Strong Light-Matter-Interactions in Nanocavities and 2D Material-Nanocavity Systems

We report on showing strong light-matter-interaction enhancements of waveguide-integrated and 2D material-based spiral nanocavities. Both exploit high Q/Vmode values outperforming diffraction-limited cavities due to high optical densities. ©2015 Optical Society of America OCIS codes: (350.4238), (250.5403), (190.4720), (230.7370) , (160.4236) , (010.1030) The deployment of nano-cavities may efficiently enhance light-matter-interaction for photonic components on-chip. Three nanoscale cavity designs are investigated including the one-dimensional (1D) photonic crystal (PhC) nanobeam cavity, inline waveguide-integrated plasmon cavity, and square plasmon resonator embedded in the 1D PhC nanobeam cavity (i.e. Combo cavity). The cavity performance such as quality factor, Purcell factor, mode volume, and light-matter-interaction strength are evaluated for each structure for comparison purposes. A deep subwavelength mode volume of 0.18 (λ 2n)! is observed in the Combo cavity. The Combo cavity exhibits an improved Purcell factor up to 428 and a 44 times enhanced interaction strength due to the compressed mode volume compared to the inline plasmon cavity. Thus, the Combo cavity shows promise to becoming a potential building block for active components of next generation on-chip photonic circuits. Figure 1. Schematic of (a) 1D PhC nanobeam cavity with air holes, and cavity length, L=260 nm; hole period of mirror section, a=250 nm; minimum hole distance of taper section, a!"#=160 nm; hole radius r=0.18a; number of taper hole pairs, n=12; number of mirror hole pairs, m=16; waveguide height, h=340 nm; (b) Inline resonant cavity with square size, w =250 nm, cavity height, H=340 nm, Au layer thickness 100 nm, and (c) Combo cavity, namely, a square plasmon cavity by cutting the semiconductor nanowire waveguide (Fig.1b) in the light propagation direction is embedded inside the photonic crystal nanobeam cavity There are two types of Q-factor calculation (i.e. low Q cavity and high Q cavity) used in this work. The Q-factor from a low Q cavity is determined from the Fourier transform of the field by finding the resonance frequencies (f!) of the signal and measuring the full width half maximum (FWHM, Δf) of the resonant peaks, i.e. Q = f! Δf, if the electromagnetic fields decay completely from the simulation in a time that can be simulated reasonably by FDTD. Otherwise, the Q-factor from a high Q cavity cannot be determined from the frequency spectrum because the FWHM of each resonance in the spectrum is limited by the time of simulation. In this case, Q-factor is calculated from a slope of the envelope of a decaying signal using the formula, Q = !!!!!!"#!" ! !! (1) where m is the slope of the logarithm of the time signal envelope. Due to the cavity length (i.e. L) sensitive to the Q-­‐factor, L is swept to study both the variation of Q factor using the high Q calculation method and the shifting property of resonance wavelengths with the use of a z oriented dipole source. In recent years the Purcell factor, F!, is used to describe LMI in laser physics as it relates a measure of spontaneous emission rate enhancement of a dipole emitter source placed in the cavity with respect to that in a homogeneous semiconductor material. A formula widely used for the evaluation of F! is given by, F! = ! !!! !! ! ! ( ! !!"#$ ) (2) where λ! is the resonant free space wavelength of the cavity, n is the material refractive index at the field antinode,. and V!"#$ is evaluated from a commonly used definition, V!"#$ = ! !(!) !!" !"# [! !(!) !] (3), where ε is the dielectric constant, E(r) is the electric field strength, and V is a quantization volume encompassing the NS3B.3.pdf Advanced Photonics © 2015 OSA resonator and with a boundary in the radiation zone of the cavity. Equation (2) indicates that a large Q and a smaller modal volume are desired for enhanced spontaneous emission rate (i.e. F!) that is proportional to Q/V!"#$. The result show a the smallest mode volume between the three cavities for the combo design of Vn = 0.18, where V! = !!"#$ ! !! ! . Utilizing Eq. (2) F! can be estimated if Q and V!"#$ are both known parameters. Using the high Q calculation method, the Q-factor of ~10000 is obtained for the 1D PhC nanobeam cavity. The Q-factors of 17 and 126 are simulated by the low Q calculation method for the inline plasmon cavity and the Combo cavity, respectively. The corresponding values of F! are 626, 14, and 428 for the three cavity structures, respectively. Although the Purcell factor in the Combo cavity is lower relative to the PCNB cavity, the interaction strength is significantly improved for the Combo cavity. For the interaction strength of third order effects (i.e. E !"# ! ×Fp) , the number of 348, 38, and 2103 are achieved for the PCNB, Inline, and Combo cavities, respectively. We can see that LMIs of 2D-confined SPPs may be enhanced by introducing an external cavity, where the interference between multiple reflections within the cavity can substantially modify the intrinsic density of states. Next we investigate strong LMI in cylindrical nanocavities comprised of 2D materials as the active absorber (Fig. 2). Semiconducting 2D transition metal dichalcogenides have provided evidence for strong light absorption relative to its thickness attributed to high density of states. Stacking a combination of metallic, insulating, and semiconducting 2D materials enables functional devices with atomic thicknesses. Here we show that taking advantage of the mechanical flexibility of 2D materials by rolling a molybdenum disulfide (MoS2)/graphene (Gr)/hexagonal boron nitride (hBN) stack to a spiral nanocavity, which allows for absorption up to 90% (here we tested solar radiation). A core-shell structure exhibits enhanced absorption and pronounced absorption peaks with respect to a spiral structure without metallic contacts. The resonances themselves suggest the cylinder spiral structure resembling a nanowire, and hence exhibiting Fabry-Perot cavity behavior. We confirm the latter via (i) investigating the modal features of this cavity (Fig. 2c), where the transverse (x-y direction, i.e. x in Fig. 2a) mode profile indicates a dipole for larger wavelength, which turns into quadruples and doubled-quadruples for blue shifting the resonance wavelength (6 to 1 in Fig. 2c). In addition the cavities’ standing waves can be seen in the cross-sectional-longitudinal modal profile (i.e. x’ in Fig. 2a), where the mode spacing decreases with wavelength (Fig. 2c). The higher Q-factors observed of the coreshell cell relative to the spiral cell are clearly visible in the crossectional mode profiles as distinct power density lopes (Fig. 2b). Interestingly, the absorbing materials (graphene and MoS2) occupy only 6% of the total volume of spiral cells. This suggests that the ratio of solar energy absorption to volume of photoactive material was ~7.67:1 compared to a bulk MoS2 photovoltaic cell of the same size. We name this ratio “enhancement” and define it as !!"#$%& !"##! !!"#$ !"## !!"#$ !"## ÷ !!"#!! !!" !!"#!! !!"! !!!" (4) where α denotes absorption and t refers to the respective physical layer thickness. This enhancement is proportional to the absorption efficiency and thickness of the hBN layer (Fig. 2d). In summary, we have compared three 1Dnano-cavity designs for waveguide-integrated devices. Towards obtainingstrong light-matter-interactions, theresults favor the Combo cavity due to thesmallest mode volume of the threecavities and deep sub-wavelength modevolume of ~0.18 (λ 2n)!. This leads tothe significantly enhanced interactionstrength in the cavity, which is beneficialfor on-chip opto-electronic. Secondly,have shown a 2D material-based spiralnanocavity design showing strongabsorption in the visible spectrumapproaching 90% due to high opticalDOS due to (a) the 2D materialabsorption, and (b) the nanocavityresonance References[1] We acknowledge AFOSR financialsupport under award numbers FA9559-14-1-0215 and FA9559-14-1-037, and the NationalScience Foundation under award numberNSF 1436330 and the Materials GenomeInitiative (MGI).Figure 2. (a) Schematic of spiral (left) and core-shell cavities (right). Horizontal(vertical) cross sections labeled by X(X’) are power monitors recording profilesshown in (c). (b) Absorption efficiency of spiral cell and core-shell structure. (c) Wavelengths correspond to absorption peaks of the core-shell structure. (d)Optimization of hBN thickness to achieve highest LMI (Eqn 4) enhancement.