A Research On The Dyadic Green’s Function In Surface Plasmon Waveguides And Its Application

Waveguides constrain electromagnetic fields.Although traditional dielectric waveguides can achieve low-loss light guiding,it is difficult to achieve miniaturization and integration of optical devices due to diffraction limits.Surface plasmons can localize light in a small space and overcome the diffraction limit of photons.Their mode area is very small so that they can make sub-wavelength size devices and have a wide application in the field of nano-photon.Therefore,this paper focuses on the surface plasmon nanowireline waveguides and hybrid waveguides.The research steps and main achievements are presented as follows:In chapter 1,this paper mainly introduces the photon dyadic Green’s function values and analytical solutions in cylindrical waveguides.The 3D finite element renormalization green’s function and structured and unstructured methods,the 2.5D numerical method based on Fourier spectrum,the 2D single-mode approximate solution by waveguide mode construction,and the derivation of spontaneous radiation and resonance energy are introduced.In chapter 2,the solution method of photon dyadic Green’s function and the enhancement characteristics of spontaneous radiation and resonance energy transfer in single-layer cylindrical waveguide are studied.Results show that when the source point in the cylindrical waveguide and sites in the same position,the green’s function is discrete,the based on 3 d finite element,using a structure and non structure of point source radiation field is poor and small volume mean-field renormalization method,can obtain accurate photons and green’s function,and half renormalization method can reduce the amount of calculation;Based on 2.5D Fourier spectrum method,the imaginary part of scattering photon green function can be obtained accurately.For 2D waveguide mode expansion method,when the source point and the field point are different,the exact photon dyadic Green’s function can be obtained,but only the imaginary part of the photon Green’s function can be obtained.The position and polarization direction of atoms play an important role in the enhancement of spontaneous emission and resonance energy transfer,which depends on the spontaneous emission rate and propagation distance.When the atom is close to the waveguide,the enhancement of spontaneous radiation is great.When the direction of atomic polarization is different,the enhancement of spontaneous radiation has obvious position dependence and radiation direction.In chapter 3,the characteristics of dyadic Green’s function and the enhancement of spontaneous radiation and resonance energy transfer in a two-layer cylindrical waveguide are studied.The results show that based on the renormalization and the difference between structured and unstructured point source radiation fields,the photon dyadic Green’s function of double-layer cylindrical waveguide can be obtained precisely.As for the enhancement characteristics of spontaneous emission and resonance energy transfer,the conclusion similar to chapter 2 is also obtained.The enhancement of spontaneous emission rate and resonance energy transfer is dependent on the position of atoms and radiation direction.The closer the atom is to the waveguide,the greater the enhancement of spontaneous emission.The spontaneous radiation enhancement and resonance energy transfer enhancement of silica cylindrical waveguide coated with silver metal are more significant than those of silica cylindrical waveguide coated with silicon metal.In chapter 4,resonance energy transfer enhancement between two two-level atoms in a hybrid waveguide is studied based on finite element method.The 2D finite element method is used to solve the waveguide mode and to obtain the approximate photon dyadic Green’s function in the waveguide.It is compared with the strict 3D finite element solution.The results show that the photon dyadic Green’s function constructed by the waveguide mode is in good agreement with the strict 3D finite element solution in the case of single mode,but the calculation amount is much less than that of the 3D finite element method.Using the 2D fast solution method,the size required for single-mode transmission of the waveguide and the effect of different waveguide sizes on the enhancement characteristics of resonant energy transfer are systematically studied at 1550 nm wavelength.The results show that the width of dielectric waveguide is narrower,the height of single mode is higher.When the width of the waveguide increases,the propagation distance increases and the resonant energy transfer enhancement factor decreases for the higher dielectric waveguide,but for the smaller dielectric waveguide height,the propagation distance increases first and then decreases,and the resonant energy transfer enhancement factor decreases sharply.With the increase of height,the propagation distance decreases sharply first and then increases slowly,while the resonance energy transfer enhancement factor increases sharply first and then changes slowly.The lower the gap height is,the smaller the propagation distance is and the larger the resonance energy transfer enhancement factor is.In chapter 5,we summarize the research and propose outlook for future studies.