Parity-time symmetry characterization and dynamics of periodically modulated four-channel optical waveguides

Abstract

The control of parity-time (PT) symmetry in cosmic-time PT symmetry system is of great significance, but the experimental realization of such an optical configuration using current technology faces enormous challenges. On the contrary, the periodic modulation method is a more feasible alternative. It is worth noting that periodic modulation in optical system is mainly performed through the cyclic change of complex refractive index materials. Unlike the traditional method of aligning periodically modulated waveguides in parallel to gain-dissipative waveguides to satisfy PT symmetry, an innovative physical model introduced in this work, features the cross-placement of these waveguides, marking it the first instance to use this configuration to manipulate PT symmetry. In this work, the influence of periodic modulation on the energy spectrum of the system in the high-frequency approximation is studied, and the dynamical evolution of light in a non-Hermitian four-channel optical waveguide is elucidated through a synergistic method of combining analytical method and numerical method. Adjusting the modulation parameter <i>A</i>/<i>ω</i> reveals a dual capability: it modulates the range of the real energy spectrum and precisely controls the PT symmetry of the system. Notably, at <i>A</i>/<i>ω </i>= 0, this structure exhibits a completely real energy spectrum, which is different from the traditional parallel four-channel waveguide configuration. Furthermore, as <i>A</i>/<i>ω</i> varies from 0 to 2.4, the relative intensity and optical periodicity in each waveguide exhibit enhanced stability compared with their traditionally arranged counterparts. Furthermore, our examination of PT symmetry’s effect on light tunneling dynamics in individual waveguide reveals that in the unbroken PT symmetry phase, light oscillates periodically between waveguides, whereas in the broken PT symmetry phase, light propagation in each waveguide becomes stable. In the presence of waveguide coupling, it is observed that each waveguide in the system can obtain steady-state light regardless of the initial light injection point. Furthermore, under weak coupling between the gain-dissipative two-channel waveguide and the neutral waveguide, light, regardless of its entry point, will localize in the gain waveguide with propagation distance, disappear from other waveguides, and ultimately reach a steady-state configuration. The findings reveal that unlike the scenario of traditional four-channel optical waveguide system, the periodic modulation not only narrows the range of existence for the fully real energy spectrum but also enables its earlier observation. Furthermore, the relative light intensity and optical periodicity in the four-channel waveguide exhibit greater stability against variations of modulation parameters. Hence, this theoretical exploration not only profoundly summarizes the universal principle of PT-symmetric tetramers, but also elucidates that spontaneous PT symmetry breaking greatly changes the optical transmission characteristics, transforming periodic light propagation into steady-state illumination, and providing an enhanced and more robust configuration for the manipulation of PT symmetry.