Manipulation Of PTSymmetry In 2D Arrays Of Optical Waveguide With Periodical Modulation

Topological character and quantum sensor of non-Hermitian composite systems are current research hotspot.Global parity-time(PT)symmetry plays a key role in determining the real energy spectrum,topological character and transport property of non-Hermitian composite system.Therefore,manipulating the global PT symmetry of a non-Hermitian composite system is a rather significative and challenging task.PT symmetric optical waveguide arrays that have many unique optical properties,provide a fertile ground to observe and utilize notions of global PT symmetry and topology.Due to it has important potential application in the photonic information processing,laser and integrated optics,it has been widely investigated recently.In this paper,based on the 2D PT-symmetric array of quadrimer waveguides,we explore how to manipulate the global PT symmetry,exceptional points and dynamics of the system by adjusting periodic modulation.The structure of this article is as following:In Chapter 1,we introduce the definition of PT-symmetry and its development in optical waveguide arrays.In Chapter 2,we investigate the effect of periodic modulation on PT-symmetry recovery,higher-order exceptional points(EPs)and dynamics for a single periodically modulated PT-symmetric quadrimer waveguides system.It is analytically and numerically revealed that the periodic modulation not only can restore the broken PT symmetry of the system,but also can manipulate the PT symmetry by tuning modulation amplitude.Furthermore,we found that multiple EPs can emerge,and as the modulation amplitude vary these EPs can collide and merge,leading to higher-order Floquet singularities.By defining average relative light intensity distribution,we explore the dynamical characteristics nearby these EPs.It is found that we can control the light tunneling direction of optical quadrimer waveguides via periodic modulation and gain/loss parameters.In Chapter 3,we investigate Floquet control of global PT symmetry in 2D arrays of quadrimer waveguides with transverse periodic structure along x-axis and longitudinal periodic modulation along z-axis.For unmodulated case with inhomogeneous inter-and intra-quadrimer coupling strength k1?k,in addition to conventional global PT-symmetric phase and PT-symmetry-breaking phase,we find that there is an exotic phase in which global PT symmetry is broken under open boundary condition,whereas it still is unbroken under periodical boundary condition.The boundary of phase is analytically given as k1?k+(?)and 1???2,where there exists a pair of zero-energy edge states with purely imaginary energy eigenvalues localized at the left boundary,whereas other 4N-2 eigenvalues are real.Especially,the domain of the exotic phase can be manipulated narrow and even disappeared by tuning modulation parameter.More interestingly,whether or not the array has initial global PT symmetry,periodic modulation not only can restore the broken global PT symmetry,but also can control it by tuning modulation amplitude.Therefore,the global property of transverse periodic structure of such a 2D array can be manipulated by only tuning modulation amplitude of longitudinal periodic modulation.In Chapter 4,we briefly summarize our results and give some outlooks.Throughout the whole article,we will explore how to control the global PT-symmetry,EPs and dynamics by applying periodic modulation for the 2D PT-symmetric array of quadrimer waveguides.Our main works are involved in chapters 2 and 3.