Monolithic metallic nanocavities for strong lightmatter interaction to quantum-well
intersubband excitations
A. Benz,1,2,* S. Campione,3 S. Liu,1,2 I. Montano,2 J. F. Klem,2 M. B. Sinclair,2
F. Capolino,3 and I. Brener1,2
1
Centre for Integrated Nanotechnologies (CINT), Sandia National Laboratories, P.O. Box 5800, Albuquerque, NM
87185, USA
2
Sandia National Laboratories, P.O. Box 5800, Albuquerque, NM 87185, USA
3
Department of Electrical Engineering and Computer Science University of California, Irvine, 4131 Engineering
Hall, Irvine, CA 92697, USA
*
[email protected]
Abstract: We present the design, realization and characterization of strong
coupling between an intersubband transition and a monolithic metamaterial
nanocavity in the mid-infrared spectral range. We use a ground plane in
conjunction with a planar metamaterial resonator for full three-dimensional
confinement of the optical mode. This reduces the mode volume by a factor
of 1.9 compared to a conventional metamaterial resonator while
maintaining the same Rabi frequency. The conductive ground plane is
implemented using a highly doped n+ layer which allows us to integrate it
monolithically into the device and simplify fabrication.
©2013 Optical Society of America
OCIS codes: (160.3918) Metamaterials; (230.5750) Resonators; (250.5590) Quantum-well,
-wire and -dot devices; (270.1670) Coherent optical effects.
References and links
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
K. J. Vahala, “Optical microcavities,” Nature 424(6950), 839–846 (2003).
A. J. Shields, “Semiconductor quantum light sources,” Nat. Photonics 1(4), 215–223 (2007).
K. Tanaka, E. Plum, J. Y. Ou, T. Uchino, and N. I. Zheludev, “Multifold enhancement of quantum dot
luminescence in plasmonic metamaterials,” Phys. Rev. Lett. 105(22), 227403 (2010).
G. Khitrova, H. M. Gibbs, M. Kira, S. W. Koch, and A. Scherer, “Vacuum Rabi splitting in semiconductors,”
Nat. Phys. 2(2), 81–90 (2006).
D. G. Lidzey, D. D. C. Bradley, A. Armitage, S. Walker, and M. S. Skolnick, “Photon-mediated hybridization of
Frenkel excitons in organic semiconductor microcavities,” Science 288(5471), 1620–1623 (2000).
J. Dintinger, S. Klein, F. Bustos, W. L. Barnes, and T. W. Ebbesen, “Strong coupling between surface plasmonpolaritons and organic molecules in subwavelength hole arrays,” Phys. Rev. B 71(3), 035424 (2005).
G. Günter, A. A. Anappara, J. Hees, A. Sell, G. Biasiol, L. Sorba, S. De Liberato, C. Ciuti, A. Tredicucci, A.
Leitenstorfer, and R. Huber, “Sub-cycle switch-on of ultrastrong light-matter interaction,” Nature 458(7235),
178–181 (2009).
G. Scalari, C. Maissen, D. Turcinková, D. Hagenmüller, S. De Liberato, C. Ciuti, C. Reichl, D. Schuh, W.
Wegscheider, M. Beck, and J. Faist, “Ultrastrong coupling of the cyclotron transition of a 2D electron gas to a
THz metamaterial,” Science 335(6074), 1323–1326 (2012).
M. Porer, J.-M. Menard, A. Leitenstorfer, R. Huber, R. Degl’Innocenti, S. Zanotto, G. Biasiol, L. Sorba, and A.
Tredicucci, “Nonadiabatic switching of a photonic band structure: Ultrastrong light-matter coupling and slowdown of light,” Phys. Rev. B 85(8), 081302 (2012).
A. Delteil, A. Vasanelli, Y. Todorov, C. Feuillet Palma, M. Renaudat St-Jean, G. Beaudoin, I. Sagnes, and C.
Sirtori, “Charge-induced coherence between intersubband plasmons in a quantum structure,” Phys. Rev. Lett.
109(24), 246808 (2012).
S. A. Maier, “Plasmonic field enhancement and SERS in the effective mode volume picture,” Opt. Express
14(5), 1957–1964 (2006).
R. Ruppin, “Electromagnetic energy density in a dispersive and absorptive material,” Phys. Lett. A 299(2–3),
309–312 (2002).
P. Jouy, A. Vasanelli, Y. Todorov, A. Delteil, G. Biasiol, L. Sorba, and C. Sirtori, “Transition from strong to
ultrastrong coupling regime in mid-infrared metal-dielectric-metal cavities,” Appl. Phys. Lett. 98, 231114
(2011).
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14. D. Dietze, A. Benz, G. Strasser, K. Unterrainer, and J. Darmo, “Terahertz meta-atoms coupled to a quantum well
intersubband transition,” Opt. Express 19(14), 13700–13706 (2011).
15. J. F. O’Hara, R. Singh, I. Brener, E. Smirnova, J. Han, A. J. Taylor, and W. Zhang, “Thin-film sensing with
planar terahertz metamaterials: sensitivity and limitations,” Opt. Express 16(3), 1786–1795 (2008).
16. H.-T. Chen, W. J. Padilla, M. J. Cich, A. K. Azad, R. D. Averitt, and A. J. Taylor, “A metamaterial solid-state
terahertz phase modulator,” Nat. Photonics 3(3), 148–151 (2009).
17. X. Ni, S. Ishii, A. V. Kildishev, and V. M. Shalaev, “Ultra-thin, planar, Babinet-inverted plasmonic metalenses,”
Light Sci. Appl. 2(4), e72 (2013).
18. N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. R. Dalvit,
and H.-T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science
340(6138), 1304–1307 (2013).
19. N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with
phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
20. J. Lin, J. P. B. Mueller, Q. Wang, G. Yuan, N. Antoniou, X.-C. Yuan, and F. Capasso, “Polarization-controlled
tunable directional coupling of surface plasmon polaritons,” Science 340(6130), 331–334 (2013).
21. A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science 339(6125),
1232009 (2013).
22. H. C. Liu and F. Capasso, Intersubband Transitions in Quantum Wells: Physics and Device Applications I
(Academic, 2000).
23. A. Gabbay and I. Brener, “Theory and modeling of electrically tunable metamaterial devices using inter-subband
transitions in semiconductor quantum wells,” Opt. Express 20(6), 6584–6597 (2012).
24. A. Gabbay, J. Reno, J. R. Wendt, A. Gin, M. C. Wanke, M. B. Sinclair, E. Shaner, and I. Brener, “Interaction
between metamaterial resonators and intersubband transitions in semiconductor quantum wells,” Appl. Phys.
Lett. 98, 203103–203101:203103 (2011).
25. J. D. Jackson, Classical electrodynamics (Wiley, New York, 1975).
26. A. E. Cetin, A. A. Yanik, C. Yilmaz, S. Somu, A. Busnaina, and H. Altug, “Monopole antenna arrays for optical
trapping, spectroscopy, and sensing,” Appl. Phys. Lett. 98, 111110 111111–111113 (2011).
27. J. Liang, C. C. Chiau, X. Chen, and C. G. Parini, “Printed circular disc monopole antenna for ultra-wideband
applications,” Electron. Lett. 40(20), 1246–1247 (2004).
28. R. A. Sadeghzadeh-Sheikhan, M. Naser-Moghadasi, E. Ebadifallah, H. Rousta, M. Katouli, and B. S. Virdee,
“Planar monopole antenna employing back-plane ladder-shaped resonant structure for ultra-wideband
performance,” IEEE Trans. Microwave Antennas Propag. 4(9), 1327–1335 (2010).
29. K. B. Alici and E. Ozbay, “Electrically small split ring resonator antennas,” J. Appl. Phys. 101, 083104 083101–
083104 (2007).
30. D. W. Peters, C. M. Reinke, P. S. Davids, J. F. Klem, D. Leonhardt, J. R. Wendt, J. K. Kim, and S. Samora,
“Nanoantenna-enabled midwave infrared focal plane arrays,” Proc. SPIE 8353, 83533B (2012).
31. G. Donzelli, A. Vallecchi, F. Capolino, and A. Schuchinsky, “Metamaterial made of paired planar conductors:
Particle resonances, phenomena and properties,” Metamaterials 3(1), 10–27 (2009).
32. M. Born and E. Wolf, Principles of optics (University Press, Cambridge, UK, 2002).
33. Lumerical, retrieved http://www.lumerical.com.
34. A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible
free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3),
687–702 (2010).
35. K. J. Russell, K. Y. M. Yeung, and E. Hu, “Measuring the mode volume of plasmonic nanocavities using
coupled optical emitters,” Phys. Rev. B 85(24), 245445 (2012).
36. R. Loudon, “The propagation of electromagnetic energy through an absorbing dielectric,” J. Phys. A 3(3), 233–
245 (1970).
37. M. W. Klein, T. Tritschler, M. Wegener, and S. Linden, “Lineshape of harmonic generation by metallic
nanoparticles and metallic photonic crystal slabs,” Phys. Rev. B 72(11), 115113 (2005).
38. M. Geiser, F. Castellano, G. Scalari, M. Beck, L. Nevou, and J. Faist, “Ultrastrong coupling regime and plasmon
polaritons in parabolic semiconductor quantum wells,” Phys. Rev. Lett. 108(10), 106402 (2012).
39. Y. Todorov, A. M. Andrews, R. Colombelli, S. De Liberato, C. Ciuti, P. Klang, G. Strasser, and C. Sirtori,
“Ultrastrong light-matter coupling regime with polariton dots,” Phys. Rev. Lett. 105(19), 196402 (2010).
40. G. Bastard, E. E. Mendez, L. L. Chang, and L. Esaki, “Variational calculations on a quantum well in an electric
field,” Phys. Rev. B 28(6), 3241–3245 (1983).
41. D. A. B. Miller, J. S. Weiner, and D. Chemla, “Electric-field dependence of linear optical properties in quantum
well structures: Waveguide electroabsorption and sum rules,” IEEE J. Quantum Electron. 22(9), 1816–1830
(1986).
1. Introduction
Light-matter interaction is a fascinating and highly active field of research [1]. In a simplified
picture, a two-level system is coupled to an optical cavity which causes both systems to
interact and therefore exchange energy. Depending on the efficiency of this energy exchange
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in relation to all the loss mechanisms present in the system, e.g. non-radiative decay of the
two-level system or light escaping the cavity (optical loss), different physical regimes can be
studied. In the weak coupling regime, the spontaneous lifetime of the two-level system can be
reduced through the so-called Purcell effect [2, 3]. Here we will focus on the strong coupling
regime, where the energy exchange between the dipole and the optical cavity is faster than all
loss mechanisms combined. Energy oscillates between the cavity and the two-level system
multiple times before it is lost. The characteristic signature of this energy transfer is a beating
in the time domain of different optical signals (observable in emission, reflection or
absorption) or a splitting of the single cavity resonance into two polariton branches in the
frequency domain. This process happens at a characteristic rate called the vacuum Rabi
frequency ΩR. Typically the Rabi frequency is only a very small fraction of the fundamental
optical carrier frequency. In other words, the optical dipole undergoes many optical cycles
before it exchanges energy with the cavity. To observe this splitting experimentally it is
therefore necessary to use cavities with a high quality factor. This makes low-loss dielectric
resonators the only feasible choice at optical wavelengths [4].
Significantly larger polariton splittings compared to the bare cavity resonance frequency
have been demonstrated recently [5–8]. These experiments used optical dipoles with
extremely large dipole matrix elements to achieve strong interaction; typical examples are
organic molecules (J-aggregates) [5, 6] or intersubband transitions (ISTs) in semiconductor
quantum-wells (QWs) [7, 8]. The resulting large splittings (values beyond 50% of the carrier
frequency have been reported [8]) lower the requirement for the optical cavity and make the
experimental observation of strong coupling signatures much easier. Therefore, a larger
variety of potential structures can now be used as optical cavities including metallic structures
such as gratings [9] or frequency selective surfaces [10]. Their main advantage is an extreme
spatial confinement of the optical mode to deep-subwavelength volumes based on localized
surface plasmons [11, 12]. Furthermore, the large enhancements in the electric field close to
resonant metallic surfaces support the strong light-matter interaction even further.
Recently, metallic metamaterial resonators have been used for studying light-matter
interaction and particularly in the strong coupling regime [8, 10, 13, 14]. These resonators are
of subwavelength dimensions and can be designed to support electric or magnetic resonances.
Planar arrays of these resonators have been recently used in a number of applications such as
sensing [15], modulation of light [16] and beam control [17–21]. Planar metamaterial
resonators can be straightforwardly combined with optical dipoles implemented using optical
transitions in semiconductor QWs. Thin layers of semiconductors with different bandgaps
form potential wells for carriers that inhibit the free electron motion along one spatial
direction. Electrons present in these QWs can only occupy discrete energy levels resulting in
atom-like absorption and emission spectra when they are promoted between these energy
levels. The optical properties such as transition energy or dipole matrix element of these ISTs
are controlled by the thickness of the individual wells and barriers, and become largely
independent of the underlying semiconductor material. One consequence of the quantization
of energy levels along only one spatial dimension that is essential to this work is the
anisotropy of the dielectric permittivity. Only light that is polarized along the growth
direction (in this manuscript referred to as z-axis) couples to the ISTs due to the dipole
selection rules [22]. Therefore, normal incidence radiation (which propagates along the
z direction and will be used in this manuscript to study the strong light-matter interaction) will
not be able to couple to ISTs. Metamaterial resonators can be used to solve this coupling
problem. In the near-field region of the resonators, most of the incoming optical field is
transferred to the perpendicular field component at the metamaterial resonance [14]. This
makes planar metamaterials an excellent platform to study light-matter interaction in subwavelength volumes.
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30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.032572 | OPTICS EXPRESS 32574
Fig. 1. Schematic of a single unit cell of the planar metamaterial. The “dogbone” resonator is
processed directly above the thin optical dipole layer (indicated by the vertical arrows)
resulting from the ISTs. The vertical confinement is provided by the conductive ground plane
underneath.
For an even stronger reduction in interaction volume it is necessary to study the cavity
near-field in more detail. Designing and controlling the spatial extent of the optical mode in
the lateral direction is fairly straightforward; the mode is restricted predominantly to the
regions directly underneath the metal traces. However, in the vertical direction (perpendicular
to the metamaterial) the electric field extent is given by the decay length of the cavity mode.
This decay length is difficult to control and in the mid-infrared (MIR) spectral range it is
typically on the order of a few hundred nanometers [23, 24]. This vertical field profile is
crucial for optimizing the position and the thickness of the QW stack; only the fraction of the
cavity mode that has a spatial overlap with the QWs contributes to the strong coupling.
Here we present an approach to realizing full three dimensional mode confinement using
monolithic metamaterial nanocavities that remains compatible with planar fabrication
processes, and discuss the strong light-matter interaction using these nanocavities. The basic
geometry for the device is shown in Fig. 1. We use a planar metamaterial resonator fabricated
on top of a semiconductor substrate and add a bottom conductive ground plane. We realize
the ground plane using a thin, highly doped n+ layer which is integrated monolithically into
the device and allows for simple fabrication. The quantum well stack containing the optical
dipoles can be very thin as the conducting ground plane limits the vertical extent of the
optical field. This additional confinement reduces the optical cavity volume by a factor of 1.9
as compared to the use of just a metamaterial resonator with no backplane. Incorporating our
semiconductor based ground plane into the device we achieve the same interaction strength
between the ISTs and the cavity field (i.e., the same Rabi frequency) using one-third the QW
stack thickness of a comparable design without ground plane.
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Fig. 2. Schematic of both sample geometries. The In.53Ga.47As/Al.48In.52As quantum-wells are
designed for a transition energy of 100 meV (top left). Both samples are grown on an InPsubstrate (blue); the quantum-well stack is indicated in purple. The monolithic metamaterial
nanocavity sample (bottom right) is confined by an 800 nm thick n+ layer (red) in the vertical
direction. The permittivity of the n+ layer is shown in the bottom left subplot where ε’ refers to
the real part and ε” to the imaginary one. The difference in “dogbone” size between the
conventional sample and the monolithic metamaterial nanocavity is required by the difference
in permittivity of the QW-stack and the ground plane. We have adjusted the sizes to keep the
metamaterial resonance frequency constant.
2. Metamaterial design and interaction volume
Conductive ground planes are a well-studied approach for the design of radio-frequency
antennas. From a modeling standpoint we can replace the region below the ground plane with
the mirror charge from above; the field profile remains identical in the entire upper half-space
[25]. This approach is commonly used to reduce the length of a dipole antenna by a factor of
two [26]. A monopole antenna placed perpendicularly on top of a ground plane gives the
same emission profile. More recently, dipoles that are oriented parallel to the ground plane
have been used to realize ultra-broadband antennas [27, 28] or small antennas based on splitring resonators [29]. Here we will focus on another aspect when using ground planes: the
efficient confinement of radiation to small volumes [30].
Instead of the antennas mentioned before, we combine the conductive ground plane with a
“dogbone”-metamaterial nanocavity [31]. We chose this particular metamaterial resonator
because of its strong near-field enhancement along the entire area of the resonator. We study
two cases: a) a “dogbone” resonator fabricated on top of a 650 nm thick stack of QWs as the
reference sample, and b) a “dogbone” resonator fabricated on top of a 195 nm thin QW-stack
with the semiconductor-based ground plane (we will call this the “monolithic metamaterial
nanocavity” in this work). A schematic of both samples is presented in Fig. 2. For the
monolithic metamaterial nanocavity we added an 800 nm In.53Ga.47As layer underneath the
thin QW-stack n-doped to a concentration of 1019 cm−3. Its behavior can be described using a
simple Drude model as indicated in Fig. 2. Below its plasma frequency of 39.3 THz the real
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part of the permittivity remains negative and it shows metallic behavior [32]. Our QWs are
based on an In.53Ga.47As/Al.48In.52As heterostructure which is lattice matched to the InP
substrate. The QW-width is set to 12.5 nm with 20 nm barriers in between and this leads to a
transition energy for the bound electrons of 100 meV (24.3 THz). Each well is doped to an
electron sheet density of 1.25 × 1012 cm−2. This basic sequence is repeated multiple times to
achieve the required thickness for the QW-stack of 195 nm for the monolithic metamaterial
nanocavity and 650 nm for the conventional sample. The QW-stacks are capped with a 30 nm
thin Al.48In.52As layer. The monolithic metamaterial nanocavity has an additional 40 nm
Al.48In.52As barrier between the QW-stack and the n+ layer. Both heterostructures are grown
using molecular beam epitaxy which allows us to control the thickness of the individual
layers (QWs, ground plane, buffer layers) precisely and integrate all layers monolithically
into the sample. Furthermore, we analyzed both samples using x-ray diffraction
measurements to ensure their crystal quality.
We study the strong light-matter interaction in the frequency domain analyzing the
theoretical and experimental optical reflectance spectra obtained at normal incidence. We
fabricated several arrays of metamaterial resonators by geometrically scaling the resonator
and unit-cell dimensions which shifts the resonance frequency and allows us to sweep this
transition across the IST. Due to the strong light-matter interaction we expect a distinct anticrossing behavior rather than just two discrete resonances crossing each other. To understand
our system we perform first a series of finite-difference time-domain (FDTD) simulations
[33, 34]. We design one unit cell according to the schematics in Fig. 2 and apply periodic
boundary conditions. It should be noted here that the conventional metamaterial and the
monolithic nanocavity sample show the same periodicity in the xy-plane. Thereby, we can
exclude any additional effect of the resonator spacing or nearest neighbor interaction on the
light-matter coupling between the two different samples and focus on the interaction at the
single resonator level. The parameters for the gold and the n+ layer (including doping
concentration and mobility) are extracted from spectral ellipsometry measurements. The QWs
are modeled as anisotropic, harmonic oscillators following the intersubband selection rules;
only light polarized along the z-axis can couple to these transitions. The optical susceptibility
is calculated following the procedure in [14, 23]. The center frequency of the absorption is set
to 24.3 THz, and the full-width at half-maximum to 2.4 THz. Both values are confirmed by
waveguide measurements using the same wafer as the conventional sample. It should be
stressed here that despite the multiple scattering mechanisms affecting the spectral width of
the IST, one phenomenological broadening term in the model is enough to capture the
underlying behavior.
The importance of adding an additional confinement dimension to the optical fields can be
seen in the spectrally and spatially resolved mode profiles shown in Fig. 3(a). The n+ layer
prevents the mode from penetrating into the substrate and increases the optical or mode
confinement. The mode volume is reduced from 2.49 × 10−3 λeff3 for the conventional sample
to 1.34 × 10−3 λeff3 for the monolithic metamaterial nanocavity, where λeff describes the
wavelength inside the semiconductor (λ/n). In both cases we define the mode volume
following the Purcell definition for dispersive media [11, 12, 35, 36] and limit the integration
volume to the semiconductor. Thereby, we can avoid the extreme field enhancement at the
metal surface that leads to numerical problems and as a consequence to unphysical solutions.
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Fig. 3. Field profiles and polariton branches simulated using finite-difference time-domain
calculations. (a) Frequency and spatially resolved Ez profiles for both samples without
quantum-well interaction. The electric field is concentrated at the air-semiconductor interface
and penetrates 600 nm into the conventional sample (left panel). The n+ layer limits the cavity
mode to the quantum-well region in case of the monolithic metamaterial nanocavity (right
panel). The quantum-wells are sandwiched between a 30 nm (above, both samples) and a 40
nm (below, only metamaterial nanocavity) Al.48In.52As buffer layer which is indicated by the
white, dashed lines. The absolute value of the Ez component is integrated across the entire unit
cell in the xy-plane to create both profiles. The field values are referenced against the
maximum for both cases. (b) Simulated reflectance curves for both types of samples using
finite-difference time-domain calculations. As the QW-stack thickness is increased for the
conventional sample the splitting between the two polariton branches increases as well. The
eigenfrequencies appear as maxima in reflectance in this case. The metamaterial nanocavity
sample experiences the same polariton splitting as the three-time thicker conventional sample
appearing as minima in reflectance. The black dashed lines represent the predicted polariton
eigenfrequencies using the coupled oscillator model.
The effect of the decay length of the electric field for the resonator without the ground
plane is analyzed by calculating the normal incidence reflectance spectra for three different
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QW stack thicknesses. As illustrated in Fig. 3(b) the splitting between the two polariton
branches increases with an increasing QW-stack thickness. To quantify this increased lightmatter coupling we calculate the Rabi frequency using a coupled harmonic oscillator model
[37] that allows us to fit the entire lineshape of the reflectance spectra for each metamaterial
geometric scaling factor. The three samples with different QW-stacks show Rabi frequencies
of 1.65 (50 nm QW stack), 2.34 (200 nm QW stack) and 2.64 THz (650 nm QW stack).
Adding the ground plane allows us to shrink the QW-stack thickness and keep a similar Rabi
splitting, as shown in Fig. 3(b). The calculated Rabi frequency for this case is 2.7 THz which
is almost the same value obtained for the 650 nm thick conventional QW-stack sample.
Therefore, the predicted polariton eigenfrequencies using the coupled oscillator model are
also almost identical for the monolithic nanocavity and the three-time thicker QW-stack using
a conventional metamaterial with no ground plane (Fig. 3(b)). The reason for the same lightmatter interaction strength despite the much thinner QW-stack is the additional mode
confinement provided by the ground plane.
Fig. 4. Fabrication and experimental reflectance curves. (a) The “dogbone” metamaterial is
defined by electron beam lithography directly on top of the semiconductor. A Ti/Au (5/100
nm) layer is evaporated followed by a standard lift-off process. The images are taken for our
monolithic metamaterial nanocavity sample. The conventional sample follows the exact same
processing recipe with slightly different resonator dimensions. (b) The conventional sample
shows a peak in reflectivity on resonance with the metamaterial. The reflectance values are
referenced against a gold mirror. The polariton branches predicted by the coupled oscillator
model are shown by the dashed black lines. (c) The polariton anti-crossing shows up as
minima in the reflectance curves. The reduced reflectance for polariton frequencies beyond 30
THz is caused by the reduced efficiency of the ground plane.
3. Measurement results and discussion
Experimentally, we confirm our theoretical findings by measuring the normal incidence
reflectance spectra for the conventional sample (650 nm QW stack) and the monolithic
metamaterial nanocavity sample. All optical measurements are performed at room
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temperature using a Nicolet Magna 860 Fourier-transform infrared spectrometer with a
microscope objective. The “dogbone”-nanocavity is defined using electron beam lithography;
a Ti/Au (5/100 nm) layer is evaporated followed by a standard lift-off process. Scanning
electron micrograph images for a processed device are presented in Fig. 4(a). It should be
stressed here that the fabrication of our monolithic metamaterial nanocavities does not require
any additional processing steps. The complex flip-chip process [38, 39] that is normally
required to realize a conductive ground plane can be avoided completely. Similar to the
procedure used in the FDTD simulations we change the metamaterial resonance by geometric
scaling and sweep it across the fixed IST. The normal incidence reflectance curves for the
conventional sample are presented in Fig. 4(b). For this sample, we calculate a Rabi
frequency of 2.1 THz following the same procedure as in the FDTD simulations. The
monolithic metamaterial nanocavity results are shown in Fig. 4(c) and we demonstrate an
increased Rabi frequency of 2.5 THz. As predicted by our FDTD simulations we were able to
use the full three-dimensional confinement to maintain the same light-matter interaction
strength while reducing the thickness of the QW stack. The reduced contrast in our
reflectance measurements compared to the simulations is attributed to the use of a microscope
objective with 0.58 NA leading to a large spread of incoming angles while the calculations
are performed for normal incidence plane wave excitation. At the same time, the microscope
objective allows us to sample an area of only 100 × 100 μm2 and thereby minimize the
influence of processing imperfections and heterostructure variations which would otherwise
lead to a broadening of the measured resonances. The overall red-shift of our intersubband
resonances for both samples compared to the calculations is attributed to a small thickness
gradient across the wafer (center vs. edge).
One major difference between the two samples that was also observed in the FDTD
simulations is the interchange of regions of high and low reflectance. The conventional
sample shows a peak in reflectance on the metamaterial resonance and low background
reflectance that is given by the refractive index contrast between air and the semiconductor.
The monolithic metamaterial nanocavity shows a reflectance coefficient close to unity at offresonance frequencies which is caused by the quasi-metallic ground plane. On resonance, the
reflectance is reduced, showing the polariton eigenfrequencies as minima. This behavior is
maintained below the bulk plasma frequency of the ground plane. When approaching 30 THz
the real part of the permittivity of the n+ layer approaches zero with a concomitant weakening
of the “metallic character” of this layer. As a result this 800 nm layer becomes partially
transmissive. Hence, the efficiency of the n+ layer to act as a metallic layer and provide mode
confinement is reduced.
4. Conclusion and outlook
In conclusion, we have presented a monolithic method to confine light in all three spatial
dimensions using metamaterial nanocavities in conjunction with a semiconductor-based
ground plane. The combination of a two-dimensional metamaterial with a buried n+ layer
leads to a reduced QW-stack thickness while maintaining the same light-matter interaction
strength compared to a conventional metamaterial sample without ground plane. Our
structures are compatible with planar processing technologies and can be realized in any
frequency region as long as the IST remains below the bulk plasma frequency of the
semiconductor ground plane. The reduction in the QW region thickness also means that the
cavity volume is further reduced compared to a conventional metamaterial resonator. We
have calculated a mode volume of 1.34 × 10−3 λeff3 for the monolithic nanocavity sample
which corresponds to a reduction by a factor of 1.9 as compared to a conventional
metamaterial resonator making our monolithic nanocavities an excellent tool to study lightmatter interaction in extremely small volumes. Our confinement concept can be extended
towards higher frequencies by carefully engineering the n+ layer. The strong light-matter
interaction itself relies on ISTs which can be realized in various semiconductor
#200079 - $15.00 USD
Received 23 Oct 2013; revised 4 Dec 2013; accepted 4 Dec 2013; published 23 Dec 2013
(C) 2013 OSA
30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.032572 | OPTICS EXPRESS 32580
heterostructures. The plasma frequency of the ground plane can be increased by using
semiconductors that allow for higher doping levels or have higher carrier mobility. The highly
scalable device concept presented in this work is well suited for the realization of actively
tunable metamaterials. The IST properties such as transition energy or dipole matrix element
can be easily controlled by an external bias using the quantum-confined Stark effect [40, 41].
Due to the strong interaction between the IST and the monolithic metamaterial nanocavity
also the response of the coupled system will be tuned. This leads to an active control of the
metamaterial resonance by an external bias. The reduction in QW-stack thickness due to the
additional mode confinement provided by the ground plane reduces the amount of active
medium and thereby simplifies device tuning.
Acknowledgments
This work was performed, in part, at the Center for Integrated Nanotechnologies, a U.S.
Department of Energy, Office of Basic Energy Sciences user facility. Portions of this work
were supported by the Laboratory Directed Research and Development program at Sandia
National Laboratories. Sandia National Laboratories is a multi-program laboratory managed
and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin
Corporation, for the U.S. Department of Energy's National Nuclear Security Administration
under contract DE-AC04-94AL85000.
#200079 - $15.00 USD
Received 23 Oct 2013; revised 4 Dec 2013; accepted 4 Dec 2013; published 23 Dec 2013
(C) 2013 OSA
30 December 2013 | Vol. 21, No. 26 | DOI:10.1364/OE.21.032572 | OPTICS EXPRESS 32581