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SUPPLEMENTARY MATERIALS
Materials and Methods
Figs. S1 to S68
Tables S1 to S6
References (39–68)
Institutes of Health provided a postdoctoral fellowship to J.M.L.; the
Shanghai Institute of Organic Chemistry, Zhejiang Medicine Co., and
Pharmaron provided a postdoctoral fellowship to J.W.; and the
University of the Basque Country provided a predoctoral fellowship
to L.P. We thank Y. Ishihara for assistance with the initial preparation
of the manuscript. We are grateful to D.-H. Huang and L. Pasternack
(The Scripps Research Institute) for assistance with nuclear magnetic
resonance (NMR) spectroscopy and A. L. Rheingold and C. E. Moore
NMR Spectra
21 October 2015; accepted 2 December 2015
10.1126/science.aad6252
◥
logram digitally encodes the Fourier transform
of a desired optical filter function (multiple
reflection resonances within the gain bandwidth
of the laser), enabling photonic DOS manipula-
tion at precise filter frequencies. In real space, a
typical hologram lattice contains a multitude of
phase shifts; the locations and sizes of scattering
sites and defects are set such that via coherent
backscattering the device enters a slow light re-
gime. Transfer matrix method (TMM) calculations
of the group delay transfer function (which is in-
trinsically linked to the photonic DOS) of an
ADFB microcavity under the influence of gain
reveal infinite-gain singularities [fig. S4; see (26)
for further details]. These singularities represent
the frequency and gain values at which self-
oscillation occurs. The ADFB microcavity can pro-
duce coherent amplification of the cavity photons
via stimulated emission processes because of the
build-up of phase coherence at the singularities (20).
ADFB structures were realized in THz quan-
tum cascade lasers (QCLs)—extremely long wave-
length semiconductor lasers with active regions
based on precisely engineered inter-subband tran-
sitions (27). Such ADFB THz QCLs provide an
ideal proving ground for graphene-controlled
gain modulation because they use SP-based wave-
guides (at a metal-semiconductor interface, Fig. 1A)
(28). The first crucial step is to excite two-dimensional
(2D) plasmons in an integrated, atomically thin
graphene sheet to take full leverage of the computer-
generated hologram principle. Hologram pixels
are introduced to the QCL waveguide as plas-
monic scattering sites along the longitudinal axis
of the laser ridge (Fig. 1B). By depositing an elec-
trically gateable graphene film onto these devices,
our goal is to switch the THz SP at each pixel “on”
or “off” by tuning ns, thereby altering the photonic
DOS and the degree to which the THz inter-
subband gain spectra follows the hologram re-
sponse. For example, by modulating the hologram
pixel scattering strength we approach the DOS
singularities, resulting in a dramatic increase of
light-matter interaction within the QCL gain me-
dia (20). Photon lifetimes (and hence modal gain
values) are thereby enhanced, leading to selective
enhancement of competing laser modes and a
concomitant suppression of others.
REPORTS
APPLIED OPTICS
Gain modulation by graphene
plasmons in aperiodic lattice lasers
S. Chakraborty,1* O. P. Marshall,1,2 T. G. Folland,1 Y.-J. Kim,2
A. N. Grigorenko,2 K. S. Novoselov2*
Two-dimensional graphene plasmon-based technologies will enable the development of fast,
compact, and inexpensive active photonic elements because, unlike plasmons in other
materials, graphene plasmons can be tuned via the doping level. Such tuning is harnessed
within terahertz quantum cascade lasers to reversibly alter their emission. This is achieved in
two key steps: first, by exciting graphene plasmons within an aperiodic lattice laser and,
second, by engineering photon lifetimes, linking graphene’s Fermi energy with the round-trip
gain. Modal gain and hence laser spectra are highly sensitive to the doping of an integrated,
electrically controllable, graphene layer. Demonstration of the integrated graphene plasmon
laser principle lays the foundation for a new generation of active, programmable plasmonic
metamaterials with major implications across photonics, material sciences, and nanotechnology.
mong the many intriguing properties of
graphene, its plasmonic characteristics are
some of the most fascinating and potentially
useful (1, 2). Long-lived, tunable intrinsic
graphene surface plasmons (SPs) have
(3, 17), giving rise to the possibility of compact
electrically controllable THz optical components
(18). We incorporated graphene into a plasmonic
THz laser microcavity to dynamically modulate
round-trip modal gain values and therefore laser
emission via EF. In this way, gated graphene be-
comes a powerful tool with which to control the
fundamental properties of a laser—a tool that is
potentially extremely fast and all electrical in na-
ture, with negligible electrical power requirements.
The interaction between light and matter can
be altered by manipulating the electromagnetic
density of states (DOS) using a microresonator
(19, 20). By incorporating a photonic lattice or
plasmonic structure into a laser, one can control
the frequency and amplification of resonant modes
and hence manipulate the properties of lasing
emission (21–23). Furthermore, by breaking the
regularity of these structures it is possible to mod-
ulate the photon DOS and hence light-matter
interaction at several frequencies simulta-
neously. This technique was used recently to de-
velop an aperiodic distributed feedback (ADFB)
cavity laser with a lattice that is in essence a
computer-generated hologram (24, 25). The ho-
A
already been demonstrated in a number of ex-
periments (3–9), including optical modulators
(10, 11), providing the potential for applications
(12, 13). In contrast to the noble metals that are
usually used in SP devices (13, 14), graphene’s
Fermi energy, EF, and carrier concentration, ns
(and therefore its conductivity and SP mode
properties), can be altered, for example, by elec-
trical gating and surface doping (3, 15, 16). Con-
sequently, the behavior of graphene SP-based
structures can be modified in situ, without the
need for structural device changes. In particular,
graphene’s optical and plasmonic properties are
tunable in the terahertz (THz) spectral region
1School of Electrical and Electronic Engineering, University of
Manchester, Manchester M13 9PL, UK. 2School of Physics and
Astronomy, University of Manchester, Manchester M13 9PL, UK.
*Corresponding author. E-mail: s.chakraborty@manchester.ac.uk
(S.C.); kostya@manchester.ac.uk (K.S.N.)
A hologram with relatively weak feedback was
chosen so that any subtle influence of graphene
plasmons on laser emission was not hidden by
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