Study On Spontaneous Emission And Energy Level Shift In Surface Plasmonic Nanostructures

Surface plasmonic is a kind of quasi-particle for the quantized oscillation of free electrons and associated electromagnetic fields.Electromagnetic field can be confined in a small region near the metal surface,which is beyond the traditional diffraction limit.Owing to this great local field enhancement effect,strong light-matter interaction can be achieved.The spontaneous emission rate and the energy level shift are not only the basic contents of quantum electrodynamics,but also the basis of many applications.Theoretically,the spontaneous emission rate and the energy level shift can be expressed by the photon Green's function(GF).In this paper,an accurate numerical method based on the finite element method for calculating the renormalized GF and scattered GF in dissipative structures is proposed.A fast and accurate method for calculating the atomic energy level shift in a surface plasmonic nanostructure is obtained by using the subtractive Kramers-Kronig(K-K)relation.The method based on solving the Schrodinger equation in the time domain and the resolvent operator method based on the retarted and advanced Green's function in the frequency domain for the decay dynamics of a two-level system in a plasmonic nanostructure are numerically investigated.It is found that the dynamics of the system can be solved quickly and accurately by the resolvent method with the energy level shift calculated by our subtractive K-K method.We also study the nonlocal effect of a nano-rod with different sizes on the spontaneous emission rate.The main contents of this thesis are as follows:(1)In the first chapter,the basic concepts and methods for the local and the non-local surface plasmonic,the photon GF,the spontaneous emission rate,the energy level shift and the decay dynamics are briefly introduced.(2)In Chapter 2,based on the finite element method,we propose an accurate numerical method for calculating the renormalized GF and scattered GF in dissipative structures.According to the quantum electrodynamics,the atomic spontaneous emission rate and the energy level shift can be expressed by the photon GF with the same space arguments.However,in a dissipative media,the real part and the imaginary part of the GF are divergent,leading to the nonphysical spontaneous emission rate and energy level shift.One treatment is to consider the actual size and its dielectric function of the atom(quantum dots,molecules).The macroscopic field is replaced by the actual field felt by the atom.In this case,the virtual cavity model or the real cavity model is usually adopted and the renormalized GF,which is the average value over the cavity,can be used to express the spontaneous emission rate and the energy level shift.In this thesis,a method based on the finite element method for calculating the renormalized GF in dissipative media for the real cavity model or the virtual cavity model is proposed.Firstly,the radiation field of a point electric dipole is calculated,and the renormalized field is obtained by averaging it over a small cavity.Then,the renormalized GF is obtained.Applying this method to the homogeneous space,we find that the numerical results agree well with the analytical ones.This clearly demonstrates the applicability and accuracy of our method.In arbitrary-shaped nano-structure,the renormalized scattered GF can be obtained by subtracting the analytical renormalized GF in the homogeneous space from the renormalized total GF.The numerical results also agree well with the analytical ones in the case of a metal nanosphere system.(3)In Chapter 3,we propose a fast and accurate numerical method for calculating the energy level shift of an atom located in a surface plasmonic nanostructure.The method based on solving the Schrodinger equation in the time domain and the resolvent operator method based on the Green's function in the frequency domain for the decay dynamics of a two-level system in a plasmonic nanostructure are numerically investigated.By the K-K relation,the principal integral form for the energy level shift is transformed into an ordinary integral on the real frequency axis.Then subtracting the energy level shift at zero frequency from that at the transition frequency,we obtain a new form for fast calculating the energy level shift.There is no need to calculate the GF with imaginary frequency or to perform a principal value integral.By using the Drude model for free electron gas,we can get the exact energy level shift by the method of using the GF with the imaginary frequency argument,which serves as a reference.We find that our subtracted K-K method converges much faster than the direct Hilbert transform method.By applying this method to the case for a atom located in a gap plasmonic nano-cavity with experimental dielectric function,we can calculate the energy level shift quickly and accurately.By numerical evaluation of the spontaneous decay dynamics,we find that the method by solving the Schrodinger equation in the time domain needs information about the photon GF over a much wider frequency range to accurately obtain the dynamic characteristics.Fortunately,it is found that the resolvent operator method based on the retarted and advanced Green's function can be used to quickly and accurately obtain the dynamic,once the energy level shift is calculated by our subtractive K-K method.(4)In Chapter 4,we systematically study the effect of the nonlocal plasmonic for nano-rod with different sizes on the enhancement of the spontaneous emission rate.The hydrodynamics model(HDM),which takes into account the pressure of a quantum electron gas,and a generalized nonlocal optical response model(GNOR),which takes into account the quantum convective diffusion effect,are numerically investigated.Nonlocal optical response of nano-rods with different sizes,for example,constant aspect ratio(ratio of height to radius)with different sizes are systematically studied.We find that the higher the nano-rod is,the larger the blue shift and the weaker the spontaneous emission enhancement is.However,when the radius decreases,it is different.The convective diffusion takes little effect and it is red shift for the resonance frequency.In addition,the enhancement becomes large.When the aspect ratio is fixed,the spontaneous emission enhancement effect becomes weaker and weaker as the size decreases,and the peak height decreases more and more obviously owing to convective diffusion.The resonance frequency for non-local are slightly blue-shifted,and their differences becomes large.We reduce the distance between the atom and the metal surface,it is found that the higher order the nonlocal surface plasmons is,the larger the blue shift is and the more obvious the peak broadening caused by convective diffusion is.(5)Chapter 5 gives a brief summary and outlook.