Article pubs.acs.org/JPCC
Efficient Magnetic Resonance Amplification and Near-Field Enhancement from Gain-Assisted Silicon Nanospheres and Nanoshells DaJian Wu,*,† HaiQun Yu,† Jie Yao,† QingYu Ma,† Ying Cheng,‡ and XiaoJun Liu*,‡ †
Jiangsu Key Lab on Optoelectronic Technology, School of Physics and Technology, Nanjing Normal University, Nanjing 210023, China ‡ School of Physics, Nanjing University, Nanjing 210093, China ABSTRACT: Strong artificial magnetic responses play a pivotal role in the unique optical properties of metamaterials, such as cloaking, Fano resonance, and negative refraction. We investigate the magnetic resonances of gain-assisted Si nanospheres and SiO2−Si nanoshells. It is found that the super-resonances occur successively at the octupole, quadrupole, and dipole magnetic modes of the active Si nanosphere or SiO2−Si nanoshell by changing the gain coefficient. At the super-resonances, the magnetic scatterings and the local electric fields are all extremely enhanced. The corresponding surface-enhanced Raman spectroscopy (SERS) enhancement factors at the magnetic super-resonances could reach about 1010−1015, which are enough for single-molecule detection. In particular, the electric scatterings of the active Si nanosphere and SiO2−Si nanoshell are all very weak at the super-resonances. Therefore, the active Si nanosphere and SiO2−Si nanoshell should be excellent SERS substrates with weak background radiation. The extremely strong magnetic resonances also could be used for designing new metamaterials and devices.
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nanoparticle interact with the Ag film, inducing extraordinary near-field enhancements and strong enhanced Raman spectra.21 Albella et al.22 presented the far-field scattering properties and the near-field enhancements for a silicon nanosphere dimer. The mutual interactions of the electric and magnetic dipolar modes of the Si nanosphere lead to the enhanced spectra. Caldarola et al.23 further found that the dimerlike silicon-based single nanoantennas produce both high surface-enhanced fluorescence and SERS with ultralow heat conversion. The SERS substrates based on nonmetallic materials could overcome the disadvantages of the metal substrates such as the catalytic effect of metals, high cost, and biotoxicity, but provide the moderate G factors. Recently, Liberal et al.24 reported an extraordinarily strong magnetic resonance of a Si nanoparticle encapsulated by a gain-doped dielectric shell, which is comparable to the electric dipole super-resonances excited in the active metal nanoparticles.12−14 Thus, the near-field enhancements in the high-refractive index dielectric nanoparticles with gain should receive attention.20,25 In this paper, the scattering spectra and the near-field enhancements of the gain-assisted Si nanoparticles and SiO2−Si nanoshells have been carefully investigated by using the Mie
INTRODUCTION Surface-enhanced Raman spectroscopy (SERS) has been widely studied because of its significant applications in chemical and biological detection,1 cell imaging,2 and medicine.3 The dominant enhancement mechanism of the SERS is the electromagnetic (EM) field enhancement, where surface plasmons (SPs) of metallic nanostructures dramatically enhance the Raman signals.4,5 To enhance this effect, many efforts have been carried out to create the largest E-fields, called “hot spots”. Some hot spots (such as sharp corners or tips, interparticle gaps, and nanopores) can achieve extremely high SERS enhancement factor (G factor), which is even enough for single-molecule detection.6−8 Recently, the gain-assisted metal nanoparticles have been reported to create enormous SERS G factors on the order of ∼1016−1019.9−11 The gain materials doped in the dielectric near the metallic surface can transfer energy to compensate the loss of SP and finally amplify the desired SP response.12−14 However, the strong background radiation of the active nanostructure should be a great technological disadvantage for SERS. In recent years, nanoparticles made of high-refractive-index dielectric materials have attracted great attention because of their strong magnetic responses with low losses and have been explored as the constitutive elements of new metamaterials and devices.15−20 As a Si nanoparticle locates on a silver film, the general electric and magnetic dipole resonances of the Si © XXXX American Chemical Society
Received: April 16, 2016 Revised: May 30, 2016
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DOI: 10.1021/acs.jpcc.6b03871 J. Phys. Chem. C XXXX, XXX, XXX−XXX
Article
The Journal of Physical Chemistry C
corresponding k-value varies from 0.01 to 3.13,24,30 Many previous researches have widely used this simple approach and obtained some important results.31−35 In this work, we assume that the high-refractive-index dielectric material is Si (nSi ∼ 3.5) and the embedding medium is air.
scattering theory. With decreasing k-value, the super-resonances occur successively at the octupole, quadrupole, and dipole magnetic modes of the active Si nanoparticles and SiO2−Si nanoshells. We focus on the near-field enhancement properties of the active Si nanoparticles and SiO2−Si nanoshells. At three magnetic super-resonances, the enormous enhancements of the E-fields have been found at the surfaces of the active Si nanoparticles and SiO2−Si nanoshells, while the corresponding electric scatterings are all very weak. Active Silicon Nanosphere and Nanoshell. The far- and near-field optical properties of a single spherical nanoparticle can be understood by means of the Mie scattering theory.26 The EM waves are expanded to spherical partial waves using vector spherical harmonics; then, Maxwell’s boundary conditions are applied to resolve the unknown expansion coefficients of the scattered and interior waves. The obtained scattering efficiency, Qsca, can be expressed as26 Q sca =
2 (kR )2
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RESULTS AND DISCUSSION We start our research from the passive Si nanosphere and SiO2−Si nanoshell (k = 0). Figure 1 shows the scattering
∞
∑ (2n + 1)(|an|2 + |bn|2 ) n=1
(1)
The scattering coefficients an and bn represent the electric and magnetic multipolar contributions, respectively. For the Si nanosphere, the scattering coefficients an and bn can be obtained as26
Figure 1. Scattering spectra of the passive Si nanosphere with radius of 150 nm.
spectra of the passive Si nanosphere with the radius of 150 nm. The dashed and dotted lines represent the electric (Qsca(an)) and magnetic (Qsca(bn)) scatterings, respectively. In the dotted line, the peaks at about 584, 758, and 1097 nm represent the octupole, quadrupole, and dipole magnetic resonances, respectively. Meanwhile, in the dashed line, the peaks at about 610 and 835 nm show the contributions of the electric quadrupole and dipole modes, respectively. Panels a, b, and c of Figure 2 show the distributions of the E-field enhancements in the y−z section of the passive Si nanosphere at the octupole, quadrupole, and dipole magnetic modes, respectively. In this case, the incident light is along the z-axis and the polarization is perpendicular to the y−z section. The E-field distributions at the magnetic resonances are similar to the results reported by Geffrin et al.20 and Gao and Huang.25 The strong displacement currents rotate in the planes parallel to the equator of the Si nanosphere, inducing the magnetic resonances.16,17,36 Panels a1, b1, and c1 of Figure 2 show the E-field distributions in the x−z section of the Si nanosphere at the octupole, quadrupole, and dipole magnetic resonances, respectively. It is obvious that the enhanced E-fields can be found in the Si nanosphere and on the surface of the Si nanosphere. The maximal enhancements on the surface of Si nanosphere can reach about 11.03, 7.04, and 3.63 for the octupole, quadrupole, and dipole magnetic resonances, respectively. Panels a and b of Figure 3 show the contour plots of the magnetic and electric contributions to the scattering spectra of the passive SiO2−Si nanoshell as a function of the inner core radius, r1. Here, the radius of the outer shell, r2, is fixed at 150 nm, and the refractive index of SiO2 is 1.43. As shown in Figure 3a, for r1 < 50 nm, the resonance wavelengths of the dipole, quadrupole, and octupole magnetic modes of the SiO2−Si nanoshell are almost invariable. As r1 > 50 nm, it is found with increasing the r1-value that the resonance wavelengths of the dipole, quadrupole, and octupole magnetic modes show distinct blue-shifts. At the same time, the electric modes of the SiO2−Si nanoshell also show blue shifts. As shown in Figure 2a−c, at the octupole, quadrupole, and dipole magnetic resonances, the strong circled E-fields locate at the
mψn(mx)ψn′(x) − ψn(x)ψn′(mx)
an =
mψn(mx)ξn′(x) − ξn(x)ψn′(mx)
(2)
ψn(mx)ψn′(x) − mψn(x)ψn′(mx)
bn =
ψn(mx)ξn′(x) − mξn(x)ψn′(mx)
(3)
where the Riccati−Bessel functions ψn(ρ) = ρjn(ρ) and ξn(ρ) = ρh(1) n (ρ); m is the relative refractive index, and x ≡ kr. For the SiO2−Si nanoshell, the obtained an and bn are26 an =
ψn(y)[ψn′(m2y) − A nχn ′(m2y)] − m2ψn′(y)[ψn(m2y) − A nχn (m2y)] ξn(y)[ψn′(m2y) − A nχn ′(m2y)] − m2ξn′(y)[ψn(m2y) − A nχn (m2y)]
(4) bn =
m2ψn(y)[ψn′(m2y) − Bnχn ′(m2y)] − ψn′(y)[ψn(m2y) − Bnχn (m2y)] m2ξn(y)[ψn′(m2y) − Bnχn ′(m2y)] − ξn′(y)[ψn(m2y) − Bnχn (m2y)]
(5)
An =
Bn =
m2ψn(m2x)ψn′(m1x) − m1ψn′(m2x)ψn(m1x) m2χn (m2x)ψn′(m1x) − m1χn ′(m2x)ψn(m1x)
(6)
m2ψn(m1x)ψn′(m2x) − m1ψn(m2x)ψn′(m1x) m2χn ′(m2x)ψn(m1x) − m1ψn′(m1x)χn (m2x)
(7)
where the Riccati−Bessel function χn(ρ) = −ρyn(ρ), x ≡ kr1, and y ≡ kr2. A program for computing an and bn is given in ref 26. Our results are calculated by using Matlab software. To a good approximation, the SERS G factor can be expressed by the fourth power of the ratio of the total electric field E⃗ loc to the incident excitation field E⃗ in.27 In principle, the accurate quantum theory should be used to represent the responses of the gain materials.28,29 For simplicity, a simple complex refractive index (ng = n + ik) with a negative imaginary part (k < 0) can be used to describe the response of the incident light to the gain doped dielectric. The k-value could be adjusted either by the external pumping power or the concentration of gain elements. The dye molecules, rare-earth ions, and quantum dots could be used as gain materials and the B
DOI: 10.1021/acs.jpcc.6b03871 J. Phys. Chem. C XXXX, XXX, XXX−XXX
Article
The Journal of Physical Chemistry C
Figure 2. Distributions of E-field enhancements in the y−z section of the passive Si nanosphere at the (a) octupole, (b) quadrupole, and (c) dipole magnetic resonances. Distributions of E-field enhancements in the x−z section at the (a1) octupole, (b1) quadrupole, and (c1) dipole magnetic resonances.
Figure 4. Magnetic scattering spectra of the active Si nanospheres with different k-values of (a) 0, (b) −0.0089, (c) −0.0397, and (d) −0.1604. Here, the radius of the Si nanosphere is fixed at 150 nm.
Figure 3. Contour plots of the (a) magnetic and (b) electric contributions to the scattering spectra of the SiO2−Si nanoshell as a function of inner core radius, r1. Here, the radius of the outer shell is fixed at 150 nm.
maximal Qsca(bn)-value of this mode increases to about 6216, which is about 6000 times that of the passive Si nanosphere. With further decreasing of the k-value, this super-resonance will be broken down. When the k-value decreased to −0.0397, a new super-resonance appears at the quadrupole magnetic mode and the corresponding Qsca(bn)-value reaches about 1.8 × 106, as shown in Figure 4c. In Figure 4d, as k = −0.1604, the superresonance of the dipole magnetic mode occurs. The Qsca(bn) of this mode increases to an extremely large value of about 5.2 × 107, which is about 3.1 × 107 times that of the passive Si nanosphere. The strong circled displacement currents in the Si nanosphere lead to the magnetic resonances.16,17,36 At the super-resonances, the photoemission of the gain materials is strongly quenched because of the energy transfer to the magnetic resonances. The large E-fields in the Si nanosphere excite the periodic perturbation on the gain medium and stimulate more emission, causing the feedback.12,37 This feedback mechanism leads to the excitation of more identical
region near the outer surface of the particle. The strong circled displacement currents in this region lead to the magnetic resonances. Meanwhile, in the region of the radius
