Research On Unconditionally Stable Finite-Difference Time-Domain Methods In Nano-Photonics

With the development of science and technology,the physical models that need to be solved in nano-photonics are becoming more and more complicated,which involve the multi-scale and multi-physics field effects.The finite-difference time-domain(FDTD)method is a commonly used method to solve the complex electromagnetic problems in nano-photonics.However,the time step size for FDTD is limited by the Courant-Friedrich-Levy(CFL)stability condition,causing a very long computation time when FDTD simulations are perfomed in nano-photonic devices.The implicit unconditionally stable locally-one-dimensional(LOD)FDTD method is very suitable for solving those nano-photonic devices.However,the unconditionally stable LOD-FDTD method with high performance is still waiting for further study,which includes three aspects.Firstly,the LOD-FDTD method with higher accuracy,higher efficiency,and wider applicability should be investigated.Secondly,LOD-FDTD based on the hybrid sub-gridding scheme should be thoroughly studied.Finally,in terms of engineering applications,the fast LOD-FDTD method with high accuracy and efficiency should be used to solve the electromagnetic and optical problems in the field of nano-photonics,and the numerical methods can also be applied to the numerical design of nano-photonic devices.This thesis aims at investigating the unconditionally stable and fast FDTD methods and their applications in the field of nano-photonics.On the one hand,the implicit unconditionally stable LOD-FDTD method,the hybrid sub-gridding LOD-FDTD method,and the numerical design method of nano-photonics devices are thoroughly and systematically studied.One the other hand,the proposed fast LOD-FDTD method are widely employed for the simulation of the nano-photonics,such as the extraordinary optical transmission(EOT)of the periodic metallic gratings,plasma photonic crystal,periodic metallic nanoparticle arrays,and numerical design of nanophotonic devices.The contents are divided into four parts shown as follows.In the first part,a frequency-dependent LOD-FDTD method based on the auxiliary differential equation is developed for the EOT analysis of periodic metallic gratings.Firstly,the dispersion of the metal,caused by the evanescent waves propagating along the interface between the metal and dielectric materials in the visible and near infrared regions,is expressed by the Drude model and solved with a generalized auxiliary differential equation(ADE)technique,and the ADE-LOD-FDTD suitable for simulating the dispersive media is obtained.Secondly,the periodic boundary condition(PBC)is applied to the two-dimensional(2-D)metallic grating structure,which extends the application area of the ADE-LOD-FDTD method.Thirdly,two numerical examples with different sub-wavelength slits are calculated and the mechanism of the EOT phenomenon is investigated.In the second part,a complex-envelope(CE)scheme is introduced into the ADE-LOD-FDTD method for the band-gap analysis of the plasma photonic crystal(PPC).Firstly,in order to reduce the numerical dispersion for large time-step sizes in LOD-FDTD,a complex-envelope scheme is introduced into the LOD-FDTD method.Secondly,in order to accurately simulate the electromagnetic problems in open regions,the CE scheme is applied to the perfectly matched layer.Thirdly,the proposed CE-ADE-LOD-FDTD is employed to simulate the PPC structures,which extends the application area of the CE-ADE-LOD-FDTD method.In the third part,a sub-gridding scheme that hybridizes the conventional ADE-FDTD method and the unconditionally stable ADE-LOD-FDTD is developed for analyzing the periodic metallic nanoparticle arrays.Firstly,a hybrid method with the explicit FDTD and implicit LOD-FDTD is proposed.Secondly,an easy-to-accomplish scheme of spatial interpolation is presented at the interface between coarse-grid and fine-grid regions,and its numerical stability is tested.Thirdly,numerical examples about extraordinary optical transmission through the periodic metallic nanoparticle array are provided to show the accuracy and efficiency of the proposed hybrid FDTD method.In the fourth part,the application of unconditionally stable LOD-FDTD method in the numerical design of nanophotonic devices is studied.Firstly,the mode excitation source technique of adiabatic guided-wave structures is introduced.Secondly,a general numerical method for designing the efficient adiabatic mode evolution structure(AMES)(referred to as NAMES)is introduced,which can be applied to adiabatic taper,adiabatic coupler,and a wide range of AMES based devices.Through these examples,we showed that the introduced numerical method is robust,stable,convergent,and general(not restricted to a particular device type or device geometry).Finally,the calculation of the mode overlap integral of any adiabatic guided-wave structures is introduced.LOD-FDTD is used to obtain the mode overlap integral of the adiabatic guided-wave structure designed by the NAMES algorithm and verify its effectiveness.