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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 1 — Jan. 14, 2013
  • pp: 431–442
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Spectral broadening effects of spontaneous emission and density of state on plasmonic enhancement in cermet waveguides

Keyong Chen, Xue Feng, Chao Zhang, Kaiyu Cui, and Yidong Huang  »View Author Affiliations


Optics Express, Vol. 21, Issue 1, pp. 431-442 (2013)
http://dx.doi.org/10.1364/OE.21.000431


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Abstract

Based on the full integration formula of Purcell factor (PF) deduced from Fermi’s Golden Rule, the plasmonic enhancement in Au(1-α)Si3N4(α) cermet waveguides is evaluated with the joint impact of finite emission linewidth and the broadening of PF spectrum. The calculation results indicate that the PF would be significantly degraded by the two broadening effects though the SPP resonance frequency can be tuned with different volume fractions (α) of Si3N4. It is also found that the critical emission linewidth is approximately linear to the PF spectrum linewidth. Thus in order to achieve strong plasmonic enhancement, both the emission and PF spectrum linewidths should be dramatically reduced.

© 2013 OSA

1. Introduction

2. Full integration formula of Purcell factor

Figure 1
Fig. 1 Schematic diagram of a SPP waveguide on the uniformly distributed QDs active layer in an air/waveguide/emitter structure, and reference coordinate system.
is the schematic setup of the SPP waveguide on top of the active layer, in which mass QDs serve as the light emitter. ε1, ε2 and ε3 are the permittivities of the air (ε1 = 1), the SPP waveguide and the active layer, respectively. The permeabilities of all media are set μ = 1. According to Fermi’s Golden Rule, the SE rate Γsp is [9

9. H. Yokoyama and K. Ujihara, eds., Spontaneous Emission and Laser Oscillation in Microcavities (CRC, 1995), Chap. 8.

]:
Γsp=2π0|f|dE(r)|i|2ρ(ω)(ω)dω,
(1)
where f|dE(r)|i is the dipole emission matrix element, d is the electro-hole pair dipole moment, E(r) is the electric field distribution, ω is the angular frequency and ħ is the reduced Planck constant. ρ(ω) is the DOS for SPP mode and (ω) is the mode density of dipole transition or SE spectrum with the normalization condition 0(ω)dω=1. Usually, the ensemble emission linewidth of mass QDs is wider than that of single QD due to the size non-uniformity. In principle, the size distribution of QDs could be reduced by optimized fabrication process, so we assume that the sizes of all QDs are the same and thus only the linewidth of SE from single QD is considered. Suppose that the homogeneous broadening is dominant, the SE spectrum for single QD could be expressed as Lorentzian function [9

9. H. Yokoyama and K. Ujihara, eds., Spontaneous Emission and Laser Oscillation in Microcavities (CRC, 1995), Chap. 8.

]:
(ωω0)=Δω/2π(ωω0)2+(Δω/2)2,
(2)
where ω0 is the central emission frequency and Δω is the emission linewidth. If Δω is much narrower than that of ρ(ω), Eq. (1) could be reduced to:
Γsp(ω0)=2π|f|dE(r)|i|2ρ(ω0).
(3)
Equation (3) is commonly used to evaluate the plasmonic enhancement [2

2. M. Gontijo, M. Boroditsky, E. Yablonovitch, S. Keller, U. Mishra, and S. DenBaars, “Coupling of InGaN quantum-well photoluminescence to silver surface plasmons,” Phys. Rev. B 60(16), 11564–11567 (1999). [CrossRef]

,6

6. Y. Y. Gong, J. Lu, S. L. Cheng, Y. Nishi, and J. Vučković, “Plasmonic enhancement of emission from Si-nanocrystals,” Appl. Phys. Lett. 94(1), 013106 (2009). [CrossRef]

,11

11. X. Hu, Y. Huang, W. Zhang, and J. Peng, “Dominating radiative recombination in a nanoporous silicon layer with a metal-rich Au(1-α)SiO2(α) cermet waveguide,” Appl. Phys. Lett. 89(8), 081112 (2006). [CrossRef]

,12

12. X. Tang, Y. Wang, W. Ke, X. Feng, Y. Huang, and J. Peng, “Internal quantum efficiency enhancement of silicon nanocrystals using double layer Au-rich cermet films,” Opt. Commun. 283(13), 2754–2757 (2010). [CrossRef]

,14

14. X. Feng, F. Liu, and Y. D. Huang, “Calculated plasmonic enhancement of spontaneous emission from silicon nanocrystals with metallic gratings,” Opt. Commun. 283(13), 2758–2761 (2010). [CrossRef]

16

16. G. Sun, J. B. Khurgin, and R. A. Soref, “Practicable enhancement of spontaneous emission using surface plasmons,” Appl. Phys. Lett. 90(11), 111107 (2007). [CrossRef]

,22

22. H. Iwase, D. Englund, and J. Vučković, “Analysis of the Purcell effect in photonic and plasmonic crystals with losses,” Opt. Express 18(16), 16546–16560 (2010). [CrossRef] [PubMed]

,24

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

]. However, for a practical emitter with finite emission linewidth, Eq. (1) should be employed. In addition, it has been found that the DOS spectrum of SPP mode would also be broadened due to the waveguide absorption loss and could also be expressed as Lorentzian function [22

22. H. Iwase, D. Englund, and J. Vučković, “Analysis of the Purcell effect in photonic and plasmonic crystals with losses,” Opt. Express 18(16), 16546–16560 (2010). [CrossRef] [PubMed]

,24

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

]:
ρ(ωωk)=ωk/2πQk(ωωk)2+(ωk/2Qk)2,
(4)
where ωk and Qk are the frequency and the quality factor for state k, respectively. Thus the SE rate should be the sum of the rates for all k states under specific ω0:
Γsp(ω0)=0k2π2|f|dEk(r)|i|2ρ(ωωk)(ωω0)dω.
(5)
For simplicity, we start from the reduced form of Γsp to deduce the PF. Firstly, |f|dEk|i|2 is rewritten as 1/3(d2|Ek|2) with an averaging factor of 1/3 for the random polarization direction of d to Ek, as in Ref [2

2. M. Gontijo, M. Boroditsky, E. Yablonovitch, S. Keller, U. Mishra, and S. DenBaars, “Coupling of InGaN quantum-well photoluminescence to silver surface plasmons,” Phys. Rev. B 60(16), 11564–11567 (1999). [CrossRef]

]. Ek is normalized to a half quantum for zero-point fluctuations within a prepared space of V = LxLyLz:
|Ek|2=ω/2|E0k(r)|21/8πLxLyLz[(εωk)/ωk]|E0k(x,y,z)|2dxdydz,
(6)
where E0k is the original electric field for state k, and ε is the frequency-dependent permittivity that also varies with different locations in the air/waveguide/emitter structure. What’s more, the integration along z direction is Lz± and in x and y directions, Ek is homogeneous so the denominator or stored energy is rewritten as LxLy/(8π)+[(εωk)/ωk]|E0k(z)|2dz. In the reciprocal space, the mode area of one SPP mode could be expressed as ΔkxΔky = (2π)2/LxLy. Then the SE rate for state k based on Eqs. (3)(6) is obtained:
Γspk(ω0)=2d2ω03|E0k(z)|2+[(εωk)/ωk]|E0k(z)|2dzρ(ω0ωk)ΔkxΔky.
(7)
This recombination rate should be compared to the SE rate Γ0(ω0) in bulk semiconductors, which is calculated by the classical equation [25

25. P. Milonni, The Quantum Vacuum: An Introduction to Quantum Electrodynamics (Academic, 1994).

]:
Γ0(ω)=4nd2ω33c3,
(8)
where c is the vacuum speed of light and n is the refractive index of active layer. With Eqs. (7) and (8), the reduced formula of PF is deduced as [2

2. M. Gontijo, M. Boroditsky, E. Yablonovitch, S. Keller, U. Mishra, and S. DenBaars, “Coupling of InGaN quantum-well photoluminescence to silver surface plasmons,” Phys. Rev. B 60(16), 11564–11567 (1999). [CrossRef]

]:
PF(z|ω0)=1+kΓspk(ω0)Γ0(ω0)=1+c32nω02k|E0k(z)|2+[(εωk)/ωk]|E0k(z)|2dzρ(ω0ωk)ΔkxΔky.
(9)
If the real space is large enough, kx and ky could be treated as continuous variables and kΔkxΔky approximates ++dkxdky. Then by integrating PF(z|ω0) in polar coordinates k = (kcosϕ,ksinϕ,0), ++dkxdky is rewritten as 02π0kdkdϕ where k is the propagation constant, independent of ϕ. So taking the SE spectrum into account, we obtain the PF in the full integral form:
PF(z|ω0)=1+πc3nω0200H(ωk)ρ(ωωk)(ωω0)kdkdωkdωkdω,
(10)
where H(ωk)=|E0k(z)|2+[(εωk)/ωk]|E0k(z)|2dz. It should be noted that k replaces dk as the integration variable by multiplying dk/dωk for convenient calculation of PF because both ρ(ω) and l(ω) are explicit functions of ω.

Till now, the full integration formula of PF has been obtained. To verify this formula, we consider two special cases. First, if the emission linewidth (Δω) is sufficiently narrow, l(ω−ω0) would be Dirac’s function δ(ω−ω0). Thus Eq. (10) is reduced to:
PF(ω0,z)=1+πc3nω020H(ωk)ρ(ω0ωk)kdkdωkdωk
(11)
which is the PF spectrum, consistent with the formula in Ref [22

22. H. Iwase, D. Englund, and J. Vučković, “Analysis of the Purcell effect in photonic and plasmonic crystals with losses,” Opt. Express 18(16), 16546–16560 (2010). [CrossRef] [PubMed]

]. Second, if absorption loss of the SPP waveguide is neglected, ρ(ω0−ωk) would also be Dirac’s function δ(ω0−ωk) so that Eq. (11) could be further simplified to PF(ω0,z)=1+πc3nω02H(ω0)kdkdω0, which is the commonly used formula to evaluate the plasmonic enhancement [2

2. M. Gontijo, M. Boroditsky, E. Yablonovitch, S. Keller, U. Mishra, and S. DenBaars, “Coupling of InGaN quantum-well photoluminescence to silver surface plasmons,” Phys. Rev. B 60(16), 11564–11567 (1999). [CrossRef]

,6

6. Y. Y. Gong, J. Lu, S. L. Cheng, Y. Nishi, and J. Vučković, “Plasmonic enhancement of emission from Si-nanocrystals,” Appl. Phys. Lett. 94(1), 013106 (2009). [CrossRef]

,11

11. X. Hu, Y. Huang, W. Zhang, and J. Peng, “Dominating radiative recombination in a nanoporous silicon layer with a metal-rich Au(1-α)SiO2(α) cermet waveguide,” Appl. Phys. Lett. 89(8), 081112 (2006). [CrossRef]

,12

12. X. Tang, Y. Wang, W. Ke, X. Feng, Y. Huang, and J. Peng, “Internal quantum efficiency enhancement of silicon nanocrystals using double layer Au-rich cermet films,” Opt. Commun. 283(13), 2754–2757 (2010). [CrossRef]

,14

14. X. Feng, F. Liu, and Y. D. Huang, “Calculated plasmonic enhancement of spontaneous emission from silicon nanocrystals with metallic gratings,” Opt. Commun. 283(13), 2758–2761 (2010). [CrossRef]

16

16. G. Sun, J. B. Khurgin, and R. A. Soref, “Practicable enhancement of spontaneous emission using surface plasmons,” Appl. Phys. Lett. 90(11), 111107 (2007). [CrossRef]

].

3. Permittivity of cermet waveguides

To analyze the plasmonic enhancement quantitatively, we consider a representative SPP waveguide based on cermet of Au(1-α)Si3N4(α), where α is the volume fraction of Si3N4 and α = 0 denotes pure Au. The cermet permittivity (ε2) is derived from the probabilistic growth model introduced by Sheng [26

26. P. Sheng, “Theory for the dielectric function of granular composite media,” Phys. Rev. Lett. 45(1), 60–63 (1980). [CrossRef]

,27

27. U. J. Gibson and R. A. Buhrman, “Optical response of cermet composite films in the microstructural transition region,” Phys. Rev. B 27(8), 5046–5051 (1983). [CrossRef]

]:
pεMetalCoatε2εMetalCoat+2ε2+(1p)εDielectricCoatε2εDielectricCoat+2ε2=0,
(12)
where the cermet material is modeled as a mixture of two types of coated spheres (i.e., metal-coated dielectric sphere and dielectric-coated metal sphere) with respective dielectric functions:
εMetalCoat=εM(2α(εDεM)+(εD+2εM))(εD+2εM)α(εDεM),
(13)
εDielectricCoat=εD(2(1α)(εMεD)+(εM+2εD))(εM+2εD)(1α)(εMεD),
(14)
and the probability of forming a metal-coated dielectric sphere is:
p=(1α1/3)3(1α1/3)3+(1(1α)1/3)3.
(15)
εM and εD are the permittivities of Au metal and Si3N4 dielectric, respectively.

4. Spectral broadening effects of SE and DOS on plasmonic enhancement

Before calculating the PF, it is necessary to acquire the dispersion curves and the electric field distributions of SPP mode propagating on the Au(1-α)Si3N4(α) cermet waveguide in order to calculate the DOS and the normalized electric field. Firstly, we assume that the active material is InP QDs embedded in GaP [8

8. F. Hatami, V. Lordi, J. S. Harris, H. Kostial, and W. T. Masselink, “Red light-emitting diodes based on InP/GaP quantum dots,” J. Appl. Phys. 97(9), 096106 (2005). [CrossRef]

] with refractive index of n = 3. The thickness of the cermet layer is set 10 nm. Then the complex propagation constant (ksp = k-ik) of SPP mode can be calculated by the following dispersion relation of TM mode [31

31. J. J. Burke, G. I. Stegeman, and T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B Condens. Matter 33(8), 5186–5201 (1986). [CrossRef] [PubMed]

]:
tanh(γ2h)(ε1ε3γ22+ε22γ1γ3)+[γ2(ε1γ3+ε3γ1)ε2]=0,
(16)
where γj2=ksp2εjk02, j = 1, 2, 3, respectively. k0 is the wave vector in vacuum and h is the thickness of the cermet layer.

Figure 3
Fig. 3 Dispersion curves of SPP mode on different Au(1-α)Si3N4(α) cermet waveguides with α = 0~0.3.
shows the calculated dispersion cures with α = 0~0.3. It should be noted that for each α, there are two branches of SPP mode (i.e., anti-symmetric and symmetric branches), but only anti-symmetric SPP mode is considered here because the symmetric one is a leaky mode at low frequencies and therefore cannot be exploited [11

11. X. Hu, Y. Huang, W. Zhang, and J. Peng, “Dominating radiative recombination in a nanoporous silicon layer with a metal-rich Au(1-α)SiO2(α) cermet waveguide,” Appl. Phys. Lett. 89(8), 081112 (2006). [CrossRef]

]. With increasing α, SPP resonance is tuned to lower frequency (the corresponding resonance energies are 2.48 eV, 2.18 eV, 1.945 eV and 1.765 eV, respectively). On the other hand, the electric field distribution can be calculated from Maxwell’s equations and boundary conditions of continuity [29

29. W. Chen, M. D. Thoreson, A. V. Kildishev, and V. M. Shalaev, “Fabrication and optical characterizations of smooth silver-silica nanocomposite films,” Laser Phys. Lett. 7(9), 677–684 (2010). [CrossRef]

]. Figure 4
Fig. 4 Normalized distributions of electric field along z at SPP resonance frequencies for α = 0~0.3.
shows the normalized distributions of electric field along z (|E0k(z)|2max(|E0k(z)|2)) at the resonance energies for different α. The field intensities in the emitter decay exponentially away from the waveguide. They are primarily localized at the cermet-emitter interface contributing to greater plasmonic enhancement at the SPP resonance frequencies. With increasing α the field distribution expands along z. After the dispersion curves are obtained, the DOS can be calculated with Eq. (4) where Qk equals ωk/(2k × dωk/dk) for lossy SPP mode [22

22. H. Iwase, D. Englund, and J. Vučković, “Analysis of the Purcell effect in photonic and plasmonic crystals with losses,” Opt. Express 18(16), 16546–16560 (2010). [CrossRef] [PubMed]

]. In addition, as seen in Fig. 3, SPP mode is forbidden to propagate when the frequency is beyond the resonance frequency (ωsp), so the integral upper limits of ∞ in Eqs. (10) and (11) could be replaced by ωsp to conveniently calculate the PF in either form.

Figure 5
Fig. 5 Calculated PF spectra at the locations of z = 5 nm, 10 nm and 15 nm, for α = 0 and 0.3, respectively.
shows the PF spectra (PF(ω,z)) at the locations of z = 5 nm, 10 nm and 15 nm beneath the Au(1-α)Si3N4(α) cermet waveguide with α = 0 and 0.3. As to the pure Au (α = 0), the PF spectrum at z = 15 nm is degraded dramatically compared with that at z = 5 nm, indicating that the plasmonic enhancement is limited in narrow space of only a few tens of nanometers. Meanwhile, the corresponding PF spectrum linewidth is significantly broadened. These phenomena, same as in Ref [22

22. H. Iwase, D. Englund, and J. Vučković, “Analysis of the Purcell effect in photonic and plasmonic crystals with losses,” Opt. Express 18(16), 16546–16560 (2010). [CrossRef] [PubMed]

], can also be found in the other cermet waveguides (e.g., α = 0.3). But with increasing α, the PF spectrum peak is red-shifted at any location, and is notably reduced at z = 5nm due to the grain size effect that arouses stronger scattering loss with decreasing Au-NC size [13

13. D. Lu, J. Kan, E. E. Fullerton, and Z. Liu, “Tunable surface plasmon polaritons in Ag composite films by adding dielectrics or semiconductors,” Appl. Phys. Lett. 98(24), 243114 (2011). [CrossRef]

]. For more clarity, we plot the peak values (PFpeak) and the corresponding energies (ħω0) at various locations of z = 0~30 nm in Fig. 6
Fig. 6 Peak values PFpeak of PF spectra (a) and corresponding energies ħω0 (b) at various locations of z = 0~30 nm for α = 0~0.3.
. It is seen that the plasmonic enhancement decays remarkably in the first ten nanometers and nearly to be 1 at z = 30 nm. Along with the PF decay, ħω0 is firstly red-shifted a little but shows prominent changes after z>15 nm, as shown in Fig. 6(b), which may result from the evanescent property of electric field in the active layer.

Based on the above PF spectra, the PFs in the full integral form (PF(z|ω0)) can be numerically calculated. To maximize overall plasmonic enhancement under varied emission linewidths (Δω), the central frequency of the emitter (ω0) should be matched with that of PF spectrum at the position where the strongest PFpeak is achieved. Clearly, this position should be at the cermet-emitter interface (z = 0 nm). But unfortunately, if the QDs approach very close to the waveguide (<5 nm), SE is almost completely coupled into lossy surface wave mode instead of SPP mode, leading to unfavorable luminescence quenching [32

32. R. R. Chance, A. Prock, and R. Silbey, “Molecular fluorescence and energy transfer near interfaces,” Adv. Chem. Phys. 37, 1–65 (1978). [CrossRef]

34

34. W. L. Barnes, “Electromagnetic crystals for surface plasmon polaritons and the extraction of light from emissive devices,” J. Lightwave Technol. 17(11), 2170–2182 (1999). [CrossRef]

]. Therefore, a spacer is necessarily added between the cermet and the emitter [2

2. M. Gontijo, M. Boroditsky, E. Yablonovitch, S. Keller, U. Mishra, and S. DenBaars, “Coupling of InGaN quantum-well photoluminescence to silver surface plasmons,” Phys. Rev. B 60(16), 11564–11567 (1999). [CrossRef]

,3

3. K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. Mater. 3(9), 601–605 (2004). [CrossRef] [PubMed]

]. Assuming that the spacer is 5 nm thick and its refractive index remains the same as that of the active layer, ω0 should then be matched with the central frequency (ω1) of PF spectrum at the spacer-emitter interface (z = 5nm), ceteris paribus. Then to evaluate overall plasmonic enhancement, PF(z|ω0) is further averaged by the following equation:
PFave=1+1DzsDz(PF(z|ω0)1)dz,
(17)
where s is the spacer thickness that is set 5 nm and thus ω0 = ω1, and Dz approximating 30 nm here is the decay length at which the peak value of PF spectrum decays to 1 within the active layer.

As shown in Fig. 7
Fig. 7 Calculated PFs in the full integral form at z = 5 nm (a) and on average over the active layer (b) with varied emission linewidth (Δω) for α = 0~0.3; the central frequency of the emitter (ω0) is matched with that of the PF spectrum (ω1) at the spacer-emitter interface (z = 5 nm).
, due to the PF decay with distance, the calculated average PF (PFave) is much smaller than the PF at z = 5nm with ħΔω = 10−3~106 meV. Specially, PFave drops to less than 10 when the emission linewidth exceeds ~0.1 eV. For narrow-linewidth emitters, increasing the doping fraction (α) would deteriorate both the PF at z = 5nm and PFave since additional loss is introduced due to the grain size effect of Au-NCs. It should be noted that the PFave curves for α = 0.1 and 0.2 overlap almost completely. This is because that besides introducing greater additional loss for decreased Au-NC size, increasing α would increase the real part of cermet permittivity (Re(ε2)) as shown in Fig. 2, which is yet helpful to improve PF. Since the grain size effect is dominant for the dielectric-doped cermet, tuning SPP resonance would be accompanied with PF degradation. However, for wide-linewidth emitters, such additional loss is helpful to obtain higher PFave. It could be understood that although such additional loss of cermet would lead to DOS spectral broadening and degrade the PF, the broadening of DOS spectrum would also enlarge the integration span and counterbalance the impact of reduced DOS value. In Fig. 8
Fig. 8 Maximum PFave and PF spectrum linewidth at the spacer-emitter interface (ΔωPF) versus central emission frequency (ω0) of the emitter for α = 0~0.3.
, with increasing α the maximum PFave decreases approximately linearly and the central emission frequency is lowered correspondingly in a wide range of ħω0 = 2.43~1.65 eV. Meanwhile, the linewidth of PF spectrum at the spacer-emitter interface, denoted as ΔωPF, increases due to the grain size effect. However, in order to achieve the maximum PFave, the emission linewidth should be sufficiently narrow.

According to the above results, some guidelines to achieve strong plasmonic enhancement could be summarized as follows:

  • (1) The central frequency of the emitter should be matched with that of PF spectrum at such a location where the highest PF is achieved.
  • (2) The emission linewidth of emitter should be matched to the PF spectrum linewidth, namely Δωω*~LωPF). Otherwise, broad emission linewidth will lead to significant PF degradation. It should be mentioned that if the active layer is thicker within the decay length (Dz) the emission linewidth of emitter could be broader.
  • (3) Both the emission linewidth and the SPP waveguide loss are the physical limitations to achieve ultrahigh PFave. As shown in Fig. 9(b), they need to be dramatically reduced. Such reduction could be achieved at low temperature as discussed in Ref [23

    23. X. Feng, K. Cui, F. Liu, and Y. Huang, “Impact of spectral broadening on plasmonic enhancement with metallic gratings,” Appl. Phys. Lett. 101(12), 121102 (2012). [CrossRef]

    ]. Therefore, low-temperature emitters with strong plasmonic enhancement would be an interesting research subject. But this is beyond the scope of the paper. We are expecting some corresponding experimental investigations.

5. Conclusion

In summary, the plasmonic enhancement for different Au(1-α)Si3N4(α) cermet waveguides including pure Au is evaluated by utilizing the deduced PF in the full integral form (PF(z|ω0)), where both the DOS spectrum (ρ(ω0−ωk)) of SPP mode and the SE spectrum of emitter (l(ω−ω0)) are involved. It is found that the cermet waveguides offer the advantages of tuning the SPP resonance whereas accompanied with the PF degradation due to the grain size effect, but in contrast, the emission linewidth and the broadening of PF spectrum (PF(ω,z)) can markedly deteriorate the plasmonic enhancement. It is also found that the critical emission linewidth (Δω*) is approximately linear to the linewidth of the highest PF spectrum (ΔωPF). These results suggest that both the emission linewidth and the PF spectrum linewidth should be dramatically reduced in order to achieve strong plasmonic enhancement.

Acknowledgments

This work was supported by the National Basic Research Program of China (No. 2011CBA00608, 2011CBA00303, 2011CB301803, and 2010CB327405) and the National Natural Science Foundation of China (Grant No. 61036010 and 61036011). The authors would like to thank Dr. Wei Zhang and Dr. Fang Liu for their valuable discussions and helpful comments.

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X. Tang, Y. Wang, W. Ke, X. Feng, Y. Huang, and J. Peng, “Internal quantum efficiency enhancement of silicon nanocrystals using double layer Au-rich cermet films,” Opt. Commun. 283(13), 2754–2757 (2010). [CrossRef]

13.

D. Lu, J. Kan, E. E. Fullerton, and Z. Liu, “Tunable surface plasmon polaritons in Ag composite films by adding dielectrics or semiconductors,” Appl. Phys. Lett. 98(24), 243114 (2011). [CrossRef]

14.

X. Feng, F. Liu, and Y. D. Huang, “Calculated plasmonic enhancement of spontaneous emission from silicon nanocrystals with metallic gratings,” Opt. Commun. 283(13), 2758–2761 (2010). [CrossRef]

15.

X. Feng, F. Liu, and Y. D. Huang, “Spontaneous emission rate enhancement of silicon nanocrystals by plasmonic bandgap on copper grating,” J. Lightwave Technol. 28(9), 1420–1430 (2010). [CrossRef]

16.

G. Sun, J. B. Khurgin, and R. A. Soref, “Practicable enhancement of spontaneous emission using surface plasmons,” Appl. Phys. Lett. 90(11), 111107 (2007). [CrossRef]

17.

J. T. Robinson, C. Manolatou, L. Chen, and M. Lipson, “Ultrasmall mode volumes in dielectric optical microcavities,” Phys. Rev. Lett. 95(14), 143901 (2005). [CrossRef] [PubMed]

18.

P. Cheng, D. Li, Z. Yuan, P. Chen, and D. Yang, “Enhancement of ZnO light emission via coupling with localized surface plasmon of Ag island film,” Appl. Phys. Lett. 92(4), 041119 (2008). [CrossRef]

19.

C. Hong, H. Kim, S. Park, and C. Lee, “Optical properties of porous silicon coated with ultrathin gold film by RF-magnetron sputtering,” J. Eur. Ceram. Soc. 30(2), 459–463 (2010). [CrossRef]

20.

M. van Exter, G. Nienhuis, and J. Woerdman, “Two simple expressions for the spontaneous emission factor β,” Phys. Rev. A 54(4), 3553–3558 (1996). [CrossRef] [PubMed]

21.

T. Baba and D. Sano, “Low-threshold lasing and Purcell effect in microdisk lasers at room temperature,” IEEE J. Sel. Top. Quantum Electron. 9(5), 1340–1346 (2003). [CrossRef]

22.

H. Iwase, D. Englund, and J. Vučković, “Analysis of the Purcell effect in photonic and plasmonic crystals with losses,” Opt. Express 18(16), 16546–16560 (2010). [CrossRef] [PubMed]

23.

X. Feng, K. Cui, F. Liu, and Y. Huang, “Impact of spectral broadening on plasmonic enhancement with metallic gratings,” Appl. Phys. Lett. 101(12), 121102 (2012). [CrossRef]

24.

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

25.

P. Milonni, The Quantum Vacuum: An Introduction to Quantum Electrodynamics (Academic, 1994).

26.

P. Sheng, “Theory for the dielectric function of granular composite media,” Phys. Rev. Lett. 45(1), 60–63 (1980). [CrossRef]

27.

U. J. Gibson and R. A. Buhrman, “Optical response of cermet composite films in the microstructural transition region,” Phys. Rev. B 27(8), 5046–5051 (1983). [CrossRef]

28.

T. Bååk, “Silicon oxynitride; a material for GRIN optics,” Appl. Opt. 21(6), 1069–1072 (1982). [CrossRef] [PubMed]

29.

W. Chen, M. D. Thoreson, A. V. Kildishev, and V. M. Shalaev, “Fabrication and optical characterizations of smooth silver-silica nanocomposite films,” Laser Phys. Lett. 7(9), 677–684 (2010). [CrossRef]

30.

N. C. Miller, B. Hardiman, and G. A. Shirn, “Transport properties, microstructure, and conduction model of cosputtered Au-SiO2 cermet films,” J. Appl. Phys. 41(4), 1850–1856 (1970). [CrossRef]

31.

J. J. Burke, G. I. Stegeman, and T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B Condens. Matter 33(8), 5186–5201 (1986). [CrossRef] [PubMed]

32.

R. R. Chance, A. Prock, and R. Silbey, “Molecular fluorescence and energy transfer near interfaces,” Adv. Chem. Phys. 37, 1–65 (1978). [CrossRef]

33.

G. W. Ford and W. H. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep. 113(4), 195–287 (1984). [CrossRef]

34.

W. L. Barnes, “Electromagnetic crystals for surface plasmon polaritons and the extraction of light from emissive devices,” J. Lightwave Technol. 17(11), 2170–2182 (1999). [CrossRef]

OCIS Codes
(130.2790) Integrated optics : Guided waves
(240.6680) Optics at surfaces : Surface plasmons
(310.3915) Thin films : Metallic, opaque, and absorbing coatings

ToC Category:
Optics at Surfaces

History
Original Manuscript: September 24, 2012
Revised Manuscript: November 14, 2012
Manuscript Accepted: December 9, 2012
Published: January 4, 2013

Citation
Keyong Chen, Xue Feng, Chao Zhang, Kaiyu Cui, and Yidong Huang, "Spectral broadening effects of spontaneous emission and density of state on plasmonic enhancement in cermet waveguides," Opt. Express 21, 431-442 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-1-431


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References

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  9. H. Yokoyama and K. Ujihara, eds., Spontaneous Emission and Laser Oscillation in Microcavities (CRC, 1995), Chap. 8.
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  11. X. Hu, Y. Huang, W. Zhang, and J. Peng, “Dominating radiative recombination in a nanoporous silicon layer with a metal-rich Au(1-α)SiO2(α) cermet waveguide,” Appl. Phys. Lett.89(8), 081112 (2006). [CrossRef]
  12. X. Tang, Y. Wang, W. Ke, X. Feng, Y. Huang, and J. Peng, “Internal quantum efficiency enhancement of silicon nanocrystals using double layer Au-rich cermet films,” Opt. Commun.283(13), 2754–2757 (2010). [CrossRef]
  13. D. Lu, J. Kan, E. E. Fullerton, and Z. Liu, “Tunable surface plasmon polaritons in Ag composite films by adding dielectrics or semiconductors,” Appl. Phys. Lett.98(24), 243114 (2011). [CrossRef]
  14. X. Feng, F. Liu, and Y. D. Huang, “Calculated plasmonic enhancement of spontaneous emission from silicon nanocrystals with metallic gratings,” Opt. Commun.283(13), 2758–2761 (2010). [CrossRef]
  15. X. Feng, F. Liu, and Y. D. Huang, “Spontaneous emission rate enhancement of silicon nanocrystals by plasmonic bandgap on copper grating,” J. Lightwave Technol.28(9), 1420–1430 (2010). [CrossRef]
  16. G. Sun, J. B. Khurgin, and R. A. Soref, “Practicable enhancement of spontaneous emission using surface plasmons,” Appl. Phys. Lett.90(11), 111107 (2007). [CrossRef]
  17. J. T. Robinson, C. Manolatou, L. Chen, and M. Lipson, “Ultrasmall mode volumes in dielectric optical microcavities,” Phys. Rev. Lett.95(14), 143901 (2005). [CrossRef] [PubMed]
  18. P. Cheng, D. Li, Z. Yuan, P. Chen, and D. Yang, “Enhancement of ZnO light emission via coupling with localized surface plasmon of Ag island film,” Appl. Phys. Lett.92(4), 041119 (2008). [CrossRef]
  19. C. Hong, H. Kim, S. Park, and C. Lee, “Optical properties of porous silicon coated with ultrathin gold film by RF-magnetron sputtering,” J. Eur. Ceram. Soc.30(2), 459–463 (2010). [CrossRef]
  20. M. van Exter, G. Nienhuis, and J. Woerdman, “Two simple expressions for the spontaneous emission factor β,” Phys. Rev. A54(4), 3553–3558 (1996). [CrossRef] [PubMed]
  21. T. Baba and D. Sano, “Low-threshold lasing and Purcell effect in microdisk lasers at room temperature,” IEEE J. Sel. Top. Quantum Electron.9(5), 1340–1346 (2003). [CrossRef]
  22. H. Iwase, D. Englund, and J. Vučković, “Analysis of the Purcell effect in photonic and plasmonic crystals with losses,” Opt. Express18(16), 16546–16560 (2010). [CrossRef] [PubMed]
  23. X. Feng, K. Cui, F. Liu, and Y. Huang, “Impact of spectral broadening on plasmonic enhancement with metallic gratings,” Appl. Phys. Lett.101(12), 121102 (2012). [CrossRef]
  24. Y. Gong and J. Vučković, “Design of plasmon cavities for solid-state cavity quantum electrodynamics applications,” Appl. Phys. Lett.90(3), 033113 (2007). [CrossRef]
  25. P. Milonni, The Quantum Vacuum: An Introduction to Quantum Electrodynamics (Academic, 1994).
  26. P. Sheng, “Theory for the dielectric function of granular composite media,” Phys. Rev. Lett.45(1), 60–63 (1980). [CrossRef]
  27. U. J. Gibson and R. A. Buhrman, “Optical response of cermet composite films in the microstructural transition region,” Phys. Rev. B27(8), 5046–5051 (1983). [CrossRef]
  28. T. Bååk, “Silicon oxynitride; a material for GRIN optics,” Appl. Opt.21(6), 1069–1072 (1982). [CrossRef] [PubMed]
  29. W. Chen, M. D. Thoreson, A. V. Kildishev, and V. M. Shalaev, “Fabrication and optical characterizations of smooth silver-silica nanocomposite films,” Laser Phys. Lett.7(9), 677–684 (2010). [CrossRef]
  30. N. C. Miller, B. Hardiman, and G. A. Shirn, “Transport properties, microstructure, and conduction model of cosputtered Au-SiO2 cermet films,” J. Appl. Phys.41(4), 1850–1856 (1970). [CrossRef]
  31. J. J. Burke, G. I. Stegeman, and T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B Condens. Matter33(8), 5186–5201 (1986). [CrossRef] [PubMed]
  32. R. R. Chance, A. Prock, and R. Silbey, “Molecular fluorescence and energy transfer near interfaces,” Adv. Chem. Phys.37, 1–65 (1978). [CrossRef]
  33. G. W. Ford and W. H. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep.113(4), 195–287 (1984). [CrossRef]
  34. W. L. Barnes, “Electromagnetic crystals for surface plasmon polaritons and the extraction of light from emissive devices,” J. Lightwave Technol.17(11), 2170–2182 (1999). [CrossRef]

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