Letter pubs.acs.org/NanoLett
Linearly Polarized Light Emission from Quantum Dots with Plasmonic Nanoantenna Arrays Mengxin Ren,†,‡ Mo Chen,‡ Wei Wu,† Lihui Zhang,‡ Junku Liu,‡ Biao Pi,† Xinzheng Zhang,† Qunqing Li,*,‡ Shoushan Fan,*,‡ and Jingjun Xu*,† †
The Key Laboratory of Weak-Light Nonlinear Photonics, Ministry of Education, School of Physics and TEDA Applied Physics Institute, Nankai University, Tianjin 300071, P.R. China ‡ Tsinghua-Foxconn Nanotechnology Research Center, Department of Physics, Tsinghua University, Beijing 100084, P.R. China S Supporting Information *
ABSTRACT: Polarizers provide convenience in generating polarized light, meanwhile their adoption raises problems of extra weight, cost, and energy loss. Aiming to realize polarizer-free polarized light sources, herein, we present a plasmonic approach to achieve direct generation of linearly polarized optical waves at the nanometer scale. Periodic slot nanoantenna arrays are fabricated, which are driven by the transition dipole moments of luminescent semiconductor quantum dots. By harnessing interactions between quantum dots and scattered fields from the nanoantennas, spontaneous emission with a high degree of linear polarization is achieved from such hybrid antenna system with polarization perpendicular to antenna slot. We also demonstrate that the polarization is engineerable in aspects of both spectrum and magnitude by tailoring plasmonic resonance of the antenna arrays. Our findings will establish a basis for the development of innovative polarized light-emitting devices, which are useful in optical displays, spectroscopic techniques, optical telecommunications, and so forth. KEYWORDS: plasmonic, nanoantanna, linear polarization, luminescence
P
along specific directions using various methods to realize polarized luminescence.7 The photonic crystal nanocavity was utilized to realize polarized emission from the embedded single quantum dots.8 More recently, linear polarized emission was observed from stacked semiconductor quantum dots (QDs) using sophisticated epitaxial growing methods.9 In this paper, we will demonstrate a simple and flexible plasmonic approach to realize linearly polarized optical wave emission. Analogous to the performance of the radio wave (or microwave) antennas, plasmonic nanoantenna arrays are fabricated, which are further functionalized by semiconductor quantum dots as dipole sources to drive the antennas. Recent research activities suggested that such hybrid nanoantenna systems show the features of accelerated/decelerated radiative rates10−16 and shapeable fluorescent spectra.15,17 Furthermore, unidirectional emission18−21 and control over the radiation patterns from optical antennas were also realized.22−25 Herein, we will focus on the polarization features of the emission from the system. The classical electromagnetic theory states that the electromagnetic waves that were previously emitted by the dipole sources undergo a series of scattering events on the
olarization, as a fundamental property of an electromagnetic wave, forms the basis for many technologies, including telecommunications, liquid-crystal displays, spectroscopic techniques, and so forth. Fascinatingly, in radio wave and microwave bands, a simply dipole antenna in free space acts as a perfect polarized radiation source with the electric field oriented along the direction of the antenna rods.1 On the other hand, in the optical band, to generate polarized light, adopting polarizers are traditionally and commercially regarded as the most straightforward methods. Also, nowadays, due to the booming developments in nanophotonics and plasmonics, polarizers with compact dimensions have been proposed and may become commercially available in the near future.2−5 However, the polarizers need to perform polarization operation in the far-field region of emitters, which would introduce inevitable extra space between emitter and polarizer leading to increase in size of the total light source.6 Adopting polarizers actually induce the problems of extra space, weight, cost, and intrinsic absorptive/reflective loss. Therefore, the uses of polarizers basically violate the trend for global miniaturization and energy consuming reduction for the related electronic and photonic devices. On the basis of the above considerations, light sources that could directly emit polarized optical light are highly demanded. For decades, researchers in materials science community began to make great efforts to achieve this goal. Optical anisotropic organic molecules were forced to orient © XXXX American Chemical Society
Received: December 14, 2014 Revised: March 18, 2015
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Nano Letters antenna elements, which would rebound back and, in turn, work as the driving field for the dipole moments. Secondary emission would be induced, which influences the total emission fields through superimposing on the previously emitted fields.11,26,27 Notably, the secondary emitted field is polarized identically to the scattering driving fields. Through designing suitable nanoantenna elements, the dipole oscillation along a certain direction could be enhanced, whereas the scattering fields along the other directions are overwhelmed. As a result, the emission with preferential polarization in the far-field may happen. On the basis of the above analysis, we hereby exploit the QD-transition dipole-moment-driven plasmonic rectangular slot nanoantennas, which show different scattering strengths for orthogonally polarizations, to directly generate the linearly polarized light. In our experiment, the emission polarization properties of such systems were quantitatively studied utilizing polarimetry technique,28 and the high degree of linear polarization (DOLP) of more than 90% is achieved, which is higher than the reported values of most organic7 and photonic crystal counterparts,8 as well as the stacked QDs.9 The emission polarization is oriented perpendicular to the longer side of the slot. Furthermore, the DOLP is proved to be engineerable by harnessing the plasmonic resonance of the antenna array. Because of the advantages of surface plasmon in localizing intense field with nanoscale distance from the metal surface, the QDs-combined nanoantenna array could be highly compact in size, which shows a total thickness of 150 nm in our case. Distinct from previous works that studied the polarization features of emission at single-nanorod level,18,22,25,29,30 we achieved polarized emission from an arrayed sample with finite area. In addition, rather than requiring quantum emitter to situated at specific position relative to a single antenna using sophisticated techniques,18,25,30−32 the QDs are allowed to be randomly distributed above the antenna arrays in our case, which simplifies the functionalization of the antenna arrays. Our methods could be applied to manufacture miniature polarized light sources without polarizers, which can be expected for wide applications, such as backlights of liquid crystal displays, illuminators in spectrometers, transmitters for quantum information transportation, and so forth. The rectangular plasmonic slot nanoantenna array combined with QDs is schematically illustrated in Figure 1a. The antenna layer was fabricated by focused ion beam milling through a 50 nm thick gold film on a silica substrate. The slot antennas are arranged in a square lattice with a lattice constant P = 300 nm and the entire array footprint is 50 μm × 50 μm. The scanning electron micrograph of an unit cell is shown in the top panel of Figure 1b. Photoluminescent cadmium selenide (CdSe) semiconductor QDs with zinc sulfide (ZnS) shell (Qdot 800 ITK, Invitrogen, sketched in the inset of Figure 1a) were used as the optical dipole sources to drive the antennas. And the QDs were dispersed using the polymer solution and then spin coated onto the structured gold film, forming a 100 nm thick illuminating layer (refer to methods for the preparation of the QDs-polymer layer). The QDs-polymer film on the naked silica substrate shows a luminescence spectrum peaking at wavelength (λ0) of 782 nm, as indicated in Figure 1b. Due to the anisotropic structure design, its spectral responses are expected to be different for orthogonally polarized light. Indeed, as shown by the measured spectra for plane wave illumination in Figure 1c, plasmonic resonances are observed in transmission (T), reflection (R), and absorption (A) spectra near 770 nm (λA) for y polarization;33−35 however, no resonance occurs for x
Figure 1. QDs-combined rectangular slot nanoantenna array and the spectral properties. (a) Schematics of nanoantenna array cut through a 50 nm thick gold film on a silica substrate and covered by QDspolymer layer. The cross section of a QD is sketched in the inset. (b) Scanning electron micrograph of the unit cell (without QDs) (top panel). Feature sizes: unit cell P = 300 nm, slot length a = 90 nm, width b = 25 nm. And the photoluminescence spectra from the QDspolymer layer on silica substrate accompanied by Gaussian fit (dashed blue lines). (c) Experimental measured spectra of transmission (T), reflection (R), and absorption (A) for the QDs-coated antenna array with a = 90 nm under plane-wave illumination. This structure shows a resonance absorption peak at 770 nm for an y-polarized incident wave.
polarization in the measured wavelength range. Such polarization-dependent responses imply the distinct scattering cross sections for different polarized electromagnetic waves and, hence, may lead to modifications to the polarization of the emitted fields of the dipoles nearby as mentioned above. To explicitly explore the polarization properties of the radiation from the above QD-antenna systems, an oscillating dipole moment p (representing a QD transition dipole moment) is assumed to situate at 10 nm above the gold surface on the central normal of an unit cell (with a = 90 nm), as shown in Figure 2a. As aforementioned, the directly emitted fields from the dipole would be scattered by the antenna and react back onto the dipole, followed by inducing secondary emission with polarization identical to the direction of the scattering fields. Using the finite element methods (COMSOL), the induced charge distributions σ (color map) and current density distributions j (red arrows, length in logarithmic scale) on the top surface of gold film, along with the scattered fields Es (black arrows) at the dipole position were simulated (shown in Figure 2a). The three panels correspond to the results under excitations of three orthogonally oriented dipoles px, py, and pz, respectively. The oscillating frequency of the dipoles is chosen according to the antenna resonance wavelength (770 nm). It can be seen that under the excitation of px, the induced current B
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resonance (770 nm). This may indicate the correlation between the emission polarization and the structural plasmonic resonances. Thus, correlation would hint at a way to control the emission DOLP through tailoring the resonances of the nanoantenna arrays, which could be achieved by adjusting the antenna geometric parameters, for example, by simply varying the slot length a. In the experiment, for the purpose of fully treating the polarization properties of the emission from the sample, the Stokes vectors (S-vectors) were adopted to represent the states of the emitted light, which are mathematically convenient to describe the states of partially polarized waves.28 The adopted experimental setup is shown in Figure 3a. The sample was illuminated by a CW laser (center wavelength at 532 nm). The polarization state of the incident laser was manipulated by a combination of a polarizer and a half wave-plate (not shown in the picture). A 10× objective with a numerical aperture (NA) of 0.25 was used to focus the laser onto the QDs side of the sample. The objective was moved toward the sample by a linear stage to ensure that the laser spot fully covered a whole antenna array. Another objective (NA = 0.28) on the opposite side was used to collect the photoluminescence in the direct transmitted direction. A long pass filter with cut-on wavelength at 550 nm was applied to isolate the pump laser. The polarization state of the photoluminescence was spectrally analyzed by a homemade polarimeter consisting of a rotating superachromatic quarterwave (QW) plate (Bernhard Halle Nachfolger GmbH), a fixed Glan−Taylor (GT) calcite polarizer (Thorlabs) and a fiber coupled spectrometer (Princeton Instruments).28 The components of S-vector of the luminescence were derived from Fourier transforming over the spectrometer recorded intensity signal (see in Methods) and shown in Figure 3b. All of them are normalized to the maximum value of the S0. The S0 basically describes the total intensity of the luminescence, which should coincide with the direct measured spectrum without suffering any polarization manipulation of the QW plate and the GT polarizer. The S1 is minus indicating the y polarization feature of the luminescence. The S2 is slightly smaller than 0 in the center wavelength range meaning that the emission has slight polarization component along the 135° direction; however, in our opinion, this is caused by the unavoidable little misalignment between orientations of sample and GT polarizer. The S3 is about zero over the whole spectral range. The degree of linear polarization (DOLP) and the degree of circular polarization (DOCP) are related to the S-vector by DOLP = ((S21 + S22)1/2)/S0 and DOCP = S3/S0, respectively, which are shown in Figure 3c. The luminescence with the DOLP as high as 90% is achieved in the spectral range between 740 and 810 nm. Outside this wavelength range, the determined DOLP is less accurate (covered by the shaded areas). This is due to the fact that the transmitted luminescence intensity was too weak to measure when θ was around 0 and 90°, which introduces errors into the Fourier transformation process. Furthermore, due to the nonchiral symmetry of the structure, no circular polarized component in the luminescence is anticipated, as confirmed by the zero DOCP. The polarization characteristic from the above QD-covered antenna could be well explained by the electromagnetic interaction between the transition dipoles and the antenna, as proved by the good consistency between the experimental DOLP curve and simulation prediction (blue dashed line in Figure 4d) in the unshaded spectral range (see in Methods for the simulation details). We may notice that the DOLP here is smaller than that predicted in Figure 2b. This
Figure 2. Antenna-scattered emission fields of a dipole and the degree of polarization of emission from system. (a) The dipole locates 10 nm directly above the center of the unit cell (a = 90 nm). In the remaining panels, snapshots of charge distributions σ (color map) and instantaneous directions of the induced current density j (small red arrows, length in logarithmic scale) on the top surface of gold film are shown. The black arrows give the scattered fields Es at the dipole position. Three panels correspond to the cases of excitation by three orthogonal oriented dipoles px, py, and pz, respectively. For the sake of clarity, Es are enlarged by 10 times for the case of px. All of the results are plotted for the resonance wavelength 770 nm. (b) The simulated DOLP of light emission in the far-field through the silica substrate.
vortices swirl in opposite directions, and the x-directional dipole-like charge distribution is formed in the tight vicinity of the slot. The scattered field at the exciting dipole position was simulated to be x-oriented (black arrow), which leads to the xpolarized secondary emission fields (more analysis on charge/ current distributions and scattering fields please see Supporting Information). For the py, the induced currents have major direction along the y direction except for the vortices near the slot ends. Furthermore, because of the existence of the distinct plasmonic resonance for y polarization (see in Figure 1c), stronger charge distributions are induced; hence, larger Es is produced. Finally, for pz, only divergent current distribution and monopole-like charge distribution appears; hence, no horizontal Es at the dipole position emerges. Thus, it has no contribution to the polarization modification for the radiation along the z axis. Noticeably, the magnitude of the induced Es for py is more than 10 times larger than that for px, which may suggest y-polarized feature of the secondary and the total emission. For a quantitative evaluation, the overall degree of the linear polarization of the radiation in the far-field was described by DOLP = (Iy − Ix)/(Iy + Ix), in which Ix and Iy are intensities of x and y components, respectively. Taking into account the fact that a real emitter normally has no fixed dipole axis, an average over various dipole orientations should be performed, that is, Ii = 1/3(∑jIi(pj)), in which Ii(pj) (i = x, y; j = x, y, z) is the intensity of i components induced by the dipole along j direction. The DOLP of the light fields exiting from the substrate side is shown in Figure 2b. Indeed confirming our prediction, the emitted light is y-polarized with DOLP larger than 98% and peak wavelength identical to the absorption C
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Figure 3. Polarimeter used in the measurement and typical results for the antenna array with a = 90 nm. (a) The experimental setup adopted to analyze the polarization states of the luminescence. (b) The retrieved S-vector components for luminescence from the sample with a = 90 nm. All of the components are normalized to the maximum value of the S0. (c) The corresponding DOLP and DOCP calculated from the S-vector components shown in (b). The derived DOLP and DOCP are not accurate at the edges of the emission spectral range as a result of the weak measured luminescence intensity (covered by the shaded areas). The blue dashed line corresponds to the calculated DOLP by the numerical simulations.
influenced by the plasmonic resonances. The derived DOLP for different structures are shown in Figure 4d. In a manner similar to the shifting of the emission peaks, the DOLP peaks are also shown to be dependent on and controllable by changing the slot lengths a. Additionally, the S1 components are minus for all structures (not shown in figure); thus, the luminescent waves from all antennas are y polarized, which further manifest the correlations between the radiation polarization manipulation and the polarization dependent plasmonic resonances. The simulated DOLP curves are given by blue dashed lines in Figure 4d, which consist with the experimental measurements well and demonstrate the essential role of electromagnetic interaction between QDs and antennas in modifying polarization radiations. Noticeably, for the structure with larger a, the DOLP curve gives larger peak value. For example, among our results, the maximum DOLP value of more than 90% appears on the red end of the spectrum for structure with a of 110 nm. This phenomenon could be explained by the smaller ohmic loss of gold in longer wavelength and larger evanescent depth inside the QDs layer; thus, more QDs intensely interact with nanoantenna, with accordingly higher polarizing quality. However, we need to notice that the enhancement in the total luminescence intensity (comparing results in Figure 4c with those in Figure 4a) is not obvious for those plasmonic antenna designs compared with previously reported works.11−15 However, if we consider the fact that at least half of the energy would be wasted by adopting a polarizer to make the emission in Figure 4a polarized, the direct polarized emission from our
could be elucidated by the fact that QDs are randomly distributed inside the polymer layer and most of the QDs are more than 10 nm away from the antennas in the experiment. The larger distances would cause much weaker coupling between QDs and the antennas and, consequently, smaller scattering driving fields and worse luminescence polarization. To identify the possibility of controlling the radiation polarization by the plasmonic resonance of the nanoantenna, more systematic results of the photoluminescence and the corresponding DOP from the systems with different a values are presented in Figure 4. Five arrays with different antenna lengths ranging from a = 70 to 110 nm in step of 10 nm were fabricated, whereas b = 25 nm and P = 300 nm were fixed. As reference, the results of the QD-polymer film on the silica substrate without gold film are listed at the top of Figure 4. The around-zero level of the obtained DOP in Figure 4b demonstrates that the emission is totally nonpolarized without showing any polarization memory effect from QDs.36 Figure 4c gives the luminescence spectra of various QDs functionalized antenna arrays under excitation of x-polarized laser. All the photoluminescence spectra in Figure 4c are normalized to the maximum luminescence value in Figure 4a. The measured absorption spectra for y-polarized plane waves are also presented by red dashed lines. As shown, by changing the slot lengths a, the absorption resonance wavelength (λA) is shifted, and the photoluminescence peak is moving toward the respective absorption resonance as well, proving the QDs are efficiently coupled to the antennas and the total emission is D
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the above polymer solution with volume ratio (v/v) of 5% and followed by ultrasonic treatment to prevent aggregation of QDs. The 100 nm thick QDs-polymer layer was finally achieved by spin-coating at 6000 rpm for 1 min. S-Vector Derivation. The emitted light was described by the S-vector in our experiment. The meanings of the components of the S-vector: S0 corresponds to the total irradiance; S1 gives the excess in intensity of light between x- and y-polarized components; S2 shows the excess in intensity of light polarized along 45° direction and that along 135° direction; S3 describes the difference between the intensity between right circular polarized (RCP) and left circular polarized (LCP) components. In such a presentation, the quarter-wave plate with fast axis oriented along θ can be presented by a Mueller matrix of
M QW
⎡1 0 0 0 ⎤ ⎥ ⎢ 1 ⎢ 0 1 + 1 cos 4θ −sin 2θ ⎥ sin 4θ ⎥ ⎢ 2 2 2 =⎢ ⎥ 1 1 1 ⎢0 − cos 4θ cos 2θ ⎥ sin 4θ 2 2 2 ⎥ ⎢ ⎢⎣ 0 −cos 2θ sin 2θ 0 ⎥⎦
The GT polarizer with optical axis along the x direction is described by
Figure 4. Emission spectra and DOLP curves for different structures. (a,b) The luminescence spectrum and DOP from the QDs-polymer film on the silica substrate. (c) The emission spectra from QDs combined nanoantenna arrays with different slot lengths a (orange curves), which are normalized to the maximum luminescence value in (a). Their Gaussian fits are given by blue dashed curves. The absorption spectra for different structures are shown by red dashed lines. The SEM images of different structures are given in the left side. (d) The corresponding DOLP curves for different structures (orange curves). The blue dashed lines present the DOLP predicted by the numerical simulations.
M GT
⎡1 ⎢ 1 1 = ⎢ 2 ⎢0 ⎢⎣ 0
1 1 0 0
0 0 0 0
0⎤ ⎥ 0⎥ 0⎥ ⎥ 0⎦
After passing through the wave plate, the polarization of the luminescence was modulated and the corresponding polarization state depends on the angle of the QW plate. The GT polarizer transformed the above polarization modulation into an intensity modulation and was recorded spectrally by the spectrometer. The S-vector of the light entered the spectrometer (Sspe) is related to that of the emitted luminescence [Slumi, components are presented by Si (i = 0, 1, 2, 3)] by
nanoantennas owns doubled efficiency. Furthermore, in the experiment, nearly identical DOLP curves were measured for ypolarized laser excitation (not shown here). It suggests that the polarized emission is only induced by the interactions between the QDs emission and the plasmonic resonances, which has no relationship with the excitation process. As a result, the above experimental results could be extended to the situations of nonpolarized optical excitation or even electricity pumping. In conclusion, the direct generation of linearly polarized light from the QDs coupled nanoantenna composites is achieved. The scattering fields are identified to act as mediators to link the driving sources with antenna elements and determine the polarization properties of the nanoantenna systems. The DOLP is proved both quantitively and spectrally controllable through the geometric parameters of the antennas. We believe that this work opens up an exciting access to the innovative nanoscale polarized light sources, which could find applications in a wealth of areas, including optical displays, quantum communications, spectroscopy, and compact biosensors. Methods. QDs-Polymer Layer Preparation. Dissolve 274.4 mg of boric acid powder and 1525.6 mg of sodium tetraborate decahydrate powder (purchased from Alfa Aesar) in deionized water in a 100 mL volumetric flask to achieve a borate buffer solution (0.2 mol/L, pH 9.0). Dilute poly(acrylic acid sodium salt) solution (PAA-Na, 225 kDa, Polysciences) using the above borate buffer solution by 5 times in a vial to prepare a polymer solution. The final QDs-polymer solution was made by adding the CdSe/ZnS QDs solution (Qdot 800 ITK, Invitrogen) to
Sspe = M GTM QW S lumi ⎡1⎛ 1 ⎞ ⎢ ⎝⎜S0 + S1⎠⎟ + 2 ⎢2 ⎢ − 1 S3sin 2θ ⎢ 2 ⎢ 1⎛ 1 ⎞ = ⎢ ⎜S0 + S1⎟ + ⎢2⎝ 2 ⎠ 1 ⎢ ⎢ − 2 S3sin 2θ ⎢ ⎢ ⎢⎣
⎤ 1 1 S1cos 4θ + S2 sin 4θ ⎥ 4 4 ⎥ ⎥ ⎥ ⎥ 1 1 S1cos 4θ + S2 sin 4θ ⎥ ⎥ 4 4 ⎥ ⎥ ⎥ 0 ⎥ ⎥⎦ 0
It is shown that the finally recorded intensity signal contains the DC part, as well as the components with periods of 90° and 180°. And all other frequencies have an amplitude of zero by theory. Through the Fourier transformation of the recorded rotation angle dependent intensity, the components of the luminescence (Slumi) could be obtained. Simulations of DOLP Curves. In the simulations, the optical behavior of gold was described by tabulated data from ref 37. The refractive index of the medium where the dipoles locate E
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was assumed as 1.45 to simulate the existence of polymer layer. Furthermore, the refractive index of the silica substrate was assumed to be 1.5. Periodic boundary conditions were imposed on the boundaries between unit cells. Perfectly matched layers were applied to the ends of the model where the waves were outgoing the structure. In the simulation for the model built in Figure 1d, a singe dipole source was adopted 10 nm above the center of an unit cell. However, in the experimental cases, as the QDs are randomly distributed inside the polymer layer, the model built in Figure 1d is not sufficient to explain the measured DOLP results in Figure 3 and 4. Alternatively, a position array was built to model the possible situations of the QDs. In the position array, the QDs are assumed to only locate in three representative planes of z = 10 nm [corresponds to the case that the QDs (radius about 7.5−10 nm) nearly contact with gold film], 50 nm (middle plane of the polymer layer), and 100 nm (the surface of the polymer layer). In addition, the spacings between the neighboring positions in the same z plane are 5 nm along the x and y directions. The contribution of a dipole to each possible position to the radiation in the far-field is calculated separately and averaged over three orthogonal orientations. If the interactions between QDs and unit cells that are not in directly below are neglected and consider that the selected QDs concentration results in a coverage of about two QDs in each unit cell on average, the total intensities of the xand y-polarized components in the far-field could be described by summing contributions from individual QDs [with position coordinates of (x, y, z)] as Ix =
n−1 Cn2
∑ x ,y,z
M.X.R., M.C., W.W, L.H.Z, B.P., and J.K.L. prepared samples. M.X.R. assembled the polarimeter and carried out the optical measurements, analyzed data, and wrote the paper. J.J.X., Q.Q.L., and X.Z.Z assisted in analyzing data and writing the paper. J.J.X. and S.S.F. supervised the work. Notes
The authors declare no competing financial interest.
n−1 Cn2
∑ x ,y,z
1 [Ix(px (x , y , z)) + Ix(py (x , y , z)) 3
1 [Iy(px (x , y , z)) + Iy(py (x , y , z)) 3
in which n is the number of position points contained in one unit cell of the hypothetical position array. Using Iy − Ix Iy + Ix
the DOLP curves are derived and shown by blue dashed curves in Figure 3c and 4d, and a positive DOLP value correspond to y polarization.
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ASSOCIATED CONTENT
S Supporting Information *
Detailed analysis on charge/current distributions inside unit cells and the scattering fields excited by different orientated dipoles. This material is available free of charge via the Internet at http://pubs.acs.org/.
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REFERENCES
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+ Iy(pz(x , y , z))]
DOLP =
ACKNOWLEDGMENTS
This work was supported by National Basic Research Program of China (2013CB328702, 2010CB934101), National Natural Science Foundation of China (11304162), the 111 Project (B07013), PCSIRT (IRT0149), SRFDP (20130031120005), China Postdoctoral Science Foundation funded project (2013M530038), and the Fundamental Research Funds for the Central Universities.
+ Ix(pz(x , y , z))], Iy =
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AUTHOR INFORMATION
Corresponding Authors
*E-mail: [email protected]. *E-mail: [email protected]. *E-mail: [email protected]. F
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Nano Letters (25) Curto, A. G.; Taminiau, T. H.; Volpe, G.; Kreuzer, M. P.; Quidant, R.; van Hulst, N. F. Nat. Commun. 2013, 4, 1750. (26) Chance, R.; Prock, A.; Silbey, R. Adv. Chem. Phys. 1978, 37, 65. (27) Novotny, L.; Hecht, B. Principles of Nano-optics; Cambridge University Press: New York, 2012. (28) Bass, M.; DeCusatis, C.; Enoch, J.; Lakshminarayanan, V.; Li, G.; Macdonald, C.; Mahajan, V.; Van Stryland, E. Handbook of Optics, 3rd ed.; McGraw-Hill, Inc.: New York, 2010; Vol. I: Geometrical and Physical Optics, Polarized Light, Components and Instruments. (29) Ming, T.; Zhao, L.; Chen, H.; Woo, K.; Wang, J.; Lin, H. Nano Lett. 2011, 11, 2296−2303. (30) Kukushkin, V. I.; Mukhametzhanov, I. M.; Kukushkin, I. V.; Kulakovskii, V. D. Phys. Rev. B 2014, 90, 235313. (31) Moerland, R. J.; Taminiau, T. H.; Novotny, L.; van Hulst, N. F. Nano Lett. 2008, 8, 606. (32) Rui, G.; Chen, W.; Don, A.; Nelson, R.; Zhan, Q. Opt. Express 2012, 20, 19297. (33) Degiron, A.; Lezec, H. J.; Yamamoto, N.; Ebbesen, T. W. Opt. Commun. 2004, 239, 61−66. (34) Van der Molen, K. L.; Klein Koerkamp, K. J.; Enoch, S.; Segerink, F. B.; Van Hulst, N. F.; Kuipers, L. Phys. Rev. B 2005, 72, 045421. (35) Garca-Vidal, F. J.; Martn-Moreno, L.; Moreno, E.; Kumar, L. K. S.; Gordon, R. Phys. Rev. B 2006, 74, 153411. (36) Poem, E.; Khatsevich, S.; Benny, Y.; Marderfeld, I.; Badolato, A.; Petroff, P.; Gershoni, D. Solid State Commun. 2009, 149, 1493. (37) Johnson, R. W.; Christy, P. B. Phys. Rev. B 1972, 6, 4370.
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DOI: 10.1021/nl5047973 Nano Lett. XXXX, XXX, XXX−XXX
Linearly Polarized Light Emission from Quantum Dots with Plasmonic Nanoantenna Arrays Mengxin Ren,†,‡ Mo Chen,‡ Wei Wu,† Lihui Zhang,‡ Junku Liu,‡ Biao Pi,† Xinzheng Zhang,† Qunqing Li,*,‡ Shoushan Fan,*,‡ and Jingjun Xu*,† †
The Key Laboratory of Weak-Light Nonlinear Photonics, Ministry of Education, School of Physics and TEDA Applied Physics Institute, Nankai University, Tianjin 300071, P.R. China ‡ Tsinghua-Foxconn Nanotechnology Research Center, Department of Physics, Tsinghua University, Beijing 100084, P.R. China S Supporting Information *
ABSTRACT: Polarizers provide convenience in generating polarized light, meanwhile their adoption raises problems of extra weight, cost, and energy loss. Aiming to realize polarizer-free polarized light sources, herein, we present a plasmonic approach to achieve direct generation of linearly polarized optical waves at the nanometer scale. Periodic slot nanoantenna arrays are fabricated, which are driven by the transition dipole moments of luminescent semiconductor quantum dots. By harnessing interactions between quantum dots and scattered fields from the nanoantennas, spontaneous emission with a high degree of linear polarization is achieved from such hybrid antenna system with polarization perpendicular to antenna slot. We also demonstrate that the polarization is engineerable in aspects of both spectrum and magnitude by tailoring plasmonic resonance of the antenna arrays. Our findings will establish a basis for the development of innovative polarized light-emitting devices, which are useful in optical displays, spectroscopic techniques, optical telecommunications, and so forth. KEYWORDS: plasmonic, nanoantanna, linear polarization, luminescence
P
along specific directions using various methods to realize polarized luminescence.7 The photonic crystal nanocavity was utilized to realize polarized emission from the embedded single quantum dots.8 More recently, linear polarized emission was observed from stacked semiconductor quantum dots (QDs) using sophisticated epitaxial growing methods.9 In this paper, we will demonstrate a simple and flexible plasmonic approach to realize linearly polarized optical wave emission. Analogous to the performance of the radio wave (or microwave) antennas, plasmonic nanoantenna arrays are fabricated, which are further functionalized by semiconductor quantum dots as dipole sources to drive the antennas. Recent research activities suggested that such hybrid nanoantenna systems show the features of accelerated/decelerated radiative rates10−16 and shapeable fluorescent spectra.15,17 Furthermore, unidirectional emission18−21 and control over the radiation patterns from optical antennas were also realized.22−25 Herein, we will focus on the polarization features of the emission from the system. The classical electromagnetic theory states that the electromagnetic waves that were previously emitted by the dipole sources undergo a series of scattering events on the
olarization, as a fundamental property of an electromagnetic wave, forms the basis for many technologies, including telecommunications, liquid-crystal displays, spectroscopic techniques, and so forth. Fascinatingly, in radio wave and microwave bands, a simply dipole antenna in free space acts as a perfect polarized radiation source with the electric field oriented along the direction of the antenna rods.1 On the other hand, in the optical band, to generate polarized light, adopting polarizers are traditionally and commercially regarded as the most straightforward methods. Also, nowadays, due to the booming developments in nanophotonics and plasmonics, polarizers with compact dimensions have been proposed and may become commercially available in the near future.2−5 However, the polarizers need to perform polarization operation in the far-field region of emitters, which would introduce inevitable extra space between emitter and polarizer leading to increase in size of the total light source.6 Adopting polarizers actually induce the problems of extra space, weight, cost, and intrinsic absorptive/reflective loss. Therefore, the uses of polarizers basically violate the trend for global miniaturization and energy consuming reduction for the related electronic and photonic devices. On the basis of the above considerations, light sources that could directly emit polarized optical light are highly demanded. For decades, researchers in materials science community began to make great efforts to achieve this goal. Optical anisotropic organic molecules were forced to orient © XXXX American Chemical Society
Received: December 14, 2014 Revised: March 18, 2015
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Nano Letters antenna elements, which would rebound back and, in turn, work as the driving field for the dipole moments. Secondary emission would be induced, which influences the total emission fields through superimposing on the previously emitted fields.11,26,27 Notably, the secondary emitted field is polarized identically to the scattering driving fields. Through designing suitable nanoantenna elements, the dipole oscillation along a certain direction could be enhanced, whereas the scattering fields along the other directions are overwhelmed. As a result, the emission with preferential polarization in the far-field may happen. On the basis of the above analysis, we hereby exploit the QD-transition dipole-moment-driven plasmonic rectangular slot nanoantennas, which show different scattering strengths for orthogonally polarizations, to directly generate the linearly polarized light. In our experiment, the emission polarization properties of such systems were quantitatively studied utilizing polarimetry technique,28 and the high degree of linear polarization (DOLP) of more than 90% is achieved, which is higher than the reported values of most organic7 and photonic crystal counterparts,8 as well as the stacked QDs.9 The emission polarization is oriented perpendicular to the longer side of the slot. Furthermore, the DOLP is proved to be engineerable by harnessing the plasmonic resonance of the antenna array. Because of the advantages of surface plasmon in localizing intense field with nanoscale distance from the metal surface, the QDs-combined nanoantenna array could be highly compact in size, which shows a total thickness of 150 nm in our case. Distinct from previous works that studied the polarization features of emission at single-nanorod level,18,22,25,29,30 we achieved polarized emission from an arrayed sample with finite area. In addition, rather than requiring quantum emitter to situated at specific position relative to a single antenna using sophisticated techniques,18,25,30−32 the QDs are allowed to be randomly distributed above the antenna arrays in our case, which simplifies the functionalization of the antenna arrays. Our methods could be applied to manufacture miniature polarized light sources without polarizers, which can be expected for wide applications, such as backlights of liquid crystal displays, illuminators in spectrometers, transmitters for quantum information transportation, and so forth. The rectangular plasmonic slot nanoantenna array combined with QDs is schematically illustrated in Figure 1a. The antenna layer was fabricated by focused ion beam milling through a 50 nm thick gold film on a silica substrate. The slot antennas are arranged in a square lattice with a lattice constant P = 300 nm and the entire array footprint is 50 μm × 50 μm. The scanning electron micrograph of an unit cell is shown in the top panel of Figure 1b. Photoluminescent cadmium selenide (CdSe) semiconductor QDs with zinc sulfide (ZnS) shell (Qdot 800 ITK, Invitrogen, sketched in the inset of Figure 1a) were used as the optical dipole sources to drive the antennas. And the QDs were dispersed using the polymer solution and then spin coated onto the structured gold film, forming a 100 nm thick illuminating layer (refer to methods for the preparation of the QDs-polymer layer). The QDs-polymer film on the naked silica substrate shows a luminescence spectrum peaking at wavelength (λ0) of 782 nm, as indicated in Figure 1b. Due to the anisotropic structure design, its spectral responses are expected to be different for orthogonally polarized light. Indeed, as shown by the measured spectra for plane wave illumination in Figure 1c, plasmonic resonances are observed in transmission (T), reflection (R), and absorption (A) spectra near 770 nm (λA) for y polarization;33−35 however, no resonance occurs for x
Figure 1. QDs-combined rectangular slot nanoantenna array and the spectral properties. (a) Schematics of nanoantenna array cut through a 50 nm thick gold film on a silica substrate and covered by QDspolymer layer. The cross section of a QD is sketched in the inset. (b) Scanning electron micrograph of the unit cell (without QDs) (top panel). Feature sizes: unit cell P = 300 nm, slot length a = 90 nm, width b = 25 nm. And the photoluminescence spectra from the QDspolymer layer on silica substrate accompanied by Gaussian fit (dashed blue lines). (c) Experimental measured spectra of transmission (T), reflection (R), and absorption (A) for the QDs-coated antenna array with a = 90 nm under plane-wave illumination. This structure shows a resonance absorption peak at 770 nm for an y-polarized incident wave.
polarization in the measured wavelength range. Such polarization-dependent responses imply the distinct scattering cross sections for different polarized electromagnetic waves and, hence, may lead to modifications to the polarization of the emitted fields of the dipoles nearby as mentioned above. To explicitly explore the polarization properties of the radiation from the above QD-antenna systems, an oscillating dipole moment p (representing a QD transition dipole moment) is assumed to situate at 10 nm above the gold surface on the central normal of an unit cell (with a = 90 nm), as shown in Figure 2a. As aforementioned, the directly emitted fields from the dipole would be scattered by the antenna and react back onto the dipole, followed by inducing secondary emission with polarization identical to the direction of the scattering fields. Using the finite element methods (COMSOL), the induced charge distributions σ (color map) and current density distributions j (red arrows, length in logarithmic scale) on the top surface of gold film, along with the scattered fields Es (black arrows) at the dipole position were simulated (shown in Figure 2a). The three panels correspond to the results under excitations of three orthogonally oriented dipoles px, py, and pz, respectively. The oscillating frequency of the dipoles is chosen according to the antenna resonance wavelength (770 nm). It can be seen that under the excitation of px, the induced current B
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resonance (770 nm). This may indicate the correlation between the emission polarization and the structural plasmonic resonances. Thus, correlation would hint at a way to control the emission DOLP through tailoring the resonances of the nanoantenna arrays, which could be achieved by adjusting the antenna geometric parameters, for example, by simply varying the slot length a. In the experiment, for the purpose of fully treating the polarization properties of the emission from the sample, the Stokes vectors (S-vectors) were adopted to represent the states of the emitted light, which are mathematically convenient to describe the states of partially polarized waves.28 The adopted experimental setup is shown in Figure 3a. The sample was illuminated by a CW laser (center wavelength at 532 nm). The polarization state of the incident laser was manipulated by a combination of a polarizer and a half wave-plate (not shown in the picture). A 10× objective with a numerical aperture (NA) of 0.25 was used to focus the laser onto the QDs side of the sample. The objective was moved toward the sample by a linear stage to ensure that the laser spot fully covered a whole antenna array. Another objective (NA = 0.28) on the opposite side was used to collect the photoluminescence in the direct transmitted direction. A long pass filter with cut-on wavelength at 550 nm was applied to isolate the pump laser. The polarization state of the photoluminescence was spectrally analyzed by a homemade polarimeter consisting of a rotating superachromatic quarterwave (QW) plate (Bernhard Halle Nachfolger GmbH), a fixed Glan−Taylor (GT) calcite polarizer (Thorlabs) and a fiber coupled spectrometer (Princeton Instruments).28 The components of S-vector of the luminescence were derived from Fourier transforming over the spectrometer recorded intensity signal (see in Methods) and shown in Figure 3b. All of them are normalized to the maximum value of the S0. The S0 basically describes the total intensity of the luminescence, which should coincide with the direct measured spectrum without suffering any polarization manipulation of the QW plate and the GT polarizer. The S1 is minus indicating the y polarization feature of the luminescence. The S2 is slightly smaller than 0 in the center wavelength range meaning that the emission has slight polarization component along the 135° direction; however, in our opinion, this is caused by the unavoidable little misalignment between orientations of sample and GT polarizer. The S3 is about zero over the whole spectral range. The degree of linear polarization (DOLP) and the degree of circular polarization (DOCP) are related to the S-vector by DOLP = ((S21 + S22)1/2)/S0 and DOCP = S3/S0, respectively, which are shown in Figure 3c. The luminescence with the DOLP as high as 90% is achieved in the spectral range between 740 and 810 nm. Outside this wavelength range, the determined DOLP is less accurate (covered by the shaded areas). This is due to the fact that the transmitted luminescence intensity was too weak to measure when θ was around 0 and 90°, which introduces errors into the Fourier transformation process. Furthermore, due to the nonchiral symmetry of the structure, no circular polarized component in the luminescence is anticipated, as confirmed by the zero DOCP. The polarization characteristic from the above QD-covered antenna could be well explained by the electromagnetic interaction between the transition dipoles and the antenna, as proved by the good consistency between the experimental DOLP curve and simulation prediction (blue dashed line in Figure 4d) in the unshaded spectral range (see in Methods for the simulation details). We may notice that the DOLP here is smaller than that predicted in Figure 2b. This
Figure 2. Antenna-scattered emission fields of a dipole and the degree of polarization of emission from system. (a) The dipole locates 10 nm directly above the center of the unit cell (a = 90 nm). In the remaining panels, snapshots of charge distributions σ (color map) and instantaneous directions of the induced current density j (small red arrows, length in logarithmic scale) on the top surface of gold film are shown. The black arrows give the scattered fields Es at the dipole position. Three panels correspond to the cases of excitation by three orthogonal oriented dipoles px, py, and pz, respectively. For the sake of clarity, Es are enlarged by 10 times for the case of px. All of the results are plotted for the resonance wavelength 770 nm. (b) The simulated DOLP of light emission in the far-field through the silica substrate.
vortices swirl in opposite directions, and the x-directional dipole-like charge distribution is formed in the tight vicinity of the slot. The scattered field at the exciting dipole position was simulated to be x-oriented (black arrow), which leads to the xpolarized secondary emission fields (more analysis on charge/ current distributions and scattering fields please see Supporting Information). For the py, the induced currents have major direction along the y direction except for the vortices near the slot ends. Furthermore, because of the existence of the distinct plasmonic resonance for y polarization (see in Figure 1c), stronger charge distributions are induced; hence, larger Es is produced. Finally, for pz, only divergent current distribution and monopole-like charge distribution appears; hence, no horizontal Es at the dipole position emerges. Thus, it has no contribution to the polarization modification for the radiation along the z axis. Noticeably, the magnitude of the induced Es for py is more than 10 times larger than that for px, which may suggest y-polarized feature of the secondary and the total emission. For a quantitative evaluation, the overall degree of the linear polarization of the radiation in the far-field was described by DOLP = (Iy − Ix)/(Iy + Ix), in which Ix and Iy are intensities of x and y components, respectively. Taking into account the fact that a real emitter normally has no fixed dipole axis, an average over various dipole orientations should be performed, that is, Ii = 1/3(∑jIi(pj)), in which Ii(pj) (i = x, y; j = x, y, z) is the intensity of i components induced by the dipole along j direction. The DOLP of the light fields exiting from the substrate side is shown in Figure 2b. Indeed confirming our prediction, the emitted light is y-polarized with DOLP larger than 98% and peak wavelength identical to the absorption C
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Figure 3. Polarimeter used in the measurement and typical results for the antenna array with a = 90 nm. (a) The experimental setup adopted to analyze the polarization states of the luminescence. (b) The retrieved S-vector components for luminescence from the sample with a = 90 nm. All of the components are normalized to the maximum value of the S0. (c) The corresponding DOLP and DOCP calculated from the S-vector components shown in (b). The derived DOLP and DOCP are not accurate at the edges of the emission spectral range as a result of the weak measured luminescence intensity (covered by the shaded areas). The blue dashed line corresponds to the calculated DOLP by the numerical simulations.
influenced by the plasmonic resonances. The derived DOLP for different structures are shown in Figure 4d. In a manner similar to the shifting of the emission peaks, the DOLP peaks are also shown to be dependent on and controllable by changing the slot lengths a. Additionally, the S1 components are minus for all structures (not shown in figure); thus, the luminescent waves from all antennas are y polarized, which further manifest the correlations between the radiation polarization manipulation and the polarization dependent plasmonic resonances. The simulated DOLP curves are given by blue dashed lines in Figure 4d, which consist with the experimental measurements well and demonstrate the essential role of electromagnetic interaction between QDs and antennas in modifying polarization radiations. Noticeably, for the structure with larger a, the DOLP curve gives larger peak value. For example, among our results, the maximum DOLP value of more than 90% appears on the red end of the spectrum for structure with a of 110 nm. This phenomenon could be explained by the smaller ohmic loss of gold in longer wavelength and larger evanescent depth inside the QDs layer; thus, more QDs intensely interact with nanoantenna, with accordingly higher polarizing quality. However, we need to notice that the enhancement in the total luminescence intensity (comparing results in Figure 4c with those in Figure 4a) is not obvious for those plasmonic antenna designs compared with previously reported works.11−15 However, if we consider the fact that at least half of the energy would be wasted by adopting a polarizer to make the emission in Figure 4a polarized, the direct polarized emission from our
could be elucidated by the fact that QDs are randomly distributed inside the polymer layer and most of the QDs are more than 10 nm away from the antennas in the experiment. The larger distances would cause much weaker coupling between QDs and the antennas and, consequently, smaller scattering driving fields and worse luminescence polarization. To identify the possibility of controlling the radiation polarization by the plasmonic resonance of the nanoantenna, more systematic results of the photoluminescence and the corresponding DOP from the systems with different a values are presented in Figure 4. Five arrays with different antenna lengths ranging from a = 70 to 110 nm in step of 10 nm were fabricated, whereas b = 25 nm and P = 300 nm were fixed. As reference, the results of the QD-polymer film on the silica substrate without gold film are listed at the top of Figure 4. The around-zero level of the obtained DOP in Figure 4b demonstrates that the emission is totally nonpolarized without showing any polarization memory effect from QDs.36 Figure 4c gives the luminescence spectra of various QDs functionalized antenna arrays under excitation of x-polarized laser. All the photoluminescence spectra in Figure 4c are normalized to the maximum luminescence value in Figure 4a. The measured absorption spectra for y-polarized plane waves are also presented by red dashed lines. As shown, by changing the slot lengths a, the absorption resonance wavelength (λA) is shifted, and the photoluminescence peak is moving toward the respective absorption resonance as well, proving the QDs are efficiently coupled to the antennas and the total emission is D
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the above polymer solution with volume ratio (v/v) of 5% and followed by ultrasonic treatment to prevent aggregation of QDs. The 100 nm thick QDs-polymer layer was finally achieved by spin-coating at 6000 rpm for 1 min. S-Vector Derivation. The emitted light was described by the S-vector in our experiment. The meanings of the components of the S-vector: S0 corresponds to the total irradiance; S1 gives the excess in intensity of light between x- and y-polarized components; S2 shows the excess in intensity of light polarized along 45° direction and that along 135° direction; S3 describes the difference between the intensity between right circular polarized (RCP) and left circular polarized (LCP) components. In such a presentation, the quarter-wave plate with fast axis oriented along θ can be presented by a Mueller matrix of
M QW
⎡1 0 0 0 ⎤ ⎥ ⎢ 1 ⎢ 0 1 + 1 cos 4θ −sin 2θ ⎥ sin 4θ ⎥ ⎢ 2 2 2 =⎢ ⎥ 1 1 1 ⎢0 − cos 4θ cos 2θ ⎥ sin 4θ 2 2 2 ⎥ ⎢ ⎢⎣ 0 −cos 2θ sin 2θ 0 ⎥⎦
The GT polarizer with optical axis along the x direction is described by
Figure 4. Emission spectra and DOLP curves for different structures. (a,b) The luminescence spectrum and DOP from the QDs-polymer film on the silica substrate. (c) The emission spectra from QDs combined nanoantenna arrays with different slot lengths a (orange curves), which are normalized to the maximum luminescence value in (a). Their Gaussian fits are given by blue dashed curves. The absorption spectra for different structures are shown by red dashed lines. The SEM images of different structures are given in the left side. (d) The corresponding DOLP curves for different structures (orange curves). The blue dashed lines present the DOLP predicted by the numerical simulations.
M GT
⎡1 ⎢ 1 1 = ⎢ 2 ⎢0 ⎢⎣ 0
1 1 0 0
0 0 0 0
0⎤ ⎥ 0⎥ 0⎥ ⎥ 0⎦
After passing through the wave plate, the polarization of the luminescence was modulated and the corresponding polarization state depends on the angle of the QW plate. The GT polarizer transformed the above polarization modulation into an intensity modulation and was recorded spectrally by the spectrometer. The S-vector of the light entered the spectrometer (Sspe) is related to that of the emitted luminescence [Slumi, components are presented by Si (i = 0, 1, 2, 3)] by
nanoantennas owns doubled efficiency. Furthermore, in the experiment, nearly identical DOLP curves were measured for ypolarized laser excitation (not shown here). It suggests that the polarized emission is only induced by the interactions between the QDs emission and the plasmonic resonances, which has no relationship with the excitation process. As a result, the above experimental results could be extended to the situations of nonpolarized optical excitation or even electricity pumping. In conclusion, the direct generation of linearly polarized light from the QDs coupled nanoantenna composites is achieved. The scattering fields are identified to act as mediators to link the driving sources with antenna elements and determine the polarization properties of the nanoantenna systems. The DOLP is proved both quantitively and spectrally controllable through the geometric parameters of the antennas. We believe that this work opens up an exciting access to the innovative nanoscale polarized light sources, which could find applications in a wealth of areas, including optical displays, quantum communications, spectroscopy, and compact biosensors. Methods. QDs-Polymer Layer Preparation. Dissolve 274.4 mg of boric acid powder and 1525.6 mg of sodium tetraborate decahydrate powder (purchased from Alfa Aesar) in deionized water in a 100 mL volumetric flask to achieve a borate buffer solution (0.2 mol/L, pH 9.0). Dilute poly(acrylic acid sodium salt) solution (PAA-Na, 225 kDa, Polysciences) using the above borate buffer solution by 5 times in a vial to prepare a polymer solution. The final QDs-polymer solution was made by adding the CdSe/ZnS QDs solution (Qdot 800 ITK, Invitrogen) to
Sspe = M GTM QW S lumi ⎡1⎛ 1 ⎞ ⎢ ⎝⎜S0 + S1⎠⎟ + 2 ⎢2 ⎢ − 1 S3sin 2θ ⎢ 2 ⎢ 1⎛ 1 ⎞ = ⎢ ⎜S0 + S1⎟ + ⎢2⎝ 2 ⎠ 1 ⎢ ⎢ − 2 S3sin 2θ ⎢ ⎢ ⎢⎣
⎤ 1 1 S1cos 4θ + S2 sin 4θ ⎥ 4 4 ⎥ ⎥ ⎥ ⎥ 1 1 S1cos 4θ + S2 sin 4θ ⎥ ⎥ 4 4 ⎥ ⎥ ⎥ 0 ⎥ ⎥⎦ 0
It is shown that the finally recorded intensity signal contains the DC part, as well as the components with periods of 90° and 180°. And all other frequencies have an amplitude of zero by theory. Through the Fourier transformation of the recorded rotation angle dependent intensity, the components of the luminescence (Slumi) could be obtained. Simulations of DOLP Curves. In the simulations, the optical behavior of gold was described by tabulated data from ref 37. The refractive index of the medium where the dipoles locate E
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was assumed as 1.45 to simulate the existence of polymer layer. Furthermore, the refractive index of the silica substrate was assumed to be 1.5. Periodic boundary conditions were imposed on the boundaries between unit cells. Perfectly matched layers were applied to the ends of the model where the waves were outgoing the structure. In the simulation for the model built in Figure 1d, a singe dipole source was adopted 10 nm above the center of an unit cell. However, in the experimental cases, as the QDs are randomly distributed inside the polymer layer, the model built in Figure 1d is not sufficient to explain the measured DOLP results in Figure 3 and 4. Alternatively, a position array was built to model the possible situations of the QDs. In the position array, the QDs are assumed to only locate in three representative planes of z = 10 nm [corresponds to the case that the QDs (radius about 7.5−10 nm) nearly contact with gold film], 50 nm (middle plane of the polymer layer), and 100 nm (the surface of the polymer layer). In addition, the spacings between the neighboring positions in the same z plane are 5 nm along the x and y directions. The contribution of a dipole to each possible position to the radiation in the far-field is calculated separately and averaged over three orthogonal orientations. If the interactions between QDs and unit cells that are not in directly below are neglected and consider that the selected QDs concentration results in a coverage of about two QDs in each unit cell on average, the total intensities of the xand y-polarized components in the far-field could be described by summing contributions from individual QDs [with position coordinates of (x, y, z)] as Ix =
n−1 Cn2
∑ x ,y,z
M.X.R., M.C., W.W, L.H.Z, B.P., and J.K.L. prepared samples. M.X.R. assembled the polarimeter and carried out the optical measurements, analyzed data, and wrote the paper. J.J.X., Q.Q.L., and X.Z.Z assisted in analyzing data and writing the paper. J.J.X. and S.S.F. supervised the work. Notes
The authors declare no competing financial interest.
n−1 Cn2
∑ x ,y,z
1 [Ix(px (x , y , z)) + Ix(py (x , y , z)) 3
1 [Iy(px (x , y , z)) + Iy(py (x , y , z)) 3
in which n is the number of position points contained in one unit cell of the hypothetical position array. Using Iy − Ix Iy + Ix
the DOLP curves are derived and shown by blue dashed curves in Figure 3c and 4d, and a positive DOLP value correspond to y polarization.
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ASSOCIATED CONTENT
S Supporting Information *
Detailed analysis on charge/current distributions inside unit cells and the scattering fields excited by different orientated dipoles. This material is available free of charge via the Internet at http://pubs.acs.org/.
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REFERENCES
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+ Iy(pz(x , y , z))]
DOLP =
ACKNOWLEDGMENTS
This work was supported by National Basic Research Program of China (2013CB328702, 2010CB934101), National Natural Science Foundation of China (11304162), the 111 Project (B07013), PCSIRT (IRT0149), SRFDP (20130031120005), China Postdoctoral Science Foundation funded project (2013M530038), and the Fundamental Research Funds for the Central Universities.
+ Ix(pz(x , y , z))], Iy =
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AUTHOR INFORMATION
Corresponding Authors
*E-mail: [email protected]. *E-mail: [email protected]. *E-mail: [email protected]. F
DOI: 10.1021/nl5047973 Nano Lett. XXXX, XXX, XXX−XXX
Letter
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DOI: 10.1021/nl5047973 Nano Lett. XXXX, XXX, XXX−XXX
