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Abstract
Epsilon near-zero photonics and surface polariton nanophotonics have become major fields within optics, leading to unusual and enhanced light-matter interaction. Specific dielectric responses are required in both cases, which can be achieved, e.g., via operation near a material’s electronic or phononic resonance. However, this condition restricts operation to a specific, narrow frequency range. It has been shown that using a thin dielectric layer can adjust the dielectric response of a surface and, therefore, the operating frequency for achieving specific photonic excitations. Here, we show that a surface’s optical properties can be tuned via the deposition/transference of ultra-thin layered van der Waals (vdW) crystals, the thicknesses of which can easily be adjusted to provide the desired response. In particular, we experimentally and theoretically show that the surface phonon resonance of a silica surface can be tuned by ∼50 cm−1 through the simple deposition of nanometer-thick exfoliated flakes of black phosphorus. The surface properties were probed by infrared nanospectroscopy, and results show a close agreement with the theory. The black phosphorus-silica layered structure effectively acts as a surface with a tunable effective dielectric constant that presents an infrared response dependent on the black phosphorus thickness. In contrast, with a lower dielectric constant, hexagonal boron nitride does not significantly tune the silica surface phonon polariton. Our approach also applies to epsilon near-zero surfaces, as theoretically shown, and to polaritonic surfaces operating at other optical ranges.
© 2021 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The area of photonics has experienced disruptive developments in recent years. Materials with near-zero dielectric constant (epsilon), for example, have been shown to present unprecedented properties such as a giant nonlinear refractive index [1] and decoupling between temporal and spatial variations in their optical field, allowing for field tunneling through randomly distorted regions of a waveguide [2]. Similarly, surface polariton waves exploiting plasmonic, phononic, and excitonic resonances of matter, especially in lamellar vdW crystals, have been shown to allow for the subdiffraction confinement and guiding of electromagnetic radiation [3,4].
Materials presenting either epsilon near-zero or allowing for polaritonic waves in the visible and infrared ranges have been identified and characterized [5,6]. Mid-infrared materials are particularly important for sensing applications, and an ultra-sensitive biomolecule sensor based on graphene plasmons has been demonstrated [7]. However, achieving the exact required value in the relevant optical parameter (e.g., a null real part of the dielectric constant or a dielectric constant of −1, in the case of surface polariton resonances at an interface with air) is not straightforward. Researchers have largely relied on operation near resonances of existing materials (e.g., the surface phonon resonance of silica at 1164 cm$^{-1}$) [8]. In this case, however, the frequency of operation is generally fixed by the crystal properties. It has been shown that nanometric dielectric layers can be used to adjust the electromagnetic environment at the surface, thus, providing some spectral tunability/tailorability [9]. Naturally, however, depositing an ultrathin layer onto a surface requires careful choice of both the material and the deposition method, with the thermal/mechanical compatibility, the reactivity of dangling bonds, and the continuity and thickness homogeneity of the film being parameters that require attention.
The lack of interlayer chemical bonds allows for atomically flat layered vdW crystals, with nano/subnanometer thicknesses, to be placed on any surface, or even stacked to form heterostructures [10]. Additionally, their thickness can be controlled during the growth processes or with post-treatment. For example, Kwon et al. and Kim et al. showed that black phosphorus thickness could be tailored by a controlled oxidation process using ozone or reactive oxygen species generated by UV radiation [11,12]. Another way to tailor the thickness of layered vdW crystals is by Laser thinning with a continuous-wave laser, which was demonstrated for $MoS_2$ by Castellanos-Gomez et al. [13] and black phosphorus by Rodrigues et al. [14].
Layered vdW crystals support their own polaritons [3,4,15], which have been extensively studied, and the momentum of which has been shown to tune with the crystal thickness in the case of hexagonal boron nitride (hBN) [16]. We note that the tunability of these polaritons by the substrate’s dielectric constant [17,18] or via hybridization with polaritons of another, adjacent, vdW material [19–23] have been demonstrated. However, the use of vdW crystals as easily obtainable/transferable nonresonant ultrathin dielectric layers to adjust the photonic/polaritonic response of the adjacent surface remains largely unexplored [24,25].
In this paper, we show that few-nanometer-thick layered vdW crystals can change the near-field optical response of a dielectric surface, with the resonances becoming dependent on the thickness of the layered material. Near-field responses were obtained by Synchrotron Infrared Nanospectroscopy (SINS), which uses a synchrotron broadband infrared beam impinging on a scattering-type scanning near-field optical microscopy (s-SNOM) tip to retrieve, by Fourier transform interferometry, the infrared spectrum from nano-sized regions of the sample [26,27]. In particular, our results show that black phosphorus (BP), a vdW direct gap semiconductor, leads to the tunability of the phononic resonance of an air-SiO$_{2}$ surface. This tunability is significantly higher than that obtained with hBN, which is attributed to the higher dielectric constant of BP. The BP-SiO$_{2}$ structure can be adjusted to offer a customized near-field optical response. The deposition or transference of layered crystals on other substrates can offer similar tunabilities at other spectral ranges, as theoretically shown for an hBN/indium tin oxide (ITO) structure.
2. Theoretical framework
We electromagnetically model the composite surfaces as a stacked structure composed by one slab of the layered vdW crystal with thickness $d$ and dielectric constant $\varepsilon _{2}$, on top of a semi-infinite section of the substrate with a dielectric function $\varepsilon _{3}$. The space above the layered structure is assumed to be filled with nitrogen with a dielectric constant $\varepsilon _{1}=1$. All interfaces are assumed to be normal to the $z$ axis. Laturia et al. showed by density functional theory that for vdW crystal such as hBN and transition metal dichalcogenides $\varepsilon _{2}$ has a small thickness dependence. They showed that the variation is between 0.1 and 0.5 for h-BN and $MoS_2$ when the number of layers changes from one to five, reaching the bulk value after five layers [28]. On the other hand, Kumar et al. showed that for BP, the dielectric constant slowly increases with the number of layers towards its bulk value [29]. Since the flakes studied here have thickness larger than 5 nm, we used the dielectric constant of bulk BP.
The expression for the net reflection coefficient from the structure (for $p$-polarized light, which is dominant in the s-SNOM configuration [8]) can be written as
Equation (3) is valid in the near field case (kz =iq) with $-\infty < qd < \infty$; where the most important in-plane momentum is $q \approx 1/a$ being a the probing tip radius ($a \approx 30 nm$). Note that, with $qd < 1$, $\varepsilon _{*}$ may significantly differ from both $\varepsilon _{2}$ and $\varepsilon _{3}$, which makes the layered structure behave as a heterostructure with an effective dielectric function $\varepsilon _{*}$. Equations (3) show that by varying the layered crystal’s thickness, $d$, $\varepsilon _{*}$ can be tuned, allowing for the near-field reflectance spectra to be adjusted to specific conditions. For example, to excite collective (polaritonic) modes, we look for the maximum of the imaginary part of the near-field reflection coefficient ($Im[R(q,k)]$) [8], which is found when $Re[\varepsilon _{*}] = -1$ and $Im[\varepsilon _{*}] \rightarrow 0$. Figure 1(a) shows this condition as a function of the $qd$ product both for a BP and hBN thin crystal on a silica substrate, near the surface phonon resonance of silica. The complex dielectric functions for BP, hBN and SiO$_{2}$ were extracted from Refs. [30,31] and [8], respectively. The value of $Im[\varepsilon _{*}]$ is shown in the color scale and should be as low as possible to minimize damping of the polaritonic wave. It can be seen that, for each $qd$ value, the $Re[\varepsilon _{*}] = -1$ condition is satisfied twice. However, the lower wavenumber corresponds to high losses and is, in practice, not observed. We will, thus, only discuss the higher wavenumber branch.
Fig. 1. Tunability of the optical properties. (a) Polaritonic wave resonance (corresponding to $Re[\varepsilon _{*}] = -1$) with BP/SiO$_2$ and hBN/SiO$_2$ structures in the mid infrared range and (b) $Re[\varepsilon _{*}] = 0$ condition in the near infrared with an hBN/ITO sample as functions of $qd$. $Im[\varepsilon _{*}]$, associated with losses, shown in color scales, where the regions of lower (higher) loss are the blue (red) ones.
For $qd \sim 0$ the maximum of the $Im[R(q,k)]$ is at $1150$ cm$^{-1}$, as previously observed for a bare SiO$_2$ surface [8]. As the layered crystal gets thicker, that is, for higher $qd$ values, the $Re[\varepsilon _{*}] = -1$ condition shifts to lower wavenumbers and a red shift in the silica optical near field response is expected. Additionally, $Im[\varepsilon _{*}]$ increases with $qd$, making the $Im[R(q,k)]$) peak loose amplitude until it is completely damped (see Supplement 1). It can be seen that the rate at which the polaritonic peak shifts with $qd$ is significantly higher with BP. Within the $0< qd < 0.2$ region, the BP/SiO$_2$ curve shows a slope of $\sim 133$ cm$^{-1}$, while for the hBN/SiO$_2$ surface the slope is $\sim 52$ cm$^{-1}$. We attribute the higher tunability of the BP/SiO$_2$ structures to the higher real part of the dielectric function of BP ($\sim 11.7$) in the spectral region of interest relative to those of hBN ($\sim 3.7$) and silica ($\sim -1$). As a consequence, the polaritonic response is expected to tune between 1150 and 1110 cm$^{-1}$ by changing the thickness of the BP overlayer. Note that for BP and $qd > 0.233$ the $Re[\varepsilon _{*}] = -1$ condition is never satisfied. Nevertheless, as will be shown, for $0.23 < qd < 1$ the low value of the denominator in $R(q,\omega )$ (Eq. 3) still yields a reflectance peak.
Another interesting example of the achievable spectral tunability with ultrathin vdW layers in the near field is the ability to tune the epsilon near-zero wavelength of a surface. Figure 1(b) shows the wavelength for which $Re[\varepsilon _{*}] = 0$ as a function of $qd$ for a slab of hBN on top an ITO substrate (ITO’s dielectric function was extracted from Ref. [1]). $Im[\varepsilon _{*}]$ is again plotted in the color scale and low values correspond to lower losses. It can be seen that the epsilon near-zero condition can be tuned over a window of more than $200$ nm ($>16\%$ tunability), reaching, e.g., spectral regions that are of interest in optical communications. The real and imaginary parts of the $\varepsilon _{*}$ spectrum for the hBN/ITO structure are shown in Supplement 1 as well as a possible experimental setup (and theoretical predictions of experimental results) to observe the proposed effect by following ITO’s surface plasmon polaritons frequency using an Otto configuration.
2.1 Self-interacting dipole model
To model the s-SNOM tip/sample interaction in the experiments, the near-field spectrum demodulated at the second harmonic of the tip oscillation frequency was theoretically obtained. For this purpose, we modeled the tip as a point dipole above of the sample. The scattered electric field $E_{s}$ at the detector is expressed as [32,33]
This equation includes the far-field factor $(1+R_{p})^{2}$ and the near-field dipole-dipole interaction $(1-\alpha G)^{-1}$. In Eq. (4), $\alpha = a^{3} \frac {\varepsilon _{tip}-1}{\varepsilon _{tip}-2}$ corresponds to the polarizability of a sphere of radius $a$ and dielectric constant $\varepsilon _{tip}$ (representing the tip); and $G$ determines the range of in-plane momenta sampled by the tip at a height $z$ above the sample:
Finally, the relation between the $n$-th harmonic demodulated s-SNOM signal and the scattered electric field can be written as
where the vertical position of the tip is defined by $z = z_{0} + \delta _{z}cos(\Omega )$.3. Experimental methods
3.1 Sample preparation
To demonstrate the simplicity and effectiveness of the proposed approach, BP/SiO$_{2}$ and hBN/SiO$_{2}$ structures were prepared by standard mechanical exfoliation, with an adhesive tape, of the layered crystals onto 300-nm-thick silicon dioxide films on silicon wafers. For BP samples the exfoliation was carried out in a nitrogen environment, with O$_{2}$ concentrations varying between 0.4 vol% and 0.9 vol%; we removed air-exposed sections of the tape, so that fresh sections were used for exfoliation. For hBN the exfoliation took place in ambient environment. The flakes were transferred onto 300 nm silicon dioxide on silicon wafers and their near-field optical response in the mid-infrared was evaluated.
3.2 SINS experiments
Near-field optical experiments were carried out in the infrared nanospectroscopy beamline of the Brazilian Synchrotron Light Laboratory (LNLS, Campinas) [34]. In this beamline, the mid-infrared fraction of an ultra-broadband synchrotron radiation is collimated and coupled into a commercial s-SNOM microscope (Neaspec GmbH) [35,36]. Fig. 2 shows the experimental setup used for the SINS experiments. The instrument consists of an AFM equipped with external optics that enables one to focus the incident synchrotron light onto the metallic AFM tip operating in tapping mode. The tip shaft acts as an antenna that enhances the incident electrical field at its apex. This generates a intense optical near field whose effective wavelength peaks at approximately the tip apex radius, thus overcoming the Abbe’s diffraction limit. The obtained optical signal is modulated by the AFM tip oscillation (ca. 300 kHz) and the near-field signal is isolated by demodulating the far-field scattered light at the second harmonic ($2\Omega$) of the tip frequency. For the acquisition of SINS spectra, the microscope is inserted in a Fourier transform spectrometer setup, using a asymmetric Michelson interferometer with a scanning mirror [35–38].
Fig. 2. Experimental setup for the scattering type scanning near-field microscopy using synchrotron radiation in the endstation of IR1 beamline of LNLS.
Using an HgCdTe detector (KolmarTechnologies), [37,39] the mid IR region between 700 cm$^{-1}$ and 5000 cm$^{-1}$ was measured and point spectra were obtained with an optical path difference in the interferometer of 1600 $\mu$m (yielding ca. 6 cm$^{-1}$ spectral resolution) and with a sampling time of 30 ms. We obtained 25 SINS spectra per point in our measurements, which were averaged to improve the signal-to-noise ratio. All spectra were normalized to the spectra acquired from a pure Au surface under the same conditions. All measurements with the s-SNOM microscope were carried out in an N$_{2}$ atmosphere with 1.9 vol% of O$_{2}$ and 2.5 vol% of humidity, which avoided BP oxidation (see Supplement 1.
4. Results and discussion
Layered vdW materials have been extensively characterized via s-SNOM, [40–42] which allows for the coupling between free-space electromagnetic radiation and surface polariton waves [3,4]. Near-field responses of BP/SiO$_2$ and hBN/SiO$_2$ were obtained by SINS. Figure 3 shows the experimental (black) theoretical (red) SINS amplitude spectra demodulated at the second harmonic ($2\Omega$) of the tip’s oscillation frequency for the BP/SiO$_2$ and hBN/SiO$_2$ samples with several flake thicknesses. As a reference, the figure also shows the spectra obtained on bare silica. Figure 3(a) shows the experimental SINS amplitude spectrum for BP/SiO$_{2}$ structures. Due to sample surface-tip coupling, the peak related to the SiO$_{2}$ surface-phonon mode, without BP, appears at $\approx 1135$ cm$^{-1}$, as previously reported [8] and well reproduced by our model. On the other hand, the presence of BP shifts, broadens and changes shape of the SiO$_2$ polaritonic peak. Furthermore, these changes are dependent on the BP thickness and agree well with our theoretical predictions.
Fig. 3. Near-field optical responses. Experimental (black) and theoretical (red) normalized $2\Omega$ intensity spectra for various flake thicknesses for (a) BP/SiO$_2$ and (b) hBN/SiO$_2$ structures.
In Fig. 3(b) we show the comparison between experimental and calculated SINS amplitude spectra for hBN/SiO$_2$ samples with various hBN thicknesses. The calculated spectra again reproduce well the SiO$_2$ surface phonon peak as well as its shift with the hBN crystal thickness. However, the predicted widths are slightly different from those observed experimentally, which could be related resonance tail disturbance of hBN phonons near the SiO$_2$ peak (see Supplement 1).
The SINS amplitude spectra show that the tunability of the SiO$_2$ surface phonon polariton is significantly smaller with hBN than with BP, which is in line with the theoretical predictions shown in Fig. 1. We stress that, even though the tip height is affected by the presence of the vdW crystals, affecting the acquired spectrum, this is not the sole reason for the observed spectral changes. Indeed, Fig. 1(a), as well as Eq. (3), are independent of the s-SNOM configuration and still indicate spectral tunability. The experimentally and theoretically obtained spectral positions of the polariton peak as a function of flake thickness, for both BP and hBN, are shown in Fig. 4, clearly confirming this trend. In particular, note that the experimental results show that, with the BP/SiO$_2$ structure, the peak can be tuned between 1135 and 1076 cm$^{-1}$ ($\sim$ 59 cm$^{-1}$). For BP flakes thinner than 30 nm (and, thus, $qd < 1$), the experimental and theoretical shifts agree very well. For thicker flakes we notice a saturation plateau for the theoretical curve, while experimentally the peaks keep shifting almost linearly with the BP thickness. This behavior suggests a more pronounced penetration of the near field into the BP crystal than predicted by the point dipole model. Moreover, for thicker flakes the SiO$_2$ volume probed by the tip diminishes and the effective dielectric constant $\varepsilon _{*}$ deviates from the condition required for resonance, both of which explain the reduction of the peak amplitude (see Supplement 1).
Fig. 4. Surface phonon polariton frequency shift with flake thickness. Spectral position of the SiO$_2$ surface phonon peak as a function of the BP (red) and hBN (blue) flake thickness in the experimental (symbols) and theoretical (lines) spectra.
5. Conclusions
In summary, we have experimentally and theoretically demonstrated that nanometer-thick layered vdW crystals can alter the optical properties of a substrate, tuning its resonant features and forming a structure with thickness-tunable effective dielectric constant. In particular, we have shown that BP/SiO$_{2}$ structures are able to tune silica’s surface polariton peak by over 50 cm$^{-1}$, while the use of hBN instead of BP leads to significantly lower tuning range due to the lower dielectric constant of hBN at the relevant spectral region. Additionally, our results predict the tunability of epsilon near-zero surfaces, with an hBN/ITO sample expected to tune ITO’s epsilon near zero point by over 200 nm. The approach presented here is also applicable to other spectral ranges, consisting of a simple and effective way to achieve optical tunability of surfaces.
Funding
Fundação de Amparo à Pesquisa do Estado de São Paulo (2012/50259-8, 2015/10405-3, 2018/25339-4, 2019/14017-9, 2015/11779-4); Conselho Nacional de Desenvolvimento Científico e Tecnológico (311327/2020-6, 311564/2018-6).
Acknowledgments
The authors thank LNLS for providing beamtime for this project. This work was funded by FAPESP (SPEC project 2012/50259-8 and Thematic Projects 2015/11779-4 and 2018/25339-4), INCT Nanocarbono and CNPq. D. Grasseschi was supported by a FAPESP fellowship (grant no. 2015/10405-3). R. O. Freitas acknowledges CNPq (grant 311564/2018-6) and FAPESP (grant 2019/14017-9). I.D.B. acknowledges the support from CNPq through the Research Grant 311327/2020-6.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
References
1. M. Z. Alam, I. De Leon, and R. W. Boyd, “Large optical nonlinearity of indium tin oxide in its epsilon-near-zero region,” Science 352(6287), 795–797 (2016). [CrossRef]
2. I. Liberal and N. Engheta, “Near-zero refractive index photonics,” Nat. Photonics 11(3), 149–158 (2017). [CrossRef]
3. D. N. Basov, M. M. Fogler, and F. J. Garcia de Abajo, “Polaritons in van der Waals materials,” Science 354(6309), aag1992 (2016). [CrossRef]
4. T. Low, A. Chaves, J. D. Caldwell, A. Kumar, N. X. Fang, P. Avouris, T. F. Heinz, F. Guinea, L. Martin-Moreno, and F. Koppens, “Polaritons in layered two-dimensional materials,” Nat. Mater. 16(2), 182–194 (2017). [CrossRef]
5. R. W. Boyd, “Physics and Applications of Epsilon-Near-Zero Materials,” in OSA Advanced Photonics Congress (AP) 2020 (IPR, NP, NOMA, Networks, PVLED, PSC, SPPCom, SOF), (Optical Society of America, 2020), p. NpTh2D.1.
6. O. Reshef, I. De Leon, M. Z. Alam, and R. W. Boyd, “Nonlinear optical effects in epsilon-near-zero media,” Nat. Rev. Mater. 4(8), 535–551 (2019). [CrossRef]
7. D. Rodrigo, O. Limaj, D. Janner, D. Etezadi, F. J. Garcia de Abajo, V. Pruneri, and H. Altug, “Mid-infrared plasmonic biosensing with graphene,” Science 349(6244), 165–168 (2015). [CrossRef]
8. L. M. Zhang, G. O. Andreev, Z. Fei, A. S. McLeod, G. Dominguez, M. Thiemens, A. H. Castro-Neto, D. N. Basov, and M. M. Fogler, “Near-field spectroscopy of silicon dioxide thin films,” Phys. Rev. B 85(7), 075419 (2012). [CrossRef]
9. P. Li, X. Yang, T. W. W. Maß, J. Hanss, M. Lewin, A.-K. U. Michel, M. Wuttig, and T. Taubner, “Reversible optical switching of highly confined phonon–polaritons with an ultrathin phase-change material,” Nat. Mater. 15(8), 870–875 (2016). [CrossRef]
10. A. K. Geim and I. V. Grigorieva, “Van der Waals heterostructures,” Nature 499(7459), 419–425 (2013). [CrossRef]
11. H. Kwon, S. W. Seo, T. G. Kim, E. S. Lee, P. T. Lanh, S. Yang, S. Ryu, and J. W. Kim, “Ultrathin and Flat Layer Black Phosphorus Fabricated by Reactive Oxygen and Water Rinse,” ACS Nano 10(9), 8723–8731 (2016). [CrossRef]
12. S. Kim, Y. Jung, J.-Y. Lee, G.-H. Lee, and J. Kim, “In situ thickness control of black phosphorus field-effect transistors via ozone treatment,” Nano Res. 9(10), 3056–3065 (2016). [CrossRef]
13. A. Castellanos-Gomez, M. Barkelid, A. M. Goossens, V. E. Calado, H. S. J. van der Zant, and G. A. Steele, “Laser-Thinning of MoS 2 : On Demand Generation of a Single-Layer Semiconductor,” Nano Lett. 12(6), 3187–3192 (2012). [CrossRef]
14. M. J. L. F. Rodrigues, C. J. S. de Matos, Y. W. Ho, H. Peixoto, R. E. P. de Oliveira, H.-Y. Wu, A. H. C. Neto, and J. Viana-Gomes, “Resonantly Increased Optical Frequency Conversion in Atomically Thin Black Phosphorus,” Adv. Mater. 28(48), 10693–10700 (2016). [CrossRef]
15. I. D. Barcelos, H. A. Bechtel, C. J. S. de Matos, D. A. Bahamon, B. Kaestner, F. C. B. Maia, and R. O. Freitas, “Probing Polaritons in 2D Materials with Synchrotron Infrared Nanospectroscopy,” Adv. Opt. Mater. 8(5), 1901091 (2020). [CrossRef]
16. S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. C. Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable Phonon Polaritons in Atomically Thin van der Waals Crystals of Boron Nitride,” Science 343(6175), 1125–1129 (2014). [CrossRef]
17. K. S. Kim, D. Trajanoski, K. Ho, L. Gilburd, A. Maiti, L. van der Velden, S. de Beer, and G. C. Walker, “The Effect of Adjacent Materials on the Propagation of Phonon Polaritons in Hexagonal Boron Nitride,” J. Phys. Chem. Lett. 8(13), 2902–2908 (2017). [CrossRef]
18. A. M. Dubrovkin, B. Qiang, H. N. S. Krishnamoorthy, N. I. Zheludev, and Q. J. Wang, “Ultra-confined surface phonon polaritons in molecular layers of van der Waals dielectrics,” Nat. Commun. 9(1), 1762 (2018). [CrossRef]
19. Z. Fei, G. O. Andreev, W. Bao, L. M. Zhang, A. S. McLeod, C. Wang, M. K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, M. M. Fogler, M. J. Tauber, A. H. Castro-Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Infrared nanoscopy of dirac plasmons at the graphene-SiO2 interface,” Nano Lett. 11(11), 4701–4705 (2011). [CrossRef]
20. S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S.-E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015). [CrossRef]
21. F. C. B. Maia, B. T. O’Callahan, A. R. Cadore, I. D. Barcelos, L. C. Campos, K. Watanabe, T. Taniguchi, C. Deneke, M. B. Raschke, and R. O. Freitas, “Rectification and gate tuning of the hyperbolic plasmon-phonon polaritons in the graphene-hexagonal boron nitride metamaterial,” arXiv (2017).
22. N. C. Passler, C. R. Gubbin, T. G. Folland, I. Razdolski, D. S. Katzer, D. F. Storm, M. Wolf, S. De Liberato, J. D. Caldwell, and A. Paarmann, “Strong Coupling of Epsilon-Near-Zero Phonon Polaritons in Polar Dielectric Heterostructures,” Nano Lett. 18(7), 4285–4292 (2018). [CrossRef]
23. E. L. Runnerstrom, K. P. Kelley, T. G. Folland, J. R. Nolen, N. Engheta, J. D. Caldwell, and J.-P. Maria, “Polaritonic Hybrid-Epsilon-near-Zero Modes: Beating the Plasmonic Confinement vs Propagation-Length Trade-Off with Doped Cadmium Oxide Bilayers,” Nano Lett. 19(2), 948–957 (2019). [CrossRef]
24. J. Taboada-Gutiérrez, G. Álvarez-Pérez, J. Duan, W. Ma, K. Crowley, I. Prieto, A. Bylinkin, M. Autore, H. Volkova, K. Kimura, T. Kimura, M.-H. Berger, S. Li, Q. Bao, X. P. A. Gao, I. Errea, A. Y. Nikitin, R. Hillenbrand, J. Martín-Sánchez, and P. Alonso-González, “Broad spectral tuning of ultra-low-loss polaritons in a van der Waals crystal by intercalation,” Nat. Mater. 19(9), 964–968 (2020). [CrossRef]
25. S. Foteinopoulou, G. C. R. Devarapu, G. S. Subramania, S. Krishna, and D. Wasserman, “Phonon-polaritonics: enabling powerful capabilities for infrared photonics,” Nanophotonics 8(12), 2129–2175 (2019). [CrossRef]
26. F. H. Feres, R. A. Mayer, I. D. Barcelos, R. O. Freitas, and F. C. B. Maia, “Acceleration of Subwavelength Polaritons by Engineering Dielectric-Metallic Substrates,” ACS Photonics 7(6), 1396–1402 (2020). [CrossRef]
27. F. H. Feres, I. D. Barcelos, R. A. Mayer, T. M. dos Santos, R. O. Freitas, M. B. Raschke, D. A. Bahamon, and F. C. B. Maia, “Dipole modelling for a robust description of subdiffractional polariton waves,” Nanoscale 11(44), 21218–21226 (2019). [CrossRef]
28. A. Laturia, M. L. Van de Put, and W. G. Vandenberghe, “Dielectric properties of hexagonal boron nitride and transition metal dichalcogenides: from monolayer to bulk,” npj 2D Mater. Appl. 2(1), 6 (2018). [CrossRef]
29. P. Kumar, B. S. Bhadoria, S. Kumar, S. Bhowmick, Y. S. Chauhan, and A. Agarwal, “Thickness and electric-field-dependent polarizability and dielectric constant in phosphorene,” Phys. Rev. B 93(19), 195428 (2016). [CrossRef]
30. H. Asahina and A. Morita, “Band structure and optical properties of black phosphorus,” J. Phys. C: Solid State Phys. 17(11), 1839–1852 (1984). [CrossRef]
31. R. Geick, C. Perry, and G. Rupprecht, “Normal Modes in Hexagonal Boron Nitride,” Phys. Rev. 146(2), 543–547 (1966). [CrossRef]
32. J. Aizpurua, T. Taubner, F. J. García de Abajo, M. Brehm, and R. Hillenbrand, “Substrate-enhanced infrared near-field spectroscopy,” Opt. Express 16(3), 1529 (2008). [CrossRef]
33. D. S. Kim, H. Kwon, A. Y. Nikitin, S. Ahn, L. Martin-Moreno, F. J. Garcia-Vidal, S. Ryu, H. Min, and Z. H. Kim, “Stacking Structures of Few-Layer Graphene Revealed by Phase-Sensitive Infrared Nanoscopy,” ACS Nano 9(7), 6765–6773 (2015). [CrossRef]
34. R. O. Freitas, C. Deneke, F. C. B. Maia, H. G. Medeiros, T. Moreno, P. Dumas, Y. Petroff, and H. Westfahl, “Low-aberration beamline optics for synchrotron infrared nanospectroscopy,” Opt. Express 26(9), 11238 (2018). [CrossRef]
35. P. Hermann, A. Hoehl, P. Patoka, F. Huth, E. Rühl, and G. Ulm, “Near-field imaging and nano-Fourier-transform infrared spectroscopy using broadband synchrotron radiation,” Opt. Express 21(3), 2913 (2013). [CrossRef]
36. P. Hermann, A. Hoehl, G. Ulrich, C. Fleischmann, A. Hermelink, B. Kästner, P. Patoka, A. Hornemann, B. Beckhoff, E. Rühl, and G. Ulm, “Characterization of semiconductor materials using synchrotron radiation-based near-field infrared microscopy and nano-FTIR spectroscopy,” Opt. Express 22(15), 17948 (2014). [CrossRef]
37. F. Huth, M. Schnell, J. Wittborn, N. Ocelic, and R. Hillenbrand, “Infrared-spectroscopic nanoimaging with a thermal source,” Nat. Mater. 10(5), 352–356 (2011). [CrossRef]
38. B. Pollard, F. C. B. Maia, M. B. Raschke, and R. O. Freitas, “Infrared Vibrational Nanospectroscopy by Self-Referenced Interferometry,” Nano Lett. 16(1), 55–61 (2016). [CrossRef]
39. F. Keilmann and R. Hillenbrand, “Near-field microscopy by elastic light scattering from a tip,” Philos. Trans. R. Soc., A 362(1817), 787–805 (2004). [CrossRef]
40. B. Knoll and F. Keilmann, “Near-field probing of vibrational absorption for chemical microscopy,” Nature 399(6732), 134–137 (1999). [CrossRef]
41. F. Zenhausern, Y. Martin, and H. K. Wickramasinghe, “Scanning Interferometric Apertureless Microscopy: Optical Imaging at 10 Angstrom Resolution,” Science 269(5227), 1083–1085 (1995). [CrossRef]
42. S. Kawata, T. Ichimura, A. Taguchi, and Y. Kumamoto, “Nano-Raman Scattering Microscopy: Resolution and Enhancement,” Chem. Rev. 117(7), 4983–5001 (2017). [CrossRef]
