Research On Localized Mode And Its Control In (Quasi-)Periodic Waveguides

The localization phenomenon exists in both periodic and quasi-periodic structures.Highquality resonator cavities,couplers,sensors,amplifiers and other functional devices can be fabricated by this physical property.Therefore,the localization of guided waves has been widely studied in various fields such as optics,acoustics,and solid mechanics.Most of these related researches are based on traditional Bragg resonance waveguides,in which the low-order modes are excited as the main component of the guided waves.However,the participation of high-order modes can not only strengthen the localization effect in traditional waveguides,but also facilitate the integration of waveguide devices.Related mode-control devices can be used not only to improve the resolution of imaging in the communication field,but also to design devices for manipulating particles such as optical tweezers and acoustic tweezers.Therefore,waveguides,which can excite high-order modes with periodically and quasi-periodically corrugated walls,are designed according to these advantages.Based on the coupled mode and the orthogonality breaking theory,the localization of guided waves in periodic and quasiperiodic structures is investigated.The mode control mechanism is further discussed based on the multi-mode interaction,so as to realize the prediction and control of the mode field on different applied conditions.The specific content is as follows:1.Localization phenomena of defect states and interface states are investigated in defect models and heterojunction models based on periodic waveguides.First,defects are introduced by inserting straight waveguides into waveguides with corrugated walls,and the defect states in the Bragg and non-Bragg gaps are investigated.Due to different resonance mechanisms of two gaps,the interface states in two gaps also exhibit their own characteristics.Experimental results show that defect states exhibit low-order mode characteristics in the Bragg gap but highorder mode characteristics in the non-Bragg gap.In addition,introducing multiple defects to the periodic waveguide can also lead to multiple defect states in the spectrum.Second,the interface states are stimulated in the heterojunction,which is fabricated by two waveguides with different duty ratios.Based on the coupled mode theory,we investigate the law that the frequency of the interface state changes with the connection phase of the interface.Researches show that as the connection phase increases,the interface state moves to the lower frequency until it completely enters the low-frequency edge of gap.At this specific phase point,a new interface state appears from the high-frequency edge of gap.The mode field distribution shows the most significant feature of the interface state,that is,the maximum energy is localized near the interface.2.Interface states with localization effect and high-quality factor are stimulated in the quasi-periodic waveguides.Most researches on traditional quasi-periodic waveguides are based on the Bragg resonances.Bragg resonances are enhanced,forming a Bragg gap with high attenuation by increasing the periods in the waveguide.Based on non-Bragg resonances,we designe a Fibonacci quasi-periodic waveguide,where the resonances can be enhanced on the condition of maintaining the waveguide volume.The interface state is excited in the non-Bragg gap by constructing the mirror symmetry structure of the Fibonacci quasi-periodic waveguide.The experimental results show that the field distribution of the interface state exhibits significant energy localization near the interface of the mirrored waveguide,and the phases at two maximum amplitudes of guided waves are completely opposite.This interface state,similar to a squashed dipole,exhibits high-order mode characteristics and high-quality factor.It can be used to optimize the traditional quasi-periodic waveguide structure and provide design ideas for various functional devices such as multi-mode filters,sensors,and couplers.3.The coupled effect of double-defect model is investigated by employing the coupledmode theory.Defects in the periodic structure can cause the localization,which is applied to many equipments and devices such as optical/acoustic tweezers,laser cavities,spatial modulators,and detectors.Two defects are inserted into a perfect waveguide with periodically corrugated walls to regulate the coupled effect of defect states.Coupled effect between two defect states are experimentally observed.The phase measured at the maximum amplitude of guided waves in the waveguide shows that two defect states have opposite symmetry on localized characteristics,and this symmetry changes alternately as the number of periods between the two defects increases.The experimental results show that the distance between the two defects and the geometric parameters of defects can influence the defect states coupled.When the distance between two defects increases,the defect coupled becomes weaker and the peaks overlap and then disappear.In addition,the maximum energy of the defect state with a longer wavelength is always localized in a longer defect.The localization of waves can be effectively manipulated by adjusting the structures with defects and related researches provide ideas on fabricating various functional devices in wave control engineering.4.The high-order modes with high transmittance and purity are stimulated by designing heterostructures based on the quasi-periodic waveguides.An extraordinary transmission with high-order mode characteristics arises near the interface of the heterojunction,which consists of two periodic structures based on different mode resonances.In general,it is difficult to develop various related functional devices by using such extraordinary transmission with low transmittance.To solve this problem,the heterostructure is assembled with a low-order mode waveguide and a high-order mode waveguide which is based on the Fibonacci quasi-periodic structures.A transmission phenomenon with high-transmittance and high-order mode characteristics is realized in the quasi-periodic waveguide by using the multi-mode resonance mechanism.The simulation results show that the field pattern of the extraordinary transmission phenomenon exhibits an anti-symmetric distribution.The localization effect only exists in the high-order mode waveguide,and the field distribution is a dipole-like.As the mode composition analysis shows,the high-order mode is mainly second-order mode,and the mode component ratio is close to 1.The localization phenomenon in high-order mode waveguides is completely different from that in low-order mode waveguides.In addition,the band structure of the quasiperiodic structure is more complex than that of the periodic structure,so the band gap structure of quasi-periodic waveguide is more abundant.This physical property is used to design a generalized Fibonacci quasi-periodic waveguide,and the function of multi-channel tunable filtering is realized by changing the number of layers of the quasi-periodic waveguide.In summary,based on the multi-mode coupled and multi-mode resonance principles,the localization can be stimulated under specific conditions by designing periodic and quasiperiodic waveguide structures.The localization effect can change the performance indicators of the original structure,and improve the properties of related functional equipments and devices.Due to these advantages,the reaserches on the localization are significant.At the same time,the regulation on the mode field of guided waves not only plays a vital role in designing various devices,but also provides feasible ideas for the development and optimization of new tunable functional devices.