Quantum optical approach for graphene plasmon scattering by quantum emitter; frequency and angular dependence.
- 주제(키워드) graphene , surface plasmon polariton , quantum emitter , quantum scattering , frequency and angular dependence
- 발행기관 고려대학교 대학원
- 지도교수 남석우
- 발행년도 2017
- 학위수여년월 2017. 2
- 학위구분 박사
- 학과 대학원 응용물리학과
- 원문페이지 97 p
- 실제URI http://www.dcollection.net/handler/korea/000000071501
- 본문언어 영어
- 제출원본 000045897854
초록/요약
Propagating plasmon formed on the graphene layer can interact with a scatterer near the graphene layer, giving rise to various features for the plasmon scattering. We investigate theoretically the differential scattering cross section of the graphene plasmon due to a nano-scale scatterer. Though the scattered plasmon could be realized by the energy flux of the classical fields of the plasmon and the scatterer, we utilize the quantum optical approach in which the transition amplitude between the second quantized states of the total system of plasmon and scatterer plays the most important role. In addition a quantum emitter as the scatterer is quantum mechanically controllable parameter in the study. Since the unique feature of the electronic structure of the graphene, represented by the Massless Dirac Fermion and chirality, gives rise to the corresponding dielectric function even in RPA, the scattering properties would reflect the characteristic graphene plasmon modes. Dispersion relation of graphene plasmon is obtained by Maxwell’s equations. We calculate the differential scattering cross section of the graphene plasmon from a quantum emitter above the graphene layer. Quantum emitter in this study has spherical shape with radius in the range of 2nm ~ 6nm, and its transition energy is in visible range. Here we consider the Rayleigh scattering whose plasmon frequency is around the THz range(10~100meV). The quantum emitter is placed very close to the layer, so that the interaction between the quantum emitter and the plasmon fields could be substantial. We are interested in the frequency and angular dependencies of the plasmon scattering from the emitter on the differential scattering cross section. As a main result of this study, the differential scattering cross section shows ω7-dependence and becomes stronger for higher spectral range. Its overall trend as a function of frequency is similar to that from the classical. In addition, the characteristics of the scattering are discussed relating to the controllable parameters including Fermi energy and the dielectric constant of substrate.
more목차
1. Introduction - 1 -
2. Graphene - 5 -
2.1. Graphene Electronic Structure - 5 -
2.2. method (Effective mass description) - 9 -
2.3. Metal Surface Plasmon Polariton - 15 -
2.4. Graphene dielectric function - 20 -
2.5. Graphene plasmon - 25 -
2.5.1 TM mode plasmon in graphene - 26 -
2.5.2 TE mode plasmon in graphene - 28 -
3. Graphene Plasmon Scattering - 32 -
3.1. System - 32 -
3.2. Kramers-Heisenberg Scattering - 36 -
3.3. Differential Scattering Cross Section - 42 -
3.4. Validity of the two-level approximation - 49 -
4. Results and Discussion - 51 -
4.1. Frequency dependence of differential scattering cross section - 51 -
4.2. Angular dependence of differential scattering cross section - 62 -
4.3. Discussion - 64 -
5. Conclusion - 67 -
Appendix - 69 -
A1. Plasmon in solid & dielectric function - 69 -
A2. Calculation of transition amplitudes - 71 -
A3. Calculation of for the TM mode - 75 -
A4. Rayleigh scattering - 76 -
References - 81 -
