Coupled nanowire-based hybrid plasmonic nanocavities on thin substrates
© Cheng et al.; licensee Springer. 2014
Received: 29 June 2014
Accepted: 12 November 2014
Published: 28 November 2014
We theoretically analyze nanowire-based hybrid plasmonic nanocavities on thin substrates at visible wavelengths. In the presence of thin suspended substrates, the hybrid plasmonic modes, formed by the coupling between a metal nanowire and a dielectric nanowire with optical gain, exhibit negligible substrate-mediated characteristics and overlap better with the gain region. Consequently, the confinement factor of the guided hybrid modes is enhanced by more than 42%. However, the presence of significant mirror loss remains the main challenge to lasing. By adding silver coatings with a sufficient thickness range on the two end facets, we show that the reflectivity is substantially enhanced to above 50%. For a coating thickness of 50 nm and cavity length of about 4 μ m, the quality factor is above 100.
Nanophotonic technologies based on nanowires have attracted much attention in the last decade. Owing to their interesting optical and electronic properties, nanowires (NWs) could serve as building blocks for novel miniaturized photonic and optoelectronic devices  with applications ranging from waveguiding [2–6] to lasing [7–11]. Recently, semiconductor NW-based nanolasers that utilize the surface plasmon polariton (SPP) effect as the optical guiding mechanism have been successfully demonstrated [8, 10]. As hybrid plasmonic structures play an important role in determining the modal behavior and lasing properties, the unavoidable metal-based nanostructure significantly increases the fabrication complexity. Cutting-edge bottom-up synthesis techniques [12, 13] enable the fabrication of various kinds of NWs with accurately controlled components, dimensions, and shapes. In this study, we analyze the guiding properties of an aligned NW pair formed by a gain NW and a metal NW, fabricated using bottom-up techniques, on a suspended dielectric substrate. We then propose a three-dimensional (3D) plasmonic Fabry-Pérot (FP) nanocavity composed of the NW pair (composed of silver and gallium nitride) truncated by two Ag-coated end facets that act as reflectors. The proposed nanocavity, which is based on the SPP modes at visible wavelengths around 450 nm, is suspended on a thin substrate of thickness t. The air gap distance d (between the two NWs) and thickness t are varied in later calculations under different metal NW radii rm and dielectric NW radii rGaN. We are particularly interested in the case of a thin substrate (t=5 nm) with low refractive index (ns=1.5) corresponding to a free-standing dielectric nanomembrane consisting of, for example, silicon dioxide (SiO 2). In this way, the bottom-up approaches for organic/inorganic nanomembranes [14, 15] may be further integrated with surface plasmonics to enable more functionalities. In addition, the substrate thickness affects the characteristics of the lasing modes. The SPP modes formed from strong coupling between the metal and dielectric NWs on thick substrates often feature substrate-mediated characteristics , which result in strong field enhancement at the interface between the substrate and metal region. The significant loss at the metal region and the low overlap with the gain region are therefore the main challenges for lasing. In contrast, hybrid plasmonic modes on a thin substrate often exhibit characteristics of dielectric NW-guided modes and lead to better confinement and lower modal loss. Except for the analysis of modal characteristics by two-dimensional (2D) finite-element method (FEM) [17, 18], we utilize 3D FEM to solve for the modal volume Vm and reflection field pattern. The orthogonality theorem of waveguide modes is applied to extract the modal reflectivity R. We also estimate the required cavity length L, quality factor QFP, and threshold gain gth necessary for the lasing action at the target wavelength of 450 nm.
In the following analysis of the plasmonic FP cavity, the resonance mode of an FP cavity is approximated as the standing wave corresponding to the specific transverse-guided mode. We performed 3D FEM to calculate the overall fields (both incident and reflected) inside the cavity. The modal reflection coefficients, relative phase shifts, and reflectivities R at the Ag reflectors are extracted from the orthogonality theorem . In order to sustain sufficient modal gain for lasing, we coated the waveguide with Ag layers of thickness 50 nm at the end facets. When compared to the configuration of bare waveguide/air interface, the Ag mirrors significantly increase the reflectivity and decrease the mirror loss. In addition to the reflectivity, the cavity length L is another relevant parameter for lasing. We deduced each cavity length that satisfies the FP round-trip phase-matching condition at the target wavelength. By collecting the information about material loss and mirror loss, we can reasonably estimate the quality factor QFP and threshold gain gth from the FP formulae [17–19].
In addition, we evaluated the quality factor Q of the configurations on substrates of two different thicknesses at a specific value of L in a more intuitive but computationally consuming way to verify QFP. In 3D FEM calculations, we excited the nanocavity with a -polarized plane wave. The spatial integration of the squared magnitude of the electric field (proportional to electric energy density) inside the gain region was then recorded when the wavelength was altered through resonance. The Q factor was solved from the ratio between the full width at half maximum (FWHM) and the peak resonance wavelengths of the corresponding lineshape. Finally, resolving the field distributions of the resonance modes enables us to determine the mode volume Vm.
Results and discussion
The hybrid plasmonic modes of the structure in Figure 1 are hybridized from the surface plasmonic guided modes of the metallic NW and the guided modes of the dielectric NW. According to , when a metallic cylinder is in the proximity of a plane, the guided modes TM 0 and HE ±1 are coupled and significantly mediated by the polarized charges on the surface of the planar structure. In the entire guiding structure, if a considerable amount of the field is distributed between the metallic region and substrate, the field may not sufficiently overlap with the dielectric NW. We hence explored the modal characteristics of the aligned NW pair with a sufficient air gap width d and two distinct substrate thicknesses t=5 and 500 nm. The coupling strengths of the fundamental hybrid modes between the two categories of modes are sensitive to variations in the NW radii, rGaN and rAg, and the width of the air gap d. Depending on the parameters, the features of each type of mode can be quite different.
We have proposed and analyzed a novel three-dimensional hybrid plasmonic Fabry-Pérot nanocavity with a metallic and dielectric nanowire pair on a thin substrate. We investigated the effect of the thin substrate on the fundamental hybrid plasmonic modes that exhibit ultrasmall mode areas. By using the finite-element method, we numerically solved for the guided modes of the hybrid plasmonic waveguide at a wavelength of 450 nm. The confinement factors, modal losses, and corresponding transparency thresholds of the guided modes on thin and thick substrates were explored for various wire radii. In comparison with the case of thick substrates (t=500 nm), we observed that for thin substrates (t=5 nm) with rAg=50 nm and rGaN=40 nm, the modal loss is lower by 10% and the waveguide confinement factor is larger by 50%. While the radii of the NW pair on the thin substrate are comparable, the fundamental hybrid plasmonic mode exhibits superior characteristics to achieve low material loss. To reduce the mirror loss, we additionally considered silver coatings at the two end facets as reflectors.The results show that the reflectivity is substantially enhanced when the substrate thickness is within the nanometer range because of better mode profile matching at the waveguide/reflector interface. Instead of increasing the reflectivity, an alternative solution to decrease the mirror loss is to increase the FP cavity length. At a coating thickness of 50 nm and a cavity length nearly equal to 4 μ m, the quality factor is above 100 and the threshold gain is lower than 1 μ m-1. The proposed nanowire-based plasmonic nanocavities on a free-standing nanomembrane are compatible with state-of-the-art bottom-up fabrication technology and could be attractive candidates for active photonic/surface plasmonic systems.
This work was sponsored by the Research Center for Applied Sciences, Academia Sinica, Taiwan and the Ministry of Science and Technology, Taiwan under Grant number MOST 102-2221-E-019-050. The authors would also like to memorize and be grateful to Professor Shun Lien Chuang at the Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, for his encouragements and fruitful discussions.
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