Deep subwavelength plasmonic whispering-gallery-mode cavity

doi:10.1364/OE.20.024918

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Deep subwavelength plasmonic whispering-gallery-mode cavity

Soon-Hong Kwon »View Author Affiliations

Optics Express, Vol. 20, Issue 22, pp. 24918-24924 (2012)
http://dx.doi.org/10.1364/OE.20.024918

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▸ Article Outline
– Abstract
1. Introduction
2. Plasmonic whispering-gallery-mode cavity for different azimuthal number
3. Size reduction of plasmonic WGM cavity
4. Conclusion
– References and links

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Abstract

We propose a plasmonic whispering-gallery-mode cavity comprising of a dielectric disk with sub-hundred nanometer thickness sandwiched by two silver disks. By reducing radius and thickness carefully based on the investigated resonant wavelength dependencies, the surface-plasmon-polariton cavity mode with a resonant wavelength of 1550 nm can be confined in a disk with a radius of 88 nm and a thickness of 10 nm, where the physical size of the cavity is 0.000064 λ₀³ (λ₀: free space wavelength). The cavity mode has a deep subwavelength mode volume of 0.010 (λ/2n)³ and a high quality factor of 1900 at 40K, consequently, a large Purcell factor of 1.1 x 10⁵.

1. Introduction

Light confinements in wavelength-scale nanocavites have been a topic that has been attracting considerable attention, owing to their ability to strongly enhance light-matter interactions. Strong interactions, represented by a high quality (Q) factor and a small mode volume (V_mode), enables nanocavities as one of key components for novel photonic devices such as low-threshold lasers [1

H.-G. Park, S.-H. Kim, S.-H. Kwon, Y.-G. Ju, J.-K. Yang, J.-H. Baek, S.-B. Kim, and Y.-H. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305(5689), 1444–1447 (2004). [CrossRef] [PubMed]

–3

M. T. Hill, Y.-S. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S.-H. Kwon, Y.-H. Lee, R. Nötzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 589–594 (2007). [CrossRef]

], efficient single photon sources [4

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vucković, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. 95(1), 013904 (2005). [CrossRef] [PubMed]

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432(7014), 197–200 (2004). [CrossRef] [PubMed]

], optical switch [6

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocaviy,” Nat. Photonics 4(7), 477–483 (2010). [CrossRef]

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E.-J. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photonics 4(3), 182–187 (2010). [CrossRef]

], and optical memories [8

M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432(7014), 206–209 (2004). [CrossRef] [PubMed]

]. Recently, metal coated dielectric cavities demonstrated the smallest mode volumes in dielectric cavities [3

K. Yu, A. Lakhani, and M. C. Wu, “Subwavelength metal-optic semiconductor nanopatch lasers,” Opt. Express 18(9), 8790–8799 (2010). [CrossRef] [PubMed]

–11

C. Manolatou and F. Rana, “Subwavelength nanopatch cavities for semiconductor plasmon lasers,” IEEE J. Quantum Electron. 44(5), 435–447 (2008). [CrossRef]

], however, further size reduction is intrinsically limited by the diffraction-limit, order of wavelength in material. In contrast to dielectric cavities, plasmonic cavities allow light confinement in the subwavelength mode volume [12

M. Kuttge, F. J. García de Abajo, and A. Polman, “Ultrasmall mode volume plasmonic nanodisk resonators,” Nano Lett. 10(5), 1537–1541 (2010). [CrossRef] [PubMed]

–18

J.-H. Kang, H.-G. Park, and S.-H. Kwon, “Room-temperature high-Q channel-waveguide surface plasmon nanocavity,” Opt. Express 19(15), 13892–13898 (2011). [CrossRef] [PubMed]

On the other hand, among dielectric cavities, whispering-gallery-mode (WGM) excited at disk or ring cavities have been studied over a wide range of applications such as optical switch [7

], memory [8

], channel-drop filters [19

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997). [CrossRef]

], and laser [20

M. Fujita, A. Sakai, and T. Baba, “Ultrasmall and ultralow threshold GaInAsP-InP microdisk injection lasers: design, fabrication, lasing characteristics, and spontaneous emission factor,” IEEE J. Sel. Top. Quantum Electron. 5(3), 673–681 (1999). [CrossRef]

] by applying its unique modal characteristics of high Q factor, efficient waveguide coupling, and mode degeneracy [21

K. Vahala, Optical Microcavities (World Scientific, 2004).

,22

R. K. Chang and A. J. Campillo, Optical Processes in Microcavities, 1st ed. (World Scientific, 1996).

]. However, as the radius of a cavity decreases, radiation loss of the WGM tends to increase due to weaker total internal reflection [21

K. Vahala, Optical Microcavities (World Scientific, 2004).

,22

R. K. Chang and A. J. Campillo, Optical Processes in Microcavities, 1st ed. (World Scientific, 1996).

]. Therefore, conventional WGM based on dielectric cavities has the limitation of size reduction, which becomes the main obstacle to miniaturize photonic devices based on the WGM. Very recently, the plasmonic WGM based on surface-plasmon-polaritons (SPPs) has been reported [12

M. Kuttge, F. J. García de Abajo, and A. Polman, “Ultrasmall mode volume plasmonic nanodisk resonators,” Nano Lett. 10(5), 1537–1541 (2010). [CrossRef] [PubMed]

,16

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(9), 3679–3683 (2010). [CrossRef] [PubMed]

,23

B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, and K. Vahala, “High-Q surface-plasmon-polariton whispering-gallery microcavity,” Nature 457(7228), 455–458 (2009). [CrossRef] [PubMed]

]. Whereas there are few studies on theoretical analysis to reduce cavity size to the deep-subwavelength dimension while the high Q and same resonant wavelength are kept.

Due to its small size, the plasmonic WGM cavity, which supports WGM properties in subwavelength size, can be a new building block for the high-density integration of photonic devices. In this letter, we propose a deep-subwavelength-sized plasmonic WGM cavity by intricately reducing radius (R) and thickness (t) simultaneously. In this cavity with R = 88 nm and t = 10 nm, the physical volume of (λ₀/30)³ (λ₀: free space wavelength), large Q of 1900 at 40K and ultrasmall mode volume (V_mode) of 0.010 (λ/2n)³ are achieved, which results in a high Purcell Factor (F_p) of 1.1 x 10⁵. In addition, we divide plasmonic cavity loss into radiation loss and metallic absorption loss and investigate which loss limits Q factors depending on the azimuthal number of the plasmonic WGM when the cavity size decreases.

2. Plasmonic whispering-gallery-mode cavity for different azimuthal number

Figure 1(a) shows a schematic diagram of the plasmonic disk cavity consisting of a dielectric disk with radius of R and thickness of t sandwiched by two silver disks with the same radii. The thicknesses of silver disks are 200 nm. This plasmonic WGM cavity can be efficiently excited by electrical injection through top and bottom metal disks [11

C. Manolatou and F. Rana, “Subwavelength nanopatch cavities for semiconductor plasmon lasers,” IEEE J. Quantum Electron. 44(5), 435–447 (2008). [CrossRef]

]. In a cavity with R = 476 nm and t = 100 nm, plasmonic WGM with an azimuthal number (N) of 6 can be excited at a resonant wavelength of 1550 nm through a three-dimensional (3D) finite-difference time-domain simulation, as shown in the electric field (E_z) profiles of Fig. 1(b) and 1(c). The horizontal view shows a similar field profile with the transverse-magnetic (TM)-like WGM in the conventional dielectric disk [21

K. Vahala, Optical Microcavities (World Scientific, 2004).

,22

R. K. Chang and A. J. Campillo, Optical Processes in Microcavities, 1st ed. (World Scientific, 1996).

], however, in the vertical direction, the electric fields in the cross-sectional view are only tightly confined inside the dielectric disk due to the top and bottom silver disks in contrast to the field extension of the conventional WGM over air [21

K. Vahala, Optical Microcavities (World Scientific, 2004).

,22

R. K. Chang and A. J. Campillo, Optical Processes in Microcavities, 1st ed. (World Scientific, 1996).

Fig. 1 (a) Schematic diagram of the plasmonic disk cavity consisting of silver (gray)/dielectric (red)/silver. R and t indicate the radius of the disk and thickness of the dielectric, respectively. (b) Horizontal and (c) cross-sectional views of the electric field (E_z) profiles of the plasmonic WGM mode with the azimuthal number, N = 6 for the cavity with R = 476 nm and t = 100 nm.

The dielectric was assumed to have a high refractive index of 3.4 (e.g. InP, Si or GaAs) and silver was modeled by the Drude model: ε(ω) = ε_∞ - ω_p² / (ω² + iγω). Experimentally determined dielectric functions of silver were fitted by the background dielectric constant ε_∞ of 3.1, the plasma frequency ω_p of 1.4 x 10¹⁶ s⁻¹ and the collision frequency γ at room temperature of 3.1 x 10¹³ s⁻¹, respectively [15

M.-K. Seo, S.-H. Kwon, H.-S. Ee, and H.-G. Park, “Full three-dimensional subwavelength high-Q surface-plasmon-polariton cavity,” Nano Lett. 9(12), 4078–4082 (2009). [CrossRef] [PubMed]

–18

J.-H. Kang, H.-G. Park, and S.-H. Kwon, “Room-temperature high-Q channel-waveguide surface plasmon nanocavity,” Opt. Express 19(15), 13892–13898 (2011). [CrossRef] [PubMed]

,24

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]

]. A spatial resolution of 1 nm was used for these calculations. We used a home-made FDTD code for numerical simulation. To excite the plasmonic WGM, a dipole emitter was placed 1 nm away from the bottom of the silver surface. The mode volume was defined as the ratio of the total energy density of the mode to the peak energy density, where the effective refractive index of metal was used [14

Y. Gong and J. Vuckovic, “Design of plasmon cavities for solid-state cavity quantum electrodynamics applications,” Appl. Phys. Lett. 90(3), 033113 (2007). [CrossRef]

–17

J.-H. Kang, Y.-S. No, S.-H. Kwon, and H.-G. Park, “Ultrasmall subwavelength nanorod plasmonic cavity,” Opt. Lett. 36(11), 2011–2013 (2011). [CrossRef] [PubMed]

In order to investigate the effects of size reduction regarding the plasmonic WGM, Q factors at 40K were calculated as a function of the azimuthal number (Fig. 2 ). The Q factor is defined as Q = ω₀(Stored Energy)/(Power Loss), and calculated from the time decay of the cavity energy. The cavity thickness is fixed at t = 100 nm and the resonant wavelength is kept at 1550 nm for fair comparison. Thus, the radius of the cavity decreases with decreasing the azimuthal number to provide the same resonant wavelength, which is shown from the corresponding radius for a given azimuthal number at the top axis in Fig. 2.

Fig. 2 Q factors of plasmonic WGM for different azimuthal numbers. The top axis shows the corresponding radius of the cavities to the azimuthal number, having the same resonant wavelength of 1550 nm. Q_total, Q_optical, and Q_absorption are indicated by black, blue, and red lines, respectively.

The Q factor calculated at 40K can provide a lower limit of Q for the solid-state quantum electrodynamics (QED) experiments since the operation temperature for single photon source or strong coupling is usually lower than 40K [4

,14

Y. Gong and J. Vuckovic, “Design of plasmon cavities for solid-state cavity quantum electrodynamics applications,” Appl. Phys. Lett. 90(3), 033113 (2007). [CrossRef]

,17

J.-H. Kang, Y.-S. No, S.-H. Kwon, and H.-G. Park, “Ultrasmall subwavelength nanorod plasmonic cavity,” Opt. Lett. 36(11), 2011–2013 (2011). [CrossRef] [PubMed]

]. The Q factor is calculated from the time decay of the mode energy. Silver at low temperature was described by scaling down the damping collision frequency, γ, by a ratio of the conductivity at low temperature and the room temperature conductivity [3

,14

Y. Gong and J. Vuckovic, “Design of plasmon cavities for solid-state cavity quantum electrodynamics applications,” Appl. Phys. Lett. 90(3), 033113 (2007). [CrossRef]

–18

J.-H. Kang, H.-G. Park, and S.-H. Kwon, “Room-temperature high-Q channel-waveguide surface plasmon nanocavity,” Opt. Express 19(15), 13892–13898 (2011). [CrossRef] [PubMed]

For the fixed thickness, the total Q factor (Q_total) decreases with the decreasing azimuthal number or radius in Fig. 2. Total loss of the plasmonic cavity can be divided into an optical loss by radiation and absorption loss by metallic ohmic loss. In order to systematically investigate the dependence of Q factors on the azimuthal number (or radius), Q_optical and Q_absorption were calculated separately where Q_optical was estimated by setting the damping constant as zero. Here, Q_optical and Q_absorption are inversely proportional to the radiation loss and absorption loss, respectively. Since the real part of the metal permittivity is barely affected by the damping constant in the telecommunication wavelength, where γ is orders of magnitude smaller than the resonant frequency, ω, zeroing γ allows calculating Q_optical separately. separately. Interestingly, when azimuthal number is larger than 4, Q_total is limited by Q_absorption and, when N is smaller than 3, Q_total is limited by Q_optical. In contrast to that Q_absorption almost remains constant as 5500 for the cavities with a fixed thickness of 100 nm regardless of the azimuthal number, Q_optical exponentially decreases with a decreasing azimuthal number, which can be understood by larger radiation loss due to the smaller radius of the curvature [21

K. Vahala, Optical Microcavities (World Scientific, 2004).

,22

R. K. Chang and A. J. Campillo, Optical Processes in Microcavities, 1st ed. (World Scientific, 1996).

]. On the other hand, the plasmonic WGM with N = 1, corresponding to the dipole resonance, serious radiation loss degrades Q to only 10 as in the case of a metal nanoparticle [25

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460(7259), 1110–1112 (2009). [CrossRef] [PubMed]

]. Therefore, unfortunately, simply decreasing radius (or azimuthal number) to miniaturize cavity size seriously deteriorates the Q factor due to increasing radiation loss.

3. Size reduction of plasmonic WGM cavity

In order to further reduce cavity size with the same resonant wavelength while a high Q is maintained, the wavelength, Q factor, and mode volume (V_mode) were systematically investigated in Fig. 3 by varying the structure parameters of the plasmonic disk, radius (R) and thickness (t) for the cavity mode with N = 6, where Q_total is limited by Q_absorption. At a fixed thickness of 100 nm, the resonant wavelength decreases linearly as the radius decreases (Fig. 3(a)) [21

K. Vahala, Optical Microcavities (World Scientific, 2004).

,22

R. K. Chang and A. J. Campillo, Optical Processes in Microcavities, 1st ed. (World Scientific, 1996).

]. On the other hand, at a fixed radius of 476 nm, the resonant wavelength increases considerably for a thinner thickness due to the stronger coupling of SPPs excited at the top and bottom silver/dielectric interfaces (Fig. 3(b)) [15

M.-K. Seo, S.-H. Kwon, H.-S. Ee, and H.-G. Park, “Full three-dimensional subwavelength high-Q surface-plasmon-polariton cavity,” Nano Lett. 9(12), 4078–4082 (2009). [CrossRef] [PubMed]

,17

J.-H. Kang, Y.-S. No, S.-H. Kwon, and H.-G. Park, “Ultrasmall subwavelength nanorod plasmonic cavity,” Opt. Lett. 36(11), 2011–2013 (2011). [CrossRef] [PubMed]

,26

H. T. Miyazaki and Y. Kurokawa, “Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity,” Phys. Rev. Lett. 96(9), 097401 (2006). [CrossRef] [PubMed]

]. The calculated resonant wavelengths were plotted as a function of R and t in Fig. 3(c). In the color map, red (top left) and violet (bottom right) represent longer and shorter wavelengths, respectively. Although the resonant wavelength of conventional nanocavites usually decreases with a reduction in size [21

K. Vahala, Optical Microcavities (World Scientific, 2004).

,22

R. K. Chang and A. J. Campillo, Optical Processes in Microcavities, 1st ed. (World Scientific, 1996).

,27

O. Painter, A. Husain, A. Scherer, P. T. Lee, I. Kim, J. D. O'Brien, and P. D. Dapkus, “Lithographic tuning of a two-dimensional photonic crystal laser array,” IEEE Photon. Technol. Lett. 12(9), 1126–1128 (2000). [CrossRef]

], the proposed plasmonic WGM cavity can have the same resonant wavelength for even a smaller cavity by cleverly decreasing R and t. Indeed, black squares in Fig. 3(c) indicate structure parameter sets (R, t) having the resonant wavelength of 1550 nm. It should be noted that the resonance remains at the same wavelength while the physical volume (πR²t) of the dielectric disk reduces considerably for the cavities with (R, t) ranging from (476 nm, 100 nm) to (214 nm, 10 nm).

Fig. 3 Resonant wavelengths, Q factors, and mode volumes of the plasmonic WGM with the azimuthal number, N = 6. (a) Resonant wavelength vs. R. Here, t of 100 nm is used. The inset shows the cavity mode. (b) Resonant wavelength vs. t. Here, R is fixed at 476 nm. (c) Resonant wavelength color map as a function of R and t. The wavelength decreases with decreasing R or increasing t. Black squares indicate (R, t) sets having the wavelength of 1550 nm. (d) Q factors at 40 K (black) and V_mode (blue) as a function of the physical volume (πR²t) of the dielectric disk. (R, t) varies from (476 nm, 100 nm) to (214 nm, 10 nm), corresponding to black squares in (c). (e) Q factors vs. the physical volume. Q_absoprtion (red) curve matches to Q_total (black) very well, thus, invisible in the graph. The break in the y-axis is used to show Q_total and Q_optical at the same time. (f) Purcell factor vs. the physical volume.

In Fig. 3(d), Q factors at 40 K and V_mode were calculated as a function of the physical volume for the cavities with structure parameters of the black squares in Fig. 3(c). Here, V_mode was defined as the ratio of the total electric field energy density to the peak energy density of the mode, considering the effective refractive index of metal [14

Y. Gong and J. Vuckovic, “Design of plasmon cavities for solid-state cavity quantum electrodynamics applications,” Appl. Phys. Lett. 90(3), 033113 (2007). [CrossRef]

–18

J.-H. Kang, H.-G. Park, and S.-H. Kwon, “Room-temperature high-Q channel-waveguide surface plasmon nanocavity,” Opt. Express 19(15), 13892–13898 (2011). [CrossRef] [PubMed]

]. The Q factor decreases to 3 times the size from 5500 to 1900 as the physical volume decreases 50 times smaller from 0.071 μm³ to 0.0014 μm³, because of the increasing metallic absorption due to more penetration of the electric field to the metal in the thinner cavity. In Fig. 3(e), total cavity loss is dominated by absorption loss over the whole investigated range of the physical volume, while optical loss is negligible, as shown in very high Q_optical. On the other hand, similar to the physical volume, V_mode decreases much faster than the Q factor from 1.6 (λ/2n)³ to 0.044 (λ/2n)³. As result of an extremely small V_mode and large Q factor for a cavity with small physical volume, the large Purcell factor (F_p), proportional to the ratio of Q factor and V_mode, of 2.6 x 10⁴ could be obtained for the cavity with R = 214 nm and t = 10 nm (Fig. 3(f)) [14

Y. Gong and J. Vuckovic, “Design of plasmon cavities for solid-state cavity quantum electrodynamics applications,” Appl. Phys. Lett. 90(3), 033113 (2007). [CrossRef]

,17

J.-H. Kang, Y.-S. No, S.-H. Kwon, and H.-G. Park, “Ultrasmall subwavelength nanorod plasmonic cavity,” Opt. Lett. 36(11), 2011–2013 (2011). [CrossRef] [PubMed]

In contrast, the Q factor of the plasmonic WGM with the azimuthal number, N = 2 rather increases 6 times larger as the cavity size decreases, although V_mode reduces to 30 times the size. First, the resonant wavelengths for the plasmonic WGM with N = 2 were investigated for the various structure parameters in Fig. 4(a) , which shows increasing wavelength for larger R and thinner t like the plasmonic WGM with N = 6. For the (R, t) sets ranging from (195 nm, 100 nm) to (88 nm, 10 nm), having a resonant wavelength of 1550 nm, Q factors and V_mode were calculated, where the physical volume changes from 1.2 x 10⁻² μm³ to 2.4 x 10⁻⁴ μm³ (Fig. 4(b)). In Fig. 2 and Fig. 4(c), the Q factor of the cavity with R = 195 nm and t = 100 nm was limited by Q_optical, related to radiation loss. However, as the physical volume decreases, Q_optical increases exponentially by two orders of magnitude in Fig. 4(c). Because a thinner metal-insulator-metal waveguide has a larger effective refractive index [26

H. T. Miyazaki and Y. Kurokawa, “Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity,” Phys. Rev. Lett. 96(9), 097401 (2006). [CrossRef] [PubMed]

], and radiation loss of WGM decreases. In contrast, Q_absorption modestly decreases to three times the size from 5700 to 1900 due to increasing metallic absorption loss. As result, Q_total rather increases from 320, limited by radiation loss, to 1900, limited by absorption loss, even though cavity size reduces 50 times smaller from (R, t) = (195 nm, 100 nm) to (88 nm, 10 nm). However, if the thickness becomes smaller, Q factor decreases due to increasing absorption loss. V_mode reduces from 0.33 (λ/2n)³ to 0.010 (λ/2n)³ with decreasing the physical volume in Fig. 4(b). As a result of the increasing Q factor and exponentially decreasing V_mode with decreasing cavity size, F_p increases dramatically upto 1.1 x 10⁵ in Fig. 4(d). Considering the average positioning of an emitter inside the cavity, still large average F_p of 2.9 x 10⁴ was also calculated. Compared with the mode with N = 6, the plasmonic WGM with N = 2 has higher Purcell factor due to smaller mode volume while Q factor, limited by the absorption loss, is identical.

Fig. 4 Resonant wavelengths, Q factors, and mode volume for the plasmonic WGM with the azimuthal number, N = 2. (a) Resonant wavelength color map as a function of R and t. Black squares indicate (R, t) sets having resonant wavelength of 1550 nm. (b) Q factors at 40 K (black) and V_mode (blue) calculated as a function of the physical volume (πR²t) of the dielectric disk. (R, t) varies from (195 nm, 100 nm) to (88 nm, 10 nm), corresponding to black squares in (a). (c) Q factors vs. the physical volume. (f) Purcell factor vs. the physical volume. The inset shows the electric field profile of the cavity mode with N = 2.

4. Conclusion

We proposed a plasmonic WGM cavity having an extremely small mode volume of 0.010 (λ/2n)³ and high Q factor of 1900 at 40K. In the dielectric disk sized by a radius of 88 nm and a thickness of 10 nm with an ultra-small physical volume of 0.000032 λ₀³ (λ₀: free space wavelength), SPPs with a wavelength of 1550 nm were strongly confined by two silver disks. The deep subwavelength mode volume allowed obtaining a large Purcell factor of 1.1 x 10⁵ at 40 K. Even though at room temperature, where metallic absorption loss seriously increases, the low Q factor of 60 is calculated, thanks to the small mode volume, still a high Purcell factor of 3600 could be achieved. The proposed plasmonic WGM cavity can be one of key components for a wide range of nanophotonic devices such as a single photon source, optical switch, optical memory, and low threshold light sources. In addition, the strategy to optimize the plasmonic cavity structure for the high Q factor, small V_mode, and the desired resonant wavelength will also be useful to design nanocavity devices for various applications.

Acknowledgments

This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (Grant No. 2012-0003438).

References and links

1.	H.-G. Park, S.-H. Kim, S.-H. Kwon, Y.-G. Ju, J.-K. Yang, J.-H. Baek, S.-B. Kim, and Y.-H. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305(5689), 1444–1447 (2004). [CrossRef] [PubMed]
2.	B. Ellis, M. A. Mayer, G. Shambat, T. Sarmiento, J. Harris, E. E. Haller, and J. Vuckovic, “Ultralow-threshold electrically pumped quantum dot photonic-crystal nanocavity laser,” Nat. Photonics 5(5), 297–300 (2011). [CrossRef]
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4.	D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vucković, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. 95(1), 013904 (2005). [CrossRef] [PubMed]
5.	J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432(7014), 197–200 (2004). [CrossRef] [PubMed]
6.	K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocaviy,” Nat. Photonics 4(7), 477–483 (2010). [CrossRef]
7.	L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E.-J. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photonics 4(3), 182–187 (2010). [CrossRef]
8.	M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432(7014), 206–209 (2004). [CrossRef] [PubMed]
9.	K. Yu, A. Lakhani, and M. C. Wu, “Subwavelength metal-optic semiconductor nanopatch lasers,” Opt. Express 18(9), 8790–8799 (2010). [CrossRef] [PubMed]
10.	M. P. Nezhad, A. Simic, O. Bondarenko, B. Slutsky, A. Mizrahi, L. Feng, V. Lomakin, and Y. Fainman, “Room-temperature subwavelength metallo-dielectric lasers,” Nat. Photonics 4(6), 395–399 (2010). [CrossRef]
11.	C. Manolatou and F. Rana, “Subwavelength nanopatch cavities for semiconductor plasmon lasers,” IEEE J. Quantum Electron. 44(5), 435–447 (2008). [CrossRef]
12.	M. Kuttge, F. J. García de Abajo, and A. Polman, “Ultrasmall mode volume plasmonic nanodisk resonators,” Nano Lett. 10(5), 1537–1541 (2010). [CrossRef] [PubMed]
13.	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(7264), 629–632 (2009). [CrossRef] [PubMed]
14.	Y. Gong and J. Vuckovic, “Design of plasmon cavities for solid-state cavity quantum electrodynamics applications,” Appl. Phys. Lett. 90(3), 033113 (2007). [CrossRef]
15.	M.-K. Seo, S.-H. Kwon, H.-S. Ee, and H.-G. Park, “Full three-dimensional subwavelength high-Q surface-plasmon-polariton cavity,” Nano Lett. 9(12), 4078–4082 (2009). [CrossRef] [PubMed]
16.	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(9), 3679–3683 (2010). [CrossRef] [PubMed]
17.	J.-H. Kang, Y.-S. No, S.-H. Kwon, and H.-G. Park, “Ultrasmall subwavelength nanorod plasmonic cavity,” Opt. Lett. 36(11), 2011–2013 (2011). [CrossRef] [PubMed]
18.	J.-H. Kang, H.-G. Park, and S.-H. Kwon, “Room-temperature high-Q channel-waveguide surface plasmon nanocavity,” Opt. Express 19(15), 13892–13898 (2011). [CrossRef] [PubMed]
19.	B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997). [CrossRef]
20.	M. Fujita, A. Sakai, and T. Baba, “Ultrasmall and ultralow threshold GaInAsP-InP microdisk injection lasers: design, fabrication, lasing characteristics, and spontaneous emission factor,” IEEE J. Sel. Top. Quantum Electron. 5(3), 673–681 (1999). [CrossRef]
21.	K. Vahala, Optical Microcavities (World Scientific, 2004).
22.	R. K. Chang and A. J. Campillo, Optical Processes in Microcavities, 1st ed. (World Scientific, 1996).
23.	B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, and K. Vahala, “High-Q surface-plasmon-polariton whispering-gallery microcavity,” Nature 457(7228), 455–458 (2009). [CrossRef] [PubMed]
24.	P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]
25.	M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460(7259), 1110–1112 (2009). [CrossRef] [PubMed]
26.	H. T. Miyazaki and Y. Kurokawa, “Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity,” Phys. Rev. Lett. 96(9), 097401 (2006). [CrossRef] [PubMed]
27.	O. Painter, A. Husain, A. Scherer, P. T. Lee, I. Kim, J. D. O'Brien, and P. D. Dapkus, “Lithographic tuning of a two-dimensional photonic crystal laser array,” IEEE Photon. Technol. Lett. 12(9), 1126–1128 (2000). [CrossRef]

OCIS Codes
(230.5750) Optical devices : Resonators
(240.6680) Optics at surfaces : Surface plasmons
(250.5403) Optoelectronics : Plasmonics

ToC Category:
Optics at Surfaces

History
Original Manuscript: September 11, 2012
Revised Manuscript: October 12, 2012
Manuscript Accepted: October 12, 2012
Published: October 16, 2012

Citation
Soon-Hong Kwon, "Deep subwavelength plasmonic whispering-gallery-mode cavity," Opt. Express 20, 24918-24924 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-22-24918

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References

H.-G. Park, S.-H. Kim, S.-H. Kwon, Y.-G. Ju, J.-K. Yang, J.-H. Baek, S.-B. Kim, and Y.-H. Lee, “Electrically driven single-cell photonic crystal laser,” Science305(5689), 1444–1447 (2004). [CrossRef] [PubMed]
B. Ellis, M. A. Mayer, G. Shambat, T. Sarmiento, J. Harris, E. E. Haller, and J. Vuckovic, “Ultralow-threshold electrically pumped quantum dot photonic-crystal nanocavity laser,” Nat. Photonics5(5), 297–300 (2011). [CrossRef]
M. T. Hill, Y.-S. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S.-H. Kwon, Y.-H. Lee, R. Nötzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics1(10), 589–594 (2007). [CrossRef]
D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vucković, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett.95(1), 013904 (2005). [CrossRef] [PubMed]
J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature432(7014), 197–200 (2004). [CrossRef] [PubMed]
K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocaviy,” Nat. Photonics4(7), 477–483 (2010). [CrossRef]
L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E.-J. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photonics4(3), 182–187 (2010). [CrossRef]
M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature432(7014), 206–209 (2004). [CrossRef] [PubMed]
K. Yu, A. Lakhani, and M. C. Wu, “Subwavelength metal-optic semiconductor nanopatch lasers,” Opt. Express18(9), 8790–8799 (2010). [CrossRef] [PubMed]
M. P. Nezhad, A. Simic, O. Bondarenko, B. Slutsky, A. Mizrahi, L. Feng, V. Lomakin, and Y. Fainman, “Room-temperature subwavelength metallo-dielectric lasers,” Nat. Photonics4(6), 395–399 (2010). [CrossRef]
C. Manolatou and F. Rana, “Subwavelength nanopatch cavities for semiconductor plasmon lasers,” IEEE J. Quantum Electron.44(5), 435–447 (2008). [CrossRef]
M. Kuttge, F. J. García de Abajo, and A. Polman, “Ultrasmall mode volume plasmonic nanodisk resonators,” Nano Lett.10(5), 1537–1541 (2010). [CrossRef] [PubMed]
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,” Nature461(7264), 629–632 (2009). [CrossRef] [PubMed]
Y. Gong and J. Vuckovic, “Design of plasmon cavities for solid-state cavity quantum electrodynamics applications,” Appl. Phys. Lett.90(3), 033113 (2007). [CrossRef]
M.-K. Seo, S.-H. Kwon, H.-S. Ee, and H.-G. Park, “Full three-dimensional subwavelength high-Q surface-plasmon-polariton cavity,” Nano Lett.9(12), 4078–4082 (2009). [CrossRef] [PubMed]
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(9), 3679–3683 (2010). [CrossRef] [PubMed]
J.-H. Kang, Y.-S. No, S.-H. Kwon, and H.-G. Park, “Ultrasmall subwavelength nanorod plasmonic cavity,” Opt. Lett.36(11), 2011–2013 (2011). [CrossRef] [PubMed]
J.-H. Kang, H.-G. Park, and S.-H. Kwon, “Room-temperature high-Q channel-waveguide surface plasmon nanocavity,” Opt. Express19(15), 13892–13898 (2011). [CrossRef] [PubMed]
B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol.15(6), 998–1005 (1997). [CrossRef]
M. Fujita, A. Sakai, and T. Baba, “Ultrasmall and ultralow threshold GaInAsP-InP microdisk injection lasers: design, fabrication, lasing characteristics, and spontaneous emission factor,” IEEE J. Sel. Top. Quantum Electron.5(3), 673–681 (1999). [CrossRef]
K. Vahala, Optical Microcavities (World Scientific, 2004).
R. K. Chang and A. J. Campillo, Optical Processes in Microcavities, 1st ed. (World Scientific, 1996).
B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, and K. Vahala, “High-Q surface-plasmon-polariton whispering-gallery microcavity,” Nature457(7228), 455–458 (2009). [CrossRef] [PubMed]
P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972). [CrossRef]
M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature460(7259), 1110–1112 (2009). [CrossRef] [PubMed]
H. T. Miyazaki and Y. Kurokawa, “Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity,” Phys. Rev. Lett.96(9), 097401 (2006). [CrossRef] [PubMed]
O. Painter, A. Husain, A. Scherer, P. T. Lee, I. Kim, J. D. O'Brien, and P. D. Dapkus, “Lithographic tuning of a two-dimensional photonic crystal laser array,” IEEE Photon. Technol. Lett.12(9), 1126–1128 (2000). [CrossRef]

Arakawa, Y.
Baba, T.
Baek, J.-H.
Baets, R.
Bakker, R.
Bartal, G.
Belgrave, A. M.
Binsma, H.
Bondarenko, O.
Christy, R. W.
Chu, S. T.
Dai, L.
Dapkus, P. D.
de Vries, T.
de Waardt, H.
Den Besten, J. H.
Dorren, H. J. S.
Ee, H.-S.
Eijkemans, T. J.
Ellis, B.
Englund, D.
Fainman, Y.
Fattal, D.
Feng, L.
Forchel, A.
Foresi, J.
Fujita, M.
García de Abajo, F. J.
Geluk, E. J.
Geluk, E.-J.
Gladden, C.
Gong, Y.
Haller, E. E.
Harris, J.
Haus, H. A.
Herz, E.
Hill, M. T.
Hofmann, C.
Husain, A.
Huybrechts, K.
Johnson, P. B.
Ju, Y.-G.
Kang, J.-H.
Keldysh, L. V.
Khoe, G. D.
Kim, I.
Kim, S.-B.
Kim, S.-H.
Kim, S.-K.
Kuhn, S.
Kulakovskii, V. D.
Kumar, R.
Kurokawa, Y.
Kuttge, M.
Kwon, S.-H.
Laine, J. P.
Lakhani, A.
Lee, P. T.
Lee, Y.-H.
Leijtens, X. J. M.
Lieber, C. M.
Little, B. E.
Liu, L.
Löffler, A.
Lomakin, V.
Ma, R.-M.
Manolatou, C.
Matsuo, S.
Mayer, M. A.
Min, B.
Miyazaki, H. T.
Mizrahi, A.
Morthier, G.
Nakaoka, T.
Narimanov, E. E.
Nezhad, M. P.
No, Y.-S.
Noginov, M. A.
Notomi, M.
Nötzel, R.
Nozaki, K.
O'Brien, J. D.
Oei, Y. S.
Oei, Y.-S.
Ostby, E.
Oulton, R. F.
Painter, O.
Park, H.-G.
Polman, A.
Rana, F.
Regreny, P.
Reinecke, T. L.
Reithmaier, J. P.
Reitzenstein, S.
Roelkens, G.
Sakai, A.
Sarmiento, T.
Sato, T.
Scherer, A.
Seassal, C.
Sek, G.
Seo, M.-K.
Shalaev, V. M.
Shambat, G.
Shinya, A.
Simic, A.
Slutsky, B.
Smalbrugge, B.
Smit, M. K.
Solomon, G.
Sorger, V.
Sorger, V. J.
Spuesens, T.
Stout, S.
Suteewong, T.
Tanabe, T.
Taniyama, H.
Turkiewicz, J. P.
Ulin-Avila, E.
Vahala, K.
van Otten, F. W. M.
Van Thourhout, D.
van Veldhoven, P. J.
Vuckovic, J.
Waks, E.
Wiesner, U.
Wu, M. C.
Yamamoto, Y.
Yang, J.-K.
Yang, L.
Yu, K.
Zentgraf, T.
Zhang, B.
Zhang, X.
Zhu, G.
Zhu, Y.

Appl. Phys. Lett.

Y. Gong and J. Vuckovic, “Design of plasmon cavities for solid-state cavity quantum electrodynamics applications,” Appl. Phys. Lett.90(3), 033113 (2007). [CrossRef]

IEEE J. Quantum Electron.

C. Manolatou and F. Rana, “Subwavelength nanopatch cavities for semiconductor plasmon lasers,” IEEE J. Quantum Electron.44(5), 435–447 (2008). [CrossRef]

IEEE J. Sel. Top. Quantum Electron.

M. Fujita, A. Sakai, and T. Baba, “Ultrasmall and ultralow threshold GaInAsP-InP microdisk injection lasers: design, fabrication, lasing characteristics, and spontaneous emission factor,” IEEE J. Sel. Top. Quantum Electron.5(3), 673–681 (1999). [CrossRef]

IEEE Photon. Technol. Lett.

O. Painter, A. Husain, A. Scherer, P. T. Lee, I. Kim, J. D. O'Brien, and P. D. Dapkus, “Lithographic tuning of a two-dimensional photonic crystal laser array,” IEEE Photon. Technol. Lett.12(9), 1126–1128 (2000). [CrossRef]

J. Lightwave Technol.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol.15(6), 998–1005 (1997). [CrossRef]

Nano Lett.

M. Kuttge, F. J. García de Abajo, and A. Polman, “Ultrasmall mode volume plasmonic nanodisk resonators,” Nano Lett.10(5), 1537–1541 (2010). [CrossRef] [PubMed]
M.-K. Seo, S.-H. Kwon, H.-S. Ee, and H.-G. Park, “Full three-dimensional subwavelength high-Q surface-plasmon-polariton cavity,” Nano Lett.9(12), 4078–4082 (2009). [CrossRef] [PubMed]
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(9), 3679–3683 (2010). [CrossRef] [PubMed]

Nat. Photonics

M. P. Nezhad, A. Simic, O. Bondarenko, B. Slutsky, A. Mizrahi, L. Feng, V. Lomakin, and Y. Fainman, “Room-temperature subwavelength metallo-dielectric lasers,” Nat. Photonics4(6), 395–399 (2010). [CrossRef]
B. Ellis, M. A. Mayer, G. Shambat, T. Sarmiento, J. Harris, E. E. Haller, and J. Vuckovic, “Ultralow-threshold electrically pumped quantum dot photonic-crystal nanocavity laser,” Nat. Photonics5(5), 297–300 (2011). [CrossRef]
M. T. Hill, Y.-S. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S.-H. Kwon, Y.-H. Lee, R. Nötzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics1(10), 589–594 (2007). [CrossRef]
K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocaviy,” Nat. Photonics4(7), 477–483 (2010). [CrossRef]
L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E.-J. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photonics4(3), 182–187 (2010). [CrossRef]

Nature

M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature432(7014), 206–209 (2004). [CrossRef] [PubMed]
J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature432(7014), 197–200 (2004). [CrossRef] [PubMed]
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,” Nature461(7264), 629–632 (2009). [CrossRef] [PubMed]
M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature460(7259), 1110–1112 (2009). [CrossRef] [PubMed]
B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, and K. Vahala, “High-Q surface-plasmon-polariton whispering-gallery microcavity,” Nature457(7228), 455–458 (2009). [CrossRef] [PubMed]

Opt. Express

Opt. Lett.

J.-H. Kang, Y.-S. No, S.-H. Kwon, and H.-G. Park, “Ultrasmall subwavelength nanorod plasmonic cavity,” Opt. Lett.36(11), 2011–2013 (2011). [CrossRef] [PubMed]

Phys. Rev. B

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972). [CrossRef]

Phys. Rev. Lett.

H. T. Miyazaki and Y. Kurokawa, “Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity,” Phys. Rev. Lett.96(9), 097401 (2006). [CrossRef] [PubMed]
D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vucković, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett.95(1), 013904 (2005). [CrossRef] [PubMed]

Science

H.-G. Park, S.-H. Kim, S.-H. Kwon, Y.-G. Ju, J.-K. Yang, J.-H. Baek, S.-B. Kim, and Y.-H. Lee, “Electrically driven single-cell photonic crystal laser,” Science305(5689), 1444–1447 (2004). [CrossRef] [PubMed]

Other

K. Vahala, Optical Microcavities (World Scientific, 2004).
R. K. Chang and A. J. Campillo, Optical Processes in Microcavities, 1st ed. (World Scientific, 1996).

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