Yes / Two fractional Fourier transforms are used to define bi-fractional displacement operators, which interpolate between displacement operators and parity operators. They are used to define bi-fractional coherent states. They are also used to define the bi-fractional Wigner function, which is a two-parameter family of functions that interpolates between the Wigner function and the Weyl function. Links to the extended phase space formalism are also discussed.

no / Bifractional displacement operators, are introduced by performing two fractional Fourier transforms on displacement operators. They are shown to be special cases of elements of the group G , that contains both displacements and squeezing transformations. Acting with them on the vacuum we get various classes of coherent states, which we call bifractional coherent states. They are special classes of squeezed states which can be used for interpolation between various quantities in phase space methods. Using them we introduce bifractional Wigner functions A(α,β;θα,θβ)A(α,β;θα,θβ), which are a two-dimensional continuum of functions, and reduce to Wigner and Weyl functions in special cases. We also introduce bifractional Q-functions, and bifractional P-functions. The physical meaning of these quantities is discussed.

In this thesis, two methods to model quantum well lasers will be examined. The first model is based on well-known techniques to determine some of the spectral and dynamical properties of the laser. For the spectral properties, an expression for TE and TM modal amplitude gain is derived. For the dynamical properties, the rate equations are shown. The spectral and dynamical properties can be examined separately for specific operating characteristics or used in conjunction with each other for a complete description of the laser. Examples will be shown to demonstrate some of the analysis and results that can be obtained. The second model used is based on Wigner functions and the quantum Boltzmann equation. It is derived from general non-equilibrium Greens functions with the application of the Kadanoff-Baym ansatz. This model is less phenomenological than the previous model and does not require the separation of physical processes such as the former spectral and dynamical properties. It therefore has improved predictive power for the performance of novel laser designs. To the Author's knowledge, this is the first time such a model has been formulated. The quantum Boltzmann equations will be derived and some calculations will be performed for a simplified system in order to illustrate some calculation techniques as well as results that can be obtained.

In this thesis, two methods to model quantum well lasers will be examined. The first model is based on well-known techniques to determine some of the spectral and dynamical properties of the laser. For the spectral properties, an expression for TE and TM modal amplitude gain is derived. For the dynamical properties, the rate equations are shown. The spectral and dynamical properties can be examined separately for specific operating characteristics or used in conjunction with each other for a complete description of the laser. Examples will be shown to demonstrate some of the analysis and results that can be obtained. The second model used is based on Wigner functions and the quantum Boltzmann equation. It is derived from general non-equilibrium Greens functions with the application of the Kadanoff-Baym ansatz. This model is less phenomenological than the previous model and does not require the separation of physical processes such as the former spectral and dynamical properties. It therefore has improved predictive power for the performance of novel laser designs. To the Author's knowledge, this is the first time such a model has been formulated. The quantum Boltzmann equations will be derived and some calculations will be performed for a simplified system in order to illustrate some calculation techniques as well as results that can be obtained.

abstract: Advanced and mature computer simulation methods exist in fluid dynamics, elec- tromagnetics, semiconductors, chemical transport, and even chemical and material electronic structure. However, few general or accurate methods have been developed for quantum photonic devices. Here, a novel approach utilizing phase-space quantum mechanics is developed to model photon transport in ring resonators, a form of en- tangled pair source. The key features the model needs to illustrate are the emergence of non-classicality and entanglement between photons due to nonlinear effects in the ring. The quantum trajectory method is subsequently demonstrated on a sequence of elementary models and multiple aspects of the ring resonator itself. / Dissertation/Thesis / Doctoral Dissertation Electrical Engineering 2020

yes / An analytic representation with Theta functions on a torus, for systems with variables in ℤ(d), is considered. Another analytic representation with Theta functions on a strip, for systems with positions in a circle S and momenta in Z, is also considered. The reproducing kernel formalism for these two systems is studied. Wigner and Weyl functions in this language, are also studied.