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Active Tuning of Mid-infrared Surface Plasmon Resonance and Its Hybridization in Black Phosphorus Sheet Array Li Han, Lin Wang, Huaizhong Xing, and Xiaoshuang Chen ACS Photonics, Just Accepted Manuscript • DOI: 10.1021/acsphotonics.8b00875 • Publication Date (Web): 25 Jul 2018 Downloaded from http://pubs.acs.org on July 26, 2018
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Active Tuning of Mid-infrared Surface Plasmon Resonance
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and Its Hybridization in Black Phosphorus Sheet Array
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Li Han1, Lin Wang2*, Huaizhong Xing1*, Xiaoshuang Chen1,2*
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1
Department of Applied Physics, Donghua University, Shanghai 201620, China
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2
State Key Laboratory of Infrared Physics, Shanghai Institute of Technical Physics,
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Chinese Academy of Sciences, Shanghai 200083, China
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*Emails:
[email protected];
[email protected];
[email protected] 8
ABSTRACT
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The behaviors of anisotropic plasmons in black phosphorus have been fully exploited
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across a complete variety of system including individual nanoribbon, vertically offset
11
paired ones, and nanoribbon/sheet hybrid system. Benefiting from its two-dimensional
12
nature, plasmons can be actively controlled by either geometrical parameters or the
13
carrier doping in black phosphorus, which allows for the emerging phenomenon of
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strong light-matter interaction at mid-infrared region. Remarkably, Rabi splitting over
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17.3 meV is observed in the plasmonic spectra of the nanoribbon/sheet hybrid
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structure as harnessed by the strong interaction of coupled plasmons. We also propose
17
a scheme that supports plasmon on a continuous monolayer black phosphorus by
18
using a diffraction grating. By adjusting the geometrical parameters of the grating and
19
the Fermi level of the black phosphorus slightly, the resonance wavelength can be
20
changed notably. The results appealing open up possibilities of devising black
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phosphorus-based plasmons in the application of optical detection and sensing within
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the deep subwavelength regime at mid-infrared region.
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KEYWORDS: black phosphorus, surface plasmons, hybridization, Rabi splitting,
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diffraction grating, mid-infrared
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Surface plasmons (SPs) are collective oscillations of electrons or holes and have
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drawn much attention due to its ability to concentrate electromagnetic energy in deep
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subwavelength regime.1,2 Because of this, a flurry of very promising experiments have
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demonstrated that SPs may have transformative impact on the way we will drive,
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manipulate, enhance and monitor chemical process,3 and offers spatial and temporal
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control over light, photochemistry with the help of resonant nanostructure. Recent
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works have witness the strong focus on engineering the SPs for the helicity-dependent
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electromagnetic propagation,4,5 wavefront engineering for achromatic metalens,6,7 and
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sub-bandgap photon harvesting on the metallic surface.8,9 Especially, SPs in
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nanostructures with the ability of reconfigurable and tunable wavelength is
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particularly required nowadays for the mid-infrared spectroscopic sensing by
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accessing the fingerprint of molecular vibrations for uniquely identify the biochemical
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building blocks, high-temperature body.10 However, such requirements inevitably
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pose a plethora of practical challenges that create a high barrier in tuning the
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plasmons toward practical applications due to the short electrostatic screening length
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in metal. Two-dimensional (2D) materials such as graphene, molybdenum disulfide
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and black phosphorus offers great potential to reshape the landscape of mid-infrared
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photonics and optoelectronics due to their unique properties such as high degree of
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tunable electronic and photonic properties.11 In particular, in contrast to the plasmons
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in noble metal, the infrared response in these two-dimensional materials is dominated
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by plasmons that can be dynamically tuned by electrostatic gating. Typically, the
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electromagnetic fields of graphene plasmons has been displayed in a way of
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extremely spatial confinement, making them extremely attractive for enhancing
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light-matter interaction.12 Therefore, it is crucial to identify the unique properties of
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SPs in these materials with the aim of overcoming the limitation of the weak field
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confinement in metallic nanostructure at mid-infrared as well as the narrow spectral
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bandwidth.
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Graphene, as a stable existed carbon-atom layer with honeycomb structure, has
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been extensive studied as a hosting materials for supporting the SPs in the past few
30
years, due to its exceptional electronic and photonic properties, e. g. intrinsic high ACS Paragon Plus Environment
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carrier's mobility as well as large electrical tunability.13-15 The SPs have been
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presented in a variety of periodic structures such as ribbons,16-18 disks,19,20 and crossed
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shapes,21,22 exhibiting superior performance in the application of biosensor, plasmonic
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waveguide. Nevertheless, carrier transport in graphene is susceptible to the surface
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imperfections, making it still a great challenge to satisfy the scalable on-chip
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optoelectronic application. As a result, the SPs in graphene is susceptible to scattering
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caused by the supporting substrate, the grain boundaries or the absorbents,23
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sophisticated interface engineering is needed in order to make SPs observable.
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Furthermore, the photodetection in graphene suffering from the large dark current due
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to its gapless nature. These practical challenges have sparked the requirement of
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exploring alternative material satisfying the tradeoff between finite bandgap and high
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mobility.
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Amongst the family of two-dimensional materials, the recently rediscovered
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black phosphorus (BP) already in its first demonstration exhibits moderate bandgap
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and decent mobility, shedding light on the possibilities of overcoming above issues.
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Similar to graphene, black phosphorus (Figure 1a) is a van der Waals material
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comprising puckered layered structure with orthorhombic unit cell. It has
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demonstrated that BP has a direct band gap of about 0.3 eV with measured Hall
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mobilities of n and p type doping approaching 105 cm2/(V·s).24 This puckered-layered
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structure gives rise to the highly anisotropic electrical and optical properties between
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armchair (x) and zigzag (y) directions, enabling the fascinating optical phenomena,
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such as linear dichroism,25 anisotropic exciton and plasmons etc. Liu et al.26
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demonstrated numerically the localized surface plasmons (LSPs) modes in monolayer
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BP using nanopatch arrays. Ni et al.27 designed a nanopatch array structure and
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demonstrated theoretically that the band non-parabolicity of BP leads to highly
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anisotropic plasmon excitation, and the mode dispersions along different
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crystallographic directions enabling polarization selectivity or spectral filtering of
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incident photons. Even so, devising the SPs in BP and its anisotropy is a demanding
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task with the aim of building advanced photonic system with high-degree
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frequency-agile as well as high efficiency at mid-infrared region. ACS Paragon Plus Environment
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Here, highly anisotropic localized surface plasmon resonance behavior in
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individual BP nanoribbon (BPNR) with different geometrical parameters and intrinsic
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doping have been studied in advance. On this basis, plasmon interactions in vertically
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offset paired BPNRs along the armchair and zigzag directions, and simultaneously, in
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the nanoribbon/sheet hybrid system are being explored. Rabi splitting due to the
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strong coupled interactions in nanoribbon/sheet hybrid system have been observed in
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the proposed system. To the end, we have developed a way toward the silicon-based
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integration via considering a continuous monolayer BP placed on a SiO2 grating to
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excite SPs along these two orthogonal crystal-lattice directions. Plasmon resonance
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can be tuned effectively either by electrostatic doping or the geometrical controlling,
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offering efficient route to the scalable optoelectronic integration at mid-infrared
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regime.
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RESULTS AND DISCUSSION
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Surface Plasmon Resonance in Individual BPNR. The SP behavior in monolayer
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BPNR array (Figure 1b) along x and y crystal directions is simulated following the
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anisotropic optical and electronic properties of BP. Here, the BPNRs are surrounded
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with dielectrics of constants ε1 and ε2 . The resonance wavelength is approximately28
λSPj = c
19
2πm j ε0 (ε1 + ε2 ) pξ ne 2
(0)
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where j denotes the crystal direction, n is the electron density for n-doped case is
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2 −1 0.5 given by n= (π h ) (mx my ) kBT ln [1 + exp( EF kBT )] ,24 mj is the electron mass
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along x and y direction which can be obtained from reference 25 and ξ = 1.42 is the
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dimensionless constant derived from the simulation of BPNRs with period p = 2w, w
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is the width of BPNR. For simplicity, we assume that BPNRs are suspended in the
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space so that ε1 = ε2 =1.
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The absorption curve along x and y directions are shown in Figure 1c. The
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geometric parameters for both x and y directions are doomed to be the same, that is,
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the period p = 0.8 µm, the BPNR width w = 0.4 µm and the Fermi level (EF) of BP is
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0.20 eV. For the electric vector along the x direction, the plasmon-induced absorption
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resonance is located at 8.6 µm, while it is red-shifting to 22.2 µm when the electric
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vector turned to the y direction. The reason for the observed phenomenon is due to
5
anisotropy of electronic effective mass, the smaller effective mass along x direction
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represents smaller inertia under action of electric field force and higher frequency.
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The corresponding electric field distributions at the resonance peaks along the
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armchair (x) and zigzag (y) directions are shown in the inset of Figure 1c. As clearly
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shown, a localized plasmon resonance behavior can be observed with the electric field
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maximum localized in a deep-subwavelength regime close to the edges of BPNR. The
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specific changes of the electric field near BP as light passes through individual
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nanoribbon can be obtained from Supporting Information.
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Figure 1. (a) Crystal structure of BP monolayer, x and y denote the armchair and zigzag
15
directions along the puckered atomic layer. (b) Periodic BPNR structure under illumination
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of TM polarized electromagnetic wave. (c) Plasmon-induced infrared absorption in BPNRs
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with its momentum along x (black line) and y (red line) crystal axis directions, and the insets
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show the corresponding electric field distributions.
19 20
To elucidate the role of geometrical parameter on the behavior of SPs in BPNR
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array, different nanoribbon periods and widths are considered in Figure 2. Figures 2a
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and 2b show the plasmon-induced absorption spectra along x and y crystal directions
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with different periods. Obviously, when the period increases, the position of the
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plasmon resonance shifts to a longer wavelength along both crystal directions, being
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conform well with the expression of eq 1. Furthermore, these FWHW of plasmon
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resonances peaks become much broader when the periods increase due to the radiative
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loss of plasmon caused by the reemission of light at longer wavelengths, the result is
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agreement with former report in graphene.29
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Figure 2. Plasmon-induced absorption spectra of BPNR array within different parameters.
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(a, b) Absorption spectra with varying period (p = 2w) corresponding to the armchair and
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zigzag directions. (c, d) Absorption spectra of plasmons along both directions with fixed
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period 0.8 µm and different ribbon widths. (e, f) Absorption spectra along x and y directions
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as EF varied from 0 eV to 0.20 eV.
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Similarly, Figures 2c and 2d show the plasmon-induced absorption spectra with
3
ribbon width w changed from 0.1 µm to 0.7 µm at p = 0.8 µm. By decreasing the
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width w, the coupling between adjacent nanoribbons is weak, and the resonance peak
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shifts to a shorter wavelength since the plasmon wave vector roughly follows
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q~π w.
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dipole caused by the small absorption cross section of narrow ribbon as well as large
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separation among them. On the contrarily, as w increases gradually, coupling between
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adjacent nanoribbons increases intensively, and the plasmon can be extensively
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excited among BPNR array, leading to the enhanced absorption. Since the localized
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field of SPs in BPNR array can extend from one ribbon to another, the net dipole of
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plasmon is increased sharply, resulting in the radiative loss and linewidth broadening
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of resonance peak. Because of this, the geometrical dependence exhibits distinctive
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difference between Figures 2a, 2b and Figures 2c, 2d, with the onset of such departure
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take places at w ~ 0.5 µm. Generally, plasmon-induced resonance shift versus the
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geometrical parameters along both the x and y crystal directions are similar, with the
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maximum absorption rate reaching at 0.5 for both directions.
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The weakness of plasmon-induced absorption is attributed to the small net
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The particular usage of two-dimensional materials for SPs lies primarily in the
19
fact that it can be actively control by tuning the Fermi level (EF) or doping with
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electrostatic gating.24 Similar to above discussions, absorption spectra of BPNRs
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corresponding to the SPs propagating along x and y crystal directions are shown in
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Figure 2e and Figure 2f with varied Fermi level of BP. The geometrical parameters of
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the nanoribbons are set with p = 0.8 µm, w = 0.4 µm, and Fermi level was changed
24
from 0 eV to 0.20 eV. As shown, resonance wavelengths of SPs along both directions
25
undergo significant shift following EF0.73, which is more notable than the graphene
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counterpart with EF0.25 due to the Dirac dispersion. The resonance wavelength of x
27
direction decreases from 28.7 µm to 8.6 µm, and that of y direction changes from 73.4
28
µm to 22.2 µm, exhibiting wider tuning range along y direction with the Fermi level
29
changed from 0.04 eV up to 0.20 eV. Even though the absorption rate becomes
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inferior with the Fermi level decreases, it is still prominent with value exceeding 0.20.
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Figure 3. Schematics of the vertically offset paired BPNRs structure.
4 5
Surface Plasmon Resonance in Vertical Offset paired BPNRs. With the above
6
understanding, in the following, plasmon resonance behavior in vertically offset
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paired BPNRs (Figure 3) is investigated. Here, the nanoribbon period (p = 0.8 µm)
8
and width (w = 0.4 µm) of the top and bottom nanoribbons are kept the same, and
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they are vertically offset with the distance d ~ 0.2 µm to ensure strong coupling. The
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Fermi level (EF) of the bottom BPNR is changed from 0 eV to 0.20 eV and the top
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BPNR remains at 0.10 eV. Figure 4a and Figure 4b display the absorption curve of the
12
paired BPNRs corresponding to the SPs along x and y crystal directions at EF = 0 eV,
13
respectively. In both cases, two resonance maxima are sparked in the spectrum. In
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typically, for plasmon along the armchair direction, a narrow peak I with absorption of
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0.49 at 12.2 µm and a broad peak II with absorption of 0.14 at 28.9 µm are facilitated.
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The inset shows the snapshots of the electric field profile corresponding to these
17
resonance maxima (see Supporting Information). It can be clearly visualized that peak
18
I is aroused by the formation of localized SPs in top BP, and peak II is attributed to the
19
formation of localized SPs in bottom BP. Similarly, for plasmon along the zigzag
20
direction, a narrow peak III with absorption of 0.49 at 31.2 µm and a broad peak IV
21
with absorption of 0.14 at 75.1 µm can be observed. The corresponding electric field
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profile are also shown in illustration, from which it can be concluded that the two
23
peaks are caused by separated excitation of plasmons from top and bottom layers.
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Figure 4. (a, b) Absorption curve of two directions with EFtop = 0.10 eV and EFbottom = 0 eV.
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The inset shows the snapshots of the electric field profile corresponding to these resonance
4
maxima. (c, d) Absorption spectra along x and y direction as EFbottom varied from 0 eV to 0.20
5
eV.
6 7
To elucidate the active tuning of the plasmon resonance behavior in this
8
composite structure, the absorption spectra corresponding to the plasmons along x and
9
y crystal directions are calculated by varying EF as shown in Figure 4c and Figure 4d.
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Obviously, along x direction, with the increase of Fermi level, the peak II gradually
11
moved closer to peak I. Especially when EF is close to 0.10 eV, the two peaks are
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nearly overlapping with each other. More interesting, the combined resonance
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between upper and lower BPNRs exhibiting significant difference in absorption
14
compared with the individual nanoribbons, leading to the anti-crossing behavior. It is
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worth to be mentioned that the individual resonance from top BPNR is suppressed
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when EF > 0.10 eV, and similar trend can be observed for both crystal directions as
17
shown in Figure 4c and Figure 4d. ACS Paragon Plus Environment
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Figure 5. Schematics of nanoribbon/sheet structure.
3 4
Strong hybridization in nanoribbon/sheet hybrid system. To understand
5
better the strong hybridization in composite BPNRs, we considered the case of hybrid
6
system that comprises of monolayer BP and BPNRs as shown in Figure 5. Here, the
7
parameters are p = 0.8 µm, w = 0.4 µm, d = 0.2 µm and EF of nanoribbon is 0.10 eV.
8
When the coupling rate between plasmons in the BPNR and monolayer BP is stronger
9
than their decay rate, system is staying in a strongly interaction regime, which faciles
10
the formation of new hybrid energy levels. Hybrid dynamics of the system by
11
changing the Fermi level of a continuous monolayer BP (from 0 eV to 0.20 eV) is
12
explored. Figure 6a and Figure 6b show the absorption spectra along both directions,
13
respectively. Unlike vertically offset paired nanoribbons, the plasmon resonance
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exhibits larger anti-crossing behavior as caused by the asymmetrical SPs in between
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BP sheet and BPNR. This phenomenon has been denominated before as a Rabi
16
splitting that reflects a strong coupling state.31 Interesting electric field changes can be
17
observed in Supporting Information.
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Figure 6. (a, b) Absorption spectra of BPNR and BP sheet hybrid system as EF varied from 0
3
eV to 0.20 eV corresponding to the SPs along x and y directions. (c, d) Theoretical
4
predictions of the BP-LSP, BP-SP, and the hybrid modes along both directions, and the blue
5
triangle is the FDTD result of the hybrid mode.
6 7 8 9
The dispersion relationship of SPs in a continuous monolayer BP can be expressed as28,32 σ jj = −
ε 0 ω ( ε1 + ε 2 ) iq
(2)
10
and the wave vector of BP plasmon wave can be straightforward retrieved from
11
formula (2) and Drude conductivity (see METHODS)
12
q j (ω ) =
m j ε 0 ( ε1 + ε 2 ) ne
2
ω 2 (1 +
i ) ωτ
(3)
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The SPs in continuous monolayer BP can be excited by incident light once the
14
in-plane wave vector matches the wave vector diffracted by BPNRs. The phase
15
matching equation can be described as33
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Re(q j (ωSPj )) =
1
ωSPj
c
sinθ +
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2π p
(4)
2
where c is the speed of light, θis the incident angle, and ωSPj is the resonance frequency.
3
For θ= 0, the resonance wavelength of continuous BP can be represented as
λSPj = c
4
5 6
2πm j ε0 (ε1 + ε2 ) p ne 2
(5)
thus, the dispersion relation of the hybrid strong coupling system is given by31,34 ω± =
ω below j + ω top j
2
±
1 2
( ω below j - ω top j ) 2 + Ω 2j
(6)
7
Based on the above formula, the dispersion curves of the BPLSP (black line),
8
BPSP (red line) and two hybrid modes (blue line) are plotted simultaneously in
9
Figures 6c and 6d for both x and y crystal directions, respectively. As shown, the two
10
curves of SPs in BPNR and BP sheet are independent from each other except at 0.06
11
eV. When both of them are in the strong coupling regime, Rabi splitting with two
12
hybrid modes are given rise and the resonance wavelength exhibit blue-shifting as the
13
Fermi level increases. Due to the destructive interference between these plasmons at
14
0.06eV, they do not cross with each other, instead, splitting as large as 2.1 µm and 5.5
15
µm in the anti-crossing is given rise along x and y crystal axis. In addition, the
16
splitting energy in x direction (17.3 meV) is greater than that in y direction (6.7 meV),
17
which is mainly due to the smaller effective mass of BP in x direction.
18
Excitation of SPs in Continuous Monolayer BP. Although it has been analyzed
19
that BP patterning can exhibit strong coupled resonance for mid-infrared photon
20
manipulation along with giant tunability, the case of particular integration with CMOS
21
compatible process should be considered. Here, the SiO2 ( ε3 = 1.97) diffraction
22
grating, as shown in Figure 7a, is implemented to excite SP at the interface. The phase
23
matching equation can also be described as33
24 25 26
R e( q j ( ωSP j )) =
ωSP j
c
sin θ +
2π Λ
(7)
Where Λ is the grating period. For an incident wave with θ= 0, with the wave vector matching condition, the
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plasmon in BP is excited and absorption peak appears. The resonance wavelength can
2
be expressed as
λSPj = c
3
2πm j ε0 (ε1 + ε3 ) Λ ne 2
(8)
4 5
Figure 7. (a) Schematics of SPs in BP supported by SiO2 diffraction grating. (b, c)
6
Absorption curve for
7
propogation along x and y crystal directions, respectively. Different orders of plasmon mode
8
are marked with numbers. (d) The electric field profile of the fundamental and second-order
9
plasmon modes in one structure period.
Λ = 0.8 µm, ∆ = 0.4 µm, h = 2.1 µm and EF = 0.20 eV with plasmon
10 11
The SP resonances along x and y directions with the grating period Λ = 0.8 µm,
12
grating width ∆ = 0.4 µm and grating height h = 2.1 µm are shown in Figure 7b and
13
Figure 7c. Second-order plasmon mode at higher frequencies can be seen for either of
14
them, except for the main fundamental peak. The side view of field profile in one
15
period of this structure at the resonance positions are shown in Figure 7d, where the
16
electric field is tightly confined within BP (see Supporting Information). For
17
second-order resonance, the electric field has a 4π phase shift in each grating period.
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1
It is worth noting that the absorption rate along y direction is relatively weak, which
2
will be mentioned in the following discussion.
3
∆
Λ
4
Figure 8. (a, b) Absorption spectra with different grating periods of
5
corresponding to the SPs along x and y crystal directions. (c, d) Absorption spectra of SPs
6
along two crystal directions with fixed period
7
Absorption spectra of two directions with different EF in monolayer BP.
Λ=
= 0.5
0.8 µm but varying widths
∆.
,
(e, f)
8 9
The specific absorption spectra as a function of the grating period are shown in
10
Figure 8a and Figure 8b, where Λ changes from 0.2 µm to 2.0 µm and ∆ = 0.5 Λ .
11
Typically, the resonance wavelength exhibits redshifting from 5.1 µm to 15.1 µm as ACS Paragon Plus Environment
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the grating period increases along the x axis. The absorption reaches its maximum of
2
0.50 when the period is 0.8 µm, corresponding to the resonance wavelength of 9.6 µm.
3
Owing the increased radiative loss, the resonant linewidth is also broadening as the
4
grating period increases. Another factor that limits the plasmon resonance in BP is the
5
grating width ∆ . Figure 8c and Figure 8d illustrate the grating width effect on the
6
plasmon resonance for both directions. For x direction, the resonance wavelength
7
redshifts from 7.6 µm to 10.7 µm as ∆ increases (0.1 µm to 0.7 µm), similar trend is
8
also applicable for y direction (19.6 µm to 27.3 µm), all following well λ ~
9
predicted by the theory. On the contrary to the case of nanoribbons (Figure 2a and
10
Figure 2b), it can be clearly seen that plasmon resonances along these two orthogonal
11
directions scale almost in the same manner when the geometrical parameters changes.
12
To demonstrate the active tuning of SPs, we fix the geometrical parameter of Λ =
13
0.8 µm, ∆ = 0.5 Λ , h = 2.1 µm, and active tuning the Fermi level from 0 eV to 0.20
14
eV. It can be seen from the results in Figure 8e and Figure 8f that the resonance
15
wavelength shifts from 31.7 µm to 9.6 µm as the carrier density increases, along with
16
stronger absorption. The absorption rate reaches a maximum 0.50 at EF = 0.20 eV,
17
being agreement with the change of SPs in the BPNRs array as demonstrated in
18
Figure 2e and Figure 2f.
Λ as
19 20
Figure 9. (a, b) Peak absorption of two directions as a function of grating height.
21 22
Figures 9a and 9b display the change of plasmon absorption along with the
23
change of the trench depth of grating. With the height of the grating increases, the
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1
absorption rate undergoes a non-monotonous process. For plasmon along the x
2
direction, the absorption rate reaches the maximum of 0.5 when h = 2.1 µm. However,
3
for y direction, the grating height at which the absorption rate reaches the maximum
4
of 0.5 is 4.9 µm. It demonstrates that the absorption rate can be adjusted by changing
5
the height of the grating. The above-mentioned problem of lower absorption rate in
6
the y direction than x direction has been solved.
7 8
Figure 10. (a) Schematics of square array grating. (b) Absorption spectra at different
9
polarization angles.
10 11
Based on the anisotropy of BP, the plasmon excitation of the square array grating
12
(Figure 10a) at different polarization angles is briefly explored. In order to compare
13
with the above results, we choose the geometrical parameters as Λ = 0.8 µm, ∆ = 0.4
14
µm, h = 2.1 µm and EF = 0.20 eV. The absorption spectra corresponding to different
15
polarization angles are shown in Figure 10b. A resonance absorption peak can be
16
observed at 9.6 µm when the polarization angle θ = 0 ° (i. e. armchair direction). With
17
the θ increases, plasmon resonances along both armchair (x) and zigzag (y) directions
18
can be observed at the same time. The plasmon resonance along y direction appears at
19
21.5 µm and reaches its maximum at θ = 90 ° . Compared with the above analysis, the
20
absorption is reduced because of the reduced filling factor in the square array grating.
21
It is worth noting that plasmon resonances along both crystal directions appear when
22
the polarization angle of incident light is deflected by a certain angle. However, the
23
absorption becomes weaker when compared with the one with polarization angle in
24
purely parallel to one of these crystal directions.
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CONCLUSION
3
In summary, we have investigated the localized surface plasmons with
4
crystal-direction dependent by constructing a variety of BP-based photonic system. In
5
individual BPNR, it is found that SPs along the y direction have a longer resonance
6
wavelength than the x direction. By changing the geometry and intrinsic doping of the
7
BPNR, efficient tuning of the plasmon resonance can be facilitated. The plasmon
8
resonances in vertically offset paired nanoribbons have also been studied with the
9
understanding of the individual properties. Flexible tuning between single and double
10
peaks has been achieved, leading to the efficient coupling induced spectra splitting. A
11
strong coherent coupling along both armchair and zigzag crystal-directions has been
12
proposed in a nanoribbon/sheet hybrid system, and Rabi splitting energy over 20 meV
13
can be obtained. Based on the above results, we proposed a model for the excitation of
14
plasmons in a continuous BP using periodic SiO2 diffractive grating. Numerical
15
simulations showed that a wide range of operating bandwidth can be achieved in both
16
directions by simply adjusting the geometry parameters of the grating or the intriguing
17
doping of BP. Finally, the behavior of polarization-dependent SP resonance in BP
18
supported on a square array of dielectric grating is demonstrated. The discoveries of
19
the peculiar properties of SPs in black phosphorus such as polarization dependence,
20
widely active tunability as well as strong coupling, enable a new platform with better
21
accessing and controlling of plasmons for the applications of biomedical sensing,
22
anisotropic nanodevice with polarization selective, and spectroscopy at mid-infrared
23
band.
24 25
METHODS
26
Due to the different structures along x and y directions, there is a significant optical
27
anisotropy at BP. The photon characteristics in monolayer BP can be described by the
28
Drude model. The approximate plasma conductivity is expressed as32
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σ jj =
1
ine 2 m j (ω + i τ j )
2
where τis the relaxation time determines the carrier mobility µ in BP asτ = µmj e .
3
Unless specified, we choose µ = 1000 cm2/(V·s) in this paper.
4
The anisotropic Drude dielectric function for monolayer BP is35 ε jj (ω ) = ε ∞ −
5
ω pj2 ω 2 + iωcj ω
6
2 2 where ε∞ = 5.76 is the high-frequency relative permittivity,36 ωpj = (ne ) (ε0mj t) is the
7
plasma frequency of BP with thickness t and ωcj = 1 τ j is the collision frequency.
8
To study the localized surface plasmons in monolayer BP, simulations are
9
performed using lumerical FDTD solutions. In the simulations, BP was modeled as a
10
thin layer with a thickness of 10 nm. Non-uniform grid is used with an accuracy in the
11
BP area as 2 nm, and the mesh size gradually increases outside the BP. The periodic
12
boundary condition is applied in the horizontal direction and the perfectly matched
13
layer (PML) is applied in the vertical direction. The source is selected as vertically
14
incident plane wave. The absorptivity (A) can be calculated with a straightforward
15
formula A = 1 – R – T, where R is the reflectivity, T is the transmissivity.
16 17
AUTHOR INFORMATION
18
Corresponding Author
19
*Emails:
[email protected];
[email protected];
[email protected] 20
Notes
21
The authors declare no competing financial interest.
22 23
ACKNOWLEDGMENTS
24
The authors acknowledge the support provided by the State Key Program for Basic
25
Research of China (Nos. 2013CB632705, 2011CB922004, 2017YFA0305500), the
26
National Natural Science Foundation of China (Nos. 10990104, 11334008, 61405230,
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61290301, 61376102, 11274225, and 61675222), and the Youth Innovation Promotion
2
Association (CAS).
3 4
SUPPORTING INFORMATION
5
The supporting information shows how the light propagates through the structures
6
including individual nanoribbon, vertically offset paired ones, nanoribbon/sheet
7
hybrid system, and diffraction grating system.
8 9 10 11 12 13 14 15
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For Table of Contents Use only
2 3
Title: Active Tuning of Mid-infrared Surface Plasmon Resonance and Its
4
Hybridization in Black Phosphorus Sheet Array
5
Authors: Li Han, Lin Wang, Huaizhong Xing, Xiaoshuang Chen
6
Synopsis: The anisotropic plasmon behaviors in black phosphorus have been fully
7
exploited across a complete variety of system including individual nanoribbon,
8
vertically offset paired ones, nanoribbon/sheet hybrid system, and diffraction grating
9
exciting model. Plasmons can be actively controlled by either geometrical parameters
10
or the carrier doping in black phosphorus. Compared with graphene, black phosphorus
11
has a faster tuning speed and a wider resonance range. Remarkably, Rabi splitting
12
over 17.3 meV is observed in the plasmonic spectra of the nanoribbon/sheet hybrid
13
structure.
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