Abstract

Photoluminescence of polyfluoren copolymers, a white-light material, was demonstrated to be enhanced selectively by coupling with either localized or propagating modes of surface plasmon resonance (SPR). The silver sub-micron cylinders with 75nm height fabricated by e-beam lithography followed by e-beam evaporation and lift-off process. The enhanced light emissions at 500nm and 533nm are attributed to the low frequency branch of localized SPR. Furthermore, a 50nm silver thin film between these cylinders and the substrate provides propagating surface plasmons under excitation and enhances the blue emission band of the polyfluoren copolymer at 438nm. This delocalized SPR is sufficient for effective plasmon to light conversion. Moreover, by effectively coupling the localized and propagating SPR, we can experimentally demonstrate that the photoluminescence of polyfluoren copolymers is enhanced by 4 to 5.4 times at different wavelengths compared to enhancement by either single mode.

© 2010 OSA

1. Introduction

The electromagnetic properties of metal/dielectric interfaces have attracted a great deal of research attention, and it is believed that spontaneous emission can be modified by resonant coupling to the external electromagnetic environment. The localized surface plasmon resonance (LSPR), the collective response of electrons on the surface of a conductor composed by metallic nanostructures to an optical field, strongly affects the spectroscopic characteristics of nearby molecules. Recently, surface plasmon resonance(SPR) from metal nanoparticles has generated considerable interest [1] with regard to bio-sensing and enhanced light emission applications [24]. An increase in the spontaneous emission rate in semiconductors and polymers caused by surface plasmon coupling has been observed when the SPR energy is matched to the emission energy of the band gap [2], and the SPR energy can be tuned by controlling metal particle geometry [5]. However, the energy conversion from SPs to heat means that localized SP coupling fluorescence is only slightly enhanced, or even reduced [6,7]. Therefore, the application of tunable SPR by varying metallic particle geometry is restricted, as the localized SP evanescence field and the improvement of fluorescence intensity is limited. In this letter, the localized and propagating SP modes of silver coupling with copolymer were studied to overcome the problem of the SP ineffective conversion efficiency. The multiple emission bands of the copolymer can be selectively enhanced by the nature of SPR shifting and splitting [8]. The intensity of delocalized SP-enhanced fluorescence at green frequency was successfully increased by five times by using plasmonic structure coupling. The energy conversion from SPR to photons with effective SP coupling length is the key to the conservation of the dispersion relation.

2. Experiment

Figure 1(a) is the schematic diagram of the designed structure in cross section for investigation, where the polyfluorene (PF) copolymer was spin-coated on a Si substrate with plasmonic structures patterned by e-beam lithography followed by a standard lift-off process. The plasmonic structure contains periodic Ag sub-micron cylinder arrays with or without a 50 nm thick Ag film at bottom. The patterned area is 50μm × 50μm square. The diameter of the sub-micron cylinder is varied from 300, 250 to 200nm corresponding to the center-to-center distance from 600, 500 to 400nm, while the height is kept at 75nm. The plan-view SEM (JSM-7000, JEOL) image in Fig. 1(b) shows the sub-micron cylinder arrays with different diameters. The PF copolymer was synthesized using fluorine monomers copolymerized with iridium (IR) complex monomer and end-capped with naphthalimide (NTI) dyes. The condensing ratio of the PF copolymer is fluorine: IR: NTI = 97: 2: 1. Photoluminescence (PL) spectroscopy (Labram HR, Jobin Yvon) was performed using a 325nm He-Cd laser, which was focused to a 10-μm-diameter spot by a 40x objective (N.A. = 0.5). The PL signals were excited and collected at normal angle and recorded using a liquid-nitrogen cooled charged coupled detector. The absorption spectrum of the PF copolymer spin-coated on a quartz substrate was performed using ultraviolet-visible (UV-VIS) spectroscopy. The absorption spectrum of the Ag cylindrical particles in the specific medium was also analyzed theoretically using discrete dipole approximation (DDA), where the plasmonic structure was approximated by a cubic array composed of polarizable dipoles. The absorption efficiency with dipole arrays was calculated by solving Maxwell’s equations with the specific location, polarization of each dipole and dielectric medium. The dielectric constants of the PF copolymer and silver used in the DDA calculations were derived from the refractive and distinction coefficients, which were measured by ellipsometry (M44, J. A. Woolam, Saturn Vac Co., Ltd.).

 

Fig. 1 (a) Schematic illustrates experimental geometry used as enhanced PL measurements of multiple plasmons (left) and LSPR only (right). The sizes are not in proportion. (b) SEM images of Ag cylinder array with the same constant height of 75nm and different diameters of 200nm, 250nm and 300nm on silicon substrates.

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3. Results and discussion

Figure 2 shows the PL and UV-VIS spectra of the PF copolymer with the molecular structure. The absorption spectrum of the PF copolymer is dominated by an intense peak at about 390nm, which comes from the fluorene unit serving as the backbone in the copolymer [9]. The absorption peaks of the NTI segment and IR complex are not detectable because of their low contents in the polymer chains [10]. The PL emissions at 438nm and 465nm are contributed by the fluorene segment, and the emission peak at 533nm is due to the oxidation of the fluorine [11]. The green emission at 500nm is from the NTI segment, but the red emission at around 590nm is not obvious as the amount of the IR complex is low. However the emission intensity of the NTI segment is larger, even though the content is even lower than the IR complex, because the energy conversion from the fluorescence to the NTI group is more efficient than to the IR complex [12].

 

Fig. 2 The UV-VIS absorption and PL emission spectrum reveal the optical properties of PF copolymer. The absorption spectrum of the PF copolymer is dominated by an intense peak at about 390nm, which comes from the fluorene unit serving as the backbone in the copolymer. The PL emissions at 438nm and 465nm are contributed by the fluorene segment, and the emission peak at 533nm is due to the oxidation of the fluorene.13 The green emission at 500nm is from the NTI segment, but the red emission at around 590nm is not obvious as the amount of the IR complex is low. The upper insert shows the structure of PF copolymer.

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Figure 3(a) shows the PL spectra of the PF copolymer alone and coupling with the plasmonic structures of the Ag sub-micron cylinder arrays of various diameters, but without an Ag film at the bottom, where D and P in the figure denotes the diameter and period (spacing), respectively. Figure 3(b) shows the enhancement factor as a function of wavelength by normalization with the intensity of the PF copolymer alone. Obviously, all the plasmonic structures can enhance light emission through LSPR, but to different degrees at different wavelengths, of which the specific pattern with the period of 400nm and the diameter of 200nm promotes two-fold PL intensity for the green emissions and less for the blue emissions. The change in the PL spectra with various pattern parameters in the silver sub-micron cylinder arrays is ascribed to SPR coupling. To realize the PL results, the SPR absorption energies of the various Ag cylinders in the PF copolymer medium are calculated by the DDA method, and the results are shown in Fig. 4 . An incident polarized EM wave with an orthogonal direction is absorbed and scattered by dipoles. The SPR frequency of the Ag cylinders shows a red-shift from ultraviolet to visible light when the medium changes from vacuum to PF copolymer. Sosa et al. have shown that in DDA simulations, the SPR absorption for cylinder structure is divided into dipolar and multi-polar absorptions [13]. The dipolar absorption energy of the Ag cylinders is located near 700nm in Fig. 4. The parameter of the cylinder diameter in the sub-micron range has little effect on the shift of the dipolar absorption peak. The multi-polar absorption in the DDA calculation shows a broadened peak near the green band in Fig. 4, and the cylinder diameter also has little effect on SPR. The SPR branch of the 200nm-diameter cylindrical particles at the green spectrum from multi-polar absorption is the major reason for the PL intensity enhancement at 465nm, 500nm and 533nm.

 

Fig. 3 (a) PL spectrum of PF copolymer coupling with 400nm, 500nm and 600nm-period Ag cylinder arrays on Si substrate. (b) PL enhancement factors transformed from Fig. 3(a) by normalizing with the intensity of PF copolymer alone.

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Fig. 4 The absorption efficiency of Ag cylinder in PF copolymer using DDA calculation.

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From the DDA approach, the multi-polar absorption efficiency is found to match the green band emission of the PF copolymer for all diameters. However, the PL intensity increases as the inter-particle spacing decreases. The period of the pattern is the major factor for effective SPR enhanced light emission, and the localized evanescence field of SP restricts the SP wave propagation and momentum modification. The change in the evanescence field can be expressed by the skin depth as:

ζ=λ2πεd'+εm'εd'2
where εm'andεd'are the real part of the dielectric constants of the PF copolymer and silver, respectively, and λ is the wavelength of the incident light. The skin depth of the Ag cylinder in the PF copolymer is 112nm for 533nm calculated using Eq. (1), which provides a guide for the range of SP interaction. The energy conversion from the exciton of the PF copolymer to the phonon of the Ag cylinders provides an extra density of states to enable the excited states of the PF to go back to the ground state. Consequently, the life time is reduced and the radiative process is accelerated [14,15]. However, for the effective SP enhanced light emission, the SPR to photon process needs to occur via wave vector loss to enhance luminescence intensity. With the restriction of the skin depth, decreasing the pattern period to increase SP wave vector modification is necessary for effective SP enhanced luminescence, and the appropriate period would lead to sufficient SP wave vector loss by periodic metal arrays. In this study, the pattern of the 400nm-period array brings maximum PL enhancement at the green emission band, which is of the nearest cylinder-to-cylinder distance compared to the skin depth, and the 400nm periods provides sufficient effects for PL enhancement compared to the 500nm and 600nm periods.

Figure 5(a) shows the PL spectra of the PF copolymer with plasmonic structure for a continuous Ag film with/without periodic Ag cylinders on the top, where C refers to the continuous film. Figure 5(b) shows the respective enhancement factor spectrum. The 50nm-thick Ag thin layer induces large enhancement only for the blue emission band of the PF copolymer at 438 nm. SP coupling emission at the interface between the silver film and the PF copolymer predominated the contribution and the SPR energy is determined by the dispersion relation given by:

kx=ωcεmεdεm+εd
where kx is the wave vector, ω is the angular frequency, c is the light constant in vacuum,εm andεd are the dielectric constants of metal and medium, respectively. According to the dispersion relation, Eq. (2), the corresponding wavelength of the SPR energy in this case is calculated to be 427nm, which is close to the blue emission band of the PF copolymer at 438nm. The close energy match between the SPR energy and the emission band of the PF copolymer makes the energy transfer directly from exciton of the organic fluorophore to the phonon of SPR with the assistance of sufficient surface roughness on the metal surface produced during the metal evaporation for the wave vector modification [16]. The major result shows that there is around five-fold PL enhancement of the PF copolymer at 438nm for effective SP coupling emission. The fluorescence at the green band shows little improvement from the Ag film coating at the same time. The calculation approach according to dispersion relation is comparable to the PL intensity measurement in this case.

 

Fig. 5 (a) PL spectrum of PF copolymer coupling with 300nm, 350nm and 400nm-period Ag cylinder arrays on 50nm Ag thin film. (b) PL enhancement factors transformed from Fig. 5(a) by normalizing with the intensity of PF copolymer alone.

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We have shown that the silver cylinder alone can enhance green light emission through SP coupling. In Fig. 5, we further show that, by combining the features of tunable SP frequency and effective momentum compensation with a wave guide structure, the green light emission has been further enhanced compared to the previous case. By controlling the silver structure from film to particles, the SPR frequency can be tuned from blue to green band and the SPR enhanced light emission can be potentially enhanced for the entire visible light spectrum. However, the distance between two metal particles is the key for effective conversion from SP to light. The PL enhancement factor of the localized SP coupling emission produced by Ag cylinders at the green spectrum is lower than that of the propagating mode produced by an Ag thin film at the blue spectrum. It is necessary for SP to have sufficient propagating distance to modify the momentum mismatch between the phonon and photon. The efficiency between localized and propagating modes is shown to present the largest enhancement factor by either cylinder or film coupling from around two-fold at 500nm in Fig. 3 to 5.4-fold at 438nm in Fig. 5. Most significantly, the cylinder-on-film plasmonic structure helps further improve the largest PL enhancement factor at 465nm emission from around 1.9-fold of solely cylinder coupling to around 5.4-fold of cylinder-on-film coupling. The enhancement at 500nm is improved from two-fold to 4.5fold, while the enhancement at 533nm is improved from two-fold to four-fold. The SP has a large propagating distance at the metal thin surface (30um for 533nm), and delocalized SP with film coating is the key to effective tunable PL enhancement [3,17].

SP splitting and shifting is observed in Fig. 5(b), and the PL enhancement at the blue and green spectrum is varied due to the collective SP phenomenon of the cylindrical Ag array. The Ag thin film makes the interaction of SP field of Ag cylinders stronger, because it enables the SP wave to propagate and interact more easily. The transverse and longitudinal SP modes induced by orthogonal field coupling make the SP frequency split and shift toward blue and red frequencies, respectively [9]. Therefore, by decreasing the period, the SP field interaction is stronger and the intensity of SP coupling fluorescence is lower.

4. Conclusions

In conclusion, we have observed up to 5.4-fold enhancement in PL intensity with PF copolymer coupling to the multiple plasmons. The fluorescence enhancement is extended to blue and green frequencies by the combination of Ag sub-micron cylinder arrays and Ag thin film. The momentum compensation is necessary for the phonon to photon process, and delocalized SP coupling emission makes the PF copolymer more radiative. Coupling to engineered plasmonic structures combines effective luminescence enhancement and extensive SP frequencies, and this should have a wide range of application.

Acknowledgments

The authors would like to thank the Center for Micro/Nano Science and Technology, National Cheng Kung University, Tainan, Taiwan, for equipment access and technical support, and also the NSC Core Facililies Laboratory for Nano-Science and Nano-Technology in the Kaohsiung-Pintung Area. This work was supported by the National Science Council of Taiwan (grant no. NSC-95-2221-E-006-082-MY3).

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. 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]  

3. J. H. Song, T. Atay, S. Shi, H. Urabe, and A. V. Nurmikko, “Large enhancement of fluorescence efficiency from CdSe/ZnS quantum dots induced by resonant coupling to spatially controlled surface plasmons,” Nano Lett. 5(8), 1557–1561 (2005). [CrossRef]   [PubMed]  

4. C. D. Geddes and J. R. Lakowiczl, “The Changing Face of Fluorescence: Addressing the Changes,” J. Fluoresc. 12, 2 (2002).

5. S. Link and M. A. El-Sayed, “Steady state and time resolved optical properties of metallic nanoparticles the surface plasmon absorption as an analytical tool to inverstigate particle properties,” Int. Rev. Phys. Chem. 19, 409 (2000). [CrossRef]  

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

7. P. A. Hobson, S. Wedge, J. A. E. Wasey, I. Sage, and W. L. Barnes, “Surface plasmon mediated emission from organic light-emitting diodes,” Adv. Mater. 14(19), 1393–1396 (2002). [CrossRef]  

8. W. Rechberger, A. Hohenau, A. Leitner, J. R. Krenn, B. Lamprecht, and F. R. Aussenegg, “Optical properties of two interacting gold nanoparticles,” Opt. Commun. 220(1-3), 137–141 (2003). [CrossRef]  

9. C. W. Wu and H. C. Lin, “Synthesis and Characterization of Kinked and Hyperbranched Carbazole/Fluorene-Based Copolymers,” Macromolecules 39(21), 7232–7240 (2006). [CrossRef]  

10. Po-I Lee, Steve Lien-Chung Hsu, and Jung-Feng Lee, “Pure white light emitting diodes from phosphorescent single polymer systems,” J. Polym. Sci. A Polym. Chem. 46, 464 (2008). [CrossRef]  

11. R. Grisorio, G. P. Suranna, P. Mastrorilli, and C. F. Nobile, “Insight into the role of oxidation in the thermally induced green band in fluorene based systems,” Adv. Funct. Mater. 17(4), 538–548 (2007). [CrossRef]  

12. W. C. Wu, C. L. Liu, and W. C. Chen, “Synthesis and characterization of new fluorene-acceptor alternating and random copolymers for light-emitting applications,” Polymer (Guildf.) 47(2), 527–538 (2006). [CrossRef]  

13. I. O. Sosa, C. Noguez, and R. G. Barrera, “Optical properties of metal nanoparticles with arbitrary shapes,” J. Phys. Chem. B 107(26), 6269–6275 (2003). [CrossRef]  

14. K. Okamoto, I. Niki, A. Scherer, Y. Narukawa, T. Mukai, and Y. Kawakami, “Surface plasmon enhanced spontaneous emission rate of ingangan quantum wells probed by time resolved photoluminescence spectroscopy,” Appl. Phys. Lett. 87(7), 071102 (2005). [CrossRef]  

15. T. D. Neal, K. Okamoto, A. Scherer, M. S. Liu, and A. K. Y. Jen, “Time resolved photoluminescence spectroscopy of surface plasmon enhanced light emission from conjugate polymers,” Appl. Phys. Lett. 89(22), 221106 (2006). [CrossRef]  

16. T. W. Lee and S. K. Gray, “Regenerated surface plasmon polaritions,” Appl. Phys. Lett. 86(14), 141105 (2005). [CrossRef]  

17. Y. Zhang, K. Aslan, M. J. R. Previte, and C. D. Geddes, “Metal enhanced fluorescence surface plasmons can radiate a fluorophore’s structured emission,” Appl. Phys. Lett. 90(5), 053107 (2007). [CrossRef]  

References

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  1. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
    [CrossRef] [PubMed]
  2. 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]
  3. J. H. Song, T. Atay, S. Shi, H. Urabe, and A. V. Nurmikko, “Large enhancement of fluorescence efficiency from CdSe/ZnS quantum dots induced by resonant coupling to spatially controlled surface plasmons,” Nano Lett. 5(8), 1557–1561 (2005).
    [CrossRef] [PubMed]
  4. C. D. Geddes and J. R. Lakowiczl, “The Changing Face of Fluorescence: Addressing the Changes,” J. Fluoresc. 12, 2 (2002).
  5. S. Link and M. A. El-Sayed, “Steady state and time resolved optical properties of metallic nanoparticles the surface plasmon absorption as an analytical tool to inverstigate particle properties,” Int. Rev. Phys. Chem. 19, 409 (2000).
    [CrossRef]
  6. G. W. Ford and W. H. Weber, “Electromagnetic interactions of molecules with metal surface,” Phys. Rep. 113(4), 195–287 (1984).
    [CrossRef]
  7. P. A. Hobson, S. Wedge, J. A. E. Wasey, I. Sage, and W. L. Barnes, “Surface plasmon mediated emission from organic light-emitting diodes,” Adv. Mater. 14(19), 1393–1396 (2002).
    [CrossRef]
  8. W. Rechberger, A. Hohenau, A. Leitner, J. R. Krenn, B. Lamprecht, and F. R. Aussenegg, “Optical properties of two interacting gold nanoparticles,” Opt. Commun. 220(1-3), 137–141 (2003).
    [CrossRef]
  9. C. W. Wu and H. C. Lin, “Synthesis and Characterization of Kinked and Hyperbranched Carbazole/Fluorene-Based Copolymers,” Macromolecules 39(21), 7232–7240 (2006).
    [CrossRef]
  10. Po-I Lee, Steve Lien-Chung Hsu, and Jung-Feng Lee, “Pure white light emitting diodes from phosphorescent single polymer systems,” J. Polym. Sci. A Polym. Chem. 46, 464 (2008).
    [CrossRef]
  11. R. Grisorio, G. P. Suranna, P. Mastrorilli, and C. F. Nobile, “Insight into the role of oxidation in the thermally induced green band in fluorene based systems,” Adv. Funct. Mater. 17(4), 538–548 (2007).
    [CrossRef]
  12. W. C. Wu, C. L. Liu, and W. C. Chen, “Synthesis and characterization of new fluorene-acceptor alternating and random copolymers for light-emitting applications,” Polymer (Guildf.) 47(2), 527–538 (2006).
    [CrossRef]
  13. I. O. Sosa, C. Noguez, and R. G. Barrera, “Optical properties of metal nanoparticles with arbitrary shapes,” J. Phys. Chem. B 107(26), 6269–6275 (2003).
    [CrossRef]
  14. K. Okamoto, I. Niki, A. Scherer, Y. Narukawa, T. Mukai, and Y. Kawakami, “Surface plasmon enhanced spontaneous emission rate of ingangan quantum wells probed by time resolved photoluminescence spectroscopy,” Appl. Phys. Lett. 87(7), 071102 (2005).
    [CrossRef]
  15. T. D. Neal, K. Okamoto, A. Scherer, M. S. Liu, and A. K. Y. Jen, “Time resolved photoluminescence spectroscopy of surface plasmon enhanced light emission from conjugate polymers,” Appl. Phys. Lett. 89(22), 221106 (2006).
    [CrossRef]
  16. T. W. Lee and S. K. Gray, “Regenerated surface plasmon polaritions,” Appl. Phys. Lett. 86(14), 141105 (2005).
    [CrossRef]
  17. Y. Zhang, K. Aslan, M. J. R. Previte, and C. D. Geddes, “Metal enhanced fluorescence surface plasmons can radiate a fluorophore’s structured emission,” Appl. Phys. Lett. 90(5), 053107 (2007).
    [CrossRef]

2008 (1)

Po-I Lee, Steve Lien-Chung Hsu, and Jung-Feng Lee, “Pure white light emitting diodes from phosphorescent single polymer systems,” J. Polym. Sci. A Polym. Chem. 46, 464 (2008).
[CrossRef]

2007 (2)

R. Grisorio, G. P. Suranna, P. Mastrorilli, and C. F. Nobile, “Insight into the role of oxidation in the thermally induced green band in fluorene based systems,” Adv. Funct. Mater. 17(4), 538–548 (2007).
[CrossRef]

Y. Zhang, K. Aslan, M. J. R. Previte, and C. D. Geddes, “Metal enhanced fluorescence surface plasmons can radiate a fluorophore’s structured emission,” Appl. Phys. Lett. 90(5), 053107 (2007).
[CrossRef]

2006 (3)

W. C. Wu, C. L. Liu, and W. C. Chen, “Synthesis and characterization of new fluorene-acceptor alternating and random copolymers for light-emitting applications,” Polymer (Guildf.) 47(2), 527–538 (2006).
[CrossRef]

C. W. Wu and H. C. Lin, “Synthesis and Characterization of Kinked and Hyperbranched Carbazole/Fluorene-Based Copolymers,” Macromolecules 39(21), 7232–7240 (2006).
[CrossRef]

T. D. Neal, K. Okamoto, A. Scherer, M. S. Liu, and A. K. Y. Jen, “Time resolved photoluminescence spectroscopy of surface plasmon enhanced light emission from conjugate polymers,” Appl. Phys. Lett. 89(22), 221106 (2006).
[CrossRef]

2005 (3)

T. W. Lee and S. K. Gray, “Regenerated surface plasmon polaritions,” Appl. Phys. Lett. 86(14), 141105 (2005).
[CrossRef]

K. Okamoto, I. Niki, A. Scherer, Y. Narukawa, T. Mukai, and Y. Kawakami, “Surface plasmon enhanced spontaneous emission rate of ingangan quantum wells probed by time resolved photoluminescence spectroscopy,” Appl. Phys. Lett. 87(7), 071102 (2005).
[CrossRef]

J. H. Song, T. Atay, S. Shi, H. Urabe, and A. V. Nurmikko, “Large enhancement of fluorescence efficiency from CdSe/ZnS quantum dots induced by resonant coupling to spatially controlled surface plasmons,” Nano Lett. 5(8), 1557–1561 (2005).
[CrossRef] [PubMed]

2004 (1)

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]

2003 (3)

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

W. Rechberger, A. Hohenau, A. Leitner, J. R. Krenn, B. Lamprecht, and F. R. Aussenegg, “Optical properties of two interacting gold nanoparticles,” Opt. Commun. 220(1-3), 137–141 (2003).
[CrossRef]

I. O. Sosa, C. Noguez, and R. G. Barrera, “Optical properties of metal nanoparticles with arbitrary shapes,” J. Phys. Chem. B 107(26), 6269–6275 (2003).
[CrossRef]

2002 (2)

P. A. Hobson, S. Wedge, J. A. E. Wasey, I. Sage, and W. L. Barnes, “Surface plasmon mediated emission from organic light-emitting diodes,” Adv. Mater. 14(19), 1393–1396 (2002).
[CrossRef]

C. D. Geddes and J. R. Lakowiczl, “The Changing Face of Fluorescence: Addressing the Changes,” J. Fluoresc. 12, 2 (2002).

2000 (1)

S. Link and M. A. El-Sayed, “Steady state and time resolved optical properties of metallic nanoparticles the surface plasmon absorption as an analytical tool to inverstigate particle properties,” Int. Rev. Phys. Chem. 19, 409 (2000).
[CrossRef]

1984 (1)

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

Aslan, K.

Y. Zhang, K. Aslan, M. J. R. Previte, and C. D. Geddes, “Metal enhanced fluorescence surface plasmons can radiate a fluorophore’s structured emission,” Appl. Phys. Lett. 90(5), 053107 (2007).
[CrossRef]

Atay, T.

J. H. Song, T. Atay, S. Shi, H. Urabe, and A. V. Nurmikko, “Large enhancement of fluorescence efficiency from CdSe/ZnS quantum dots induced by resonant coupling to spatially controlled surface plasmons,” Nano Lett. 5(8), 1557–1561 (2005).
[CrossRef] [PubMed]

Aussenegg, F. R.

W. Rechberger, A. Hohenau, A. Leitner, J. R. Krenn, B. Lamprecht, and F. R. Aussenegg, “Optical properties of two interacting gold nanoparticles,” Opt. Commun. 220(1-3), 137–141 (2003).
[CrossRef]

Barnes, W. L.

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

P. A. Hobson, S. Wedge, J. A. E. Wasey, I. Sage, and W. L. Barnes, “Surface plasmon mediated emission from organic light-emitting diodes,” Adv. Mater. 14(19), 1393–1396 (2002).
[CrossRef]

Barrera, R. G.

I. O. Sosa, C. Noguez, and R. G. Barrera, “Optical properties of metal nanoparticles with arbitrary shapes,” J. Phys. Chem. B 107(26), 6269–6275 (2003).
[CrossRef]

Chen, W. C.

W. C. Wu, C. L. Liu, and W. C. Chen, “Synthesis and characterization of new fluorene-acceptor alternating and random copolymers for light-emitting applications,” Polymer (Guildf.) 47(2), 527–538 (2006).
[CrossRef]

Dereux, A.

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

Ebbesen, T. W.

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

El-Sayed, M. A.

S. Link and M. A. El-Sayed, “Steady state and time resolved optical properties of metallic nanoparticles the surface plasmon absorption as an analytical tool to inverstigate particle properties,” Int. Rev. Phys. Chem. 19, 409 (2000).
[CrossRef]

Ford, G. W.

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

Geddes, C. D.

Y. Zhang, K. Aslan, M. J. R. Previte, and C. D. Geddes, “Metal enhanced fluorescence surface plasmons can radiate a fluorophore’s structured emission,” Appl. Phys. Lett. 90(5), 053107 (2007).
[CrossRef]

C. D. Geddes and J. R. Lakowiczl, “The Changing Face of Fluorescence: Addressing the Changes,” J. Fluoresc. 12, 2 (2002).

Gray, S. K.

T. W. Lee and S. K. Gray, “Regenerated surface plasmon polaritions,” Appl. Phys. Lett. 86(14), 141105 (2005).
[CrossRef]

Grisorio, R.

R. Grisorio, G. P. Suranna, P. Mastrorilli, and C. F. Nobile, “Insight into the role of oxidation in the thermally induced green band in fluorene based systems,” Adv. Funct. Mater. 17(4), 538–548 (2007).
[CrossRef]

Hobson, P. A.

P. A. Hobson, S. Wedge, J. A. E. Wasey, I. Sage, and W. L. Barnes, “Surface plasmon mediated emission from organic light-emitting diodes,” Adv. Mater. 14(19), 1393–1396 (2002).
[CrossRef]

Hohenau, A.

W. Rechberger, A. Hohenau, A. Leitner, J. R. Krenn, B. Lamprecht, and F. R. Aussenegg, “Optical properties of two interacting gold nanoparticles,” Opt. Commun. 220(1-3), 137–141 (2003).
[CrossRef]

Hsu, Steve Lien-Chung

Po-I Lee, Steve Lien-Chung Hsu, and Jung-Feng Lee, “Pure white light emitting diodes from phosphorescent single polymer systems,” J. Polym. Sci. A Polym. Chem. 46, 464 (2008).
[CrossRef]

Jen, A. K. Y.

T. D. Neal, K. Okamoto, A. Scherer, M. S. Liu, and A. K. Y. Jen, “Time resolved photoluminescence spectroscopy of surface plasmon enhanced light emission from conjugate polymers,” Appl. Phys. Lett. 89(22), 221106 (2006).
[CrossRef]

Kawakami, Y.

K. Okamoto, I. Niki, A. Scherer, Y. Narukawa, T. Mukai, and Y. Kawakami, “Surface plasmon enhanced spontaneous emission rate of ingangan quantum wells probed by time resolved photoluminescence spectroscopy,” Appl. Phys. Lett. 87(7), 071102 (2005).
[CrossRef]

Krenn, J. R.

W. Rechberger, A. Hohenau, A. Leitner, J. R. Krenn, B. Lamprecht, and F. R. Aussenegg, “Optical properties of two interacting gold nanoparticles,” Opt. Commun. 220(1-3), 137–141 (2003).
[CrossRef]

Lakowiczl, J. R.

C. D. Geddes and J. R. Lakowiczl, “The Changing Face of Fluorescence: Addressing the Changes,” J. Fluoresc. 12, 2 (2002).

Lamprecht, B.

W. Rechberger, A. Hohenau, A. Leitner, J. R. Krenn, B. Lamprecht, and F. R. Aussenegg, “Optical properties of two interacting gold nanoparticles,” Opt. Commun. 220(1-3), 137–141 (2003).
[CrossRef]

Lee, Jung-Feng

Po-I Lee, Steve Lien-Chung Hsu, and Jung-Feng Lee, “Pure white light emitting diodes from phosphorescent single polymer systems,” J. Polym. Sci. A Polym. Chem. 46, 464 (2008).
[CrossRef]

Lee, Po-I

Po-I Lee, Steve Lien-Chung Hsu, and Jung-Feng Lee, “Pure white light emitting diodes from phosphorescent single polymer systems,” J. Polym. Sci. A Polym. Chem. 46, 464 (2008).
[CrossRef]

Lee, T. W.

T. W. Lee and S. K. Gray, “Regenerated surface plasmon polaritions,” Appl. Phys. Lett. 86(14), 141105 (2005).
[CrossRef]

Leitner, A.

W. Rechberger, A. Hohenau, A. Leitner, J. R. Krenn, B. Lamprecht, and F. R. Aussenegg, “Optical properties of two interacting gold nanoparticles,” Opt. Commun. 220(1-3), 137–141 (2003).
[CrossRef]

Lin, H. C.

C. W. Wu and H. C. Lin, “Synthesis and Characterization of Kinked and Hyperbranched Carbazole/Fluorene-Based Copolymers,” Macromolecules 39(21), 7232–7240 (2006).
[CrossRef]

Link, S.

S. Link and M. A. El-Sayed, “Steady state and time resolved optical properties of metallic nanoparticles the surface plasmon absorption as an analytical tool to inverstigate particle properties,” Int. Rev. Phys. Chem. 19, 409 (2000).
[CrossRef]

Liu, C. L.

W. C. Wu, C. L. Liu, and W. C. Chen, “Synthesis and characterization of new fluorene-acceptor alternating and random copolymers for light-emitting applications,” Polymer (Guildf.) 47(2), 527–538 (2006).
[CrossRef]

Liu, M. S.

T. D. Neal, K. Okamoto, A. Scherer, M. S. Liu, and A. K. Y. Jen, “Time resolved photoluminescence spectroscopy of surface plasmon enhanced light emission from conjugate polymers,” Appl. Phys. Lett. 89(22), 221106 (2006).
[CrossRef]

Mastrorilli, P.

R. Grisorio, G. P. Suranna, P. Mastrorilli, and C. F. Nobile, “Insight into the role of oxidation in the thermally induced green band in fluorene based systems,” Adv. Funct. Mater. 17(4), 538–548 (2007).
[CrossRef]

Mukai, T.

K. Okamoto, I. Niki, A. Scherer, Y. Narukawa, T. Mukai, and Y. Kawakami, “Surface plasmon enhanced spontaneous emission rate of ingangan quantum wells probed by time resolved photoluminescence spectroscopy,” Appl. Phys. Lett. 87(7), 071102 (2005).
[CrossRef]

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]

Narukawa, Y.

K. Okamoto, I. Niki, A. Scherer, Y. Narukawa, T. Mukai, and Y. Kawakami, “Surface plasmon enhanced spontaneous emission rate of ingangan quantum wells probed by time resolved photoluminescence spectroscopy,” Appl. Phys. Lett. 87(7), 071102 (2005).
[CrossRef]

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]

Neal, T. D.

T. D. Neal, K. Okamoto, A. Scherer, M. S. Liu, and A. K. Y. Jen, “Time resolved photoluminescence spectroscopy of surface plasmon enhanced light emission from conjugate polymers,” Appl. Phys. Lett. 89(22), 221106 (2006).
[CrossRef]

Niki, I.

K. Okamoto, I. Niki, A. Scherer, Y. Narukawa, T. Mukai, and Y. Kawakami, “Surface plasmon enhanced spontaneous emission rate of ingangan quantum wells probed by time resolved photoluminescence spectroscopy,” Appl. Phys. Lett. 87(7), 071102 (2005).
[CrossRef]

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]

Nobile, C. F.

R. Grisorio, G. P. Suranna, P. Mastrorilli, and C. F. Nobile, “Insight into the role of oxidation in the thermally induced green band in fluorene based systems,” Adv. Funct. Mater. 17(4), 538–548 (2007).
[CrossRef]

Noguez, C.

I. O. Sosa, C. Noguez, and R. G. Barrera, “Optical properties of metal nanoparticles with arbitrary shapes,” J. Phys. Chem. B 107(26), 6269–6275 (2003).
[CrossRef]

Nurmikko, A. V.

J. H. Song, T. Atay, S. Shi, H. Urabe, and A. V. Nurmikko, “Large enhancement of fluorescence efficiency from CdSe/ZnS quantum dots induced by resonant coupling to spatially controlled surface plasmons,” Nano Lett. 5(8), 1557–1561 (2005).
[CrossRef] [PubMed]

Okamoto, K.

T. D. Neal, K. Okamoto, A. Scherer, M. S. Liu, and A. K. Y. Jen, “Time resolved photoluminescence spectroscopy of surface plasmon enhanced light emission from conjugate polymers,” Appl. Phys. Lett. 89(22), 221106 (2006).
[CrossRef]

K. Okamoto, I. Niki, A. Scherer, Y. Narukawa, T. Mukai, and Y. Kawakami, “Surface plasmon enhanced spontaneous emission rate of ingangan quantum wells probed by time resolved photoluminescence spectroscopy,” Appl. Phys. Lett. 87(7), 071102 (2005).
[CrossRef]

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]

Previte, M. J. R.

Y. Zhang, K. Aslan, M. J. R. Previte, and C. D. Geddes, “Metal enhanced fluorescence surface plasmons can radiate a fluorophore’s structured emission,” Appl. Phys. Lett. 90(5), 053107 (2007).
[CrossRef]

Rechberger, W.

W. Rechberger, A. Hohenau, A. Leitner, J. R. Krenn, B. Lamprecht, and F. R. Aussenegg, “Optical properties of two interacting gold nanoparticles,” Opt. Commun. 220(1-3), 137–141 (2003).
[CrossRef]

Sage, I.

P. A. Hobson, S. Wedge, J. A. E. Wasey, I. Sage, and W. L. Barnes, “Surface plasmon mediated emission from organic light-emitting diodes,” Adv. Mater. 14(19), 1393–1396 (2002).
[CrossRef]

Scherer, A.

T. D. Neal, K. Okamoto, A. Scherer, M. S. Liu, and A. K. Y. Jen, “Time resolved photoluminescence spectroscopy of surface plasmon enhanced light emission from conjugate polymers,” Appl. Phys. Lett. 89(22), 221106 (2006).
[CrossRef]

K. Okamoto, I. Niki, A. Scherer, Y. Narukawa, T. Mukai, and Y. Kawakami, “Surface plasmon enhanced spontaneous emission rate of ingangan quantum wells probed by time resolved photoluminescence spectroscopy,” Appl. Phys. Lett. 87(7), 071102 (2005).
[CrossRef]

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]

Shi, S.

J. H. Song, T. Atay, S. Shi, H. Urabe, and A. V. Nurmikko, “Large enhancement of fluorescence efficiency from CdSe/ZnS quantum dots induced by resonant coupling to spatially controlled surface plasmons,” Nano Lett. 5(8), 1557–1561 (2005).
[CrossRef] [PubMed]

Shvartser, A.

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]

Song, J. H.

J. H. Song, T. Atay, S. Shi, H. Urabe, and A. V. Nurmikko, “Large enhancement of fluorescence efficiency from CdSe/ZnS quantum dots induced by resonant coupling to spatially controlled surface plasmons,” Nano Lett. 5(8), 1557–1561 (2005).
[CrossRef] [PubMed]

Sosa, I. O.

I. O. Sosa, C. Noguez, and R. G. Barrera, “Optical properties of metal nanoparticles with arbitrary shapes,” J. Phys. Chem. B 107(26), 6269–6275 (2003).
[CrossRef]

Suranna, G. P.

R. Grisorio, G. P. Suranna, P. Mastrorilli, and C. F. Nobile, “Insight into the role of oxidation in the thermally induced green band in fluorene based systems,” Adv. Funct. Mater. 17(4), 538–548 (2007).
[CrossRef]

Urabe, H.

J. H. Song, T. Atay, S. Shi, H. Urabe, and A. V. Nurmikko, “Large enhancement of fluorescence efficiency from CdSe/ZnS quantum dots induced by resonant coupling to spatially controlled surface plasmons,” Nano Lett. 5(8), 1557–1561 (2005).
[CrossRef] [PubMed]

Wasey, J. A. E.

P. A. Hobson, S. Wedge, J. A. E. Wasey, I. Sage, and W. L. Barnes, “Surface plasmon mediated emission from organic light-emitting diodes,” Adv. Mater. 14(19), 1393–1396 (2002).
[CrossRef]

Weber, W. H.

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

Wedge, S.

P. A. Hobson, S. Wedge, J. A. E. Wasey, I. Sage, and W. L. Barnes, “Surface plasmon mediated emission from organic light-emitting diodes,” Adv. Mater. 14(19), 1393–1396 (2002).
[CrossRef]

Wu, C. W.

C. W. Wu and H. C. Lin, “Synthesis and Characterization of Kinked and Hyperbranched Carbazole/Fluorene-Based Copolymers,” Macromolecules 39(21), 7232–7240 (2006).
[CrossRef]

Wu, W. C.

W. C. Wu, C. L. Liu, and W. C. Chen, “Synthesis and characterization of new fluorene-acceptor alternating and random copolymers for light-emitting applications,” Polymer (Guildf.) 47(2), 527–538 (2006).
[CrossRef]

Zhang, Y.

Y. Zhang, K. Aslan, M. J. R. Previte, and C. D. Geddes, “Metal enhanced fluorescence surface plasmons can radiate a fluorophore’s structured emission,” Appl. Phys. Lett. 90(5), 053107 (2007).
[CrossRef]

Adv. Funct. Mater. (1)

R. Grisorio, G. P. Suranna, P. Mastrorilli, and C. F. Nobile, “Insight into the role of oxidation in the thermally induced green band in fluorene based systems,” Adv. Funct. Mater. 17(4), 538–548 (2007).
[CrossRef]

Adv. Mater. (1)

P. A. Hobson, S. Wedge, J. A. E. Wasey, I. Sage, and W. L. Barnes, “Surface plasmon mediated emission from organic light-emitting diodes,” Adv. Mater. 14(19), 1393–1396 (2002).
[CrossRef]

Appl. Phys. Lett. (4)

K. Okamoto, I. Niki, A. Scherer, Y. Narukawa, T. Mukai, and Y. Kawakami, “Surface plasmon enhanced spontaneous emission rate of ingangan quantum wells probed by time resolved photoluminescence spectroscopy,” Appl. Phys. Lett. 87(7), 071102 (2005).
[CrossRef]

T. D. Neal, K. Okamoto, A. Scherer, M. S. Liu, and A. K. Y. Jen, “Time resolved photoluminescence spectroscopy of surface plasmon enhanced light emission from conjugate polymers,” Appl. Phys. Lett. 89(22), 221106 (2006).
[CrossRef]

T. W. Lee and S. K. Gray, “Regenerated surface plasmon polaritions,” Appl. Phys. Lett. 86(14), 141105 (2005).
[CrossRef]

Y. Zhang, K. Aslan, M. J. R. Previte, and C. D. Geddes, “Metal enhanced fluorescence surface plasmons can radiate a fluorophore’s structured emission,” Appl. Phys. Lett. 90(5), 053107 (2007).
[CrossRef]

Int. Rev. Phys. Chem. (1)

S. Link and M. A. El-Sayed, “Steady state and time resolved optical properties of metallic nanoparticles the surface plasmon absorption as an analytical tool to inverstigate particle properties,” Int. Rev. Phys. Chem. 19, 409 (2000).
[CrossRef]

J. Fluoresc. (1)

C. D. Geddes and J. R. Lakowiczl, “The Changing Face of Fluorescence: Addressing the Changes,” J. Fluoresc. 12, 2 (2002).

J. Phys. Chem. B (1)

I. O. Sosa, C. Noguez, and R. G. Barrera, “Optical properties of metal nanoparticles with arbitrary shapes,” J. Phys. Chem. B 107(26), 6269–6275 (2003).
[CrossRef]

J. Polym. Sci. A Polym. Chem. (1)

Po-I Lee, Steve Lien-Chung Hsu, and Jung-Feng Lee, “Pure white light emitting diodes from phosphorescent single polymer systems,” J. Polym. Sci. A Polym. Chem. 46, 464 (2008).
[CrossRef]

Macromolecules (1)

C. W. Wu and H. C. Lin, “Synthesis and Characterization of Kinked and Hyperbranched Carbazole/Fluorene-Based Copolymers,” Macromolecules 39(21), 7232–7240 (2006).
[CrossRef]

Nano Lett. (1)

J. H. Song, T. Atay, S. Shi, H. Urabe, and A. V. Nurmikko, “Large enhancement of fluorescence efficiency from CdSe/ZnS quantum dots induced by resonant coupling to spatially controlled surface plasmons,” Nano Lett. 5(8), 1557–1561 (2005).
[CrossRef] [PubMed]

Nat. Mater. (1)

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]

Nature (1)

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

Opt. Commun. (1)

W. Rechberger, A. Hohenau, A. Leitner, J. R. Krenn, B. Lamprecht, and F. R. Aussenegg, “Optical properties of two interacting gold nanoparticles,” Opt. Commun. 220(1-3), 137–141 (2003).
[CrossRef]

Phys. Rep. (1)

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

Polymer (Guildf.) (1)

W. C. Wu, C. L. Liu, and W. C. Chen, “Synthesis and characterization of new fluorene-acceptor alternating and random copolymers for light-emitting applications,” Polymer (Guildf.) 47(2), 527–538 (2006).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

(a) Schematic illustrates experimental geometry used as enhanced PL measurements of multiple plasmons (left) and LSPR only (right). The sizes are not in proportion. (b) SEM images of Ag cylinder array with the same constant height of 75nm and different diameters of 200nm, 250nm and 300nm on silicon substrates.

Fig. 2
Fig. 2

The UV-VIS absorption and PL emission spectrum reveal the optical properties of PF copolymer. The absorption spectrum of the PF copolymer is dominated by an intense peak at about 390nm, which comes from the fluorene unit serving as the backbone in the copolymer. The PL emissions at 438nm and 465nm are contributed by the fluorene segment, and the emission peak at 533nm is due to the oxidation of the fluorene.13 The green emission at 500nm is from the NTI segment, but the red emission at around 590nm is not obvious as the amount of the IR complex is low. The upper insert shows the structure of PF copolymer.

Fig. 3
Fig. 3

(a) PL spectrum of PF copolymer coupling with 400nm, 500nm and 600nm-period Ag cylinder arrays on Si substrate. (b) PL enhancement factors transformed from Fig. 3(a) by normalizing with the intensity of PF copolymer alone.

Fig. 4
Fig. 4

The absorption efficiency of Ag cylinder in PF copolymer using DDA calculation.

Fig. 5
Fig. 5

(a) PL spectrum of PF copolymer coupling with 300nm, 350nm and 400nm-period Ag cylinder arrays on 50nm Ag thin film. (b) PL enhancement factors transformed from Fig. 5(a) by normalizing with the intensity of PF copolymer alone.

Equations (2)

Equations on this page are rendered with MathJax. Learn more.

ζ = λ 2 π ε d ' + ε m ' ε d ' 2
k x = ω c ε m ε d ε m + ε d

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