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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 7 — Apr. 7, 2014
  • pp: 8490–8502
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Whispering gallery mode nanodisk resonator based on layered metal-dielectric waveguide

Fei Lou, Min Yan, Lars Thylen, Min Qiu, and Lech Wosinski  »View Author Affiliations


Optics Express, Vol. 22, Issue 7, pp. 8490-8502 (2014)
http://dx.doi.org/10.1364/OE.22.008490


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Abstract

This paper proposes a layered metal-dielectric waveguide consisting of a stack of alternating metal and dielectric films which enables an ultracompact mode confinement. The properties of whispering gallery modes supported by disk resonators based on such waveguides are investigated for achieving a large Purcell factor. We show that by stacking three layers of 10 nm thick silver with two layers of 50 nm dielectric layers (of refractive index n) in sequence, the disk radius can be as small as 61 nm λ 0 /(7n) and the mode volume is only 0.0175 ( λ 0 /(2n)) 3 . When operating at 40 K, the cavity’s Q-factor can be ~670; Purcell factor can be as large as 2.3× 10 4 , which is more than five times larger than that achievable in a metal-dielectric-metal disk cavity in the same condition. When more dielectric layers with smaller thicknesses are used, even more compact confinement can be achieved. For example, the radius of a cavity consisting of seven dielectric-layer waveguide can be shrunk down to λ 0 /(13.5n) , corresponding to a mode volume of 0.005 λ 0 /(2n) ) 3 , and Purcell factor can be enhanced to 7.3× 10 4 at 40 K. The influence of parameters like thicknesses of dielectric and metal films, cavity size, and number of dielectric layers is also comprehensively studied. The proposed waveguide and nanodisk cavity provide an alternative for ultracompact light confinement, and can find applications where a strong light-matter interaction is necessary.

© 2014 Optical Society of America

1. Introduction

In this paper, we propose a layered metal-dielectric (LMD) waveguide whose geometry resembles a hyperbolic metamaterial waveguide, while its guiding principle is similar as MDM waveguide and dielectric-metal-dielectric (DMD) waveguide. In contrast to MDM and DMD waveguides, the proposed LMD waveguide achieves much more compact confinement due to the strong mode coupling between multiple metal and dielectric layers. The physical properties of WGM nanodisks based on the LMD waveguide will be systematically studied, including Q-factor, mode volume and Purcell factor, as well as influence of the metal and dielectric thicknesses. We show that when the metal and/or dielectric layer is thin, strong inter-layer coupling occurs and the propagation constant can increase significantly. Simulations show that the radius of the disk cavity can be shrunk down to 61 nm, i.e. λ0/(7n) (here n is the dielectric’s index) when stacking three layers of 10 nm thick silver alternatively with two layers of 50 nm dielectric layers. The cavity’s mode volume is calculated as small as 0.0175(λ0/(2n))3, and a Purcell factor around 2.3×104 can be achieved at 40 K. The calculated Purcell factor is more than five times larger than that achievable in a metal-dielectric-metal disk cavity with identical dielectric thickness. We also show that when using a LMD waveguide with more dielectric layers, the cavity’s properties can be further enhanced. For example, when the number of dielectric layers changes from 1 to 7, the disk radius can be shrunk from 92 nm to 33 nm λ0/(13.5n), and Purcell factor can be dramatically increased from about 1860 to 7.3×104.

The remainder of the paper is organized as follows. Section 2 explains the waveguiding principle by considering an analytical model of a 1D straight waveguide composed of three layers of metal and two layers of dielectric films. Section 3 studies the cavity properties including Q-factor, mode volume and Purcell factor of a WGM disk based on the proposed waveguide, and compares with a traditional MDM-based cavity. Then the influence of geometry parameters on the LMD cavity properties is systematically studied in Section 4. Section 5 presents the situation when increasing the number of dielectric layers. Finally conclusions are given in Section 6.

2. Waveguiding principles

The proposed layered metal-dielectric waveguide, i.e., LMDN (N = 1, 2 …) is composed by interlacing N + 1 metal layers with N dielectric layers. As schematically shown in Fig. 1(a)
Fig. 1 (a) Schematic diagram of a 1D LMD2 waveguide. The propagation direction is along x + . (b) Field distributions of the even (TM1) mode supported in the 1D LMD2 waveguide. (c) Field distributions of the odd (TM2) mode supported in the 1D LMD2 waveguide.
, a simple 1-dimensional (1D) LMD waveguide with N = 2 is firstly considered, to explain the waveguiding principle. Here, no spatial variation along y direction is assumed. The SPP wave propagates along x direction. The thickness of each metal and dielectric is denoted by hM and h2, respectively. Then the concerned waveguide’s propagation constant can be analyzed analytically. In the study, metal is assumed as silver; its permittivity is described by Drude model εm=εωp2/(ω2+iγω), where ε is 3.1, the plasma frequency ωp is 1.4×1016s1, and the collision frequency γ is 3.1×1013s1 [21

21. S.-H. Kwon, “Deep subwavelength plasmonic whispering gallery-mode cavity,” Opt. Express 20, 918–924 (2012).

, 27

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

]. The dielectric can be various materials such as III-V, Ge, doped Si, etc. A permittivity of 12.25 is assumed without losing generality.

Figures 1(b) and 1(c) show the field distributions of two highly-confined eigen modes supported by the LMD2 waveguide, namely even TM1 mode and odd TM2 mode. The frequency considered is 193.55 THz for 1550 nm operation, which is much lower than the plasmon frequency of silver. In the simulation, the silver thickness is hM=10nm, and the dielectric thickness is h2=50nm. From the figures, one can see that the even mode has a symmetric Ez field across the metal separation in the middle, while the Ez field of the odd mode is asymmetric. In addition, the effective wavelength of the odd mode is relatively smaller than that of the even mode, implying that the corresponding propagation constant is larger. Basically, the LMD2 waveguide can be regarded as a N = 2 stack consisting of two LMD1 waveguides separated by a metal layer with thickness of hM. When hM is thin enough for light penetrating through, the isolated LMD1 modes would symmetrically and asymmetrically couple with each other. The mode hybridization can result in mode splitting and create bonding and anti-bonding modes [28

28. Y. Francescato, V. Giannini, and S. A. Maier, “Strongly confined gap plasmon modes in graphene sandwiches and graphene-on-silicon,” New J. Phys. 15(6), 063020 (2013). [CrossRef]

, 29

29. Q. Wang, H. Zhao, X. Du, W. Zhang, M. Qiu, and Q. Li, “Hybrid photonic-plasmonic molecule based on metal/Si disks,” Opt. Express 21(9), 11037–11047 (2013). [CrossRef] [PubMed]

], i.e. the even and odd modes as shown in Figs. 1(b) and 1(c). Due to the phase matching condition, the bonding and anti-bonding eigen modes in the LMD2 waveguide would satisfy: βp±βpΔ, where βp+ and βp are propagation constants of even and odd modes, and βp is the propagation constant of the fundamental mode in LMD1 waveguide, while Δ represents the momentum shifts due to the mode couplings.

In order to quantitatively analyze the mode splitting, effective refractive indices and propagation lengths of the concerned modes as functions of metal and dielectric thicknesses are plotted in Fig. 2
Fig. 2 Influence of metal and dielectric thicknesses on the effective refractive indices and propagation lengths of the concerned modes. Standard parameters are hM=10nm and h2=50nm. (a) and (b) are variation of effective indices and propagation lengths when changing hM, respectively. (c) and (d) are variation of effective indices and propagation lengths when changing h2, respectively.
. In the analysis, effective mode indices are given by ne±=(βp±)/k0, and propagation lengths are evaluated by Le±=k02/2I(βp±), depicting the 1/e plasmon decay length along x direction. One can see from Fig. 2(a) and 2(c) that for any given geometry, effective indices of bonding and anti-bonding modes satisfy 2ne=ne++ne and ne+<ne. The mode splitting (nene+) decreases as increasing hM due to the decreased mode hybridization since less light can penetrate through the metal when metal gets thicker. When the metal is thick enough (hM >~100nm), the LMD waveguide degenerates into MDM waveguide, and in this case, ne and ne+ approach asymptotically the effective index of a MDM mode, which has a much lower refractive index as shown in Fig. 2(a). To analyze the influence of substrate, nsub± denoting the effective indices of a LMD2 waveguide sitting on a silica substrate are also calculated, as shown in Fig. 2(a). One can see that nsub± are almost identical with ne±, suggesting that the substrate hardly affects the waveguide performance. For simplicity, air is used as cladding and substrate material in the following analysis. As for the influence of dielectric thickness h2, one can see in Fig. 2(c) that ne and ne increase simultaneously with decreasing h2, which is similar as in a MDM waveguide, where better confinement can be achieved with a thinner dielectric. In addition, the mode splitting is relatively less sensitive to the variation of h2 than to the silver thickness variation, mainly because the mode coupling is mostly determined by the field penetration through the metal layer. As a comparison to the traditional MDM waveguide, we also plot the effective index nMDM of a MDM waveguide with 100 nm thick metal in Fig. 2(c). As one can see for a given dielectric thickness, the anti-bonding mode’s effective index ne is significantly larger than nMDM, suggesting that the mode confinement can be significantly enhanced by operating with TM2 mode in a LMD2 waveguide. We then study the propagation lengths of the LMD waveguide as shown in Figs. 2(b) and 2(d). One can find that in the proposed LMD waveguide, there also exists a tradeoff between effective index (confinement) and propagation length. Note that similar tradeoffs exist in all plasmonic waveguides, and one needs to choose suitable design according to specific applications.

3. Nanodisk cavity based on layered metal-dielectric waveguide with N = 2 (LMD2)

4. Influence of metal and dielectric thicknesses on TM2 LMD2 nanodisk cavity

5. Nanodisk cavity based on LMDN waveguide with N > 2

Firstly, WGM nanodisks based on LMD3 waveguides are analyzed. Similarly as the mode splitting in a LMD2 waveguide, the multi-layer coupling in a LMD3 waveguide also results in three hybridized TM modes, namely TM1, TM2 and TM3. The corresponding Ez field distributions of the WGM cavities operating under these modes are shown in Fig. 7(a)
Fig. 7 (a) Ez field distributions of WGM disks based on LMD waveguide with N = 3, 4… 7. (b) Selected radius and the corresponding effective mode index as functions of N. (c) Q-factors and normalized mode volume as functions of N. (d) Purcell factor as a function of N.
, and the respective cavity radii are 86 nm, 60 nm and 48 nm for an azimuthal number m = 1. One may find that similar as the TM2 mode in a LMD2 waveguide, the TM3 mode in a LMD3 waveguide with asymmetric Ez fields across each metal separation also possesses the largest propagation constant. In fact, such reversed mode ordering applies not only for LMD waveguide with N = 2 and 3, but also for N > 3 LMD waveguide. Generally, a LMDN waveguide can be regarded as Nth cascading of LMD1 waveguides separated by a thin metal section. As discussed in Section 2, the asymmetric coupling (anti-bonding) between adjacent LMD1 modes would result in the enhancement of the propagation constant. Hence, when each LMD1 mode asymmetrically couples with adjacent ones, the overall enhancement of the propagation constant is the largest. In Fig. 7(a), the WGM distributions of the nanodisks based on LMDN (N = 4, 5, 6 and 7) waveguides are also shown. One can see that each waveguide has an asymmetric field which has the most compact confinement. Figure 7(b) shows the selected disk radius for m = 1 and the WGM effective index as functions of the number of dielectric layers. When N increases from 1 to 7, the corresponding disk radius drops from 92 nm to 33 nm ~λ0/(13.5n), and neWGM increases from about 2.7 to 7.5. Then, the Q-factors and mode volume of the LMDN cavities are simulated, as shown in Fig. 7(c). On one hand, when N increases from 2 to 7, Q decreases gradually from 680 to 615 due to the enhanced metal absorption loss. On the other hand, Q drops dramatically to ~190 for N = 1. The sudden drop can be understood by comparing the radiation Q-factors for N = 1 and N = 2 cavities. As shown in Fig. 7(c), Qrad for LMD1 cavity is only 215, while Qrad is as large as 2.86×104 for a LMD2 cavity, as discussed in Section 4. Hence, for N>1, since Qrad >> Qabs for N>1, Q is determined by Qabs. On the contrary, the cavity’s Q is largely limited by Qrad for N = 1, resulting in the discontinuity as shown in Fig. 7(c). At last, the normalized mode volume and Purcell factor of each cavity are plotted in Fig. 7(c) and 7(d). One can see that by increasing the number of dielectric layer from 1 to 7, V can be decreased from about 0.06 to 0.005, while Purcell factor can be enhanced from around 1860 to 7.3×104 which is about two times larger than that of a N = 2 cavity.

Note that above studied LMDN cavities of hD = 100 nm and hM = 10 nm are only serving as examples to elaborate the principle of scaling the number of metal-dielectric layers. Since LMDN has similar waveguiding principle as LMD2, varying the metal and dielectric thicknesses has similar influence on LMDN (N>2) cavities as on LMD2 cavity as discussed in section 4. Namely, the bending radii and normalized mode volume decrease when reducing the silver and dielectric thicknesses, while Purcell factors increase. To fabricate the proposed LMDN cavities, methods used to realize hyperbolic metamaterial devices can be applied. For examples, one can use either liftoff processes to deposit multiple metal-dielectric layers as explained in Ref [25

25. X. Yang, J. Yao, J. Rho, X. Yin, and X. Zhang, “Experimental realization of three-dimensional indefinite cavities at the nanoscale with anomalous scaling laws,” Nat. Photonics 6(7), 450–454 (2012). [CrossRef]

], or focused ion beam to define and etch the as-deposited multi-layer structures as in Ref [32

32. J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008). [CrossRef] [PubMed]

]. In practical implementations, one can balance the desired performance and needed fabrication requirements, and choose proper design of layer numbers as well as metal-dielectric thicknesses.

6. Conclusions

Acknowledgment

The work described in this paper was partly supported by the Swedish Research Council (VR) through its Linnæus Center of Excellence ADOPT and proj. VR-621-2010-4379.

References and links

1.

K. J. Vahala, “Optical microcavities,” Nature 424(6950), 839–846 (2003). [CrossRef] [PubMed]

2.

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Demonstration of ultra-high-Q small mode volume toroid microcavities on a chip,” Appl. Phys. Lett. 85(25), 6113–6115 (2004). [CrossRef]

3.

K. Srinivasan, M. Borselli, O. Painter, A. Stintz, and S. Krishna, “Cavity Q, mode volume, and lasing threshold in small diameter AlGaAs microdisks with embedded quantum dots,” Opt. Express 14(3), 1094–1105 (2006). [CrossRef] [PubMed]

4.

H. Y. Ryu, M. Notomi, and Y. H. Lee, “High-quality-factor and small-mode-volume hexapole modes in photonic-crystal-slab nanocavities,” Appl. Phys. Lett. 83(21), 4294–4296 (2003). [CrossRef]

5.

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

6.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010). [CrossRef]

7.

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. Notzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 589–594 (2007). [CrossRef]

8.

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]

9.

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]

10.

R. M. Briggs, J. Grandidier, S. P. Burgos, E. Feigenbaum, and H. A. Atwater, “Efficient coupling between dielectric-loaded plasmonic and silicon photonic waveguides,” Nano Lett. 10(12), 4851–4857 (2010). [CrossRef] [PubMed]

11.

A. V. Krasavin, S. Randhawa, J.-S. Bouillard, J. Renger, R. Quidant, and A. V. Zayats, “Optically-programmable nonlinear photonic component for dielectric-loaded plasmonic circuitry,” Opt. Express 19(25), 25222–25229 (2011). [CrossRef] [PubMed]

12.

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]

13.

R.-M. Ma, R. F. Oulton, V. J. Sorger, G. Bartal, and X. Zhang, “Room-temperature sub-diffraction-limited plasmon laser by total internal reflection,” Nat. Mater. 10(2), 110–113 (2011). [CrossRef] [PubMed]

14.

Y. Song, J. Wang, M. Yan, and M. Qiu, “Subwavelength hybrid plasmonic nanodisk with high Q factor and Purcell factor,” J. Opt. 13(7), 075001 (2011). [CrossRef]

15.

F. Lou, D. Dai, L. Thylen, and L. Wosinski, “Design and analysis of ultra-compact EO polymer modulators based on hybrid plasmonic microring resonators,” Opt. Express 21(17), 20041–20051 (2013). [CrossRef] [PubMed]

16.

M. Khajavikhan, A. Simic, M. Katz, J. H. Lee, B. Slutsky, A. Mizrahi, V. Lomakin, and Y. Fainman, “Thresholdless nanoscale coaxial lasers,” Nature 482(7384), 204–207 (2012). [CrossRef] [PubMed]

17.

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.

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]

19.

R. Zia, M. D. Selker, P. B. Catrysse, and M. L. Brongersma, “Geometries and materials for subwavelength surface plasmon modes,” J. Opt. Soc. Am. A 21(12), 2442–2446 (2004). [CrossRef] [PubMed]

20.

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006). [CrossRef]

21.

S.-H. Kwon, “Deep subwavelength plasmonic whispering gallery-mode cavity,” Opt. Express 20, 918–924 (2012).

22.

M. Yan, L. Thylén, and M. Qiu, “Layered metal-dielectric waveguide: subwavelength guidance, leveraged modulation sensitivity in mode index, and reversed mode ordering,” Opt. Express 19(4), 3818–3824 (2011). [CrossRef] [PubMed]

23.

Y. He, S. He, J. Gao, and X. Yang, “Nanoscale metamaterial optical waveguides with ultrahigh refractive indices,” J. Opt. Soc. Am. B 29(9), 2559–2566 (2012). [CrossRef]

24.

Y. He, L. Sun, S. He, and X. Yang, “Deep subwavelength beam propagation in extremely loss-anisotropic metamaterials,” J. Opt. 15(5), 055105 (2013). [CrossRef]

25.

X. Yang, J. Yao, J. Rho, X. Yin, and X. Zhang, “Experimental realization of three-dimensional indefinite cavities at the nanoscale with anomalous scaling laws,” Nat. Photonics 6(7), 450–454 (2012). [CrossRef]

26.

H. N. S. Krishnamoorthy, Z. Jacob, E. Narimanov, I. Kretzschmar, and V. M. Menon, “Topological Transitions in Metamaterials,” Science 336(6078), 205–209 (2012). [CrossRef] [PubMed]

27.

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

28.

Y. Francescato, V. Giannini, and S. A. Maier, “Strongly confined gap plasmon modes in graphene sandwiches and graphene-on-silicon,” New J. Phys. 15(6), 063020 (2013). [CrossRef]

29.

Q. Wang, H. Zhao, X. Du, W. Zhang, M. Qiu, and Q. Li, “Hybrid photonic-plasmonic molecule based on metal/Si disks,” Opt. Express 21(9), 11037–11047 (2013). [CrossRef] [PubMed]

30.

W. Chen, M. D. Thoreson, S. Ishii, A. V. Kildishev, and V. M. Shalaev, “Ultra-thin ultra-smooth and low-loss silver films on a germanium wetting layer,” Opt. Express 18(5), 5124–5134 (2010). [CrossRef] [PubMed]

31.

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]

32.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008). [CrossRef] [PubMed]

OCIS Codes
(230.5750) Optical devices : Resonators
(250.5300) Optoelectronics : Photonic integrated circuits
(250.5403) Optoelectronics : Plasmonics

ToC Category:
Integrated Optics

History
Original Manuscript: January 3, 2014
Revised Manuscript: March 17, 2014
Manuscript Accepted: March 19, 2014
Published: April 2, 2014

Citation
Fei Lou, Min Yan, Lars Thylen, Min Qiu, and Lech Wosinski, "Whispering gallery mode nanodisk resonator based on layered metal-dielectric waveguide," Opt. Express 22, 8490-8502 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-7-8490


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References

  1. K. J. Vahala, “Optical microcavities,” Nature 424(6950), 839–846 (2003). [CrossRef] [PubMed]
  2. T. J. Kippenberg, S. M. Spillane, K. J. Vahala, “Demonstration of ultra-high-Q small mode volume toroid microcavities on a chip,” Appl. Phys. Lett. 85(25), 6113–6115 (2004). [CrossRef]
  3. K. Srinivasan, M. Borselli, O. Painter, A. Stintz, S. Krishna, “Cavity Q, mode volume, and lasing threshold in small diameter AlGaAs microdisks with embedded quantum dots,” Opt. Express 14(3), 1094–1105 (2006). [CrossRef] [PubMed]
  4. H. Y. Ryu, M. Notomi, Y. H. Lee, “High-quality-factor and small-mode-volume hexapole modes in photonic-crystal-slab nanocavities,” Appl. Phys. Lett. 83(21), 4294–4296 (2003). [CrossRef]
  5. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).
  6. D. K. Gramotnev, S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010). [CrossRef]
  7. 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. Notzel, M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 589–594 (2007). [CrossRef]
  8. S.-H. Kwon, J.-H. Kang, C. Seassal, S.-K. Kim, P. Regreny, Y.-H. Lee, C. M. Lieber, H.-G. Park, “Subwavelength plasmonic lasing from a semiconductor nanodisk with silver nanopan cavity,” Nano Lett. 10(9), 3679–3683 (2010). [CrossRef] [PubMed]
  9. B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, K. Vahala, “High-Q surface-plasmon-polariton whispering-gallery microcavity,” Nature 457(7228), 455–458 (2009). [CrossRef] [PubMed]
  10. R. M. Briggs, J. Grandidier, S. P. Burgos, E. Feigenbaum, H. A. Atwater, “Efficient coupling between dielectric-loaded plasmonic and silicon photonic waveguides,” Nano Lett. 10(12), 4851–4857 (2010). [CrossRef] [PubMed]
  11. A. V. Krasavin, S. Randhawa, J.-S. Bouillard, J. Renger, R. Quidant, A. V. Zayats, “Optically-programmable nonlinear photonic component for dielectric-loaded plasmonic circuitry,” Opt. Express 19(25), 25222–25229 (2011). [CrossRef] [PubMed]
  12. R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009). [CrossRef] [PubMed]
  13. R.-M. Ma, R. F. Oulton, V. J. Sorger, G. Bartal, X. Zhang, “Room-temperature sub-diffraction-limited plasmon laser by total internal reflection,” Nat. Mater. 10(2), 110–113 (2011). [CrossRef] [PubMed]
  14. Y. Song, J. Wang, M. Yan, M. Qiu, “Subwavelength hybrid plasmonic nanodisk with high Q factor and Purcell factor,” J. Opt. 13(7), 075001 (2011). [CrossRef]
  15. F. Lou, D. Dai, L. Thylen, L. Wosinski, “Design and analysis of ultra-compact EO polymer modulators based on hybrid plasmonic microring resonators,” Opt. Express 21(17), 20041–20051 (2013). [CrossRef] [PubMed]
  16. M. Khajavikhan, A. Simic, M. Katz, J. H. Lee, B. Slutsky, A. Mizrahi, V. Lomakin, Y. Fainman, “Thresholdless nanoscale coaxial lasers,” Nature 482(7384), 204–207 (2012). [CrossRef] [PubMed]
  17. M. Kuttge, F. J. García de Abajo, A. Polman, “Ultrasmall mode volume plasmonic nanodisk resonators,” Nano Lett. 10(5), 1537–1541 (2010). [CrossRef] [PubMed]
  18. H. T. Miyazaki, 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]
  19. R. Zia, M. D. Selker, P. B. Catrysse, M. L. Brongersma, “Geometries and materials for subwavelength surface plasmon modes,” J. Opt. Soc. Am. A 21(12), 2442–2446 (2004). [CrossRef] [PubMed]
  20. J. A. Dionne, L. A. Sweatlock, H. A. Atwater, A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006). [CrossRef]
  21. S.-H. Kwon, “Deep subwavelength plasmonic whispering gallery-mode cavity,” Opt. Express 20, 918–924 (2012).
  22. M. Yan, L. Thylén, M. Qiu, “Layered metal-dielectric waveguide: subwavelength guidance, leveraged modulation sensitivity in mode index, and reversed mode ordering,” Opt. Express 19(4), 3818–3824 (2011). [CrossRef] [PubMed]
  23. Y. He, S. He, J. Gao, X. Yang, “Nanoscale metamaterial optical waveguides with ultrahigh refractive indices,” J. Opt. Soc. Am. B 29(9), 2559–2566 (2012). [CrossRef]
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