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 systems holds paramount significance, yet experimental realization of such optical configurations using current technologies poses formidable challenges. Conversely, the approach of periodic modulation emerges as a more viable alternative. Notably, periodic modulation in optical systems is predominantly executed through the cyclic alteration of complex refractive index materials. Distinct from conventional approaches that align periodically modulated waveguides in parallel with gain-dissipative counterparts to satisfy PT symmetry, this paper innovatively introduces a physical model featuring the cross-placement of these waveguides, marking the first instance of leveraging this configuration to manipulate PT symmetry. This paper examines the effect of periodic modulation on the energy spectrum of the system within the high-frequency approximation, elucidating the dynamical evolution of light in a non-Hermitian four-channel optical waveguide through a synergistic approach that combines analytical and numerical methods. Adjusting the modulation parameter <i>A/ω</i> reveals a dual capability: it modulates the extent of the real energy spectrum and precisely controls the PT symmetry of the system. Notably, at <i>A/ω</i>=0, the structure exhibits a fully real energy spectrum, diverging from conventional parallel four-channel waveguide configurations. Furthermore, as <i>A/ω</i> varies from 0 to 2.4, the relative intensity and optical periodicity within each waveguide exhibit enhanced stability compared to their conventionally arranged counterparts. Furthermore, our examination of PT symmetry's effect on light tunneling dynamics within individual waveguides reveals that in the unbroken PT symmetry phase, light oscillates periodically between waveguides, whereas in the broken PT symmetry phase, light propagation within each waveguide becomes stable. In the presence of waveguide coupling, it is observed that each waveguide within the system attains 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, becomes localized in the gain waveguide with propagation distance, vanishing from other waveguides, ultimately reaching a steady-state configuration. The findings reveal that, in contrast to traditional four-channel optical waveguide systems, 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 within the four-channel waveguide exhibit greater stability against variations in modulation parameters. Hence, this theoretical inquiry not only profoundly encapsulates the ubiquitous principle of PT-symmetric tetramers, elucidating that spontaneous PT symmetry breaking drastically alters optical transmission properties, transforming periodic light propagation into steady-state illumination, but also presents an enhanced, more robust configuration for the manipulation of PT symmetry.