自從雷射的出現，長距離光通信系統大多以此光源來產生光信號。這種優先於其他基本光源，例如，發光二極管（LED）的使用是起因於雷射利用了受激發射（Stimulated emission），使此光源可獲得較高的輸出功率，較窄的線寬和較大的帶寬容量。然而，當涉及到諸如片上光通信之類的短規模通信網絡時，這些發光器件由於採用大腔體以及高功耗而造成其不適合作為此類通訊網路的發光器件。
另一方面，LED由於仰賴自發發射（Spontaneous emission）來出光，其較不會被尺寸或雷射所要求的閾值條件給限制。因此，它們不會佔用太多空間，也不會消耗大量的能量來進行操作。不幸的是，LED的調變速度不足一直是讓該設備在現代通信世界中”發光”的阻礙點。這起因於LED固有的低自發發射率及其與輸出功率無關的特性，造成這個發光設備只能以200MHz左右的速率被直接調變，這與典型調製速度約為50 GHz的雷射相比實在太慢了。幸運的是，發光器的自發輻射率不是固定的。相反地，通過適當地設計發射器的周圍電磁環境，我們是可以將自發發射率提高好幾個數量級。
在本文中，我們通過採用光學槽式天線作為光學環境的變化，來探索自發發射率的這種特性。具體來說，我們研究這些光學結構的幾何參數在近紅外（NIR）光譜區域中與耦合發射器的自發發射率之間的關係。另外，我們還討論了這些幾何參數對增強量的共振位置和發射極量子效率的影響。通過我們的調查，我們發現，通過實際設計和設計合理的光學槽式天線，我們可以在進紅外光的頻率範圍內獲得整體速率約1000倍的提升，同時具有足夠的輻射效率。該發現暗示了創作高速電信波長LED的可能性，該LED可用作芯片上光通信的有效光源。

Lasers, since their creation, have been heavily employed in long distance optical communications for the generation of optical signals. Such a preference over the other basic light source, the light emitting diodes (LEDs), stems from lasers’ utilization of stimulated emission (STE), providing them with comparatively high output power, narrow linewidths, and large bandwidth capacities. However, when it comes to short-scale communication networks, such as on-chip optical communications, these light emitting devices may not be a suitable candidate due to their adoption of large cavities as well as high power consumption, which are both needed to overcome the required threshold to successfully instigate STE and then reap the aforementioned benefits.
On the other hand, LEDs, are known not to be limited by size or by the threshold condition required in lasers given their reliance on spontaneous emission (SE) for lighting. Consequently, they do not take up too much space, nor do they consume huge amount of power to operate. Unfortunately, inadequacy in the modulation bandwidth of an LED has been a serious problem for the device’s usage in the modern communication world. Indeed, due to the inherently low SE rate and its output power-irrelevant nature, an LED can only be directly modulated at rate around 200MHz, which is way too slow as compared to a laser with a typical modulation speed of ~50 GHz. Luckily, the SE rate of a light emitter is not a fixed property; rather, by properly engineering the ambient electromagnetic environment of the emitter, its SE rate can be potentially enhanced by several orders of magnitude.
In this thesis, we numerically explore such a characteristic of the SE rate by employing optical slot antennas as a change in the optical environments. Specifically, we investigate the role that the geometric parameters of these optical structures play in modifying the SE rate of a coupled emitter in the near-infrared (NIR) spectral region. Also in discussion are the influences of these parameters on the enhancement’s resonance position and the emitter’s quantum efficiency. Through our investigation, we find it achievable for a practically and properly designed optical slot antenna to offer an exemplified emitter up to ~1000 overall rate enhancement with adequate radiation efficiency in the NIR frequency range. This finding implies the possibility of creating a high speed, telecommunication wavelength LEDs, which can serve as an efficient light source for on-chip optical communication.

Abstract.....I
中文摘要.....III
Acknowledgement.....V
Table of Contents.....VI
List of Figures.....VIII
Chapter 1 Introduction.....1
1.1 Motivation.....1
1.2 Optical Slot Antenna for Modifying the Spontaneous Emission Rate.....3
1.3 Outline of This Thesis.....5
Chapter 2 Electric Dipole for Classical Description of Spontaneous Emission.....8
2.1 Introduction.....8
2.2 Electromagnetic Field Distribution of an Oscillating Dipole.....9
2.3 Energy Dissipation Rate of an Oscillating Dipole.....14
2.4 Energy Dissipation Rate Enhancement in Inhomogeneous Spaces.....16
Chapter 3 Spontaneous Emission.....19
3.1 Introduction.....19
3.2 Quantum Electrodynamics (QED) Description of the Spontaneous Emission Rate.....20
3.3 The Purcell Effect.....26
3.4 Enhanced Modulation Bandwidth.....31
Chapter 4 Optical Antennas.....36
4.1 Introduction.....36
4.2 Conventional Antennas vs Optical Antennas.....37
4.3 Effect of Optical Antennas on Quantum Objects.....41
4.3.1 Increased Absorption Cross Section.....41
4.3.2 Local Density of States Engineering.....43
4.4 Resonance of Antennas.....44
4.4.1 Resonance Wavelength Scaling for Conventional Antennas.....45
4.4.2 Resonance Wavelength Scaling for Optical Antennas.....45
4.5 Optical Slot Antennas.....50
4.5.1 Radiation Pattern of Optical Slot Antennas.....54
4.5.2 Resonance of Optical Slot Antennas.....56
Chapter 5 Numerical Investigation of the Optical Properties of a Slot Antenna-Coupled Optical Emitter.....59
5.1 Introduction.....59
5.2 Energy Flow in an Antenna-Emitter Coupling System.....62
5.3 Optical Response of a Slot Antenna-Coupled Emitter to Different Slot Lengths and Widths.....67
5.4 Optical Response of a Slot Antenna-Coupled Emitter to Different Slot Thicknesses.....76
5.5 Practical Design of Optical Slot Antennas Coupled with an Exemplified Emitter at the Emission Wavelength of 1550 nm.....80
5.5.1 Effective Spontaneous Emission Rate Enhancement.....87
5.5.2 Overall Spontaneous Emission Rate Enhancement.....91
Chapter 6 Conclusion and Future Work.....95
Bibliography.....99

[1] S. Mishra, N. K. Chaudhary and K. Singh, "Overview of optical interconnect technology," Int. J. Sci. Eng. Res., vol. 3, no. 4, pp. 390-396, 4 2012.
[2] M. S. Eggleston, Metal Optics Based nanoLEDs: In Search of a Fast, Efficient, Nanoscale Light Emitter, University of California, Berkeley, 2015.
[3] S. Fortuna, Integrated Nanoscale Antenna-LED for On-Chip Optical Communication, University of California, Berkeley, 2017.
[4] S. L. Chuang, Physics of Photonic Devices, vol. Second edition, Wiley Publishing, 2009.
[5] O. Painter, "Two-Dimensional Photonic Band-Gap Defect Mode Laser," Science, vol. 284, p. 1819–1821, 1999.
[6] H.-G. Park, "Electrically Driven Single-Cell Photonic Crystal Lase," Science, vol. 305, p. 1444– 1447, 2004.
[7] M. Pelton, "Modified spontaneous emission in nanophotonic structures," Nature Photonics, vol. 9, p. 427–435, 2015.
[8] S. A. Maier, Plasmonics: Fundamentals and Applications, Bath: springer, 2007.
[9] E. K. Lau, A. Lakhani, R. S. Tucker and M. C. Wu, "Enhanced modulation bandwidth of nanocavity light emitting devices," Opt. Express, vol. 17, no. 10, pp. 7790-7799, 2009.
[10] S. K. Patel and C. Argyropoulos, "Plasmonic nanoantennas: enhancing light-matter interactions at the nanoscale," EPJ Appl. Metamaterials, vol. 2, no. 4, 2015.
[11] L. Allen and J. H. Eberly, Optical Resonance and Two-level Atoms, Mineola, NY: Dover publications, 1987.
[12] L. Novotny and B. Hecht, Principles of Nano-optics, vol. Second eidtion, Cambridge: Cambridge University Press, 2012.
[13] J. D. Jackson, Classical Electrodynamics, vol. Second edition , New York: Wiley , 1975.
[14] Y. Hiroyuki and K. Ujihara, Spontaneous Emission and Laser Oscillation in Microcavities, CRC Press, 1995.
[15] E. M. Purcell, H. C. Torrey and R. V. Pound, "Resonance Absorption by Nuclear Magnetic Moments in a Solid," Phys. Rev., vol. 69, no. 37, 1946.
[16] R.Loudon, The Quantum Theory of Light, vol. Second edition, Oxford: Oxford University Press, 1983.
[17] G. Grynberg, A. Aspect and C. Fabre, Quantum Optics, Paris: Cambridge University Press, 2010.
[18] L. C. Andreani, G. Panzarini and J.-M. Gérard, "Strong-coupling regime for quantum boxes in pillar microcavities: Theory," Phys. Rev. B, vol. 60, no. 19, 1999.
[19] T. Baba, "Photonic crystals and microdisk cavities based on GaInAsP-InP system," IEEE J. Sel. Top. Quantum Electron, vol. 3, no. 3, pp. 808 - 830 , 1997.
[20] C. A. Balanis, Antenna theory: analysis and design, vol. Second edition, New York: John Wiley and Sons, 1997.
[21] C. A. B. A. Bharadwaj, B. Deutsch and 4. (. 2. L. Novotny Adv. Opt. Photonics 1, "Optical antennas," Adv. Opt. Photonics, vol. 1, no. 3, p. 438–483, 2009.
[22] P. B. Johnson and R. W. Christy, "Optical Constants of the Noble Metals," Phys. Rev. B, vol. 6, no. 4370, 1972.
[23] Y. N. Xia and N. Halas, "Shape-controlled synthesis and surface plasmonic properties of metallic nanostructures," MRS Bulletin, vol. 30, no. 5, pp. 338-344, 2005.
[24] K. L. Kelly, E. Coronado, L. L. Zhao and G. C. Schatz, "The Optical Properties of Metal Nanoparticles:  The Influence of Size, Shape, and Dielectric Environment," J. Phys. Chem. B, vol. 107, no. 3, pp. 668-677, 2003.
[25] L. S. MODE Solutions.
[26] Y. Chen, T. R. Nielsen, N. Gregersen, P. Lodahl and J. Mørk, "Finite-element modeling of spontaneous emission of a quantum emitter at nanoscale proximity to plasmonic waveguides," Phys. Rev. B, vol. 81, no. 125431, 2010.
[27] D. K. Cheng, Field and wave electromagnetics, vol. Second edition, New York: Addison Wesley, 1989.
[28] L. Novotny, "Effective Wavelength Scaling for Optical Antennas," Phys. Rev. Lett. 98, 266802, vol. 98, no. 266802, 2007.
[29] C. T. Middlebrook, P. M. Krenz, B. A. Lail and G. D. Boreman, "Infrared phased‐array antenna," ‎Microw. Opt. Technol. Lett., vol. 50, no. 3, pp. 719-723, 2008.
[30] A. G.Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant and N. F. v. Hulst, "Unidirectional emission of a quantum dot coupled to a nanoantenna.," Science, vol. 29, no. 5994, pp. 930-3, 2010.
[31] Y. Wang, Plasmonic Antennas and Arrays for Optical Imaging and Sensing Applications, Toronto: University of Toronto, 2013.
[32] H. U. Yang, R. L. Olmon, K. S. Deryckx, X. G. Xu, H. A. Bechtel, Y. Xu, B. A. Lail and M. B. Raschke, "Accessing the Optical Magnetic Near-Field through Babinet’s Principle," ACS Photonics, vol. 1, no. 9, pp. 894-899, 2014.
[33] Y. Park, J. Kim, Y.-G. Roh and Q. -H. Park, "Optical slot antennas and their applications to photonic devices," Nanophotonics, vol. 7, no. 10, p. 1617–1636, 2018.
[34] T. Kosako, Y. Kadoya and H. F. Hofmann, "Directional control of light by a nano-optical Yagi–Uda antenna," Nat. Photonics, vol. 4, p. 312–315, 2010.
[35] M. Ren, M. Chen, W. Wu, L. Zhang, J. Liu, B. Pi, X. Zhang, Q. Li, S. Fan and J. Xu, "Linearly Polarized Light Emission from Quantum Dots with Plasmonic Nanoantenna Arrays," Nano Lett, vol. 15, no. 5, pp. 2951-2957, 2015.
[36] J. R. Lakowicz, "Radiative decay engineering 5: Metal-enhanced fluorescence and plasmon emission," Anal. Biochem, vol. 337, no. 2, pp. 171-94, 2005.
[37] D. E. Chang, A. S. Sørensen, P. R. Hemmer and M. D. Lukin, "Strong coupling of single emitters to surface plasmons," Phys. Rev. B, vol. 76, no. 3, 2007.
[38] P. Bharadwaj and L. Novotny, "Spectral dependence of single molecule fluorescence enhancement," Opt. Express, vol. 15, no. 21, pp. 14266-14274, 2007.
[39] M. Agio, "Optical antennas as nanoscale resonators," Nanoscale, vol. 4, no. 3, pp. 692-706, 2012.
[40] L. Wang, W. Xie, D. V.Thourhout, Y. Zhang, H. Yu and S. Wang, "Nonlinear silicon nitride waveguides based on a PECVD deposition platform," Opt. Express, vol. 26, no. 8, pp. 9645-9654, 2018.
[41] C. Cheng, J. Lia and X. Cheng, "Photoluminescence lifetime and absorption spectrum of PbS nanocrystal quantum dots," J. Lumin., vol. 188, pp. 252-257, 2017.
[42] G. M. Akselrod, M. C. Weidman, Y. Li, C. Argyropoulos, W. A. Tisdale and M. H. Mikkelsen, "Efficient Nanosecond Photoluminescence from Infrared PbS Quantum Dots Coupled to Plasmonic Nanoantennas," ACS Photonics, vol. 3, no. 10, pp. 1741-1746.
[43] H. Guo, T. P. Meyrath, T. Zentgraf, N. Liu, L. Fu, H. Schweizer and H. Giessen, "Optical resonances of bowtie slot antennas and their geometry and material dependence," vol. 16, no. 11, pp. 7756-7766, 2008.