Plasmonic directional couplers using channel waveguides in random arrays of metal nanoparticles

: Plasmonic directional couplers based on channel waveguides embedded in random arrays of metal nanoparticles (NPs) operating in near-infrared are fabricated using electron-beam lithography and investigated experimentally characterizing their performance with leakage-radiation microscopy. The power exchange between coupled waveguides, its spatial period and efficiency, along with the overall power transmission, are determined in the wavelength range from 700 to 800 nm. We introduce a simple coupled-mode approach based on three coupled waveguides. The composite system considers a waveguide consisting of NP-filled stripe with characteristics distinctly different from those of the channel waveguides. Using this model, we describe the performance of investigated composite plasmonic configurations and obtain good qualitative agreement with experimental observations.


Introduction
Plasmon-based photonic, or simply plasmonic devices represent, in general, nano-optical components that are designed to generate and detect, guide and control surface plasmonpolariton (SPP) modes.The intrinsic characteristic of SPP modes to be confined in subwavelength volumes persists to be one of the main motivations for their study [1].A substantial amount of plasmonic devices, with many diverse functions and geometries, have been proposed, designed, and characterized in the past decade.Dielectric-loaded waveguides [2,3], channel and slot waveguides [4,5], nano-lenses [6,7], antennas [8,9], and plasmonic metamaterial components [10], are just a few examples of a long list of recently developed plasmonic devices with different purposes, which include multiplexing [11], beam splitting [12], filtering [13], nano-focusing [7], and directional coupling [14], among others.
Optical directional couplers (ODCs) consist of two or more closely-located optical waveguides, whose modes can couple evanescently and thereby exchange their powers, realizing, under certain conditions, complete power transfer between waveguides [15].In general, ODCs with weakly-coupled waveguides can equivalently be viewed as independent waveguides with mode power exchange due to their coupling or as a single composite (multimode) waveguide structure, in which the power distribution across the structure varies with the propagation due to the mode interference [15,16].Plasmonic directional couplers (PDCs) have also been explored in several configurations based on different coupling schemes and functions.Efficient power transfer and switching has been demonstrated in PDCs based on long-range plasmonic waveguides at telecom wavelengths [17][18][19][20], hybrid waveguide systems [21], slot metal-insulator-metal waveguides [22], and dielectric-loaded waveguides [23].
#367360 https://doi.org/10.1364/OE.27.022753In this work, we consider a completely new alternative for the PDC design, which is based on two channel waveguides embedded in random arrays of metal nanoparticles (NPs) separated by a stripe filled also with NPs.The proof of concept for this type of waveguides was investigated in the previous work with straight waveguides, bends and splitters being designed and experimentally characterized [24].The fundamental idea behind such structures is that the NP-free channels support plasmonic guided modes, while the SPP propagation through random and strongly interacting NPs is prohibited due to the SPP elastic multiple scattering resulting in the SPP localization [25][26][27][28].In a recent study, the effect of multiple scattering of SPPs produced by random arrays of NPs has demonstrated to be able to maximize the deliverable number of input-to-output plasmonic channels for improved performance in optoelectronic devices by exploiting the decorrelation of SPP modes [29].In the configuration presented here, the occurrence of coupling between two NP-free channels implies SPP transmission through the stripe of randomly positioned NPs.Surprisingly, the interpretation of experimental observations led us to assume that the NP stripe acts as a third waveguide that mediates the coupling between SPP modes supported by NP-free channels.Using a simple coupled-mode approach based on three coupled waveguides, we describe the performance of investigated composite plasmonic configurations obtaining good qualitative agreement with the experimental observations.

Materials and methods
The structures were fabricated using standard electron-beam lithography (EBL) and lift-off patterning.First, a 70-nm-thick gold film was deposited on top of a 0.17-mm-thick silica substrate.The lithographic mask consisted of a thin film of polymethyl-methacrylate (PMMA) spin-coated over the gold film, which acted as a positive resist.Then, the sample was patterned using the EBL process for subsequent development.A second evaporation process was performed to fabricate the cylindrical gold NPs, to finally remove the mask, and thus completing the lift-off process.The PDCs consisted of a pair of 2-μm-wide NP-free channel waveguides enclosed by a relatively high-density array of gold NPs (~75 per square micron).The design height and width of the NPs was set to h = 70 nm, and w = 50 nm, respectively.The particles were randomly distributed over the designed areas on top of the gold film [Figs.1(a) and 1(b)].The PDCs are composed of two parallel waveguides separated by a 500-nm-wide stripe filled with NPs.It is important to mention that the ND-filled stripe has also a random distribution and that it serves as the coupling mechanism for this specific device.The separation distance between the two plasmonic waveguides was chosen following the experimental characterization conducted for different widths of the NP-filled stripe [see Appendix A].The best coupling occurred for a separation distance of 500 nm.The interaction length L of the PDCs consists of the longitudinal distance where the two waveguides are in close proximity to each other, and where the power transfer takes place.The fabricated structures had L varied from 12 to 18 μm.The excitation of SPPs was performed using single metallic (gold) ridge, placed at 5 μm from the PDC; where a tapered channel was added to reduce the coupling losses [Fig.1(b)].
The characterization of the samples was performed using leakage-radiation microscopy (LRM) and postprocessing image analysis in the wavelength interval from 700 to 800 nm.The basic setup and principle of operation of the LRM setup can be found in [30].Our light source consisted of a tunable continuous-wave Ti:Saphire laser (SpectraPhysics 3900S), where the laser beam was linearly polarized and focused onto the sample using a 20x objective.The leakage radiation was collected using a 63x oil-immersion objective, which has a numerical aperture NA = 1.25; sufficient to collect the leakage radiation of the SPP modes propagating at a gold-air interface.The power distribution of the SPPs was monitored using a charge-coupled device (CCD) camera in the image plane of the microscope, and the intensity profiles were extracted from the captured digital images.
While we observed clear signs of power redistribution along the propagation, and the coupling region was clearly long enough to sustain power transfer oscillations, the power transfer was never complete [Fig.1(c)].Looking for the simplest approach to model this (unexpected) feature, we realized that one should either assume one of the two following possibilities: (1) that the two coupled waveguides (nominally of the same width) have very different propagation characteristics destroying the phase-matching of coupled SPP modes, or (2), considering the NP stripe as a third waveguide (with characteristics distinctly different from those of the channel waveguides) mediating the coupling between SPP modes supported by NP-free channels.The latter seems better fitting to the expectations and experimental observations

Three-waveguide directional-coupler model
The coupling arrangement investigated in this work was thereby considered using a threewaveguide coupled-mode approach with the PDC fields being represented by normal modes of three individual waveguides that are coupled with each other [Fig.2(a)].The coupled differential equations can be expressed in a matrix form as follows: .
The field distributions of the j-th waveguide are denoted here as A j (z), as well as the corresponding wavevectors β j (j = 1, 2, 3), where z is the propagation direction.The interaction between the waveguides is determined by the coupling coefficients κ jk (j ≠ k = 1, 2, 3), which describe strength of the coupling from the j-th to the k-th waveguide.For most symmetrical systems, κ jk = κ kj , therefore we used such criterion for this model.Waveguides 1 and 3 are treated as the direct and the adjacent channel waveguides, respectively, and their wavevectors are assumed to be equal (β 1 = β 3 = β c ), since the geometrical parameters are, at some extent due to the randomness, the same.Waveguide 2 corresponds to the array of random NPs between the channels (β 2 = β r ).The degrees of freedom associated to the coupling coefficients was decreased by assuming that the coupling from the channel modes to the random N coupling betw be rewritten w The system finding the ei propagation c conditions.A in [15].For s where k 0 = 2π We tested [Figs.2(b)-2( obtained from 1.09 to 1.12 wavelength in as well as the experimental

Analysis
The character we discuss the from 700 to 8 to the NP-fill longer wavele the adjacent w there is a hig excited at sho applying the enhancement that directiona From simple wavelengths.important fea adjacent wave filled stripe an

Transmis
The transmiss the input port the intensity increase for la transfer from the structures coupling) [Fi characterized the direct w complement there was a m down to 70%,

Beating p
The beating p averaging the was generally were averaged gave an avera wavelength [F the mode effe the array prod estimate of th using the mo estimation of from 700 to 8 It is worth as the ones composed of

Fig. 1 .
Fig. 1.(a) Schematic design of the plasmonic directional coupler and (b) scanning electron microscopy (SEM) image showing the principal waveguide (1) and the coupling channel, or adjacent waveguide (2) surrounded by the random array of metallic nanoparticles (NPs).The interaction length is denoted here as L. The inset in (a) corresponds to an SEM amplification image that shows the individual NPs which constitute the array.(c) Saturated leakage radiation microscopy image of a plasmonic directional coupler with L = 18 μm illuminated at a wavelength λ 0 = 780 nm.The position of the input and output ports (A and B) are indicated with white arrows.
Fig. 2 distrib region wavel nm. ( (Im[n The main distribution [F Fig. 3 that p wavel transp waveg experiThe struct performed me to the mode c Fig. 6 direct and m structu Fig. 7 The b measu functi The c5. ConclusioIn summary, embedded in Fig. 8 width image structu Funding Consejo Naci Council; Villu