Open Access
Add to BibSonomyAbstract
In this paper, surface plasmon polariton (SPP) modes on silver nanowire (AgNW), with different field symmetric, are studied by different near field methods, respectively. In the experiment, the excitation and detection of SPPs are performed by two probes of near field scanning optical microscope (NSOM) simultaneously, which realizes the study of SPPs in complete near field. By controlling the experimental conditions, two of the fundamental SPP modes are detected separately and their intensity distributions on AgNW are given by the NSOM images. In the discussion, creeping wave (CW) is introduced to analyze the experimental results, which improves the coincidence of the experimental results and the theoretical calculations. A detailed characterization of SPPs modes in near field, which gives a further insight into optical properties of AgNW, will benefit integrated optical circuits.
© 2014 Optical Society of America
1. Introduction
The integration of optical circuits calls for binding light into nanoscale. Surface Plasmon Polariton (SPP) has attracted numerous attentions, since it is collective oscillation of electrons on metal and can be confined in a sub-wavelength volume [1]. SPP is free from light diffraction limit and can propagate along the interface between metal and dielectric, where its energy is bounded. Because of its unique properties, SPP has been used in many areas, such as antenna [2], optical trapping [3], super-resolution imaging [4], invisible cloak [5, 6], and so on. One of the most promising applications is in the photonic integration circuits (PICs).
Silver nanowire (AgNW), as one of the typical SPP nanowaveguide [7–11], holds several advantages for practical applications, such as easy preparation, regular and uniform geometry, and relatively low absorption losses [12, 13]. Great efforts have been devoted to study the optical properties of AgNW, where subwavelength waveguiding [14–18], quantum properties of SPPs [19–21] and information processing [22, 23] have been reported. Those studies are mostly performed through free space excitation or collection, for instance, coupling light from far field to the nanowire end and detecting electromagnetic field by near field scanning optical microscope (NSOM). As a result, the detected SPPs usually contain several modes and the properties of individual mode can not be revealed exactly. In order to give a further insight into SPP on AgNW, it is necessary to study the properties of individual SPP mode experimentally and theoretically.
In this work, complete near field methods, where both excitation and detection of SPPs are performed in near field, are used to study SPPs on AgNW, which realize the separated detection of different SPP modes. In the experiment, a near field scanning optical microscope (NSOM) with two probes is used to study SPP on AgNW, where one probe is used for excitation and the other one for collection. The intensity distributions of SPP2 and SPP3 are given by NSOM images and theoretical analysis is also given for comparison and further study. In the analysis of SPPs on AgNW, we find that creeping wave (CW), one kind of surface wave, may also exist, which changes the intensity distribution of SPPs on AgNW. Such an analysis of SPPs on AgNW will benefit the development of integrated optical circuit, and a more comprehensive analysis is expected.
2. Experimental setup and methods
The AgNW used in the experiment is prepared by chemical method [24, 25]. They have an average diameter of 250 nm and are coated with 25-nm-thick SiO2, as shown in the inset of Fig. 1(a). The alcoholic solution (containing AgNW) is spun on the SiO2 substrate and covered with 50-nm-thick Polymethyle Methacrylate (PMMA) after volatilization.
Fig. 1 The schematic of the studied structure. (a) The cross section of SiO2-coated AgNW covered by a layer of PMMA on SiO2 substrate (not to scale). The inset is the SEM image of SiO2-coated AgNW. (b) and (c) The experimental setups of SE and DE methods, respectively. (d)–(f) The electric field distributions of SPP1, SPP2 and SPP3, respectively, on the cross section of AgNW.
In the experiment, two Au/Cr–coated NSOM probes are utilized simultaneously, with the excitation probe connected to the Laser at λ = 671 nm and the collection probe connected to an Avalanche Photo Diode (APD). The tip diameters are 100 nm for the collection probe and 200 nm for the excitation probe. Two MultiView 4000TM systems control the probes independently and acquire data to produce topography and NSOM images [26, 27]. To study surface waves on the AgNW, two different methods are adopted: (1) dynamic collection and static excitation (SE), (2) static collection and dynamic excitation (DE). In the SE method as shown in Fig. 1(b), surface waves are excited by the NSOM probe resting on one end facet of AgNW and are detected by the other probe scanning along the AgNW. While in the DE method as shown in Fig. 1(c), surface waves are excited by the scanning probe and collected by the static probe at the end facet of AgNW.
The cross section of the studied structure is illustrated in Fig. 1(a). For uniform AgNW, SPP modes could be excited and propagate along it with their electric field varying as e−iωt+i2πneffz/λ, where ω and λ are laser frequency and vacuum wavelength. Here, the effective mode refractive index neff is a complex number, whose real and imaginary parts relate to propagation phase evolution and loss. With finite element method, we numerically calculated three bounded propagation modes of the AgNW, which are signed as SPP1, SPP2 and SPP3, with the electric field distributions shown in Figs. 1(d)–1(f). The effective refractive indices are n1 = 1.67 + 0.0138i, n2 = 1.53 + 0.0113i and n3 = 1.48 + 0.0116i for SPP1, SPP2 and SPP3, respectively. In the simulation, the permittivity of Ag is −18.445 + 1.203i corresponding to λ = 671 nm, and the indexes of SiO2 and PMMA are 1.47 and 1.49, respectively [28].
3. Results and discussions
Figure 2(a) gives the NSOM image of surface waves on a 5-μm-long AgNW obtained by SE method, with a three-dimensional intensity image in the inset. There are several obvious intensity nodes along the AgNW and a big peak at the end facet. The intensity profile along blue dashed cut line is plotted in Fig. 2(b). From the excitation end (down left) to the distal end (up right) of the AgNW, the average intensity of surface waves decays at first and recovers near the distal end, with an intensity node period (distance between adjacent nodes) about 267 nm.
Fig. 2 Experimental result of surface waves detected by SE method. (a) NSOM image of AgNW detected by SE method. The inset is three-dimensional intensity image of surface waves. (b) Intensity profile of surface waves on AgNW. The red solid line is intensity profile of surface waves along the blue dashed cut line in (a). The black (purple) solid line is the calculated result fitted with SPP3 and CW (only SPP3 with a normalized intensity offset of −0.2). The inset is the illustration of surface waves propagating on AgNW with SE method. S and C are the end facets of AgNW. D is a point on the surface of AgNW.
In the SE method, the excitation probe is at the end facet S of AgNW as shown in the inset of Fig. 2(b). Since the probe is Au/Cr–coated, it can work as a metal antenna to enhance the coupling efficiency [11, 29]. The excitation polarization is manipulated to make SPP1 and SPP3 modes being excited efficiently. Since SPP2 is an odd symmetric mode and its excitation polarization is different from those of SPP1 and SPP3 [17], the excitation of SPP2 is neglected in the SE method. What is more, SPP1 is difficult to be detected since its energy is mostly localized on the interface between AgNW and SiO2 substrate. The effective mode area of SPP1 is about 0.028 μm2 [16, 30]. while the distance between the location of SPP1 and the detection probe is about 350 nm, which make the intensity of SPP1 attenuate dramatically to be 0.03 in the unit of that in the interface. So the energy of SPP1 detected by the probe can also be neglected, and it is reasonable to suppose that SPP3 mainly determines the energy distribution on the AgNW except at the end facet as shown in Fig. 2(a). When SPP3 reaches the end facet, it will be scattered and reflected, thus counter-propagating SPP3 mode is involved, too. Then, the field detected by the scanning probe can be described as
where is the vacuum wave vector, Ã3 is the detected field amplitude of SPP3, and η3 is the detected amplitude of backward SPP3. Note that, the field at end facet C is very complex and can not be simply described by Eq. (1), which is only applicable for the electric field on the uniform side surface. According to Eq. (1), a calculated field intensity distribution is given by I(z) = |Edet,SPP3(z)|2 with Ã3 = 10.0 and η3 = 1.0, as shown by the purple curve in Fig. 2(b) (offset −0.2 for clarity).It should be noted that, there is a modulation on the envelope of the detected intensity, which does not exist on the calculated result, where only SPP3 is considered. What is more, the detected period of intensity nodes (267 nm) greatly shifts from the interference period caused by counter-propagating SPP3, which is 232nm obtained by λ/2Re (n3). So it is supposed that some other kind of surface waves are detected together with SPP3. In previous studies of near field optics, creeping wave (CW), which accompanies with the excitation of SPPs, has been found to play an important role in surface waves on flat metallic surface [31–34]. It is transverse wave propagating along the surface of metal with its amplitude suffering a attenuation, with z being the distance from the excitation point [33]. Therefore, we take CW into consideration when analyzing SPP modes on AgNW. Since the length of the studied AgNW is short, the model of CW can be taken as an approximate field form of for simplicity, with a propagation length of 1–2 μm, and a propagation wave vector kCW ≈ k0. Then the field detected by the scanning probe in the SE method can be given as
where ÃCW is the detected field amplitude of CW. Considering the effect of CW, a revised result is given by I(z) = |Edet,tot (z)|2, as shown by the black curve in Fig. 2(b), with ÃCW = 12.0, Ã3 = 1.0 and η3 = 4.2. The intensity node period of the fitted black curve is more consistent with the experimental result (red line), compared with the purple curve given by Eq. (1). Besides, the period of the calculated intensity nodes is 260 nm as considering CW, which agrees well with the experimental result 267 nm. It should be noted that, the beating phenomenon between SPP3 and CW (1.4 μm) is not obvious in the detected intensity profile (red line), which may attribute to experimental noise and ambient disturbance.To further study the SPPs on AgNW, we investigated another 6-μm-length AgNW by DE method, where the collection probe is resting at the left end facet (S) and the excitation probe scans along the AgNW with an optimized excitation polarization for SPP2. When the probe reaches one side of the AgNW, the electric field polarized on x-direction excites SPP2 efficiently. The excitation probe used in the DE method is an asymmetric excitation source, which is different from the case in the SE method that the excitation probe is a symmetric excitation source. To make SPP2 being detected efficiently, the detection probe is positioned on the end facet with a small departure from the center, since the intensity distribution of different SPP modes on the cross section of the AgNW are different. The intensity of the NSOM image in Fig. 3(a) corresponds to the signal detected at the end facet S. In contrast to the SE method, there is almost no signal detected when the excitation probe is directly over the AgNW [35], and the intensity distribution around the AgNW is separated into two parallel parts. The intensity along the blue dashed cut line in Fig. 3(a) is shown in Fig. 3(b). It decays rapidly and then resonates with a big peak at the right end, with intensity node period of 253 nm and beating period of 1.1 μm. Compared to SPP3 on the 5-μm-length AgNW, the beating phenomenon is prominent for SPP2 on the 6-μm-length AgNW, which may attribute to the relative less influence of the end facet in a longer AgNW.
Fig. 3 Experimental result of surface waves detected by DE method. (a) NSOM image of AgNW detected by DE method. (b) Intensity profile of surface waves on AgNW. The red line is detected intensity profile of surface waves along the blue dashed cut line in (a). The black (purple) solid line is the calculated result fitted with SPP2 and CW (SPP2 only, with an normalized intensity offset of −0.2). The inset is the illustration of surface waves propagating along AgNW.
With DE method, the detected field can be given as
where B̃CW and B̃2 are the detected amplitudes of CW and SPP2 from the excited probe, respectively, η2 is the detected amplitude of backward SPP2 due to the reflection at end facet C.We plot the intensity profile according to Eq. (3) with B̃CW = 8.7, B̃2 = 1.0 and η2 = 3.9, as shown in Fig. 3(b) (black solid curve). The calculated curve agrees well with the detected intensity profile except the abrupt enhancement near the end facet C, which corresponds to enhanced excitation of CW and SPP modes at the AgNW end facet. The well agreement shows a definite evidence of the co-existence of SPPs and CW, which can be further confirmed by the unmatched purple solid line fitted only with SPP2 mode as shown in Fig. 3(b). We can see that, CW accounts for the main part of surface waves since B̃CW is much bigger than B̃2. Regardless of the end peak, the propagation length of surface waves on AgNW is fitted to be 1.3 μm, which is between those of CW and SPP3.
4. Conclusions
In this work, different SPP modes on AgNW are studied in near field separately, and a reasonable theoretical analysis is given as well. SPP2 and SPP3 on AgNW are identified by DE and SE methods respectively, which are both realized by two NSOM probes. What is more, CW is taken into consideration in the analysis of SPP on AgNW, which improves the consistence of theoretical and experimental results. Such an analysis of individual SPP mode propagating along the AgNW is important for information transmission, which will promote the application of AgNW in nano-optical circuits.
Acknowledgments
This work was funded by NBRP (grant nos. 2011CBA00200 and 2011CB921200), the Innovation Funds from the Chinese Academy of Sciences (grant no. 60921091), NNSF (grant nos. 10904137, 10934006 and 11374289), the Fundamental Research Funds for the Central Universities (grant no. WK2470000005), and NCET. H.T.L acknowledges financial supports from 973 Program ( 2013CB328701), NSFC ( 61322508) and NSFT ( 11JCZDJC15400). A.P.L acknowledges financial supports from NNSF (grant nos. 11274178, 11311140250 and 61475197), the Scientific Research Foundation of Nanjing University of Posts and Telecommunications (grant no. NY212011).
References and links
1. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998). [CrossRef]
2. J. Dorfmülle, R. Vogelgesang, W. Khunsin, C. Rockstuhl, C. Etrich, and K. Kern, “Plasmonic nanowire antennas: experiment, simulation, and theory,” Nano Lett. 10, 3596–3603 (2010). [CrossRef]
3. K. Wang, E. Schonbrun, P. Steinvurzel, and K. B. Crozier, “Scannable plasmonic trapping using a gold stripe,” Nano Lett. 10, 3506–3511 (2010). [CrossRef] [PubMed]
4. N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308, 534–537 (2005). [CrossRef] [PubMed]
5. H. F. Ma and T. J. Cui, “Three-dimensional broadband ground-plane cloak made of metamaterials,” Nat. Commun. 1, 21 (2010). [CrossRef] [PubMed]
6. X. Chen, Y. Luo, J. Zhang, K. Jiang, J. B. Pendry, and S. Zhang, “Macroscopic invisibility cloaking of visible light,” Nat. Commun. 2, 176 (2011). [CrossRef] [PubMed]
7. J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter,” Opt. Lett. 22, 475–477 (1997). [CrossRef] [PubMed]
8. H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95, 257403 (2005). [CrossRef] [PubMed]
9. A. L. Pyayt, B. Wiley, Y. Xia, A. Chen, and L. Dalton, “Integration of photonic and silver nanowire plasmonic waveguides,” Nat. Nanotech. 3, 660–665 (2008). [CrossRef]
10. C.-H. Dong, X.-F. Ren, R. Yang, J.-Y. Duan, J.-G. Guan, G.-C. Guo, and G.-P. Guo, “Coupling of light from an optical fiber taper into silver nanowires,” Appl. Phys. Lett. 95, 221109 (2009). [CrossRef]
11. Z. Fang, L. Fan, C. Lin, D. Zhang, A. J. Meixner, and X. Zhu, “Plasmonic coupling of bow tie antennas with Ag nanowire,” Nano Lett. 11, 1676–1680 (2011). [CrossRef] [PubMed]
12. X. Guo, Y. Ma, Y. Wang, and L. Tong, “Nanowire plasmonic waveguides, circuits and devices,” Laser Photon. Rev. 7, 855–881 (2013). [CrossRef]
13. X. Xiong, C.-L. Zou, X.-F. Ren, A.-P. Liu, Y.-X. Ye, F.-W. Sun, and G.-C. Guo, “Silver nanowires for photonics applications,” Laser Photon. Rev. 7, 901–919 (2013). [CrossRef]
14. A. W. Sanders, D. A. Routenberg, B. J. Wiley, Y. Xia, E. R. Dufresne, and M. A. Reed, “Observation of plasmon propagation, redirection, and Fan-out in silver nanowires,” Nano Lett. 6, 1822–1826 (2006). [CrossRef] [PubMed]
15. D. Solis, W.-S. Chang, B. P. Khanal, K. Bao, P. Nordlander, E. R. Zubarev, and S. Link, “Bleach-imaged plasmon propagation (BlIPP) in single gold nanowires,” Nano Lett. 10, 3482–3485 (2010). [CrossRef] [PubMed]
16. C. L. Zou, F. W. Sun, Y. F. Xiao, C. H. Dong, X. D. Chen, J. M. Cui, Q. Gong, Z. F. Han, and G. C. Guo, “Plasmon modes of silver nanowire on a silica substrate,” Appl. Phys. Lett. 97, 183102 (2010). [CrossRef]
17. S. Zhang, H. Wei, K. Bao, U. Håkanson, N. J. Halas, P. Nordlander, and H. Xu, “Chiral surface plasmon polaritons on metallic nanowires,” Phys. Rev. Lett. 107, 096801 (2011). [CrossRef] [PubMed]
18. A. Paul, D. Solis, K. Bao, W.-S. Chang, S. Nauert, L. Vidgerman, E. R. Zubarev, P. Nordlander, and S. Link, “Identification of higher order long-propagation-length surface plasmon polariton modes in chemically prepared gold nanowires,” ACS Nano 6, 8105–8113 (2012). [CrossRef] [PubMed]
19. A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, “Generation of single optical plasmons in metallic nanowires coupled to quantum dots,” Nature 450, 402–406 (2007). [CrossRef] [PubMed]
20. R. Kolesov, B. Grotz, G. Balasubramanian, R. J. Stöhr, A. A. L. Nicolet, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, “Wave-particle duality of single surface plasmon polaritons,” Nat. Phys. 5, 470–474 (2009). [CrossRef]
21. A. L. Falk, F. H. L. Koppens, C. L. Yu, K. Kang, N. de Leon Snapp, A. V. Akimov, M.-H. Jo, M. D. Lukin, and H. Park, “Near-field electrical detection of optical plasmons and single-plasmon sources,” Nat. Phys. 5, 475–479 (2009). [CrossRef]
22. H. Wei, Z. Wang, X. Tian, M. Käll, and H. Xu, “Cascaded logic gates in nanophotonic plasmon networks,” Nat. Commun. 2, 387 (2011). [CrossRef] [PubMed]
23. H. Wei, S. Zhang, X. Tian, and H. Xu, “Highly tunable propagating surface plasmons on supported silver nanowires,” PNAS 110, 4494–4499 (2013). [CrossRef] [PubMed]
24. Y. Sun and Y. Xia, “Large-scale synthesis of uniform silver nanowires through a soft, self-seeding, polyol process,” Adv. Mater. 14, 833–837 (2002). [CrossRef]
25. Y. Yin, Y. Lu, Y. Sun, and Y. Xia, “Silver nanowires can be directly coated with amorphous silica to generate well-controlled coaxial nanocables of silver/silica,” Nano Lett. 2, 427–430 (2002). [CrossRef]
26. R. Dallapiccola, C. Dubois, A. Gopinath, F. Stellacci, and L. Dal Negro, “Near-field excitation and near-field detection of propagating surface plasmon polaritons on Au waveguide structures,” Appl. Phys. Lett. 94, 243118 (2009). [CrossRef]
27. X. Ren, A. Liu, C. Zou, L. Wang, Y. Cai, F. Sun, G. Guo, and G. Guo, “Interference of surface plasmon polaritons from a “point” source,” Appl. Phys. Lett. 98, 201113 (2011). [CrossRef]
28. E. D. Palik, Handbook of Optical Constants of Solids (Academic, New York, 1998).
29. Z. Fand, Y. Lu, L. Fan, C. Lin, and X. Zhu, “Surface plasmon polariton enhancement in silver nanowire-nanoatenna structure,” Plasmonics 5, 57–62 (2010). [CrossRef]
30. Y. Wang, Y. Ma, X. Guo, and L. Tong, “Single-mode plasmonic waveguiding properties of metal nanowires with dielectric substrates,” Opt. Express 20, 19006–19015 (2012). [CrossRef] [PubMed]
31. G. Gay, O. Alloschery, B. Viaris de Lesegno, C. O’Dwyer, J. Weiner, and H. J. Lezec, “The optical response of nanostructured surfaces and the composite diffracted evanescent wave model,” Nat. Phys. 2, 262–267 (2006). [CrossRef]
32. P. Lalanne and J. P. Hugonin, “Interaction between optical nano-objects at metallo-dielectric interfaces,” Nat. Phys. 2, 551–556 (2006). [CrossRef]
33. H. Liu and P. Lalanne, “Microscopic theory of the extraordinary optical transmission,” Nature 452, 728–731 (2008). [CrossRef] [PubMed]
34. X. Y. Yang, H. T. Liu, and P. Lalanne, “Cross conversion between surface plasmon polaritons and quasicylindrical waves,” Phys. Rev. Lett. 102, 153903 (2009). [CrossRef] [PubMed]
35. N. Liu, Z. Li, and H. Xu, “Polarization-dependent study on propagating surface plasmons in silver nanowires launched by a near-field scanning optical fiber tip,” Small 8, 2641–2646 (2012). [CrossRef] [PubMed]
