Abstract

We have investigated second harmonic generation (SHG) from Ag-coated LiNbO3 (LN) core-shell nanocuboids and found that giant SHG can occur via deliberately designed double plasmonic resonances. By controlling the aspect ratio, we can tune fundamental wave (FW) and SHG signal to match the longitudinal and transverse plasmonic modes simultaneously, and achieve giant enhancement of SHG by 3 × 105 in comparison to a bare LN nanocuboid and by about one order of magnitude to the case adopting only single plasmonic resonance. The underlying key physics is that the double-resonance nanoparticle enables greatly enhanced trapping and harvesting of incident FW energy, efficient internal transfer of optical energy from FW to the SHG signal, and much improved power to transport the SHG energy from the nanoparticle to the far-field region. The proposed double-resonance nanostructure can serve as an efficient subwavelength coherent light source through SHG and enable flexible engineering of light-matter interaction at nanoscale.

© 2014 Optical Society of America

1. Introduction

Surface plasmon resonance (SPR) induced optical field enhancement and localization have been of great interests and widely applied in many optical phenomena [1, 2], such as surface enhanced Raman scattering, near-field microscope, enhanced fluorescence emission and nonlinear interaction [3], e.g. second harmonic generation (SHG). In this regard, the enhancement of SHG has been observed in metal nanoparticles [4], a sharp metal tip [5], planar metallic structures [6–8], and multifrequency gold nano-antenna [9]. Recently, SHG has been achieved efficiently in a plasmonic nanocavity which consists of a noncentrosymmetric medium sphere [10] and nanowire [11, 12] enclosed in a metal shell. The fundamental wave (FW) at frequency ω was observe to get strongly confined in nanocavities when interacting with the SPR mode of a metal-coated nanoparticle or nanowire and then overlap with the nonlinear medium very well, leading to more efficient SHG at frequency 2ω (with an enhancement factor over 50) than the bare core (without the metal shell). However, only FW is resonant with the nanoparticle in these cases. The direct effects of SPR on the SHG signal are still unclear. A natural question arises: How if both FW and SHW are simultaneously on-resonant with two SPR modes of nanoparticles?

In this work we will address this problem by insightful design. The most important thing is to look for a nanoparticle with double SPR modes. For this purpose, we turn to nanoparticles of anisotropic geometry, among which nanorods have attracted great attention due to their dimension induced wavelength tunability and polarization sensitivity [13–15]. One can control the aspect ratio of nanorods easily and obtain double SPR modes simultaneously, which are associated with the longitudinal and transverse SPR modes [16,17]. Moreover, the optical cross-sections of nanorods are much higher than those of nanospheres, and this has attributed nanorods promising features in wide applications like low-threshold surface plasmon amplification [18,19] and ultrafast optical devices [20]. The two SPR modes can be designed to enable their wavelengths matched to the absorption bands and emission bands of fluorescent molecules absorbed in gold nanorods [21] for enhancing their fluorescence intensity. It would be expected that this double-resonance mechanism should also play a very good role in enhancing SHG intensity of nanostructured materials.

To illustrate and confirm this hypothesis, we propose and design an anisotropic nanoparticle, a Ag-coated LiNbO3 (LN) core-shell nanocuboid [Ag-LN in Fig. 1(a)] to further enhance nanoscale SHG, where longitudinal and transverse SPR modes are obtained simultaneously and match exactly the wavelengths of FW and SHG signal. Note that SHG occurs only from LN materials but not from Ag materials, but the SPR induced by Ag materials will significantly enhance SHG from LN the materials. We will show via numerical calculations that the SHG signal from Ag-LN with double SPR modes is much more efficient than the bare LN core (>3 × 105X) where no SPR mode occurs [Fig. 1(b)].

 figure: Fig. 1

Fig. 1 (a) Schematic diagram of a Ag-coated nanocuboid. The nonlinear core, 16 × 72 × 16 nm3, is lithium niobate (LiNbO3, LN) which is coated by a 5 nm thick Ag shell. The fundamental wave (FW, ω) propagates along the x-direction, and excites second harmonic generation (SHG, 2ω) signal in all directions. (b) Calculated SHG signal in three different cases, Ag-coated LiNbO3 nanocuboid (Ag-LN, yy-z utilizing d32), Ag-LN (yy-y, d22), and bare LN (yy-y, d22) for comparison. Here yy-z representss that the SHG signal with z-component (E2z) is excited by FW with E1y. Assume d32 = d22 = d0. P0 is the unit power.

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2. Theoretical model

Note that several theoretical methods such as the perturbation theory [22], nonlinear Mie theory [23] and reciprocity theory combined with linear Mie scattering [24], have been adopted to describe SHG cases in nanoparticles. However, most of these methods are limited to handle spherical nanoparticles, and a universal model is still rare for nanoparticles in arbitrary shapes. Here, we develop a nonlinear discrete-dipole approximation (DDA) method to analyze SHG case conveniently in arbitrary nanoparticles in the framework of rigorous Maxwell’s equations solution. As is known, the DDA method is an effective and powerful tool to calculate the linear optical properties of nanoparticles, such as extinction, scattering and absorption [25, 26]. This approach is efficient equally for nonlinear optical problem solutions.

Assume a plane wave FW at the frequency of ω1 is incident upon a nonlinear particle. The FW electric field E1 satisfies Maxwell’s equation

××E1k12E1=k12P1,
where P1 is the linear polarization of FW, k1=ω1/c, c is light speed in vacuum. To use the DDA [25, 26] to solve Eq. (1), the particle is assumed as a cubic array of N electric dipoles, and the total electric field in the jth dipole at location rjcan be described by
E1,j=E10,jkjNΑjkP1,k,
where E10,j=E10exp(ik1njrj),P1,j=α1,jE1,j, nj=rj/|rj|, α1,j=3d3(ε1,jεb)/[4π(ε1,j+2εb)] is the polarizability and εI,j is the dielectric function of the jth dipole at ω1, εb is the background dielectric constant, d is the length of each cubic unit (or dipole). AjkP1,kis the secondary radiation electric field at rj from dipole P1,k at rk, and given by,
AjkP1,k=exp(ik1rjk)rjk3{k12rjk×(rjk×P1,k)+1ik1rjkrjk2[rjk2P1,k3rjk(rjkP1,k)]},
where rjk=rjrk and rjk=|rjk|. Each element Ajk is a 3 × 3 matrix. After definingAjj=αj1, Eq. (2) can reduce to be a simple algebraic form of
E10,j=k=1NΑjkP1,k.
Once all the dipoles P1,k are calculated self-consistently by solving the linear equations [Eq. (4)], the total scattering cross-section can be given by a spherical integral over the entire 4π solid angle,
Csca=k14|E10|2dΩ|k=1N[P1,knk(nkP1,k)]exp(ik1nkrk)|2,
and the extinction cross-section is

Cext=4πk1|E10|2k=1NIm(E10,k*P1,k).

In the SHG case, the SHG signal at the frequency of ω2 = 2ω1 has its electric field E2 satisfying the following nonlinear coupled equation [27, 28],

××E2k22E2=k22P2+k22P(2),
where k2=ω2/c, P2 is the linear polarization of the SHG signal, and P(2) denotes the second-order nonlinear polarization. Similar to the linear case in Eq. (2), the total electric field of the SHG signal in the jth dipole is derived as

E2,j=E20,jkjNBjkP2,k,

Assume α2,j=3d3(ε2,jεb)/[4π(ε2,j+2εb)] is the polarizability, ε2,j is the dielectric function of the jth dipole at ω2, P2,j=α2,jE2,j. Similar to Ajk, Bjk reflects the interaction between the jth and kth dipoles at ω2 and follows,

BjkP2,k=exp(ik2rjk)rjk3{k22rjk×(rjk×P2,k)+1ik2rjkrjk2[rjk2P2,k3rjk(rjkP2,k)]},
In Eq. (8), E20,j is the electric filed that is due to P(2). It can also be written in the context of DDA as
E20,j=Pj(2)/α2,jkjNBjkPk(2),
where Pj(2)/α2,j represents the self-induced radiation field by Pj(2) at rj. BjkPk(2) has a similar expression as Eq. (9) where P2,k is replaced by Pk(2), and represents the secondary radiation electric field induced by nonlinear dipole Pk(2) at rk. Each nonlinear dipole Pj(2) can be given as
Pj(2)=d34πεb(3εbεm+2εb)2χ(2):E1,jE1,j,
where εm stands for the dielectric constant of studied medium, and χ(2) represents the second-order nonlinear tensor. Note that E1,jspecifies the external filed of the jth dipole, thus the factor [3εb/(εm+2εb)]2 should be considered in Eq. (11).

Now we have made relevant deviations of the nonlinear DDA method. Note that the conversion efficiency of SHG is usually low in nanoparticles, the undepleted pump approximation (UPA) is adopted. The nonlinear DDA method can be summarized as follows: when FW is incident upon the particle, each dipole P1,jand the total electric field E1,jare calculated by means of DDA [shown in Eqs. (1)-(6)]; then the nonlinear dipole Pj(2) is induced by E1,jin the second-order nonlinear process, and regarded as the radiation source of the SHG signal. Subsequently, E20,jand P2,jare solved self-consistently [shown in Eqs. (7)-(11)]. Once the total dipole distribution of SHW P (=P2,j+Pj(2)) is obtained, we can give the scattering SHG power by

Wscak24dΩ|k=1N[Pknk(nkPk)]exp(ik2nkrk)|2.
This formula is analogous to Eq. (5) and is used to evaluate the SHG radiation generated from the particle.

Now we take a closer look at Eq. (11), which is one of the key ingredients of the nonlinear DDA method. It describes the nonlinear polarization (P(2)) which irradiates the SHG signal. P(2) depends both on the local FW electric field and on the nonlinear susceptibility by the following matrix equation [28],

(Px(2)Py(2)Pz(2))=(d11d12d13d14d15d16d21d22d23d24d25d26d31d32d33d34d35d36)(E1x2E1y2E1z22E1yE1z2E1zE1x2E1xE1y),
where {dij}depicts the second-order nonlinear tensor of the nanoparticle material. In the current study, the nonlinear material is the LN core, where only d15, d16, d21, d22, d24, d31, d32, and d33 are non-vanishing. As shown in Eqs. (7)-(13), the SHG process can be described in two steps: the nonlinear polarization generation in the LN core (depending on FW and {dij}) and SHG radiation out of the Ag shell. Simply speaking, the SHG radiation power of the core-shell nonlinear nanoparticle relies on two apparent factors: the efficiency to create a strong local nonlinear polarization and the efficiency to transport the local SHG energy from the near-field region of nanoparticle to its far-field region. In the first factor, the local electric field and the nonlinear susceptibility both play important roles. SPR resonant with the incident FW will induce a greatly enhanced linear local field and contribute much to the first factor, while SPR resonant with the SHW will contribute much to the second factor. A giant enhancement of SHG should be expected when a nonlinear nanoparticle possesses double SPRs that match both with the FW and SHW simultaneously. To achieve this highly desirable goal, deliberate design on the geometric configuration must be implemented.

3. Numerical results and discussion

We assume the pump amplitude (of FW) is 1.0 V/m and the second-order nonlinear coefficient is d0 = 4 pm/V. As shown in Fig. 1(a), the plane-wave FW propagates in the x-axis and is polarized in the yz plane. We only consider SHG from the LN core of which the second-order nonlinear coefficient is much larger than the metal shell and surface, as is the case for Ag shell [29], and suppose this core-shell nanoparticle is embedded in the water background (εb = 1.33). The refractive index of LN (εm) is chosen as 2.17 near 900 nm, while 2.23 near 450 nm. By means of the nonlinear DDA method developed above, we have calculated and compared SHG in three different cases [Fig. 1(b)], (1) Ag-LN where y-polarized FW (E1y) excites z-polarized SHG signal (E1z) by utilizing the nonlinear coefficient of d32 (E1yE1y-E2z, or yy-z), (2) Ag-LN (E1yE1y-E1y, or yy-y with d22) and (3) bare LN core (yy-y). It is seen that the SHG signal is very poor from the bare LN and has no any feature. However, the nonlinear signal exhibits an obvious peak (~450 nm) in Ag-LN with yy-z, much stronger (>3 × 105X) than the bare LN. More interestingly, the yy-z process seems to be more efficient (~10X) than yy-y even if d32 = d22 = d0. Here we only consider d32 and d22 for comparison.

In order to explore the underlying mechanism, we have calculated the extinction cross-section (Cext) of these structures (Ag-LN and bare) in Fig. 2. Under the y-polarized excitation (along long side), there is a resonance mode around 900 nm in Ag-LN, corresponding to the longitudinal SPR mode (LSPR) [Fig. 2(a)], while no remarkable feature is observed in the bare LN [Figs. 2(c) and 2(d)]. Therefore if FW is tuned to match LSPR exactly (~900 nm) in Ag-LN, it can get intensified greatly in the yy-y process and then enhance the nonlinear polarization generation, which serves as an efficient light source of SHG radiation [>104X enhancement achieved in comparison to the bare LN in Fig. 1(b)]. Note that there is no peak of Cext around 450 nm under the y-polarized excitation [Inset of Fig. 2(a)]. Only FW is on-resonance in the yy-y process (single SPR mode) while the SHG signal is off-resonance, similar to previous study [10–12]. Figure 2(b) shows two resonance modes take place in the short wavelength region if the excitation light is polarized along the z-axis (the short side). One of them is located near 450 nm (double frequency of FW at 900 nm) and is related to the transverse SPR mode (TSPR), which could also facilitate the light emission [30]. In the yy-z process, FW is tuned at the LSPR mode (similar to yy-y) and the generated SHG signal matches the TSPR mode exactly. Therefore the double SPR modes in this case (yy-z) result in much stronger SHG radiation (~10X) than the single SPR mode (yy-y) [Fig. 1(b)].

 figure: Fig. 2

Fig. 2 Extinction cross-section (Cext) of Ag-coated and bare LN nanocuboid. (a) Ag-LN under the y-polarized excitation. Insets: diagram of the excitation polarization and enlarged figure of Cext wihtin the wavelength range of 400-500 nm. (b) Ag-LN under the z-polarized excitation. Similar to Panel (a), one of insets shows the enlarged figure of Cext within 800-1000 nm. Bare LN under the y-polarized (c) and z-polarized (d) excitation.

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To further understand these differences, we also show the FW electric field intensity distribution (Iω) of Ag-LN and bare LN in different cases [Fig. 3]. At the LSPR mode (~900 nm) of Ag-LN, the light is strongly confined in the plasmonic nanocavity, ~250X amplification in the most LN body and >500X in the Ag/LN interface [Fig. 3(a)], which is very constructive for the SHG process (strong field overlapping with the nonlinear core). In contrast, the light concentration is very poor (<5X) in the bare LN under the same excitation condition [Fig. 3(c)], corresponding to the inefficient SHG [Fig. 1(b)]. Moreover, the TSPR mode (~450 nm) in Ag-LN exhibits much better concentration of light in the nanocavity (>10X) [Fig. 3(b)] than the bare LN under the z-polarized excitation [Fig. 3(d)]. Therefore, Ag-LN is a better candidate for efficient SHG (due to the double SPR modes) than the bare LN. In this system with double SPR modes, the overlap between FW and SH field modal profile (e.g. yy-z), κ=|d32E1yE1yE2zdV|, is another critical parameter to affect the SHG radiation [8] and seems to be good in our case [Figs. 3(a) and 3(b)]. Note that the SHG signal is generated only from the LN core, the field distribution is only plotted in the LN core (even in Ag-LN).

 figure: Fig. 3

Fig. 3 Field distribution (yz-plane) of Ag-coated and bare LN nanocuboid at the wavelengths of 900 nm and 450 nm. (a) Ag-LN under the y-polarized excitation and at 900 nm (resonance). (b) Ag-LN under the z-polarized excitation and at 450 nm (resonance). (c) Bare LN under the y-polarized excitation and at 900 nm. (d) Bare LN under the z-polarized excitation and at 450 nm. Here only the LN core (of Ag-LN) is plotted.

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To study the anisotropic properties of SHG as naturally expected for the geometrically anisotropic Ag-LN core-shell nanoparticle, we tune the FW excitation polarization angle from θ = 0° (along the y-axis) to 90° (along the z-axis) and show the calculated z-polarized SHG signal from Ag-LN by setting FW at 900 nm in Fig. 4(a). When θ = 0°, FW is polarized along the y-axis and then matches the LSPR mode [Fig. 2(a)], leading to the efficient SHG radiation [Fig. 1(b)]. However, there is no or weak resonance mode near 900 nm under the z-polarized excitation (θ = 90°) [Inset of Fig. 2(b)]. Therefore, the SHG signal is observed to decrease monotonically as the polarization angle increases [Fig. 4(a)]. Here the nonlinear coefficients d32 ( = d0) and d33 ( = 7d0) are involved. If FW is polarized along the x-axis (isotropic or identical to the z-axis due to the same side length) and propagates along the y-axis, the SHG signal (xx-y and xx-z) is very poor in comparison to the yy-z process [Fig. 1(b)] but still exhibits some peak feature [Fig. 4(b)], very similar to the FW behavior in the extinction spectrum [Inset of Fig. 2(b)] where a small peak is observed (weakly-resonant). Furthermore, the xx-z process (d31) appears to be more efficient than xx-y (d21) even if d31 = d21 = d0 as a result of the TSPR mode excited by the z-polarized SHG signal [Fig. 2(b)]. Another interesting thing is that the SHG signal in the xx-z process is maximum at ~445 nm, red-shifting from the xx-y case (~440 nm) but blue-shifting from the TSPR mode (~450 nm), which is probably due to the joint contribution of the weakly-resonant FW and TSPR mode in the xx-z process.

 figure: Fig. 4

Fig. 4 (a) Excitation polarization dependence of the z-polarized SHG signals. Inset: polarization angle of FW (yz-plane), θ, is set with respect to the y-axis. (b) Calculated SHG signal in the cases of xx-z (utilizing d31) and xx-y (d21) when FW is polarized in the xz-plane (propagating along the y-axis). Assume d31 = d21 = d0.

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In the above discussion we tune FW at the longitudinal SPR mode (~900 nm) and the SHG signal at the transverse one (~450 nm), and achieve nanoscale SHG efficiently in a Ag-coated nonlinear nanocuboid where the aspect ratio of geometry is strictly required. We have shown an example of demonstrating double plasmonic resonance-enhanced SHG at nanoscale. This principle can also be applicable to other anisotropic nanoparticles, such as nanorods which are commonly-used and exhibit controlled aspect ratios [21]. Moreover, the absorptive loss (or imaginary part of refractive index) of Ag instead of LN (transparent in the studied region) has been taken into account in our model (see α1, j and α2, j related to the dielectric function). Note that the nonlinear coefficients utilized are assumed to be the same for comparison. One may achieve even higher conversion efficiency of SHG by combining double SPR modes with the largest nonlinear coefficient (e.g. d33 in LN) if adjusting the orientation of nanoparticles. In terms of conversion efficiency, the theoretical method is straightforward adopted to make direct and quantitative comparison between different nanostructures (Ag-coated and bare) of our system, and also possible to compare results here with other systems by considering the system difference. Moreover, we only exploit SHG in an isolated nanocuboid here for simplification, which holds true in the system with sparse nanocuboids. However if nanocuboids are packed densely and aligned by some methods, such as a stretched-film method [16,17], plasmonic coupling or interaction between nanocuboids could be strong and remarkable [30], probably contributing more to the SHG radiation. As double SPR modes closely rely on the aspect ratio of a nanocuboid [13–21, 31], one can tune them to desired wavelengths for efficient SHG and enhanced fluorescence radiation [21]. If the nanocuboid is anisotropic in x-, y- and z-axis, three modes could be obtained simultaneously and therefore be adopted to enhance third harmonic generation (THG) [32]. Another point that is worthwhile to mention is that in the nanocuboid particle, the TSPR mode is much weaker than the LSPR mode in the strength of both optical cross section and field enhancement. It is expected that by considering other double SPR nanosystems with equally strong resonant strength, the SHG can become even stronger by orders of magnitude.

4. Conclusion

In summary, a Ag-coated nonlinear nanocuboid has been proposed and demonstrated as an efficient subwavelength coherent light source through SHG, which can help to study various optical phenomena in nanoscale size. The study is based on numerical simulation using a home-made nonlinear DDA method that can rigorously solve SHG from arbitrary nonlinear nanoparticles. We have found that when FW and SHW are tuned to match the longitudinal and transverse SPR modes of the nanocuboid particle simultaneously, nanoscale SHG radiation can be enhanced by ~10 times in comparison to the single SPR mode (yy-y) and >3 × 105 times to the bare LN [Fig. 1(b)]. In general, double SPR modes in anisotropic nanocuboids can be harnessed to achieve efficient nanoscale SHG, strong luminescence, enhanced fluorescence absorption and emission, and other applications like high-resolution cell imaging and biomedical labeling [33], and will open a new avenue to manipulate light-matter interaction in nanoscale plasmonic systems [34–36].

Acknowledgments

This work was supported by the State Key Development Program for Basic Research of China at No. 2013CB632704, and the National Natural Science Foundation of China at Nos. 11104342 and 11374357.

References and links

1. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2006).

2. J. F. Li and Z. Y. Li, “Manipulation of plasmonic wavefront and light-matter interaction in metallic nanostructures: A brief review,” Chin. Phys. B23, (2014).

3. M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6(11), 737–748 (2012). [CrossRef]  

4. J. Butet, J. Duboisset, G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, and P. F. Brevet, “Optical Second Harmonic Generation of Single Metallic Nanoparticles Embedded in a Homogeneous Medium,” Nano Lett. 10(5), 1717–1721 (2010). [CrossRef]   [PubMed]  

5. A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, “Near-field second-harmonic generation induced by local field enhancement,” Phys. Rev. Lett. 90(1), 013903 (2003). [CrossRef]   [PubMed]  

6. J. A. H. van Nieuwstadt, M. Sandtke, R. H. Harmsen, F. B. Segerink, J. C. Prangsma, S. Enoch, and L. Kuipers, “Strong modification of the nonlinear optical response of metallic subwavelength hole arrays,” Phys. Rev. Lett. 97(14), 146102 (2006). [CrossRef]   [PubMed]  

7. C. K. Chen, A. R. B. Decastro, and Y. R. Shen, “Surface-Enchanced 2nd-Harmonic Generation,” Phys. Rev. Lett. 46(2), 145–148 (1981). [CrossRef]  

8. B. L. Wang, R. Wang, R. J. Liu, X. H. Lu, J. M. Zhao, and Z. Y. Li, “Origin of Shape Resonance in Second-Harmonic Generation from Metallic Nanohole Arrays,” Sci Rep 3, 2358 (2013). [PubMed]  

9. H. Harutyunyan, G. Volpe, R. Quidant, and L. Novotny, “Enhancing the Nonlinear Optical Response Using Multifrequency Gold-Nanowire Antennas,” Phys. Rev. Lett. 108(21), 217403 (2012). [CrossRef]   [PubMed]  

10. Y. Pu, R. Grange, C. L. Hsieh, and D. Psaltis, “Nonlinear optical properties of core-shell nanocavities for enhanced second-harmonic generation,” Phys. Rev. Lett. 104(20), 207402 (2010). [CrossRef]   [PubMed]  

11. J. Richter, A. Steinbruck, T. Pertsch, A. Tunnermann, and R. Grange, “Plasmonic Core-Shell Nanowires for Enhanced Second-Harmonic Generation,” Plasmonics 8(1), 115–120 (2013). [CrossRef]  

12. M. L. Ren, W. Liu, C. O. Aspetti, L. Sun, and R. Agarwal, “Enhanced second-harmonic generation from metal-integrated semiconductor nanowires via highly confined whispering gallery modes,” Nat. Commun. 5, 5432 (2013).

13. T. Ming, L. Zhao, Z. Yang, H. J. Chen, L. D. Sun, J. F. Wang, and C. H. Yan, “Strong Polarization Dependence of Plasmon-Enhanced Fluorescence on Single Gold Nanorods,” Nano Lett. 9(11), 3896–3903 (2009). [CrossRef]   [PubMed]  

14. P. Zijlstra, J. W. M. Chon, and M. Gu, “Five-dimensional optical recording mediated by surface plasmons in gold nanorods,” Nature 459(7245), 410–413 (2009). [CrossRef]   [PubMed]  

15. Q. K. Liu, Y. X. Cui, D. Gardner, X. Li, S. L. He, and I. I. Smalyukh, “Self-Alignment of Plasmonic Gold Nanorods in Reconfigurable Anisotropic Fluids for Tunable Bulk Metamaterial Applications,” Nano Lett. 10(4), 1347–1353 (2010). [CrossRef]   [PubMed]  

16. J. F. Li, S. Y. Liu, Y. Liu, F. Zhou, and Z. Y. Li, “Anisotropic and enhanced absorptive nonlinearities in a macroscopic film induced by aligned gold nanorods,” Appl. Phys. Lett. 96(26), 263103 (2010). [CrossRef]  

17. S. Y. Liu, J. F. Li, and Z. Y. Li, “Macroscopic Polarized Emission from Aligned Hybrid Gold Nanorods Embedded in a Polyvinyl Alcohol Film,” Adv. Opt. Mater. 1(3), 227–231 (2013). [CrossRef]  

18. S. Y. Liu, J. F. Li, F. Zhou, L. Gan, and Z. Y. Li, “Efficient surface plasmon amplification from gain-assisted gold nanorods,” Opt. Lett. 36(7), 1296–1298 (2011). [CrossRef]   [PubMed]  

19. C. Shi, S. Soltani, and A. M. Armani, “Gold Nanorod Plasmonic Upconversion Microlaser,” Nano Lett. 13(12), 5827–5831 (2013). [CrossRef]   [PubMed]  

20. K. F. MacDonald, Z. L. Samson, M. I. Stockman, and N. I. Zheludev, “Ultrafast active plasmonics,” Nat. Photonics 3(1), 55–58 (2009). [CrossRef]  

21. S. Y. Liu, L. Huang, J. F. Li, C. Wang, Q. Li, H. X. Xu, H. L. Guo, Z. M. Meng, Z. Shi, and Z. Y. Li, “Simultaneous Excitation and Emission Enhancement of Fluorescence Assisted by Double Plasmon Modes of Gold Nanorods,” J. Phys. Chem. C 117(20), 10636–10642 (2013). [CrossRef]  

22. X. M. Hua and J. I. Gersten, “Theory of 2nd-Harmonic Generation by Small Metal Spheres,” Phys. Rev. B 33(6), 3756–3764 (1986). [CrossRef]  

23. Y. Pavlyukh and W. Hubner, “Nonlinear Mie scattering from spherical particles,” Phys. Rev. B 70(24), 245434 (2004). [CrossRef]  

24. A. G. F. de Beer and S. Roke, “Nonlinear Mie theory for second-harmonic and sum-frequency scattering,” Phys. Rev. B 79(15), 155420 (2009). [CrossRef]  

25. B. T. Draine and P. J. Flatau, “Discrete-Dipole Approximation for Scattering Calculations,” J. Opt. Soc. Am. A 11(4), 1491–1499 (1994). [CrossRef]  

26. F. Zhou, Z. Y. Li, Y. Liu, and Y. N. Xia, “Quantitative Analysis of Dipole and Quadrupole Excitation in the Surface Plasmon Resonance of Metal Nanoparticles,” J. Phys. Chem. C 112(51), 20233–20240 (2008). [CrossRef]  

27. Z. Y. Li, B. Y. Gu, and G. Z. Yang, “Strong localization of near-field second-harmonic generation for nonlinear mesoscopic surface structures,” Phys. Rev. B 59(19), 12622–12626 (1999). [CrossRef]  

28. R. W. Boyd, Nonlinear Optics (Academic, 2008).

29. M. L. Ren, X. L. Zhong, B. Q. Chen, and Z. Y. Li, “An all-optical diode based on plasmonic attenuation and nonlinear frequency conversion,” Chin. Phys. Lett. 30(9), 097301 (2013). [CrossRef]  

30. B. L. Wang, M. L. Ren, J. F. Li, and Z. Y. Li, “Plasmonic coupling effect between two gold nanospheres for efficient second-harmonic generation,” J. Appl. Phys. 112(8), 083102 (2012). [CrossRef]  

31. B. J. Wiley, Y. C. Chen, J. M. McLellan, Y. J. Xiong, Z. Y. Li, D. Ginger, and Y. N. Xia, “Synthesis and optical properties of silver nanobars and nanorice,” Nano Lett. 7(4), 1032–1036 (2007). [CrossRef]   [PubMed]  

32. B. Q. Chen, M. L. Ren, R. J. Liu, C. Zhang, Y. Sheng, B. Q. Ma, and Z. Y. Li, “Simultaneous broadband generation of second and third harmonics from chirped nonlinear photonic crystals,” Light Sci. Appl. 3(7), e189 (2014). [CrossRef]  

33. C. L. Hsieh, R. Grange, Y. Pu, and D. Psaltis, “Three-dimensional harmonic holographic microcopy using nanoparticles as probes for cell imaging,” Opt. Express 17(4), 2880–2891 (2009). [CrossRef]   [PubMed]  

34. Z. Y. Li and J. F. Li, “Recent progress in engineering and application of surface plasmon resonance in metal nanostructures,” Chin. Sci. Bull.(Chinese Ver.) 56(32), 2631 (2011). [CrossRef]  

35. J. F. Li, H. L. Guo, and Z. Y. Li, “Microscopic and macroscopic manipulation of gold nanorod and its hybrid nanostructures,” Photon. Res. 1(1), 28 (2013). [CrossRef]  

36. Z. Y. Li, “Nanophotonics in China: Overviews and highlights,” Front. of Phys. 7(6), 601–631 (2012). [CrossRef]  

References

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  1. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2006).
  2. J. F. Li and Z. Y. Li, “Manipulation of plasmonic wavefront and light-matter interaction in metallic nanostructures: A brief review,” Chin. Phys. B23, (2014).
  3. M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6(11), 737–748 (2012).
    [Crossref]
  4. J. Butet, J. Duboisset, G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, and P. F. Brevet, “Optical Second Harmonic Generation of Single Metallic Nanoparticles Embedded in a Homogeneous Medium,” Nano Lett. 10(5), 1717–1721 (2010).
    [Crossref] [PubMed]
  5. A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, “Near-field second-harmonic generation induced by local field enhancement,” Phys. Rev. Lett. 90(1), 013903 (2003).
    [Crossref] [PubMed]
  6. J. A. H. van Nieuwstadt, M. Sandtke, R. H. Harmsen, F. B. Segerink, J. C. Prangsma, S. Enoch, and L. Kuipers, “Strong modification of the nonlinear optical response of metallic subwavelength hole arrays,” Phys. Rev. Lett. 97(14), 146102 (2006).
    [Crossref] [PubMed]
  7. C. K. Chen, A. R. B. Decastro, and Y. R. Shen, “Surface-Enchanced 2nd-Harmonic Generation,” Phys. Rev. Lett. 46(2), 145–148 (1981).
    [Crossref]
  8. B. L. Wang, R. Wang, R. J. Liu, X. H. Lu, J. M. Zhao, and Z. Y. Li, “Origin of Shape Resonance in Second-Harmonic Generation from Metallic Nanohole Arrays,” Sci Rep 3, 2358 (2013).
    [PubMed]
  9. H. Harutyunyan, G. Volpe, R. Quidant, and L. Novotny, “Enhancing the Nonlinear Optical Response Using Multifrequency Gold-Nanowire Antennas,” Phys. Rev. Lett. 108(21), 217403 (2012).
    [Crossref] [PubMed]
  10. Y. Pu, R. Grange, C. L. Hsieh, and D. Psaltis, “Nonlinear optical properties of core-shell nanocavities for enhanced second-harmonic generation,” Phys. Rev. Lett. 104(20), 207402 (2010).
    [Crossref] [PubMed]
  11. J. Richter, A. Steinbruck, T. Pertsch, A. Tunnermann, and R. Grange, “Plasmonic Core-Shell Nanowires for Enhanced Second-Harmonic Generation,” Plasmonics 8(1), 115–120 (2013).
    [Crossref]
  12. M. L. Ren, W. Liu, C. O. Aspetti, L. Sun, and R. Agarwal, “Enhanced second-harmonic generation from metal-integrated semiconductor nanowires via highly confined whispering gallery modes,” Nat. Commun. 5, 5432 (2013).
  13. T. Ming, L. Zhao, Z. Yang, H. J. Chen, L. D. Sun, J. F. Wang, and C. H. Yan, “Strong Polarization Dependence of Plasmon-Enhanced Fluorescence on Single Gold Nanorods,” Nano Lett. 9(11), 3896–3903 (2009).
    [Crossref] [PubMed]
  14. P. Zijlstra, J. W. M. Chon, and M. Gu, “Five-dimensional optical recording mediated by surface plasmons in gold nanorods,” Nature 459(7245), 410–413 (2009).
    [Crossref] [PubMed]
  15. Q. K. Liu, Y. X. Cui, D. Gardner, X. Li, S. L. He, and I. I. Smalyukh, “Self-Alignment of Plasmonic Gold Nanorods in Reconfigurable Anisotropic Fluids for Tunable Bulk Metamaterial Applications,” Nano Lett. 10(4), 1347–1353 (2010).
    [Crossref] [PubMed]
  16. J. F. Li, S. Y. Liu, Y. Liu, F. Zhou, and Z. Y. Li, “Anisotropic and enhanced absorptive nonlinearities in a macroscopic film induced by aligned gold nanorods,” Appl. Phys. Lett. 96(26), 263103 (2010).
    [Crossref]
  17. S. Y. Liu, J. F. Li, and Z. Y. Li, “Macroscopic Polarized Emission from Aligned Hybrid Gold Nanorods Embedded in a Polyvinyl Alcohol Film,” Adv. Opt. Mater. 1(3), 227–231 (2013).
    [Crossref]
  18. S. Y. Liu, J. F. Li, F. Zhou, L. Gan, and Z. Y. Li, “Efficient surface plasmon amplification from gain-assisted gold nanorods,” Opt. Lett. 36(7), 1296–1298 (2011).
    [Crossref] [PubMed]
  19. C. Shi, S. Soltani, and A. M. Armani, “Gold Nanorod Plasmonic Upconversion Microlaser,” Nano Lett. 13(12), 5827–5831 (2013).
    [Crossref] [PubMed]
  20. K. F. MacDonald, Z. L. Samson, M. I. Stockman, and N. I. Zheludev, “Ultrafast active plasmonics,” Nat. Photonics 3(1), 55–58 (2009).
    [Crossref]
  21. S. Y. Liu, L. Huang, J. F. Li, C. Wang, Q. Li, H. X. Xu, H. L. Guo, Z. M. Meng, Z. Shi, and Z. Y. Li, “Simultaneous Excitation and Emission Enhancement of Fluorescence Assisted by Double Plasmon Modes of Gold Nanorods,” J. Phys. Chem. C 117(20), 10636–10642 (2013).
    [Crossref]
  22. X. M. Hua and J. I. Gersten, “Theory of 2nd-Harmonic Generation by Small Metal Spheres,” Phys. Rev. B 33(6), 3756–3764 (1986).
    [Crossref]
  23. Y. Pavlyukh and W. Hubner, “Nonlinear Mie scattering from spherical particles,” Phys. Rev. B 70(24), 245434 (2004).
    [Crossref]
  24. A. G. F. de Beer and S. Roke, “Nonlinear Mie theory for second-harmonic and sum-frequency scattering,” Phys. Rev. B 79(15), 155420 (2009).
    [Crossref]
  25. B. T. Draine and P. J. Flatau, “Discrete-Dipole Approximation for Scattering Calculations,” J. Opt. Soc. Am. A 11(4), 1491–1499 (1994).
    [Crossref]
  26. F. Zhou, Z. Y. Li, Y. Liu, and Y. N. Xia, “Quantitative Analysis of Dipole and Quadrupole Excitation in the Surface Plasmon Resonance of Metal Nanoparticles,” J. Phys. Chem. C 112(51), 20233–20240 (2008).
    [Crossref]
  27. Z. Y. Li, B. Y. Gu, and G. Z. Yang, “Strong localization of near-field second-harmonic generation for nonlinear mesoscopic surface structures,” Phys. Rev. B 59(19), 12622–12626 (1999).
    [Crossref]
  28. R. W. Boyd, Nonlinear Optics (Academic, 2008).
  29. M. L. Ren, X. L. Zhong, B. Q. Chen, and Z. Y. Li, “An all-optical diode based on plasmonic attenuation and nonlinear frequency conversion,” Chin. Phys. Lett. 30(9), 097301 (2013).
    [Crossref]
  30. B. L. Wang, M. L. Ren, J. F. Li, and Z. Y. Li, “Plasmonic coupling effect between two gold nanospheres for efficient second-harmonic generation,” J. Appl. Phys. 112(8), 083102 (2012).
    [Crossref]
  31. B. J. Wiley, Y. C. Chen, J. M. McLellan, Y. J. Xiong, Z. Y. Li, D. Ginger, and Y. N. Xia, “Synthesis and optical properties of silver nanobars and nanorice,” Nano Lett. 7(4), 1032–1036 (2007).
    [Crossref] [PubMed]
  32. B. Q. Chen, M. L. Ren, R. J. Liu, C. Zhang, Y. Sheng, B. Q. Ma, and Z. Y. Li, “Simultaneous broadband generation of second and third harmonics from chirped nonlinear photonic crystals,” Light Sci. Appl. 3(7), e189 (2014).
    [Crossref]
  33. C. L. Hsieh, R. Grange, Y. Pu, and D. Psaltis, “Three-dimensional harmonic holographic microcopy using nanoparticles as probes for cell imaging,” Opt. Express 17(4), 2880–2891 (2009).
    [Crossref] [PubMed]
  34. Z. Y. Li and J. F. Li, “Recent progress in engineering and application of surface plasmon resonance in metal nanostructures,” Chin. Sci. Bull.(Chinese Ver.) 56(32), 2631 (2011).
    [Crossref]
  35. J. F. Li, H. L. Guo, and Z. Y. Li, “Microscopic and macroscopic manipulation of gold nanorod and its hybrid nanostructures,” Photon. Res. 1(1), 28 (2013).
    [Crossref]
  36. Z. Y. Li, “Nanophotonics in China: Overviews and highlights,” Front. of Phys. 7(6), 601–631 (2012).
    [Crossref]

2014 (1)

B. Q. Chen, M. L. Ren, R. J. Liu, C. Zhang, Y. Sheng, B. Q. Ma, and Z. Y. Li, “Simultaneous broadband generation of second and third harmonics from chirped nonlinear photonic crystals,” Light Sci. Appl. 3(7), e189 (2014).
[Crossref]

2013 (8)

J. F. Li, H. L. Guo, and Z. Y. Li, “Microscopic and macroscopic manipulation of gold nanorod and its hybrid nanostructures,” Photon. Res. 1(1), 28 (2013).
[Crossref]

S. Y. Liu, L. Huang, J. F. Li, C. Wang, Q. Li, H. X. Xu, H. L. Guo, Z. M. Meng, Z. Shi, and Z. Y. Li, “Simultaneous Excitation and Emission Enhancement of Fluorescence Assisted by Double Plasmon Modes of Gold Nanorods,” J. Phys. Chem. C 117(20), 10636–10642 (2013).
[Crossref]

M. L. Ren, X. L. Zhong, B. Q. Chen, and Z. Y. Li, “An all-optical diode based on plasmonic attenuation and nonlinear frequency conversion,” Chin. Phys. Lett. 30(9), 097301 (2013).
[Crossref]

J. Richter, A. Steinbruck, T. Pertsch, A. Tunnermann, and R. Grange, “Plasmonic Core-Shell Nanowires for Enhanced Second-Harmonic Generation,” Plasmonics 8(1), 115–120 (2013).
[Crossref]

M. L. Ren, W. Liu, C. O. Aspetti, L. Sun, and R. Agarwal, “Enhanced second-harmonic generation from metal-integrated semiconductor nanowires via highly confined whispering gallery modes,” Nat. Commun. 5, 5432 (2013).

B. L. Wang, R. Wang, R. J. Liu, X. H. Lu, J. M. Zhao, and Z. Y. Li, “Origin of Shape Resonance in Second-Harmonic Generation from Metallic Nanohole Arrays,” Sci Rep 3, 2358 (2013).
[PubMed]

S. Y. Liu, J. F. Li, and Z. Y. Li, “Macroscopic Polarized Emission from Aligned Hybrid Gold Nanorods Embedded in a Polyvinyl Alcohol Film,” Adv. Opt. Mater. 1(3), 227–231 (2013).
[Crossref]

C. Shi, S. Soltani, and A. M. Armani, “Gold Nanorod Plasmonic Upconversion Microlaser,” Nano Lett. 13(12), 5827–5831 (2013).
[Crossref] [PubMed]

2012 (4)

H. Harutyunyan, G. Volpe, R. Quidant, and L. Novotny, “Enhancing the Nonlinear Optical Response Using Multifrequency Gold-Nanowire Antennas,” Phys. Rev. Lett. 108(21), 217403 (2012).
[Crossref] [PubMed]

M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6(11), 737–748 (2012).
[Crossref]

B. L. Wang, M. L. Ren, J. F. Li, and Z. Y. Li, “Plasmonic coupling effect between two gold nanospheres for efficient second-harmonic generation,” J. Appl. Phys. 112(8), 083102 (2012).
[Crossref]

Z. Y. Li, “Nanophotonics in China: Overviews and highlights,” Front. of Phys. 7(6), 601–631 (2012).
[Crossref]

2011 (2)

Z. Y. Li and J. F. Li, “Recent progress in engineering and application of surface plasmon resonance in metal nanostructures,” Chin. Sci. Bull.(Chinese Ver.) 56(32), 2631 (2011).
[Crossref]

S. Y. Liu, J. F. Li, F. Zhou, L. Gan, and Z. Y. Li, “Efficient surface plasmon amplification from gain-assisted gold nanorods,” Opt. Lett. 36(7), 1296–1298 (2011).
[Crossref] [PubMed]

2010 (4)

Y. Pu, R. Grange, C. L. Hsieh, and D. Psaltis, “Nonlinear optical properties of core-shell nanocavities for enhanced second-harmonic generation,” Phys. Rev. Lett. 104(20), 207402 (2010).
[Crossref] [PubMed]

Q. K. Liu, Y. X. Cui, D. Gardner, X. Li, S. L. He, and I. I. Smalyukh, “Self-Alignment of Plasmonic Gold Nanorods in Reconfigurable Anisotropic Fluids for Tunable Bulk Metamaterial Applications,” Nano Lett. 10(4), 1347–1353 (2010).
[Crossref] [PubMed]

J. F. Li, S. Y. Liu, Y. Liu, F. Zhou, and Z. Y. Li, “Anisotropic and enhanced absorptive nonlinearities in a macroscopic film induced by aligned gold nanorods,” Appl. Phys. Lett. 96(26), 263103 (2010).
[Crossref]

J. Butet, J. Duboisset, G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, and P. F. Brevet, “Optical Second Harmonic Generation of Single Metallic Nanoparticles Embedded in a Homogeneous Medium,” Nano Lett. 10(5), 1717–1721 (2010).
[Crossref] [PubMed]

2009 (5)

T. Ming, L. Zhao, Z. Yang, H. J. Chen, L. D. Sun, J. F. Wang, and C. H. Yan, “Strong Polarization Dependence of Plasmon-Enhanced Fluorescence on Single Gold Nanorods,” Nano Lett. 9(11), 3896–3903 (2009).
[Crossref] [PubMed]

P. Zijlstra, J. W. M. Chon, and M. Gu, “Five-dimensional optical recording mediated by surface plasmons in gold nanorods,” Nature 459(7245), 410–413 (2009).
[Crossref] [PubMed]

K. F. MacDonald, Z. L. Samson, M. I. Stockman, and N. I. Zheludev, “Ultrafast active plasmonics,” Nat. Photonics 3(1), 55–58 (2009).
[Crossref]

C. L. Hsieh, R. Grange, Y. Pu, and D. Psaltis, “Three-dimensional harmonic holographic microcopy using nanoparticles as probes for cell imaging,” Opt. Express 17(4), 2880–2891 (2009).
[Crossref] [PubMed]

A. G. F. de Beer and S. Roke, “Nonlinear Mie theory for second-harmonic and sum-frequency scattering,” Phys. Rev. B 79(15), 155420 (2009).
[Crossref]

2008 (1)

F. Zhou, Z. Y. Li, Y. Liu, and Y. N. Xia, “Quantitative Analysis of Dipole and Quadrupole Excitation in the Surface Plasmon Resonance of Metal Nanoparticles,” J. Phys. Chem. C 112(51), 20233–20240 (2008).
[Crossref]

2007 (1)

B. J. Wiley, Y. C. Chen, J. M. McLellan, Y. J. Xiong, Z. Y. Li, D. Ginger, and Y. N. Xia, “Synthesis and optical properties of silver nanobars and nanorice,” Nano Lett. 7(4), 1032–1036 (2007).
[Crossref] [PubMed]

2006 (1)

J. A. H. van Nieuwstadt, M. Sandtke, R. H. Harmsen, F. B. Segerink, J. C. Prangsma, S. Enoch, and L. Kuipers, “Strong modification of the nonlinear optical response of metallic subwavelength hole arrays,” Phys. Rev. Lett. 97(14), 146102 (2006).
[Crossref] [PubMed]

2004 (1)

Y. Pavlyukh and W. Hubner, “Nonlinear Mie scattering from spherical particles,” Phys. Rev. B 70(24), 245434 (2004).
[Crossref]

2003 (1)

A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, “Near-field second-harmonic generation induced by local field enhancement,” Phys. Rev. Lett. 90(1), 013903 (2003).
[Crossref] [PubMed]

1999 (1)

Z. Y. Li, B. Y. Gu, and G. Z. Yang, “Strong localization of near-field second-harmonic generation for nonlinear mesoscopic surface structures,” Phys. Rev. B 59(19), 12622–12626 (1999).
[Crossref]

1994 (1)

1986 (1)

X. M. Hua and J. I. Gersten, “Theory of 2nd-Harmonic Generation by Small Metal Spheres,” Phys. Rev. B 33(6), 3756–3764 (1986).
[Crossref]

1981 (1)

C. K. Chen, A. R. B. Decastro, and Y. R. Shen, “Surface-Enchanced 2nd-Harmonic Generation,” Phys. Rev. Lett. 46(2), 145–148 (1981).
[Crossref]

Agarwal, R.

M. L. Ren, W. Liu, C. O. Aspetti, L. Sun, and R. Agarwal, “Enhanced second-harmonic generation from metal-integrated semiconductor nanowires via highly confined whispering gallery modes,” Nat. Commun. 5, 5432 (2013).

Armani, A. M.

C. Shi, S. Soltani, and A. M. Armani, “Gold Nanorod Plasmonic Upconversion Microlaser,” Nano Lett. 13(12), 5827–5831 (2013).
[Crossref] [PubMed]

Aspetti, C. O.

M. L. Ren, W. Liu, C. O. Aspetti, L. Sun, and R. Agarwal, “Enhanced second-harmonic generation from metal-integrated semiconductor nanowires via highly confined whispering gallery modes,” Nat. Commun. 5, 5432 (2013).

Bachelier, G.

J. Butet, J. Duboisset, G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, and P. F. Brevet, “Optical Second Harmonic Generation of Single Metallic Nanoparticles Embedded in a Homogeneous Medium,” Nano Lett. 10(5), 1717–1721 (2010).
[Crossref] [PubMed]

Benichou, E.

J. Butet, J. Duboisset, G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, and P. F. Brevet, “Optical Second Harmonic Generation of Single Metallic Nanoparticles Embedded in a Homogeneous Medium,” Nano Lett. 10(5), 1717–1721 (2010).
[Crossref] [PubMed]

Beversluis, M.

A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, “Near-field second-harmonic generation induced by local field enhancement,” Phys. Rev. Lett. 90(1), 013903 (2003).
[Crossref] [PubMed]

Bouhelier, A.

A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, “Near-field second-harmonic generation induced by local field enhancement,” Phys. Rev. Lett. 90(1), 013903 (2003).
[Crossref] [PubMed]

Brevet, P. F.

J. Butet, J. Duboisset, G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, and P. F. Brevet, “Optical Second Harmonic Generation of Single Metallic Nanoparticles Embedded in a Homogeneous Medium,” Nano Lett. 10(5), 1717–1721 (2010).
[Crossref] [PubMed]

Butet, J.

J. Butet, J. Duboisset, G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, and P. F. Brevet, “Optical Second Harmonic Generation of Single Metallic Nanoparticles Embedded in a Homogeneous Medium,” Nano Lett. 10(5), 1717–1721 (2010).
[Crossref] [PubMed]

Chen, B. Q.

B. Q. Chen, M. L. Ren, R. J. Liu, C. Zhang, Y. Sheng, B. Q. Ma, and Z. Y. Li, “Simultaneous broadband generation of second and third harmonics from chirped nonlinear photonic crystals,” Light Sci. Appl. 3(7), e189 (2014).
[Crossref]

M. L. Ren, X. L. Zhong, B. Q. Chen, and Z. Y. Li, “An all-optical diode based on plasmonic attenuation and nonlinear frequency conversion,” Chin. Phys. Lett. 30(9), 097301 (2013).
[Crossref]

Chen, C. K.

C. K. Chen, A. R. B. Decastro, and Y. R. Shen, “Surface-Enchanced 2nd-Harmonic Generation,” Phys. Rev. Lett. 46(2), 145–148 (1981).
[Crossref]

Chen, H. J.

T. Ming, L. Zhao, Z. Yang, H. J. Chen, L. D. Sun, J. F. Wang, and C. H. Yan, “Strong Polarization Dependence of Plasmon-Enhanced Fluorescence on Single Gold Nanorods,” Nano Lett. 9(11), 3896–3903 (2009).
[Crossref] [PubMed]

Chen, Y. C.

B. J. Wiley, Y. C. Chen, J. M. McLellan, Y. J. Xiong, Z. Y. Li, D. Ginger, and Y. N. Xia, “Synthesis and optical properties of silver nanobars and nanorice,” Nano Lett. 7(4), 1032–1036 (2007).
[Crossref] [PubMed]

Chon, J. W. M.

P. Zijlstra, J. W. M. Chon, and M. Gu, “Five-dimensional optical recording mediated by surface plasmons in gold nanorods,” Nature 459(7245), 410–413 (2009).
[Crossref] [PubMed]

Cui, Y. X.

Q. K. Liu, Y. X. Cui, D. Gardner, X. Li, S. L. He, and I. I. Smalyukh, “Self-Alignment of Plasmonic Gold Nanorods in Reconfigurable Anisotropic Fluids for Tunable Bulk Metamaterial Applications,” Nano Lett. 10(4), 1347–1353 (2010).
[Crossref] [PubMed]

de Beer, A. G. F.

A. G. F. de Beer and S. Roke, “Nonlinear Mie theory for second-harmonic and sum-frequency scattering,” Phys. Rev. B 79(15), 155420 (2009).
[Crossref]

Decastro, A. R. B.

C. K. Chen, A. R. B. Decastro, and Y. R. Shen, “Surface-Enchanced 2nd-Harmonic Generation,” Phys. Rev. Lett. 46(2), 145–148 (1981).
[Crossref]

Draine, B. T.

Duboisset, J.

J. Butet, J. Duboisset, G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, and P. F. Brevet, “Optical Second Harmonic Generation of Single Metallic Nanoparticles Embedded in a Homogeneous Medium,” Nano Lett. 10(5), 1717–1721 (2010).
[Crossref] [PubMed]

Enoch, S.

J. A. H. van Nieuwstadt, M. Sandtke, R. H. Harmsen, F. B. Segerink, J. C. Prangsma, S. Enoch, and L. Kuipers, “Strong modification of the nonlinear optical response of metallic subwavelength hole arrays,” Phys. Rev. Lett. 97(14), 146102 (2006).
[Crossref] [PubMed]

Flatau, P. J.

Gan, L.

Gardner, D.

Q. K. Liu, Y. X. Cui, D. Gardner, X. Li, S. L. He, and I. I. Smalyukh, “Self-Alignment of Plasmonic Gold Nanorods in Reconfigurable Anisotropic Fluids for Tunable Bulk Metamaterial Applications,” Nano Lett. 10(4), 1347–1353 (2010).
[Crossref] [PubMed]

Gersten, J. I.

X. M. Hua and J. I. Gersten, “Theory of 2nd-Harmonic Generation by Small Metal Spheres,” Phys. Rev. B 33(6), 3756–3764 (1986).
[Crossref]

Ginger, D.

B. J. Wiley, Y. C. Chen, J. M. McLellan, Y. J. Xiong, Z. Y. Li, D. Ginger, and Y. N. Xia, “Synthesis and optical properties of silver nanobars and nanorice,” Nano Lett. 7(4), 1032–1036 (2007).
[Crossref] [PubMed]

Grange, R.

J. Richter, A. Steinbruck, T. Pertsch, A. Tunnermann, and R. Grange, “Plasmonic Core-Shell Nanowires for Enhanced Second-Harmonic Generation,” Plasmonics 8(1), 115–120 (2013).
[Crossref]

Y. Pu, R. Grange, C. L. Hsieh, and D. Psaltis, “Nonlinear optical properties of core-shell nanocavities for enhanced second-harmonic generation,” Phys. Rev. Lett. 104(20), 207402 (2010).
[Crossref] [PubMed]

C. L. Hsieh, R. Grange, Y. Pu, and D. Psaltis, “Three-dimensional harmonic holographic microcopy using nanoparticles as probes for cell imaging,” Opt. Express 17(4), 2880–2891 (2009).
[Crossref] [PubMed]

Gu, B. Y.

Z. Y. Li, B. Y. Gu, and G. Z. Yang, “Strong localization of near-field second-harmonic generation for nonlinear mesoscopic surface structures,” Phys. Rev. B 59(19), 12622–12626 (1999).
[Crossref]

Gu, M.

P. Zijlstra, J. W. M. Chon, and M. Gu, “Five-dimensional optical recording mediated by surface plasmons in gold nanorods,” Nature 459(7245), 410–413 (2009).
[Crossref] [PubMed]

Guo, H. L.

S. Y. Liu, L. Huang, J. F. Li, C. Wang, Q. Li, H. X. Xu, H. L. Guo, Z. M. Meng, Z. Shi, and Z. Y. Li, “Simultaneous Excitation and Emission Enhancement of Fluorescence Assisted by Double Plasmon Modes of Gold Nanorods,” J. Phys. Chem. C 117(20), 10636–10642 (2013).
[Crossref]

J. F. Li, H. L. Guo, and Z. Y. Li, “Microscopic and macroscopic manipulation of gold nanorod and its hybrid nanostructures,” Photon. Res. 1(1), 28 (2013).
[Crossref]

Harmsen, R. H.

J. A. H. van Nieuwstadt, M. Sandtke, R. H. Harmsen, F. B. Segerink, J. C. Prangsma, S. Enoch, and L. Kuipers, “Strong modification of the nonlinear optical response of metallic subwavelength hole arrays,” Phys. Rev. Lett. 97(14), 146102 (2006).
[Crossref] [PubMed]

Hartschuh, A.

A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, “Near-field second-harmonic generation induced by local field enhancement,” Phys. Rev. Lett. 90(1), 013903 (2003).
[Crossref] [PubMed]

Harutyunyan, H.

H. Harutyunyan, G. Volpe, R. Quidant, and L. Novotny, “Enhancing the Nonlinear Optical Response Using Multifrequency Gold-Nanowire Antennas,” Phys. Rev. Lett. 108(21), 217403 (2012).
[Crossref] [PubMed]

He, S. L.

Q. K. Liu, Y. X. Cui, D. Gardner, X. Li, S. L. He, and I. I. Smalyukh, “Self-Alignment of Plasmonic Gold Nanorods in Reconfigurable Anisotropic Fluids for Tunable Bulk Metamaterial Applications,” Nano Lett. 10(4), 1347–1353 (2010).
[Crossref] [PubMed]

Hsieh, C. L.

Y. Pu, R. Grange, C. L. Hsieh, and D. Psaltis, “Nonlinear optical properties of core-shell nanocavities for enhanced second-harmonic generation,” Phys. Rev. Lett. 104(20), 207402 (2010).
[Crossref] [PubMed]

C. L. Hsieh, R. Grange, Y. Pu, and D. Psaltis, “Three-dimensional harmonic holographic microcopy using nanoparticles as probes for cell imaging,” Opt. Express 17(4), 2880–2891 (2009).
[Crossref] [PubMed]

Hua, X. M.

X. M. Hua and J. I. Gersten, “Theory of 2nd-Harmonic Generation by Small Metal Spheres,” Phys. Rev. B 33(6), 3756–3764 (1986).
[Crossref]

Huang, L.

S. Y. Liu, L. Huang, J. F. Li, C. Wang, Q. Li, H. X. Xu, H. L. Guo, Z. M. Meng, Z. Shi, and Z. Y. Li, “Simultaneous Excitation and Emission Enhancement of Fluorescence Assisted by Double Plasmon Modes of Gold Nanorods,” J. Phys. Chem. C 117(20), 10636–10642 (2013).
[Crossref]

Hubner, W.

Y. Pavlyukh and W. Hubner, “Nonlinear Mie scattering from spherical particles,” Phys. Rev. B 70(24), 245434 (2004).
[Crossref]

Jonin, C.

J. Butet, J. Duboisset, G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, and P. F. Brevet, “Optical Second Harmonic Generation of Single Metallic Nanoparticles Embedded in a Homogeneous Medium,” Nano Lett. 10(5), 1717–1721 (2010).
[Crossref] [PubMed]

Kauranen, M.

M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6(11), 737–748 (2012).
[Crossref]

Kuipers, L.

J. A. H. van Nieuwstadt, M. Sandtke, R. H. Harmsen, F. B. Segerink, J. C. Prangsma, S. Enoch, and L. Kuipers, “Strong modification of the nonlinear optical response of metallic subwavelength hole arrays,” Phys. Rev. Lett. 97(14), 146102 (2006).
[Crossref] [PubMed]

Li, J. F.

S. Y. Liu, L. Huang, J. F. Li, C. Wang, Q. Li, H. X. Xu, H. L. Guo, Z. M. Meng, Z. Shi, and Z. Y. Li, “Simultaneous Excitation and Emission Enhancement of Fluorescence Assisted by Double Plasmon Modes of Gold Nanorods,” J. Phys. Chem. C 117(20), 10636–10642 (2013).
[Crossref]

S. Y. Liu, J. F. Li, and Z. Y. Li, “Macroscopic Polarized Emission from Aligned Hybrid Gold Nanorods Embedded in a Polyvinyl Alcohol Film,” Adv. Opt. Mater. 1(3), 227–231 (2013).
[Crossref]

J. F. Li, H. L. Guo, and Z. Y. Li, “Microscopic and macroscopic manipulation of gold nanorod and its hybrid nanostructures,” Photon. Res. 1(1), 28 (2013).
[Crossref]

B. L. Wang, M. L. Ren, J. F. Li, and Z. Y. Li, “Plasmonic coupling effect between two gold nanospheres for efficient second-harmonic generation,” J. Appl. Phys. 112(8), 083102 (2012).
[Crossref]

Z. Y. Li and J. F. Li, “Recent progress in engineering and application of surface plasmon resonance in metal nanostructures,” Chin. Sci. Bull.(Chinese Ver.) 56(32), 2631 (2011).
[Crossref]

S. Y. Liu, J. F. Li, F. Zhou, L. Gan, and Z. Y. Li, “Efficient surface plasmon amplification from gain-assisted gold nanorods,” Opt. Lett. 36(7), 1296–1298 (2011).
[Crossref] [PubMed]

J. F. Li, S. Y. Liu, Y. Liu, F. Zhou, and Z. Y. Li, “Anisotropic and enhanced absorptive nonlinearities in a macroscopic film induced by aligned gold nanorods,” Appl. Phys. Lett. 96(26), 263103 (2010).
[Crossref]

J. F. Li and Z. Y. Li, “Manipulation of plasmonic wavefront and light-matter interaction in metallic nanostructures: A brief review,” Chin. Phys. B23, (2014).

Li, Q.

S. Y. Liu, L. Huang, J. F. Li, C. Wang, Q. Li, H. X. Xu, H. L. Guo, Z. M. Meng, Z. Shi, and Z. Y. Li, “Simultaneous Excitation and Emission Enhancement of Fluorescence Assisted by Double Plasmon Modes of Gold Nanorods,” J. Phys. Chem. C 117(20), 10636–10642 (2013).
[Crossref]

Li, X.

Q. K. Liu, Y. X. Cui, D. Gardner, X. Li, S. L. He, and I. I. Smalyukh, “Self-Alignment of Plasmonic Gold Nanorods in Reconfigurable Anisotropic Fluids for Tunable Bulk Metamaterial Applications,” Nano Lett. 10(4), 1347–1353 (2010).
[Crossref] [PubMed]

Li, Z. Y.

B. Q. Chen, M. L. Ren, R. J. Liu, C. Zhang, Y. Sheng, B. Q. Ma, and Z. Y. Li, “Simultaneous broadband generation of second and third harmonics from chirped nonlinear photonic crystals,” Light Sci. Appl. 3(7), e189 (2014).
[Crossref]

J. F. Li, H. L. Guo, and Z. Y. Li, “Microscopic and macroscopic manipulation of gold nanorod and its hybrid nanostructures,” Photon. Res. 1(1), 28 (2013).
[Crossref]

M. L. Ren, X. L. Zhong, B. Q. Chen, and Z. Y. Li, “An all-optical diode based on plasmonic attenuation and nonlinear frequency conversion,” Chin. Phys. Lett. 30(9), 097301 (2013).
[Crossref]

S. Y. Liu, J. F. Li, and Z. Y. Li, “Macroscopic Polarized Emission from Aligned Hybrid Gold Nanorods Embedded in a Polyvinyl Alcohol Film,” Adv. Opt. Mater. 1(3), 227–231 (2013).
[Crossref]

S. Y. Liu, L. Huang, J. F. Li, C. Wang, Q. Li, H. X. Xu, H. L. Guo, Z. M. Meng, Z. Shi, and Z. Y. Li, “Simultaneous Excitation and Emission Enhancement of Fluorescence Assisted by Double Plasmon Modes of Gold Nanorods,” J. Phys. Chem. C 117(20), 10636–10642 (2013).
[Crossref]

B. L. Wang, R. Wang, R. J. Liu, X. H. Lu, J. M. Zhao, and Z. Y. Li, “Origin of Shape Resonance in Second-Harmonic Generation from Metallic Nanohole Arrays,” Sci Rep 3, 2358 (2013).
[PubMed]

B. L. Wang, M. L. Ren, J. F. Li, and Z. Y. Li, “Plasmonic coupling effect between two gold nanospheres for efficient second-harmonic generation,” J. Appl. Phys. 112(8), 083102 (2012).
[Crossref]

Z. Y. Li, “Nanophotonics in China: Overviews and highlights,” Front. of Phys. 7(6), 601–631 (2012).
[Crossref]

Z. Y. Li and J. F. Li, “Recent progress in engineering and application of surface plasmon resonance in metal nanostructures,” Chin. Sci. Bull.(Chinese Ver.) 56(32), 2631 (2011).
[Crossref]

S. Y. Liu, J. F. Li, F. Zhou, L. Gan, and Z. Y. Li, “Efficient surface plasmon amplification from gain-assisted gold nanorods,” Opt. Lett. 36(7), 1296–1298 (2011).
[Crossref] [PubMed]

J. F. Li, S. Y. Liu, Y. Liu, F. Zhou, and Z. Y. Li, “Anisotropic and enhanced absorptive nonlinearities in a macroscopic film induced by aligned gold nanorods,” Appl. Phys. Lett. 96(26), 263103 (2010).
[Crossref]

F. Zhou, Z. Y. Li, Y. Liu, and Y. N. Xia, “Quantitative Analysis of Dipole and Quadrupole Excitation in the Surface Plasmon Resonance of Metal Nanoparticles,” J. Phys. Chem. C 112(51), 20233–20240 (2008).
[Crossref]

B. J. Wiley, Y. C. Chen, J. M. McLellan, Y. J. Xiong, Z. Y. Li, D. Ginger, and Y. N. Xia, “Synthesis and optical properties of silver nanobars and nanorice,” Nano Lett. 7(4), 1032–1036 (2007).
[Crossref] [PubMed]

Z. Y. Li, B. Y. Gu, and G. Z. Yang, “Strong localization of near-field second-harmonic generation for nonlinear mesoscopic surface structures,” Phys. Rev. B 59(19), 12622–12626 (1999).
[Crossref]

J. F. Li and Z. Y. Li, “Manipulation of plasmonic wavefront and light-matter interaction in metallic nanostructures: A brief review,” Chin. Phys. B23, (2014).

Liu, Q. K.

Q. K. Liu, Y. X. Cui, D. Gardner, X. Li, S. L. He, and I. I. Smalyukh, “Self-Alignment of Plasmonic Gold Nanorods in Reconfigurable Anisotropic Fluids for Tunable Bulk Metamaterial Applications,” Nano Lett. 10(4), 1347–1353 (2010).
[Crossref] [PubMed]

Liu, R. J.

B. Q. Chen, M. L. Ren, R. J. Liu, C. Zhang, Y. Sheng, B. Q. Ma, and Z. Y. Li, “Simultaneous broadband generation of second and third harmonics from chirped nonlinear photonic crystals,” Light Sci. Appl. 3(7), e189 (2014).
[Crossref]

B. L. Wang, R. Wang, R. J. Liu, X. H. Lu, J. M. Zhao, and Z. Y. Li, “Origin of Shape Resonance in Second-Harmonic Generation from Metallic Nanohole Arrays,” Sci Rep 3, 2358 (2013).
[PubMed]

Liu, S. Y.

S. Y. Liu, J. F. Li, and Z. Y. Li, “Macroscopic Polarized Emission from Aligned Hybrid Gold Nanorods Embedded in a Polyvinyl Alcohol Film,” Adv. Opt. Mater. 1(3), 227–231 (2013).
[Crossref]

S. Y. Liu, L. Huang, J. F. Li, C. Wang, Q. Li, H. X. Xu, H. L. Guo, Z. M. Meng, Z. Shi, and Z. Y. Li, “Simultaneous Excitation and Emission Enhancement of Fluorescence Assisted by Double Plasmon Modes of Gold Nanorods,” J. Phys. Chem. C 117(20), 10636–10642 (2013).
[Crossref]

S. Y. Liu, J. F. Li, F. Zhou, L. Gan, and Z. Y. Li, “Efficient surface plasmon amplification from gain-assisted gold nanorods,” Opt. Lett. 36(7), 1296–1298 (2011).
[Crossref] [PubMed]

J. F. Li, S. Y. Liu, Y. Liu, F. Zhou, and Z. Y. Li, “Anisotropic and enhanced absorptive nonlinearities in a macroscopic film induced by aligned gold nanorods,” Appl. Phys. Lett. 96(26), 263103 (2010).
[Crossref]

Liu, W.

M. L. Ren, W. Liu, C. O. Aspetti, L. Sun, and R. Agarwal, “Enhanced second-harmonic generation from metal-integrated semiconductor nanowires via highly confined whispering gallery modes,” Nat. Commun. 5, 5432 (2013).

Liu, Y.

J. F. Li, S. Y. Liu, Y. Liu, F. Zhou, and Z. Y. Li, “Anisotropic and enhanced absorptive nonlinearities in a macroscopic film induced by aligned gold nanorods,” Appl. Phys. Lett. 96(26), 263103 (2010).
[Crossref]

F. Zhou, Z. Y. Li, Y. Liu, and Y. N. Xia, “Quantitative Analysis of Dipole and Quadrupole Excitation in the Surface Plasmon Resonance of Metal Nanoparticles,” J. Phys. Chem. C 112(51), 20233–20240 (2008).
[Crossref]

Lu, X. H.

B. L. Wang, R. Wang, R. J. Liu, X. H. Lu, J. M. Zhao, and Z. Y. Li, “Origin of Shape Resonance in Second-Harmonic Generation from Metallic Nanohole Arrays,” Sci Rep 3, 2358 (2013).
[PubMed]

Ma, B. Q.

B. Q. Chen, M. L. Ren, R. J. Liu, C. Zhang, Y. Sheng, B. Q. Ma, and Z. Y. Li, “Simultaneous broadband generation of second and third harmonics from chirped nonlinear photonic crystals,” Light Sci. Appl. 3(7), e189 (2014).
[Crossref]

MacDonald, K. F.

K. F. MacDonald, Z. L. Samson, M. I. Stockman, and N. I. Zheludev, “Ultrafast active plasmonics,” Nat. Photonics 3(1), 55–58 (2009).
[Crossref]

McLellan, J. M.

B. J. Wiley, Y. C. Chen, J. M. McLellan, Y. J. Xiong, Z. Y. Li, D. Ginger, and Y. N. Xia, “Synthesis and optical properties of silver nanobars and nanorice,” Nano Lett. 7(4), 1032–1036 (2007).
[Crossref] [PubMed]

Meng, Z. M.

S. Y. Liu, L. Huang, J. F. Li, C. Wang, Q. Li, H. X. Xu, H. L. Guo, Z. M. Meng, Z. Shi, and Z. Y. Li, “Simultaneous Excitation and Emission Enhancement of Fluorescence Assisted by Double Plasmon Modes of Gold Nanorods,” J. Phys. Chem. C 117(20), 10636–10642 (2013).
[Crossref]

Ming, T.

T. Ming, L. Zhao, Z. Yang, H. J. Chen, L. D. Sun, J. F. Wang, and C. H. Yan, “Strong Polarization Dependence of Plasmon-Enhanced Fluorescence on Single Gold Nanorods,” Nano Lett. 9(11), 3896–3903 (2009).
[Crossref] [PubMed]

Novotny, L.

H. Harutyunyan, G. Volpe, R. Quidant, and L. Novotny, “Enhancing the Nonlinear Optical Response Using Multifrequency Gold-Nanowire Antennas,” Phys. Rev. Lett. 108(21), 217403 (2012).
[Crossref] [PubMed]

A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, “Near-field second-harmonic generation induced by local field enhancement,” Phys. Rev. Lett. 90(1), 013903 (2003).
[Crossref] [PubMed]

Pavlyukh, Y.

Y. Pavlyukh and W. Hubner, “Nonlinear Mie scattering from spherical particles,” Phys. Rev. B 70(24), 245434 (2004).
[Crossref]

Pertsch, T.

J. Richter, A. Steinbruck, T. Pertsch, A. Tunnermann, and R. Grange, “Plasmonic Core-Shell Nanowires for Enhanced Second-Harmonic Generation,” Plasmonics 8(1), 115–120 (2013).
[Crossref]

Prangsma, J. C.

J. A. H. van Nieuwstadt, M. Sandtke, R. H. Harmsen, F. B. Segerink, J. C. Prangsma, S. Enoch, and L. Kuipers, “Strong modification of the nonlinear optical response of metallic subwavelength hole arrays,” Phys. Rev. Lett. 97(14), 146102 (2006).
[Crossref] [PubMed]

Psaltis, D.

Y. Pu, R. Grange, C. L. Hsieh, and D. Psaltis, “Nonlinear optical properties of core-shell nanocavities for enhanced second-harmonic generation,” Phys. Rev. Lett. 104(20), 207402 (2010).
[Crossref] [PubMed]

C. L. Hsieh, R. Grange, Y. Pu, and D. Psaltis, “Three-dimensional harmonic holographic microcopy using nanoparticles as probes for cell imaging,” Opt. Express 17(4), 2880–2891 (2009).
[Crossref] [PubMed]

Pu, Y.

Y. Pu, R. Grange, C. L. Hsieh, and D. Psaltis, “Nonlinear optical properties of core-shell nanocavities for enhanced second-harmonic generation,” Phys. Rev. Lett. 104(20), 207402 (2010).
[Crossref] [PubMed]

C. L. Hsieh, R. Grange, Y. Pu, and D. Psaltis, “Three-dimensional harmonic holographic microcopy using nanoparticles as probes for cell imaging,” Opt. Express 17(4), 2880–2891 (2009).
[Crossref] [PubMed]

Quidant, R.

H. Harutyunyan, G. Volpe, R. Quidant, and L. Novotny, “Enhancing the Nonlinear Optical Response Using Multifrequency Gold-Nanowire Antennas,” Phys. Rev. Lett. 108(21), 217403 (2012).
[Crossref] [PubMed]

Ren, M. L.

B. Q. Chen, M. L. Ren, R. J. Liu, C. Zhang, Y. Sheng, B. Q. Ma, and Z. Y. Li, “Simultaneous broadband generation of second and third harmonics from chirped nonlinear photonic crystals,” Light Sci. Appl. 3(7), e189 (2014).
[Crossref]

M. L. Ren, X. L. Zhong, B. Q. Chen, and Z. Y. Li, “An all-optical diode based on plasmonic attenuation and nonlinear frequency conversion,” Chin. Phys. Lett. 30(9), 097301 (2013).
[Crossref]

M. L. Ren, W. Liu, C. O. Aspetti, L. Sun, and R. Agarwal, “Enhanced second-harmonic generation from metal-integrated semiconductor nanowires via highly confined whispering gallery modes,” Nat. Commun. 5, 5432 (2013).

B. L. Wang, M. L. Ren, J. F. Li, and Z. Y. Li, “Plasmonic coupling effect between two gold nanospheres for efficient second-harmonic generation,” J. Appl. Phys. 112(8), 083102 (2012).
[Crossref]

Richter, J.

J. Richter, A. Steinbruck, T. Pertsch, A. Tunnermann, and R. Grange, “Plasmonic Core-Shell Nanowires for Enhanced Second-Harmonic Generation,” Plasmonics 8(1), 115–120 (2013).
[Crossref]

Roke, S.

A. G. F. de Beer and S. Roke, “Nonlinear Mie theory for second-harmonic and sum-frequency scattering,” Phys. Rev. B 79(15), 155420 (2009).
[Crossref]

Russier-Antoine, I.

J. Butet, J. Duboisset, G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, and P. F. Brevet, “Optical Second Harmonic Generation of Single Metallic Nanoparticles Embedded in a Homogeneous Medium,” Nano Lett. 10(5), 1717–1721 (2010).
[Crossref] [PubMed]

Samson, Z. L.

K. F. MacDonald, Z. L. Samson, M. I. Stockman, and N. I. Zheludev, “Ultrafast active plasmonics,” Nat. Photonics 3(1), 55–58 (2009).
[Crossref]

Sandtke, M.

J. A. H. van Nieuwstadt, M. Sandtke, R. H. Harmsen, F. B. Segerink, J. C. Prangsma, S. Enoch, and L. Kuipers, “Strong modification of the nonlinear optical response of metallic subwavelength hole arrays,” Phys. Rev. Lett. 97(14), 146102 (2006).
[Crossref] [PubMed]

Segerink, F. B.

J. A. H. van Nieuwstadt, M. Sandtke, R. H. Harmsen, F. B. Segerink, J. C. Prangsma, S. Enoch, and L. Kuipers, “Strong modification of the nonlinear optical response of metallic subwavelength hole arrays,” Phys. Rev. Lett. 97(14), 146102 (2006).
[Crossref] [PubMed]

Shen, Y. R.

C. K. Chen, A. R. B. Decastro, and Y. R. Shen, “Surface-Enchanced 2nd-Harmonic Generation,” Phys. Rev. Lett. 46(2), 145–148 (1981).
[Crossref]

Sheng, Y.

B. Q. Chen, M. L. Ren, R. J. Liu, C. Zhang, Y. Sheng, B. Q. Ma, and Z. Y. Li, “Simultaneous broadband generation of second and third harmonics from chirped nonlinear photonic crystals,” Light Sci. Appl. 3(7), e189 (2014).
[Crossref]

Shi, C.

C. Shi, S. Soltani, and A. M. Armani, “Gold Nanorod Plasmonic Upconversion Microlaser,” Nano Lett. 13(12), 5827–5831 (2013).
[Crossref] [PubMed]

Shi, Z.

S. Y. Liu, L. Huang, J. F. Li, C. Wang, Q. Li, H. X. Xu, H. L. Guo, Z. M. Meng, Z. Shi, and Z. Y. Li, “Simultaneous Excitation and Emission Enhancement of Fluorescence Assisted by Double Plasmon Modes of Gold Nanorods,” J. Phys. Chem. C 117(20), 10636–10642 (2013).
[Crossref]

Smalyukh, I. I.

Q. K. Liu, Y. X. Cui, D. Gardner, X. Li, S. L. He, and I. I. Smalyukh, “Self-Alignment of Plasmonic Gold Nanorods in Reconfigurable Anisotropic Fluids for Tunable Bulk Metamaterial Applications,” Nano Lett. 10(4), 1347–1353 (2010).
[Crossref] [PubMed]

Soltani, S.

C. Shi, S. Soltani, and A. M. Armani, “Gold Nanorod Plasmonic Upconversion Microlaser,” Nano Lett. 13(12), 5827–5831 (2013).
[Crossref] [PubMed]

Steinbruck, A.

J. Richter, A. Steinbruck, T. Pertsch, A. Tunnermann, and R. Grange, “Plasmonic Core-Shell Nanowires for Enhanced Second-Harmonic Generation,” Plasmonics 8(1), 115–120 (2013).
[Crossref]

Stockman, M. I.

K. F. MacDonald, Z. L. Samson, M. I. Stockman, and N. I. Zheludev, “Ultrafast active plasmonics,” Nat. Photonics 3(1), 55–58 (2009).
[Crossref]

Sun, L.

M. L. Ren, W. Liu, C. O. Aspetti, L. Sun, and R. Agarwal, “Enhanced second-harmonic generation from metal-integrated semiconductor nanowires via highly confined whispering gallery modes,” Nat. Commun. 5, 5432 (2013).

Sun, L. D.

T. Ming, L. Zhao, Z. Yang, H. J. Chen, L. D. Sun, J. F. Wang, and C. H. Yan, “Strong Polarization Dependence of Plasmon-Enhanced Fluorescence on Single Gold Nanorods,” Nano Lett. 9(11), 3896–3903 (2009).
[Crossref] [PubMed]

Tunnermann, A.

J. Richter, A. Steinbruck, T. Pertsch, A. Tunnermann, and R. Grange, “Plasmonic Core-Shell Nanowires for Enhanced Second-Harmonic Generation,” Plasmonics 8(1), 115–120 (2013).
[Crossref]

van Nieuwstadt, J. A. H.

J. A. H. van Nieuwstadt, M. Sandtke, R. H. Harmsen, F. B. Segerink, J. C. Prangsma, S. Enoch, and L. Kuipers, “Strong modification of the nonlinear optical response of metallic subwavelength hole arrays,” Phys. Rev. Lett. 97(14), 146102 (2006).
[Crossref] [PubMed]

Volpe, G.

H. Harutyunyan, G. Volpe, R. Quidant, and L. Novotny, “Enhancing the Nonlinear Optical Response Using Multifrequency Gold-Nanowire Antennas,” Phys. Rev. Lett. 108(21), 217403 (2012).
[Crossref] [PubMed]

Wang, B. L.

B. L. Wang, R. Wang, R. J. Liu, X. H. Lu, J. M. Zhao, and Z. Y. Li, “Origin of Shape Resonance in Second-Harmonic Generation from Metallic Nanohole Arrays,” Sci Rep 3, 2358 (2013).
[PubMed]

B. L. Wang, M. L. Ren, J. F. Li, and Z. Y. Li, “Plasmonic coupling effect between two gold nanospheres for efficient second-harmonic generation,” J. Appl. Phys. 112(8), 083102 (2012).
[Crossref]

Wang, C.

S. Y. Liu, L. Huang, J. F. Li, C. Wang, Q. Li, H. X. Xu, H. L. Guo, Z. M. Meng, Z. Shi, and Z. Y. Li, “Simultaneous Excitation and Emission Enhancement of Fluorescence Assisted by Double Plasmon Modes of Gold Nanorods,” J. Phys. Chem. C 117(20), 10636–10642 (2013).
[Crossref]

Wang, J. F.

T. Ming, L. Zhao, Z. Yang, H. J. Chen, L. D. Sun, J. F. Wang, and C. H. Yan, “Strong Polarization Dependence of Plasmon-Enhanced Fluorescence on Single Gold Nanorods,” Nano Lett. 9(11), 3896–3903 (2009).
[Crossref] [PubMed]

Wang, R.

B. L. Wang, R. Wang, R. J. Liu, X. H. Lu, J. M. Zhao, and Z. Y. Li, “Origin of Shape Resonance in Second-Harmonic Generation from Metallic Nanohole Arrays,” Sci Rep 3, 2358 (2013).
[PubMed]

Wiley, B. J.

B. J. Wiley, Y. C. Chen, J. M. McLellan, Y. J. Xiong, Z. Y. Li, D. Ginger, and Y. N. Xia, “Synthesis and optical properties of silver nanobars and nanorice,” Nano Lett. 7(4), 1032–1036 (2007).
[Crossref] [PubMed]

Xia, Y. N.

F. Zhou, Z. Y. Li, Y. Liu, and Y. N. Xia, “Quantitative Analysis of Dipole and Quadrupole Excitation in the Surface Plasmon Resonance of Metal Nanoparticles,” J. Phys. Chem. C 112(51), 20233–20240 (2008).
[Crossref]

B. J. Wiley, Y. C. Chen, J. M. McLellan, Y. J. Xiong, Z. Y. Li, D. Ginger, and Y. N. Xia, “Synthesis and optical properties of silver nanobars and nanorice,” Nano Lett. 7(4), 1032–1036 (2007).
[Crossref] [PubMed]

Xiong, Y. J.

B. J. Wiley, Y. C. Chen, J. M. McLellan, Y. J. Xiong, Z. Y. Li, D. Ginger, and Y. N. Xia, “Synthesis and optical properties of silver nanobars and nanorice,” Nano Lett. 7(4), 1032–1036 (2007).
[Crossref] [PubMed]

Xu, H. X.

S. Y. Liu, L. Huang, J. F. Li, C. Wang, Q. Li, H. X. Xu, H. L. Guo, Z. M. Meng, Z. Shi, and Z. Y. Li, “Simultaneous Excitation and Emission Enhancement of Fluorescence Assisted by Double Plasmon Modes of Gold Nanorods,” J. Phys. Chem. C 117(20), 10636–10642 (2013).
[Crossref]

Yan, C. H.

T. Ming, L. Zhao, Z. Yang, H. J. Chen, L. D. Sun, J. F. Wang, and C. H. Yan, “Strong Polarization Dependence of Plasmon-Enhanced Fluorescence on Single Gold Nanorods,” Nano Lett. 9(11), 3896–3903 (2009).
[Crossref] [PubMed]

Yang, G. Z.

Z. Y. Li, B. Y. Gu, and G. Z. Yang, “Strong localization of near-field second-harmonic generation for nonlinear mesoscopic surface structures,” Phys. Rev. B 59(19), 12622–12626 (1999).
[Crossref]

Yang, Z.

T. Ming, L. Zhao, Z. Yang, H. J. Chen, L. D. Sun, J. F. Wang, and C. H. Yan, “Strong Polarization Dependence of Plasmon-Enhanced Fluorescence on Single Gold Nanorods,” Nano Lett. 9(11), 3896–3903 (2009).
[Crossref] [PubMed]

Zayats, A. V.

M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6(11), 737–748 (2012).
[Crossref]

Zhang, C.

B. Q. Chen, M. L. Ren, R. J. Liu, C. Zhang, Y. Sheng, B. Q. Ma, and Z. Y. Li, “Simultaneous broadband generation of second and third harmonics from chirped nonlinear photonic crystals,” Light Sci. Appl. 3(7), e189 (2014).
[Crossref]

Zhao, J. M.

B. L. Wang, R. Wang, R. J. Liu, X. H. Lu, J. M. Zhao, and Z. Y. Li, “Origin of Shape Resonance in Second-Harmonic Generation from Metallic Nanohole Arrays,” Sci Rep 3, 2358 (2013).
[PubMed]

Zhao, L.

T. Ming, L. Zhao, Z. Yang, H. J. Chen, L. D. Sun, J. F. Wang, and C. H. Yan, “Strong Polarization Dependence of Plasmon-Enhanced Fluorescence on Single Gold Nanorods,” Nano Lett. 9(11), 3896–3903 (2009).
[Crossref] [PubMed]

Zheludev, N. I.

K. F. MacDonald, Z. L. Samson, M. I. Stockman, and N. I. Zheludev, “Ultrafast active plasmonics,” Nat. Photonics 3(1), 55–58 (2009).
[Crossref]

Zhong, X. L.

M. L. Ren, X. L. Zhong, B. Q. Chen, and Z. Y. Li, “An all-optical diode based on plasmonic attenuation and nonlinear frequency conversion,” Chin. Phys. Lett. 30(9), 097301 (2013).
[Crossref]

Zhou, F.

S. Y. Liu, J. F. Li, F. Zhou, L. Gan, and Z. Y. Li, “Efficient surface plasmon amplification from gain-assisted gold nanorods,” Opt. Lett. 36(7), 1296–1298 (2011).
[Crossref] [PubMed]

J. F. Li, S. Y. Liu, Y. Liu, F. Zhou, and Z. Y. Li, “Anisotropic and enhanced absorptive nonlinearities in a macroscopic film induced by aligned gold nanorods,” Appl. Phys. Lett. 96(26), 263103 (2010).
[Crossref]

F. Zhou, Z. Y. Li, Y. Liu, and Y. N. Xia, “Quantitative Analysis of Dipole and Quadrupole Excitation in the Surface Plasmon Resonance of Metal Nanoparticles,” J. Phys. Chem. C 112(51), 20233–20240 (2008).
[Crossref]

Zijlstra, P.

P. Zijlstra, J. W. M. Chon, and M. Gu, “Five-dimensional optical recording mediated by surface plasmons in gold nanorods,” Nature 459(7245), 410–413 (2009).
[Crossref] [PubMed]

Adv. Opt. Mater. (1)

S. Y. Liu, J. F. Li, and Z. Y. Li, “Macroscopic Polarized Emission from Aligned Hybrid Gold Nanorods Embedded in a Polyvinyl Alcohol Film,” Adv. Opt. Mater. 1(3), 227–231 (2013).
[Crossref]

Appl. Phys. Lett. (1)

J. F. Li, S. Y. Liu, Y. Liu, F. Zhou, and Z. Y. Li, “Anisotropic and enhanced absorptive nonlinearities in a macroscopic film induced by aligned gold nanorods,” Appl. Phys. Lett. 96(26), 263103 (2010).
[Crossref]

Chin. Phys. Lett. (1)

M. L. Ren, X. L. Zhong, B. Q. Chen, and Z. Y. Li, “An all-optical diode based on plasmonic attenuation and nonlinear frequency conversion,” Chin. Phys. Lett. 30(9), 097301 (2013).
[Crossref]

Chin. Sci. Bull.(Chinese Ver.) (1)

Z. Y. Li and J. F. Li, “Recent progress in engineering and application of surface plasmon resonance in metal nanostructures,” Chin. Sci. Bull.(Chinese Ver.) 56(32), 2631 (2011).
[Crossref]

Front. of Phys. (1)

Z. Y. Li, “Nanophotonics in China: Overviews and highlights,” Front. of Phys. 7(6), 601–631 (2012).
[Crossref]

J. Appl. Phys. (1)

B. L. Wang, M. L. Ren, J. F. Li, and Z. Y. Li, “Plasmonic coupling effect between two gold nanospheres for efficient second-harmonic generation,” J. Appl. Phys. 112(8), 083102 (2012).
[Crossref]

J. Opt. Soc. Am. A (1)

J. Phys. Chem. C (2)

F. Zhou, Z. Y. Li, Y. Liu, and Y. N. Xia, “Quantitative Analysis of Dipole and Quadrupole Excitation in the Surface Plasmon Resonance of Metal Nanoparticles,” J. Phys. Chem. C 112(51), 20233–20240 (2008).
[Crossref]

S. Y. Liu, L. Huang, J. F. Li, C. Wang, Q. Li, H. X. Xu, H. L. Guo, Z. M. Meng, Z. Shi, and Z. Y. Li, “Simultaneous Excitation and Emission Enhancement of Fluorescence Assisted by Double Plasmon Modes of Gold Nanorods,” J. Phys. Chem. C 117(20), 10636–10642 (2013).
[Crossref]

Light Sci. Appl. (1)

B. Q. Chen, M. L. Ren, R. J. Liu, C. Zhang, Y. Sheng, B. Q. Ma, and Z. Y. Li, “Simultaneous broadband generation of second and third harmonics from chirped nonlinear photonic crystals,” Light Sci. Appl. 3(7), e189 (2014).
[Crossref]

Nano Lett. (5)

B. J. Wiley, Y. C. Chen, J. M. McLellan, Y. J. Xiong, Z. Y. Li, D. Ginger, and Y. N. Xia, “Synthesis and optical properties of silver nanobars and nanorice,” Nano Lett. 7(4), 1032–1036 (2007).
[Crossref] [PubMed]

C. Shi, S. Soltani, and A. M. Armani, “Gold Nanorod Plasmonic Upconversion Microlaser,” Nano Lett. 13(12), 5827–5831 (2013).
[Crossref] [PubMed]

Q. K. Liu, Y. X. Cui, D. Gardner, X. Li, S. L. He, and I. I. Smalyukh, “Self-Alignment of Plasmonic Gold Nanorods in Reconfigurable Anisotropic Fluids for Tunable Bulk Metamaterial Applications,” Nano Lett. 10(4), 1347–1353 (2010).
[Crossref] [PubMed]

T. Ming, L. Zhao, Z. Yang, H. J. Chen, L. D. Sun, J. F. Wang, and C. H. Yan, “Strong Polarization Dependence of Plasmon-Enhanced Fluorescence on Single Gold Nanorods,” Nano Lett. 9(11), 3896–3903 (2009).
[Crossref] [PubMed]

J. Butet, J. Duboisset, G. Bachelier, I. Russier-Antoine, E. Benichou, C. Jonin, and P. F. Brevet, “Optical Second Harmonic Generation of Single Metallic Nanoparticles Embedded in a Homogeneous Medium,” Nano Lett. 10(5), 1717–1721 (2010).
[Crossref] [PubMed]

Nat. Commun. (1)

M. L. Ren, W. Liu, C. O. Aspetti, L. Sun, and R. Agarwal, “Enhanced second-harmonic generation from metal-integrated semiconductor nanowires via highly confined whispering gallery modes,” Nat. Commun. 5, 5432 (2013).

Nat. Photonics (2)

M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6(11), 737–748 (2012).
[Crossref]

K. F. MacDonald, Z. L. Samson, M. I. Stockman, and N. I. Zheludev, “Ultrafast active plasmonics,” Nat. Photonics 3(1), 55–58 (2009).
[Crossref]

Nature (1)

P. Zijlstra, J. W. M. Chon, and M. Gu, “Five-dimensional optical recording mediated by surface plasmons in gold nanorods,” Nature 459(7245), 410–413 (2009).
[Crossref] [PubMed]

Opt. Express (1)

Opt. Lett. (1)

Photon. Res. (1)

Phys. Rev. B (4)

X. M. Hua and J. I. Gersten, “Theory of 2nd-Harmonic Generation by Small Metal Spheres,” Phys. Rev. B 33(6), 3756–3764 (1986).
[Crossref]

Y. Pavlyukh and W. Hubner, “Nonlinear Mie scattering from spherical particles,” Phys. Rev. B 70(24), 245434 (2004).
[Crossref]

A. G. F. de Beer and S. Roke, “Nonlinear Mie theory for second-harmonic and sum-frequency scattering,” Phys. Rev. B 79(15), 155420 (2009).
[Crossref]

Z. Y. Li, B. Y. Gu, and G. Z. Yang, “Strong localization of near-field second-harmonic generation for nonlinear mesoscopic surface structures,” Phys. Rev. B 59(19), 12622–12626 (1999).
[Crossref]

Phys. Rev. Lett. (5)

A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, “Near-field second-harmonic generation induced by local field enhancement,” Phys. Rev. Lett. 90(1), 013903 (2003).
[Crossref] [PubMed]

J. A. H. van Nieuwstadt, M. Sandtke, R. H. Harmsen, F. B. Segerink, J. C. Prangsma, S. Enoch, and L. Kuipers, “Strong modification of the nonlinear optical response of metallic subwavelength hole arrays,” Phys. Rev. Lett. 97(14), 146102 (2006).
[Crossref] [PubMed]

C. K. Chen, A. R. B. Decastro, and Y. R. Shen, “Surface-Enchanced 2nd-Harmonic Generation,” Phys. Rev. Lett. 46(2), 145–148 (1981).
[Crossref]

H. Harutyunyan, G. Volpe, R. Quidant, and L. Novotny, “Enhancing the Nonlinear Optical Response Using Multifrequency Gold-Nanowire Antennas,” Phys. Rev. Lett. 108(21), 217403 (2012).
[Crossref] [PubMed]

Y. Pu, R. Grange, C. L. Hsieh, and D. Psaltis, “Nonlinear optical properties of core-shell nanocavities for enhanced second-harmonic generation,” Phys. Rev. Lett. 104(20), 207402 (2010).
[Crossref] [PubMed]

Plasmonics (1)

J. Richter, A. Steinbruck, T. Pertsch, A. Tunnermann, and R. Grange, “Plasmonic Core-Shell Nanowires for Enhanced Second-Harmonic Generation,” Plasmonics 8(1), 115–120 (2013).
[Crossref]

Sci Rep (1)

B. L. Wang, R. Wang, R. J. Liu, X. H. Lu, J. M. Zhao, and Z. Y. Li, “Origin of Shape Resonance in Second-Harmonic Generation from Metallic Nanohole Arrays,” Sci Rep 3, 2358 (2013).
[PubMed]

Other (3)

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2006).

J. F. Li and Z. Y. Li, “Manipulation of plasmonic wavefront and light-matter interaction in metallic nanostructures: A brief review,” Chin. Phys. B23, (2014).

R. W. Boyd, Nonlinear Optics (Academic, 2008).

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Figures (4)

Fig. 1
Fig. 1 (a) Schematic diagram of a Ag-coated nanocuboid. The nonlinear core, 16 × 72 × 16 nm3, is lithium niobate (LiNbO3, LN) which is coated by a 5 nm thick Ag shell. The fundamental wave (FW, ω) propagates along the x-direction, and excites second harmonic generation (SHG, 2ω) signal in all directions. (b) Calculated SHG signal in three different cases, Ag-coated LiNbO3 nanocuboid (Ag-LN, yy-z utilizing d32), Ag-LN (yy-y, d22), and bare LN (yy-y, d22) for comparison. Here yy-z representss that the SHG signal with z-component (E2 z ) is excited by FW with E1 y . Assume d32 = d22 = d0. P0 is the unit power.
Fig. 2
Fig. 2 Extinction cross-section (Cext) of Ag-coated and bare LN nanocuboid. (a) Ag-LN under the y-polarized excitation. Insets: diagram of the excitation polarization and enlarged figure of Cext wihtin the wavelength range of 400-500 nm. (b) Ag-LN under the z-polarized excitation. Similar to Panel (a), one of insets shows the enlarged figure of Cext within 800-1000 nm. Bare LN under the y-polarized (c) and z-polarized (d) excitation.
Fig. 3
Fig. 3 Field distribution (yz-plane) of Ag-coated and bare LN nanocuboid at the wavelengths of 900 nm and 450 nm. (a) Ag-LN under the y-polarized excitation and at 900 nm (resonance). (b) Ag-LN under the z-polarized excitation and at 450 nm (resonance). (c) Bare LN under the y-polarized excitation and at 900 nm. (d) Bare LN under the z-polarized excitation and at 450 nm. Here only the LN core (of Ag-LN) is plotted.
Fig. 4
Fig. 4 (a) Excitation polarization dependence of the z-polarized SHG signals. Inset: polarization angle of FW (yz-plane), θ, is set with respect to the y-axis. (b) Calculated SHG signal in the cases of xx-z (utilizing d31) and xx-y (d21) when FW is polarized in the xz-plane (propagating along the y-axis). Assume d31 = d21 = d0.

Equations (13)

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× × E 1 k 1 2 E 1 = k 1 2 P 1 ,
E 1 , j = E 10 , j k j N Α j k P 1 , k ,
A j k P 1 , k = exp ( i k 1 r j k ) r j k 3 { k 1 2 r j k × ( r j k × P 1 , k ) + 1 i k 1 r j k r j k 2 [ r j k 2 P 1 , k 3 r j k ( r j k P 1 , k ) ] } ,
E 10 , j = k = 1 N Α j k P 1 , k .
C s c a = k 1 4 | E 10 | 2 d Ω | k = 1 N [ P 1 , k n k ( n k P 1 , k ) ] exp ( i k 1 n k r k ) | 2 ,
C e x t = 4 π k 1 | E 10 | 2 k = 1 N Im ( E 10 , k * P 1 , k ) .
× × E 2 k 2 2 E 2 = k 2 2 P 2 + k 2 2 P ( 2 ) ,
E 2 , j = E 20 , j k j N B j k P 2 , k ,
B j k P 2 , k = exp ( i k 2 r j k ) r j k 3 { k 2 2 r j k × ( r j k × P 2 , k ) + 1 i k 2 r j k r j k 2 [ r j k 2 P 2 , k 3 r j k ( r j k P 2 , k ) ] } ,
E 20 , j = P j ( 2 ) / α 2 , j k j N B j k P k ( 2 ) ,
P j ( 2 ) = d 3 4 π ε b ( 3 ε b ε m + 2 ε b ) 2 χ ( 2 ) : E 1 , j E 1 , j ,
W s c a k 2 4 d Ω | k = 1 N [ P k n k ( n k P k ) ] exp ( i k 2 n k r k ) | 2 .
( P x ( 2 ) P y ( 2 ) P z ( 2 ) ) = ( d 11 d 12 d 13 d 14 d 15 d 16 d 21 d 22 d 23 d 24 d 25 d 26 d 31 d 32 d 33 d 34 d 35 d 36 ) ( E 1 x 2 E 1 y 2 E 1 z 2 2 E 1 y E 1 z 2 E 1 z E 1 x 2 E 1 x E 1 y ) ,

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