Research Article
Vol. 55, No. 5 / February 10 2016 / Applied Optics
1029
Design of high Q-factor metallic nanocavities using plasmonic bandgaps HO-SEOK EE,1 HONG-GYU PARK,1
AND
SUN-KYUNG KIM2,*
1
Department of Physics, Korea University, Seoul 136-701, South Korea Department of Applied Physics, Kyung Hee University, Gyeonggi-do 17104, South Korea *Corresponding author: [email protected]
2
Received 28 October 2015; revised 22 December 2015; accepted 5 January 2016; posted 6 January 2016 (Doc. ID 252839); published 8 February 2016
The surface plasmon polariton modes often excited in metallic nanocavities enable the miniaturization of photonic devices, even beyond the diffraction limit, yet their severe optical losses deteriorate device performance. This study proposes a design of metallic nanorod cavities coupled to plasmonic crystals with the aim of reducing the radiation loss of surface plasmon modes. Periodic Ag disks placed on an insulator–metal substrate open a substantial amount of plasmonic bandgaps (e.g., Δλ 290 nm at λ 1550 nm) by modifying their diameter and thickness. When an Ag nanorod with a length of ∼400 nm is surrounded by the periodic Ag disks, its Q-factor increases up to 127, yielding a 16-fold enhancement compared with a bare Ag nanorod, while its mode volume can be as small as 0.03λ∕2n3 . Ag nanorods with gradually increasing lengths exhibit high Q-factor plasmonic modes that are tunable within the plasmonic bandgap. These numerical studies on low-radiation-loss plasmonic modes excited in metallic nanocavities will promote the development of ultrasmall plasmonic devices. © 2016 Optical Society of America OCIS codes: (240.6680) Surface plasmons; (160.5293) Photonic bandgap materials; (260.3910) Metal optics. http://dx.doi.org/10.1364/AO.55.001029
1. INTRODUCTION Surface plasmon polaritons (SPPs) are photon–electron coupled states that are localized at the interface between a metal and a dielectric [1]. The electric field distribution of SPPs, which decays exponentially in the direction of both the metal and dielectric materials, has been exploited to develop optoelectronic devices with ultrasmall mode volume [2,3]. In particular, metallic nanorods are attracting considerable interest as plasmonic cavities because of their bottom-up fabrication, capacity for tuning plasmonic resonances, and ease of integration with other optical devices [4]. These advantages of metallic nanorods enable the use of plasmonic lasers [3], waveguides [5,6], and optical sensors [7,8], which will be essential components in next-generation photonic integrated circuits [9]. However, large optical losses in metallic nanorods are considered an unavoidable problem that impedes the extension of plasmonic device applications. For example, the Q-factor of a single Au nanorod was recorded to be ∼25 at room temperature [10–13]. In general, the optical losses of metallic nanocavities consist of material absorption loss and cavity radiation loss [Fig. 1(A)]. The material absorption loss in a metal has a strong temperature dependence due to free electron collisions with lattice vibrations, and thus accounts for a significant portion of the total optical losses at room temperature [2]. Meanwhile, to 1559-128X/16/051029-05$15/0$15.00 © 2016 Optical Society of America
manage the radiation loss of metallic nanocavities, a variety of plasmonic cavity designs, including metal–insulator–metal (MIM) structures, have been proposed [13–16]. For example, Seo et al. designed metal-coated dielectric nanorods with bandcutoff plasmonic mirrors wherein no plasmonic propagation mode exists in the two end mirrors at the operating wavelengths [16]. The estimated maximum Q-factor of the metal-coated dielectric nanorod was ∼100 at 300 K. However, incorporating such plasmonic cavities into a planar circuit is a nontrivial issue. In this study, we propose plasmonic-bandgap-coupled metallic nanorod cavities where a single Ag nanorod is surrounded by periodic Ag disks [Fig. 1(B)]. The plasmonic bandgaps of periodic Ag disks were examined by varying their diameter, thickness, and pitch size, and by conducting finite-difference time-domain (FDTD) simulations. The Q-factor, defined by 2π (energy stored)/(energy dissipated per cycle), of a single Ag nanorod was compared with and without the introduction of periodic Ag disks. The radiation loss of the plasmonicbandgap-coupled single Ag nanorod was further suppressed by tailoring the diameter of Ag disks near the Ag nanorod. Finally, a single pronounced peak was sequentially tuned within the plasmonic bandgap by modulating the length of the Ag nanorod, thus suggesting the feasibility of tunable optical filters and lasers for use in photonic integrated circuits.
1030
Vol. 55, No. 5 / February 10 2016 / Applied Optics
Fig. 1. Schematic illustrations showing, A, a bare Ag nanorod plasmonic cavity and, B, an Ag nanorod coupled to a plasmonic crystal formed by periodic Ag disks.
2. PLASMONIC BANDGAPS OF PERIODIC Ag DISKS Prior to the design of plasmonic bandgaps formed by periodic metallic patterns, we first investigated the ω − k dispersions of MIM slabs while varying the thickness (t) of the top metal layer by conducting FDTD simulations in which the Bloch boundary conditions are applied [Fig. 2(A)] [17]. A dispersive Ag material was handled via the Drude model for the top and bottom metal layers. The permittivity at infinite frequency, and the plasma and collision frequencies used in the model were ε∞ 3.91364, ωp 9.17111 ℏ−1 eV, and γ 0.0207945 ℏ−1 eV, respectively, where ħ is the reduced Planck’s constant. These values were obtained by fitting measured optical dispersion [18] over the wavelength range of 400–2000 nm. For the embedded insulator layer, a dielectric material with a constant refractive index of 3.2, which corresponds to InP-based materials around λ 1550 nm, was introduced. Note that these MIM slabs with an ambient medium of SiO2 can be prepared by the conventional wafer bonding technique [19]. In these simulations, the temporal and spatial resolutions were 5c −1 nm and 10 nm, respectively, where c is the speed of light. The calculated result showed that the plasmonic
Fig. 2. A, calculated dispersions of SiO2 ∕InP∕Ag and SiO2 ∕Ag∕ InP∕Ag slabs while varying the thickness of the top Ag layer. The inset shows the schematic of the calculated structure. B, calculated first (black squares), second (red dots), and third (blue triangles) lowest plasmonic band dispersion of the MIM plasmonic crystal. C, electric field profiles normal to the slabs at the M-point on the second band (top) and the K-point on the first band (bottom).
Research Article dispersion characteristics of the MIM slabs differed distinctly with and without (i.e., t 0 nm) the introduction of the upper metal part. For these simulations, the thickness of the dielectric was fixed at 90 nm. In particular, with regards to the telecommunication frequencies, the effective index, defined by kmode ∕ω, increased significantly with the existence of the top Ag layer. This implies that MIM slabs are effective structures to highly confine surface plasmon (SP) propagation modes, even for low normalized frequencies. In particular, at λ 1550 nm (i.e., normalized frequency 0.645), the effective index of the MIM slabs was ∼4.2, which is much larger than that of the structure without the top Ag layer (∼2.0). The large effective index SPP propagating modes in the MIM slabs opens a possibility of plasmonic bandgaps when periodic metal patterns are introduced into them [20–22]. SP modes must be excited readily with transverse magnetic polarization (i.e., electric field oscillation perpendicular to the interface), and, hence, rod-type (cf. hole-type) patterns are preferred for the opening of the bandgaps [23]. The FDTD simulations showed that periodic Ag disks placed on an insulator–metal substrate exhibited a plasmonic bandgap of ∼0.035 (in terms of normalized frequency) between a K-point on the first band (K1) and an M-point on the second band (M2) [Fig. 2(B)]. The electric fields of K1 and M2 were strongly localized at the edges of the periodic Ag disks, which is indicative of plasmonic modes [Fig. 2(C)]. For these plasmonic band dispersion calculations, the spatial resolutions along pthe ffiffiffi xΓ − K , yM − K , and z (vertical) directions were 10, 5 3, and 10 nm, respectively, to exactly match the unit cell with the hexagonal symmetry structure. To maximize the plasmonic bandgap, we varied the pitch size (a), diameter (D), and thickness (t) of the periodic Ag disks and the thickness (h) of the dielectric in the simulated structures [Figs. 3(A) and 3(B)]. First, the wavelengths of K1 and M2 increased gradually with an increase in a; if one wishes to form a plasmonic bandgap around λ 1550 nm, 270 nm < a < 330 nm should be chosen [Fig. 3(A), left panel]. For these simulations, D was fixed at a − 50 nm. With a fixed value of a 300 nm, the bandgap opens at D > 100 nm and continues to increase until D 250 nm, which is similar to the trend of dielectric photonic crystals [Fig. 3(A), right panel] [23]. The plasmonic bandgap also depended on the thickness (t) of the periodic disks and the height (h) of the insulator slab [Fig. 3(B)]. Interestingly, the plasmonic bandgap increased steadily with decreasing t and h; the wavelength was redshifted for K1, whereas it was blueshifted for M1. In MIM or insulator–metal–insulator slabs, the effective index of lower energy plasmonic propagation modes generally increases when the thicknesses of the middle insulator or metal layer decrease [24,25], which indicates that the plasmonic field becomes more tightly localized at the metal–dielectric interface with the thinner layers. The increase in effective index contrast finally leads to the extension of plasmonic bandgaps. 3. Ag NANOROD CAVITIES COUPLED TO PLASMONIC BANDGAPS The optical losses of plasmonic modes in metallic nanorod cavities are mainly responsible for limiting practical applications.
Research Article
Fig. 3. Calculated free-space wavelengths of the K1 and M2 bandedge modes as a function of pitch size a [left panel of (A), t 30 nm, h 90 nm, D a − 50 nm], diameter of disk D [right panel of (A), a 300 nm, t 30 nm, h 90 nm], thickness of Ag disk t [left panel of (B), a 300 nm, D 250 nm, h 90 nm], and height of the insulator h [right panel of (B), a 300 nm, D 250 nm, t 30 nm]. The insets show the top (A) and side (B) views of the calculated structure.
To suppress the radiation loss of plasmonic modes, we modeled a single Ag nanorod surrounded by periodic Ag disks sustaining plasmonic bandgaps. For the periodic Ag disks, a 300 nm, D 250 nm, t 30 nm, and h 90 nm were chosen to attain a sufficiently large plasmonic bandgap around λ 1550 nm [Fig. 4(A)]. To situate the Ag nanorod on the center of the plasmonic crystal, two Ag disks were removed. To further reduce the radiation loss, the pitch
Fig. 4. A, schematic illustration of a plasmonic crystal coupled metal nanorod cavity structure. B, calculated Q-factor and mode volume (V mode ) of the plasmonic mode as a function of Δd . C, calculated spectra of the plasmonic-crystal-coupled Ag nanorod cavities with gradually increasing lengths. D, calculated spectra of bare Ag nanorod cavities with gradually increasing lengths.
Vol. 55, No. 5 / February 10 2016 / Applied Optics
1031
(a 0 a − Δd ∕2) and the diameter (d D − Δd ) of the eight Ag disks near an Ag nanorod were slightly modified [26]. The Q-factor and the mode volume of an Ag nanorod with a length, width, and thickness of L 390 nm, w 50 nm, and t 30 nm were calculated as a function of Δd [Fig. 4(B)]. The Q-factor of the Ag nanorod was larger than 120 at Δd 40 nm, while the mode volume was as small as ∼0.03 λ∕2n3 . It is worth mentioning that the Q-factor and the mode volume of the Ag nanorod cavities are not very strongly correlated [27]. The high Q-factor plasmonic resonance was more apparent in the frequency domain; a single pronounced peak was gradually tuned to longer wavelengths within the plasmonic bandgap as L increased [Fig. 4(C)], which suggests that the implementation of tunable optical filters may be possible. For comparison, the spectra of bare Ag nanorods with the same increasing lengths were calculated [Fig. 4(D)]; relatively broadened peaks appeared, due to the increase of radiation loss. To clearly visualize the suppression of radiation loss by plasmonic bandgaps, the electric field intensity profiles of the Ag nanorods (L 390 and 610 nm) with and without the plasmonic crystal were calculated [Figs. 5(A) and 5(B), respectively]. For the L 610 nm structure, three central disks were missing and the 10 nearest disks were modified. First, the plasmonic crystal significantly suppressed the side radiation loss, while it did not distort the original mode profile inside the Ag nanorod cavity; the Ag nanorod with L 390 nm (610 nm) exhibited three (four) intensity antinodes along the axial direction. Second, the suppression of radiation loss by plasmonic bandgaps was a generic phenomenon, regardless of the length of the metallic nanorods.
Fig. 5. Time-averaged electric field intensity profiles of a plasmonic mode excited in 390 nm long (A) and 610 nm long (B) Ag nanorod cavities with (top) and without (bottom) a plasmonic crystal. Calculated total (C) and intrinsic (D) Q-factors of a plasmonic mode excited in plasmonic-crystal-coupled Ag nanorod cavities as a function of L with respect to the number of missing Ag disks.
1032
Research Article
Vol. 55, No. 5 / February 10 2016 / Applied Optics
Fig. 6. A, schematic illustration of a misaligned metallic nanorod cavity with x- and y-directional displacement. B, calculated total Q-factors of a 390 nm long Ag nanorod cavity as a function of displacement with respect to the x and y directions.
Next, we calculated the total [Fig. 5(C)] and intrinsic [Fig. 5(D)] Q-factors of the Ag nanorods for a wide range of lengths. Here, the intrinsic Q-factor indicates that the material absorption loss in a metal is completely ignored, which corresponds to low-temperature experiments [2]. The Q-factors were plotted with respect to the number of missing Ag disks; Ag nanorods with the same number of the missing Ag disks sustained the same cavity mode. The total and intrinsic Q-factors were significantly changed for different L. Interestingly, the Q-factors of the plasmonic modes steadily increased as their resonant wavelengths approached the wavelength at the K1 band-edge point of nearest disks, whose lattice pitch and disk diameter are a 0 and d , respectively. The space between antinodes in the upper panel of Figs. 5(A) and 5(B) are similar to π∕kK 1 210 nm, where k K 1 is the wavevector at the K1 point of the nearest disks, which provides better mode matching and thus reduces the side radiation loss [28]. The maximum total Q-factor of the Ag nanorod was ∼120 in the range considered for L. For the intrinsic Q-factor, the maximum values of all the Ag nanorods were larger than 1000. Such high Q-factor plasmonic modes in the metallic nanorods could enable the use of room-temperature plasmonic lasers if the bottom dielectric has a gain medium. The plasmonic nanorod laser cavities can be fabricated via the following procedure. First, well-defined Ag nanorods and plasmonic crystals are prepared on an InGaAsP/InP wafer by electron-beam lithography and a lift-off process. Second, the InGaAsP/InP wafer is bonded to a transparent substrate with a bonding material such as epoxy or SU-8 [19]. Last, the bottom InP substrate is selectively dissolved by HCl and an Ag film is deposited on the other side of the InGaAsP layer. To make the design on the metallic nanorod cavities more useful for real fabrication, we conducted additional simulations to investigate the variation of the Q-factor of an Ag nanorod cavity (L 390 nm) with an increase of the displacement between the center of the nanorod and the plasmonic crystal [Fig. 6(A)]. Even with displacement of 70 nm with respect to the x and y directions, the total Q-factor of the nanorod cavity was degraded by less than 10% compared with its original Q-factor [Fig. 6(B)], indicating the robustness of the developed nanorod cavities against misalignment in fabrication. 4. CONCLUSIONS We studied low-radiation-loss plasmonic modes in plasmoniccrystal-coupled Ag nanorod cavities. With the help of plasmonic
bandgaps formed by periodic Ag disks on an insulator– metal substrate, the maximum Q-factors of Ag nanorods with L 100–900 nm were larger than 100, while their mode volumes were much smaller than λ∕2n3 . These numerical findings for the high Q-factor plasmonic modes in metallic Ag nanorods will provide a platform to develop ultrasmall photonic devices, such as light sources and optical filters. Furthermore, the Ag nanorod cavities proposed herein will facilitate the integration of other photonic devices fabricated on plasmonic crystals. Funding. Basic Science Research Program; National Research Foundation of Korea (NRF) (NRF2013R1A1A1059423); Ministry of Science, ICT and Future Planning (MSIP) (No. 2009-0081565). REFERENCES 1. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003). 2. S.-H. Kwon, J.-H. Kang, C. Seassal, S.-K. Kim, P. Regreny, Y.-H. Lee, C. M. Lieber, and H.-G. Park, “Subwavelength plasmonic lasing from a semiconductor nanodisk with silver nanopan cavity,” Nano Lett. 10, 3679–3683 (2010). 3. R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009). 4. T. Kang, W. Choi, I. Yoon, H. Lee, M.-K. Seo, Q.-H. Park, and B. Kim, “Rainbow radiating single-crystal Ag nanowire nanoantenna,” Nano Lett. 12, 2331–2336 (2012). 5. Jitender, A. Kumar, R. K. Varshney, and M. Kumar, “Calculation of propagation characteristics of surface plasmons in gold/silver nanowires,” Appl. Opt. 54, 3715–3719 (2015). 6. T. Iqbal, “Propagation length of surface plasmon polaritons excited by a 1D plasmonic grating,” Curr. Appl. Phys. 15, 1445–1452 (2015). 7. Q. Zhan, J. Qian, X. Li, and S. He, “A study of mesoporous silicaencapsulated gold nanorods as enhanced light scattering probes for cancer cell imaging,” Nanotechnology 21, 055704 (2009). 8. M. Zekriti, D. V. Nesterenko, and Z. Sekkat, “Long-range surface plasmons supported by a bilayer metallic structure for sensing applications,” Appl. Opt. 54, 2151–2157 (2015). 9. A. Hryciw, Y. C. Jun, and M. L. Brongersma, “Electrifying plasmonics on silicon,” Nat. Mater. 9, 3–4 (2010). 10. J. S. Sekhon and S. S. Verma, “Optimal dimensions of gold nanorod for plasmonic nanosensors,” Plasmonics 6, 163–169 (2011). 11. E. J. R. Vesseur, R. de Waele, H. J. Lezec, H. A. Atwater, F. J. García de Abajo, and A. Polman, “Surface plasmon polariton modes in a single-crystal Au nanoresonator fabricated using focused-ion-beam milling,” Appl. Phys. Lett. 92, 083110 (2008). 12. D. J. Hill, C. W. Pinion, J. D. Christesen, and J. F. Cahoon, “Waveguide scattering microscopy for dark-field imaging and spectroscopy of photonic nanostructures,” ACS Photon. 1, 725–731 (2014). 13. C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, J. Feldmann, O. Wilson, and P. Mulvaney, “Drastic reduction of plasmon damping in gold nanorods,” Phys. Rev. Lett. 88, 077402 (2002). 14. M. T. Hill, M. Marell, E. S. P. Leong, B. Smalbrugge, Y. Zhu, M. Sun, P. J. van Veldhoven, E. J. Geluk, F. Karouta, Y.-S. Oei, R. Nötzel, C.-Z. Ning, and M. K. Smit, “Lasing in metal-insulator-metal subwavelength plasmonic waveguides,” Prog. Photovoltaics 19, 11107– 11112 (2009). 15. H. Yang, J. Li, and G. Xiao, “Significantly increased surface plasmon polariton mode excitation using a multilayer insulation structure in a metal–insulator–metal plasmonic waveguide,” Appl. Opt. 53, 3642–3646 (2014). 16. M.-K. Seo, S.-H. Kwon, H.-S. Ee, and H.-G. Park, “Full threedimensional subwavelength high-Q surface-plasmon-polariton cavity,” Nano Lett. 9, 4078–4082 (2009).
Research Article 17. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005). 18. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972). 19. J. Van Campenhout, P. Rojo-Romeo, P. Regreny, C. Seassal, D. Van Thourhout, S. Verstuyft, L. Di Cioccio, J.-M. Fedeli, C. Lagahe, and R. Baets, “Electrically pumped InP-based microdisk lasers integrated with a nanophotonic silicon-on-insulator waveguide circuit,” Opt. Express 15, 6744–6749 (2007). 20. L. Feng, M.-H. Lu, V. Lomakin, and Y. Fainman, “Plasmonic photonic crystal with a complete band gap for surface plasmon polariton waves,” Appl. Phys. Lett. 93, 231105 (2008). 21. C.-W. Cheng, M. N. Abbas, M.-H. Shih, and Y.-C. Chang, “Characterization of the surface plasmon polariton band gap in an Ag/SiO2/Ag T-shaped periodical structure,” Opt. Express 19, 23698–23705 (2011). 22. A. Kocabas, S. S. Senlik, and A. Aydinli, “Plasmonic band gap cavities on biharmonic gratings,” Phys. Rev. B 77, 195130 (2008).
Vol. 55, No. 5 / February 10 2016 / Applied Optics
1033
23. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008). 24. J. Chen, G. A. Smolyakov, S. R. J. Brueck, and K. J. Malloy, “Surface plasmon modes of finite, planar, metal-insulator-metal plasmonic waveguides,” Opt. Express 16, 14902–14909 (2008). 25. M. Kuttge, W. Cai, F. J. G. de Abajo, and A. Polman, “Dispersion of metal-insulator-metal plasmon polaritons probed by cathodoluminescence imaging spectroscopy,” Phys. Rev. B 80, 033409 (2009). 26. Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “Fine-tuned high-Q photonic-crystal nanocavity,” Opt. Express 13, 1202–1214 (2005). 27. H.-G. Park, J.-K. Hwang, J. Huh, H.-Y. Ryu, S.-H. Kim, J.-S. Kim, and Y.-H. Lee, “Characteristics of modified single-defect two-dimensional photonic crystal lasers,” IEEE J. Quantum Electron. 38, 1352–1365 (2002). 28. S.-K. Kim, R. W. Day, J. F. Cahoon, T. J. Kempa, K.-D. Song, H.-G. Park, and C. M. Lieber, “Tuning light absorption in photovoltaic silicon nanowires through morphological design,” Nano Lett. 12, 4971–4976 (2012).
Vol. 55, No. 5 / February 10 2016 / Applied Optics
1029
Design of high Q-factor metallic nanocavities using plasmonic bandgaps HO-SEOK EE,1 HONG-GYU PARK,1
AND
SUN-KYUNG KIM2,*
1
Department of Physics, Korea University, Seoul 136-701, South Korea Department of Applied Physics, Kyung Hee University, Gyeonggi-do 17104, South Korea *Corresponding author: [email protected]
2
Received 28 October 2015; revised 22 December 2015; accepted 5 January 2016; posted 6 January 2016 (Doc. ID 252839); published 8 February 2016
The surface plasmon polariton modes often excited in metallic nanocavities enable the miniaturization of photonic devices, even beyond the diffraction limit, yet their severe optical losses deteriorate device performance. This study proposes a design of metallic nanorod cavities coupled to plasmonic crystals with the aim of reducing the radiation loss of surface plasmon modes. Periodic Ag disks placed on an insulator–metal substrate open a substantial amount of plasmonic bandgaps (e.g., Δλ 290 nm at λ 1550 nm) by modifying their diameter and thickness. When an Ag nanorod with a length of ∼400 nm is surrounded by the periodic Ag disks, its Q-factor increases up to 127, yielding a 16-fold enhancement compared with a bare Ag nanorod, while its mode volume can be as small as 0.03λ∕2n3 . Ag nanorods with gradually increasing lengths exhibit high Q-factor plasmonic modes that are tunable within the plasmonic bandgap. These numerical studies on low-radiation-loss plasmonic modes excited in metallic nanocavities will promote the development of ultrasmall plasmonic devices. © 2016 Optical Society of America OCIS codes: (240.6680) Surface plasmons; (160.5293) Photonic bandgap materials; (260.3910) Metal optics. http://dx.doi.org/10.1364/AO.55.001029
1. INTRODUCTION Surface plasmon polaritons (SPPs) are photon–electron coupled states that are localized at the interface between a metal and a dielectric [1]. The electric field distribution of SPPs, which decays exponentially in the direction of both the metal and dielectric materials, has been exploited to develop optoelectronic devices with ultrasmall mode volume [2,3]. In particular, metallic nanorods are attracting considerable interest as plasmonic cavities because of their bottom-up fabrication, capacity for tuning plasmonic resonances, and ease of integration with other optical devices [4]. These advantages of metallic nanorods enable the use of plasmonic lasers [3], waveguides [5,6], and optical sensors [7,8], which will be essential components in next-generation photonic integrated circuits [9]. However, large optical losses in metallic nanorods are considered an unavoidable problem that impedes the extension of plasmonic device applications. For example, the Q-factor of a single Au nanorod was recorded to be ∼25 at room temperature [10–13]. In general, the optical losses of metallic nanocavities consist of material absorption loss and cavity radiation loss [Fig. 1(A)]. The material absorption loss in a metal has a strong temperature dependence due to free electron collisions with lattice vibrations, and thus accounts for a significant portion of the total optical losses at room temperature [2]. Meanwhile, to 1559-128X/16/051029-05$15/0$15.00 © 2016 Optical Society of America
manage the radiation loss of metallic nanocavities, a variety of plasmonic cavity designs, including metal–insulator–metal (MIM) structures, have been proposed [13–16]. For example, Seo et al. designed metal-coated dielectric nanorods with bandcutoff plasmonic mirrors wherein no plasmonic propagation mode exists in the two end mirrors at the operating wavelengths [16]. The estimated maximum Q-factor of the metal-coated dielectric nanorod was ∼100 at 300 K. However, incorporating such plasmonic cavities into a planar circuit is a nontrivial issue. In this study, we propose plasmonic-bandgap-coupled metallic nanorod cavities where a single Ag nanorod is surrounded by periodic Ag disks [Fig. 1(B)]. The plasmonic bandgaps of periodic Ag disks were examined by varying their diameter, thickness, and pitch size, and by conducting finite-difference time-domain (FDTD) simulations. The Q-factor, defined by 2π (energy stored)/(energy dissipated per cycle), of a single Ag nanorod was compared with and without the introduction of periodic Ag disks. The radiation loss of the plasmonicbandgap-coupled single Ag nanorod was further suppressed by tailoring the diameter of Ag disks near the Ag nanorod. Finally, a single pronounced peak was sequentially tuned within the plasmonic bandgap by modulating the length of the Ag nanorod, thus suggesting the feasibility of tunable optical filters and lasers for use in photonic integrated circuits.
1030
Vol. 55, No. 5 / February 10 2016 / Applied Optics
Fig. 1. Schematic illustrations showing, A, a bare Ag nanorod plasmonic cavity and, B, an Ag nanorod coupled to a plasmonic crystal formed by periodic Ag disks.
2. PLASMONIC BANDGAPS OF PERIODIC Ag DISKS Prior to the design of plasmonic bandgaps formed by periodic metallic patterns, we first investigated the ω − k dispersions of MIM slabs while varying the thickness (t) of the top metal layer by conducting FDTD simulations in which the Bloch boundary conditions are applied [Fig. 2(A)] [17]. A dispersive Ag material was handled via the Drude model for the top and bottom metal layers. The permittivity at infinite frequency, and the plasma and collision frequencies used in the model were ε∞ 3.91364, ωp 9.17111 ℏ−1 eV, and γ 0.0207945 ℏ−1 eV, respectively, where ħ is the reduced Planck’s constant. These values were obtained by fitting measured optical dispersion [18] over the wavelength range of 400–2000 nm. For the embedded insulator layer, a dielectric material with a constant refractive index of 3.2, which corresponds to InP-based materials around λ 1550 nm, was introduced. Note that these MIM slabs with an ambient medium of SiO2 can be prepared by the conventional wafer bonding technique [19]. In these simulations, the temporal and spatial resolutions were 5c −1 nm and 10 nm, respectively, where c is the speed of light. The calculated result showed that the plasmonic
Fig. 2. A, calculated dispersions of SiO2 ∕InP∕Ag and SiO2 ∕Ag∕ InP∕Ag slabs while varying the thickness of the top Ag layer. The inset shows the schematic of the calculated structure. B, calculated first (black squares), second (red dots), and third (blue triangles) lowest plasmonic band dispersion of the MIM plasmonic crystal. C, electric field profiles normal to the slabs at the M-point on the second band (top) and the K-point on the first band (bottom).
Research Article dispersion characteristics of the MIM slabs differed distinctly with and without (i.e., t 0 nm) the introduction of the upper metal part. For these simulations, the thickness of the dielectric was fixed at 90 nm. In particular, with regards to the telecommunication frequencies, the effective index, defined by kmode ∕ω, increased significantly with the existence of the top Ag layer. This implies that MIM slabs are effective structures to highly confine surface plasmon (SP) propagation modes, even for low normalized frequencies. In particular, at λ 1550 nm (i.e., normalized frequency 0.645), the effective index of the MIM slabs was ∼4.2, which is much larger than that of the structure without the top Ag layer (∼2.0). The large effective index SPP propagating modes in the MIM slabs opens a possibility of plasmonic bandgaps when periodic metal patterns are introduced into them [20–22]. SP modes must be excited readily with transverse magnetic polarization (i.e., electric field oscillation perpendicular to the interface), and, hence, rod-type (cf. hole-type) patterns are preferred for the opening of the bandgaps [23]. The FDTD simulations showed that periodic Ag disks placed on an insulator–metal substrate exhibited a plasmonic bandgap of ∼0.035 (in terms of normalized frequency) between a K-point on the first band (K1) and an M-point on the second band (M2) [Fig. 2(B)]. The electric fields of K1 and M2 were strongly localized at the edges of the periodic Ag disks, which is indicative of plasmonic modes [Fig. 2(C)]. For these plasmonic band dispersion calculations, the spatial resolutions along pthe ffiffiffi xΓ − K , yM − K , and z (vertical) directions were 10, 5 3, and 10 nm, respectively, to exactly match the unit cell with the hexagonal symmetry structure. To maximize the plasmonic bandgap, we varied the pitch size (a), diameter (D), and thickness (t) of the periodic Ag disks and the thickness (h) of the dielectric in the simulated structures [Figs. 3(A) and 3(B)]. First, the wavelengths of K1 and M2 increased gradually with an increase in a; if one wishes to form a plasmonic bandgap around λ 1550 nm, 270 nm < a < 330 nm should be chosen [Fig. 3(A), left panel]. For these simulations, D was fixed at a − 50 nm. With a fixed value of a 300 nm, the bandgap opens at D > 100 nm and continues to increase until D 250 nm, which is similar to the trend of dielectric photonic crystals [Fig. 3(A), right panel] [23]. The plasmonic bandgap also depended on the thickness (t) of the periodic disks and the height (h) of the insulator slab [Fig. 3(B)]. Interestingly, the plasmonic bandgap increased steadily with decreasing t and h; the wavelength was redshifted for K1, whereas it was blueshifted for M1. In MIM or insulator–metal–insulator slabs, the effective index of lower energy plasmonic propagation modes generally increases when the thicknesses of the middle insulator or metal layer decrease [24,25], which indicates that the plasmonic field becomes more tightly localized at the metal–dielectric interface with the thinner layers. The increase in effective index contrast finally leads to the extension of plasmonic bandgaps. 3. Ag NANOROD CAVITIES COUPLED TO PLASMONIC BANDGAPS The optical losses of plasmonic modes in metallic nanorod cavities are mainly responsible for limiting practical applications.
Research Article
Fig. 3. Calculated free-space wavelengths of the K1 and M2 bandedge modes as a function of pitch size a [left panel of (A), t 30 nm, h 90 nm, D a − 50 nm], diameter of disk D [right panel of (A), a 300 nm, t 30 nm, h 90 nm], thickness of Ag disk t [left panel of (B), a 300 nm, D 250 nm, h 90 nm], and height of the insulator h [right panel of (B), a 300 nm, D 250 nm, t 30 nm]. The insets show the top (A) and side (B) views of the calculated structure.
To suppress the radiation loss of plasmonic modes, we modeled a single Ag nanorod surrounded by periodic Ag disks sustaining plasmonic bandgaps. For the periodic Ag disks, a 300 nm, D 250 nm, t 30 nm, and h 90 nm were chosen to attain a sufficiently large plasmonic bandgap around λ 1550 nm [Fig. 4(A)]. To situate the Ag nanorod on the center of the plasmonic crystal, two Ag disks were removed. To further reduce the radiation loss, the pitch
Fig. 4. A, schematic illustration of a plasmonic crystal coupled metal nanorod cavity structure. B, calculated Q-factor and mode volume (V mode ) of the plasmonic mode as a function of Δd . C, calculated spectra of the plasmonic-crystal-coupled Ag nanorod cavities with gradually increasing lengths. D, calculated spectra of bare Ag nanorod cavities with gradually increasing lengths.
Vol. 55, No. 5 / February 10 2016 / Applied Optics
1031
(a 0 a − Δd ∕2) and the diameter (d D − Δd ) of the eight Ag disks near an Ag nanorod were slightly modified [26]. The Q-factor and the mode volume of an Ag nanorod with a length, width, and thickness of L 390 nm, w 50 nm, and t 30 nm were calculated as a function of Δd [Fig. 4(B)]. The Q-factor of the Ag nanorod was larger than 120 at Δd 40 nm, while the mode volume was as small as ∼0.03 λ∕2n3 . It is worth mentioning that the Q-factor and the mode volume of the Ag nanorod cavities are not very strongly correlated [27]. The high Q-factor plasmonic resonance was more apparent in the frequency domain; a single pronounced peak was gradually tuned to longer wavelengths within the plasmonic bandgap as L increased [Fig. 4(C)], which suggests that the implementation of tunable optical filters may be possible. For comparison, the spectra of bare Ag nanorods with the same increasing lengths were calculated [Fig. 4(D)]; relatively broadened peaks appeared, due to the increase of radiation loss. To clearly visualize the suppression of radiation loss by plasmonic bandgaps, the electric field intensity profiles of the Ag nanorods (L 390 and 610 nm) with and without the plasmonic crystal were calculated [Figs. 5(A) and 5(B), respectively]. For the L 610 nm structure, three central disks were missing and the 10 nearest disks were modified. First, the plasmonic crystal significantly suppressed the side radiation loss, while it did not distort the original mode profile inside the Ag nanorod cavity; the Ag nanorod with L 390 nm (610 nm) exhibited three (four) intensity antinodes along the axial direction. Second, the suppression of radiation loss by plasmonic bandgaps was a generic phenomenon, regardless of the length of the metallic nanorods.
Fig. 5. Time-averaged electric field intensity profiles of a plasmonic mode excited in 390 nm long (A) and 610 nm long (B) Ag nanorod cavities with (top) and without (bottom) a plasmonic crystal. Calculated total (C) and intrinsic (D) Q-factors of a plasmonic mode excited in plasmonic-crystal-coupled Ag nanorod cavities as a function of L with respect to the number of missing Ag disks.
1032
Research Article
Vol. 55, No. 5 / February 10 2016 / Applied Optics
Fig. 6. A, schematic illustration of a misaligned metallic nanorod cavity with x- and y-directional displacement. B, calculated total Q-factors of a 390 nm long Ag nanorod cavity as a function of displacement with respect to the x and y directions.
Next, we calculated the total [Fig. 5(C)] and intrinsic [Fig. 5(D)] Q-factors of the Ag nanorods for a wide range of lengths. Here, the intrinsic Q-factor indicates that the material absorption loss in a metal is completely ignored, which corresponds to low-temperature experiments [2]. The Q-factors were plotted with respect to the number of missing Ag disks; Ag nanorods with the same number of the missing Ag disks sustained the same cavity mode. The total and intrinsic Q-factors were significantly changed for different L. Interestingly, the Q-factors of the plasmonic modes steadily increased as their resonant wavelengths approached the wavelength at the K1 band-edge point of nearest disks, whose lattice pitch and disk diameter are a 0 and d , respectively. The space between antinodes in the upper panel of Figs. 5(A) and 5(B) are similar to π∕kK 1 210 nm, where k K 1 is the wavevector at the K1 point of the nearest disks, which provides better mode matching and thus reduces the side radiation loss [28]. The maximum total Q-factor of the Ag nanorod was ∼120 in the range considered for L. For the intrinsic Q-factor, the maximum values of all the Ag nanorods were larger than 1000. Such high Q-factor plasmonic modes in the metallic nanorods could enable the use of room-temperature plasmonic lasers if the bottom dielectric has a gain medium. The plasmonic nanorod laser cavities can be fabricated via the following procedure. First, well-defined Ag nanorods and plasmonic crystals are prepared on an InGaAsP/InP wafer by electron-beam lithography and a lift-off process. Second, the InGaAsP/InP wafer is bonded to a transparent substrate with a bonding material such as epoxy or SU-8 [19]. Last, the bottom InP substrate is selectively dissolved by HCl and an Ag film is deposited on the other side of the InGaAsP layer. To make the design on the metallic nanorod cavities more useful for real fabrication, we conducted additional simulations to investigate the variation of the Q-factor of an Ag nanorod cavity (L 390 nm) with an increase of the displacement between the center of the nanorod and the plasmonic crystal [Fig. 6(A)]. Even with displacement of 70 nm with respect to the x and y directions, the total Q-factor of the nanorod cavity was degraded by less than 10% compared with its original Q-factor [Fig. 6(B)], indicating the robustness of the developed nanorod cavities against misalignment in fabrication. 4. CONCLUSIONS We studied low-radiation-loss plasmonic modes in plasmoniccrystal-coupled Ag nanorod cavities. With the help of plasmonic
bandgaps formed by periodic Ag disks on an insulator– metal substrate, the maximum Q-factors of Ag nanorods with L 100–900 nm were larger than 100, while their mode volumes were much smaller than λ∕2n3 . These numerical findings for the high Q-factor plasmonic modes in metallic Ag nanorods will provide a platform to develop ultrasmall photonic devices, such as light sources and optical filters. Furthermore, the Ag nanorod cavities proposed herein will facilitate the integration of other photonic devices fabricated on plasmonic crystals. Funding. Basic Science Research Program; National Research Foundation of Korea (NRF) (NRF2013R1A1A1059423); Ministry of Science, ICT and Future Planning (MSIP) (No. 2009-0081565). REFERENCES 1. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003). 2. S.-H. Kwon, J.-H. Kang, C. Seassal, S.-K. Kim, P. Regreny, Y.-H. Lee, C. M. Lieber, and H.-G. Park, “Subwavelength plasmonic lasing from a semiconductor nanodisk with silver nanopan cavity,” Nano Lett. 10, 3679–3683 (2010). 3. R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009). 4. T. Kang, W. Choi, I. Yoon, H. Lee, M.-K. Seo, Q.-H. Park, and B. Kim, “Rainbow radiating single-crystal Ag nanowire nanoantenna,” Nano Lett. 12, 2331–2336 (2012). 5. Jitender, A. Kumar, R. K. Varshney, and M. Kumar, “Calculation of propagation characteristics of surface plasmons in gold/silver nanowires,” Appl. Opt. 54, 3715–3719 (2015). 6. T. Iqbal, “Propagation length of surface plasmon polaritons excited by a 1D plasmonic grating,” Curr. Appl. Phys. 15, 1445–1452 (2015). 7. Q. Zhan, J. Qian, X. Li, and S. He, “A study of mesoporous silicaencapsulated gold nanorods as enhanced light scattering probes for cancer cell imaging,” Nanotechnology 21, 055704 (2009). 8. M. Zekriti, D. V. Nesterenko, and Z. Sekkat, “Long-range surface plasmons supported by a bilayer metallic structure for sensing applications,” Appl. Opt. 54, 2151–2157 (2015). 9. A. Hryciw, Y. C. Jun, and M. L. Brongersma, “Electrifying plasmonics on silicon,” Nat. Mater. 9, 3–4 (2010). 10. J. S. Sekhon and S. S. Verma, “Optimal dimensions of gold nanorod for plasmonic nanosensors,” Plasmonics 6, 163–169 (2011). 11. E. J. R. Vesseur, R. de Waele, H. J. Lezec, H. A. Atwater, F. J. García de Abajo, and A. Polman, “Surface plasmon polariton modes in a single-crystal Au nanoresonator fabricated using focused-ion-beam milling,” Appl. Phys. Lett. 92, 083110 (2008). 12. D. J. Hill, C. W. Pinion, J. D. Christesen, and J. F. Cahoon, “Waveguide scattering microscopy for dark-field imaging and spectroscopy of photonic nanostructures,” ACS Photon. 1, 725–731 (2014). 13. C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, J. Feldmann, O. Wilson, and P. Mulvaney, “Drastic reduction of plasmon damping in gold nanorods,” Phys. Rev. Lett. 88, 077402 (2002). 14. M. T. Hill, M. Marell, E. S. P. Leong, B. Smalbrugge, Y. Zhu, M. Sun, P. J. van Veldhoven, E. J. Geluk, F. Karouta, Y.-S. Oei, R. Nötzel, C.-Z. Ning, and M. K. Smit, “Lasing in metal-insulator-metal subwavelength plasmonic waveguides,” Prog. Photovoltaics 19, 11107– 11112 (2009). 15. H. Yang, J. Li, and G. Xiao, “Significantly increased surface plasmon polariton mode excitation using a multilayer insulation structure in a metal–insulator–metal plasmonic waveguide,” Appl. Opt. 53, 3642–3646 (2014). 16. M.-K. Seo, S.-H. Kwon, H.-S. Ee, and H.-G. Park, “Full threedimensional subwavelength high-Q surface-plasmon-polariton cavity,” Nano Lett. 9, 4078–4082 (2009).
Research Article 17. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005). 18. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972). 19. J. Van Campenhout, P. Rojo-Romeo, P. Regreny, C. Seassal, D. Van Thourhout, S. Verstuyft, L. Di Cioccio, J.-M. Fedeli, C. Lagahe, and R. Baets, “Electrically pumped InP-based microdisk lasers integrated with a nanophotonic silicon-on-insulator waveguide circuit,” Opt. Express 15, 6744–6749 (2007). 20. L. Feng, M.-H. Lu, V. Lomakin, and Y. Fainman, “Plasmonic photonic crystal with a complete band gap for surface plasmon polariton waves,” Appl. Phys. Lett. 93, 231105 (2008). 21. C.-W. Cheng, M. N. Abbas, M.-H. Shih, and Y.-C. Chang, “Characterization of the surface plasmon polariton band gap in an Ag/SiO2/Ag T-shaped periodical structure,” Opt. Express 19, 23698–23705 (2011). 22. A. Kocabas, S. S. Senlik, and A. Aydinli, “Plasmonic band gap cavities on biharmonic gratings,” Phys. Rev. B 77, 195130 (2008).
Vol. 55, No. 5 / February 10 2016 / Applied Optics
1033
23. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008). 24. J. Chen, G. A. Smolyakov, S. R. J. Brueck, and K. J. Malloy, “Surface plasmon modes of finite, planar, metal-insulator-metal plasmonic waveguides,” Opt. Express 16, 14902–14909 (2008). 25. M. Kuttge, W. Cai, F. J. G. de Abajo, and A. Polman, “Dispersion of metal-insulator-metal plasmon polaritons probed by cathodoluminescence imaging spectroscopy,” Phys. Rev. B 80, 033409 (2009). 26. Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “Fine-tuned high-Q photonic-crystal nanocavity,” Opt. Express 13, 1202–1214 (2005). 27. H.-G. Park, J.-K. Hwang, J. Huh, H.-Y. Ryu, S.-H. Kim, J.-S. Kim, and Y.-H. Lee, “Characteristics of modified single-defect two-dimensional photonic crystal lasers,” IEEE J. Quantum Electron. 38, 1352–1365 (2002). 28. S.-K. Kim, R. W. Day, J. F. Cahoon, T. J. Kempa, K.-D. Song, H.-G. Park, and C. M. Lieber, “Tuning light absorption in photovoltaic silicon nanowires through morphological design,” Nano Lett. 12, 4971–4976 (2012).
