1077-260X (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/JSTQE.2016.2617619, IEEE Journal of Selected Topics in Quantum Electronics JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS 1 Graphene Integrated Plasmonic Structure for Optical Third Harmonic Generation Behrooz Semnani, Student Member, IEEE, S. Mohsen Raeis-Zadeh, Student Member, IEEE, Arash Rohani, Amir Hamed Majedi, Senior Member, IEEE, and Safieddin Safavi-Naeini Fellow, IEEE Abstract—In this work a general recipe is proposed to design an efficient graphene integrated plasmonic structure for third harmonic generation (THG). Specifically, the design procedure for an integrated graphene based ultra-violet light generator is presented. In order to enhance the field intensity at the graphene layer, two distinct mechanisms are utilized. A multilayer Bragg structure is used as a Perfect Magnetic Conductor (PMC) to make a constructive interference between incident and reflected field at the graphene layer. A periodic array of shaped resonant gold nanoparticles is placed on top of the graphene sheet to enhance the field intensity due to the plasmonic resonance at the fundamental frequency. A hybrid and fast numerical method based on scattering matrix of Floquet modes and the Generalized Multipole Technique (GMT) is also proposed to analyze the periodic structure. This numerical method is used to optimize the dimensions of the multilayer structure and boost the nonlinear conversion efficiency by more than 10 6 times. Index Terms—Graphene, integerated nonlinear optics, third harmonic generation, plasmonic, I. I NTRODUCTION Nonlinear up-conversion of the visible and near infrared light to the higher harmonics has been the topic of intense research in recent years [1]-[3]. Applications are diverse and encompass many areas ranging from photonics and laser tech- nology to biomedical imaging and sensing [4]-[6]. The con- ventional up-conversion techniques rely on the phase matching of the intense electromagnetic fields in bulk nonlinear crystals. The bulk nonlinear structures take advantage of the phase matching to efficiently utilize the cascaded nonlinear processes and accumulation of nonlinear interactions within a long prop- agation path [7]. The guided-wave frequency mixing methods essentially suffer from an excessive amount of absorption loss that limits the conversion efficiency. In order to perform non- linear operations in a highly integrated fashion with low power consumption, one would require to hire effective mechanisms to enhance the field intensity inside the nonlinear medium. Recent rapid advancements in nanofabrication technologies have widened the realm of possibilities in nanophotonics, nonlinear and sub-wavelength optics. Realizing nonlinear op- tics in sub-wavelength scale paves the way for low cost integrated photonics [8]. The ultra-high-Q photonic crystal nanocavities [9]-[10] and nanostructured materials are exam- ples of such structures. Specifically, the plasmonic plasmonic metasurfaces offer very small mode volume guaranteeing highly enhanced field intensity [8]. The region of nonlinear Authors are with the Department of Electrical and Computer Engineering; and Waterloo Institute for Nanotechnology (WIN), at the University of Waterloo, Waterloo, ON, Canada. interaction nonetheless is limited to the mode extend. That hinders the efficient adoption of the bulk nonlinear mediums for frequency mixing applications. To circumvent this issue, the integration of artificial quantum materials such as highly nonlinear multiple-quantum-well semiconductor heterostruc- tures and plasmonic nanostructures made of noble metals has been proposed recently[11]-[12]. This paper proposes the integration of the plasmonic metasurfaces and the recently discovered 2D-materials [13] to perform nonlinear frequency mixing. Among 2D materials, graphene has been demonstrated to be optically nonlinear [14]-[16]. The band structure of graphene differs substantially from that of the other known semiconduc- tors. The honeycomb crystalline structure of graphene intro- duces the chiral quasiparticles obeying the Dirac equation. The symmetries of the graphene lattice entail significantly strong nonlinear optical properties making graphene a compelling candidate for integrated nonlinear optics [14]. Though some metals may also exhibit strong nonlinearity, they are generally opaque and highly refractive [17]. Unlike metals, graphene is almost transparent maintaining the optical structure intact. In the wavelength conversion device introduced in this article, graphene acts as the nonlinear medium. The centrosymmetry of the graphene lattice prevents even-ordered nonlinear pro- cesses and hence the first nonlinear term is the third order term [14]. Accordingly the structure is designed for third harmonic generation (THG). The main objective of this paper is twofold. First, a design methodology for an efficient plasmonic graphene-based third harmonic generator is proposed. As a particular example, we focus on a frequency tripler converting an optical beam in the near infrared wavelengths (∼ 800nm) to its third harmonic at UV range of frequency. Second, a fast hybrid numerical method is introduced to analyze and optimize the dimensions of the structure. The proposed structure is composed of a graphene layer transfered over a multilayer structure. A periodic array of shaped gold nanoparticles, designed to be resonant around the wavelength of 800nm, is positioned on top of the graphene sheet. The dimensions of the multilayer structure and nanopar- ticles are optimized to tune the plasmonic resonance frequency and maximize the enhancement factor both at the fundamental frequency and its third harmonics. The multilayer structure is designed to act as a Bragg mirror which provides an additional enhancement of the field intensity due to the reflection from the band gap medium. The numerical method introduced in this paper is used