Mid-infrared epsilon-near-zero modes in ultra-thin phononic films

In polar optoelectronic materials, the strong absorption of light by phonons poses a significant impediment to the development of optoelectronic devices at wavelengths within, or spectrally adjacent to, a material's Reststrahlen band, the frequency range bounded by the material's transverse optical (TO) and longitudinal optical (LO) phonon energies. This results in an effective gap in the wavelength coverage of any individual material, and a larger, collective gap, from wavelengths of approximately $20–60μm$⁠, for the III-V semiconductors. At the same time, this strong interaction provides a tantalizing opportunity to harness lattice vibrations for potential approaches to the development of new types of optical structures or optoelectronic devices. Such efforts fall into the broader category of Reststrahlen Optics,¹ referring to optical devices, materials, or structures with functionality in or near a material's Reststrahlen band. For traditional III-V materials, phonons provide a potential mechanism for accessing the aforementioned $20–60μm$ wavelength range.² Materials with higher energy phonons provide lower loss alternatives to plasmonic materials for mid-IR applications, relying on a negative permittivity resulting from lattice vibrations as opposed to free charge oscillations. Already, there has been significant effort made to harness surface phonon (SPh) modes for optical functionality akin to that achieved using the more ubiquitous surface plasmons (SPs), largely utilizing the high energy (10.6–12 μm) phonons of SiC.^3–9 However, the range of wavelengths, and ultimately applications, for which phononic materials have utility is arguably more limited than their plasmonic counterparts.

Spectrally, the interface between a phononic and dielectric material can sustain SPh modes across the majority of the (typically narrow) Reststrahlen band. However, at lower energies, SPh loss increases due to increased material absorption near the TO phonon energy. At the higher energy side of the narrow Reststrahlen band, near the LO phonon, such modes can only exist when $Reϵph<0$ and $ϵph>ϵd$⁠, where $ϵph$ and $ϵd$ are the permittivity of the phononic material and the adjacent dielectric, respectively. Moreover, recent work has argued that these phononic modes also differ from their plasmonic counterparts, due to a significant portion of the modes' energy residing in the mechanical energy of the lattice instead of the electric field.¹⁰ For the above reasons, perhaps the most intriguing phenomena associated with phononic materials occur at or near the LO phonon energy. Here, $ReϵphωLO≈0$ and $ImϵphωLO$ can be much smaller than that of a plasmonic material's permittivity (⁠$ϵpl$⁠) at the plasma frequency (⁠$ωp$⁠, where $Reϵplωp≈0$⁠). However, traditional localized or propagating surface modes cannot be sustained at this epsilon-near-zero (ENZ) frequency (though hybrid phonon-plasmon modes have been demonstrated at the LO phonon energy¹¹).

The field of ENZ materials has been of increasing interest over the past decade due to a host of intriguing optical effects associated with these materials' vanishing permittivity. ENZ phenomena have been predicted theoretically^12–14 and demonstrated experimentally,^15–25 at frequencies spanning a significant portion of the electromagnetic (EM) spectrum, using composites designed to mimic the characteristics of bulk ENZ materials,^15–21 at the plasma frequency of plasmonic materials,^22,24–27 or near the LO phonon energy for phononic materials.^23,27,28 Together, the broad range of ENZ materials developed thus far have been leveraged to demonstrate a range of novel optical effects, including but not limited to enhanced transmission through subwavelength apertures,²² strong subwavelength field enhancement,²³ “photonic wires,”²⁹ and tailoring of the response of optical antennas.²⁷ For this reason, there is significant interest in structures which can support optical modes at ENZ frequencies. One such mode is the Berreman mode,³⁰ originally thought to be a longitudinal optical mode, but later more accurately described as a TM-polarized leaky polariton mode.^31,32 The Berreman mode offers strong field enhancement in thin layers at near-ENZ frequencies. In plasmonic materials, these modes can be supported at optical frequencies with diluted plasma,³³ but for phononic materials, these energies coincide with the material's LO phonon energy, offering a route towards strong coupling between light and longitudinal phonons via these hybridized modes.

Here, we demonstrate coupling to such optical modes at mid-IR wavelengths in thin layers of polar semiconductor materials. Our samples are characterized experimentally by angle-, polarization-, and temperature-dependent infrared reflection and emission spectroscopy and simulated using frequency domain mode matching software,³⁴ which for planar structures reduces to a straightforward transfer matrix method (TMM).^35,36 We demonstrate near perfect absorption and strong field localization in ultra-thin (⁠$t<λ/100$⁠) layers and map the Berreman mode dispersion as a function of layer thickness. In addition, we demonstrate that such structures can serve as polarization-dependent selective thermal emitters at or near the LO phonon energy, with minimal angular dispersion. Although here we utilize the high energy phonons of AlN, the work presented can be extended to the lower energy phonons of polar materials more traditionally used for optoelectronic devices.

The samples studied consist of a Si carrier substrate, a 100 nm molybdenum (Mo) ground plane, followed by sputtered, polycrystalline AlN films of varying thicknesses (⁠$t=100, 1200, 1400, 1600, and 1800 nm)$⁠, purchased from OEM Group, Inc. Reflection spectra were collected using a Bruker V70 Fourier transform infrared (FTIR) spectrometer with a custom-built reflection set-up allowing for angle- and polarization-dependent reflectivity measurements for incident angles 20–65° from normal and sample temperatures from room temperature (RT) to 200 °C. Collected spectra are normalized to reflection from RT Au (offering nearly 100% reflection at long wavelengths). A KRS-5 wire-grid polarizer was used to obtain both transverse electric (TE) and transverse magnetic (TM) polarized reflection spectra [Fig. 1(a)].

For emission experiments, thermal emission of the heated sample is spatially filtered by an aperture, collected by a ZnSe lens, and then refocused into a Bruker V80v FTIR through an IR polarizer [Fig. 1(b)]. The emitted thermal spectra are background corrected by subtracting the “background” spectra from an Au-coated (high reflectivity, low emissivity) sample of the same size at the same temperature. The background corrected spectra are then normalized to the background-corrected emission from a known blackbody reference source, fabricated using the technique of Refs. 37 and 38. While the Au sample offers near-zero emissivity (due to the high mid-IR reflectivity of the Au), its emissivity will not be identically zero, and thus, the resulting extracted sample emissivity will be a slight underestimation of the sample's actual emissivity. Our samples were modeled using TMM assuming an isotropic AlN permittivity with a complex dielectric permittivity described by a temperature-dependent single oscillator Lorentzian³⁹ 

with constant $ϵ∞=4.6$⁠, temperature dependent TO and LO phonon energies,⁴⁰ and the scattering rate $γ(T)$ serving as a fitting parameter. Here we used $ωLO=889.977 cm−1$⁠, $ωTO=656.779 cm−1$ and $γ=9 cm−1$ for room temperature and $ωLO=885.8 cm−1$⁠, $ωTO=653.588 cm−1$ and $γ=16 cm−1$ for 200 °C. Figure 1(c) shows the real and imaginary AlN permittivity model used in this work.

The TMM-modeled reflection from bulk, semi-infinite AlN is shown in Figs. 2(a) and 2(b), with the LO phonon energy marked by a dashed line. As can be seen from the simulations, high reflectivity is seen across the Reststrahlen band extending from $λ≈11.2 μm$ to $λ≈15.8 μm$⁠, and only weak coupling to bulk AlN is observed at ENZ (⁠$ωLO$⁠), resulting only from the imaginary component of the AlN permittivity when $ReϵAlN=0$⁠. The optical properties of the AlN films change dramatically however, when the bulk AlN is replaced by a thin AlN film above a Mo ground plane. Figures 2(c)–2(f) show angle-dependent TMM-modeled TE- and TM-polarized reflectivity for such samples with AlN thicknesses of $t=1.2 μm$ [Figs. 2(c) and 2(d)] and $t=100 nm$ [Figs. 2(e) and 2(f)]. In each of these panels, the LO phonon energy, and thus the ENZ frequency, is marked with a dashed line. From the TM-polarized simulations [Figs. 2(c) and 2(e)], we clearly observe strong absorption features in close spectral proximity to the AlN ENZ wavelength. These absorption features correspond to coupling to the Berreman mode. For the thicker AlN sample (⁠$t=1.2 μm$⁠), we observe a Berreman mode with moderate dispersion, close to the LO phonon energy at low incident angles, but moving further from ENZ at larger angles of incidence. For the thin (⁠$t=100 nm≈λENZ/110$⁠) AlN, the observed mode is nearly dispersion-free and overlaps strongly with the AlN LO phonon energy for the entirety of the angular range investigated. We also observe absorption from the AlN TO phonon in the thicker (⁠$t=1.2 μm$⁠) sample, which is barely noticeable in the thin (⁠$t=100 nm$⁠) AlN sample, due to the longer AlN optical path length of the reflected light in the thick sample.

Figure 3 shows the room temperature TE and TM experimental reflection data from the $t=1.2 μm$ and $t=100 nm$ samples for angles 20° to 65° from normal. The experimental data closely match our TMM simulations, showing a clear absorption feature near the AlN LO phonon for both samples. Again, the thicker sample shows a stronger dispersion, with the resonant absorption moving away from the LO phonon with increasing incidence angle, while the thin AlN sample shows an absorption feature with nearly constant spectral position as a function of incidence angle. Absorption from the TO phonon is also observed in our experimental data, again with the stronger TO phonon absorption in the thicker sample. In Fig. 4, we plot the dispersion extracted from our TMM-simulated and experimental reflection spectra with respect to the LO phonon energy (dashed line) and the free space light line (solid). Also shown, in the inset to Fig. 4, is the strong simulated field enhancement obtained in the AlN layer for the thin AlN sample, indicative of a strongly confined ENZ mode at the LO phonon energy. The dispersion of the Berreman mode, similar to any leaky mode in planar geometry, can be understood from simple analytical considerations. The Berreman resonance represents a minimum in reflectivity of the three-layer system, given by:

where $r̃mn$ is the complex (amplitude) reflection coefficient between layers m and n (with layers 1, 2, and 3 referring to air, AlN, and Mo, respectively), and $kzm=ω/cϵm−sin2θ1$ is the wavevector component of light in the $m$-th layer. Assuming that the Mo behaves approximately as a perfect electrical conductor at mid-IR wavelengths (⁠$r̃23≈−1$⁠), the condition for the Berreman mode (⁠$r̃=0$⁠) simplifies to $r̃12=e2ikz2d$⁠. In the limit of optically thin AlN layers, the latter expression can be further transformed to a simple relationship that reveals the spectral response of the Berreman mode:

The excellent agreement between the approximation in Eq. (3), the TMM, and the experimental results is illustrated in Fig. 4, with the approximation of Eq. (3) predicting the spectral position of the Berreman mode particularly well for the 100 nm AlN sample. The Berreman mode in this ultra-thin AlN sample shows a practically angle-independent dispersion, nearly coincident with the LO phonon energy of the AlN, while the thicker AlN layer exhibits significant dispersion of the Berreman mode.

The observed strong absorption of light opens the door to ENZ-based selective thermal emitters leveraging Kirchoff's Law, which states that the emissivity [$ε(ω)$] of a surface is equivalent to its absorptivity. Selective thermal emission is a particularly appealing application for mid-IR plasmonic and phononic structures, given the mid-IR's position as the home to the peak thermal emission for blackbodies with temperatures ranging from 200 to 1400 K,⁴¹ and the (often) undesirable tendency of most, if not all, plasmonic structures to rather efficiently absorb light. In the mid-IR, this near-universal deficiency (strong absorption) of plasmonic or phononic structures can be leveraged and engineered to develop selective thermal emitters.^42–44 Such emitters could serve as cost-effective sources for IR sensing, scene projection, and beaconing applications. Particularly appealing for the Berreman mode observed in our system is not only the strong, selective absorption but the straightforward, planar nature of the absorber (no subwavelength coupling features required) and the insensitivity to the angle in the emission. Moreover, the ultrathin layer of AlN, and the underlying, highly reflective metal, ensures that the observed absorption (and subsequent thermal emission) would be spectrally localized at the LO phonon energy and not obscured by any additional absorption features elsewhere in the mid-IR.

In Fig. 5, we show the simulated [Figs. 5(a) and 5(b)] and experimental [Figs. 5(c) and 5(d)] 200 °C emissivity from our 100 nm AlN sample. Strong agreement is observed between our experiment and the simulated emissivity. The emissivity shows a narrow peak (FWHM = $0.3736 μm≅λo/30$⁠) centered on the LO phonon energy and effectively independent of the angle. As expected, the TM-polarized nature of the Berreman Mode results in a strong polarization dependence in the sample's thermal emission, with strong, spectrally narrow TM-polarized emission, and extremely weak TE-polarized emission observed. Notably, the emissivity feature associated with the Berreman mode remains strong and narrow at elevated temperatures, one of the advantages associated with the high temperature stability of the III-Nitrides. Our sample thus provides strong spectral selectivity for thermal emission in the mid-IR and little to no angular dispersion. In addition, and perhaps more intriguing, the results presented indicate efficient outcoupling of thermal energy at the LO phonon energy, an effect which would not be observed from bulk polar materials.

In summary, we have investigated the coupling of mid-IR light to ENZ modes on thin films of polar materials deposited upon metallic ground planes. We observe strong absorption from the Berreman mode in reflection experiments and are able to use these data to extract the dispersion of the modes, in agreement with our TMM simulations and an analytic approximation used to determine the spectral position of leaky modes in a planar three-layer system. Finally, we demonstrate strong spectrally selective thermal emission from our planar, thin-film structures, suggesting efficient outcoupling of thermal energy at the LO phonon frequency. The work presented here offers a potential route towards narrowband, angle-independent mid-IR thermal emitters, in addition to intriguing possibilities for coupling longitudinal lattice excitations to free-space photons.

The authors gratefully acknowledge funding from the Army Research Office, Award No. W911NF‐16‐1‐0417 (L.N.) and the National Science Foundation, Award Nos. DMR-1629330 (V.A.P.), ECCS-1609912 (L.N. and D.W.), and ECCS-1609363 (A.J.H.).