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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 5 — Mar. 1, 2010
  • pp: 4006–4011
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Surface plasmons amplifications in single Ag nanoring

Zhong-Jian Yang, Nam-Chol Kim, Jian-Bo Li, Mu-Tian Cheng, Shao-Ding Liu, Zhong-Hua Hao, and Qu-Quan Wang  »View Author Affiliations


Optics Express, Vol. 18, Issue 5, pp. 4006-4011 (2010)
http://dx.doi.org/10.1364/OE.18.004006


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Abstract

The stimulated amplifications of surface plasmons (SPs) propagating along a single silver nanoring is theoretically investigated by considering the interactions between SPs and activated semiconductor quantum dots (SQDs). Threshold condition for the stimulated amplifications, the SP density as a function of propagation length and the maximum SP density are obtained. The SPs can be nonlinearly amplified when the pumping rate of SQDs is larger than the threshold, and the maximum value of SP density increases linearly with the pumping rate of SQDs.

© 2010 OSA

1. Introduction

In recent years, there has been a great interest in studying plasmonics for various applications such as photonics and electronics [1

1. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]

3

3. S. A. Maier, “Plasmonics: The Promise of Highly Integrated Optical Devices,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1671–1677 (2006). [CrossRef]

], sensing [4

4. K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. Dasari, and M. S. Feld, “Single molecule detection using surface-enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78(9), 1667–1670 (1997). [CrossRef]

, 5

5. S. Lal, S. Link, and N. S. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics 1(11), 641–648 (2007). [CrossRef]

], nanolithography [6

6. W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic nanolithography,” Nano Lett. 4(6), 1085–1088 (2004). [CrossRef]

] and microscopy [7

7. I. I. Smolyaninov, J. Elliott, A. V. Zayats, and C. C. Davis, “Far-field optical microscopy with a nanometer-scale resolution based on the in-plane image magnification by surface plasmon polaritons,” Phys. Rev. Lett. 94(5), 057401 (2005). [CrossRef] [PubMed]

, 8

8. Z. W. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007). [CrossRef] [PubMed]

]. Plasmonics as a discipline is concerned with the study of surface plasmons and using the properties of surface plasmons (SPs) to manipulate light at the nanoscale. SPs can be strongly localized in metal nanopartilces and nanoholes, and can also propagate in metal nanowires and thin films. The nanosized optical dipole emitters can strongly couple to both localized and nonlocalized SPs.

Based on the strong interaction between nanosized emitters and localized SPs, Bergman and Stockman first proposed a project of Surface Plasmon Amplification by Stimulated Emission of Radiation (SPASER) [9

9. D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90(2), 027402 (2003). [CrossRef] [PubMed]

]. Associated with the idea of SPASER, several theoretical schemes and experimental studies about amplification of SPs have been reported [10

10. N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing Spaser,” Nat. Photonics 2(6), 351–354 (2008). [CrossRef]

22

22. A. Kumar, S. F. Yu, X. F. Li, and S. P. Lau, “Surface plasmonic lasing via the amplification of coupled surface plasmon waves inside dielectric-metal-dielectric waveguides,” Opt. Express 16(20), 16113–16123 (2008). [CrossRef] [PubMed]

].

The interaction between a nanosized emitter and propagating SPs in metal nanowires was systematically studied by Chang et al. [23

23. D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett. 97(5), 053002 (2006). [CrossRef] [PubMed]

, 24

24. D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Strong coupling of single emitters to surface plasmons,” Phys. Rev. B 76(3), 035420 (2007). [CrossRef]

]. By optimizing nanostructures, the nanosized optical dipole can efficiently couple to the propagating SPs. Single plasmons propagating in Ag nanowire was successfully demonstrated [25

25. A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, “Generation of single optical plasmons in metallic nanowires coupled to quantum dots,” Nature 450(7168), 402–406 (2007). [CrossRef] [PubMed]

]. Very recently, the Ag nanorings with smooth surface and bi-crystal were successfully synthesized, which can support standing waves of SPs and were free from the end-loss of SPs in nanowires [26

26. H. M. Gong, L. Zhou, X. R. Su, S. Xiao, S. D. Liu, and Q. Q. Wang, “Illuminating Dark Plasmons of Silver Nanoantenna Rings to Enhance Exciton–Plasmon Interactions,” Adv. Funct. Mater. 19(2), 298–303 (2009). [CrossRef]

, 27

27. S. D. Liu, Z. S. Zhang, and Q. Q. Wang, “High sensitivity and large field enhancement of symmetry broken Au nanorings: effect of multipolar plasmon resonance and propagation,” Opt. Express 17(4), 2906–2917 (2009). [CrossRef] [PubMed]

]. Semiconductor quantum dots (SQDs) with their potential applications in quantum computation and quantum information, have been studied widely in the past years [28

28. T. H. Stievater, X. Li, D. G. Steel, D. Gammon, D. S. Katzer, D. Park, C. Piermarocchi, and L. J. Sham, “Rabi oscillations of excitons in single quantum dots,” Phys. Rev. Lett. 87(13), 133603 (2001). [CrossRef] [PubMed]

31

31. X. Li, Y. Wu, D. Steel, D. Gammon, T. H. Stievater, D. S. Katzer, D. Park, C. Piermarocchi, and L. J. Sham, “An all-optical quantum gate in a semiconductor quantum dot,” Science 301(5634), 809–811 (2003). [CrossRef] [PubMed]

]. These theoretical and experimental achievements motivate us to study the amplification of propagating SPs in Ag nanorings through strong coupling of exciton and plasmon.

2. Theoretical model and analysis

Figures 1(a)
Fig. 1 (a) Schematic of the cross section of an Ag nanoring surrounded by SQDs. The nanoring and SQDs are embedded in a dielectric with electric permittivity ε 1. (b) Schematic of a small part of the ring with a SQD to show the stimulated emission. (c) Energy-level diagram of a two-level SQD, |1and |0are excited and ground states of the SQD, respectively.
and 1(b) illustrate the structure of our nanosystem consisting of an Ag nanoring and the surrounding active SQDs. The Ag nanoring and SQDs are embedded in a dielectric with dielectric constant ε 1. d is the center-to-center distance between a SQD and the Ag nanowire, and all the SQDs have the same distance to the Ag nanowire. The SQDs spatial distribution is designed as the largest linear density surrounding the Ag nanoring for a given distance d. Assuming the largest linear population densities of SQDs is η, which depends on the structure parameters of the system with the relationship η = 2πd/(πRSQD2), where R SQD is the radius of the sphere SQD. Figure 1(c) shows the energy-level diagram of the two-level SQD coupling with SPs. Γ rad and Γ nonrad are the rates of spontaneous emission into free space and the non-radiative emission into Ag nanoring, respectively. Γsp(SpE) and Γsp(StE) denote the spontaneous emission rate and stimulated emission rate into SPs, Γsp(StA) is the stimulated absorption rate and W 01 is the pumping rate of the SQD. In the following part, we first discuss the stimulated interactions of a single SQD and SPs. Then we consider the interactions of many SQDs with SPs, and discuss the steady state solutions of this nano-system.

First, we consider the coupling between a single two-level SQD and SPs. The ring circumference is considered to be much longer than the wire radius, so the ring can be approximately taken as a straight cylinder wire to get the electromagnetic field. Only a fundamental mode of the electromagnetic field is allowed due to the nanowire limit [24

24. D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Strong coupling of single emitters to surface plasmons,” Phys. Rev. B 76(3), 035420 (2007). [CrossRef]

]. The fundamental mode can be expressed as Ei(r,t)=aQi(r)exp(ik//ziωspt), where i = 1, 2 represent the electric fields outside and inside the cylinder, respectively.
Q1(r)=[H0(k1r)×(ik//k1/k12)r^+H0(k1r)×(k12/k12)z^],
Q2(r)=[H0(k1R)/J0(k2R)][J0(k2r)×(ik//k1/k22)r^+J0(k2r)×(k2k1/k22)z^],where k i⊥and k //, are transverse and longitudinal wave vectors, J 0 and H 0 are Bessel function and Hankel function of the first kind, respectively. a is a constant. r^and z^denote the orientation. The SP is quantized using the method of harmonic oscillator quantization [32

32. P. W. Milonni, “Field quantization and radiative processes in dispersive dielectric media,” J. Mod. Opt. 42(10), 1991–2004 (1995). [CrossRef]

]. For simplicity, here we neglect the damping of SPs. Under the rotating wave approximation, the exciton-plasmon interaction Hamiltonian is written as
Hint=g[a^σ10exp(ik//ziωspt)+a^+σ01exp(ik//z+iωspt)],
(1)
where a^+,a^are the creation and annihilation operators of a SP, σ10=|10|, σ01=|01|, |1and |0are excited and ground states of SQDs, respectively. ω sp is the frequency of SPs, which is approximately equal to the dipole transitions frequency ω 10 of the SQD under the resonant excitation condition ω spω 10ω. g is the coupling factor of the SQDs and SPs. g = ω 1/2 μ 10·Q 1(r) / (2 1/2) with μ 10 being the transition matrix element of SQDs. The SQDs emission rate into SPs is obtained from the Fermi's golden rule, ΓSP(ω10)=ΓSP(StE)+ΓSP(SpE)=2π|g|2(n+1)DSP(ωSP),where ΓSP(StE)=2π|g|2nDsp(ω) and ΓSP(SpE)=2π|g|2Dsp(ω). D SP(ω) is the SP density of states, and (n+1) is the total number of SPs attributed to the stimulated and spontaneous emissions of SQDs. The value of Γsp(StA) is equal to that of Γsp(StE). It should be noted that in our discussion the spontaneous emission into free space Γ rad and the non-radiative emission into Ag nanoring Γ nonrad are ignored. In Ref. 24

24. D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Strong coupling of single emitters to surface plasmons,” Phys. Rev. B 76(3), 035420 (2007). [CrossRef]

a Purcell factor is defined by P'=Γsp(SpE)/(Γrad+Γnonrad) to denote the efficiency of spontaneous emission into SPs, and the dependences of Pas functions of wire radius and SQD position are discussed in details. In our system we define a modified Purcell factor as P=(Γsp(SpE)+Γsp(StE))/(Γrad+Γnonrad) to include the contribution of stimulated emissions, so P = (n + 1) P. For our nanosystem, the wire diameter is generally ~100nm, and the distance d between the SQD and the Ag nanowire is ~60nm, which means P ~100. When n>>1, P is very large and Γ rad and Γ nonrad can be ignored in the SP rate equations.

We now discuss the interactions of many SQDs with SPs. According to the energy-level diagram, the rate equations for the nanosystem can be written as follows,
dNsp(l)υsp=Γsp(StE)ρeffdl,
(2)
dρeffdt=η(W01Γsp(SpE))ρeff(W01+Γsp(SpE)+2Γsp(StE)),
(3)
where N sp(l) is the number of SPs per unit length after the SPs propagate the distance l along the ring. The total number of the SPs satisfies n = N sp(l)L', where L' is the quantization length, which is assumed to be equal to the circumference L of the ring. υ sp is the group velocity of the SPs. ρ eff = ρ 1 - ρ 0 is the population inversion with ρ 1 being the linear population densities of SQDs in the excited states and ρ 0 in the ground states. The linear population density of SQDs is η = ρ 1 + ρ 0. In Eq. (2) Γsp(SpE) is neglected because Γsp(SpE)<<Γsp(StE). For simplification, the interactions between the SQDs are ignored and the orientation of each SQD dipole moment is assumed to be random, so we use the average of |g|2denoted by|g|2instead of |g|2in the following calculation.

The steady state solution for the population inversion ρ eff can be obtained from Eq. (3),
ρeff=ρeff0/(1+Nsp(l)/N'),
(4)
whereρeff0=η(Γsp(SpE)+W01)/(Γsp(SpE)+W01), N'=(Γsp(SpE)+W01)/(2LΓsp(SpE)). N' is a constant for a given W 01 in our system with the dimension of linear population density. Defining the gain coefficient G' = dN sp(l)/[Nsp(l)dl] and substituting Eq. (4) into Eq. (2) yields the gain coefficient G=Γsp(SpE)Lρeff/[υsp(1+Nsp(l)/N)], which shows that G' is decreasing with the increasing of N sp(l). Under small-signal condition, namely N sp(l) << N', the small-signal gain coefficient is written as G0=Γsp(SpE)Lρeff0/υsp. Taking the loss of SPs into account with the loss coefficient α = 2Imk //, the net gain coefficient is given by

G=G0/[1+Nsp(l)/N']α.
(5)

The small-signal gain coefficient is modified as G 0-α. It should be noted that G 0 should at least satisfy G 0 >α to realize the amplification of SPs, thus G 0 = α is interpreted as the threshold condition. The solution of W 01 from the equation G 0 = α is the threshold value of pumping rate denoted by W01c. Substituting dN sp(l)/[N sp(l)dl] into the left-hand side of Eq. (5), and integrating from 0 to l yields the variation of N sp(l) with propagating length:
ln[Nsp(l)Nsp0]=(G0α)l+G0αlnG0α[1+Nsp(l)/N']G0α[1+Nsp0/N'],
(6)
where Nsp0=Nsp(0) is the number of SPs per unit length at the starting point. From Eq. (5), one can see that the net gain coefficient G decreases with the increasing of N sp(l), and when N sp(l) reaches to a certain value, G turns to be almost zero, which means that the number of SPs becomes saturated and reaches the maximum. The maximum value of SP number per unit length denoted by Nspmax could be obtained from Eq. (5)

Nspmax=N'(G0/α1).
(7)

Under the condition of G 0 >>α, Eq. (7) can be approximately written as Nspmax = η(-Γsp(SpE) +W 01)/(2αυ sp), where it is assumed that the SP dispersion relation satisfies ω = υ sp k //, and it shows clearly the relationships between Nspmax and the parameters of the system.

3. Numerical results

We now calculate the amplification properties in a realistic system with the parameters D W=100nm, the wavelength in vacuum λ 0=1000nm, d=60nm, L=5λ sp= 2.99μm. ε 1=2, ε 2= −50+0.6i and μ 10 = 1.9×1017 esu [9

9. D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90(2), 027402 (2003). [CrossRef] [PubMed]

]. The Ag permittivity is taken from Ref [33

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

]. The corresponding loss coefficient α is calculated to be 0.033μm−1. We take R SQD=5nm for the SQD radius, and then we obtain η = 4.8 × 103μm−1, ρ eff 0=1.4×101μm−1, ΓSP(SpE)=2π|g|2Dsp(ω)=2.8215×1011s1,where Dsp(ω)=(L/2π)(dk///dω)=L/(2πυsp). The threshold pumping rate is W01c=1.00582Γsp(SpE)=2.8379×1011s1.The number of SPs per unit at the starting point N sp(0) is assumed to be far smaller than N' to ensure that the small signal approximation is satisfied at the starting point. Here we assume N sp(0)/ N' = 0.01 at W10=9W01c, namely, N sp(0) = 0.033μm−1.

Figure 2
Fig. 2 The change of N sp(l) within short propagating length l. (a) W10W01c. (b) W10W01c.
shows the change of SP number per unit length N sp(l) within a very short propagating length l. Figure 2 (a) shows that when the pumping rate is larger than the pumping rate threshold W01c, Nsp(l) will increase exponentially with the propagating length, which means that the SPs amplification is realized. The larger the pumping rate, the faster the SPs number increases. For the pumping rate W10=W01c, the number of SPs keeps unchanged, i.e., SPs is neither amplified nor reduced. For W10<W01c, the number of SPs decreases with the propagating length, and the amplification cannot be realized, as shown in Fig. 2(b).

When W10>W01c, N sp(l) at first increases dramatically with the propagating length l, which leads to the decrease of the gain coefficient G, then N sp(l) turns to be saturated when the gain equals to the loss, as shown in Fig. 3(a)
Fig. 3 (a) The calculated N sp(l) as a function of l after long distance propagation when W10>W01c. (b) The maximum SPs number per unit length Nspmaxas a function of the pumping rate of SQDs.
. Therefore, at first the SP field is first amplified as propagating along the nanoring, then reaches to its saturated value after circling for several rounds and at last the SP field in the nanoring is equivalent everywhere. As the pumping rate increases, the maximum value of SP number becomes larger. Figure 3(b) shows the maximum value of N sp(l) as a function of the pumping rate W 01. It shows that when W10>W01c, Nspmax is linearly increased with the pumping rate W 01.

4. Conclusion

In conclusion, we have investigated the stimulated emission of SQDs into SPs propagating along an Ag nanoring, and obtained the steady-state solution for SPs amplification by using the rate equations. We obtained the threshold condition for amplification, SPs numbers per unit length as a function of propagation length, and the maximum SPs number per unit length, respectively. Numerical calculations show that when the pumping rate of SQDs W 01 is larger than the pumping threshold W01c, at first the SPs number first increases quickly within short propagating length, and then becomes saturated after long propagating distance. The saturated or maximum value of the SPs number per unit length is linearly dependent on the pumping rate. We note that the maximum value of SPs number is proportional to the pumping rate. There are many prospective applications in plasmonic devices for Ag nanoring SPs amplification.

Acknowledgments

This work was supported by the Natural Science Foundation of China (10534030, 10874134), the National Program on Key Science Research (2006CB921504 and 2007CB935300), Key Project of Ministry of Education (708063) and the fund of Anhui province for young teachers under Grant No.2010SQRL037ZD.

References and links

1.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]

2.

E. Ozbay, “Plasmonics: Merging Photonics and Electronics at Nanoscale Dimensions,” Science 311(5758), 189–193 (2006). [CrossRef] [PubMed]

3.

S. A. Maier, “Plasmonics: The Promise of Highly Integrated Optical Devices,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1671–1677 (2006). [CrossRef]

4.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. Dasari, and M. S. Feld, “Single molecule detection using surface-enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78(9), 1667–1670 (1997). [CrossRef]

5.

S. Lal, S. Link, and N. S. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics 1(11), 641–648 (2007). [CrossRef]

6.

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic nanolithography,” Nano Lett. 4(6), 1085–1088 (2004). [CrossRef]

7.

I. I. Smolyaninov, J. Elliott, A. V. Zayats, and C. C. Davis, “Far-field optical microscopy with a nanometer-scale resolution based on the in-plane image magnification by surface plasmon polaritons,” Phys. Rev. Lett. 94(5), 057401 (2005). [CrossRef] [PubMed]

8.

Z. W. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007). [CrossRef] [PubMed]

9.

D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90(2), 027402 (2003). [CrossRef] [PubMed]

10.

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing Spaser,” Nat. Photonics 2(6), 351–354 (2008). [CrossRef]

11.

E. Plum, V. A. Fedotov, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Towards the lasing spaser: controlling metamaterial optical response with semiconductor quantum dots,” Opt. Express 17(10), 8548–8551 (2009). [CrossRef] [PubMed]

12.

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]

13.

M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, and V. A. Podolskiy, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. 101(22), 226806 (2008). [CrossRef] [PubMed]

14.

M. A. Noginov, V. A. Podolskiy, G. Zhu, M. Mayy, M. Bahoura, J. A. Adegoke, B. A. Ritzo, and K. Reynolds, “Compensation of loss in propagating surface plasmon polariton by gain in adjacent dielectric medium,” Opt. Express 16(2), 1385–1392 (2008). [CrossRef] [PubMed]

15.

M. A. Noginov, G. Zhu, M. Bahoura, J. Adegoke, C. E. Small, B. A. Ritzo, V. P. Drachev, and V. M. Shalaev, “Enhancement of surface plasmons in an Ag aggregate by optical gain in a dielectric medium,” Opt. Lett. 31(20), 3022–3024 (2006). [CrossRef] [PubMed]

16.

J. Seidel, S. Grafström, and L. Eng, “Stimulated emission of surface plasmons at the interface between a silver film and an optically pumped dye solution,” Phys. Rev. Lett. 94(17), 177401 (2005). [CrossRef] [PubMed]

17.

M. Ambati, S. H. Nam, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Observation of Stimulated Emission of Surface Plasmon Polaritons,” Nano Lett. 8(11), 3998–4001 (2008). [CrossRef] [PubMed]

18.

M. Ambati, D. A. Genov, R. F. Oulton, and X. Zhang, “Active Plasmonics: Surface Plasmon Interaction With Optical Emitters,” IEEE J. Sel. Top. Quantum Electron. 14(6), 1395–1403 (2008). [CrossRef]

19.

D. A. Genov, M. Ambati, and X. Zhang, “Surface Plasmon Amplification in Planar Metal Films,” IEEE J. Quantum Electron. 43(11), 1104–1108 (2007). [CrossRef]

20.

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]

21.

I. D. Leon and P. Berini, “Theory of surface plasmon-polariton amplification in planar structures incorporating dipolar gain media,” Phys. Rev. 78, 161401 (2008). [CrossRef]

22.

A. Kumar, S. F. Yu, X. F. Li, and S. P. Lau, “Surface plasmonic lasing via the amplification of coupled surface plasmon waves inside dielectric-metal-dielectric waveguides,” Opt. Express 16(20), 16113–16123 (2008). [CrossRef] [PubMed]

23.

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett. 97(5), 053002 (2006). [CrossRef] [PubMed]

24.

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Strong coupling of single emitters to surface plasmons,” Phys. Rev. B 76(3), 035420 (2007). [CrossRef]

25.

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, “Generation of single optical plasmons in metallic nanowires coupled to quantum dots,” Nature 450(7168), 402–406 (2007). [CrossRef] [PubMed]

26.

H. M. Gong, L. Zhou, X. R. Su, S. Xiao, S. D. Liu, and Q. Q. Wang, “Illuminating Dark Plasmons of Silver Nanoantenna Rings to Enhance Exciton–Plasmon Interactions,” Adv. Funct. Mater. 19(2), 298–303 (2009). [CrossRef]

27.

S. D. Liu, Z. S. Zhang, and Q. Q. Wang, “High sensitivity and large field enhancement of symmetry broken Au nanorings: effect of multipolar plasmon resonance and propagation,” Opt. Express 17(4), 2906–2917 (2009). [CrossRef] [PubMed]

28.

T. H. Stievater, X. Li, D. G. Steel, D. Gammon, D. S. Katzer, D. Park, C. Piermarocchi, and L. J. Sham, “Rabi oscillations of excitons in single quantum dots,” Phys. Rev. Lett. 87(13), 133603 (2001). [CrossRef] [PubMed]

29.

A. Zrenner, E. Beham, S. Stufler, F. Findeis, M. Bichler, and G. Abstreiter, “Coherent properties of a two-level system based on a quantum-dot photodiode,” Nature 418(6898), 612–614 (2002). [CrossRef] [PubMed]

30.

Q. Q. Wang, A. Muller, M. T. Cheng, H. J. Zhou, P. Bianucci, and C. K. Shih, “Coherent control of a V-type three-level system in a single quantum dot,” Phys. Rev. Lett. 95(18), 187404 (2005). [CrossRef] [PubMed]

31.

X. Li, Y. Wu, D. Steel, D. Gammon, T. H. Stievater, D. S. Katzer, D. Park, C. Piermarocchi, and L. J. Sham, “An all-optical quantum gate in a semiconductor quantum dot,” Science 301(5634), 809–811 (2003). [CrossRef] [PubMed]

32.

P. W. Milonni, “Field quantization and radiative processes in dispersive dielectric media,” J. Mod. Opt. 42(10), 1991–2004 (1995). [CrossRef]

33.

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

OCIS Codes
(230.7370) Optical devices : Waveguides
(240.6680) Optics at surfaces : Surface plasmons
(230.4480) Optical devices : Optical amplifiers
(250.5590) Optoelectronics : Quantum-well, -wire and -dot devices

ToC Category:
Optics at Surfaces

History
Original Manuscript: December 18, 2009
Revised Manuscript: January 21, 2010
Manuscript Accepted: January 26, 2010
Published: February 16, 2010

Citation
Zhong-Jian Yang, Nam-Chol Kim, Jian-Bo Li, Mu-Tian Cheng, Shao-Ding Liu, Zhong-Hua Hao, and Qu-Quan Wang, "Surface plasmons amplifications in single Ag nanoring," Opt. Express 18, 4006-4011 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-5-4006


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References

  1. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]
  2. E. Ozbay, “Plasmonics: Merging Photonics and Electronics at Nanoscale Dimensions,” Science 311(5758), 189–193 (2006). [CrossRef] [PubMed]
  3. S. A. Maier, “Plasmonics: The Promise of Highly Integrated Optical Devices,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1671–1677 (2006). [CrossRef]
  4. K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. Dasari, and M. S. Feld, “Single molecule detection using surface-enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78(9), 1667–1670 (1997). [CrossRef]
  5. S. Lal, S. Link, and N. S. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics 1(11), 641–648 (2007). [CrossRef]
  6. W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic nanolithography,” Nano Lett. 4(6), 1085–1088 (2004). [CrossRef]
  7. I. I. Smolyaninov, J. Elliott, A. V. Zayats, and C. C. Davis, “Far-field optical microscopy with a nanometer-scale resolution based on the in-plane image magnification by surface plasmon polaritons,” Phys. Rev. Lett. 94(5), 057401 (2005). [CrossRef] [PubMed]
  8. Z. W. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007). [CrossRef] [PubMed]
  9. D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90(2), 027402 (2003). [CrossRef] [PubMed]
  10. N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing Spaser,” Nat. Photonics 2(6), 351–354 (2008). [CrossRef]
  11. E. Plum, V. A. Fedotov, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Towards the lasing spaser: controlling metamaterial optical response with semiconductor quantum dots,” Opt. Express 17(10), 8548–8551 (2009). [CrossRef] [PubMed]
  12. 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]
  13. M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, and V. A. Podolskiy, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. 101(22), 226806 (2008). [CrossRef] [PubMed]
  14. M. A. Noginov, V. A. Podolskiy, G. Zhu, M. Mayy, M. Bahoura, J. A. Adegoke, B. A. Ritzo, and K. Reynolds, “Compensation of loss in propagating surface plasmon polariton by gain in adjacent dielectric medium,” Opt. Express 16(2), 1385–1392 (2008). [CrossRef] [PubMed]
  15. M. A. Noginov, G. Zhu, M. Bahoura, J. Adegoke, C. E. Small, B. A. Ritzo, V. P. Drachev, and V. M. Shalaev, “Enhancement of surface plasmons in an Ag aggregate by optical gain in a dielectric medium,” Opt. Lett. 31(20), 3022–3024 (2006). [CrossRef] [PubMed]
  16. J. Seidel, S. Grafström, and L. Eng, “Stimulated emission of surface plasmons at the interface between a silver film and an optically pumped dye solution,” Phys. Rev. Lett. 94(17), 177401 (2005). [CrossRef] [PubMed]
  17. M. Ambati, S. H. Nam, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Observation of Stimulated Emission of Surface Plasmon Polaritons,” Nano Lett. 8(11), 3998–4001 (2008). [CrossRef] [PubMed]
  18. M. Ambati, D. A. Genov, R. F. Oulton, and X. Zhang, “Active Plasmonics: Surface Plasmon Interaction With Optical Emitters,” IEEE J. Sel. Top. Quantum Electron. 14(6), 1395–1403 (2008). [CrossRef]
  19. D. A. Genov, M. Ambati, and X. Zhang, “Surface Plasmon Amplification in Planar Metal Films,” IEEE J. Quantum Electron. 43(11), 1104–1108 (2007). [CrossRef]
  20. 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]
  21. I. D. Leon and P. Berini, “Theory of surface plasmon-polariton amplification in planar structures incorporating dipolar gain media,” Phys. Rev. 78, 161401 (2008). [CrossRef]
  22. A. Kumar, S. F. Yu, X. F. Li, and S. P. Lau, “Surface plasmonic lasing via the amplification of coupled surface plasmon waves inside dielectric-metal-dielectric waveguides,” Opt. Express 16(20), 16113–16123 (2008). [CrossRef] [PubMed]
  23. D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett. 97(5), 053002 (2006). [CrossRef] [PubMed]
  24. D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Strong coupling of single emitters to surface plasmons,” Phys. Rev. B 76(3), 035420 (2007). [CrossRef]
  25. A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, “Generation of single optical plasmons in metallic nanowires coupled to quantum dots,” Nature 450(7168), 402–406 (2007). [CrossRef] [PubMed]
  26. H. M. Gong, L. Zhou, X. R. Su, S. Xiao, S. D. Liu, and Q. Q. Wang, “Illuminating Dark Plasmons of Silver Nanoantenna Rings to Enhance Exciton–Plasmon Interactions,” Adv. Funct. Mater. 19(2), 298–303 (2009). [CrossRef]
  27. S. D. Liu, Z. S. Zhang, and Q. Q. Wang, “High sensitivity and large field enhancement of symmetry broken Au nanorings: effect of multipolar plasmon resonance and propagation,” Opt. Express 17(4), 2906–2917 (2009). [CrossRef] [PubMed]
  28. T. H. Stievater, X. Li, D. G. Steel, D. Gammon, D. S. Katzer, D. Park, C. Piermarocchi, and L. J. Sham, “Rabi oscillations of excitons in single quantum dots,” Phys. Rev. Lett. 87(13), 133603 (2001). [CrossRef] [PubMed]
  29. A. Zrenner, E. Beham, S. Stufler, F. Findeis, M. Bichler, and G. Abstreiter, “Coherent properties of a two-level system based on a quantum-dot photodiode,” Nature 418(6898), 612–614 (2002). [CrossRef] [PubMed]
  30. Q. Q. Wang, A. Muller, M. T. Cheng, H. J. Zhou, P. Bianucci, and C. K. Shih, “Coherent control of a V-type three-level system in a single quantum dot,” Phys. Rev. Lett. 95(18), 187404 (2005). [CrossRef] [PubMed]
  31. X. Li, Y. Wu, D. Steel, D. Gammon, T. H. Stievater, D. S. Katzer, D. Park, C. Piermarocchi, and L. J. Sham, “An all-optical quantum gate in a semiconductor quantum dot,” Science 301(5634), 809–811 (2003). [CrossRef] [PubMed]
  32. P. W. Milonni, “Field quantization and radiative processes in dispersive dielectric media,” J. Mod. Opt. 42(10), 1991–2004 (1995). [CrossRef]
  33. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]

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