips into LiNbO3 substrate. Relaxed beam splitters were produced using Ti diffused waveguides in a directional coupler configuration with 3.5mm long coupling region, 0.6º bending angle, and separation gap of 11μm and 13μm between waveguides. Tunable TE↔TM polarization mode converters with 99.8%

A polarization-independent electro-optically tunable add/drop filter utilizing non-polarizing novel relaxed beam splitters has been developed in LiNbO3 at the 1.55μm wavelength regime. The operation of this filter is based on passive directional coupler type beam splitters and strain-induced phase-matched TE↔TM polarization mode converters on an asymmetric Mach-Zehnder interferometer waveguide configuration. Fabrication parameters for channel waveguides, relaxed beam splitters and polarization mode converters were optimized individually then integrated to produce the final device. Single mode channel waveguides for both TE and TM polarizations were realized by the diffusion of 7μm wide Ti strips into LiNbO3 substrate. Relaxed beam splitters were produced using Ti diffused waveguides in a directional coupler configuration with 3.5mm long coupling region, 0.6º bending angle, and separation gap of 11μm and 13μm between waveguides. Tunable TE↔TM polarization mode converters with 99.8%

The currently used DSL splitters or filters are designed for ADSL band up to 1104 KHz and ADSL2+ band up to 2208 KHz. To meet faster internet access, DSL technology has evolved from ADSL into VDSL2 with an operating band up to 30 MHz. However, the splitters in VDSL2 band have some design difficulties in longitudinal conversion loss and isolation. The main purpose of this thesis is to find some solutions to overcome these design difficulties for splitters operating in VDSL2 band. The proposed solutions include the use of common-mode choke and compensation circuit. The final testing results of the splitters can validate the proposed solutions.

Multiport beam splitter is a new research topic in quantum communication. To improve the security system, the dimension/capacity of quantum communication should increase. In this thesis, design, simulation and methodology of NXN multiport beam splitter on a photonic integrated circuit is explained. Photonic integrated circuit has more advantages than other optical components to design a multiport beam splitter. Multiport beam splitter on a photonic chip gives configuration stability, a compact prototype for future quantum network.

<p> 1-by-N optical power splitters are primary components in the field of integrated optics and optical transmission systems. Planar waveguide optical power splitters are key devices to realize low-cost optical transmission systems through photonic integration. The goal of this thesis is to design, model and simulate a novel planar waveguide optical power splitter for optical transmission systems and Fiber to the Home (FTTH) networks.</p> <p> The first chapter is an introduction. This chapter gives the background of power splitter, reviews the existing devices and explains why our novel design is needed.</p> <p> The idea of this novel power splitter is presented in Chapter 2, including analytical formulations, theoretical calculations and designs. This serves as a theoretical foundation for the development and verification of different parts presented in Chapter 3. The novel power splitter design is composed of a series of waveguide lenses and waveguide phase shifts. The analytical formulations are derived and intensive numerical simulations are performed to verify and investigate this new power splitter. Also the conventional Beam Propagation Method (BPM) is studied in this chapter, which provides a numerical preparation for the device simulation and design in the subsequent chapter.</p> <p> The design results are shown in Chapter 4. The novel power splitter design predicts good performance with more compact device size, better output and smaller wavelength dependence. This chapter demonstrated the possibility of new power splitter working as a better approach to the existing MMI or other structures.</p> <p> Finally, Chapter 5 gives a conclusion to this thesis. The limitations of this work are presented and the future works are proposed.</p> / Thesis / Master of Applied Science (MASc)

O presente trabalho é o início de um estudo da aplicação do método de otimização conhecido como adjunto em escoamentos incompressíveis, viscosos e periódicos, envolvendo um problema de bastante interesse: a análise da aplicação de splitter plates em cilindros de seção circular. Conhecido por sua simplicidade, o splitter plate, que consiste em uma placa plana alinhada ao escoamento e colocada a jusante do corpo, é um dispositivo efetivo na mudança de comportamento da esteira de vórtices de Von Kárman. A partir da revisão bibliográfica foi possível entender a dinâmica do escoamento, proporcionando uma calibração dos modelos numéricos. Complementando esta etapa, foi efetuada uma análise da qualidade das malhas computacionais. Através de uma geração de diversas malhas computacionais, o espaço de soluções foi explorado buscando encontrar o mínimo arrasto para diversos comprimentos de splitter plate e diferentes números de Reynolds (Re). Foi observada a influência da placa na formação da esteira de vórtices, obtendo uma redução dos coeficientes de força do cilindro. Com esses dados, foi possível desenvolver o método de otimização voltado para análise do gradiente de sensibilidade conhecido como método adjunto baseado nas equações de Navier Stokes utilizando o problema descrito como base para validação dos resultados. A abordagem do método adjunto caracteriza-se pela busca dos extremos de funções conhecidas como medidas de mérito. Essas funções podem ser integrais de sustentação e arrasto por exemplo. Na literatura, o método adjunto é apresentado como possuindo duas grandes vantagens: a primeira é a imposição das equações do escoamento como restrições do problema, o que sempre confinará as variações da medida de mérito dentro do universo de soluções realizáveis; já a segunda é conseqüência da primeira, pois as restrições permitem uma simplificação no cálculo do gradiente de sensibilidade, reduzindo o custo computacional. Para o cálculo do gradiente de sensibilidade, o objetivo é otimizar o arrasto do cilindro sob efeito do splitter plate variando os parâmetros de controle (comprimento e posicionamento do splitter plate). A direção de busca e o cálculo do passo da geometria são obtidos a partir da relação entre a solução numérica do escoamento e as variáveis adjuntas calculadas. Nesta dissertação, será apresentada a pesquisa bibliográfica, os resultados do método tentativa e erro, a formulação do método adjunto baseado nas equações de Navier Stokes e um exemplo de sua solução numérica, demonstrando sua existência. / The report is the beginning of a research about the application of the so called adjoint method in the optimization of incompressive, viscous and periodic flows. The study involves a problem of great interest: an analysis of the implementation of splitter plates in the flow around cylinders with circular section. Widely recognized for its simplicity, the splitter plate consists of a flat plate, which is placed in the wake of a cylinder, in the stream wise direction, and it works by changing the way the shear layers interact with one another. Based on a literature survey, it is possible to understand the physics of this class of flows. As a better result, one learns what to expect from the numerical solutions and hence, one can calibrate its parameters. Moreover, we study the best configuration of the computational mesh, thus reducing the computational cost. After the generation of meshes, the universe of solutions was explored to find the minimum drag for various lengths of splitter plate and Reynolds number (Re). The influence of the plate in the interaction of the shear layers was observed in the reduction of drag coefficient. These results form a the basis for comparison, upon one can develop the optimization by the adjoint method. The adjoint method can be used to search the extreme of objective functionals. These functionals can be the lift and drag integrals for example. The theory presents two advantages to the method: first, the imposing the equations that govern the flow as variational constraints one limits the variations to the universe of realizable solutions; second, these constrains simplify the computation of the sensitivity gradient, by reducing its computational cost. To compute the sensitivity gradient, the objective functional can be defined as the average drag coefficient of the circular cylinder with a splitter plate. The control parameters are the length of the plate and the distance between it and the body, which known as gap. The search direction and the variation of geometry can be obtained by the relationship between the solutions to the flow and the adjoint equations. This final report shows the literature survey, the results of trial and error method and the formulation and one result of adjoint equations based on the incompressible NavierStokes equations.

O presente trabalho é o início de um estudo da aplicação do método de otimização conhecido como adjunto em escoamentos incompressíveis, viscosos e periódicos, envolvendo um problema de bastante interesse: a análise da aplicação de splitter plates em cilindros de seção circular. Conhecido por sua simplicidade, o splitter plate, que consiste em uma placa plana alinhada ao escoamento e colocada a jusante do corpo, é um dispositivo efetivo na mudança de comportamento da esteira de vórtices de Von Kárman. A partir da revisão bibliográfica foi possível entender a dinâmica do escoamento, proporcionando uma calibração dos modelos numéricos. Complementando esta etapa, foi efetuada uma análise da qualidade das malhas computacionais. Através de uma geração de diversas malhas computacionais, o espaço de soluções foi explorado buscando encontrar o mínimo arrasto para diversos comprimentos de splitter plate e diferentes números de Reynolds (Re). Foi observada a influência da placa na formação da esteira de vórtices, obtendo uma redução dos coeficientes de força do cilindro. Com esses dados, foi possível desenvolver o método de otimização voltado para análise do gradiente de sensibilidade conhecido como método adjunto baseado nas equações de Navier Stokes utilizando o problema descrito como base para validação dos resultados. A abordagem do método adjunto caracteriza-se pela busca dos extremos de funções conhecidas como medidas de mérito. Essas funções podem ser integrais de sustentação e arrasto por exemplo. Na literatura, o método adjunto é apresentado como possuindo duas grandes vantagens: a primeira é a imposição das equações do escoamento como restrições do problema, o que sempre confinará as variações da medida de mérito dentro do universo de soluções realizáveis; já a segunda é conseqüência da primeira, pois as restrições permitem uma simplificação no cálculo do gradiente de sensibilidade, reduzindo o custo computacional. Para o cálculo do gradiente de sensibilidade, o objetivo é otimizar o arrasto do cilindro sob efeito do splitter plate variando os parâmetros de controle (comprimento e posicionamento do splitter plate). A direção de busca e o cálculo do passo da geometria são obtidos a partir da relação entre a solução numérica do escoamento e as variáveis adjuntas calculadas. Nesta dissertação, será apresentada a pesquisa bibliográfica, os resultados do método tentativa e erro, a formulação do método adjunto baseado nas equações de Navier Stokes e um exemplo de sua solução numérica, demonstrando sua existência. / The report is the beginning of a research about the application of the so called adjoint method in the optimization of incompressive, viscous and periodic flows. The study involves a problem of great interest: an analysis of the implementation of splitter plates in the flow around cylinders with circular section. Widely recognized for its simplicity, the splitter plate consists of a flat plate, which is placed in the wake of a cylinder, in the stream wise direction, and it works by changing the way the shear layers interact with one another. Based on a literature survey, it is possible to understand the physics of this class of flows. As a better result, one learns what to expect from the numerical solutions and hence, one can calibrate its parameters. Moreover, we study the best configuration of the computational mesh, thus reducing the computational cost. After the generation of meshes, the universe of solutions was explored to find the minimum drag for various lengths of splitter plate and Reynolds number (Re). The influence of the plate in the interaction of the shear layers was observed in the reduction of drag coefficient. These results form a the basis for comparison, upon one can develop the optimization by the adjoint method. The adjoint method can be used to search the extreme of objective functionals. These functionals can be the lift and drag integrals for example. The theory presents two advantages to the method: first, the imposing the equations that govern the flow as variational constraints one limits the variations to the universe of realizable solutions; second, these constrains simplify the computation of the sensitivity gradient, by reducing its computational cost. To compute the sensitivity gradient, the objective functional can be defined as the average drag coefficient of the circular cylinder with a splitter plate. The control parameters are the length of the plate and the distance between it and the body, which known as gap. The search direction and the variation of geometry can be obtained by the relationship between the solutions to the flow and the adjoint equations. This final report shows the literature survey, the results of trial and error method and the formulation and one result of adjoint equations based on the incompressible NavierStokes equations.

Previous work on rigid splitter plates in the wake of a bluff body has shown that the primary vortex shedding can be suppressed for sufficiently long splitter plates. In the present work, we study the problem of a flexible splitter plate in the wake of a circular cylinder. In this case, the splitter plate can deform due to the fluid forces acting on it, and hence the communication between the two sides of the wake is not totally disrupted like in the rigid splitter plate case. In particular, we study two kinds of flexible splitter plates. In the first case, the splitter plate is rigid but is flexibly mounted (hinged) to the cylinder, while in the second case, the entire splitter plate is flexible. We are interested in both the dynamics of the splitter plate, if they do vibrate at all, and in the wake dynamics downstream of the flexible splitter plates. The main parameters in the problem are the splitter plate length (L) to cylinder diameter (D) ratio, the relative mass of the plate, the Reynolds number, and the stiffness and internal damping associated with the flexible plate. In our study, we investigate this problem in the limit where the stiffness and internal damping of the plate are negligible and hence are not parameters of interest. For the hinged-rigid splitter plate case, experiments show that the splitter plate oscillations increase with Reynolds numbers at low values of Re, and are found to reach a saturation amplitude level at higher Re. This type of saturation amplitude level that appears to continue indefinitely with Re, appears to be related to the fact that there is no structural restoring force in this case, and has been seen previously for elastically-mounted cylinders with no restoring force. In the present case, the saturation tip amplitude level can be up to 0.45D,where D is the cylinder diameter. For this hinged-rigid splitter plate case, it is found that the splitter plate length to cylinder diameter (L/D) ratio is crucial in determining the character and magnitude of the oscillations. For small splitter plate lengths (L/D ≤ 3.0), the oscillations appear to be nearly periodic with tip amplitudes of about 0.45D nearly independent of L/D. The non-dimensional oscillation frequencies (fD/U ) on the other hand are found to continuously vary with L/D from fD/U ≈ 0.2at L/D =1 to fD/U ≈ 0.1 at L/D = 3. As the splitter plate length is further increased beyond L/D ≥ 4.0, the character of the splitter plate oscillations suddenly changes. The oscillations become aperiodic with much smaller amplitudes. In this long splitter plate regime, the spectra of the oscillations become broadband, and are reminiscent of the change in character of the wake oscillations seen in the earlier fixed-rigid splitter plate case for L/D ≥ 5.0. It appears that the vortex shedding is nearly inhibited for L/D ≥ 4.0 in the present case. This is also supported by measurements of the wake vorticity field from Particle-Image Velocimetry (PIV). The phase-averaged PIV vorticity fields show that the strength of the shed vortices decreases rapidly as the splitter plate length increases. For longer splitter plates, L/D ≥ 4.0, the plate oscillations are no longer periodic, and hence it appears that the wake vortices are not synchronized with the splitter plate motions. For the entirely-flexible splitter plate case, the splitter plate deformations appear to be in the form of a travelling wave. In this case, the tip amplitudes are significantly larger of the order of 1.1D, and the non-dimensional oscillation frequency (fD/U )is close to 0.2, approximately the same as the Strouhal number for the bare cylinder. In sharp contrast to the hinged-rigid splitter plate case, the non-dimensional amplitude and frequency appear to be nearly independent of the normalized splitter plate length (L/D)even up to L/D =7.0. PIV measurements of the wake vorticity field indicates that there appears to be a nearly continuous sheet of vorticity on both sides of the flexible splitter plate, and the vortex sheet sheds and forms distinct vortices only at the trailing edge of the plate. The strength of these shed vortices appears to be close to that of the bare cylinder at similar Re. The results appear to suggest that in this entirely-flexible case, the vortices form at the same frequency and are of the same strength as in the bare cylinder case, but their formation is just pushed further downstream. This would suggest that in this case, the base suction and drag could be lower than the bare cylinder. Further, the formation of vortices further downstream of the body could imply that this type of flexible splitter plate could be useful to suppress vortex-induced vibrations (VIV).

Transmission lines are the basic building blocks of any RF and microwave circuits. The width of a microstripline increases as the characteristic impedance is lowered for a given substrate. Wide microstriplines suffer from spurious and higher order modes at higher frequencies and may not behave as transmission lines. This means the lower limitation for a realisable microstripline is about 10 ohm. In this project microstriplines with characteristic impedances of 7 ohm and 25 ohm at a frequency of 2 GHz were designed and realised using the artificial transmission lines (ATL) concept. Detailed theoretical analysis and circuit and EM simulations were used for the design and implementation of the ATLs. Taconic TLY-5 substrate was used for the PCB fabrication. The substrate thickness was 0.787 mm and the dielectric constant was 2.2. The measured results were de-embedded and compared with the simulation results. The detailed procedure of modelling and de-embedding of an SMA connector is also given. The 25 ohm ATL was realised using microstriplines only, where as microstriplines and chip capacitors were used in realising the 7 ohm ATL. The measured characteristic impedance of the 25 ohm ATL was 24.4 ohm and the measured electrical length of the 25 ohm ATL was 180 degrees at 2.1 GHz. To realise a 25 ohm ATL with 90 degrees electrical length, the half-wavelength 25 ohm ATL geometry was cut into half and one of the half geometries was EM simulated. The EM simulated electrical length of the 25 ohm ATL was 90 degrees at 1.9 GHz. The measured characteristic impedance of the 7 ohm ATL was 5.9 ohm and the measured electrical length of the 7 ohm ATL was 90 degrees at 1.8 GHz. The main advantage of an ATL is size reduction. A 25 ohm meandered microstrip line (substrate thickness = 0.787 mm, dielectric constant = 2.2) with 180 degrees electrical length at 2 GHz has a size of 34 mm x 15 mm. The 25 ohm ATL with 180 degrees electrical length at 2.1 GHz was realised in a size of 22 mm x 19 mm. The design of the 25 Ω ATL resulted in 18 percent reduction in area compared to the meander line. A 7 ohm conventional microstripline (substrate thickness = 0.787 mm, dielectric constant = 2.2) with 90 degrees electrical length at 1.8 GHz has a size of about 28 mm x 27 mm. The 7 ohm ATL with 90 degrees electrical length at 1.8 GHz was realised in a size of 7 mm x 8.4 mm which is only 8 percent of the conventional 7 ohm microstripline area. In general, a spacing of 3h where h is the substrate thickness is required between the adjacent microstriplines. In this project detailed investigations were done to see if the spacing can be reduced without any detrimental coupling affects and a spacing of 0.6 mm was used. This reduction in spacing has resulted in reduced size of the ATL. For an asymmetrical power splitter based on the Wilkinson topology, the power splitter output power split ratio depends on the square of the characteristic impedances of the quarter-wavelength arms. In this project an asymmetrical power splitter was designed and realised using a 7 ohm ATL and a 25 ohm ATL as the quarter-wavelength arms. The desired centre frequency of the power splitter was 2 GHz and the measured centre frequency was 1.6 GHz. At the centre frequency the phase difference between the output ports of the power splitter will be zero. The simulated power split ratio was 10.1 dB and the measured power split ratio was 13 dB. The power split ratio calculated using the measured characteristic impedances of the ATLs (24.4 ohm and 5.9 ohm) will be 12.4 dB which is very close to the measured power split ratio.