Phang, Sendy
(2016)
Theory and numerical modelling of paritytime symmetric structures for photonics.
PhD thesis, University of Nottingham.
Abstract
This thesis presents the study of a relatively new class of photonic structures invoking ParityTime (PT)symmetry. PTsymmetric structures in photonics, as a realisation of PTsymmetric Quantum Mechanics problems, are constructed by a judicious design of refractive index modulation which requires the real part of the refractive index to be an even function and the imaginary part of the refractive index to be an odd function in space. PTsymmetric structures in the form of Bragg gratings, coupled resonators and chain resonators are the main conﬁgurations studied in this thesis. These PTsymmetric structures feature a spontaneous symmetry breaking at which interesting wave behaviour such as an asymmetric response depending on the direction of the incident wave, unidirectional invisibility, simultaneous coherentperfect absorber lasing and localised termination modes are observed; these behaviours are presented in this thesis. Theoretical and numerical studies of these PTsymmetric structures are undertaken which assume realistic material parameters,including material dispersion and material nonlinearity. Moreover,in this thesis, potential applications of these PTsymmetric structures are explored.
The ﬁrst part of the thesis considers PTsymmetric Bragg grating structures which are formed by introducing a PTsymmetric refractive index modulation into a Bragg grating structure. If gain/loss dispersion is considered, it is shown that dispersion limits the PTsymmetric operation to just a single frequency. As such spontaneous symmetry breaking can only be achieved by varying the gain/loss parameter. Nevertheless, it is shown that by switching the gain/loss in the system, a switching operation can be achieved by using the PTBragg grating at a single frequency. Subsequently,anonlinear PTBragg grating is investigated by using a timedomain numerical method, namely the TransmissionLine modelling (TLM) method. For the present work a TLM code is developed from scratch in order to ensure fullﬂexibility when modelling a dispersive and nonlinear material. Using the TLM solver, it is demonstrated that gain/loss saturation is an important material property which should be considered as it may impact the practical applications of a PTsymmetrybased device. In the context of a nonlinear PTBragg grating (NPTBG), the gain/loss saturation aﬀects the interplay between the PTsymmetric opearation and the Kerr nonlinear eﬀect. It is further shown that gain/loss saturation plays a crucial role in securing a stable operation of nonlinear PTbased devices. For practical applications, it is demonstrated that a nonlinear PTsymmetric Bragg grating oﬀers an additional degree of freedom in their operation,by modulating the gain/loss and the intensity of the input signal,compared to a passive structure which can only be manipulated by the input signal intensity. Two applications based on the interplay of PTsymmetric behaviour and Kerr nonlinearity are demonstrated,namely a memory device and a logicgate device.
The second part of the thesis studies PTsymmetric resonator structures as a coupled system and as a periodic chain system. For these studies, a semianalytical method based on the Boundary Integral Equation (BIE) method is developed and used together with a twodimensional TLM method. The impact of realistic material parameter on the spectral properties of the structure is again investigated. It is shown that the PTsymmetric behaviour can be observed at a single frequency. Moreover, it is shown that PTsymmetrylike behaviour is observed but with complex eigenfrequencies due to the radiation losses; this is a deviation of the strict deﬁnition of a PTsymmetric structure with balanced gain and loss. Lowering lasing threshold by increasing loss in the system is demonstrated; this occurs due to induced early symmetry breaking. The ﬁnal part of the thesis studies the spectral properties of an inﬁnite and ﬁnite chain of PTsymmetric resonators. It is shown that the type of modulation along the PTchain aﬀects the position of the breaking point of the PTstructure. For a ﬁnite PTchain structure, and for a particular type of refractive index modulation, early PTsymmetry breaking is observed and shown to cause the presence of termination states which are localised at the edge of the ﬁnitechain resulting in localised lasing and dissipative modes at each end of the chain.
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