Polaritonic hybrid-epsilon-near-zero modes: beating the plasmonic

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Polaritonic hybrid-epsilon-near-zero modes: beating the plasmonic confinement vs. propagationlength tradeoff with doped cadmium oxide bilayers Evan L. Runnerstrom, Kyle P Kelley, Thomas Folland, Joshua Ryan Nolen, Nader Engheta, Joshua D Caldwell, and Jon-Paul Maria Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.8b04182 • Publication Date (Web): 24 Dec 2018 Downloaded from http://pubs.acs.org on December 25, 2018

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Polaritonic hybrid-epsilon-near-zero modes: beating the plasmonic confinement vs. propagation-length tradeoff with doped cadmium oxide bilayers Evan L. Runnerstrom1†, Kyle P. Kelley1†, Thomas G. Folland2, J. Ryan Nolen2,3, Nader Engheta4, Joshua D. Caldwell2*, Jon-Paul Maria1,5*

Department of Materials Science and Engineering, North Carolina State University, Raleigh, NC 27695 2 Department of Mechanical Engineering, Vanderbilt University, Nashville, TN 37212 3 Interdisciplinary Materials Science Program, Vanderbilt University, Nashville, TN 37212 4 Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA 19104 5 Department of Materials Science and Engineering, The Pennsylvania State University, University Park, PA 16802 † These authors contributed equally to this work * To whom correspondence should be addressed: [email protected]; [email protected] 1

Abstract: Polaritonic materials that support epsilon-near-zero (ENZ) modes offer the opportunity to design light-matter interactions at the nanoscale through extreme subwavelength light confinement, producing phenomena like resonant perfect absorption. However, the utility of ENZ modes in nanophotonic applications has been limited by a flat spectral dispersion, which leads to small group velocities and extremely short propagation lengths. Here, we overcome this constraint by hybridizing ENZ and surface plasmon polariton (SPP) modes in doped cadmium oxide epitaxial bilayers. This results in strongly coupled hybrid modes that are characterized by an anti-crossing in the polariton dispersion and a large spectral splitting on the order of 1/3 of the mode frequency. These hybrid modes simultaneously achieve modal propagation and ENZ mode-like interior field confinement, adding propagation character to ENZ mode properties. We subsequently tune the resonant frequencies, dispersion, and coupling of these polaritonic-hybrid-epsilon-near-zero (PH-ENZ) modes by tailoring the modal oscillator strength and the ENZ-SPP spectral overlap. PH-ENZ modes ultimately leverage the most desirable characteristics of both ENZ and SPP modes, allowing us to overcome the canonical plasmonic tradeoff between confinement and propagation length. Keywords: Epsilon-near-zero, surface plasmon, strong coupling, mode confinement, infrared, nanophotonics, epitaxy.

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Extraordinary light-matter interactions become possible when the effective dielectric permittivity of a material vanishes. Such epsilon-near-zero (ENZ) phenomena occur near the frequency where the real part of the dielectric function changes sign and are characterized by electromagnetic modes with light wavelengths and phase velocities in the ENZ medium diverging toward infinity, along with decoupled spatial and temporal electromagnetic fields.1,2 Harnessing this behavior has recently become a major objective in nanophotonics research; examples include total light absorption and concentration in deeply sub-wavelength thin films,3-6 length-invariant antenna resonances,7 wave-front engineering,8 controlled thermal emissivity,9,10 and extraordinary transmission by supercoupling.11 Practically, an ENZ condition can be realized in any material or system where the real part of the effective dielectric function passes through zero, and thus occurs naturally in materials such as doped semiconductors4,6,12 and polar crystals.13-17 Thin layers of these materials can support polaritonic “ENZ modes”, which strongly confine light and electric fields within the interior of deeply sub-wavelength films, leading to resonant perfect absorption and a photonic density of states diverging towards infinity.2-5 ENZ modes have the distinguishing and related characteristic of being nearly dispersion-less, as their resonant energy does not change significantly with the longitudinal component of the incident wavevector. Consequently, ENZ modes have a very low group velocity: in fact, a perfect ENZ material (lossless and unbound) cannot transmit energy or information.2 While propagating ENZ behavior can be engineered within artificially structured metamaterials,1,2,18,19 such metamaterials often use metallic components that suffer high optical losses and/or require complicated and laborious fabrication procedures.19 These shortcomings motivate our goal to engineer low-loss natural ENZ modes using simple, coupled-layer structures in order to induce propagation, manipulate the modal dispersion, and control operating frequencies in nanophotonic devices that exploit ENZ behavior.

Doped semiconductors naturally sustain spectrally tunable ENZ behavior near the screened plasma frequency, especially in the infrared (IR).6,12,20 However, when most materials are doped to resonate at energies of interest in the near- to mid-IR, they suffer a steep drop in carrier mobility due to ionized impurity scattering. This prohibitively increases optical losses. Doped cadmium oxide (CdO) is an important exception, as thin films are shown to support low-loss plasmonic modes over a broad spectral range pursuant to tunable carrier concentrations that range from 1019 to 1021 e-/cm3 while maintaining carrier mobilities over 300 cm2/V·s (peak values >500 cm2/V·s).6,21,22 Optically, CdO supports tunable, low-loss surface plasmon polaritons (SPPs) and ENZ modes over the entire mid-IR.6,21 However, as discussed above, low group velocities limit the implementation of ENZ films in applications such as waveguide design, where some of the extraordinary behaviors would be most beneficial. Conversely, SPP modes propagate at much faster group velocities, but the strong interfacial confinement renders them highly sensitive to surface morphology and carrier scattering losses.23 Here, we demonstrate a strategy to simultaneously overcome the shortcomings of SPP and ENZ modes by coupling SPP and ENZ resonances into a new class of hybrid modes within a monolithic bilayer system.

Coupling between photonic and/or electronic states24-26 occurs when the two constituent states interact with sufficient strength to form a hybrid system where energy is exchanged between the states more quickly than it decays out of the system. Such a coupling interaction between two degenerate energy states changes the spatial and spectral dispersion of the two modes and causes the modes to repel, resulting in ACS Paragon Plus Environment

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symmetric and antisymmetric modes with a well-defined splitting in energy (analogous to the vacuum Rabi splitting).27 Notably, this changes the properties of both modes and strongly modifies the microscopic behavior of the hybrid mode. Well-known examples include coupling between high-quality optical resonators and excitons in dye molecules, J-aggregates, and quantum dots,27-30 split-ring resonators coupled to plasmonic modes,4,26 and vibrational states coupled to optical cavities.31-34 Herein, we demonstrate analogous, cavity-free, and tunable strong coupling between SPP and ENZ modes in homoepitaxial CdO ENZ-on-SPP bilayers. The coupling is characterized by a very large spectral splitting that is on the order of the mode frequency itself. The result is a hybrid of both SPP and ENZ modes that combines the high field confinement and minimal phase variation characteristics of an ENZ mode with the modal propagation of an SPP mode. We call this hybrid mode a polaritonic-hybrid-epsilon-near-zero or “PH-ENZ” mode. We further demonstrate that the strong coupling in PH-ENZ modes is highly tunable by varying either the carrier concentration and/or thickness of the individual layers. This work identifies and explores the benefits of combining ENZ modes with SPP behavior in propagating nanophotonic systems built around the concept of monolithic metamaterial structures.

In the following, we investigate a series of ENZ-on-SPP bilayers to explore ENZ-SPP hybridization. All of the bilayer structures studied here commonly contain a 300 nm-thick indium-doped CdO (In:CdO) heteroepitaxial layer grown on r-plane sapphire using reactive high-power impulse magnetron sputtering (R-HiPIMS, see SI for detailed description of growth, including structural characterization in Fig. S1). This In:CdO layer, hereafter referred to as the “SPP layer”, has an electron concentration of 2.5x1020 e-/cm3, a mobility of 375 cm2/V·s, and exhibits strong wavevector-dependent absorption due to polaritonic dispersion across the mid-IR when probed using the Kretschmann configuration. These reflectance measurements exhibit the typical asymptotic dispersion 𝑘𝑘 [𝑘𝑘 = 𝑛𝑛prism sin(𝜃𝜃)] characteristic of an SPP mode (Fig. 1a). When the film thickness is 0

reduced well below the optical skin depth of In:CdO, the SPP modes at the top and bottom film interfaces hybridize into the well-known long- and short-range (symmetric/high energy and anti-symmetric/low energy) SPP modes. In the extremely thin limit (about 50× smaller than the plasma wavelength),4 the dispersion of the symmetric mode is asymptotically pinned along the light line and the screened plasma frequency, resulting in a nominally flat spectral dispersion near the ENZ condition and confinement of the electric field to the film interior: this is the ENZ mode.5,6 We observe ENZ mode behavior in the dispersion relation for a 100 nm-thick In:CdO layer (the “ENZ layer”, Fig. 1b) doped to 8.1x1019 e-/cm3 (µ=400 cm2/V·s). Comparing the spectral dispersions of SPP and ENZ modes side by side in Fig. 1a-b leads to a natural question: given their very strong overlap in frequency, momentum and space, how will these SPP and ENZ modes interact when placed in direct proximity? Here, we address the three components of this question through homoepitaxial growth of a bilayer structure comprised of an ENZ layer on top of an SPP layer (identical thicknesses and carrier densities as in the isolated cases, see insets of Fig. 1a-c), which dramatically modifies the spectral dispersion (Fig. 1c). We emphasize that bilayer growth requires no lithography, patterning, or other micro-/nanofabrication.


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Figure 1: a) IR reflectivity spectral map (Kretschmann configuration) of a bare SPP mode. Inset: geometry/electron concentration of the SPP layer. b) Reflectivity map of a bare ENZ mode. Inset: geometry/electron concentration of the ENZ layer. c) Reflectivity map of a coupled PH-ENZ mode, with the coupling point and splitting energy noted. Inset: geometry/electron concentration of the bilayer. d) Theoretical dispersion curves of coupled upper/lower branches (thick blue/red lines) resulting from strong coupling between bare SPP/ENZ dispersion curves (dashed orange/green lines). e) Simulated (transfer matrix method) reflectivity map of the coupled ENZ-on-SPP bilayer. f) Simulated (CST) reflectivity map of the coupled ENZ-on-SPP bilayer. g) Calculated propagation lengths for the experimental SPP dispersion in part (a), the experimental ENZ mode in part (b) the experimental coupled modes in part (c), and the simulated coupled modes in part (f). h) Aggregate figure of merit (propagation length times confinement factor) for the experimental SPP, ENZ, and upper/lower branch PH-ENZ modes. Note: reflectivity maps plot R= Rp/Rs (the ratio of reflected p-polarized to s-polarized light) on the color axis, energy (wavenumbers) on the y-axis, and the film-parallel component of incident wavevector (normalized by k0=ω/c at each frequency) on the x-axis. See Fig. S2 for a comparison between angle, wavevector, and normalized wavevector for the dispersion relation plotted in part (c).

This cavity-free bilayer sample exhibits clear anti-crossing between the ENZ and SPP modes (Fig. 1c), splitting into upper and lower branches that acquire dispersive character over a significant portion of the measured spectral range. The anti-crossing occurs at the spectral location where the ‘bare’ ENZ and SPP modes are tuned to cross (see Fig. 1d), which opens up a spectral transparency window. This signature of strong coupling produces a 717 cm-1 spectral splitting (Fig. 1c and 1d). To confirm this interpretation, we model strong coupling between an ENZ and SPP mode using the following expression:27,29 UB,LB 𝐸𝐸coupled (𝑘𝑘𝑥𝑥 )

1

𝐸𝐸SPP (𝑘𝑘𝑥𝑥 ) + 𝐸𝐸ENZ (𝑘𝑘𝑥𝑥 ) 1 2 2 2 = ± �ΩR + �𝐸𝐸SPP (𝑘𝑘𝑥𝑥 ) − 𝐸𝐸ENZ (𝑘𝑘𝑥𝑥 )� � (1) 2 2

UB,LB where 𝐸𝐸coupled (𝑘𝑘𝑥𝑥 ) is the dispersion relation of the coupled upper and lower branches (UB/LB), 𝐸𝐸SPP (𝑘𝑘𝑥𝑥 ) is the dispersion relation of the uncoupled SPP mode,35 𝐸𝐸ENZ (𝑘𝑘𝑥𝑥 ) is the dispersion relation of the uncoupled ENZ mode,36 and ΩR is the splitting energy.37 This model is presented in Fig. 1d and quantitatively matches our experimental results well,


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supporting our interpretation that a hybrid PH-ENZ mode evolves through polaritonic strong coupling. Qualitatively, this behavior can be described as follows (Fig. 1d): distinct upper and lower branches result from this coupling and the associated spectral splitting at the intersection of the bare SPP and bare ENZ dispersion curves. At the coupling point, the UB (LB) is associated with a hybrid symmetric (antisymmetric) PH-ENZ mode that has both SPP and ENZ character. Spectrally removed from the coupling point, the UB and LB asymptotically approach the bare SPP and bare ENZ dispersion curves, respectively, and the mode profiles primarily adopt the behavior of the asymptote to which the branch is closest. In addition to the clear anti-crossing observed, strong coupling requires that the following inequality is satisfied:27,29 1 (𝛾𝛾 + 𝛾𝛾ENZ ) (2) 2 SPP where 𝛾𝛾SPP and 𝛾𝛾ENZ are the damping frequencies of the SPP and ENZ layers, respectively. This implies that the two modes share resonant energy at a rate faster than their average decay rate: our coupled system (Fig. 1c) clearly meets this criterion, with ΩR = 717 cm-1 , 𝛾𝛾SPP = 550 cm−1, and 𝛾𝛾ENZ = 400 cm−1 . This underscores the point that using high mobility In:CdO as the low-loss building block for our bilayers is a critical prerequisite for realizing strong coupling in such a bilayer polaritonic system. Note that the splitting energy is greater than ¼ of the resonant energy at the coupling point (2580 cm-1), which arguably qualifies this effect as ultra-strong coupling (where strong coupling is defined as spectral splitting greater than the mode linewidth, and ultra-strong coupling is defined as spectral splitting having the same order of magnitude as the resonant energy).27 ΩR >

We are also able to accurately simulate the hybrid PH-ENZ mode of this same ENZ-onSPP bilayer using two different computational methods, a MATLAB-based transfer matrix method (TMM, Fig. 1e) and a commercial finite-element technique (CST Studio, Fig. 1f). Good quantitative agreement between our simulations and the experimental results demonstrates the utility of both TMM and CST simulations for interpreting the physical attributes of PH-ENZ modes. We further calculate the frequency-dependent imaginary part of the wavevector of the coupled system (Fig. S3) to gain insight into the loss and propagation characteristics of coupled PH-ENZ modes. This reveals that PH-ENZ modes have non-negligible propagation lengths on the order of 5 – 40 µm (Fig. 1g), which are comparable to the SPP propagation lengths and up to two orders of magnitude larger than the ENZ propagation lengths (0.1 – 0.15 µm) at the same frequencies. Finally, we define and calculate an aggregated figure of merit (Φ) for PH-ENZ modes by multiplying the propagation length by the confinement factor: ∫bilayer�𝐸𝐸𝑧𝑧 𝐻𝐻𝑦𝑦 �𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 1 Φ = 𝐿𝐿 × Γ = (3) 2Im(𝑘𝑘𝑥𝑥 ) ∫∞ �𝐸𝐸𝑧𝑧 𝐻𝐻𝑦𝑦 �𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 −∞

where Im(𝑘𝑘𝑥𝑥 ) is the imaginary component of the wavevector in the longitudinal/in-plane direction, 𝐸𝐸𝑧𝑧 is the transverse/out-of plane component of the electric field, and 𝐻𝐻𝑦𝑦 is the in-plane component of the magnetic field orthogonal to 𝑘𝑘𝑥𝑥 and 𝐸𝐸𝑧𝑧 . The confinement factor Γ is easily calculated by summing �𝐸𝐸𝑧𝑧 𝐻𝐻𝑦𝑦 � (calculated at discrete points using CST) over all points within the SPP-ENZ bilayer and dividing by the sum of �𝐸𝐸𝑧𝑧 𝐻𝐻𝑦𝑦 � over all points in the simulation.38 This analysis (Fig. 1h and Table 1) underscores the novel behavior of PHENZ modes, which combine SPP-comparable propagation lengths with ENZ-comparable confinement factors to achieve Φ values 5 – 17× higher than SPP modes. This ‘confined ACS Paragon Plus Environment

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propagation’ overcomes the characteristic plasmonic tradeoff between high confinement and long propagation, providing a new paradigm for integrating ENZ-mode behavior within waveguide-based nanophotonics. Table 1: Representative confinement factors and propagation lengths in ENZ, SPP, and PH-ENZ modes

Mode energy Propagation length L

Confinement factor Γ Figure of merit Φ

ENZ mode

SPP mode (low w)

PH-ENZ mode (LB)

19.0 µm

17.2 µm

2450 cm-1

2500 cm-1

0.19

0.0075

0.14 µm 0.03

0.03

SPP mode (high w)

PH-ENZ mode (UB)

2.6 µm

4.8 µm

2200 cm-1

3820 cm-1

0.046

0.14

0.79

0.48

Confinement Strong Propagation, Moderate Confinement, vs. confinement, no confinement low propagation? no propagation confinement with propagation propagation

3330 cm-1 0.19 0.91

Strong confinement and propagation.

To further understand PH-ENZ mode tunability, we grew a number of ENZ-on-SPP bilayers with systematically decreasing carrier concentration in the 100 nm-thick ENZ layer, effectively tuning or detuning the SPP-ENZ interaction and spectral overlap. Our experimental (top row) and calculated (bottom row) spectra are provided in Fig. 2 a-d and demonstrate that changing the plasma frequency of the ENZ layer directly controls the spectral overlap and coupling between the ENZ and SPP dispersions. As expected, when the ENZ layer has a much higher electron concentration than the SPP layer, there is no spectral overlap between the two dispersion relations and little to no coupling results (Fig. 2a). As the carrier density decreases, the ENZ condition spectrally approaches the asymptote of the SPP dispersion, which occurs in this system once the carrier concentration of the ENZ layer drops to ~1.5x1020 e-/cm3 (Fig. 2b). At this point, ENZSPP hybridization occurs. As the electron concentration continues to decrease, the spectral overlap and the coupling point shift to lower energy and wavevector (Fig. 2c,d). We note that tuning in this experiment is made specifically possible by the tunable carrier concentrations of In:CdO. Although similar ENZ-based polaritonic coupling behavior has been observed polar dielectric heterostructures,17 coupled modes in phonon-based polaritonic systems are limited to material-specific phonon frequencies and are thus not broadly or easily tunable without changing the material system. Here, tunability is easily achieved by controlling the carrier concentration of the CdO ENZ layer through doping, and dynamic tuning of PH-ENZ modes could, in principle, be realized through electrostatic/electrochemical gating39,40 and/or ultra-fast optical pumping approaches,41-43 as was recently demonstrated for localized surface phonon polariton nanostructures42 and for In:CdO ENZ layers.43 Such an approach could allow for dynamic tuning and/or multiplexing in PH-ENZ-based nanophotonic waveguide modulators: the thin ENZ layer could be manipulated with optical pulses or applied fields, moving the spectral splitting window to transmit or block travelling waves. Controlling the ACS Paragon Plus Environment

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dispersion in this way could also be used to selectively transmit, block, or reroute components of optical signals multiplexed between UB and LB PH-ENZ modes.

Figure 2: Tuning PH-ENZ modes by changing electron concentration in the ENZ layer. Top row: experimental IR reflectivity maps. Bottom row: TMM simulations. a) ENZ layer electron concentration: 3.5x1020 e-/cm3. b) ENZ layer electron concentration: 1.5x1020 e-/cm3. c) ENZ layer electron concentration: 9.5x1019 e-/cm3. d) ENZ layer electron concentration: 4.0x1019 e-/cm3. The ENZ layer is 100 nm thick. The SPP layer is 300 nm thick and has an electron concentration of 2.5x1020 e-/cm3. The bare SPP and ENZ frequencies are denoted as dashed lines for reference.

A second critical element that controls coupling is the oscillator strength of the constituent modes. This can be readily tuned by changing the ENZ layer thickness at a constant carrier density: as the thickness changes, so will the magnitude of the electric field overlap integral that determines the spectral splitting in the hybrid dispersion. For this experiment, we grew two additional ENZ-on-SPP bilayers, comparable to that in Fig. 2b, but one with an 80 nm-thick ENZ layer and the second with a 20 nm-thick ENZ layer, each with a carrier density of 1.5x1020 e-/cm3. Experimental dispersion relationships (Fig. 3a,d) of these bilayers show a clear and systematic decrease in the spectral splitting between the UB and LB as the ENZ layer thickness is reduced. Once again, both TMM (Fig. 3b,e) and CST simulations (Fig. 3c,f) capture this behavior.


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Figure 3: Tuning PH-ENZ modes in ENZ-on-SPP bilayers by changing ENZ layer thickness. a) Experimental IR reflectivity map of an ENZ-on-SPP bilayer with an 80 nm thick ENZ layer. Inset: geometry/electron concentration of the bilayer. b) Simulated (TMM) reflectivity map of the structure in the inset of (a). c) Simulated (CST) reflectivity map of the structure in the inset of (a). d) Experimental IR reflectivity map of an ENZ-on-SPP bilayer with a 20 nm thick ENZ layer. Inset: geometry/electron concentration of the bilayer. e) Simulated (TMM) reflectivity map of the structure in the inset of (d). f) Simulated (CST) reflectivity map of the structure in the inset of (d). The asterisks denote the points simulated in Figure 4.

To investigate how hybridization influences the near-field behavior of PH-ENZ modes, we use CST simulations to visualize the optical modes and electric field profiles of the 20 nm ENZ / 300 nm SPP bilayer at discrete points along the dispersion branches labeled a-f in Fig. 3f. These field profiles (electric field magnitude in the transverse/film normal/zdirection) and Poynting vectors are provided in Fig. 4a-f, where each specific panel corresponds to the position in Fig. 3f of the same letter label. The corresponding longitudinal/x-direction electric field profiles are provided in Fig. S5a-f. We analyze this particular structure because the regions of the dispersion relationship where both the UB and LB exhibit evidence of strong coupling (Fig. 4b,e) are clearly delineated from the regions where the modes are uncoupled (Fig. 4a,d) and/or weakly coupled (Fig. 4c,f).


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Figure 4: Electric field/mode profiles of the ENZ-on-SPP bilayer simulated in Figure 3f (see structure in Figure 3d inset). The maximum field amplitude and Poynting vector amplitude is denoted for each profile. a) Uncoupled upper branch mode profile (point a in Fig. 3f) with predominant ENZ character. Detail view: Field confinement within the 20 nm ENZ layer with low propagation. Poynting vector field is overlaid in all detail views. b) Strongly coupled upper branch PH-ENZ mode profile (point b in Fig. 3f) with hybrid ENZSPP behavior. The field profile is symmetric/in phase. Detail view: Symmetric simultaneous field confinement within the ENZ layer and evanescent decay into the free space above with propagation in the ENZ layer and at the bilayer surface. c) Uncoupled upper branch mode profile (point c in Fig. 3f) with predominant SPP character. Detail view: Evanescent field decay into free space and into the bulk of the SPP layer. d) Uncoupled lower branch mode profile (point d in Fig. 3f) with predominant SPP character. Detail view: Evanescent field decay into free space, with the propagating mode confined to the bilayer surface. e) Strongly coupled lower branch PH-ENZ mode profile (point e in Fig. 3f) with hybrid ENZ-SPP behavior. This field profile is antisymmetric/out of phase. Detail view: Antisymmetric simultaneous field confinement within the ENZ layer and evanescent decay into the free space above, with ENZ layer propagation in the opposite direction as at the bilayer surface. f) Uncoupled lower branch mode profile (point f in Fig. 3f) with


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predominant ENZ character. Detail view: Field confinement and low propagation within the 20 nm ENZ layer. Note that, while the mode profiles in the pairs of panels a/d, b/e, and c/f are simulated for the same kx/k0, the actual kx for each panel is unique due to the normalization factor k0, which is unique at each frequency. Hence, the mode profile periodicity (proportional to non-normalized kx) is slightly different in each panel.

At low wavevectors, the SPP and ENZ modes have sufficient spectral separation to limit significant coupling. Thus, we anticipate that these positions along the UB (Fig. 4a) and LB (Fig. 4d) should largely resemble the uncoupled ENZ and SPP modes, respectively. Indeed, the electric fields in Fig. 4a are largely confined within the 20 nm thick ENZ layer, as in an uncoupled ENZ mode. Likewise, the power flow (Poynting vector) is largely confined within the ENZ layer and the magnitude of the energy flux is low. In contrast, the LB at this wavevector (Fig. 4d) exhibits an optical mode that is confined at the bilayer surface with electric fields that evanescently decay into the surrounding medium, resembling an uncoupled SPP mode. For this SPP-like mode, the Poynting vector is directed along the bilayer surface and in the surrounding medium with correspondingly long propagation.

As the two branches converge and reach the anti-crossing point, they couple strongly. Here (Fig. 4b,e for the UB and LB, respectively), the modal profiles simultaneously resemble ENZ and SPP modes. In the UB (Fig. 4b), the symmetric PH-ENZ mode exhibits strong field confinement within the ENZ layer with simultaneous evanescent decay into the surrounding medium. The power flow is significantly modified, with the energy flux distributed throughout the ENZ layer and surrounding medium, and, to a small extent, the SPP layer. Importantly, power flow is greatest within the ENZ layer itself and is more than three times greater in PH-ENZ mode than in the comparable ENZ-like mode (compare Fig. 4a and 4b detail views). We calculate propagation lengths on the order of 5 – 10 µm (Fig. 1g) for this coupled PH-ENZ mode in the upper branch, thanks to the induced spectral dispersion and the fact that the electric fields are no longer entirely confined to the ENZ layer. The lower branch (Fig. 4e) consists of the anti-symmetric PHENZ mode, which again exhibits simultaneously strong evanescent fields and field confinement within the ENZ layer, but with the fields in the two layers out of phase. Here, the energy flux is again mostly confined within the ENZ layer. Because of the larger maximum Poynting vector magnitude, propagation distances are higher for this antisymmetric PH-ENZ mode (Fig. 1g).

Finally, at wavevectors well above the strong coupling point (Fig. 4c,f), the UB, which initially began with ENZ character, transitions to SPP-like behavior (Fig. 4c), while the opposite is observed in the LB, where the original SPP character transitions to ENZ behavior with limited power flow and slow propagation (Fig. 4f). Interestingly, the UB at high wavevectors exhibits electric field decay into the CdO SPP layer and substrate (Fig. 4c); because of the low carrier densities (relative to metals) employed here, the skin depth at these frequencies is on the order of hundreds of nanometers to microns,6 so the SPP-like mode can decay into both the dielectric ambient as well as into the CdO film itself.

We conclude our investigation with additional TMM simulations to thoroughly characterize how the tuning parameters influence coupling and the strength of spectral splitting in ENZ-on-SPP bilayers. To do so, we simulate the reflectivity spectra for bilayers with varying ENZ layer carrier concentration and thickness and determine the splitting by finding the smallest UB/LB peak separation. Fig. 5a displays the results of this analysis, with the splitting plotted against the detuning energy, which is defined here as the difference in plasma frequency between the SPP and ENZ layers. Two trends are ACS Paragon Plus Environment

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immediately apparent. First, the splitting is maximized at detuning energies ranging from 2000 – 4000 cm-1, which corresponds to ENZ layer carrier concentrations of 1 – 1.5×1020 e-/cm3. As seen above, this detuning energy is consistent with the strongest overlap of the bare ENZ and SPP dispersion curves (SPP layer: 2.5x1020 e-/cm3, 300 nm), and the splitting energy reaches 1/3 of the PH-ENZ mode energy. The slight shift of the splitting maximum to higher detuning energies with ENZ layer thickness is likely the result of the increasing thickness changing the effective dielectric constant ‘felt’ by the SPP layer via the effective medium approximation, which suppresses the bare SPP dispersion curve and requires a slightly lower ENZ layer carrier concentration for maximum overlap. The second clear trend is that the splitting monotonically and categorically increases with ENZ layer thickness/oscillator strength as predicted (Fig. 5b). The fact that the ENZ layer carrier concentration so strongly influences the spectral splitting even for very thin (10 – 50 nm) ENZ layers, which would be more easily modulated, indicates that dynamic control of the electronic properties of the ENZ layer will enable actively tunable PH-ENZ modes and nanophotonic waveguides.


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Figure 5: TMM simulations of coupling and spectral splitting for a wide range of ENZ layer electron concentration and ENZ layer thickness. a) PH-ENZ mode spectral splitting vs. detuning energy, which is defined as the difference between the SPP layer’s plasma frequency and the ENZ layer’s plasma frequency. Experimental results (filled circles) for ENZ-on-SPP bilayers with 100 nm thick ENZ layers are included for comparison. b) PH-ENZ mode spectral splitting vs. ENZ layer thickness. The ENZ carrier concentration is set at 1.5x1020 e-/cm3. Experimental results (filled circles) are included for comparison.

We have demonstrated that ENZ-on-SPP bilayer In:CdO structures exhibit characteristics of (ultra-) strong coupling as indicated by strong spectral splitting of the constituent dispersion curves: the experimentally observed splitting can reach 1/3 of the incident field energy. The resulting hybrid SPP-ENZ modes, or PH-ENZ modes, combine the most attractive features of SPP and ENZ modes by simultaneously achieving increased group velocity and electric field confinement within the bilayer, thereby beating the canonical plasmonic tradeoff between confinement and propagation. PH-ENZ modes concentrate propagating electromagnetic energy within the plasmonic bilayer at ENZ frequencies, which is impossible to achieve with more typical plasmonic bilayers like Ag metalinsulator-metal structures. This unique feature means that our bilayers can leverage ENZ mode behaviors like resonant perfect absorption in the far-field and extreme light confinement in the near-field simultaneously with mode propagation. Propagating modes in both the UB and LB of the dispersion also invites the use of PH-ENZ modes to carry multiplexed optical signals, and because PH-ENZ modes are highly tailorable through changes to the ENZ layer thickness (electric field overlap) and the carrier concentration of either the ENZ or SPP layer (spectral overlap), they could be made dynamic with actively tunable configurations in future work. We note that this study is the first to combine tunable ENZ modes with the appreciable propagation characteristics necessary for enabling such investigations.

We finally suggest that additional potential applications for strongly coupled PH-ENZ modes may include quantum information processing or thresholdless lasing through strong coupling between polaritonic modes and quantum emission sources.27,44-46 The resonant absorption properties of PH-ENZ modes could also be highly useful for narrowband thermal emitters.47,48 The tunable nature of PH-ENZ modes additionally offers the opportunity to tailor modal energies to simultaneously resonate with multiple specific electronic levels or vibrational states for improved surface-enhanced infrared sensing and catalysis.34,46,49-51 Combined with the ease of our bilayer fabrication, we expect PHENZ modes to quickly find applications in one or more of these areas. Experimental:

Extensive descriptions of our methods for depositing doped CdO thin films can be found in the Supporting Information. Briefly, we deposit heteroepitaxial CdO onto epi-ready double side polished r-plane sapphire using reactive high-power impulse magnetron sputtering (R-HiPIMS) from a 99.9999% pure metallic Cd target. Doping is achieved by RF co-sputtering from a 99.99% pure metallic In target. Thickness/deposition rate and carrier concentration are calibrated using X-ray reflectivity and Hall effect measurements, respectively. To form doped CdO bilayers, we first deposit 300 nm In:CdO (the SPP layer) with an electron concentration of 2.5x1020 e-/cm3. After a 2 minute rest without breaking vacuum, a homoepitaxial In:CdO layer (the ENZ layer) is deposited on top of the SPP layer. The electron concentration and thickness of the ENZ layer are controlled by the RF power applied to the In target and the deposition time, respectively. Post-deposition, the bilayers are annealed at 700°C in pure oxygen for 30 minutes. X-ray diffraction confirms that the ENZ-on-SPP bilayers are homo-/heteroepitaxial, and ACS Paragon Plus Environment

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secondary ion mass spectroscopy confirms that the In3+ donors are localized to the SPP and ENZ layers in different concentrations, as expected.

Optical properties (polarized reflectivity spectra) were characterized using a Woollam IR-VASE ellipsometer. A 90° calcium fluoride (CaF2) prism and n=1.720 index matching fluid were used to couple IR light into our plasmonic films through the polished substrate in the Kretschmann-Raether configuration. All reflectivity data were recorded with p- and s-polarized light and are plotted using R=rp/rs as the color/z-coordinate, energy (in cm-1) as the y-coordinate, and normalized wavevector as the x-coordinate (kx/k0, unitless, where kx is the component of the incident light wavevector parallel to the film surface, and k0=ω/c).

To simulate the optical response of our bilayer films, we use a combination of the transfer matrix model and the CST Studio software. Our TMM model is based on a homebuilt Matlab code that includes frequency-dependent dielectric dispersions for CaF2 and sapphire and generates frequency-dependent dielectric functions for each plasmonic layer based on the Drude model. This provides a computationally inexpensive method to simulate the reflectivity spectra of our coupled bilayers. The CST software solves Maxwell’s equations using the finite element method, allowing us to simulate electric field profiles in addition to reflectivity spectra. Supporting Information:

Detailed descriptions of thin film growth, XRD and ToF-SIMS structural/compositional characterization of bilayers, additional dispersion relations in angle and un-normalized wavevector space, description and additional plot of complex wavevector calculations and propagation lengths, descriptions of TMM and CST simulations, additional electric field profiles, Poynting vector profiles. Acknowledgements:

We gratefully acknowledge support for this work by NSF grant CHE-1507947, by Army Research Office grants W911NF- 16-1-0406 and W911NF-16-1-0037, and by Office of Naval Research grant N00014-18-12107. TF and JDC both acknowledge support from Vanderbilt School of Engineering through the latter’s startup funding package. NE acknowledges the partial support from the Vannevar Bush Faculty Fellowship program sponsored by the Basic Research Office of the Assistant Secretary of Defense for Research and Engineering and funded by the Office of Naval Research through grant N00014-16-1-2029. In addition, this work was performed in part at the Analytical Instrumentation Facility (AIF), which is supported by the State of North Carolina and the National Science Foundation (award number ECCS-1542015). The AIF is a member of the North Carolina Research Triangle Nanotechnology Network (RTNN), a site in the National Nanotechnology Coordinated Infrastructure (NNCI). We additionally thank the Efimenko and Genzer groups (NCSU, CBE) for providing use of their IR-VASE and would also like to acknowledge Andrew Klump for performing ToF-SIMS measurements. References: (1)

Liberal, I.; Engheta, N. The Rise of Near-Zero-Index Technologies. Science 2017, 358, 1540–1541. ACS Paragon Plus Environment

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Moitra, P.; Yang, Y.; Anderson, Z.; Kravchenko, I. I.; Briggs, D. P.; Valentine, J. Realization of an All-Dielectric Zero-Index Optical Metamaterial. Nature Photon. 2013, 7, 791–795. Maas, R.; Parsons, J.; Engheta, N.; Polman, A. Experimental Realization of an Epsilon-Near-Zero Metamaterial at Visible Wavelengths. Nature Photon. 2013, 7, 907. Taylor, A. M.; Wasserman, D.; Adams, D. C.; Law, S. Mid-Infrared Designer Metals. Opt. Express 2012, 20, 12155–12165. Sachet, E.; Shelton, C. T.; Harris, J. S.; Gaddy, B. E.; Irving, D. L.; Curtarolo, S.; Donovan, B. F.; Hopkins, P. E.; Sharma, P. A.; Sharma, A. L.; et al. DysprosiumDoped Cadmium Oxide as a Gateway Material for Mid-Infrared Plasmonics. Nature Mater. 2015, 14, 414–420. Kelley, K. P.; Sachet, E.; Shelton, C. T.; Maria, J.-P. High Mobility Yttrium Doped Cadmium Oxide Thin Films. APL Materials 2017, 5, 076105. Bozhevolnyi, S. I.; Volkov, V. S.; Leosson, K. Localization and Waveguiding of Surface Plasmon Polaritons in Random Nanostructures. Phys. Rev. Lett. 2002, 89, 186801. Vahala, K. J. Optical Microcavities. Nature 2003, 424, 839. Campione, S.; Wendt, J. R.; Keeler, G. A.; Luk, T. S. Near-Infrared Strong Coupling Between Metamaterials and Epsilon-Near-Zero Modes in Degenerately Doped Semiconductor Nanolayers. ACS Photonics 2016, 3, 293–297. Jun, Y. C.; Reno, J.; Ribaudo, T.; Shaner, E.; Greffet, J.-J.; Vassant, S.; Marquier, F.; Sinclair, M.; Brener, I. Epsilon-Near-Zero Strong Coupling in MetamaterialSemiconductor Hybrid Structures. Nano Lett. 2013, 13, 5391–5396. Törmä, P.; Barnes, W. L. Strong Coupling Between Surface Plasmon Polaritons and Emitters: a Review. Rep. Prog. Phys. 2015, 78, 013901. Hakala, T. K.; Toppari, J. J.; Kuzyk, A.; Pettersson, M.; Tikkanen, H.; Kunttu, H.; Törmä, P. Vacuum Rabi Splitting and Strong-Coupling Dynamics for SurfacePlasmon Polaritons and Rhodamine 6G Molecules. Phys. Rev. Lett. 2009, 103, 053602. Schlather, A. E.; Large, N.; Urban, A. S.; Nordlander, P.; Halas, N. J. Near-Field Mediated Plexcitonic Coupling and Giant Rabi Splitting in Individual Metallic Dimers. Nano Lett. 2013, 13, 3281–3286. Gomez, D. E.; Vernon, K. C.; Mulvaney, P.; Davis, T. J. Surface Plasmon Mediated Strong Exciton-Photon Coupling in Semiconductor Nanocrystals. Nano Lett. 2010, 10, 274–278. Dunkelberger, A. D.; Spann, B. T.; Fears, K. P.; Simpkins, B. S.; Owrutsky, J. C. Modified Relaxation Dynamics and Coherent Energy Exchange in Coupled Vibration-Cavity Polaritons. Nat. Commun. 2016, 7. Simpkins, B. S.; Fears, K. P.; Dressick, W. J.; Spann, B. T.; Dunkelberger, A. D.; Owrutsky, J. C. Spanning Strong to Weak Normal Mode Coupling Between Vibrational and Fabry-Perot Cavity Modes Through Tuning of Vibrational Absorption Strength. ACS Photonics 2015, 2, 1460–1467. Shalabney, A.; George, J.; Hutchison, J.; Pupillo, G.; Genet, C.; Ebbesen, T. W. Coherent Coupling of Molecular Resonators with a Microcavity Mode. Nat. Commun. 2015, 6, 5981. Autore, M.; Li, P.; Dolado, I.; Alfaro-Mozaz, F. J.; Esteban, R.; Atxabal, A.; Casanova, F.; Hueso, L. E.; Alonso-González, P.; Aizpurua, J.; et al. Boron Nitride ACS Paragon Plus Environment

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Nanoresonators for Phonon-Enhanced Molecular Vibrational Spectroscopy at the Strong Coupling Limit. Light: Science & Applications 2018 7:4 2018, 7, 17172. 𝑘𝑘𝑥𝑥 =

𝜔𝜔

𝜀𝜀 𝜀𝜀

1/2

� 1 2� 𝑐𝑐 𝜀𝜀 +𝜀𝜀 1

2

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medium (here, set to 2 to roughly account for the combined presence of the ENZ layer and air above the SPP layer), and 𝜀𝜀2 (𝜔𝜔) = 𝜀𝜀∞ −

2 𝜔𝜔𝑝𝑝

𝜔𝜔 2 +𝑖𝑖𝑖𝑖𝑖𝑖

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function of the plasmonic layer (𝜀𝜀∞ , 𝜔𝜔𝑝𝑝 , 𝛾𝛾: high frequency dielectric constant, plasma frequency, damping frequency). 𝑘𝑘 𝑑𝑑 𝛾𝛾 𝜔𝜔 ≈ 𝜔𝜔𝑝𝑝 �1 − 𝑥𝑥4 � − 𝑖𝑖 2, where d is film thickness, after Ref. 5. The spatial overlap between the ENZ and SPP electric fields: Ω(r) ∝ ∫ EENZ (r)∙ESPP (r)d𝑉𝑉, (Ref. 29) here simply set to 717 cm-1. Zia, R.; Selker, M. D.; Catrysse, P. B.; Brongersma, M. L. Geometries and Materials for Subwavelength Surface Plasmon Modes. J. Opt. Soc. Am. A 2004, 21, 2442– 2446. Garcia, G.; Buonsanti, R.; Runnerstrom, E. L.; Mendelsberg, R. J.; Llordés, A.; Anders, A.; Richardson, T. J.; Milliron, D. J. Dynamically Modulating the Surface Plasmon Resonance of Doped Semiconductor Nanocrystals. Nano Lett. 2011, 11, 4415–4420. Park, J.; Kang, J.-H.; Liu, X.; Brongersma, M. L. Electrically Tunable Epsilon-NearZero (ENZ) Metafilm Absorbers. Sci. Rep. 2015, 5, 205. Kim, J.; Carnemolla, E. G.; DeVault, C.; Shaltout, A. M.; Faccio, D.; Shalaev, V. M.; Kildishev, A. V.; Ferrera, M.; Boltasseva, A. Dynamic Control of Nanocavities with Tunable Metal Oxides. Nano Lett. 2018, 18, 740–746. Dunkelberger, A. D.; Ellis, C. T.; Ratchford, D. C.; Giles, A. J.; Kim, M.; Kim, C. S.; Spann, B. T.; Vurgaftman, I.; Tischler, J. G.; Long, J. P.; et al. Active Tuning of Surface Phonon Polariton Resonances via Carrier Photoinjection. Nature Photon. 2018, 12, 50–56. Yang, Y.; Kelley, K.; Sachet, E.; Campione, S.; Luk, T. S.; Maria, J.-P.; Sinclair, M. B.; Brener, I. Femtosecond Optical Polarization Switching Using a Cadmium OxideBased Perfect Absorber. Nature Photon. 2017, 11, 390. Chikkaraddy, R.; de Nijs, B.; Benz, F.; Barrow, S. J.; Scherman, O. A.; Rosta, E.; Demetriadou, A.; Fox, P.; Hess, O.; Baumberg, J. J. Single-Molecule Strong Coupling at Room Temperature in Plasmonic Nanocavities. Nature 2016, 535, 127. Tame, M. S.; McEnery, K. R.; Özdemir, Ş. K.; Lee, J.; Maier, S. A.; Kim, M. S. Quantum Plasmonics. Nature Physics 2013 9:6 2013, 9, 329. Cao, E.; Lin, W.; Sun, M.; Liang, W.; Song, Y. Exciton-Plasmon Coupling Interactions: From Principle to Applications. Nanophotonics 2018, 7, 145–167. Greffet, J.-J.; Carminati, R.; Joulain, K.; Mulet, J.-P.; Mainguy, S.; Chen, Y. Coherent Emission of Light by Thermal Sources. Nature 2002, 416, 61–64. Wang, T.; Li, P.; Chigrin, D. N.; Giles, A. J.; Bezares, F. J.; Glembocki, O. J.; Caldwell, J. D.; Taubner, T. Phonon-Polaritonic Bowtie Nanoantennas: Controlling Infrared Thermal Radiation at the Nanoscale. ACS Photonics 2017, 4, 1753–1760. Hutchison, J. A.; Schwartz, T.; Genet, C.; Devaux, E.; Ebbesen, T. W. Modifying Chemical Landscapes by Coupling to Vacuum Fields. Angew. Chem. Int. Ed. 2012, 51, 1592–1596. Agrawal, A.; Singh, A.; Yazdi, S.; Singh, A.; Ong, G. K.; Bustillo, K.; Johns, R. W.; Ringe, E.; Milliron, D. J. Resonant Coupling Between Molecular Vibrations and ACS Paragon Plus Environment

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Localized Surface Plasmon Resonance of Faceted Metal Oxide Nanocrystals. Nano Lett. 2017, 17, 2611–2620. Yoo, D.; Mohr, D. A.; Vidal-Codina, F.; John-Herpin, A.; Jo, M.; Kim, S.; Matson, J.; Caldwell, J. D.; Jeon, H.; Nguyen, N.-C.; et al. High-Contrast Infrared Absorption Spectroscopy via Mass-Produced Coaxial Zero-Mode Resonators with Sub10 nm Gaps. Nano Lett. 2018, 18, 1930–1936.


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kx/k0

1.2

1.3

0

a

max. field magnitude: 1.6x107 V/m max. 1 |S|: 1.0x1011 W/m2

c

b

Upper branch, low kx/k0: ENZ-like

Page 21 of 23

1 μm

2 3 4 5 6 7 8 space free 9 10 bilayer 11 substrate 12 200 nm 13 ENZ 14 layer (20nm) 15 SPP 16 layer (300nm) 17 Poynting vector length scale: = 1012 W/m2 18 d19 Lower branch, low kx/k0: SPP-like 20 max. field magnitude: 21 7 V/m 1.9x10 22 |S|: 8.8x1011 W/m2 max. 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 12 = 10

Upper branch, coupling point: Letters hybrid ENZ-SPPNano mode (symmetric) max. field magnitude: 1.7x107 V/m max. |S|: 3.3x1011 W/m2

Upper branch, high kx/k0: SPP-like pos.

max. field magnitude: 9.9x106 V/m max. |S|: 2.0x1011 W/m2

0

neg.

= 1012

e

Lower branch, coupling point: hybrid ENZ-SPP mode (anti-symmetric) max. field magnitude: 1.6x107 V/m max. |S|: 3.8x1011 W/m2

= 1012

f

Lower branch, high kx/k0: ENZ-like

max. field magnitude: 1.6x107 V/m max. |S|: 1.5x1011 W/m2

ACS Paragon Plus Environment = 1012

= 1012

a 1000

ENZ layer carrier concentration (/1019 cm-3) Letters 25 20 15Nano10 8 7 6 5 4 Page 3 22 of 23 exp. (100 nm) simulated ENZ layer thickness

Spectral splitting (cm-1)

Spectral splitting (cm-1)

1 2 800 3 4 5 600 6 7 8 400 9 10 11 200 12 13 14 0 15 0 16 b17 181000 19 20 800 21 22 23 600 24 25 26 400 27 28 29 200 30 31 32 0 0 33 34

300 nm 200 nm 100 nm 50 nm 25 nm 10 nm 5 nm SPP layer: 300 nm thick, n=2.5×10 cm-3 20

2000 4000 6000 Detuning energy (cm-1)

8000

experiment simulated

ENZ layer: n=1.5×1020 cm-3 SPP layer: 300 nm thick, n=2.5×1020 cm-3

ACS Paragon Plus Environment 50 100 150 200 250 ENZ layer thickness (nm)

300

Page 23 of 23 1 2 3 4

Nano Letters


Polaritonic hybrid-epsilon-near-zero modes: beating the plasmonic

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