Letter pubs.acs.org/NanoLett
Epsilon-Near-Zero Strong Coupling in Metamaterial-Semiconductor Hybrid Structures Young Chul Jun,*,†,‡,§ John Reno,† Troy Ribaudo,‡ Eric Shaner,‡ Jean-Jacques Greffet,∥ Simon Vassant,∥ Francois Marquier,∥ Mike Sinclair,‡ and Igal Brener*,†,‡ †
Center for Integrated Nanotechnologies, Sandia National Laboratories, Albuquerque, New Mexico 87185, United States Sandia National Laboratories, Albuquerque, New Mexico 87185, United States § Department of Physics, Inha University, Incheon 402-751, Republic of Korea ∥ Laboratoire Charles Fabry, Institut d’Optique, Univ. Paris-Sud, CNRS, 2 av Fresnel, 91127 Palaiseau, France
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‡
S Supporting Information *
ABSTRACT: We present a new type of electrically tunable strong coupling between planar metamaterials and epsilon-near-zero modes that exist in a doped semiconductor nanolayer. The use of doped semiconductors makes this strong coupling tunable over a wide range of wavelengths through the use of different doping densities. We also modulate this coupling by depleting the doped semiconductor layer electrically. Our hybrid approach incorporates strong optical interactions into a highly tunable, integrated device platform. KEYWORDS: Nano-optics, metamaterials, semiconductors, strong coupling, optoelectronics, infrared
E
as the resonance frequency of the MM resonators is varied using geometric scaling. A clear anticrossing in the measured spectra is observed at room temperature. Finally, to demonstrate the usefulness of this phenomenon for potential device applications, we dynamically modulate this coupling by depleting the doped ENZ layer electrically. Because the zero crossing of the permitiviy (Re[ε(ω)] = 0) in a doped semiconductor originates from the plasmon contribution of the electrons, the ENZ frequency can be tuned in a wide range of infrared (IR) frequencies by controlling the doping density. Therefore, our approach naturally incorporates strong optical interactions into a highly tunable, integrated device platform. These results provide a path to a new type of plasmonic devices,12−14 which can be valuable for a variety of imaging and sensing applications.15 Figure 1a shows the schematic of our hybrid structure. A planar MM layer is patterned on a semiconductor substrate containing an ultrathin ENZ layer (30 nm n+ GaAs, ND ∼ 5.5 × 1018 cm−3). Incident light is directed normal to the sample surface, that is, it does not have an electric field component normal to the ENZ interface. But, it is polarized orthogonal to the split ring resonator (SRR) gap in order to excite its fundamental resonance. The resonantly excited SRRs produce a strong normal electric field component to the interface, which is further intensified at the ENZ layer due to the boundary condition ε1E1⊥ = ε2E2⊥. Figure 1b shows the dielectric constant of our ENZ layer (see Figure S1 in Supporting Information for the detailed wafer structure) as a function of
psilon-near-zero (ENZ) materials exhibit highly unusual and intriguing optical properties. It has been shown that perfect coupling can be achieved between two waveguides through a very narrow ENZ channel of arbitrary shape and length.1−4 The associated large field enhancement of highly squeezed fields in the thin ENZ channel was also considered for enhanced nonlinear optical interactions, such as optical switching and bistability.5 ENZ materials were also employed for antenna directivity and radiation pattern control,6,7 thermal emission control,8 and coherent perfect absorption.9 Recently it was shown that thin layers of an ENZ material can support a new type of guided modes near the epsilon zero frequency, called ENZ modes.10,11 These modes do not couple to free space but can be excited locally with an electric field normal to the layers (TM) and cause enhanced optical fields inside the layer. For a symmetric structure, the ENZ modes are similar to long-range (LR) surface plasmon polariton (SPP) modes in thin metal films. Both have the same field symmetry (i.e., symmetric normal electric field); however, the electric field magnitude is maximum inside the film for ENZ modes, and minimum for LR SPP modes.11 It has also been pointed out that ENZ modes can exist in nonsymmetric configurations.10 Strong field enhancement in ENZ modes can be useful for enhancing light-matter interactions at the nanoscale. In this paper, we demonstrate a novel type of optical strong coupling in a hybrid structure consisting of planar metamaterials (MMs) and a doped semiconductor ENZ nanolayer. To the best of our knowledge, this type of strong coupling has never been reported before. This coupling is enabled by the generation of TM field components in the near field of the MM resonators. The strong coupling between the MM resonance and ENZ modes is evidenced by a very large spectral splitting © 2013 American Chemical Society
Received: August 5, 2013 Revised: October 9, 2013 Published: October 14, 2013 5391
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(Re[ε(ω)] = −1) in the very large wavevector region. As shown in Figure 2b, as the ENZ thickness increases, the dispersion curve redshifts and approaches the surface plasmon frequency (∼745 cm−1). Now we consider dipole emission above a three-layer structure, as shown in Figure 2a. The dipole oscillates normal to the surface and is placed above the ENZ layer. The emitted dipole power can be obtained as follows16,17 P 0⊥ 3 = Im P0 2
frequency, measured using spectral ellipsometry (J.A. Woollam IR VASE). The real part of the dielectric constant becomes zero in the mid-IR around 780 cm−1. We first show that this hybrid structure should excite ENZ modes efficiently. We consider a simpler case that can provide more physical intuition. Light scattering from a deep subwavelength particle provides a wide range of wavevector components and can be modeled as dipole emission. In fact, emission from a dipole above a planar multilayer can be studied analytically. In this calculation, we can obtain the emitted dipole power as a function of in-plane wavevector, and thus we can directly compare it with the dispersion relation of the multilayer structure. Here we perform dipole emission calculations for a simple three-layer structure (Figure 2a, Air/ENZ/Substrate) and compare it with the dispersion relation of the ENZ mode (Figure 2b). We find that the dipole emission spectrum lies on top of the ENZ mode dispersion exactly (Figure 2c), suggesting that the dipole emission couples to the ENZ modes efficiently. The dispersion relation for a TM mode in an asymmetric three-layer structure can be obtained by matching field components and applying boundary conditions at each interface
(1)
where kzn = (εnω /c The solutions of this relation for several different ENZ thicknesses are plotted in Figure 2b (here, the ENZ layer is n-doped GaAs with a doping density ND ∼ 5.5 × 1018 cm−3). For a very thin layer, these modes are termed ENZ modes.10,11 The ENZ mode lies around the epsilon-zero frequency (Re[ε(ω)] = 0) for a small wavevector region, but the mode dispersion redshifts for larger wavevectors. It finally approaches the surface plasmon frequency 2
2
∞
du
̂ u3 [1 + r321e − 2l3d ] l3
(2)
where the indices 1−3 correspond to each layer, u = k||/k3 and lj = −i(εj/ε3 − u2)1/2 are the normalized in-plane and out-ofplane wavevectors, kj = (εj)1/2ω/c, and r||321 is the three-layer reflection coefficient.17 The normalized distance is defined as d̂ = k3d, where d is the dipole-surface distance. The dipole emission power is normalized to that of a dipole in free-space (P0). We use experimentally measured dielectric constants for the ENZ (n+ GaAs) layer, and assume a fixed dielectric constant ε = 10.89 for the GaAs substrate. The integrand of eq 2 gives the wavevector spectrum of dipole emission. We calculated the dipole power spectrum for a range of dipole emission frequencies (640−890 cm−1) and obtained twodimensional plots of the emission power density spectrum for several different ENZ thicknesses (t) and dipole-surface distances (d). As shown in Figure 2c, the dipole emission has resonant distribution in both frequency and wavevector domains. When the ENZ thickness t increases, the resonance frequency slightly redshifts. But as the dipole-surface distance d increases, it blueshifts. In both cases, the dipole power distribution changes in the frequency and wavevector domains. We can superimpose the dispersion curves on the dipole emission spectra for comparison. The white lines in Figure 2c are the ENZ dispersion curves for a given ENZ thickness t and spacer distance d. We can see that the dipole emission spectrum lies on top of the ENZ dispersion exactly, suggesting that the dipole emission couples to the ENZ modes. A subwavelength structure like an SRR provides near-field components with a wide range of wavevectors, and therefore the SRR should excite the ENZ mode too. We have strong field enhancement in the ENZ layer due to the boundary condition ε1E1⊥ = ε2E2⊥. From the measured dielectric constants (Figure 1b), we find that we can have a very large field intensity enhancement for the normal electric field component (about 70 times) at the ENZ frequency (Figure S2, Supporting Information). We verified this field enhancement using numerical simulations too (Figure S3, Supporting Information). We use this remarkable field enhancement in ENZ modes to demonstrate a novel type of optical strong coupling that can have far reaching consequences for optoelectronic devices. Arrays of gold SRR MMs were patterned using a JEOL JBX6300FS electron-beam lithography system, followed by electron beam evaporation of 5 nm Ti and 55 nm Au and lift-off process (Figure 3a). The substrate includes a 30 nm n+ doped GaAs layer grown by molecular beam epitaxy (MBE) (Wafer A in Supporting Information Figure S1). We use a modified SRR as our MM, because it has strong field enhancement at two gaps, though other MM structures could be used too. We performed Fourier transform infrared (FTIR) measurements at room temperature to characterize our sample. Transmission spectra through the MM samples were measured
Figure 1. (a) Schematic of the metamaterial-semiconductor hybrid structure. The semiconductor substrate includes a doped semiconductor ENZ nanolayer. (b) Dielectric constant of n+ GaAs (ND ∼ 5.5 × 1018 cm−3) as a function of frequency, measured by ellipsometry. We have field intensity enhancement due to the boundary condition ε1E1⊥ = ε2E2⊥ at the n+ GaAs/GaAs interface for the normal electric field component. If ε2 goes to zero, E2⊥ should diverge. But the electric field magnitude still remains finite due to the nonzero imaginary part of the dielectric constant. Nevertheless, we can still obtain very large field enhancements near the ENZ frequency.
⎛ ⎛ε k εk ⎞ εk ⎞ ⎜1 + 1 z3 ⎟ = i tan(kz 2d)⎜ 2 z3 + 1 z 2 ⎟ ε3kz1 ⎠ ε2kz1 ⎠ ⎝ ⎝ ε3kz 2
∫0
−k2|| )1/2.
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Figure 2. (a) Geometry of the three-layer structure that we study for the dipole emission and dispersion relation. The ENZ layer is n-doped GaAs with a doping density ND ∼ 5.5 × 1018 cm−3. (b) Dispersion relations of ENZ modes for several different values of t. (c) Dipole emission power spectra for different ENZ thicknesses (t) and the emitter-surface distances (d). The color scale is dipole emission power density normalized by free space emission. White lines are the ENZ mode dispersion curves for each t and d.
The ENZ damping rate was determined to be γENZ = 73.8 cm−1 by fitting a Lorentzian line shape to numerically simulated absorption spectrum of the ENZ mode
with a Bruker IFS 66v/S FTIR spectrometer using a DTGS detector. FTIR spectra were referenced to a bare substrate region that did not have SRR structures. A series of SRR MMs with different SRR scale factors were fabricated, so that the MM resonance frequency gradually shifted across the ENZ frequency. When the MM resonance matched the ENZ frequency (780 cm−1) of the doped semiconductor layer, we observed a clear spectral splitting (scale 1.6 in Figure 3b). Clear anticrossing in the transmission spectra was observed as well. The obtained spectral splitting was as large as 195 cm−1. This kind of avoided crossing has been observed in various physical systems and is indicative of strong coupling between two coupled resonant modes.18,19 We can estimate the coupling strength in our hybrid MM/ ENZ structure. From the two-coupled damped oscillator model, we obtain the following relation for spectral splitting (Δω) and coupling strength (V) (e.g., see Chapter 4 in ref 20) Δω =
4V 2 − (γMM − γENZ)2
αENZ(ω) =
AγENZ (ω − ωENZ)2 + γENZ 2
(4)
where A is a parameter describing the absorption strength. In the numerical simulation, we used experimentally measured dielectric constants for the ENZ layer. Here, the SRR resonance was far away from the ENZ frequency (i.e., we excited the ENZ mode by an off-resonant SRR), so that the resonant interaction is negligible. The MM damping rate was obtained by similar Lorentzian fitting. We used numerically simulated SRR absorption spectra without the ENZ layer (i.e., we obtained intrinsic loss of the SRR resonance at the epsilon zero frequency) and obtained γMM = 77.8 cm−1. From the splitting Δω = 190 cm−1, we obtain the coupling strength of V = 95 cm−1. This coupling strength can be tuned further by adjusting
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obtained (Figure 3c). Numerical simulations agree remarkably well with experimental data. The spectral splitting from simulations (∼190 cm−1) was very close to the experimental one. In both cases, the anticrossing was centered at the ENZ frequency. We also calculated the absorption (A) spectra by obtaining transmission (T) and reflection (R) from the same structure (A = 1 − T − R), and observed a similar spectral splitting (Figure S4, Supporting Information). This anticrossing in the absorption spectra is a necessary and sufficient condition for strong coupling.20 We prepared another MBE grown semiconductor substrate with a lower doping level (wafer B in Supporting Information Figure S1, n+ GaAs, ND ∼ 2.2 × 1018 cm−3) and fabricated a similar MM/semiconductor hybrid sample. Because of the lower doping density, now the ENZ frequency shifted to a lower frequency (∼530 cm−1). We measured the transmission through this sample and obtained a similar spectral splitting and anticrossing (Figure 3d). This was again verified by numerical simulations (Figure 3e). We could obtain the same strong coupling in a different material system too (n+ InAs, ND ∼ 1.1 × 1019 cm−3, Figure S5, Supporting Information). These experimental and simulation results clearly show that this ENZ strong coupling is a general phenomenon and the frequency where anticrossing occurs can be tuned over a wide range of wavelengths by altering semiconductor materials or doping levels. Finally, to demonstrate the usefulness of this novel phenomenon for potential device applications, we dynamically modulate this coupling by depleting the doped ENZ layer electrically. To test this concept, we fabricated interconnected SRR arrays on wafer B (Figure 4). Using I−V (current−
Figure 3. (a) Scanning electron microscope image of gold SRR MM (scale factor 1; red scale bar, 2 μm). L = 720 nm, W = 130 nm, G = 110 nm, and the period is 1.4 μm for scale factor 1. (b) FTIR transmission spectra for a series of SRR scale factors (wafer A, ND ∼ 5.5 × 1018 cm−3). Clear anticrossing was observed at room temperature. (c) Numerically simulated transmission spectra. (d) FTIR transmission spectra (wafer B, ND ∼ 2.2 × 1018 cm−3). Because of a lower doping level, the ENZ frequency shifted to a lower frequency (∼530 cm−1). Anticrossing was observed again. (e) Numerically simulated transmission spectra. Figure 4. Schematic of the electrically tunable MM/ENZ hybrid device. Optical coupling between MM and ENZ layers can be electrically tuned by depleting the doped semiconductor ENZ layer.
the barrier or the ENZ layer thickness. MM designs can be also improved to increase the interaction strength further. We also performed numerical simulations (three-dimensional finite difference time domain, or 3D FDTD) and verified this strong coupling behavior (Figure 3c). We used experimentally measured dielectric constants for the ENZ (n+ GaAs) and SRR (gold) layers. A broadband pulse was incident from the top and polarized orthogonal to the gap. Transmission was measured on the substrate side. We repeated simulations for different SRR scale factors. The SRR resonance peak gradually redshifted as the scale factor increased, and clear anticrossing behavior was
voltage) and C−V (capacitance−voltage) measurements, we first verified that the depletion width gradually increases with a negative bias (Figure S6, Supporting Information). Upon the application of a negative bias, we are able to deplete the doped layer and effectively reduce the ENZ layer thickness. This weakens the coupling between the MM resonators and the ENZ mode. 5394
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MM resonance position due to this coupling (indicated by a red arrow in Figure 5b). These two arrows correspond to the two branches of the anticrossed modes. With negative bias voltages, we depleted the carriers and reduced this coupling. Thus, the spectrum became more symmetric (i.e., returning back to the original position of the isolated/uncoupled MM resonance) at −3.5 V (red curve). This is a gradual change with biasing. At −2 V, the spectrum was in between those measured at 0 and −3.5 V (dotted green curve). Leakage current was very small during this measurement (e.g., ∼2 μA at −2 V), thus eliminating the possibility of thermal effects. Moreover, thermal heating rather induces a red-shift of the spectrum.23 In our previous work,21,22 we studied electrical tuning of MM resonances due to a permittivity change of the substrate. In that work, SRRs were made on a thick (∼700 nm) doped semiconductor substrate, and the device was operating far away from the ENZ frequency of the doped semiconductor. We could observe a small “redshift” (
