The complex transverse waveguide geometries of integrated photonic devices warrant the application of intricate
Numerical Methods when modelling these types of Planar Lightwave Circuits (PLC). To aggravate the problem,
difficulties also arise when dealing with back-reflections at interfaces, counter-propagating signals and other
associated losses. Routines such as the Finite Element Method (FEM) and Finite Difference Method (FDM) are utilised
in simulating the propagation of light through the core waveguide structures of these PLCs. In this paper a novel FEM
reliant upon device cross-sectional symmetry is proposed, developed and discussed in regards to its advantages in
precision over other procedures. Upon completion of this analysis, the propagation constant and effective refractive
indices are known and extensions may be employed to accurately model propagation through the device and outline any
reflections or losses that may ensue. A clear and concise review of some of the foremost available schemes is also
presented here. These techniques, such as the Bidirectional Eigenmode Propagation Method (BEP) and the Beam
Propagation Method (BPM) will be discussed and an effective and precise 3-dimensional model is presented. Due to
the myriad of available techniques and algorithms, a comparative study is drawn, listing the advantages and failures of
the major methods while suggesting improvements to their application. Necessary considerations such as simulation
time and the trade-off between computer memory requirements and accuracy of the solution are also acknowledged.
Optical transmission technologies such as Dense-Wavelength Division Multiplexing (DWDM) have emerged in recent years to meet the demand for higher bandwidths and data rates. In order to implement such technologies, accurate determination of channel wavelengths is required. The Fabry-Perot Interferometer (FPI) offers the ability to resolve wavelengths with a 2-5 pm precision in resolution. We present here a novel Generic Lightwave Integrated Chip (GLIC) founded on the FPI. The device has been realised on a Planar Lightwave Circuit (PLC) in SiO2 on Silicon as a means to achieve the desired rapid wavelength monitoring with high resolution. In this paper, the simulation and characterisation of the device is reported and the advantages of this technology are revealed. The theory is founded on employing the concept of quadrature between 2 phase-shifted signals provided by 2 similar Fabry-Perot cavities to determine the wavelength in question with a sub-microsecond response time. The compact features of the device make it an ideal candidate for application in future silica based PLC DWDM networks. By its generic nature, the device is also an attractive choice for applications in optical sensing and biophotonics.
The complex transverse waveguide geometries twinned with the transcendental rate equations governing Erbium-Doped Waveguide Amplifiers (EDWA) warrant the application of intricate Numerical Methods. To date all models approaching the problem have incorporated a finite element scheme for the modal analysis of the waveguide in conjunction with either a Beam Propagation Method (BPM) or an explicit Runge-Kutta procedure towards solving the channel propagation equations. In deploying these models, a certain ambiguity lies in their practical utilisation enforcing a trade-off between simulation time and demands on computer memory. The underlying theory of the finite element method (FEM) for optical waveguide simulations comprises of a multitude of approaches to solving the scalar Helmholtz equation. Past FEM techniques were based on a combination of matrix sparsity manipulations and iterative techniques but today, even modest computers can be utilised in more direct but denser methods for eigenvalue solutions. This paper aspires to demonstrate an efficient modal analysis technique founded on an appropriate mesh with due consideration for both computational complexity and available Random Access Memory requirements. It is then trivial to continue from this modal field definition to the solution of the aforementioned rate equations for channel gain, noise or nonlinear losses including upconversion and cross relaxation in the EDWA by implementing a suitable boundary value problem approach.
The behaviour of Erbium-Doped Fibre Amplifiers (EDFA) is investigated as a function of basic fibre constituents and length in order to provide sufficient parameters for any modelling of its gain or noise profiles. The efficiency of the amplifier is found to be strongly dependent on the erbium ion concentration, the excited-state lifetime, the overlap integral of the erbium with the optical mode and the absorption and emission cross-sections. For convenience, these factors can then be lumped into two fibre specific parameters, namely the intrinsic saturation, PkIS, and absorption coefficients, ak. The topics addressed in this paper include the calculation of these parameters in order to provide a model for the gain or noise in an EDFA operating in the steady-state regime. Mechanisms that may deplete the gain achievable are identified and it is described how some of these might be overcome by finding the optimum amplifier length to obtain maximum gain. This paper presents comprehensive analysis to be coupled with available numerical and implicit analytical methods and will enable a systematic design and performance study of the EDFA.
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