Polariton design and modulation via van der Waals / doped semiconductor heterostructures

Polariton design and modulation via van der Waals / doped semiconductor heterostructures | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Polariton design and modulation via van der Waals / doped semiconductor heterostructures Mingze He, Joseph Matson, Mingyu Yu, Angela Cleri, Sai Sunku, and 8 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-2744039/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Hyperbolic phonon polaritons (HPhPs) can be supported in highly anisotropic materials, where the real parts of their permittivities along different directions are opposite in sign as a result of spectrally offset optical phonons. Compared to surface polaritons, HPhPs offer further confinement of long-wavelength light to deeply subdiffractional scales, and volume propagation that enables control of the polariton wavevector by changing the underlying medium. This allows for greater control of polaritonic resonators and near-field polariton propagation without deleterious etching of hyperbolic materials. Yet, conventionally used noble metal and dielectric substrates restrict the tunability of this approach, leaving most of the wavevector inaccessible. To overcome this challenge, we demonstrate that using doped semiconductors, e.g., InAs and CdO, can enable near-continuous tuning and access to both the maximum and minimum wavevectors (~8.3 times experimentally demonstrated). We further elucidate HPhP tuning with the plasma frequency of an InAs substrate, which features a significant wavevector discontinuity and modal order transition when the substrate permittivity crosses -1 in the Reststrahlen band. Around the transition point, the HPhP system is sensitive to perturbations, e.g., the working frequency, InAs plasma frequency and superstrate, thus it is suitable for sensing and modulation applications. We also illustrate that the hBN/InAs platform allows for active modulation at picosecond timescales by photo-injecting carriers into the InAs substrate, demonstrating a dynamic wavevector change of ~20%. Overall, the demonstrated hBN/doped semiconductor platform offers significant improvements towards manipulating HPhPs, and enormous potential for engineered and modulated polaritonic systems for applications in on-chip photonics and planar metasurface optics. Physical sciences/Optics and photonics/Optical materials and structures/Metamaterials Physical sciences/Nanoscience and technology/Nanoscale devices/Nanophotonics and plasmonics Figures Figure 1 Figure 2 Figure 3 Figure 4 Introduction Due to the long free-space wavelength of mid- to far-infrared (IR) light, the realization of deeply subdiffractional photon confinement via the stimulation of polaritons 1 is critical for flat IR nanophotonic applications, such as miniaturized optical components 2 , 3 , on-chip photonics, polariton waveguides 4 and nanolasers 5 . Specifically, hyperbolic polaritons supported in extremely anisotropic media, i.e., those featuring permittivity tensor components with opposite signs along different optical axes, can offer significant promise for many nanophotonic applications 6 where stronger confinement and improved control over propagation is beneficial. Applications of these properties include hyperlensing 7 – 9 , metasurface-based optical components, 10 quantum optics 11 , and probes of nanoscale defects 12 . While hyperbolicity was first demonstrated with artificial dielectric/metal stacks 8 , it was later discovered that a list of natural materials 1 , 13 , including hexagonal boron nitride (hBN 14 , 15 ), MoO 3 16,17 , V 2 O 5 18 , support hyperbolic phonon polaritons (HPhPs). These opportunities are further expanded within low symmetry systems as demonstrated by the report of so-called ‘Ghost-polaritons’ in off-cuts of calcite 19 and hyperbolic shear polaritons in monoclinic crystals such as β-Ga 2 O 3 20 . Such HPhPs in natural crystals feature exceptionally low optical losses 21 – 23 , as the polaritons are derived from optic phonons 22 , 24 instead of scattering from free carriers 25 . Although HPhPs are volume-confined, they can still interact with the local environment through the evanescent field, and HPhP wavevectors are demonstrated to be tuned and engineered by changing the substrate permittivity in a list of studies 4,26−31 , with this effect having been generalized by Fali. et al 26 . Additionally, HPhPs propagating across domains with varying permittivities will be refracted, with the behavior described by Snell’s law 26 and the continuity of tangential components of the wavevectors. With those fundamentals, patterned substrates can be used to manipulate polaritons supported in pristine hyperbolic media, such as polaritonic refraction 26 , 32 , 33 (e.g., prism and lensing), structured HPhPs 32 , 34 , 35 (e.g., waveguiding), photonic crystals 36 , 37 and accelerated HPhPs 38 . Like dielectric optics, those effects rely on wavevector differences for the HPhPs over different substrate regions, and some results can be enhanced with more significant contrast 38 . Additionally, the platform is ideally flat, as placing thin vdW materials over uneven surfaces (e.g., silicon pillars) will modify the morphology and/or induce strain 39 and scattering 40 . However, all existing demonstrations have either used 3D structures to induce a large contrast in the wavevectors, e.g., silicon versus air (etched silicon 35 ), or provided fundamentally limited polaritonic wavevector change (~ 1.6 times for phase change materials 32 , 34 ) with microsecond modulation. Therefore, it is prudent to search for a platform that provides a planar surface and sufficient wavevector contrast that can be actively controlled. Here, we demonstrate a hyperbolic material/doped semiconductor platform capable of controlling HPhPs at an unprecedented level with ultralow surface roughness (sub-nanometer). This platform allows for nearly continuous tuning of HPhP wavevectors, with maximum contrast of ~ 8.3 times being experimentally demonstrated. This doubles the value that can be achieved with noble metals and dielectrics. Moreover, we illustrate a sharp modal order transition when the plasma frequency of the doped semiconductor passes through the transitional frequency, leading to a wavevector discontinuity suitable for modulation and sensing applications. Finally, we show that the hBN/doped semiconductor system can be modulated by photo-injection, with an experimentally demonstrated polaritonic wavelength change of ~ 20% on a picosecond timescale. Although we focus primarily on uniformly doped semiconductors, we provided a proof-of-concept demonstration of hBN over in-plane varying plasma frequency with tuned wavevectors, offering significant freedom to manipulate HPhPs along a planar surface. Importantly, the platform is not limited to hBN, as plasma frequencies of doped semiconductors can be tuned over an extended range of frequencies for other hyperbolic materials (e.g., α-MoO 3 ), providing a significant toolbox for manipulating HPhPs. Concept of tuning HPhPs via substrate permittivity Although HPhPs are volume-confined modes, they remain sensitive to the local environment 4 , 26 , 28 – 31 , 41 , e.g., the dielectric function of the substrate. The dependence of HPhP wavevectors ( k HPhP ) over substrate permittivity can be described by an analytical solution 14 : \(k\left(\omega \right)={k}^{{\prime }}+i{k}^{{\prime }{\prime }}=-\frac{\psi }{d}\left[\text{atan}\left(\frac{{\epsilon }_{o}}{{\epsilon }_{t}\psi }\right)+\text{atan}\left(\frac{{\epsilon }_{s}}{{\epsilon }_{t}\psi }\right)+\pi l\right], \psi =-i\sqrt{\frac{{\epsilon }_{z}}{{\epsilon }_{t}}}\) (1) where d represents the hBN thickness, ɛ o and ɛ s the complex dielectric functions of the superstrate (air here) and the substrate, respectively, and ɛ t and ɛ z are dielectric functions of hBN along the in and out of plane axes. l is non-negative integer representing the HPhP mode order (0,1,2…), as infinite modes can be supported in hyperbolic systems simultaneously, and we here focus on the supported mode with lowest wavevector (referred to as fundamental mode 14 , 42 ) because it usually is dominating in both near- and far-field studies. Note that the substrate-induced wavevector difference is independent of hBN thickness, as Eq. (1) can be written in the following form: $$k\left(\omega \right)d=-\psi \left[\text{atan}\left(\frac{{\epsilon }_{o}}{{\epsilon }_{t}\psi }\right)+\text{atan}\left(\frac{{\epsilon }_{s}}{{\epsilon }_{t}\psi }\right)+\pi l\right], \psi =-i\sqrt{\frac{{\epsilon }_{z}}{{\epsilon }_{t}}}$$ 2 For a hBN/doped semiconductor heterostructure, the HPhPs supported can be indirectly engineered by changing the carrier concentration (therefore the plasma frequency, ω p, and dielectric function) of the underlying doped semiconductors, even with same hBN thickness. Therefore, HPhPs propagating in different domains possess different wavevectors, as shown in the schematic in Fig. 1 a. We first demonstrate the substrate-induced polariton tuning with a hBN/InAs heterostructure. To this end, we grew InAs samples with different ω p by controlling the as-grown dopant concentration and transferred hBN slabs onto these InAs substrates. We then utilized scattering-type scanning near field microscopy (s-SNOM) to measure the HPhP dispersion via a standard procedure, and some exemplary data analyses are included in SI, section 1 . To minimize the role of hBN thickness in dictating HPhP wavevectors, similar hBN thicknesses (~ 51–55 nm) were used in this set of comparisons. The calculated dispersion plots along with the experimentally extracted data points validate that HPhP dispersions can be manipulated by varying the InAs ω p (Fig. 1 b-d). Notably, the HPhP modal number in those systems are different: l = 0 branch is only supported when InAs is dielectric (Fig. 1 b-c versus Fig. 1 d) due to the mirror symmetry. Thus, the k HPhP supported by uniform hBN can be engineered by the underlying doped semiconductor, for applications such as far-field resonators 26 , 34 or the near-field polariton propagation 26 , 32 – 36 , 38 , so that etch-induced material damage to hBN can be avoided. While it is possible to tune HPhPs by adjusting the substrate dielectric function, quantitative analysis of the dependence of the k HPhP upon the substrate permittivity is required enable the engineering of devices using this concept. Due to the substantial variation in hBN thickness between exfoliations, we discuss the influence of substrate permittivity (ε s ) on normalized wavevector \(k\left(\omega \right)d\) in Eq. ( 2 ), as shown in Fig. 2 . Notably, l = 0 branch is only supported when on a dielectric substrate, and it is forbidden over a metallic substrate due to the mirror symmetry 27 . Consequently, for the fundamental mode, the modal orders are different: l = 0 (low confinement) for dielectric substrates and l = 1 branch (high confinement) for metallic substrates. Notice that the cut-off of l = 0 branch happens at Re(ε s )= -ε superstrate (air in our case) instead of Re(ε s ) = 0, and more related discussions are included in SI, section 2 . Furthermore, the wavevectors can also be manipulated by changing the substrate permittivity even within the same modal branch: increasing Re(ε s ) leads to reduced k HPhP . Importantly, the majority of k HPhP values are realized within a small range of Re(ε s ) (between − 10 and 10), encompassing both the highest and lowest k HPhP values and resulting in the largest polaritonic refraction effects. While the tunability of HPhPs via substrate is promising, traditional metallic substrates (noble metals) do not provide access to the high wavevector range, as they exhibit |Re(ε s )| over 100 in the mid-infrared. Quantitatively, the maximum wavevector contrast achievable with noble metals and dielectrics (air) is 4.2 times at 1500 cm − 1 . To exploit the tunability of HPhP wavevectors, here we employed doped semiconductors, with the plasma frequencies tuned from below to above the Reststrahlen band of hBN. Therefore, we used InAs 43 and cadmium oxide (CdO 44 ) as substrates, with achievable plasma frequencies being 500–2000 cm − 1 and 1500–15000 cm − 1 , respectively. Experimentally, we grew InAs and CdO substrates with varying ω p , and h 10 BN flakes 42 were transferred onto them, with k HPhP measured and extracted by Fourier analysis ( SI, section 1 ). The experimental data are plotted as symbols in Fig. 2 , showing excellent agreement with analytical solutions. Notably, with InAs substrates, we experimentally obtained both the highest and lowest k HPhP at 1500 cm − 1 , with a k HPhP difference of ~ 8.3 times, which could be used to exploit polaritonic in-plane refractive behavior. With doped CdO and InAs, we have unlocked almost the entire potential of controlling the k HPhP through tuning substrate permittivity, with only a small range of k HPhP not accessible (~ 13%), where high refractive index dielectrics (|Re(ε s )|>10) would be required. Unlike noble metals, which typically feature high surface roughness 45 (unless realized via specialized growth 45 and/or fabrication 40 ), the doped semiconductors employed here possess low surface roughness (below 1 nm, SI, section 3 ), which is crucial for HPhP platforms 40 , 45 . Importantly, semiconductors with varying in-plane ω p can be realized ( SI, section 4 ), and we experimentally demonstrated that HPhPs supported in a hBN slab exhibit different wavevector in different domains, further facilitating the manipulation of HPhPs for applications like waveguiding 34 , lensing 32 and resonators 34 . Therefore, those doped semiconductors can serve as ultrasmooth platforms to enable the tuning of HPhPs over an extended range of k HPhP . Modal order transition in hBN/InAs heterostructures To realize practical devices using doped semiconductor platforms, we must develop an understanding of the dependence of the wavevector on the substrate ω p . In particular, the hBN/InAs heterostructure offers an ideal tuning range for engineering the HPhPs. To that end, we calculated how k HPhP changes with InAs ω p , at a working frequency of 1500 cm − 1 , as shown in Fig. 3 a. When the InAs carrier concentration increases such that the ω p surpasses the excitation (working) frequency, InAs exhibit a change from a dielectric to metallic behavior (grey and magenta shaded in Fig. 3 a, respectively). This dielectric to metallic evolution of the substrate further induces a HPhP modal order transition from l = 0 to l = 1 branch, leading to the wavevector discontinuity (Fig. 2 ). Additionally, in both dielectric and metallic regimes (grey and magenta shaded in Fig. 3 a, respectively), an increase in InAs ω p causes a decline in Re(ε InAs ), resulting in a monotonical decrease in k HPhP . By correlating k HPhP with InAs ω p , HPhP propagations can be manipulated with designable wavevectors over different domains, for both polaritonic refraction devices and/or resonators with significant design freedom. It is important to note that both minimum and maximum k HPhP occur around the transitional point, with 8.3 times difference being experimentally demonstrated. Since the InAs permittivity is dispersive, the modal transition can also occur in the frequency domain. When the InAs Re(ε s ) passes through − 1 within the Reststrahlen band of hBN, a modal order transition occurs, splitting the fundamental HPhPs into two supported modal orders, as shown in Fig. 3 b. As such, the dispersion plot features highly confined HPhPs below the transition frequency ( l = 1 mode), while showing reduced confinement of the HPhPs above it ( l = 0 mode) (Fig. 3 b). By using an InAs sample with a ω p at a frequency within the Reststrahlen band, we experimentally demonstrated the transition discontinuity (Fig. 3 b, green triangles), with good agreement with calculations. The dispersion is analogous to two stacked hyperbolic dispersions, and we observed intriguing behaviors in both frequency (coexisting absorption and reflection modes) and real space (guiding in different regions at different frequencies) in numerical simulations ( SI, section 5 ). The modal order transition criteria can be generalized for both the InAs ω p (substrate-tuning) and modified working frequency, as shown in Fig. 3 c. A clear transition line distinguishes the two modal orders, separating k HPhP into two regimes: one with highly confined HPhPs (right side) and one supporting less confined modes (left). At any transition point, the modal order transition could happen if the InAs ω p or the working frequency is changed, i.e., along the InAs ω p axis or wavenumber axis in Fig. 3 c, respectively. Three representative s-SNOM images showing the highly and poorly confined HPhPs are presented in Fig. 3 d, clearly showing the transitions. As a consequence of the modal order transition and wavevector discontinuity, around the transition line, k HPhP experiences large variations with perturbations to the working conditions, e.g., InAs ω p , working frequency, and local environment ( SI, section 7 ). Therefore, a HPhP system working around the transition point, such as resonators, can be modulated effectively and/or used for refractive index sensing. Note that for any working frequency inside the Reststrahlen band of hBN, there is a corresponding InAs ω p to enable this transition, while such tunability of InAs 43 lends this concept to be expanded to other hyperbolic materials, e.g., MoO 3 . Ultrafast modulation of HPhPs Besides manipulating HPhPs in static structures, the hBN/doped semiconductor platform also enables the dynamic modulation of HPhPs. Both permittivity tensors of InAs and CdO can be modulated at the surface by electrical biasing 46 and photo-carrier injection 47 , 48 , and here we demonstrate ultrafast modulation in a hBN/InAs heterostructure. When a ~ 100-fs, 80-MHz repetition rate pulsed laser source at 0.78 eV (1590 nm free-space wavelength) irradiates the hBN/InAs heterostructure, the photons will only be absorbed by InAs since it is above InAs bandgap (0.35 eV), yet well below that of hBN (5.95 eV) 49 . This process will generate a surplus of free-charge carriers at the InAs surface, locally increasing ω p with a rise time below 1 ps, while those free carriers will subsequently recombine with a lifetime of ~ 8 ps, as shown in Fig. 4 c. Because of this locally modulated InAs ω p , k HPhP values supported in the hBN/InAs heterostructure can be modulated at picosecond timescales. To experimentally demonstrate such modulation, we conducted a near-field pump-probe measurement on one of the hBN/InAs heterostructures, with the detailed set-up provided in the Methods . Before the pump signal arrives ( pre-pump ), we observe a polariton wavelength of ~ 1.15 µm at 1450 cm − 1 for the HPhPs supported, with the InAs ω p at 990 cm − 1 . When the pump arrives ( at-pump ), the InAs ω p at the surface is shifted to a higher frequency (1150 cm − 1 ), leading to a decreased k HPhP as mentioned, and we experimentally observe a stretched polariton wavelength by ~ 20% (~ 1.37 µm). Since the time constant of modulated InAs ω p is ~ 8 ps, the modulated HPhP wavevector recovers within a similar temporal scale. Experimentally, the polaritonic behavior ( λ HPhP = 1.29 µm) relaxes to a state between pre-pump and at-pump after 7 ps of the pump signal (green curve in Fig. 4 a). Those effects are also manifested in the dispersion plots extracted from nano-FTIR scans ( SI, section 8 ). Importantly, the InAs ω p was pumped from 990 cm − 1 to 1150 cm − 1 , which are both well below the transition point discussed above. Therefore, we expect a stronger modulation if an InAs ω p is modulated to surpass the transition frequencies and to induce modal order transitions. In addition to the modification of the polariton wavelength, we can also monitor how the resonant frequency of a given HPhP system change when the InAs is pumped. For a proof-of-concept demonstration, we measured the nano-FTIR spectra at a spatial position ~ 0.35 µm from the hBN edge, which corresponds to a constant wavevector of HPhP system ( k ≈ 7×10 4 cm − 1 ) for tip launched mode, and the frequency amplitude peaks indicate the modal frequency. When InAs ω p is increased, the wavevector at a fixed frequency is reduced; therefore, for a constant wavevector, the corresponding frequency blueshifts. Experimentally, the modal frequency indeed experienced a blue shift when the InAs was pumped, with a time constant of ~ 6 ps. This implies that we can modulate HPhP resonators at ultrafast time scales with un-pumped phonon materials for potentially lower loss, and the ultrafast switching of HPhPs has important implications for device applications in modulated optical sources 50 , beacons and other areas. Importantly, we do not pump the polaritonic material itself (unlike reference where polar materials are directly pumped 51 ), which can be a challenge due to wide bandgaps 49 , 52 , and our approach can be universally applied to other HPhP supporting materials. Our approach thereby offers a great degree of flexibility in terms of doped substrates, as well as other hyperbolic materials, and could provide a foundation for more complex heterostructures. Summary In summary, we proposed and demonstrated a hyperbolic material/doped semiconductor platform to manipulate HPhPs at an unprecedented level. Our heterostructure platform offers significant improvements by providing access to almost all (~ 87%) possible HPhP wavevectors, with both maximum and minimum values accessible (~ 8.3 times difference experimentally demonstrated). This is in contrast to conventional noble metal and dielectric substrates that only provide access to discrete wavevectors with limited differences (~ 4.2 time). Moreover, when the plasma frequency of the doped semiconductor passes through the polariton frequency, a sharp modal order transition of HPhP will happen, and the HPhP system is sensitive to the local environment around the transition point, which could be used for sensing and modulation purposes. Finally, we demonstrate an ultrafast modulation of HPhPs at picosecond time scales by photoinjecting free carriers into semiconductors, with a polaritonic wavelength change of ~ 20%. With advances in semiconductor manufacturing, enabling further reduced ohmic losses and in-plane variations in doping 53 , we expect doped semiconductors to be an increasingly important platform to manipulate HPhPs, in both the near- and far-fields. Importantly, the concept is not limited to hBN, and these effects can be realized over an extended spectral range and hyperbolic materials (e.g., α-MoO 3 16 , β-Ga 2 O 3 20 , calcite 19 ), opening a whole new toolbox to manipulate in-plane HPhPs. Methods Device fabrication. In-doped CdO (n-type) was deposited on 2-inch r -plane (012) sapphire single crystal substates at 400 ° C by a reactive co-sputtering process employing high-power impulse magnetron sputtering (HiPIMS) and radio frequency (RF) sputtering from 2-inch diameter metal cadmium and indium targets, respectively. HiPIMS drive conditions were 800-Hz frequency and 80-µs pulse time, yielding a 1250-µs period and 6.4% duty cycle. Film growth occurs in a mixed argon (20 sccm) and oxygen (14.4 sccm) environment at a total pressure of 10 mTorr. Post-deposition, samples were annealed in a static oxygen atmosphere at 635°C for 30 minutes. Si-doped InAs (n-type) was grown by molecular beam epitaxy (MBE) on the epi-ready GaAs (100) substrates, using a Veeco GENxplor MBE in the University of Delaware Materials Growth Facility. In this system, the substrate temperature was measured by a band edge thermometer and the source flux was monitored as beam equivalent pressure (BEP). It provides an ultra-high vacuum environment with pressures as low as 1×10 − 10 Torr for growth. GaAs substrates were fully deoxidized at 620°C prior to growth. To prepare a smooth surface for the growth of Si-doped InAs, a GaAs buffer layer with a thickness of 100nm was deposited at 580°C first. Thereafter, the substrate was cooled to 420°C. Then the Si-doped InAs layer was grown by opening the Si, In, As, and Bi source cells simultaneously. The As2:In BEP ratio and growth rate were kept around 20, and 1.7 um/h, respectively. A small amount of Bi (In:Bi BEP ratio was 50) was added as a surfactant to suppress the segregation of Si dopants on the surface 54 . The Si doping concentration was varied by changing the Si flux while using the same growth rate. The doping density and carrier mobility were detected by room-temperature Hall effect measurements in a van der Pauw configuration. 10 B enriched hBN (~ 99% enriched 42,55 ) flakes were exfoliated and transferred onto the InAs and CdO substrates using low contamination transfer techniques. The hBN crystals were grown with a boron source that was nearly 100% 10 B isotope, as previously described 56 . Calculations. In our heterostructures, the doped semiconductors are treated as substrate, as they are significantly thicker (~ 500 nm or 1 µm thick) than the evanescent field of HPhPs. The analytical solution is calculated by Eq. (1) in the main text, and the contour plots in Fig. 1 and Fig. 3 b are calculated by the transfer matrix method. Near-field measurements. Near-field nano-imaging experiments were carried out in a commercial Neaspec ( www.neaspec.com ) s-SNOM and nano-FTIR based around a tapping-mode atomic force microscope. A metal-coated Si-tip of apex radius R ≈ 20 nm that oscillates at a frequency of Ω ≈ 280 kHz and tapping amplitude of about 100 nm is illuminated by a laser beam (probe laser, in the mid-infrared) at an angle 60° off normal to the sample surface. Scattered light launches HPhPs in the device and the tip then re-scatters light (described more completely in the main text) for detection in the far-field. Background signals are efficiently suppressed by demodulating the detector signal at harmonics of the tip oscillation frequency and employing pseudo-heterodyne interferometric detection. Static measurements . For static measurements, the incident beam is a single-frequency quantum cascade laser. The laser frequency can be tuned, and s-SNOM mapping were conducted in a single-wavelength measuring scheme. Ultrafast measurements . For ultrafast measurements, the probe laser is a pulsed broadband (~ 1000–2000 cm − 1 ) different frequency generation laser (fiber laser), and the pulse width is ~ 200 fs after considering the dispersion of beam splitter. The pump laser is a pulsed single-frequency laser at 1590 nm, and the pulse width is ~ 100 fs. Those pulse widths set the time resolution of our system: ~0.3 ps. The repetition rates of both lasers are 80 MHz. The time delay is controlled by a delay stage on the pump beam line. In the ultrafast pumped heterostructure, we also notice that the HPhPs are experiencing a collective effect during the propagation in the temporal domain. HPhPs have small group velocities, and they will propagate for ~ 0.5-2 ps before being collected. As the lifetime of InAs free-carriers is ~ 8 ps (see fitting in SI, section 10 ), the observed HPhPs will experience decreasing InAs ω p during the propagation, i.e., increasing k HPhP , if we assume uniform InAs pumping. Therefore, the as-measured ultra-fast HPhP response is convoluted within a certain time scale, depends on the group velocity. Declarations Data availability. The authors declare that the data supporting the findings of this study are available within the paper and its Supplementary Information files. Additional data is available from the authors upon request. Acknowledgement M. H., J. R. M. and J-P. M. gratefully acknowledge support for this work by Office of Naval Research Grant N00014-22-12035. J-P. M, and J. D. C. acknowledge support from the Army Research Office Research Grant W911NF-21-1-0119. A. J. C. and J-P. M. acknowledge support from the Army Research Office W911NF-16-1-0406. Support for hBN crystal growth was provided by the Office of Naval Research, award number N000142212582. M. Y. and S. L. acknowledge funding from the National Science Foundation, Division of Materials Research under Award No. 1904760 and the Division of Electrical, Communications, and Cyber systems under Award No. 2102027. M. Y. and S. L. acknowledge the use of the Materials Growth Facility (MGF) at the University of Delaware, which is partially supported by UD-CHARM a National Science Foundation MRSEC under Award No. DMR-2011824. T. G. F would like to acknowledge the University of Iowa startup funding. Work at Columbia was supported primarily by the Center on Precision-Assembled Quantum Materials, funded through the US National Science Foundation (NSF) Materials Research Science and Engineering Centers (award no. DMR-2011738). DNB is the Vannevar Bush Faculty Fellow ONR-VB: N00014-19-1-2630. Contributions M. H., J. R. M., T. G. F., J-P. M. and J.D.C. conceived the idea. M. H., S. S. S. and T. G. F. conducted the static near-field measurements, and M. H., J. R. M. and S. 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Nat Nanotechnol 10:2–6. 10.1038/nnano.2014.310 Foteinopoulou S, Devarapu GCR, Subramania GS, Krishna S, Wasserman D (2019) Phonon-polaritonics: enabling powerful capabilities for infrared photonics. Nanophotonics 8:2129–2175 Fali A et al (2019) Refractive Index-Based Control of Hyperbolic Phonon-Polariton Propagation. Nano Lett 19:7725–7734 Ambrosio A et al (2018) Selective excitation and imaging of ultraslow phonon polaritons in thin hexagonal boron nitride crystals. Light: Sci Appl 7:1–9 Dai S et al (2019) Phase-Change Hyperbolic Heterostructures for Nanopolaritonics: A Case Study of hBN/VO2. Adv Mater 31:1900251. 10.1002/adma.201900251 Dai S et al (2019) Hyperbolic Phonon Polaritons in Suspended Hexagonal Boron Nitride. Nano Lett 19:1009–1014. 10.1021/acs.nanolett.8b04242 Kim KS et al (2017) The Effect of Adjacent Materials on the Propagation of Phonon Polaritons in Hexagonal Boron Nitride. 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Acceleration of subwavelength polaritons by engineering dielectric-metallic substrates. Acs Photonics 7:1396–1402 Blundo E et al (2022) Vibrational Properties in Highly Strained Hexagonal Boron Nitride Bubbles.Nano Letters Lee I-H, Yoo D, Avouris P, Low T, Oh S-H (2019) Graphene acoustic plasmon resonator for ultrasensitive infrared spectroscopy.Nature nanotechnology,1 Ambrosio A et al (2018) Selective excitation and imaging of ultraslow phonon polaritons in thin hexagonal boron nitride crystals. Light: Sci Appl 7:27. 10.1038/s41377-018-0039-4 Giles AJ et al (2018) Ultralow-loss polaritons in isotopically pure boron nitride. Nat Mater 17:134 Law S, Liu R, Wasserman D (2014) Doped semiconductors with band-edge plasma frequencies. J Vacuum Sci Technol B Nanatechnol Microelectronics: Mater Process Meas Phenom 32:052601 Nolen JR et al (2020) Ultraviolet to far-infrared dielectric function of n-doped cadmium oxide thin films. Phys Rev Mater 4:025202 Menabde SG et al (2022) Near-field probing of image phonon-polaritons in hexagonal boron nitride on gold crystals. Sci Adv 8:eabn0627 Park J et al (2018) Dynamic thermal emission control with InAs-based plasmonic metasurfaces. Sci Adv 4:eaat3163 Wagner M et al (2014) Ultrafast dynamics of surface plasmons in InAs by time-resolved infrared nanospectroscopy. Nano Lett 14:4529–4534 Yang Y et al (2017) Femtosecond optical polarization switching using a cadmium oxide-based perfect absorber. Nat Photonics 11:390–395 Cassabois G, Valvin P, Gil B (2016) Hexagonal boron nitride is an indirect bandgap semiconductor. Nat Photonics 10:262 Xiao Y, Charipar NA, Salman J, Piqué A, Kats MA (2019) Nanosecond mid-infrared pulse generation via modulated thermal emissivity. Light: Sci Appl 8:1–8 Dunkelberger AD et al (2018) Active tuning of surface phonon polariton resonances via carrier photoinjection. Nat Photonics 12:50–56 Galazka Z (2018) β-Ga2O3 for wide-bandgap electronics and optoelectronics. Semicond Sci Technol 33:113001 Miyauchi E, Hashimoto HJNI, Materials MiP (1987) R. S. B. B. I. w. & Atoms. Maskless ion implantation system for three-dimensional fine doping structures in III–V compound semiconductors. 21, 104–111 Wei D, Maddox S, Sohr P, Bank S, Law S (2020) Enlarged growth window for plasmonic silicon-doped InAs using a bismuth surfactant. Opt Mater Express 10:302–311 Vuong T et al (2018) Isotope engineering of van der Waals interactions in hexagonal boron nitride. Nat Mater 17:152 Liu S et al (2018) Single crystal growth of millimeter-sized monoisotopic hexagonal boron nitride. Chem Mater 30:6222–6225 Additional Declarations There is NO Competing Interest. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-2744039","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":188587682,"identity":"e206e1da-0822-4747-83d0-d9469441ddef","order_by":0,"name":"Mingze He","email":"","orcid":"https://orcid.org/0000-0001-8773-1268","institution":"Vanderbilt University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Mingze","middleName":"","lastName":"He","suffix":""},{"id":188587683,"identity":"1f568c97-5834-4904-9c7e-00c023e95416","order_by":1,"name":"Joseph Matson","email":"","orcid":"https://orcid.org/0000-0002-7183-2686","institution":"Vanderbilt University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Joseph","middleName":"","lastName":"Matson","suffix":""},{"id":188587684,"identity":"3c591503-80b3-4295-aba9-6337cfcbcd07","order_by":2,"name":"Mingyu Yu","email":"","orcid":"","institution":"University of Delaware","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Mingyu","middleName":"","lastName":"Yu","suffix":""},{"id":188587685,"identity":"9ae4ce90-d9d8-4e3f-90b9-ca93da79e96c","order_by":3,"name":"Angela Cleri","email":"","orcid":"","institution":"The Pennsylvania State University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Angela","middleName":"","lastName":"Cleri","suffix":""},{"id":188587686,"identity":"82396304-39c9-40bc-9728-85fd079a5f97","order_by":4,"name":"Sai Sunku","email":"","orcid":"","institution":"Columbia University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Sai","middleName":"","lastName":"Sunku","suffix":""},{"id":188587687,"identity":"bcc7ca9b-a2ab-4989-b185-72ac311c6ef7","order_by":5,"name":"Eli Jenzen","email":"","orcid":"","institution":"Kansas State University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Eli","middleName":"","lastName":"Jenzen","suffix":""},{"id":188587688,"identity":"b070466b-30d6-4fb7-ba41-56ead0a37c73","order_by":6,"name":"Stefan Mastel","email":"","orcid":"","institution":"Attocube Systems AG","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Stefan","middleName":"","lastName":"Mastel","suffix":""},{"id":188587689,"identity":"bb9c48b7-eb46-4365-811d-4ed45a48e119","order_by":7,"name":"Thomas G. Folland","email":"","orcid":"","institution":"Vanderbilt University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Thomas","middleName":"G.","lastName":"Folland","suffix":""},{"id":188587690,"identity":"3258eef3-6ea3-4532-bb8d-cc50f7d9638b","order_by":8,"name":"James Edgar","email":"","orcid":"https://orcid.org/0000-0003-0918-5964","institution":"Kansas State University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"James","middleName":"","lastName":"Edgar","suffix":""},{"id":188587691,"identity":"78c50e3a-aca1-44f5-b1fa-0a6c2b903297","order_by":9,"name":"Dmitri Basov","email":"","orcid":"https://orcid.org/0000-0001-9785-5387","institution":"Columbia University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Dmitri","middleName":"","lastName":"Basov","suffix":""},{"id":188587692,"identity":"0c6fd63f-fdbb-4b96-9d42-a3473c59876e","order_by":10,"name":"Jon-Paul Maria","email":"","orcid":"","institution":"The Pennsylvania State University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Jon-Paul","middleName":"","lastName":"Maria","suffix":""},{"id":188587693,"identity":"d74b6734-77b0-40f9-82c5-702ce2c439b2","order_by":11,"name":"Stephanie Law","email":"","orcid":"","institution":"The Pennsylvania State University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Stephanie","middleName":"","lastName":"Law","suffix":""},{"id":188587694,"identity":"6f14a086-3883-4f30-b8c6-e551283a766c","order_by":12,"name":"Joshua Caldwell","email":"data:image/png;base64,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","orcid":"https://orcid.org/0000-0003-0374-2168","institution":"Vanderbilt University, Mechanical Engineering Department","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Joshua","middleName":"","lastName":"Caldwell","suffix":""}],"badges":[],"createdAt":"2023-03-27 22:25:31","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-2744039/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-2744039/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":35297546,"identity":"a94d4333-9744-4e52-8cf8-9f1140005780","added_by":"auto","created_at":"2023-04-04 22:46:13","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":669617,"visible":true,"origin":"","legend":"\u003cp\u003eTuned HPhP dispersion of hBN/doped semiconductor heterostructure by controlling semiconductor ω\u003csub\u003ep\u003c/sub\u003e. a, Schematic of the platform. For the same hBN, the HPhP wavelength changes as a function of the plasma frequency of semiconductor. hBN are represented with multi-layer hexagonal structures, with HPhPs shown as waves over it. \u0026nbsp;In this example, the InAs on the right side (magenta color) is highly doped, shrinking the HPhP wavelength. b-d, Dispersion plots of hBN over InAs of different plasma frequencies. The plasma frequencies are noted on the corresponding panels, and the thicknesses of hBN are 51, 51 and 55 nm, respectively. The contour plots and dashed curves are calculated by transfer matrix method (TMM) and Eq. (1), respectively, and the triangles are extracted from s-SNOM data.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-2744039/v1/bd5515df60daeec6110a8dcb.png"},{"id":35296893,"identity":"fa0efae5-6ab7-49b4-990e-0c4bb1ade93a","added_by":"auto","created_at":"2023-04-04 22:38:13","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":78152,"visible":true,"origin":"","legend":"\u003cp\u003eFull control of \u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003eHPhP\u003c/em\u003e\u003c/sub\u003e with doped semiconductors. The normalized \u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003eHPhP\u003c/em\u003e\u003c/sub\u003e varies with the Re(ε\u003csub\u003es\u003c/sub\u003e) of the substrate. All curves are calculated by Eq. (2), while all symbols are experimental data. Colored shadows indicate the tunable range of \u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003eHPhP\u003c/em\u003e\u003c/sub\u003e with that substrate with achievable doping. Solid symbols represent fundamental modes, while open symbols represent high-order modes. Data with dielectric (metallic) InAs are plotted with black (purple) stars. Data with metallic CdO are plotted with purple rectangles. Note that all noble metals lead to nearly identical \u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003eHPhP, \u003c/em\u003e\u003c/sub\u003eand the color box on the y-axis is extended for visualization purposes. Due to the accessible carrier concentration and high-frequency permittivity values, the tuning range of Re(ε\u003csub\u003es\u003c/sub\u003e) of InAs and CdO are -10 to 10, and -100 to -1, respectively.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-2744039/v1/34393dfa9cd92589e3801367.png"},{"id":35296894,"identity":"34107d44-dadd-4c0a-8b1c-27c8627900a5","added_by":"auto","created_at":"2023-04-04 22:38:13","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":396021,"visible":true,"origin":"","legend":"\u003cp\u003eModal order transition of HPhPs in hBN/InAs heterostructure. a, The relationship between normalized \u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003eHPhP\u003c/em\u003e\u003c/sub\u003e and InAs ω\u003csub\u003ep\u003c/sub\u003e. All curves are calculated by Eq. (1), while all symbols are experimental data. Solid symbols represent fundamental modes, while open symbols represent high-order modes. Data with dielectric (metallic) InAs are plotted with black (purple) symbols. The colored shades indicate whether InAs behaves as dielectrics or metals. b, The modal order transition observed in the frequency domain. The contour plot is calculated by TMM and triangles are experimental data. For experimental data points above the transitional frequency, a different method is employed to extract wavevectors due to high polaritonic loss, and details are given in SI, section 6. c, \u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003eHPhP \u003c/em\u003e\u003c/sub\u003e\u003csub\u003e­\u003c/sub\u003eat different wavenumber and InAs ω\u003csub\u003ep\u003c/sub\u003e, with larger \u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003eHPhP \u003c/em\u003e\u003c/sub\u003e\u003csub\u003e­\u003c/sub\u003eplotted with the brighter color. The modal order clearly transits when InAs ω\u003csub\u003ep \u003c/sub\u003epasses the Reststrahlen band of hBN. d, Three representative s-SNOM images plotted with the same scale bar showing the engineered \u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003eHPhP\u003c/em\u003e\u003c/sub\u003e. While the hBN thickness in subpanel-1 is 51 nm, the hBN thickness in subpanel-2,3 is 75 nm. The normalized wavevectors for the three subpanels are 0.235, 1.35, and 0.24, respectively.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-2744039/v1/409511a546c79b069eac9bd1.png"},{"id":35296896,"identity":"dee6c7ef-c98c-4107-9450-3374808ac025","added_by":"auto","created_at":"2023-04-04 22:38:13","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":352326,"visible":true,"origin":"","legend":"\u003cp\u003eUltrafast modulation of HPhPs. a, The line profiles extracted from pump-probe nano-FTIR scans at different time delays. The noisy curves are raw data, and we applied a non-linear curve fitting to extract the HPhP wavelengths following the method in reference\u003csup\u003e18\u003c/sup\u003e, with the fitted data plotted as solid curves. b, The ultrafast nano-FTIR probed at a constant spatial position (~ 0.35 µm from the edge, \u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003eHPhP\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e≈\u003c/em\u003e7×10\u003csup\u003e4\u003c/sup\u003e cm\u003csup\u003e-1\u003c/sup\u003e). The data here are processed with FFT filters to remove noise, and the raw data and signal process can be found in SI, section 9. Note that the high optical amplitude at 1400 cm\u003csup\u003e-1\u003c/sup\u003e is the TO phonon of hBN, and it was not modulated in our configuration. c, The ultrafast nano-FTIR measurements on InAs substrate. The reflection dip position is correlated to the plasma frequency of InAs, and the dielectric function fitting in the near-field can be found in SI, Fig. S10. The InAs static plasma frequency is 990 cm\u003csup\u003e-1\u003c/sup\u003e, and the hBN thickness is 55 nm.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-2744039/v1/06ce1751a9a9e74a3ad3c368.png"},{"id":36606273,"identity":"85b61ca9-2ebe-4d83-9c74-48c5d83ed842","added_by":"auto","created_at":"2023-05-04 09:01:34","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2137594,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2744039/v1/2f49caff-dfc0-4b52-9ec6-bd81f43994d9.pdf"},{"id":35296897,"identity":"9990b189-3e1f-4468-abae-264e020646dd","added_by":"auto","created_at":"2023-04-04 22:38:14","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":4171438,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"InAshBNmanuscriptSIv10.0.docx","url":"https://assets-eu.researchsquare.com/files/rs-2744039/v1/66cb641a42ceb89fb890ed13.docx"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Polariton design and modulation via van der Waals / doped semiconductor heterostructures","fulltext":[{"header":"Introduction","content":"\u003cp\u003eDue to the long free-space wavelength of mid- to far-infrared (IR) light, the realization of deeply subdiffractional photon confinement via the stimulation of polaritons\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e is critical for flat IR nanophotonic applications, such as miniaturized optical components\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e2\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e, on-chip photonics, polariton waveguides\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/sup\u003e and nanolasers\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e. Specifically, hyperbolic polaritons supported in extremely anisotropic media, i.e., those featuring permittivity tensor components with opposite signs along different optical axes, can offer significant promise for many nanophotonic applications\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e where stronger confinement and improved control over propagation is beneficial. Applications of these properties include hyperlensing\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e7\u003c/span\u003e\u0026ndash;\u003cspan class=\"CitationRef\"\u003e9\u003c/span\u003e\u003c/sup\u003e, metasurface-based optical components,\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e10\u003c/span\u003e\u003c/sup\u003e quantum optics\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e11\u003c/span\u003e\u003c/sup\u003e, and probes of nanoscale defects\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003e. While hyperbolicity was first demonstrated with artificial dielectric/metal stacks\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e8\u003c/span\u003e\u003c/sup\u003e, it was later discovered that a list of natural materials\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e1\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e13\u003c/span\u003e\u003c/sup\u003e, including hexagonal boron nitride (hBN\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e14\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003e), MoO\u003csub\u003e3\u003c/sub\u003e\u003csup\u003e16,17\u003c/sup\u003e, V\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e5\u003c/sub\u003e\u003csup\u003e18\u003c/sup\u003e, support hyperbolic phonon polaritons (HPhPs). These opportunities are further expanded within low symmetry systems as demonstrated by the report of so-called \u0026lsquo;Ghost-polaritons\u0026rsquo; in off-cuts of calcite\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e and hyperbolic shear polaritons in monoclinic crystals such as \u0026beta;-Ga\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e\u003csup\u003e20\u003c/sup\u003e. Such HPhPs in natural crystals feature exceptionally low optical losses\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e21\u003c/span\u003e\u0026ndash;\u003cspan class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e, as the polaritons are derived from optic phonons\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e22\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e instead of scattering from free carriers\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eAlthough HPhPs are volume-confined, they can still interact with the local environment through the evanescent field, and HPhP wavevectors are demonstrated to be tuned and engineered by changing the substrate permittivity in a list of studies\u003csup\u003e4,26\u0026minus;31\u003c/sup\u003e, with this effect having been generalized by Fali. et al\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e26\u003c/span\u003e\u003c/sup\u003e. Additionally, HPhPs propagating across domains with varying permittivities will be refracted, with the behavior described by Snell\u0026rsquo;s law\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e26\u003c/span\u003e\u003c/sup\u003e and the continuity of tangential components of the wavevectors. With those fundamentals, patterned substrates can be used to manipulate polaritons supported in pristine hyperbolic media, such as polaritonic refraction\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e26\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e32\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e33\u003c/span\u003e\u003c/sup\u003e (e.g., prism and lensing), structured HPhPs\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e32\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e34\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e35\u003c/span\u003e\u003c/sup\u003e (e.g., waveguiding), photonic crystals\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e36\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e37\u003c/span\u003e\u003c/sup\u003e and accelerated HPhPs\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e38\u003c/span\u003e\u003c/sup\u003e. Like dielectric optics, those effects rely on wavevector differences for the HPhPs over different substrate regions, and some results can be enhanced with more significant contrast\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e38\u003c/span\u003e\u003c/sup\u003e. Additionally, the platform is ideally flat, as placing thin vdW materials over uneven surfaces (e.g., silicon pillars) will modify the morphology and/or induce strain\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e39\u003c/span\u003e\u003c/sup\u003e and scattering\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e40\u003c/span\u003e\u003c/sup\u003e. However, all existing demonstrations have either used 3D structures to induce a large contrast in the wavevectors, e.g., silicon versus air (etched silicon\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e35\u003c/span\u003e\u003c/sup\u003e), or provided fundamentally limited polaritonic wavevector change (~\u0026thinsp;1.6 times for phase change materials\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e32\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e34\u003c/span\u003e\u003c/sup\u003e) with microsecond modulation. Therefore, it is prudent to search for a platform that provides a planar surface and sufficient wavevector contrast that can be actively controlled.\u003c/p\u003e\n\u003cp\u003eHere, we demonstrate a hyperbolic material/doped semiconductor platform capable of controlling HPhPs at an unprecedented level with ultralow surface roughness (sub-nanometer). This platform allows for nearly continuous tuning of HPhP wavevectors, with maximum contrast of ~\u0026thinsp;8.3 times being experimentally demonstrated. This doubles the value that can be achieved with noble metals and dielectrics. Moreover, we illustrate a sharp modal order transition when the plasma frequency of the doped semiconductor passes through the transitional frequency, leading to a wavevector discontinuity suitable for modulation and sensing applications. Finally, we show that the hBN/doped semiconductor system can be modulated by photo-injection, with an experimentally demonstrated polaritonic wavelength change of ~\u0026thinsp;20% on a picosecond timescale. Although we focus primarily on uniformly doped semiconductors, we provided a proof-of-concept demonstration of hBN over in-plane varying plasma frequency with tuned wavevectors, offering significant freedom to manipulate HPhPs along a planar surface. Importantly, the platform is not limited to hBN, as plasma frequencies of doped semiconductors can be tuned over an extended range of frequencies for other hyperbolic materials (e.g., \u0026alpha;-MoO\u003csub\u003e3\u003c/sub\u003e), providing a significant toolbox for manipulating HPhPs.\u003c/p\u003e\n\u003cdiv class=\"Section2\" id=\"Sec2\"\u003e\n \u003ch2\u003eConcept of tuning HPhPs via substrate permittivity\u003c/h2\u003e\n \u003cp\u003eAlthough HPhPs are volume-confined modes, they remain sensitive to the local environment\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e4\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e26\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e28\u003c/span\u003e\u0026ndash;\u003cspan class=\"CitationRef\"\u003e31\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e41\u003c/span\u003e\u003c/sup\u003e, e.g., the dielectric function of the substrate. The dependence of HPhP wavevectors (\u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003eHPhP\u003c/em\u003e\u003c/sub\u003e) over substrate permittivity can be described by an analytical solution\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e14\u003c/span\u003e\u003c/sup\u003e:\u003c/p\u003e\n \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u0026nbsp;\u003cspan class=\"mathinline\"\u003e\\(k\\left(\\omega \\right)={k}^{{\\prime }}+i{k}^{{\\prime }{\\prime }}=-\\frac{\\psi }{d}\\left[\\text{atan}\\left(\\frac{{\\epsilon }_{o}}{{\\epsilon }_{t}\\psi }\\right)+\\text{atan}\\left(\\frac{{\\epsilon }_{s}}{{\\epsilon }_{t}\\psi }\\right)+\\pi l\\right], \\psi =-i\\sqrt{\\frac{{\\epsilon }_{z}}{{\\epsilon }_{t}}}\\)\u003c/span\u003e\u0026nbsp;\u003c/span\u003e (1)\u0026nbsp;\u003cbr\u003e\u003cbr\u003ewhere \u003cem\u003ed\u003c/em\u003e represents the hBN thickness, \u003cem\u003eɛ\u003c/em\u003e\u003csub\u003e\u003cem\u003eo\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eɛ\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e the complex dielectric functions of the superstrate (air here) and the substrate, respectively, and \u003cem\u003eɛ\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eɛ\u003c/em\u003e\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e are dielectric functions of hBN along the in and out of plane axes. \u003cem\u003el\u003c/em\u003e is non-negative integer representing the HPhP mode order (0,1,2\u0026hellip;), as infinite modes can be supported in hyperbolic systems simultaneously, and we here focus on the supported mode with lowest wavevector (referred to as fundamental mode\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e14\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e42\u003c/span\u003e\u003c/sup\u003e) because it usually is dominating in both near- and far-field studies. Note that the substrate-induced wavevector difference is independent of hBN thickness, as Eq.\u0026nbsp;(1) can be written in the following form:\u003c/p\u003e\n \u003cdiv class=\"Equation\" id=\"Equ1\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e$$k\\left(\\omega \\right)d=-\\psi \\left[\\text{atan}\\left(\\frac{{\\epsilon }_{o}}{{\\epsilon }_{t}\\psi }\\right)+\\text{atan}\\left(\\frac{{\\epsilon }_{s}}{{\\epsilon }_{t}\\psi }\\right)+\\pi l\\right], \\psi =-i\\sqrt{\\frac{{\\epsilon }_{z}}{{\\epsilon }_{t}}}$$\u003c/div\u003e\n \u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003eFor a hBN/doped semiconductor heterostructure, the HPhPs supported can be indirectly engineered by changing the carrier concentration (therefore the plasma frequency, \u0026omega;\u003csub\u003ep,\u003c/sub\u003e and dielectric function) of the underlying doped semiconductors, even with same hBN thickness. Therefore, HPhPs propagating in different domains possess different wavevectors, as shown in the schematic in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ea.\u003c/p\u003e\n \u003cp\u003eWe first demonstrate the substrate-induced polariton tuning with a hBN/InAs heterostructure. To this end, we grew InAs samples with different \u0026omega;\u003csub\u003ep\u003c/sub\u003e by controlling the as-grown dopant concentration and transferred hBN slabs onto these InAs substrates. We then utilized scattering-type scanning near field microscopy (s-SNOM) to measure the HPhP dispersion via a standard procedure, and some exemplary data analyses are included in \u003cstrong\u003eSI, section 1\u003c/strong\u003e. To minimize the role of hBN thickness in dictating HPhP wavevectors, similar hBN thicknesses (~\u0026thinsp;51\u0026ndash;55 nm) were used in this set of comparisons. The calculated dispersion plots along with the experimentally extracted data points validate that HPhP dispersions can be manipulated by varying the InAs \u0026omega;\u003csub\u003ep\u003c/sub\u003e (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003eb-d). Notably, the HPhP modal number in those systems are different: \u003cem\u003el\u0026thinsp;=\u0026thinsp;0\u003c/em\u003e branch is only supported when InAs is dielectric (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003eb-c versus Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ed) due to the mirror symmetry. Thus, the \u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003eHPhP\u003c/em\u003e\u003c/sub\u003e supported by uniform hBN can be engineered by the underlying doped semiconductor, for applications such as far-field resonators\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e26\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e34\u003c/span\u003e\u003c/sup\u003e or the near-field polariton propagation\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e26\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e32\u003c/span\u003e\u0026ndash;\u003cspan class=\"CitationRef\"\u003e36\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e38\u003c/span\u003e\u003c/sup\u003e, so that etch-induced material damage to hBN can be avoided.\u003c/p\u003e\n \u003cp\u003eWhile it is possible to tune HPhPs by adjusting the substrate dielectric function, quantitative analysis of the dependence of the \u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003eHPhP\u003c/em\u003e\u003c/sub\u003e upon the substrate permittivity is required enable the engineering of devices using this concept. Due to the substantial variation in hBN thickness between exfoliations, we discuss the influence of substrate permittivity (\u0026epsilon;\u003csub\u003es\u003c/sub\u003e) on normalized wavevector \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(k\\left(\\omega \\right)d\\)\u003c/span\u003e\u003c/span\u003e in Eq.\u0026nbsp;(\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e), as shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e. Notably, \u003cem\u003el\u0026thinsp;=\u0026thinsp;0\u003c/em\u003e branch is only supported when on a dielectric substrate, and it is forbidden over a metallic substrate due to the mirror symmetry\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e27\u003c/span\u003e\u003c/sup\u003e. Consequently, for the fundamental mode, the modal orders are different: \u003cem\u003el\u0026thinsp;=\u0026thinsp;0\u003c/em\u003e (low confinement) for dielectric substrates and \u003cem\u003el\u0026thinsp;=\u0026thinsp;1\u003c/em\u003e branch (high confinement) for metallic substrates. Notice that the cut-off of \u003cem\u003el\u0026thinsp;=\u0026thinsp;0\u003c/em\u003e branch happens at Re(\u0026epsilon;\u003csub\u003es\u003c/sub\u003e)= -\u0026epsilon;\u003csub\u003esuperstrate\u003c/sub\u003e (air in our case) instead of Re(\u0026epsilon;\u003csub\u003es\u003c/sub\u003e)\u0026thinsp;=\u0026thinsp;0, and more related discussions are included in \u003cstrong\u003eSI, section 2\u003c/strong\u003e. Furthermore, the wavevectors can also be manipulated by changing the substrate permittivity even within the same modal branch: increasing Re(\u0026epsilon;\u003csub\u003es\u003c/sub\u003e) leads to reduced \u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003eHPhP\u003c/em\u003e\u003c/sub\u003e. Importantly, the majority of \u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003eHPhP\u003c/em\u003e\u003c/sub\u003e values are realized within a small range of Re(\u0026epsilon;\u003csub\u003es\u003c/sub\u003e) (between \u0026minus;\u0026thinsp;10 and 10), encompassing both the highest and lowest \u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003eHPhP\u003c/em\u003e\u003c/sub\u003e values and resulting in the largest polaritonic refraction effects.\u003c/p\u003e\n \u003cp\u003eWhile the tunability of HPhPs via substrate is promising, traditional metallic substrates (noble metals) do not provide access to the high wavevector range, as they exhibit |Re(\u0026epsilon;\u003csub\u003es\u003c/sub\u003e)| over 100 in the mid-infrared. Quantitatively, the maximum wavevector contrast achievable with noble metals and dielectrics (air) is 4.2 times at 1500 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e. To exploit the tunability of HPhP wavevectors, here we employed doped semiconductors, with the plasma frequencies tuned from below to above the Reststrahlen band of hBN. Therefore, we used InAs\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e43\u003c/span\u003e\u003c/sup\u003e and cadmium oxide (CdO\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e44\u003c/span\u003e\u003c/sup\u003e) as substrates, with achievable plasma frequencies being 500\u0026ndash;2000 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e and 1500\u0026ndash;15000 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, respectively. Experimentally, we grew InAs and CdO substrates with varying \u0026omega;\u003csub\u003ep\u003c/sub\u003e, and h\u003csup\u003e10\u003c/sup\u003eBN flakes\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e42\u003c/span\u003e\u003c/sup\u003e were transferred onto them, with \u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003eHPhP\u003c/em\u003e\u003c/sub\u003e measured and extracted by Fourier analysis (\u003cstrong\u003eSI, section 1\u003c/strong\u003e). The experimental data are plotted as symbols in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e, showing excellent agreement with analytical solutions. Notably, with InAs substrates, we experimentally obtained both the highest and lowest \u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003eHPhP\u003c/em\u003e\u003c/sub\u003e at 1500 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, with a \u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003eHPhP\u003c/em\u003e\u003c/sub\u003e difference of ~\u0026thinsp;8.3 times, which could be used to exploit polaritonic in-plane refractive behavior.\u003c/p\u003e\n \u003cp\u003eWith doped CdO and InAs, we have unlocked almost the entire potential of controlling the \u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003eHPhP\u003c/em\u003e\u003c/sub\u003e through tuning substrate permittivity, with only a small range of \u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003eHPhP\u003c/em\u003e\u003c/sub\u003e not accessible (~\u0026thinsp;13%), where high refractive index dielectrics (|Re(\u0026epsilon;\u003csub\u003es\u003c/sub\u003e)|\u0026gt;10) would be required. Unlike noble metals, which typically feature high surface roughness\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e45\u003c/span\u003e\u003c/sup\u003e (unless realized via specialized growth\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e45\u003c/span\u003e\u003c/sup\u003e and/or fabrication\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e40\u003c/span\u003e\u003c/sup\u003e), the doped semiconductors employed here possess low surface roughness (below 1 nm, \u003cstrong\u003eSI, section 3\u003c/strong\u003e), which is crucial for HPhP platforms\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e40\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e45\u003c/span\u003e\u003c/sup\u003e. Importantly, semiconductors with varying in-plane \u0026omega;\u003csub\u003ep\u003c/sub\u003e can be realized (\u003cstrong\u003eSI, section 4\u003c/strong\u003e), and we experimentally demonstrated that HPhPs supported in a hBN slab exhibit different wavevector in different domains, further facilitating the manipulation of HPhPs for applications like waveguiding\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e34\u003c/span\u003e\u003c/sup\u003e, lensing\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e32\u003c/span\u003e\u003c/sup\u003e and resonators\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e34\u003c/span\u003e\u003c/sup\u003e. Therefore, those doped semiconductors can serve as ultrasmooth platforms to enable the tuning of HPhPs over an extended range of \u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003eHPhP\u003c/em\u003e\u003c/sub\u003e.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv class=\"Section2\" id=\"Sec3\"\u003e\n \u003ch2\u003eModal order transition in hBN/InAs heterostructures\u003c/h2\u003e\n \u003cp\u003eTo realize practical devices using doped semiconductor platforms, we must develop an understanding of the dependence of the wavevector on the substrate \u0026omega;\u003csub\u003ep\u003c/sub\u003e. In particular, the hBN/InAs heterostructure offers an ideal tuning range for engineering the HPhPs. To that end, we calculated how \u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003eHPhP\u003c/em\u003e\u003c/sub\u003e changes with InAs \u0026omega;\u003csub\u003ep\u003c/sub\u003e, at a working frequency of 1500 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, as shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003ea. When the InAs carrier concentration increases such that the \u0026omega;\u003csub\u003ep\u003c/sub\u003e surpasses the excitation (working) frequency, InAs exhibit a change from a dielectric to metallic behavior (grey and magenta shaded in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003ea, respectively). This dielectric to metallic evolution of the substrate further induces a HPhP modal order transition from \u003cem\u003el\u0026thinsp;=\u0026thinsp;0\u003c/em\u003e to \u003cem\u003el\u0026thinsp;=\u0026thinsp;1\u003c/em\u003e branch, leading to the wavevector discontinuity (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e). Additionally, in both dielectric and metallic regimes (grey and magenta shaded in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003ea, respectively), an increase in InAs \u0026omega;\u003csub\u003ep\u003c/sub\u003e causes a decline in Re(\u0026epsilon;\u003csub\u003eInAs\u003c/sub\u003e), resulting in a monotonical decrease in \u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003eHPhP\u003c/em\u003e\u003c/sub\u003e. By correlating \u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003eHPhP\u003c/em\u003e\u003c/sub\u003e with InAs \u0026omega;\u003csub\u003ep\u003c/sub\u003e, HPhP propagations can be manipulated with designable wavevectors over different domains, for both polaritonic refraction devices and/or resonators with significant design freedom. It is important to note that both minimum and maximum \u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003eHPhP\u003c/em\u003e\u003c/sub\u003e occur around the transitional point, with 8.3 times difference being experimentally demonstrated.\u003c/p\u003e\n \u003cp\u003eSince the InAs permittivity is dispersive, the modal transition can also occur in the frequency domain. When the InAs Re(\u0026epsilon;\u003csub\u003es\u003c/sub\u003e) passes through \u0026minus;\u0026thinsp;1 within the Reststrahlen band of hBN, a modal order transition occurs, splitting the fundamental HPhPs into two supported modal orders, as shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003eb. As such, the dispersion plot features highly confined HPhPs below the transition frequency (\u003cem\u003el\u0026thinsp;=\u0026thinsp;1\u003c/em\u003e mode), while showing reduced confinement of the HPhPs above it (\u003cem\u003el\u0026thinsp;=\u0026thinsp;0\u003c/em\u003e mode) (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003eb). By using an InAs sample with a \u0026omega;\u003csub\u003ep\u003c/sub\u003e at a frequency within the Reststrahlen band, we experimentally demonstrated the transition discontinuity (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003eb, green triangles), with good agreement with calculations. The dispersion is analogous to two stacked hyperbolic dispersions, and we observed intriguing behaviors in both frequency (coexisting absorption and reflection modes) and real space (guiding in different regions at different frequencies) in numerical simulations (\u003cstrong\u003eSI, section 5\u003c/strong\u003e).\u003c/p\u003e\n \u003cp\u003eThe modal order transition criteria can be generalized for both the InAs \u0026omega;\u003csub\u003ep\u003c/sub\u003e (substrate-tuning) and modified working frequency, as shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003ec. A clear transition line distinguishes the two modal orders, separating \u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003eHPhP\u003c/em\u003e\u003c/sub\u003e into two regimes: one with highly confined HPhPs (right side) and one supporting less confined modes (left). At any transition point, the modal order transition could happen if the InAs \u0026omega;\u003csub\u003ep\u003c/sub\u003e or the working frequency is changed, i.e., along the InAs \u0026omega;\u003csub\u003ep\u003c/sub\u003e axis or wavenumber axis in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003ec, respectively. Three representative s-SNOM images showing the highly and poorly confined HPhPs are presented in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003ed, clearly showing the transitions. As a consequence of the modal order transition and wavevector discontinuity, around the transition line, \u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003eHPhP\u003c/em\u003e\u003c/sub\u003e experiences large variations with perturbations to the working conditions, e.g., InAs \u0026omega;\u003csub\u003ep\u003c/sub\u003e, working frequency, and local environment (\u003cstrong\u003eSI, section 7\u003c/strong\u003e). Therefore, a HPhP system working around the transition point, such as resonators, can be modulated effectively and/or used for refractive index sensing. Note that for any working frequency inside the Reststrahlen band of hBN, there is a corresponding InAs \u0026omega;\u003csub\u003ep\u003c/sub\u003e to enable this transition, while such tunability of InAs\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e43\u003c/span\u003e\u003c/sup\u003e lends this concept to be expanded to other hyperbolic materials, e.g., MoO\u003csub\u003e3\u003c/sub\u003e.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv class=\"Section2\" id=\"Sec4\"\u003e\n \u003ch2\u003eUltrafast modulation of HPhPs\u003c/h2\u003e\n \u003cp\u003eBesides manipulating HPhPs in static structures, the hBN/doped semiconductor platform also enables the dynamic modulation of HPhPs. Both permittivity tensors of InAs and CdO can be modulated at the surface by electrical biasing\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e46\u003c/span\u003e\u003c/sup\u003e and photo-carrier injection\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e47\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e48\u003c/span\u003e\u003c/sup\u003e, and here we demonstrate ultrafast modulation in a hBN/InAs heterostructure. When a\u0026thinsp;~\u0026thinsp;100-fs, 80-MHz repetition rate pulsed laser source at 0.78 eV (1590 nm free-space wavelength) irradiates the hBN/InAs heterostructure, the photons will only be absorbed by InAs since it is above InAs bandgap (0.35 eV), yet well below that of hBN (5.95 eV)\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e49\u003c/span\u003e\u003c/sup\u003e. This process will generate a surplus of free-charge carriers at the InAs surface, locally increasing \u0026omega;\u003csub\u003ep\u003c/sub\u003e with a rise time below 1 ps, while those free carriers will subsequently recombine with a lifetime of ~\u0026thinsp;8 ps, as shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ec. Because of this locally modulated InAs \u0026omega;\u003csub\u003ep\u003c/sub\u003e, \u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003eHPhP\u003c/em\u003e\u003c/sub\u003e values supported in the hBN/InAs heterostructure can be modulated at picosecond timescales.\u003c/p\u003e\n \u003cp\u003eTo experimentally demonstrate such modulation, we conducted a near-field pump-probe measurement on one of the hBN/InAs heterostructures, with the detailed set-up provided in the \u003cstrong\u003eMethods\u003c/strong\u003e. Before the pump signal arrives (\u003cem\u003epre-pump\u003c/em\u003e), we observe a polariton wavelength of ~\u0026thinsp;1.15 \u0026micro;m at 1450 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e for the HPhPs supported, with the InAs \u0026omega;\u003csub\u003ep\u003c/sub\u003e at 990 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e. When the pump arrives (\u003cem\u003eat-pump\u003c/em\u003e), the InAs \u0026omega;\u003csub\u003ep\u003c/sub\u003e at the surface is shifted to a higher frequency (1150 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e), leading to a decreased \u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003eHPhP\u003c/em\u003e\u003c/sub\u003e as mentioned, and we experimentally observe a stretched polariton wavelength by ~\u0026thinsp;20% (~\u0026thinsp;1.37 \u0026micro;m). Since the time constant of modulated InAs \u0026omega;\u003csub\u003ep\u003c/sub\u003e is ~\u0026thinsp;8 ps, the modulated HPhP wavevector recovers within a similar temporal scale. Experimentally, the polaritonic behavior (\u003cem\u003e\u0026lambda;\u003c/em\u003e\u003csub\u003e\u003cem\u003eHPhP\u003c/em\u003e\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;1.29 \u0026micro;m) relaxes to a state between \u003cem\u003epre-pump\u003c/em\u003e and \u003cem\u003eat-pump\u003c/em\u003e after 7 ps of the pump signal (green curve in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ea). Those effects are also manifested in the dispersion plots extracted from nano-FTIR scans (\u003cstrong\u003eSI, section 8\u003c/strong\u003e). Importantly, the InAs \u0026omega;\u003csub\u003ep\u003c/sub\u003e was pumped from 990 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e to 1150 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, which are both well below the transition point discussed above. Therefore, we expect a stronger modulation if an InAs \u0026omega;\u003csub\u003ep\u003c/sub\u003e is modulated to surpass the transition frequencies and to induce modal order transitions.\u003c/p\u003e\n \u003cp\u003eIn addition to the modification of the polariton wavelength, we can also monitor how the resonant frequency of a given HPhP system change when the InAs is pumped. For a proof-of-concept demonstration, we measured the nano-FTIR spectra at a spatial position\u0026thinsp;~\u0026thinsp;0.35 \u0026micro;m from the hBN edge, which corresponds to a constant wavevector of HPhP system (\u003cem\u003ek\u0026thinsp;\u0026asymp;\u003c/em\u003e\u0026thinsp;7\u0026times;10\u003csup\u003e4\u003c/sup\u003e cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) for tip launched mode, and the frequency amplitude peaks indicate the modal frequency. When InAs \u0026omega;\u003csub\u003ep\u003c/sub\u003e is increased, the wavevector at a fixed frequency is reduced; therefore, for a constant wavevector, the corresponding frequency blueshifts. Experimentally, the modal frequency indeed experienced a blue shift when the InAs was pumped, with a time constant of ~\u0026thinsp;6 ps. This implies that we can modulate HPhP resonators at ultrafast time scales with un-pumped phonon materials for potentially lower loss, and the ultrafast switching of HPhPs has important implications for device applications in modulated optical sources\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e50\u003c/span\u003e\u003c/sup\u003e, beacons and other areas. Importantly, we do not pump the polaritonic material itself (unlike reference where polar materials are directly pumped\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e51\u003c/span\u003e\u003c/sup\u003e), which can be a challenge due to wide bandgaps\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e49\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e52\u003c/span\u003e\u003c/sup\u003e, and our approach can be universally applied to other HPhP supporting materials. Our approach thereby offers a great degree of flexibility in terms of doped substrates, as well as other hyperbolic materials, and could provide a foundation for more complex heterostructures.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv class=\"Section2\" id=\"Sec5\"\u003e\n \u003ch2\u003eSummary\u003c/h2\u003e\n \u003cp\u003eIn summary, we proposed and demonstrated a hyperbolic material/doped semiconductor platform to manipulate HPhPs at an unprecedented level. Our heterostructure platform offers significant improvements by providing access to almost all (~\u0026thinsp;87%) possible HPhP wavevectors, with both maximum and minimum values accessible (~\u0026thinsp;8.3 times difference experimentally demonstrated). This is in contrast to conventional noble metal and dielectric substrates that only provide access to discrete wavevectors with limited differences (~\u0026thinsp;4.2 time). Moreover, when the plasma frequency of the doped semiconductor passes through the polariton frequency, a sharp modal order transition of HPhP will happen, and the HPhP system is sensitive to the local environment around the transition point, which could be used for sensing and modulation purposes. Finally, we demonstrate an ultrafast modulation of HPhPs at picosecond time scales by photoinjecting free carriers into semiconductors, with a polaritonic wavelength change of ~\u0026thinsp;20%. With advances in semiconductor manufacturing, enabling further reduced ohmic losses and in-plane variations in doping\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e53\u003c/span\u003e\u003c/sup\u003e, we expect doped semiconductors to be an increasingly important platform to manipulate HPhPs, in both the near- and far-fields. Importantly, the concept is not limited to hBN, and these effects can be realized over an extended spectral range and hyperbolic materials (e.g., \u0026alpha;-MoO\u003csub\u003e3\u003c/sub\u003e\u003csup\u003e16\u003c/sup\u003e, \u0026beta;-Ga\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e\u003csup\u003e20\u003c/sup\u003e, calcite\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e), opening a whole new toolbox to manipulate in-plane HPhPs.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"Methods","content":"\u003cp\u003e \u003cb\u003eDevice fabrication.\u003c/b\u003e In-doped CdO (n-type) was deposited on 2-inch \u003cem\u003er\u003c/em\u003e-plane (012) sapphire single crystal substates at 400\u003csup\u003e\u0026deg;\u003c/sup\u003eC by a reactive co-sputtering process employing high-power impulse magnetron sputtering (HiPIMS) and radio frequency (RF) sputtering from 2-inch diameter metal cadmium and indium targets, respectively. HiPIMS drive conditions were 800-Hz frequency and 80-\u0026micro;s pulse time, yielding a 1250-\u0026micro;s period and 6.4% duty cycle. Film growth occurs in a mixed argon (20 sccm) and oxygen (14.4 sccm) environment at a total pressure of 10 mTorr. Post-deposition, samples were annealed in a static oxygen atmosphere at 635\u0026deg;C for 30 minutes.\u003c/p\u003e \u003cp\u003eSi-doped InAs (n-type) was grown by molecular beam epitaxy (MBE) on the epi-ready GaAs (100) substrates, using a Veeco GENxplor MBE in the University of Delaware Materials Growth Facility. In this system, the substrate temperature was measured by a band edge thermometer and the source flux was monitored as beam equivalent pressure (BEP). It provides an ultra-high vacuum environment with pressures as low as 1\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;10\u003c/sup\u003e Torr for growth. GaAs substrates were fully deoxidized at 620\u0026deg;C prior to growth. To prepare a smooth surface for the growth of Si-doped InAs, a GaAs buffer layer with a thickness of 100nm was deposited at 580\u0026deg;C first. Thereafter, the substrate was cooled to 420\u0026deg;C. Then the Si-doped InAs layer was grown by opening the Si, In, As, and Bi source cells simultaneously. The As2:In BEP ratio and growth rate were kept around 20, and 1.7 um/h, respectively. A small amount of Bi (In:Bi BEP ratio was 50) was added as a surfactant to suppress the segregation of Si dopants on the surface\u003csup\u003e\u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e\u003c/sup\u003e. The Si doping concentration was varied by changing the Si flux while using the same growth rate. The doping density and carrier mobility were detected by room-temperature Hall effect measurements in a van der Pauw configuration.\u003c/p\u003e \u003cp\u003e \u003csup\u003e10\u003c/sup\u003eB enriched hBN (~\u0026thinsp;99% enriched\u003csup\u003e42,55\u003c/sup\u003e) flakes were exfoliated and transferred onto the InAs and CdO substrates using low contamination transfer techniques. The hBN crystals were grown with a boron source that was nearly 100% \u003csup\u003e10\u003c/sup\u003eB isotope, as previously described\u003csup\u003e\u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e56\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003e \u003cb\u003eCalculations.\u003c/b\u003e In our heterostructures, the doped semiconductors are treated as substrate, as they are significantly thicker (~\u0026thinsp;500 nm or 1 \u0026micro;m thick) than the evanescent field of HPhPs. The analytical solution is calculated by Eq.\u0026nbsp;(1) in the main text, and the contour plots in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb are calculated by the transfer matrix method.\u003c/p\u003e \u003cp\u003e \u003cb\u003eNear-field measurements.\u003c/b\u003e Near-field nano-imaging experiments were carried out in a commercial Neaspec (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e\u003ca href=\"http://www.neaspec.com\" target=\"_blank\"\u003ewww.neaspec.com\u003c/a\u003e\u003c/span\u003e\u003cspan address=\"http://www.neaspec.com\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e) s-SNOM and nano-FTIR based around a tapping-mode atomic force microscope. A metal-coated Si-tip of apex radius R\u0026thinsp;\u0026asymp;\u0026thinsp;20 nm that oscillates at a frequency of Ω\u0026thinsp;\u0026asymp;\u0026thinsp;280 kHz and tapping amplitude of about 100 nm is illuminated by a laser beam (probe laser, in the mid-infrared) at an angle 60\u0026deg; off normal to the sample surface. Scattered light launches HPhPs in the device and the tip then re-scatters light (described more completely in the main text) for detection in the far-field. Background signals are efficiently suppressed by demodulating the detector signal at harmonics of the tip oscillation frequency and employing pseudo-heterodyne interferometric detection.\u003c/p\u003e \u003cp\u003e \u003cem\u003eStatic measurements\u003c/em\u003e. For static measurements, the incident beam is a single-frequency quantum cascade laser. The laser frequency can be tuned, and s-SNOM mapping were conducted in a single-wavelength measuring scheme.\u003c/p\u003e \u003cp\u003e \u003cem\u003eUltrafast measurements\u003c/em\u003e. For ultrafast measurements, the probe laser is a pulsed broadband (~\u0026thinsp;1000\u0026ndash;2000 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) different frequency generation laser (fiber laser), and the pulse width is ~\u0026thinsp;200 fs after considering the dispersion of beam splitter. The pump laser is a pulsed single-frequency laser at 1590 nm, and the pulse width is ~\u0026thinsp;100 fs. Those pulse widths set the time resolution of our system: ~0.3 ps. The repetition rates of both lasers are 80 MHz. The time delay is controlled by a delay stage on the pump beam line. In the ultrafast pumped heterostructure, we also notice that the HPhPs are experiencing a collective effect during the propagation in the temporal domain. HPhPs have small group velocities, and they will propagate for ~\u0026thinsp;0.5-2 ps before being collected. As the lifetime of InAs free-carriers is ~\u0026thinsp;8 ps (see fitting in \u003cb\u003eSI, section 10\u003c/b\u003e), the observed HPhPs will experience decreasing InAs ω\u003csub\u003ep\u003c/sub\u003e during the propagation, i.e., increasing \u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003eHPhP\u003c/em\u003e\u003c/sub\u003e, if we assume uniform InAs pumping. Therefore, the as-measured ultra-fast HPhP response is convoluted within a certain time scale, depends on the group velocity.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eData availability.\u003c/strong\u003e The authors declare that the data supporting the findings of this study are available within the paper and its Supplementary Information files. Additional data is available from the authors upon request.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eAcknowledgement\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eM. H., J. R. M. and J-P. M. gratefully acknowledge support for this work by Office of Naval Research Grant N00014-22-12035. J-P. M, and J. D. C. acknowledge support from the Army Research Office Research Grant W911NF-21-1-0119. A. J. C. and J-P. M. acknowledge support from the Army Research Office W911NF-16-1-0406. Support for hBN crystal growth was provided by the Office of Naval Research, award number N000142212582.\u0026nbsp;M. Y. and S. L. acknowledge funding from the National Science Foundation, Division of Materials Research under Award No. 1904760 and the Division of Electrical, Communications, and Cyber systems under Award No. 2102027. M. Y. and S. L. acknowledge the use of the Materials Growth Facility (MGF) at the University of Delaware, which is partially supported by UD-CHARM a National Science Foundation MRSEC under Award No. DMR-2011824. T. G. F would like to acknowledge the University of Iowa startup funding. Work at Columbia was supported primarily by the Center on Precision-Assembled Quantum Materials, funded through the US National Science Foundation (NSF) Materials Research Science and Engineering Centers (award no. DMR-2011738). DNB is the Vannevar Bush Faculty Fellow ONR-VB: N00014-19-1-2630.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eContributions\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eM. H., J. R. M., T. G. F., J-P. M. and J.D.C. conceived the idea. M. H., S. S. S. and T. G. F. conducted the static near-field measurements, and M. H., J. R. M. and S. M. performed the ultrafast measurements. M. Y. fabricated the InAs samples, and A. C. fabricated CdO samples. E. J. grew the hBN crystal. M. H. carried out the modeling and data analysis. All participated in the writing.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003e\u003cspan\u003eBasov DN, Asenjo-Garcia A, Schuck PJ, Zhu X, Rubio A (2021) Polariton panorama. Nanophotonics 10:549\u0026ndash;577\u003c/span\u003e\u003c/li\u003e\n \u003cli\u003e\u003cspan\u003eAbedini Dereshgi S et al (2020) Lithography-free IR polarization converters via orthogonal in-plane phonons in \u0026alpha;-MoO3 flakes. Nat Commun 11:1\u0026ndash;9\u003c/span\u003e\u003c/li\u003e\n \u003cli\u003e\u003cspan\u003eDixit S, Sahoo NR, Mall A, Kumar A (2021) Mid infrared polarization engineering via sub-wavelength biaxial hyperbolic van der Waals crystals. Sci Rep 11:1\u0026ndash;9\u003c/span\u003e\u003c/li\u003e\n \u003cli\u003e\u003cspan\u003eFolland TG et al (2018) Reconfigurable infrared hyperbolic metasurfaces using phase change materials. 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Chem Mater 30:6222\u0026ndash;6225\u003c/span\u003e\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-2744039/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-2744039/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eHyperbolic phonon polaritons (HPhPs) can be supported in highly anisotropic materials, where the real parts of their permittivities along different directions are opposite in sign as a result of spectrally offset optical phonons. Compared to surface polaritons, HPhPs offer further confinement of long-wavelength light to deeply subdiffractional scales, and volume propagation that enables control of the polariton wavevector by changing the underlying medium. This allows for greater control of polaritonic resonators and near-field polariton propagation without deleterious etching of hyperbolic materials. Yet, conventionally used noble metal and dielectric substrates restrict the tunability of this approach, leaving most of the wavevector inaccessible. To overcome this challenge, we demonstrate that using doped semiconductors, e.g., InAs and CdO, can enable near-continuous tuning and access to both the maximum and minimum wavevectors (~8.3 times experimentally demonstrated). We further elucidate HPhP tuning with the plasma frequency of an InAs substrate, which features a significant wavevector discontinuity and modal order transition when the substrate permittivity crosses -1 in the Reststrahlen band. Around the transition point, the HPhP system is sensitive to perturbations, e.g., the working frequency, InAs plasma frequency and superstrate, thus it is suitable for sensing and modulation applications. We also illustrate that the hBN/InAs platform allows for active modulation at picosecond timescales by photo-injecting carriers into the InAs substrate, demonstrating a dynamic wavevector change of ~20%. Overall, the demonstrated hBN/doped semiconductor platform offers significant improvements towards manipulating HPhPs, and enormous potential for engineered and modulated polaritonic systems for applications in on-chip photonics and planar metasurface optics.\u003c/p\u003e","manuscriptTitle":"Polariton design and modulation via van der Waals / doped semiconductor heterostructures","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2023-04-04 22:38:08","doi":"10.21203/rs.3.rs-2744039/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"00f6d842-23c9-4cbe-a6ef-e6fb09444a09","owner":[],"postedDate":"April 4th, 2023","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":20399339,"name":"Physical sciences/Optics and photonics/Optical materials and structures/Metamaterials"},{"id":20399340,"name":"Physical sciences/Nanoscience and technology/Nanoscale devices/Nanophotonics and plasmonics"}],"tags":[],"updatedAt":"2023-06-19T08:41:10+00:00","versionOfRecord":[],"versionCreatedAt":"2023-04-04 22:38:08","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-2744039","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-2744039","identity":"rs-2744039","version":["v1"]},"buildId":"cBFmMYwuxLRRLfASyISRj","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}