Collective Optical Responses Of Multiple Surface Lattice Resonances Generated With Nanoparticles Array Hybridized Structures

With the rapid development of micro-nano photonic devices towards miniaturization,integration and high performance,plasmonic micro-nano structures（such as metallic nanoparticles）have attracted great interest from researchers due to their effective focusing of incident field energy and high sensitivity to changes in the external environment.However,localized surface plasmon resonances（LSPRs）of metallic nanoparticles have strong radiation losses,which reduces the quality factor of resonances,weakens the local field intensity and hinders the development of high-performance photonic devices.In the periodic array composed of nanoparticles,the collective response is affected by the coupling of LSPRs of individual nanoparticles and Rayleigh anomalies,and the resulting surface lattice resonances（SLRs）have a very narrow linewidth,which effectively suppresses the radiation losses and increases the quality factor of resonance.At the same time,the coupling effect between the nanoparticles in the array also makes the local field intensity at the resonance further enhanced relative to the localized resonance.Therefore,SLRs based on nanoparticle arrays can effectively enhance the interaction between light and matter at the nanoscale,which is an important system for designing high-performance micro-nano photonic devices.However,arrays composed of individual nanoparticles often only support a single SLR,limiting their ability to suppress radiation losses to a narrowband,which hinders the development of multiple-wavelength related photonic devices such as optical frequency combs,high-sensitivity bio-sensors,and multi-mode lasers et al.Therefore,achieving effective excitation of multiple SLRs in the nanoparticles array system can simultaneously suppress radiation losses in multiple spectral positions,which increases the quality factor of resonances and local field strength,and provide an important platform for the study of linear and nonlinear micro-nano photonic devices for multiplexing.Effective modulation of multiple SLRs in the nanoparticles array is key to achieving above applications.Therefore,this study constructs a nanoparticles array hybridized system through the introduction of metallic films and the design of multi-element nanoparticles array,and achieves the effective excitation and modulation of multiple SLRs based on the surface plasmons polaritonons（SPPs）,Fabry-Pe rot（FP）modes,coupling between electric and magnetic dipole modes of nanoparticles,and the adjustment effect of phase change materials on optical properties.The specific research contents are as follows:（1）An analytical calculation model based on the coupled dipole approximation（CDA）theory is constructed,which can be used for nanoparticles array hybridized system,and it provided theoretical guidance for the generation mechanism and optical properties modulation of multiple SLRs.The study focused on three array systems:single nanoparticles array,bipartite nanoparticles array,and overlapped nanoparticles array system with different periods.As any nanoparticle in the array system is influenced both by the incident field and the scattered field from surrounding nanoparticles,the main idea is to establish a relationship between the dipole moment（or quadrupole tensor）of the nanoparticles and the incident field.By solving the effective electric/magnetic dipole（or electric quadrupole）polarizability of the nanoparticles,the scattering and extinction spectra of individual nanoparticle and the transmission and reflection spectra of the array are calculated.Finally,the correctness of the theoretical model is verified.（2）A hybridized system composed of nanoparticles array and metal film is constructed to achieve a pair of narrowband perfect absorption related to phase singularities through the coupling between SLRs and FP modes.In addition,multiple hybridized resonance modes are excited through the strong coupling between SLRs and SPP modes,significantly improving the quality factor of resonances and local field strength relative to LSPR.The study shows that the interesting constructive and destructive interference effects between SLRs,SPP modes,and FP cavity modes are observed in the reflection spectra as the cavity length increased in the coupled system of long-spacing periodic array.The optical responses of the coupled system are calculated by the CDA theory and the classical two-layer reflection model.Due to the enhancement of the polarizability of individual nanodisk by the excitation of SLRs,a pair of narrowband perfect absorption related to phase singularities are observed in the reflection spectra,the quality factor of the absorption peak is about 89,and the observation results are verified using the two-layer reflection model.Furthermore,the SPP modes and SLRs could be independently adjusted by manipulating the period P_xand P_y.When the SPP modes and SLRs are overlapped,an anti-crossing phenomenon is observed in the reflection spectra,and the strong coupling between SPP modes and SLRs is verified using the coupled oscillator model.At the same time,the quality factor（～167）and local field strength|E|/|E₀|≈44)of the generated multiple hybridized resonance modes are greatly enhanced.（3）To overcome the limitation of the hybridized system composed of nanoparticles array and metal film only suitable for reflection working modes,a bipartite nanoparticles array system is constructed to achieve selective excitation of hybridized electric and magnetic SLRs and narrowband perfect absorption through the simultaneous introduction and intercoupling of electric and magnetic dipole modes.The study shows that by adjusting the coupling strength and phase between two Ag/Ge core/shell nanospheres in a unit cell,the electric and magnetic SLRs of single nanoparticles array and hybridized electric and magnetic SLRs of bipartite nanoparticles array are selectively excited.The above results are verified using the CDA theory and are consistent with numerical calculations（FDTD）.By adjusting the array period,when the hybridized magnetic SLR overlaps with the localized electric dipole mode,the generalized Kerker condition and the critical coupling condition in the array system are simultaneously satisfied,leading to narrowband perfect absorption.In this case,the quality factors of the perfect absorption peaks at higher and lower energies are approximately 50 and77,respectively.In addition,considering that the nanodisk structure is more in line with current nanofabrication techniques,the realization of narrowband perfect absorption in bipartite Ag/Ge core/shell nanodisks array is also studied,and the quality factor of the absorption peak is further increased to approximately 107.The study find that the relative displacement between the nanoparticles in a unit cell has almost no effect on achieving narrowband perfect absorption.Under oblique incidence,TM polarization has a significant impact on the optical responses of the array system.The energy mismatches between the hybridized magnetic SLR and the localized electric dipole mode resulted in a rapid decrease in absorption at the resonance.（4）To further improve the spectral stability of multiple SLRs in bipartite nanoparticles array,a overlapped nanoparticles array system with different periods is constructed.By overlapping two original arrays with different periods,multiple SLRs are excited at the expected spectral positions.The study shows that due to the compensation of in-phase and out-of-phase interactions between nanoparticles in a supercell,the spectral positions of multiple SLRs in the overlapped nanoparticles array system are consistent with the SLRs supported in the two original arrays.In addition,by adjusting the relative positions between the original arrays,the spectral positions and intensities of multiple SLRs remain almost unchanged,and the physical mechanism behind this spectral stability is analyzed using CDA theory.（5）To improve the issue of passive tuning of multiple SLRs by structural parameters in the aforementioned array systems,a nanoparticles array system with phase-change materials is constructed to achieve the active tuning of the spectral responses of electric and magnetic SLRs by flexibly adjusting the crystallinity of germanium telluride（Ge Te）.The study shows that by adjusting the radius ratio of the Au/Ge Te core/shell nanospheres,the electric and magnetic dipole modes are better separated at R_core=0.4R_shell.At a specific period,both electric and magnetic SLRs are simultaneously supported in the array,and the generation mechanism of electric and magnetic SLRs is analyzed by using CDA theory.Due to Ge Te can transition between amorphous and crystalline states,the spectral positions of electric and magnetic responses in the array could be actively tuned by adjusting the crystallinity of the Ge Te.Additionally,by adjusting the period P_xto overlap the spectra of magnetic and electric SLRs in the amorphous and crystallized states,a lattice Kerker effect is achieved in the array.However,the electric SLR moves away from the magnetic SLR as period P_yincreased,a lattice Kerker effect can not be achieved in this case.