All-epitaxial long-range surface plasmon polariton structures with integrated active materials

Surface plasmon polaritons (SPPs) are hybrid excitations of collective charge oscillations in a metal (⁠$εm<0$⁠), coupled to electromagnetic waves in a dielectric (⁠$εd>0$⁠), propagating at the metal/dielectric interface. The dispersion relation for such a polaritonic mode, propagating at the interface between a semi-infinite metal and a semi-infinite dielectric, can be written as¹ 

For such a system, when $εm+εd≈0$ (which occurs at the surface plasmon frequency $ωsp$⁠), $βSPP$ can far exceed its free space counterpart $ko=ω/c$⁠. Thus, at $ω=ωsp$⁠, the penetration depth of the SPP mode into the dielectric (⁠$δd$⁠) will be significantly smaller than the wavelength of light in free space, or even the surrounding dielectric $δd≪λo/εd$⁠. This strong confinement achievable at or near the surface plasmon frequency $ωsp$ has long been a driving rationale for the use of plasmonic structures for sub-diffraction-limited waveguides in nano-scale plasmonic sources and detectors, sensors, or for on-chip optical interconnect applications.^2–11 However, this strong mode confinement comes at a price. Plasmonic materials, in addition to having a negative real permittivity, also have an imaginary component of the permittivity, which results in a propagation loss for the SPP mode. The nearer the SPP mode’s frequency is to the surface plasmon frequency, the stronger the confinement, but also the larger the loss. Intuitively, this is not surprising, as the more tightly bound the mode is to the metal (with its high concentration of free carriers), the more light will be absorbed by the metal’s free carriers. Thus, while sub-diffraction-limited waveguiding of light has been a driving force behind the field of plasmonics, the appreciable losses associated with tightly bound SPP modes have provided a significant obstacle to the development of SPP-based waveguides.

The straightforward metal/dielectric SPP, however, is not the only plasmonic structure available for waveguiding applications. Three-layer systems, such as metal–dielectric–metal (MDM) or dielectric–metal–dielectric (DMD) structures can also support and guide plasmonic modes.¹² For large dielectric (metal) layers, these MDM (DMD) systems will support two isolated, degenerate single-interface propagating SPPs at opposite interfaces of the central dielectric (metal) and surrounding metal (dielectric). However, as the central dielectric (metal) layer shrinks to thicknesses commensurate with the modes’ penetration depth into the dielectric (metal), the once-isolated, degenerate modes couple and form two distinct symmetric (s) and anti-symmetric (a) modes, where the symmetry refers to the profile of the transverse component of the electric field. MDM structures can offer strong confinement of plasmonic modes for nanophotonic applications such as nano-lasers or modulators, but at the cost of additional loss.^4,13–17 The modes supported by the DMD structure are often referred to as the short-range (anti-symmetric) and long-range (symmetric) surface plasmon polariton modes (SRSPP and LRSPP, respectively).^18–21 The LRSPP is more weakly bound to the metal, and thus lower loss. In the case of the metal thickness approaching zero, the symmetric mode (LRSPP) effectively becomes a transverse electromagnetic (TEM) plane wave propagating in the dielectric. Thus, the LRSPP offers a controlled trade-off between the long propagation lengths of the TEM plane wave and the mode confinement of the SPP by control of the waveguide geometry. Consequently, the LRSPP has been successfully leveraged for lower-loss sub-diffraction-limited waveguides, modulators, and nano-scale plasmonic sources.^22–24 

The majority of plasmonic structures are designed for visible and near-IR light, using traditional plasmonic metals (typically noble metals such as Au and Ag). There has been significant interest over the past decade in the development and demonstration of plasmonic materials designed for use in specific wavelength ranges, such as the short wavelengths of the UV, the long wavelengths of the mid-infrared (⁠$3–30μm$⁠), or even the THz.²⁵ At longer wavelengths, however, the plasmonic materials used for near-IR and visible applications become increasingly less plasmonic, in that the real part of their permittivity becomes increasingly negative. As this happens, these materials quickly begin to behave, optically, more like perfect electrical conductors than plasmonic materials, and can no longer support the strongly confined modes associated with plasmonic response.²⁶ For these longer wavelengths, plasmonic materials could have an important role to play in alleviating the even greater mismatch between photon wavelength and optoelectronic device length scales. However, the traditional metals used for plasmonic applications at shorter wavelengths do not offer the same confinement into the mid-IR, and such applications thus require alternative plasmonic materials. In the mid-IR, an intriguing candidate for such applications is the highly doped semiconductor class of plasmonic materials. Similar to noble metals, doped semiconductors, or “designer” plasmonic materials, can be modeled using the Drude formalism, where their permittivity can be described by

where $εb$ is the semiconductor background permittivity (the infrared dielectric constant of the material), $γ$ is the free carrier scattering rate, and $ωp$ is the plasma frequency of the material, which depends on doping concentration $n$ and effective mass $m∗$⁠. For many semiconductors, small effective mass (typically for electrons) and the ability to achieve high carrier concentrations (free carrier density greater than $1019cm−3$⁠) offer the potential to push the plasma frequency into the mid-IR. Plasmonic response in highly doped semiconductors has been demonstrated with a range of materials^27–30 and for varying geometries or structures.^31–33 For III-V semiconductors, specifically narrow bandgap III-V materials, the combination of both small electron effective masses and high doping concentrations allows for plasma wavelengths (⁠$λp=2πc/ωp$⁠) as short as $λp≈5μm$⁠.^27,31,34 Moreover, these materials can be grown epitaxially, allowing for the integration of single-crystal semiconductor plasmonic materials with active optoelectronic devices in a monolithic, all-epitaxial architecture. Recent work has demonstrated that such an approach can strongly enhance light emission^35,36 or detection^37,38 in the infrared via the strong mode localization afforded at plasmonic interfaces. However, all of the passive and active structures using doped semiconductor materials either rely on the plasmonic modes at single “metal”/dielectric interfaces or in MDM structures, where the role of metal is played by a highly doped semiconductor.³⁹ The demonstration of DMD plasmonic waveguides, however, would open intriguing possibilities for new optoelectronic device and system architectures in the infrared. First, the long propagation length of the LRSPP supported by such an architecture offers the opportunity to link infrared optoelectronic devices (sources and receivers) on the same chip. At the same time, the double-interface nature of the LRSPP mode allows for simultaneous interaction of the propagating mode with different active regions integrated into the upper and lower dielectrics. Such capability would offer a path toward dual-wavelength, bias-switchable, and/or dual functionality mid-IR optoelectronic devices.

Here we demonstrate an all-epitaxial structure capable of supporting LRSPP modes at long-wave infrared (LWIR) wavelengths. In addition, we demonstrate the integration of type-II superlattice (T2SL) emitters with LWIR cutoff wavelengths (⁠$λco$⁠) into the dielectric layers above and below our $n++$ semiconductor plasmonic film. Our structures are characterized by angle- and polarization-dependent infrared reflection and photoluminescence (PL) spectroscopy, from which we are able to extract the dispersion of both the symmetric and anti-symmetric SPP modes supported on the DMD interfaces. Our samples are modeled analytically with a simplified three-layer model and numerically using rigorous coupled wave analysis (RCWA), with excellent agreement to our experimental results. The structures investigated offer a novel approach for new LWIR optoelectronic device architectures leveraging dual-interface SPP modes.

Our structure is grown by molecular beam epitaxy in a Varian Gen-II system with effusion sources for gallium, indium, aluminum, and silicon, and valved cracker sources for arsenic and antimony. The LRSPP structure is grown on an n-type doped GaSb substrate, with the layer stack shown in Figs. 1(a) and 1(b). Four different superlattices were used in our LRSPP structure. The first is a very-long-wave infrared (VLWIR) T2SL with a period of 45 ML, an alloy composition of $InAs/InAs0.5Sb0.5$⁠, and an InAs/InAsSb ratio of 37.125/7.875 ML. The second is a LWIR T2SL with a period of 40 ML, an alloy composition of $InAs/InAs0.5Sb0.5$⁠, and an InAs/InAsSb ratio of 33/7 ML. The third is a mid-wave infrared (MWIR) T2SL with a period of 20 ML, an alloy composition of $InAs/InAs0.5Sb0.5$⁠, and an InAs/InAsSb ratio of 16.5/3.5 ML. Lastly, we use a carrier blocking (CB) superlattice⁴⁰ with a total period of 27 ML, and individual thickness and compositions of 4/3/4/3/4/9 ML (⁠$InAs/AlAs0.5Sb0.5/InAsSb0.5Sb0.5_$⁠). The as-grown layer stack for our plasmonic system is shown in Fig. 1(a). Following a 200 nm GaSb buffer, we form our first dielectric slab by growing 11 periods (151.0 nm) of VLWIR T2SL, then 18 periods (⁠$148.2nm$⁠) of CB superlattice, then 29 more periods of VLWIR T2SL (⁠$398.0nm$⁠). To form the plasmonic slab, we grow 74 periods (⁠$451.4nm$⁠) of $n++$ Si:MWIR T2SL (doped $n++≈5×1019cm−3$⁠). We then grow the final dielectric slab, consisting of 25 periods (⁠$305.0nm$⁠) of LWIR T2SL, then 18 periods (⁠$148.2nm$⁠) of CB superlattice, then 4 more periods of LWIR T2SL (⁠$48.8nm$⁠). The above layer stack effectively forms a three-layer LRSPP structure, with the highly doped MWIR T2SL serving as the central plasmonic material. Note that while we use a T2SL as our plasmonic layer to simplify the lattice-matching to the layers above and below the plasmonic film, this T2SL can simply be treated as a Drude metal. This is due to the combination of the MWIR cutoff and state filling from the high doping concentration (Burstein Moss shift),^41,42 which ensures that the only loss in the layer comes from the Drude scattering term (⁠$γ$⁠). Below the $n++$ layer, the VLWIR T2SL is designed for a cutoff wavelength of $λco,VLWIR=15μm$⁠, with the carrier blocking layer designed to confine photoexcited electron hole pairs to the VLWIR T2SL for improved PL emission. Similarly, the LWIR T2SL above the $n++$ film is designed with $λco,LWIR=13μm$ and also includes a carrier blocking layer for improved PL. Both T2SL dielectric layers effectively serve as infrared “luminescent tags,” allowing for a spectral/spatial mapping of the SPP modes in the system.

The as-grown sample reflection is measured using a Bruker V80 Fourier transform infrared (FTIR) spectrometer coupled to an IR microscope, and shown in Fig. 1(d). In order to couple to the SPP modes in our structure, the as-grown sample is patterned with periodic Au gratings (period $Λ=2.8μm$⁠) using a UV lithography, metallization, and lift-off process. Angle-dependent reflection spectra were collected using a Bruker V70 Fourier transform infrared (FTIR) spectrometer with a custom-built reflection setup allowing for angle- and polarization-dependent reflectance measurements for incident angles $15°–65°$ from normal.⁴³ Collected spectra are normalized to reflection from a Au-coated substrate offering nearly 100% reflection at long wavelengths. A ZnSe wire-grid polarizer was used to obtain both transverse electric (TE) and transverse magnetic (TM) polarized reflection spectra.

We fabricate two grating-patterned samples, the first a large-area grating with grating period $Λ=2.8μm$ and a grating width designed to be $w=Λ/2$ for angle-resolved reflection measurements, and the second comprising an array of small-area grating patterns with grating periods ranging from $Λ=2–3.1μm$ in $0.1μm$ steps (and grating widths $w=Λ/2$⁠) for normal incidence reflection measurements. The large-area patterned LRSPP samples were also characterized using modulation step-scan photoluminescence (PL) spectroscopy. Specifically, the PL from the sample was measured using a microphotoluminescence setup, with the sample held in a temperature-controlled cryostat with a ZnSe window. The sample is optically pumped by an 808 nm laser outputting 1 W and modulated at 10 kHz. The pump laser light is transmitted through a dichroic beam splitter and focused onto the sample using an all-reflective Cassegrain $15×$ objective. PL emitted from the sample is collected by the same objective and reflected by the dichroic beam splitter. The reflected light is passed through a $3.6μm$ long-pass filter and into an FTIR equipped with a cooled (77 K) HgCdTe detector. The FTIR is operated in amplitude-modulation step-scan mode to dramatically reduce infrared background.

The optical response of the sample is numerically modeled using rigorous coupled wave analysis (RCWA).⁴⁴ The $n++$ layer is treated as a Drude metal, with a plasma wavelength $λp=6μm$ and a scattering rate $γ=1013rad/s$⁠. The carrier blocking layer is treated as having a constant permittivity $εCB=12.15$⁠. The LWIR and VLWIR T2SLs are modeled as having a constant real permittivity determined by the weighted average of their constituent materials^45,46 (⁠$εLWIR′=εVLWIR′=12.56$⁠), and an imaginary permittivity extracted from the T2SL’s absorption coefficient, which we model as $α=αo(E−Eo)$⁠. $αo$ and $Eco$ are extracted by fitting to our experimental reflection data.

Finally, we analytically model our epitaxial system as a symmetric DMD structure, assuming lossless, semi-infinite T2SL layers as the dielectric cladding (permittivity $εd$⁠), and $n++$ semiconductor as the central metal [thickness $a$ and complex permittivity $εm$ from Eq. (2)]. Doing so results in the transcendental equations,^1,12

where $km$ is the transverse wavevector in the doped semiconductor and $kd$ is the transverse wavevector of the mode in the dielectric. We use $εd=12.56$⁠, determined by using a weighted average of the dielectric constants of the T2SL constituent materials. Equations (3a)(i,ii) are solved numerically to calculate a dispersion relationship for the idealized system. This results in a symmetric solution [Eq. (3a)(i)] corresponding to the LRSPP, and an anti-symmetric solution [Eq. (3a)(ii)] corresponding to the SRSPP. The results from this idealized model are compared to our numerical and experimental results and used to guide our understanding of the observed spectral features in our optical characterization.

Figure 2 shows contour plots of the angle-dependent reflection from the large-area, $Λ=2.8μm$⁠, patterned sample for TE- and TM-polarized light for incidence angles from $15°$ to $65°$⁠. For TE-polarized light, a clear, angle-independent dip at $λ≈7.75μm$ is observed in the reflection spectra, attributed to destructive interference in the surface-patterned epitaxial stack. At longer wavelengths, the TE reflection from the patterned surface is near unity, as the $Λ=2.8μm$ gratings behave like a wire-grid polarizer, reflecting all TE-polarized light at wavelengths $λ≫Λ$⁠. Because the LRSPP and SRSPP modes are TM-polarized, features associated with coupling to these modes will only be observed for TM-polarized incident light. From the simple three-layer DMD SPP dispersion from Fig. 1(c), we expect to observe coupling to SPP modes at wavelengths longer than $λ≈8.5μm$⁠. In this wavelength range, significant structure is observed in the TM-reflection spectra, attributed to coupling to SPP modes. Coupling to these modes requires momentum matching between incident light and the SPPs supported on the $n++$ film. The momentum matching condition can be written as

where $m$ is an integer associated with the grating momentum (⁠$2π/Λ$⁠) required to couple to the SRSPP and LRSPP modes which both lie largely outside the light cone. From Eq. (4), it can be recognized that for normal incidence light, the $β+$ and $β−$ SPPs are degenerate. However, this degeneracy is lifted as the incidence angle is increased from normal, and incident light is able to couple into the forward and backward propagating SPPs at different frequencies. We can identify at least two sets of reflection dips in these spectra, each of which split with an increasing angle of incidence, corresponding to the forward and backward propagating SPP modes (⁠$β+,β−$⁠) supported by the $n++$ film. In order to identify the features in our angle-dependent reflection data, we model normal incidence coupling to our grating-patterned structure as a function of grating period $Λ$⁠. Assuming that $m=±1$ from Eq. (4), we can convert our grating period to a SPP wavevector $βSPP±=±2π/Λ$ and map out the SPP dispersion of our system. Figure 3(a) shows the resulting reflection contour plot, with dips in the reflection corresponding to coupling to modes in our grating-patterned epitaxial stack. In addition, we indicate experimentally observed coupling to the modes in our system from the small-area grating samples fabricated and characterized by normal incidence reflection spectroscopy. Two clear higher energy features are observed in Fig. 3(a), and by overlaying the three-layer dispersion from Fig. 1(b), we can identify these features as the LRSPP and SRSPP modes (corresponding to the white long-dashed and short-dashed lines in the overlaid dispersion, respectively). In Figs. 3(b) and 3(c), we show the simulated transverse magnetic field profiles for the large-area sample’s grating period $Λ=2.8μm$⁠, associated with the (b) LRSPP and (c) SRSPP modes. As can be seen in the field plots, the SRSPP field in Fig. 3(c) clearly crosses through $|Hy|=0$ in the $n++$ semiconductor layer, supporting this mode’s identification as the anti-symmetric SRSPP mode, while the magnetic field amplitude in Fig. 3(b) remains positive (⁠$|Hy|>0$⁠) through the $n++$ layer, as would be expected for the symmetric LRSPP mode.

Note that the contour plot in 3(a) presumes coupling via the $m=±1$ grating modes, which is a reasonable assumption for much of the parameter space plotted. However, for larger period gratings, coupling to SPP modes via the $m=±2$ grating mode can be achieved. This coupling can be observed in the contour plot in the region corresponding to the largest grating periods, at energies $∼115meV$⁠. This effect contributes to the broadening of the LRSPP feature (and its deviation from the analytical model at longer wavelengths). However, the bulk of the deviation from the analytically calculated LRSPP dispersion at low β's is attributed to the weaker confinement of the LRSPP for smaller wavenumbers. This will result in a larger overlap with the patterned Au and the air above the epi-stack, at which point the simple three-layer model with semi-infinite and lossless T2SL layers would be expected to break down. In addition, we do observe a third feature in the contour plot of our simulated reflection, extending from $β=2–9rad/μm$⁠. We attribute this to excitation of MDM modes between the Au grating and the $n++$ semiconductor, which grows increasingly metallic at these longer wavelengths. The nature of this absorption feature is confirmed with field plots, of which a representative example is presented in Fig. 3(d). This plot shows a mode clearly localized between the Au grating and the $n++$ layer. Because the calculated dispersion overlaid in Fig. 3(a) assumes lossless T2SL layers and does not include the effect of the patterned Au on the sample top surface, the aforementioned deviations observed in our numerical contour plot (when compared with the simple three-layer model) are expected. Nonetheless, the numerical simulation of our structure clearly reproduces the primary features of the analytical LRSPP dispersion, and the extracted field plots clearly show the field profiles expected from the LRSPP and SRSPP modes.

The T2SLs grown both above and below the $n++$ film can serve not only as luminescent tags to further probe the SPP modes in our system, but perhaps more importantly, as evidence that our all-epitaxial plasmonic architecture can be monolithically integrated with active optoelectronic epitaxial materials. Figure 4 shows the un-polarized low-temperature (⁠$T=83K$⁠) photoluminescence (PL) from the large-area, $Λ=2.8μm$⁠, patterned sample, from which are clearly observed four distinct PL features. The shortest wavelength feature (i) is associated with the TE-polarized reflection dip in the layer stack. The three longer wavelength features at (ii) $λ=10.5μm$⁠, (iii) $λ=12.7μm$⁠, and (iv) $λ=15.5μm$ can be attributed to out-coupling of light emitted into the (ii) LRSPP, (iii) SRSPP, and (iv) MDM modes identified in Fig. 3. The MDM mode is experimentally observed at a shorter wavelength than the predicted $λ=18.5μm$ in Fig. 3 due to the width of the $Λ=2.8μm$ large-area gratings, which is closer to $1.12μm$ rather than $1.4μm$⁠. Figure 4 also includes low-temperature TE- and TM-polarized reflection data obtained with the same objective lens used for the PL experiments, in order to maintain the same collection optics and thus angular spread for collected light. Not only does the PL in Fig. 4 support the identification of the SPP and MDM modes in Fig. 3, but it also demonstrates the potential for integrating long-wavelength infrared active materials into our all-epitaxial long- and short-range SPP-supporting material.

In summary, we demonstrate all-epitaxial structures supporting long-range surface plasmon polariton modes in the long-wave infrared portion of the electromagnetic spectrum. The structures investigated consist of type-II superlattice materials quantum engineered for cutoff wavelengths in the LWIR, sandwiching a heavily doped (⁠$n++$⁠) semiconductor layer acting as our plasmonic thin film. We investigate coupling to SPP modes on the $n++$ semiconductor by angle- and polarization-dependent reflection spectroscopy on a grating-patterned sample. Numerical simulations of the reflection match our experimental results with excellent agreement and allow for the visualization of the fields assigned to the modes supported by the grating-patterned structure. We note that our system supports both SRSPP and LRSPP modes, as well as a metal–dielectric–metal mode at longer wavelengths. Finally, we show that the integration of T2SL materials with our plasmonic layer structure allows for luminescent probing of the modes supported in the layer stack and demonstrates the potential for integrating active optoelectronic materials into our all-epitaxial plasmonic system. The presented structure offers a path toward all-epitaxial plasmonic optoelectronics in the long-wavelength infrared. The epitaxial nature of the system offers not only atomic-layer resolution of film thickness and the ability to quantum engineer the optoelectronic active regions, but also significant design flexibility by epitaxial control of doping concentration and layer thicknesses. Finally, the ability to access two plasmonic/dielectric interfaces opens the door to the design of dual-wavelength or multi-spectral LWIR optoelectronic devices operating on either side of the central plasmonic film. The variety of optical modes accessible in such a plasmonic system, as well as the significant design flexibility afforded by epitaxial growth, offers an intriguing path toward a variety of all-epitaxial plasmonic-optoelectronic devices, optical interconnects, modulators, and optical systems for a range of applications in the LWIR.

L.N. and P.P. contributed equally to this work.

D.W. and L.N. gratefully acknowledge support from the National Science Foundation (ECCS-1926187). This work was partly done at the Texas Nanofabrication Facility supported by the NSF grant (No. NNCI-1542159). This work was also supported by the Laboratory Directed Research and Development (LDRD) program at Sandia National Laboratories. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under Contract No. DE-NA0003525. This paper describes the objective technical results and analysis. Any subjective views or opinions that might be expressed in this paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government.

The data that support the findings of this study are available from the corresponding author upon reasonable request.