PHYSICAL REVIEW B 103, 205423 (2021) Band shaping and emission control via waveguide plasmon polaritons Augusto Martins, 1 Aimi Abass, 2 Ben-Hur V. Borges, 1 and Emiliano R. Martins 1, * 1 Department of Electrical and Computer Engineering, University of São Paulo, CEP 13566-590, São Carlos, SP, Brazil 2 Herzogstrasse 12, 52070, Aachen, Germany (Received 18 March 2021; revised 26 April 2021; accepted 28 April 2021; published 19 May 2021) Photonic nanostructures can improve the efficiency and functionality of optoelectronic devices by controlling propagation and extraction of light in waveguides. The paradigmatic example is the extraction of light by matching the grating and waveguide mode momenta. A higher functionality can be achieved, however, via strong coupling between waveguide and plasmon modes. Here, we show that such hybridized systems provide a convenient strategy to tailor the dispersion band of the waveguide. By controlling the metallic grating height, the bands evolve from a Dirac cone to a flatband and a parabolic profile. We show an application of this system to light emitting waveguides, where a flatband leads to a sharply defined emission cone, with a 1.8 fold gain in emission efficiency and a Purcell factor of 2.4. We show that 72.2% of all radiated power is contained within the flatband region and is eight times larger than the total emission by the dipole in a homogenous medium. The system thus combines efficiency gain with the opportunity of beam shaping. DOI: 10.1103/PhysRevB.103.205423 I. INTRODUCTION Though light propagation can be controlled with vari- ous macro-optical components involving mirrors and lenses, such solutions are often costly and come with large spatial requirements, as they rely on geometrical optics. Both spa- tial requirements and costs can easily exceed by orders of magnitude what is required for the emitter. As a result, com- pact alternative photonic solutions provided by nanostructures have gained widespread interest over the last two decades. In particular, these structures can be used to control the spon- taneous emission of quantum dots (QDs) or dye molecules [1–5] by altering their local photonic density of states (PDOS) [6–8]. The emission rate and angular pattern can be readily tailored by engineering the nanostructures with a judicious choice of materials and geometry [9,10]. One promising approach is to use photonic cavities, which offer the opportunity to simultaneously control the photonic density of states and angular emission [11,12]. A common approach is to embed the emitters in waveguides, thereby confining light in at least one dimension, and then employ nanostructures to extract light trapped by total internal re- flection [11,13]. The nanostructures can also act as the cavity itself, and multiple cavities (or resonators) can be associated to form a metasurface [3]. These approaches have led to emitters with directional radiation patterns [14–16] or with engineered profiles [7,17–20] without the need of external optical components or complex surface shaping. Here, we explore the physics in sculpting the dispersion of hybridized photonic-plasmonic systems and demonstrate the ability to realize various dispersion shapes, from a Dirac cone to a flatband and a parabolic band. We demonstrate * erm@usp.br interesting radiation distribution achieved by this route, such as a homogeneous light intensity distribution within a sharply defined angular window. The ease in controlling the coupling of photonic and plasmonic modes adds an important degree of freedom to the control of light emission and band shaping, with applications in light emitting devices (LEDs), sensors, camera flashes, automotive lighting, slow light, and to the growing field of photonic flatbands [21]. In Sec. II, we focus our attention on how hybridized photonic-plasmonic modes (i.e., a supermode that arises from strong coupling between these two modes) can lead to band shaping and, in particular, to the emergence of flat dispersion bands. In Sec. III, we show that the same effect can be achieved in a simplified system. In Sec. IV, we explore a flat dispersion band to taylor the light emitting properties of waveguides, achieving emission in a well defined angular cone. The paper is concluded in Sec. V. II. DISPERSION MANAGEMENT IN A HYBRID PLASMONICWAVEGUIDE SYSTEM We begin the analysis by considering the hybridization between a waveguide mode with a plasmonic mode forming a waveguide plasmon polariton (WPP) [22]. Recently, it has been shown that such coupled systems can support bound states in the continuum (BICs), which are exotic modes with infinite lifetime in spite of being coupled to radiative channels [23]. One important advantage of waveguide plasmon polari- ton modes is the opportunity of combining the strong light interaction of plasmonic modes with the low material losses of photonic waveguide modes. To identify the mechanisms behind the modes coupling, we first consider a slab waveguide (300 nm thick) embedded in an n = 1.45 medium as shown in Fig. 1 with a double grat- ing system. Though seemingly complex, this double grating waveguide system is a suitable model that provides clarity 2469-9950/2021/103(20)/205423(7) 205423-1 ©2021 American Physical Society