On-Chip Hybrid Photonic-Plasmonic Waveguides with Ultrathin

Oct 19, 2018 - The configuration is made with robust fabrication techniques, CMOS-compatible materials, and features a straightforward design with die...
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On-Chip Hybrid Photonic-Plasmonic Waveguides with Ultrathin Titanium Nitride Films Soham Saha,† Aveek Dutta,† Nathaniel Kinsey,‡ Alexander V. Kildishev,† Vladimir M. Shalaev,† and Alexandra Boltasseva*,† †

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School of Electrical and Computer Engineering and Birck Nanotechnology Center, Purdue University, West Lafayette Indiana 47907, United States ‡ Department of Electrical and Computer Engineering, Virginia Commonwealth University, Richmond, Virginia 23284, United States

ABSTRACT: A solid-state hybrid photonic−plasmonic (HPP) waveguide geometry has been experimentally demonstrated with plasmonic titanium nitride. The configuration is made with robust fabrication techniques, CMOS-compatible materials, and features a straightforward design with dielectric cladding layers that exhibit a significant index mismatch with the substrate. The resulting waveguide is shown to reduce both the propagation loss (0.6 dB/mm) and mode size (7.7 μm) when compared to previously reported long-range surface plasmon polariton (LRSPP) waveguides using both noble metal and alternative metals of similar configurations. In addition, the structure removes the need to match the cladding indices with the substrate index, allowing for a thin film superstrate cladding (∼300 nm) that can be readily deposited using numerous methods. This flexibility allows for additional optimization factors to be considered in the design, such as metal film epitaxy, etching selectivity, device function, and compatibility with subsequent fabrication steps. For example, the top cladding layer can be made of silicon nitride for photonic circuits, a gain medium for loss compensation, as well as lithium niobate or zinc oxide for electrical or optical modulation, without sacrificing performance. KEYWORDS: optical materials, titanium nitride, plasmonics, hybrid plasmonic waveguides, HPPW, ultrathin TiN he field of plasmonics deals with the oscillations of free electrons in a metal coupled to an electromagnetic field. Surface plasmon polaritons are such electromagnetic excitations that propagate along a dielectric−conductor interface, evanescently confined in the perpendicular direction. The large wave-vector associated with these oscillations enables light to be localized in volumes much smaller than the diffraction limit.1 Over the last few decades, plasmonics has emerged as a promising technology for data communications,2 offering advantages such as compact sizes, high data bandwidths at comparable or even lower power consumption than electronics.3−6 Various strategies such as hybrid plasmonic−photonic integrated circuits,7 that use photonics for data transfer and plasmonics for modulation show great promise. Selective, controlled usage of the losses in plasmonics with specially designed structures has also resulted in integrated plasmonic components that show exceptional speeds, compact sizes, and broadband performance.8 This calls for not only the development of good plasmonic films but also the investigation of different designs of geometries that enable us to engineer the mode sizes, propagation losses, and the coupling between photonic, hybrid, and plasmonic modes.9

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© XXXX American Chemical Society

Noble metals that are commonly used to demonstrate plasmonic devices are not CMOS compatible, and hence their use in practical devices on an industrial scale is not feasible. The growing need for plasmonic materials which are robust, costeffective, and CMOS-compatible has led to the study of alternative plasmonic materials.10,11 For the visible and near-infrared ranges, titanium nitride has been shown to be a suitable metal for plasmonic applications.12−15 The CMOS compatible metals, copper, and aluminum have also been investigated for plasmonic waveguiding,16,17 but issues like surface oxidation18,19 still offer resistance to their large-scale use in plasmonic applications. Furthermore, on-chip application of Cu and Al typically involves the application of a TiN layer as a diffusion barrier.20,21 The interest in titanium nitride stems from its many unique features such as gold-like optical properties, tailorability,22 CMOS compatibility, refractory nature,13,23,24 resonance in the biological transparency window, and native oxide layer, which enable surface functionalization.22,25 Moreover, TiN can be grown into atomically smooth, ultrathin films down to 2 nm.26 It is also compatible Received: June 30, 2018 Published: October 19, 2018 A

DOI: 10.1021/acsphotonics.8b00885 ACS Photonics XXXX, XXX, XXX−XXX

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Re[ε] and a smaller value of Im[ε] than amorphous/ polycrystalline films, to maximize waveguiding performance. This type of waveguide has the added advantage that it enables the mixing and matching of substrates and superstrates of different indices, unlocking the potential for the use of this waveguide in several applications. For example, the top cladding layer can be made of silicon nitride for photonic circuits, a gain medium for loss compensation, as well as lithium niobate or zinc oxide for electrical or optical modulation.

with current nanofabrication technologies, is resistant to oxidation, with a self-limiting oxynitride layer on the surface,27,28 and can be epitaxially grown on silicon, c-sapphire, and magnesium oxide.10,29 TiN can be deposited using several methods including magnetron sputtering,30−32 atomic layer deposition (ALD),33 and pulsed laser deposition (PLD),29,34 which produce films of varying optical properties. Typically, the best optical qualities are observed for epitaxial films deposited at high temperatures (500 °C and above),27,35 and higher ion energies.28 Such features are critical advantages for many plasmonic applications such as loss compensation using active gain media,36 resonance-based absorption,37 and experiments in nonlinear optics,13,38 among others. As a result, TiN is a promising material for on-chip plasmonic devices such as modulators and waveguides. Although surface plasmon polaritons (SPPs) can confine light at the metal−dielectric interface to subdiffraction limited dimensions, the presence of a lossy metallic component results in propagation distances on the order of several tens of microns, significantly smaller than what is achievable by photonic components. To counteract this low propagation length, the confinement of the mode to the metal layer can be reduced. This can be accomplished by sandwiching a thin metal layer between two dielectric slabs, forming an insulator−metal−insulator (IMI) geometry. As was proposed and demonstrated by Berini et al.,39 the geometry supports symmetric modes, called long-range surface plasmon polaritons (LR-SPPs), which can propagate for several millimeters.40 Such waveguides have been utilized in integrated optical components,41 in sensing platforms,42,43 to demonstrate optically pumped amplification of plasmonic signals,44 and also have been shown to have extraordinary coupling efficiencies with photonic waveguides,45 that makes them a promising candidate for on-chip plasmonic applications. For on-chip applications, the reduction in confinement to improve loss is not a suitable trade-off, as this reduces the potential component density. Additionally, LRSPP waveguides should have a matching top and the bottom dielectric layer surrounding the metal,46 and the performance of the waveguide is extremely sensitive to even slight mismatches in the layer indices.47 This limits the choice of substrate/cladding materials that can be used for LRSPP applications due to the strict requirement of the refractive index match between the substrate and superstrate. Previous demonstrations of the LRSPP waveguides utilized polymers or index matching oils to achieve the required index match between the top and bottom layers. Several variants of the LRSSP waveguide have been studied, employing semi-infinite multilayer structure,48 1D photonic crystal structures,49 and asymmetrical layer structures,50,51 that support long-distance propagating modes. Most of these designs still employ either a cladding layer identical to the substrate or very complex fabrication techniques. In this work, we demonstrate a hybrid, long-range waveguiding structure using epitaxial TiN film on sapphire that is cladded with a silicon nitride dielectric, introducing a significant cladding index mismatch. The structure is fabricated using a simple process, and demonstrates propagation length and mode confinement that exceeds similar LRSPP waveguides reported in the literature. We demonstrate through numerical simulations that, for metal strips of identical parameters (width, height, and optical properties), the hybrid photonic-plasmonic waveguide generally has a larger figure of merit, originating from a smaller mode size and a larger propagation length than the standard LRSPP configuration. The geometry allows us to select a sapphire substrate to achieve epitaxial TiN, with larger negative

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HYBRID PHOTONIC−PLASMONIC WAVEGUIDE Long range surface plasmon polariton waveguides using TiN have previously been demonstrated.15 Figure 1a shows the crosssectional schematic of a typical LRSPP waveguide,15 and compares it to that of the hybrid waveguide (Figure 1d). The symmetric configuration has a 10 nm high, 10 μm wide strip of TiN surrounded by a dielectric film, chosen to be sapphire (n = 1.75 at 1550 nm). In the experiment by Kinsey et al.,15 an index matching oil was used to match the index of the top layer to the index of sapphire. In this configuration, the waveguide supports a symmetric electric-field distribution on both sides (Figure 1b,c), guiding an LRSPP mode. However, the use of an index matching oil limits practicality of the structure. Here, we look to overcome this limitation and improve the performance by employing a hybrid photonic-plasmonic (HPP) waveguide. The structure comprises an identical TiN strip on a sapphire substrate, with a silicon nitride cladding. In this configuration, the wave has a sinusoidal electric field distribution in the superstrate, and an exponential decay in the substrate, highlighting the hybrid nature of the mode, as shown in Figure 1e,f. By properly choosing the thickness of the cladding, the effective index of the superstrate can match that of the substrate to achieve efficient guiding.52 This enables the design of long-range waveguides that are plasmonic in nature even with a significant mismatch between the superstrate and the substrate index. Finite element method (FEM) based simulations were performed using COMSOL to investigate the effects of the strip width and the cladding thickness on the propagation length and the mode size of the waveguide. A 10 nm thick strip of epitaxial TiN on sapphire was chosen as the waveguide. The optical properties of TiN thin films are thicknessdependent.26 For our simulations in this section, we used the data for a 10 nm film of TiN (εTiN = −75 + 23i), sapphire (nsapphire = 1.75), and silicon nitride (nSi3N4 = 1.98) at 1.55 μm from the work of Kinsey et al.15 Silicon nitride was chosen as the cladding, as it has a higher refractive index than sapphire, making it suitable for the hybrid waveguide design. To give a fair comparison between different waveguides, we have defined our figure of merit (FOM) as FOM =

L nδz

(1)

L is the propagation length defined as the distance the wave travels for its intensity to decrease to 1/e of its initial value; n is the effective mode index, which, in the case of an HPP waveguide, closely matches the substrate index; and δz is the mode size, defined as the distance into the substrate where the E-field falls to 1/e of its original value. Keeping the width constant at 10 μm and the thickness at 10 nm, the cladding height is changed from 354 to 365 nm and Figure 2a−c illustrate the resulting trend for the HPP waveguide. For comparison, an identical strip of TiN in the LRSPP B

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Figure 1. (a) Cross-sectional schematic and (b) electric field profile showing the normalized electric field (|E|) of a long-range surface plasmon polariton (LRSPP) waveguide, y = 0 is defined as the intersection between the TiN and the sapphire. (c) Mode-profile of an LRSPP waveguide showing the normalized electric field |E|. (d) Cross-sectional schematic and (e) electric field profile (|E|) of a hybrid waveguide. (f) Mode-profile of a hybrid photonic-plasmonic (HPP) waveguide showing the normalized electric field |E|.

Figure 2. (a) Mode size, (b) propagation length, and (c) figure of merit (FOM) vs cladding thickness of 10 nm high, 10 μm wide TiN waveguides. (d) Mode size, (e) propagation length, and (f) FOM vs strip width of 10 nm high TiN waveguides with 360 nm Si3N4 cladding.

configuration has a mode size of 8.0 μm and a propagation length of 4.9 mm, with a FOM of 351. Below a critical thickness of the silicon nitride layer (354 nm), the hybrid mode is not supported by the structure. At the critical height of silicon nitride (354 nm), the waveguide has the longest propagation distance (7.27 mm), a mode size of 7.82 μm and the largest FOM (531), which is significantly larger than that of the LRSPP configuration. Above this thickness, as the height of the cladding increases, both the mode size and the propagation length decrease. There is also a steady decrease in the figure of merit with the cladding height, although the value remains comparable to that of the LRSPP comparison.

Keeping the height of the silicon nitride constant at 360 nm and the strip height of the ridge at 10 nm, the width was varied from 6 to 15 μm. With the decrease in the waveguide width, the electromagnetic field penetrates deeper into the substrate, increasing the mode size. At a certain critical width, which is 6 μm for our particular geometry, the mode size exceeds the strip width, and the mode becomes coupled into a leaky substrate mode that is predominantly photonic in nature. Above the critical width, as the strip width increases, the mode confinement increases and the propagation length decreases, and the figure of merit remains comparable to those of gold or TiN LRSPP waveguides. C

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Figure 3. (a) TEM of epitaxial TiN on Sapphire. (b) Real and imaginary permittivities of the grown film.

Figure 4. (a) SEM of TiN waveguides. (b) Optical image showing the waveguides with respect to the polarization maintaining fiber.

carriers resulting in greater Drude damping, and have a lower plasma frequency due to surface oxidation effects.54 An SEM image of the patterned TiN guides with a measured width of 8.7 μm is shown in Figure 4a and microscope image of the finished structure is shown in Figure 4b. The schematic of the experimental setup is shown in Figure 5a. It consists of an NKT Photonics Super-K EW-6 white light source with a filter for 1.55 μm wavelength. A polarizer was placed at the output of the source which was then coupled through a polarization-maintaining (PM) fiber and into a polarization controller. The other end of the fiber was placed at the input waveguide facet. A near-infrared (NIR) camera was focused at the output end of the waveguide to observe the out-coupled mode. The power density of the outcoupled mode at the output facet of the HPP waveguide as observed by the NIR camera is shown in Figure 5b. To obtain the vertical mode size, the power density data of six waveguides was taken along a vertical cut-line through the center of the profiles, as depicted in Figure 5c. The power intensities versus the distance along the y-axis were then averaged and normalized with respect to the maximum intensity. The photonic side of the outcoupled mode is fitted with a 2 Gaussian decay (I = e−2(y/c) ) and the plasmonic side with an exponential decay (I = e−by). The 1/e2 decay point was chosen as the average mode size which was found to be 7.7 μm. To measure the propagation length of the waveguides, a cutback approach was used. First, the output power was measured for the full-length of the waveguide. Then the measurement was repeated after slicing the waveguides roughly in half. The log of the measured intensity is taken for each length. The slope of the corresponding fit line (y = mz + b, where m = 2k″ mm−1) measures the attenuation of the structure per unit length (α = 8.68k″ dB/mm). The structure was measured for waveguide lengths of 7.81 and 3.78 mm. Coupling and fabrication

For the confinement of the mode in the lateral direction, it is possible to modify the hybrid structure to a ridge configuration, similar to the long-range dielectric-loaded surface plasmon polariton structure demonstrated by Bozhevolnyi et al.,53 employing a thin metal film embedded in a dielectric ridge. Further reduction of mode sizes is possible maintaining similar figures of merit by using a substrate and a superstrate with a higher refractive index.

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EXPERIMENTAL SECTION For our experiments, we chose to keep the width of the waveguides around 9 μm to maximize the mode overlap between the hybrid mode and that of a standard, single mode polarization maintaining fiber. The substrate was chosen to be sapphire because of two reasons. Firstly, epitaxial grade TiN can be grown on c-sapphire, and secondly, sapphire is a substrate used for the fabrication of optoelectronic devices with III−V nitrides.35 We investigated the strip waveguide structure as opposed to a ridge structure to provide for a direct comparison with the LRSPP waveguides previously reported.15 Also, ridge waveguides would have an additional surface roughness contribution to losses, which would be difficult to decouple from the plasmonic losses. The final waveguide structure was fabricated using reactive magnetron sputtering, photolithography, etching, and chemical vapor deposition. The thickness of the TiN layer was determined to be 8.8 nm using TEM, shown in Figure 3a (see Methods for fabrication details). The optical properties of the titanium nitride layer were determined using variable angle spectroscopic ellipsometry (VASE) measurements. The VASE data was fitted with a Drude-Lorentz model and Figure 3b shows the optical properties of the film. At a wavelength of 1550 nm, the permittivity was found to be −59 + 24i. The films exhibit slightly lower negative part of the dielectric permittivity and higher losses than that reported by Kinsey et al.15 This is because, with decreasing thickness, the films are more prone to surface scattering of D

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Figure 5. (a) Schematic of the experimental setup. (b) Experimentally measured mode profile from the output facet of the TiN strip waveguide. The horizontal white line is added to show the boundary between silicon nitride and air. (c) Experimental data and the fitting of the cutline. The left 2 (photonic) side of the outcoupled mode is fit with a Gaussian decay I = e−2(y/c) and the right (plasmonic) side with an exponential decay I = e−by. (d) Simulated modal profile showing the normalized electric field |E|, from COMSOL Multiphysics. (e) The cutline from simulation, with the normalized power, given by the time averaged Poynting vector in the z-direction, showing a close match with experimental results.

Table 1. Comparison of Titanium Nitride and Gold on-Chip Plasmonic Interconnects metal

ε at 1.55 μm

thickness (nm)

width (μm)

mode size, δz (μm)

propagation length (mm)

figure of merit

gold (LRSPP waveguide) TiN15 (LRSPP waveguide) TiN (HPP waveguide)

−132 + 13i −75 + 23i −59 + 24i

10 10 8.8

8 9.38 8.7

20 9.8 7.7 (experiment) 7.75 (simulation)

7 5.5 7.2 (experiment) 7.52 (simulation)

229 321 534 554

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decreases to 1/e2 of its maximum value is taken to be the mode size. For a cladding thickness of 358.7 nm, the simulated mode size was found to be 7.75 μm. The software also computes the wavevector kspp = k′ + k″ from which the propagation length (L = 1/2k′′) is calculated to be 7.52 mm, showing a strong match between the experimental and the simulated results within the bounds of experimental error. Table 1 shows a comparison of the fabricated solid-state waveguide with other waveguides in literature. It has a higher propagation length and smaller mode size than previously reported LRSPP waveguides with both gold41 and titanium nitride,15 resulting in a higher overall figure of merit than both works. This is achieved despite a reduction of the base optical

irregularities contributed to 10% error. The measured attenuation of our waveguides was 0.60 dB/mm, and the propagation length was 7.2 ± 0.6 mm. Additional details of the measurement are included in the Methods section. Simulations were done using the commercially available software COMSOL considering a 2D geometry. Details of the simulation are elaborated in the Methods section. Figure 5d shows the mode profile |E| of the waveguide as obtained from simulations, and Figure 5e shows the normalized time-averaged Poynting vector in the z-direction through a vertical crosssection of the waveguide along its center. The intersection between the TiN and the sapphire is set to be y = 0, and the distance from this position to the point where the power E

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Figure 6. (a) Mode size, (b) propagation length, and (c) FOMs of TiN HPP waveguides with different cladding materials on sapphire.

properties of the TiN film. This can be explained by considering the material properties and structure of the waveguide geometries, whereby a thin metallic film is required. First, the reduction in the magnitude of the real permittivity of TiN allows more light to exist inside the metal, thereby reducing the size of the plasmonic mode. Typically, this would result in a reduction of the FoM due to the additional loss, however, the morphology of the films must be considered. Gold is well-known to possess nanometer scale roughness for films with thickness less than ∼15 nm.41 This roughness thereby limits the attainable propagation loss in the structure. For the two TiN-based structures, smooth epitaxial films are used that possess sub-nm surface roughness. As a result, the losses are able to approach the theoretical limit for films below 10 nm and able to outperform the gold structure. However, it is important to note that this advantage is not as impactful for thick films and the reduction in the optical properties of TiN can be harmful, as was shown for dielectric-loaded waveguides.55

commonly used in sensing,56 and its refractive index can be changed by optical pumping.57 The top layer for an HPP waveguide can be switched with ZnO to transform the waveguide into a refractive index sensor or an optically controlled switch. Lithium niobate is another material that changes its refractive index under an applied voltage and is used in the design of ultrafast optical modulators.58 Hybrid LRSPP waveguides with LiNbO3 claddings can be used to design electrical modulators or on-chip nonlinear optical operations. Other potential applications of the waveguides may employ silicon claddings for application in silicon photonic circuits or III−V nitride platforms for loss compensation using an active gain medium.

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CONCLUSION We report on the experimental demonstration of titanium nitride-based hybrid photonic-plasmonic waveguides. At the telecommunication wavelength of 1.55 μm, the waveguides show a propagation length of 7.2 mm, with a mode size of 7.7 μm. The fabricated waveguide has an outstanding figure of merit of 534 (defined as the ratio or the propagation length to the normalized mode size and the effective mode index), outperforming previously reported gold (FOM = 229) and TiN (FOM = 321) long-range surface plasmon polariton waveguides. Furthermore, simulations show that the HPP waveguide geometry with a critical cladding thickness has an overall FOM better than that of an LRSPP waveguide with an identical metal strip geometry, made with the same material. In addition, the design is based on an all-solid-state platform without using polymers or oil for index matching, enabling more flexibility in substrate selection and device design. Finally, we demonstrate through simulations the use of different dielectric capping layers for the HPP waveguide configuration, demonstrating its potential use across an array of on-chip sensing, modulation, and interconnect applications.

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HPP WAVEGUIDE WITH DIFFERENT CLADDING MATERIALS In the subsequent analysis, HPP waveguides with claddings of Si3N4 (n = 1.98), ZnO (n = 1.93), and LiNbO3 (n = 2.21) are compared with a LRSPP waveguide (embedded in a cladding of n = 1.75) for the same TiN strip geometry. We chose a 10 μm wide TiN strip with a thickness of 8.8 nm, and the propagation loss, the mode size and the figures of merit of the waveguides are compared. The permittivity of TiN is taken to be εTiN = −59 + 24i at 1.55 μm, as obtained from our experiments. The difference in refractive index (Δn) is computed by subtracting the refractive index of sapphire from that of the superstrate at 1.55 μm wavelength, that is, Δn = nsuperstrate − nsapphire

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(2)

METHODS TiN Film Growth. To fabricate our HPP waveguide structure, titanium nitride was deposited on c-sapphire using DC magnetron sputtering at 800 °C. A 99.995% pure titanium target of 2 in. diameter was used. The DC power was set at 200 W. To maintain a high purity of the grown films, the chamber was pumped down to 3 × 10−8 Torr prior to deposition and backfilled to 5 mTorr during the sputtering process with argon. The throw length was kept at 20 cm, ensuring a uniform thickness of the grown TiN layer throughout the 1.5 cm by 1.5 cm sapphire substrate. After heating, the pressure increased to 1.2 × 10−7 Torr. An argon−nitrogen mixture at a rate of 4 sccm/6 sccm was flowed into the chamber. The deposition rate was 2.2 Å per minute. By controlling the deposition time, it is possible to grow ultrathin films of titanium nitride down to 2 nm in thickness with 5% accuracy.

For each cladding, depending on the cladding index, the hybrid mode is supported by a specific cladding thickness, tcladding. Figure 6 illustrates the results. It can be seen that despite a significant difference in refractive indices of ZnO (Δn = 0.18, tcladding = 407 nm), Si3N4 (Δn = 0.23, tcladding = 358 nm), and LiNbO3 (Δn = 0.46, tcladding = 246 nm), the claddings support hybrid modes, with propagation lengths and mode sizes generally superior to the LRSPP modes of TiN on sapphire. The application of an index-mismatched cladding for the hybrid waveguide design allows for the combination of different substrates and claddings, to implement waveguides for different applications. For example, Si3N4 can be used for high-efficiency coupling between hybrid plasmonic waveguides and nitridebased photonic interconnects. Zinc oxide (ZnO) is a material F

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Fabrication of the Waveguides. The titanium nitride film was patterned using photolithography with AZ1518 photoresist. The photoresist was spin-coated at 4000 rpm for 40 s with a 2 s ramp and then soft-baked for 2 min at 100 °C on a hot plate. The subsequent UV exposure was of duration 20 s, with a peak intensity of 10 mW/cm2 at a wavelength of 405 nm. The resist was developed for 20 s using MF-26 developer and rinsed with deionized water. After lithography, the titanium nitride ridges were made by dry etching with chlorine-based chemistry in a plasma etcher. The chlorine gas flow rate was 26 sccm with a chamber pressure of 0.6 Pa. The RF source power was 150 W and the RF bias power was 26 W. The etch rate was found to be around 20 nm/min. The residual photoresist was removed by immersing the sample in acetone overnight. The width of the ridges was measured with scanning electron microscopy (SEM). The width is seen to vary between 8.5 to 9 μm between waveguides, with the average to be 8.7 μm. After photoresist removal, a 360 nm layer of Si3N4 film was deposited by chemical vapor deposition on the material through a reaction of dichlorosilane (DCS) with ammonia (NH3) at 800 °C. The thickness of the silicon nitride film is verified by spectroscopic ellipsometry to be 360 nm, with a variance of ±2 nm across the 1.5 cm substrate. Simulations. FEM simulations were done using the commercial software COMSOL Multiphysics, RF Module, considering a 2D geometry. A domain of 160 μm was used. Perfectly matched layer (PML) boundary conditions were used to prevent reflection at the boundaries. An epsilon value of −59 + 24i was used for titanium nitride at 1.55 μm wavelength, as obtained from variable angle spectroscopic ellipsometry (VASE) measurements. The refractive index of the c-sapphire was set at 1.75 and the refractive index of silicon nitride at 1.98 for a wavelength of 1.55 μm. The titanium nitride thickness was taken to be 8.8 nm and the width to be 8.7 μm, as determined from TEM/SEM. Cutback Measurement. The NIR camera was calibrated to act as a relative power meter by measuring the total pixel intensity captured within a fixed pixel area for a fixed camera position and a fixed excitation condition. In this configuration, for a fixed waveguide, the only variable which can affect the measured output intensity is the coupling condition. A difficulty we encountered was in cleaving the sapphire after waveguide fabrication. Unlike silicon, sapphire does not have a weak plane which cleaves under the application of pressure. The sapphire sample had to be cleaved a total of three times: input facet, output facet, and the center. We mitigated the problem by taking measurements from waveguides that had a flat cleaved facet after both sets of cleaving. Any waveguide with a nonsmooth edge was not considered for measurement. We performed the mode profile measurement for six waveguides that survived the input and output facet cleaving with smooth edges. To measure the intensity for loss measurement, for each waveguide, the fiber was carefully aligned, maximizing the output intensity for each length. After every reading, the fiber was completely misaligned and realigned, and the output intensity was maximized prior to taking the subsequent measurement. The intensity for each waveguide was measured four times and then averaged to account for the waveguide to waveguide variations. Following this, we cleaved the sample in the middle and repeated the measurement on the two waveguides that survived with a smooth input and output facet after both cleaves. The measured propagation length varied from 6.6 to 7.8 mm between the waveguides.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +1 765 494 0301. ORCID

Alexandra Boltasseva: 0000-0002-5988-7625 Author Contributions

S.S. and A.D. contributed equally in this work. S.S. carried out the simulations and the fabrication of the waveguides. A.D. carried out the measurements. N.K. and A.K. analyzed the results. V.S. and A.B. conceived the project and contributed to writing the paper. Funding

This research was supported by the Air Force Office of Scientific Research Grant FA9550-17-1-0243 and Sandia National Laboratory Grant 1757154. A.V.K. acknowledges the support by the DARPA/DSO Extreme Optics and Imaging (EXTREME) Program, Award HR00111720032. Notes

The authors declare no competing financial interest.

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