Open Access
Add to BibSonomyAbstract
We report a hybrid plasmonic waveguide consisting of a nanofiber coupled with a copper film on a silicon substrate. The nanofiber can be flexibly placed on the copper film to generate a highly localized optical field. Due to the easy attachment of the nanofiber to the metal surface, it is convenient to reconfigure the hybrid plasmonic waveguide. We investigate two waveguide systems with either a straight or a curved nanofiber coupled with the copper film. The straight nanofiber could excite two hybrid plasmonic modes, leading to periodic field oscillation along the metal surface. In contrast, the curved nanofiber can only excite the fundamental mode, owing to the adiabatic mode conversion before the hybrid waveguide. The propagation loss of the fundamental hybrid plasmonic mode is measured to be around 25.32 dB/mm for a nanofiber radius of 0.8 μm.
© 2015 Optical Society of America
1. Introduction
Surface plasmon-polaritons (SPP) [1–7] are attracting more and more attentions due to the field intensity enhancement at the interface and the ability to confine light beyond the diffraction limit. However, there is a tradeoff between the propagation loss and field confinement for SPP waveguides [8–11]. Deep sub-wavelength confinement of light is often obtained at the expense of large propagation loss [12]. On the other hand, the high propagation loss always inhibits the practical use of SPP waveguides. In order to get a relatively long propagation distance under a reasonably high confinement [1, 13], a variety of hybrid plasmonic waveguide (HPWG) structures have been explored, such as a SOI ridge waveguide clad by a metal cap with a silica spacer [14, 15], a hybrid waveguide in a metal V-groove [16, 17], a triangle hybrid plasmonic waveguide [18], a hybrid waveguide on a metallic bump structure [19], and a cylindrical hybrid waveguide [20]. As the optical field is strong near the metal surface, the light-matter interaction is greatly enhanced. The HPWG could be used in a variety of devices, for instance, passive integrated devices [21, 22], modulators and switches [7], nonlinear devices [23], sensors [24, 25], and nanofocusing devices [26].
The HPWGs mentioned above have a low propagation loss and meanwhile maintain a high optical confinement. However, it is quite challenging to excite hybrid plasmonic modes due to the mismatch of light momentum with that of regular waveguides. In this paper, we propose a HPWG consisting of a nanofiber situated on a copper (Cu) substrate. The hybrid plasmonic mode is generated due to the coupling between the nanofiber dielectric mode and the metal SPP mode. The nanofiber can be freely moved on the Cu film, making it flexible to adjust the waveguide length and position. This is a quite good merit when a local light-matter interaction, e.g., molecular Raman scattering or quantum electrodynamics, is to be studied on a special positon. The paper is organized as follows. In section 2, we introduce two waveguide systems that can both excite hybrid plasmonic modes. Eigenmode analysis and optical wave propagation are conducted. Section 3 describes the experimental characterization of both waveguide systems. The measurement results are compared to the simulation ones. Section 4 concludes our work.
2. Waveguide structures and simulations
As the nanofiber is very flexible and easily bent, it could reside on the Cu film in two different fashions as schematically shown in Figs. 1(a) and 1(b). In Fig. 1(a), the nanofiber is pulled straight to contact the Cu film. In Fig. 1(b), the nanofiber is loosed slightly to form a bend with the apex touching the Cu film. The attachment of the nanofiber to the Cu surface is enabled by Van der Waals and electrostatic forces [23]. Although the HPWGs in the two systems are similar, the mode excitation is different as we will show later. A good merit of the HPWGs lies in its easy mobility and reconfiguration. The nanofiber can be drawn from a standard single mode fiber (SMF) [27–29], featuring direct connection to fiber-optic systems with low loss. With an adiabatic taper, the conversation efficiency between the SMF and the nanofiber can exceed 99% [21]. The HPWG length is denoted as L, determined either by the Cu film size (straight nanofiber case) or by the contact length (curved nanofiber case). Figure 1(c) shows the cross-section of the HPWG. The nanofiber has a radius of R and the Cu film has a thickness of 200 nm which is thick enough so that the optical field will not penetrate through it.
Fig. 1 (a) and (b) Schematic diagrams of the two HPWG systems in which either (a) a straight nanofiber or (b) a curved nanofiber is attached to the metal film. (c) Cross-sectional structure of the HPWG.
2.1 Hybrid plasmonic modes
We first use the finite-difference time-domain (FDTD) simulation to numerically study the basic modal properties of the HPWG. The permittivity of Cu is assumed to be εCu = −166 + 28.6i around 1550 nm wavelength [30]. The silica fiber has a permittivity of εsilica = 2.08. Figure 2 shows the electric-field intensity profiles for the first two transverse-magnetic (TM) and transverse-electric (TE) modes with R = 0.7 μm. Here, the TM mode is defined as the one whose major electric field is perpendicular to the Cu film, and TE mode is the one with its major electric field parallel to the Cu film. The hybrid plasmonic modes are excited only when the incident light is TM polarized. The effective refractive indices of the TM0 (fundamental) and TM1 (first order) mode are 1.326 + 0.00125i and 1.125 + 0.00175i, respectively. It can be seen that the electric field is greatly enhanced near the Cu film, and in particular, there are two sharp field peaks in the air slots beside the fiber contact point. The enhancement of the electric field is contributed both by the SPP excitation and the electric field discontinuity at the air-silica interface. When the incident light is TE polarized, only the dielectric fiber mode is excited with additional loss incurred from the metal film. The effective refractive indices of the TE0 and TE1 modes are 1.26 + 0.00016i and 1.02 + 0.00022i, respectively. In contrast to the TM modes, the intensity maximum of TE modes is at the center (TE0) or at the air-silica interface along the x-axis (TE1) rather than at the metal surface. Because they have less interaction with the metal film, the TE modes have a lower propagation loss than the TM modes.
Fig. 2 Calculated electric field intensity profiles for (a) TM0, (b) TM1, (c) TE0, and (d) TE1 modes of the HPWG.
The effective refractive indices of the HPWG modes are dependent on the nanofiber radius as shown in Figs. 3(a) and 3(b). The real part of the effective index decreases with the reduced nanofiber radius, which is expectable since more light is squeezed from the fiber to the air. The TE1 mode is cut off at R = 0.7 μm and TM1 mode at R = 0.55 μm. The modal losses for TM0, TE0, and TE1 all increase with the reduced radius. However, the TM1 mode has a loss peak around R = 0.7 μm.
Fig. 3 (a) Effective refractive index (real part) and (b) propagation loss of the lowest four modes as a function of nanofiber radius.
To investigate the origin of the abnormality in TM1 loss, we plot its electric field intensity distribution along x = 0 for different radii as shown in Fig. 4. The mode profile exhibits three peaks at the two material interfaces as well as in the nanofiber core. When the nanofiber radius is 0.9 μm, a large part of optical power is located in the silica core. When the radius is reduced to 0.7 μm, the optical field is squeezed to interact more with the metal film, leading to a higher loss. However, further decreasing the radius to 0.6 μm results in less confinement of light in the nanofiber with a large part extending to the air cladding, leading to a reduced loss.
Fig. 4 Electric field intensity distribution along x = 0 for the TM1 mode. (a) R = 0.9 μm; (b) R = 0.8 μm; (c) R = 0.7 μm; (d) R = 0.6 μm.
2.2 Straight nanofiber HPWG system
Next we study the optical field propagation in the straight nanofiber HPWG system by using 3D FDTD simulations. When the input light is TE polarized, the hybrid plasmonic mode will not be excited and the optical power is transmitted primarily in the nanofiber. Figure 5(a) shows the electric field intensity pattern along the propagation direction when the nanofiber TE mode is launched. The nanofiber radius is 0.7 μm. Reflection occurs at the entrance interface of the HPWG, leading to standing-wave pattern in the input nanofiber. As the TE mode has low interaction with the metal, the transmission loss is relatively low, with 83.9% optical power transmitted through the 80 μm long HPWG. Negligible radiation leakage is observed at the interface. When the nanofiber TM mode is launched from the input end, the hybrid plasmonic mode will be excited as shown in Fig. 5(b). There is also some back reflection occurred at the interface and no significant radiation leakage is observed. The electric field is significantly enhanced at the nanofiber-metal interface compared to the incident field in the nanofiber. The maximum field intensity enhancement can be up to ~8 times. It is also observable that the electric field oscillates between the metal surface and the nanofiber core in the HPWG, owing to the co-excitation of the first two hybrid plasmonic modes. To more clearly show the oscillation and attenuation of the electric field, we plot the one dimensional field distribution at the metal surface in Fig. 5(c). The large oscillation is originated from the mode beating and the tiny fringe imposed on it is due to the Fabry-Perot resonances formed by the two HPWG facets. The field weakens more rapidly along the propagation direction compared to the TE mode, as the light field in the plasmonic mode strongly interacts with the electrons in the metal.
Fig. 5 (a) and (b) Electric field intensity pattern in the y-z plane with (a) TE and (b) TM mode excitation in the straight nanofiber system. (c) Electric field intensity along a cut-line at y = 0 for the TM mode excitation.
There are only two TM modes present in the 0.7-μm-radius nanofiber. Therefore, the electric field in the HPWG can be expressed as:
where k0 = 2π/λ0 is the free space propagation constant, neff1,2 are the effective refractive indices (real part) of the two hybrid plasmonic modes, α1,2 are the power attenuation coefficients of the two modes, C1,2 are the coupling coefficients from the nanofiber mode to the HPWG modes. C1,2 can be calculated from the overlap integral aswhere is the electric field of the nanofiber mode, are the magnetic fields of HPWG modes, S is the infinite cross-section, is the unit vector in the propagation direction. The fields are all normalized. At the exit end of the HPWG, the hybrid plasmonic modes convert back to the nanofiber mode, and therefore the electric field in the nanofiber is given byOne sees that the beating of two modes gives rise to the optical power oscillation along the metal surface. The oscillation period Λ is determined the effective index difference of the two plasmonic modes, and is given byFrom Fig. 5(c), we get Λ = 7.58 μm at λ0 = 1550 nm, and therefore, Δneff is deduced to be around 0.2, consistent with the mode simulation.2.3 Curved nanofiber HPWG system
We next study the optical field propagation in the curved nanofiber HPWG system. Figure 6 shows the electric field intensity along the light propagation direction. The nanofiber core radius is 0.8 μm and the bending radius is 1 mm. The curved part of the nanofiber works as a adiabatic mode converter between the dielectric and the hybrid plasmonic modes. It can be seen that the optical power on the metal surface gradually increases before the nanofiber touch point (z = 15 μm). In this case, the fundamental hybrid plasmonic mode is dominantly excited with in Eq. (1). No significant optical field oscillation is observed in the HPWG.
Fig. 6 Electric field intensity pattern in the y-z plane with TM dielectric mode excitation in the curved nanofiber system.
3. Experiments
Figures 7(a) and 7(b) show the photo of the experimental setup to characterize the HPWG. A tunable laser was used as the light source with its polarization controlled by a polarization controller. The laser wavelength was scanned from 1530 nm to 1560 nm and the output spectrum was recorded by an optical spectrum analyzer. The nanofiber with a radius of around 0.7 μm, measured from the scanning electron microscope (SEM) image, is clamped and pulled straight by two high-precision translation stages. The chip was prepared by sputtering-deposition of a Cu film on a silicon carrier just before experiment to avoid surface oxidation. The chip was carried by another translation stage and positioned below the nanofiber.
Fig. 7 (a) Experimental setup to characterize the HPWG. (b) Zoom in microscope view of the nanofiber residing on top of a Cu-coated silicon chip. (c) Normalized transmission spectra of the HPWG for TE and TM polarizations. The contact length L is around 1.1 mm.
We first measured light transmission through the nanofiber without coupling with the Cu film. Then the chip was elevated to approach the nanofiber. In principle, as long as the Cu film surface is clean and flat, the nanofiber can tightly cling to it without any gap due to the Van der Waals and electrostatic forces. By adjusting the polarization controller with the wavelength fixed at 1550 nm, we got high transmission for TE polarization and low transmission for TM polarization. Figure 7(c) shows the TE and TM transmission spectra normalized to the nanofiber for a HPWG length of 1.1 mm. The TM mode has a loss of about 30 dB higher than the TE mode around 1550 nm. The loss of the TM mode is about 31.5 dB/mm, which is smaller than the simulation value of 43.94 dB/mm. The deviation might be due to the uncertainty in fiber radius measurement (through SEM image) or the Cu surface defect-induced loose contact of nanofiber with the Cu film. Its spectrum exhibits periodic fluctuation with a free spectral range (FSR) of 10.3 nm, which is due to the beating of the two TM modes as analyzed previously. From the FSR and the contact length, we derive the effective refractive index difference to be Δneff = λ2/(FSR·L) = 0.21, consistent with the simulation result. The TM transmission increases when the wavelength is away from 1550 nm because we used single mode fiber whose polarization is not maintained. Slight polarization deviation from TM mode will increase the transmission.
To build the curved nanofiber HPWG system, we moved the two translation stages closer so that the nanofiber becomes curved. The contact length L is tunable by adjusting the vertical position of the chip. Figures 8(a) and 8(b) show the side and top optical microscope images of the HPWG. The nanofiber radius in this experiment is around 0.8 μm. The normalized transmission spectra for TE and TM polarizations are presented in Fig. 8(c). It can be seen that smooth spectra are obtained for both polarizations. It suggests that the curved nanofiber allows for adiabatic mode conversion from the dielectric mode to the fundamental hybrid plasmonic mode, as predicted by the FDTD simulation in Fig. 6.
Fig. 8 (a) Side-view photograph of a curved nanofiber residing on a Cu film. The mirror image of the nanofiber is formed at the Cu film surface. (b) Top-view photograph of the contact region. (c) Transmission spectra for TE and TM polarizations. The contact length L is around 1.09 mm. (d) Loss of TE and TM transmissions as a function of L. The dots are measurement results and the straight lines are linear fitting lines.
To obtain the HPWG propagation loss, we measured the insertion loss for various contact lengths as shown in Fig. 8(d). The TM loss rises faster with the increasing contact length than the TE loss does. From the slope of the linear fitting, we get the propagation losses of 25.32 dB/mm (TE) and 5.43 dB/mm (TM). The measured values are smaller than the simulation ones of about 35.3 dB/mm (TE) and 3.8 dB/mm (TM).
4. Conclusion
In summary, we have investigated flexible hybrid plasmonic waveguide systems composed of a nanofiber situated on a Cu film. The nanofiber can either be straight or curved in coupling with the Cu film. For the straight nanofiber system, it can excite high order hybrid plasmonic modes if the radius is larger than 0.55 μm due to the abrupt junction at the HPWG interfaces. In contrast, the curved nanofiber can only excite the fundamental mode, as the fiber bending provides natural mode conversion from the dielectric nanofiber mode to the fundamental hybrid plasmonic mode. We performed experiments on both waveguide systems, and measurement indicates that TE and TM excitations have significant loss difference. The straight nanofiber system exhibits sinusoidal TM transmission spectrum due to the mode beating occurred in the HPWG. Measurement of the curved nanofiber system reveals that the TM hybrid mode loss is about 25.32 dB/mm and TE loss 5.43 dB/mm for a nanofiber radius of 0.8 μm. The hybrid plasmonic waveguide platform provides an effective way to study the highly localized light-matter interaction and nonlinear effects. Moreover, the flexibility in construction makes it cost-effective to build such a hybrid waveguide system.
Acknowledgment
This work was supported in part by the 973 program (ID2011CB301700), the 863 program (2013AA014402), the National Natural Science Foundation of China (NSFC) (61422508) and SRFDP of MOE (Grant No. 20130073130005).
References and links
1. R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008). [CrossRef]
2. C. Delacour, S. Blaize, P. Grosse, J. M. Fedeli, A. Bruyant, R. Salas-Montiel, G. Lerondel, and A. Chelnokov, “Efficient directional coupling between silicon and copper plasmonic nanoslot waveguides: toward metal-oxide-silicon nanophotonics,” Nano Lett. 10(8), 2922–2926 (2010). [CrossRef] [PubMed]
3. M. Février, P. Gogol, G. Barbillon, A. Aassime, R. Mégy, B. Bartenlian, J. M. Lourtioz, and B. Dagens, “Integration of short gold nanoparticles chain on SOI waveguide toward compact integrated bio-sensors,” Opt. Express 20(16), 17402–17410 (2012). [CrossRef] [PubMed]
4. I. Goykhman, B. Desiatov, and U. Levy, “Experimental demonstration of locally oxidized hybrid silicon-plasmonic waveguide,” Appl. Phys. Lett. 97(14), 141106 (2010). [CrossRef]
5. Z. Han, A. Y. Elezzabi, and V. Van, “Experimental realization of subwavelength plasmonic slot waveguides on a silicon platform,” Opt. Lett. 35(4), 502–504 (2010). [CrossRef] [PubMed]
6. C. C. Huang, “Ultra-long-range symmetric plasmonic waveguide for high-density and compact photonic devices,” Opt. Express 21(24), 29544–29557 (2013). [CrossRef] [PubMed]
7. X. Sun, L. Zhou, X. Li, Z. Hong, and J. Chen, “Design and analysis of a phase modulator based on a metal-polymer-silicon hybrid plasmonic waveguide,” Appl. Opt. 50(20), 3428–3434 (2011). [CrossRef] [PubMed]
8. Y. Song, J. Wang, Q. Li, M. Yan, and M. Qiu, “Broadband coupler between silicon waveguide and hybrid plasmonic waveguide,” Opt. Express 18(12), 13173–13179 (2010). [CrossRef] [PubMed]
9. Y. Wang, Y. Ma, X. Guo, and L. Tong, “Single-mode plasmonic waveguiding properties of metal nanowires with dielectric substrates,” Opt. Express 20(17), 19006–19015 (2012). [CrossRef] [PubMed]
10. M. Wu, Z. Han, and V. Van, “Conductor-gap-silicon plasmonic waveguides and passive components at subwavelength scale,” Opt. Express 18(11), 11728–11736 (2010). [CrossRef] [PubMed]
11. R. Yang, R. A. Wahsheh, Z. Lu, and M. A. G. Abushagur, “Efficient light coupling between dielectric slot waveguide and plasmonic slot waveguide,” Opt. Lett. 35(5), 649–651 (2010). [CrossRef] [PubMed]
12. X. Li, X. Guo, D. Wang, and L. Tong, “Propagation losses in gold nanowires,” Opt. Commun. 323, 119–122 (2014). [CrossRef]
13. J. M. M Z. Alam, J S. Aitchison, and M Mojahedi “Super mode propagation in low index medium,” Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper JThD112 (2007).
14. D. Dai and S. He, “A silicon-based hybrid plasmonic waveguide with a metal cap for a nano-scale light confinement,” Opt. Express 17(19), 16646–16653 (2009). [CrossRef] [PubMed]
15. D. Dai, Z. Wang, N. Julian, and J. E. Bowers, “Compact broadband polarizer based on shallowly-etched silicon-on-insulator ridge optical waveguides,” Opt. Express 18(26), 27404–27415 (2010). [PubMed]
16. M. Z. Alam, J. S. Aitchison, and M. Mojahedi, “A marriage of convenience: Hybridization of surface plasmon and dielectric waveguide modes,” Laser Photon. Rev. 8(3), 394–408 (2014). [CrossRef]
17. Z.-X. Chen, Z.-J. Wu, Y. Ming, X.-J. Zhang, and Y.-Q. Lu, “Hybrid plasmonic waveguide in a metal V-groove,” AIP Advances 4(1), 017103 (2014). [CrossRef]
18. Q. Lu, C.-L. Zou, D. Chen, P. Zhou, and G. Wu, “Extreme light confinement and low loss in triangle hybrid plasmonic waveguide,” Opt. Commun. 319, 141–146 (2014). [CrossRef]
19. B. Olyaeefar and H. Khoshsima, “Low-loss ultra-subwavelength hybrid plasmonic waveguide based on metallic bump structures,” J. Phys. D Appl. Phys. 47(10), 105105 (2014). [CrossRef]
20. D. Chen, “Cylindrical hybrid plasmonic waveguide for subwavelength confinement of light,” Appl. Opt. 49(36), 6868–6871 (2010). [CrossRef] [PubMed]
21. C.-L. Zou, F.-W. Sun, C.-H. Dong, Y.-F. Xiao, X.-F. Ren, L. Lv, X.-D. Chen, J.-M. Cui, Z.-F. Han, and G.-C. Guo, “Movable fiber-integrated hybrid plasmonic waveguide on metal film,” IEEE Photon. Technol. Lett. 24(6), 434–436 (2012). [CrossRef]
22. M. Z. Alam, J. S. Aitchison, and M. Mojahedi, “Compact and silicon-on-insulator-compatible hybrid plasmonic TE-pass polarizer,” Opt. Lett. 37(1), 55–57 (2012). [CrossRef] [PubMed]
23. Y. Wu, B. Yao, Y. Cheng, Y. Rao, Y. Gong, X. Zhou, B. Wu, and K. S. Chiang, “Four-wave mixing in a microfiber attached onto a graphene film,” IEEE Photon. Technol. Lett. 26(3), 249–252 (2014). [CrossRef]
24. L. Zhou, X. Sun, X. Li, and J. Chen, “Miniature microring resonator sensor based on a hybrid plasmonic waveguide,” Sensors (Basel) 11(12), 6856–6867 (2011). [CrossRef] [PubMed]
25. M. Z. Alam, F. Bahrami, J. S. Aitchison, and M. Mojahedi, “Analysis and optimization of hybrid plasmonic waveguide as a platform for biosensing,” IEEE Photonics Journal 6(4), 1–10 (2014). [CrossRef]
26. H. Choo, M.-K. Kim, M. Staffaroni, T. J. Seok, J. Bokor, S. Cabrini, P. J. Schuck, M. C. Wu, and E. Yablonovitch, “Nanofocusing in a metal–insulator–metal gap plasmon waveguide with a three-dimensional linear taper,” Nat. Photonics 6(12), 838–844 (2012). [CrossRef]
27. Z. Hong, L. Zhou, X. Li, W. Zou, X. Sun, S. Li, J. Shen, H. Luo, and J. Chen, “Design and analysis of a highly efficient coupler between a micro/nano optical fiber and an SOI waveguide,” Appl. Opt. 51(16), 3410–3415 (2012). [CrossRef] [PubMed]
28. L. Tong, F. Zi, X. Guo, and J. Lou, “Optical microfibers and nanofibers: A tutorial,” Opt. Commun. 285(23), 4641–4647 (2012). [CrossRef]
29. L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426(6968), 816–819 (2003). [CrossRef] [PubMed]
30. D. R. Lide, CRC Handbook of Chemistry and Physics (CRC press, 2004).
