## Plasmon-enhanced spectral changes in surface sum-frequency generation with polychromatic light |

Optics Express, Vol. 21, Issue 12, pp. 14159-14168 (2013)

http://dx.doi.org/10.1364/OE.21.014159

Acrobat PDF (2986 KB)

### Abstract

We theoretically explore the spectral behavior of the fundamental and sum-frequency waves generated from the surface of a thin metal film in the Kretschmann configuration with coherent ultrashort pulses. We show that the spectra of reflected sum-frequency waves exhibit pronounced shifts for the incident fundamental waves close to the plasmon coupling angle. We also demonstrate that the scale of discovered plasmon-enhanced spectral changes is strongly influenced by the magnitude of the incidence angle and the bandwidth of the source spectrum.

© 2013 OSA

## 1. Introduction

1. M. I. Stockman, “Nanoplasmonics: past, present, and glimpse into future,” Opt. Express **19**, 22029–22106 (2011) [CrossRef] [PubMed] .

2. P. N. Prasad, *Nanophotonics* (Wiley, 2004) [CrossRef] .

3. L. Novotny and B. Hechi, *Principles of Nano-Optics* (Cambridge University, 2006) [CrossRef] .

4. L. M. Zhang and D. Uttamchandani, “Optical chemical sensing employing surface plasmon resonance,” Electron. Lett. **23**, 1469–1470 (1988) [CrossRef] .

5. J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sersors: review,” Sensors and Actuators B **54**, 3–15 (1999) [CrossRef] .

1. M. I. Stockman, “Nanoplasmonics: past, present, and glimpse into future,” Opt. Express **19**, 22029–22106 (2011) [CrossRef] [PubMed] .

6. H. J. Simon, D. E. Mitchell, and J. G. Watson, “Optical second-harmonic genernation with surfance plasmons in silver films,” Phys. Rev. Lett. **33**, 1531–1534 (1974) [CrossRef] .

7. A. Bouhelier, M. Beverslius, A. Hartschuh, and L. Novotny, “Near-field second-harmonic generation induced by local field enhancement,” Phys. Rev. Lett. **90**, 13903–1–4 (2003) [CrossRef] .

8. S. I. Bozhevolny, J. Beermann, and V. Coello, “Direct observation of localized second-harmonic enhancement in random metal nanostructures,” Phys. Rev. Lett. **90**, 197403–1–4 (2003) [PubMed] .

10. M. I. Stockman, D. G. Bergman, C. Anceau, S. Brasselet, and J. Zyss, “Enhanced second-harmonic generation by metal surfaces with nanoscale roughness: Nanoscale dephasing, depolarization, and correlations,” Phys. Rev. Lett. **92**, 057402–1–4 (2004) [CrossRef] [PubMed] .

11. N. I. Zheludev and V. I. Emelyanov, “Phase-matched second harmonic generation from nanostructured metal surfaces,” J. Opt. A. **6**, 26–28 (2004) [CrossRef] .

12. A. Liebsch, “Theory of sum frequency generation from metal surfaces,” Appl. Phys. B **68**, 301–304 (1999) [CrossRef] .

13. E. M. M. van der Ham, Q. H. F. Vrehen, E. R. Eltel, V. A. Yakovlev, E. V. Alieva, L. A. Kuzik, J. E. Petrov, V. A. Sychugov, and A. F. G. van der Meer, “Giant enhancement of sum-frequency yeild by surface-plasmon excitation,” J. Opt. Soc. Am. B **16**, 1146–1152 (1999) [CrossRef] .

14. A. T. Georges and N. E. Karatzas, “Optimizing the excitation of surface plasmon polaritions by difference-frequency generation on a gold surface,” Phys. Rev. B **85**, 155442–1–5 (2012) [CrossRef] .

15. F. DeMartini, F. G. Giuliani, M. Mataloni, E. Palange, and Y. R. Shen, “Study of Surface Polaritons in GaP by Optical Four-Wave Mixing,” Phys. Rev. Lett. **37**, 440–443 (1976) [CrossRef] .

16. S. Polomba and L. Novotny, “Nonlinear excitation of surface plasmon polaritons by four-wave mixing,” Phys. Rev. Lett. **101**, 056802–1–4 (2008) [PubMed] .

17. R. M. Corn and D. A. Higgins, “Optical second harmonic generation as a probe of surface chemistry,” Chem. Rev. **94**, 107–125 (1994) [CrossRef] .

18. J. Vydra and M. Eich, “Mapping of the lateral polar orientational distribution in second-order nonlinear thin films by scanning second-harmonic microscopy,” Appl. Phys. Lett. **72**, 275–277 (1998) [CrossRef] .

*linear*optical response of homogenous [19

19. T.-H. Lan, Y.-K. Chyng, J. Li, and C.-H. Tien, “Plasmonic rainbow rings induced by white radial polarization,” Opt. Lett. **37**, 1205–1207 (2012) [CrossRef] [PubMed] .

20. Y. Nishijima, L. Roza, and S. Juodkazis, “Surface plasmon resonances in periodic and random patterns of gold nano-disks for broadband light harvesting,” Opt. Express **20**, 11466–11477 (2012) [CrossRef] [PubMed] .

*nonlinear*optical processes, excited by polychromatic light sources, have not yet been studied. In this context, it is especially instructive to learn whether plasmons, excited on the surface of a conducting material or nanostructure, leave any signatures in the far-field spectra of generated second-order nonlinear waves. The affirmative answer to this question can trigger new developments in surface nonlinear spectroscopy, microscopy, and surface morphology studies.

## 2. Theory

21. L. Mandel and E. Wolf, *Optical Coherence and Quantum Optics* (Cambridge University, Cambridge, 1995) [CrossRef] .

22. S. A. Ponomarenko, H. Roychowdhury, and E. Wolf, “Physical significance of complete spatial coherence of optical fields,” Phys. Lett. A **345**, 10–12 (2005) [CrossRef] .

*p*-polarized polychromatic plane wave from glass (

*ε*

_{1}= 2.25) at the angle of incidence

*θ*. The gold film has a thickness

_{i}*d*and relative dielectric permittivity

*ε*

_{2}(

*ω*). The incident wave with the spectral amplitude

*A*(

*ω*) can be represented as where

**k**

_{1}= (

*k*, 0,

_{x}*k*

_{1z}) and

**e**

*and*

_{x}**e**

*are unit vectors in the*

_{z}*x*- and

*z*-directions, respectively. The components of the wave vector

**k**

_{1}can be expressed as

*k*=

_{x}*k*

_{1}sin

*θ*and

_{i}*k*

_{1z}=

*k*

_{1}cos

*θ*. The finite bandwidth of the incident light can originate either from partial temporal coherence or from a pulsed nature of the source. We assume henceforth that the incident light wave is produced by a coherent femtosecond laser source which provides sufficiently large input intensities to generate a nonlinear optical response of the system. Thus, we introduce the energy spectrum of the incident pulse by the expression [24

_{i}24. S. A. Ponomarenko, G. P. Agrawal, and E. Wolf, “Energy spectrum of nonstationary ensemble of pulses,” Opt. Lett. **29**, 394–396 (2004) [CrossRef] [PubMed] .

*r̃*

_{12}(

*ω*,

*θ*) is the double-interface Fresnel reflection coefficient for

_{i}*p*-polarization given by [25] where

*i*’th component (

*i*=

*x*,

*y*, or

*z*) of the sum-frequency polarization field can be written as [26] where

*ω*

_{1}and

*ω*

_{2}are pump frequencies while

*ω*

_{3}=

*ω*

_{1}+

*ω*

_{2}represents the generated nonlinear frequency, and

**r**= (

*x*,

*y*,

*z*);

27. W. Hübner, K. H. Bennemann, and K. Böhmer, “Theory for the nonlinear optical response of transition metals: Polarization dependence as a fingerprint of the electronic structure at surfaces and interfaces,” Phys. Rev. B **50**, 17597–17605 (1994) [CrossRef] .

*λ*≥ 690 nm for gold), the leading contribution to the nonlinear polarization comes from the diagonal surface component

29. D. Krause, C. W. Teplin, and C. T. Rogers, “Optical surface second harmonic measurements of isotropic thin-film metals: Gold, silver, copper, aluminum, and tantalum,” J. Appl. Phys. **96**, 3626–3634 (2004) [CrossRef] .

14. A. T. Georges and N. E. Karatzas, “Optimizing the excitation of surface plasmon polaritions by difference-frequency generation on a gold surface,” Phys. Rev. B **85**, 155442–1–5 (2012) [CrossRef] .

*χ*

^{(2)}hereafter. Therefore, we will only need the

*z*-component of the field at the top and bottom of the film to determine the polarization fields in Eq. (6).

*z*= 0. In addition, on applying the boundary condition for the normal components of the field on both sides of the lower interface, we obtain the field on the metal side of the lower interface as Similarly, the total FW field in the film is a superposition of the waves transmitted and reflected by the upper interface. The corresponding normal component of the field can be represented as At the upper interface

*z*=

*d*, we have where On substituting from Eqs. (8) and (10) into Eq. (6), the polarization fields at the upper and lower interfaces read where

*k*(

_{x}*ω*

_{3}) =

*k*

_{1}(

*ω*

_{3}) sin

*θ*,

_{i}*i*’th Cartesian component of the resulting sum-frequency field is determined from Maxwell’s equations to be Here

*G*(

_{ij}**r**,

**r′**,

*ω*) is the dyadic Green’s tensor which can be expressed as [3

3. L. Novotny and B. Hechi, *Principles of Nano-Optics* (Cambridge University, 2006) [CrossRef] .

*G*

_{0}(

**r**,

**r′**,

*ω*) is the scalar free-space Green’s function representing an outgoing spherical wave from a point source. We use the Weyl identity to expand the spherical wave into an angular spectrum of plane waves [3

3. L. Novotny and B. Hechi, *Principles of Nano-Optics* (Cambridge University, 2006) [CrossRef] .

21. L. Mandel and E. Wolf, *Optical Coherence and Quantum Optics* (Cambridge University, Cambridge, 1995) [CrossRef] .

**r**= (

*x*, 0,

*z*) and

**r**′ = (

*x*′, 0,

*z*′). The nonlinear polarization field at the lower interface

**P**

^{<}gives rise to a contribution to the SFW through the field directly reflected into the lower half-space. It can be obtained by substituting from Eqs. (12) and (17) into Eq. (16), and using Eq. (18), yielding where

**k**

_{1}(

*ω*

_{3}) =

*k*(

_{x}*ω*

_{3})

**e**

*+*

_{x}*k*

_{1z}(

*ω*

_{3})

**e**

*. By the same token, the other contribution from*

_{z}**P**to the SF field, partially transmitted into the film and eventually reflected back to the lower half-space, is

*ω*

_{3}=

*ω*

_{1}+

*ω*

_{2}while

**P**

^{>}is determined as

## 3. Results

^{13}to 1.0×10

^{14}s

^{−1}assuming a Gaussian pulse profile; typical Ti-sapphire lasers generate femtosecond pulses in this temporal range [30]. The carrier wavelength of the source spectrum is assumed to be

*λ*

_{0}= 1162 nm. The gold film has a thickness of

*d*= 50 nm. To describe linear dielectric properties of the film, we employ a modified Drude-Sommerfeld model which takes into account the contributions from free and bound (interband transitions) electrons resulting in [3

3. L. Novotny and B. Hechi, *Principles of Nano-Optics* (Cambridge University, 2006) [CrossRef] .

*ω*= 13.8 × 10

_{p}^{15}

*s*

^{−1}and

*ω̃*= 4.5 × 10

_{p}^{15}

*s*

^{−1}; damping rates, = 1.075 × 10

^{15}

*s*

^{−1}and

*γ*= 9 × 10

^{14}

*s*

^{−1}; bound electron resonant frequency,

*ω*

_{0}= 4.187 × 10

^{15}

*s*

^{−1}. The surface nonlinear susceptibility is described within the framework of a hydrodynamic model developed in [31

31. J. A. Maytorena, W. L. Mochán, and B. S. Mendoza, “Hydrodynamic model of sum and difference frequency generation at metal surfaces,” Phys. Rev. B **57**, 2580–2585 (1998) [CrossRef] .

*n*is the equilibrium free-electron density in the bulk. The dimensionless parameter

_{B}*a*(

*ω*

_{1},

*ω*

_{2}) is essentially frequency-independent whenever the two pump frequencies

*ω*

_{1}and

*ω*

_{2}lie well below the volume plasma frequency

*ω*. In our case, Δ

_{p}*ω*< 0.1

*ω*

_{0}and

*ω*

_{0}/

*ω*≈ 0.117, implying that any frequency within the source bandwidth is much smaller than

_{p}*ω*. Hence, we may safely treat

_{p}*a*(

*ω*

_{1},

*ω*

_{2}) as a constant. The evaluated

^{−18}m

^{2}/V (10

^{−12}cm

^{2}/statvolt in Gaussian units), showing excellent agreement with the experimental results of [29

29. D. Krause, C. W. Teplin, and C. T. Rogers, “Optical surface second harmonic measurements of isotropic thin-film metals: Gold, silver, copper, aluminum, and tantalum,” J. Appl. Phys. **96**, 3626–3634 (2004) [CrossRef] .

3. L. Novotny and B. Hechi, *Principles of Nano-Optics* (Cambridge University, 2006) [CrossRef] .

*θ*(

_{c}*ω*

_{0}) ≈ 42.3°. Under these conditions, free electrons in the film respond collectively to incident light waves by oscillating in resonance with the FW, i.e., surface plasmon resonance (SPR) occurs. It can be clearly seen in Fig. 2(a) that due to the efficient coupling to surface plasmons, the reflected FW has a hole in the far-field spectrum. The electromagnetic energy is localized near the film-air interface, dramatically enhancing the efficiency of SFG. The generated SFW is then reflected from the glass back to the detector and a large spectral peak, clearly visible in Fig. 2(b), is registered. Notice that the SFW is much better localized than the FW. For symmetric source spectra, one would expect the SFW spectrum to have a maximum at half the carrier wavelength of the FW (581 nm). However, the peak is actually blue-shifted with respect to the expected position. We conclude that the SPR leaves unambiguous signatures in the far-field spectrum of generated SFW.

*θ*and display the result in Fig. 3. In Fig. 3(a), we exhibited the SFW spectrum in a narrow range of incidence angles around the plasmon coupling angle. It can be inferred from the figure that the SPR gives rises to an overall blue-shift of the SFW spectrum. Displaying a wider incidence angle range in Fig. 3(b), we can observe that there is another (smaller) spectral shift toward the blue around 46°. This results from the SPR at SFW wavelengths: as long as the SFW is generated due to the strong FW enhancement, it can also be coupled to surface plasmons resulting in SPR excitation in the SFW. The corresponding plasmon coupling angle can be determined from the equation identical to Eq. (25), except

_{i}*ε*

_{2}is evaluated at 2

*ω*

_{0}leading to

*θ*or

_{c}*θ*= 42.47° for the input pulse of

_{i}*t*= 30 fs duration. Qualitatively, the present spectral switch is similar to the one previously discovered in Fraunhofer diffraction of light by a circular aperture [32

_{p}32. S. A. Ponomarenko and E. Wolf, “Spectral anomalies in Fraunhofer diffraction,” Opt. Lett. **27**, 1211–1213 (2002) [CrossRef] .

*linear*plasmonic sensor configurations [3

3. L. Novotny and B. Hechi, *Principles of Nano-Optics* (Cambridge University, 2006) [CrossRef] .

5. J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sersors: review,” Sensors and Actuators B **54**, 3–15 (1999) [CrossRef] .

*nonlinear*wave spectra can help attain, perhaps, a single-atom level of accuracy. This point is illustrated in Fig. 5(b) where we show that the SFW spectral behavior at the switch angle is sensitive to the angle variations of just a fraction of a degree.

## 4. Summary

## References and links

1. | M. I. Stockman, “Nanoplasmonics: past, present, and glimpse into future,” Opt. Express |

2. | P. N. Prasad, |

3. | L. Novotny and B. Hechi, |

4. | L. M. Zhang and D. Uttamchandani, “Optical chemical sensing employing surface plasmon resonance,” Electron. Lett. |

5. | J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sersors: review,” Sensors and Actuators B |

6. | H. J. Simon, D. E. Mitchell, and J. G. Watson, “Optical second-harmonic genernation with surfance plasmons in silver films,” Phys. Rev. Lett. |

7. | A. Bouhelier, M. Beverslius, A. Hartschuh, and L. Novotny, “Near-field second-harmonic generation induced by local field enhancement,” Phys. Rev. Lett. |

8. | S. I. Bozhevolny, J. Beermann, and V. Coello, “Direct observation of localized second-harmonic enhancement in random metal nanostructures,” Phys. Rev. Lett. |

9. | M. Labardi, M. Allegrini, M. Zavelani-Rossi, D. Polli, G. Cerullo, S. D. Silvestri, and O. Sveto, “Highly efficient second-harmonic nanosource for near-field optics and microscopy,” Opt. Lett. |

10. | M. I. Stockman, D. G. Bergman, C. Anceau, S. Brasselet, and J. Zyss, “Enhanced second-harmonic generation by metal surfaces with nanoscale roughness: Nanoscale dephasing, depolarization, and correlations,” Phys. Rev. Lett. |

11. | N. I. Zheludev and V. I. Emelyanov, “Phase-matched second harmonic generation from nanostructured metal surfaces,” J. Opt. A. |

12. | A. Liebsch, “Theory of sum frequency generation from metal surfaces,” Appl. Phys. B |

13. | E. M. M. van der Ham, Q. H. F. Vrehen, E. R. Eltel, V. A. Yakovlev, E. V. Alieva, L. A. Kuzik, J. E. Petrov, V. A. Sychugov, and A. F. G. van der Meer, “Giant enhancement of sum-frequency yeild by surface-plasmon excitation,” J. Opt. Soc. Am. B |

14. | A. T. Georges and N. E. Karatzas, “Optimizing the excitation of surface plasmon polaritions by difference-frequency generation on a gold surface,” Phys. Rev. B |

15. | F. DeMartini, F. G. Giuliani, M. Mataloni, E. Palange, and Y. R. Shen, “Study of Surface Polaritons in GaP by Optical Four-Wave Mixing,” Phys. Rev. Lett. |

16. | S. Polomba and L. Novotny, “Nonlinear excitation of surface plasmon polaritons by four-wave mixing,” Phys. Rev. Lett. |

17. | R. M. Corn and D. A. Higgins, “Optical second harmonic generation as a probe of surface chemistry,” Chem. Rev. |

18. | J. Vydra and M. Eich, “Mapping of the lateral polar orientational distribution in second-order nonlinear thin films by scanning second-harmonic microscopy,” Appl. Phys. Lett. |

19. | T.-H. Lan, Y.-K. Chyng, J. Li, and C.-H. Tien, “Plasmonic rainbow rings induced by white radial polarization,” Opt. Lett. |

20. | Y. Nishijima, L. Roza, and S. Juodkazis, “Surface plasmon resonances in periodic and random patterns of gold nano-disks for broadband light harvesting,” Opt. Express |

21. | L. Mandel and E. Wolf, |

22. | S. A. Ponomarenko, H. Roychowdhury, and E. Wolf, “Physical significance of complete spatial coherence of optical fields,” Phys. Lett. A |

23. | E. Kretschmann and H. Raether, “Radiative decay of non-radiative surface plasmons excited by light,” Z. Naturforsch. A |

24. | S. A. Ponomarenko, G. P. Agrawal, and E. Wolf, “Energy spectrum of nonstationary ensemble of pulses,” Opt. Lett. |

25. | W. C. Chew, |

26. | R. W. Boyd, |

27. | W. Hübner, K. H. Bennemann, and K. Böhmer, “Theory for the nonlinear optical response of transition metals: Polarization dependence as a fingerprint of the electronic structure at surfaces and interfaces,” Phys. Rev. B |

28. | F. X. Wang, F. J. Rodriguez, W. M. Albers, R. Ahorinta, J. E. Sipe, and M. Kauranen, “Surface and bulk contributions to the second-order nonlinear optical response of a gold film,” Phys. Rev. B |

29. | D. Krause, C. W. Teplin, and C. T. Rogers, “Optical surface second harmonic measurements of isotropic thin-film metals: Gold, silver, copper, aluminum, and tantalum,” J. Appl. Phys. |

30. | J.-C. Diels and W. Rudolph, |

31. | J. A. Maytorena, W. L. Mochán, and B. S. Mendoza, “Hydrodynamic model of sum and difference frequency generation at metal surfaces,” Phys. Rev. B |

32. | S. A. Ponomarenko and E. Wolf, “Spectral anomalies in Fraunhofer diffraction,” Opt. Lett. |

**OCIS Codes**

(190.4350) Nonlinear optics : Nonlinear optics at surfaces

(240.6680) Optics at surfaces : Surface plasmons

(300.6170) Spectroscopy : Spectra

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: March 27, 2013

Revised Manuscript: May 28, 2013

Manuscript Accepted: May 29, 2013

Published: June 6, 2013

**Citation**

Luyu Wang, Franklin Che, Sergey A. Ponomarenko, and Zhizhang (David) Chen, "Plasmon-enhanced spectral changes in surface sum-frequency generation with polychromatic light," Opt. Express **21**, 14159-14168 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-12-14159

Sort: Year | Journal | Reset

### References

- M. I. Stockman, “Nanoplasmonics: past, present, and glimpse into future,” Opt. Express19, 22029–22106 (2011). [CrossRef] [PubMed]
- P. N. Prasad, Nanophotonics (Wiley, 2004). [CrossRef]
- L. Novotny and B. Hechi, Principles of Nano-Optics (Cambridge University, 2006). [CrossRef]
- L. M. Zhang and D. Uttamchandani, “Optical chemical sensing employing surface plasmon resonance,” Electron. Lett.23, 1469–1470 (1988). [CrossRef]
- J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sersors: review,” Sensors and Actuators B54, 3–15 (1999). [CrossRef]
- H. J. Simon, D. E. Mitchell, and J. G. Watson, “Optical second-harmonic genernation with surfance plasmons in silver films,” Phys. Rev. Lett.33, 1531–1534 (1974). [CrossRef]
- A. Bouhelier, M. Beverslius, A. Hartschuh, and L. Novotny, “Near-field second-harmonic generation induced by local field enhancement,” Phys. Rev. Lett.90, 13903–1–4 (2003). [CrossRef]
- S. I. Bozhevolny, J. Beermann, and V. Coello, “Direct observation of localized second-harmonic enhancement in random metal nanostructures,” Phys. Rev. Lett.90, 197403–1–4 (2003). [PubMed]
- M. Labardi, M. Allegrini, M. Zavelani-Rossi, D. Polli, G. Cerullo, S. D. Silvestri, and O. Sveto, “Highly efficient second-harmonic nanosource for near-field optics and microscopy,” Opt. Lett.29, 62–64 (2004). [CrossRef] [PubMed]
- M. I. Stockman, D. G. Bergman, C. Anceau, S. Brasselet, and J. Zyss, “Enhanced second-harmonic generation by metal surfaces with nanoscale roughness: Nanoscale dephasing, depolarization, and correlations,” Phys. Rev. Lett.92, 057402–1–4 (2004). [CrossRef] [PubMed]
- N. I. Zheludev and V. I. Emelyanov, “Phase-matched second harmonic generation from nanostructured metal surfaces,” J. Opt. A.6, 26–28 (2004). [CrossRef]
- A. Liebsch, “Theory of sum frequency generation from metal surfaces,” Appl. Phys. B68, 301–304 (1999). [CrossRef]
- E. M. M. van der Ham, Q. H. F. Vrehen, E. R. Eltel, V. A. Yakovlev, E. V. Alieva, L. A. Kuzik, J. E. Petrov, V. A. Sychugov, and A. F. G. van der Meer, “Giant enhancement of sum-frequency yeild by surface-plasmon excitation,” J. Opt. Soc. Am. B16, 1146–1152 (1999). [CrossRef]
- A. T. Georges and N. E. Karatzas, “Optimizing the excitation of surface plasmon polaritions by difference-frequency generation on a gold surface,” Phys. Rev. B85, 155442–1–5 (2012). [CrossRef]
- F. DeMartini, F. G. Giuliani, M. Mataloni, E. Palange, and Y. R. Shen, “Study of Surface Polaritons in GaP by Optical Four-Wave Mixing,” Phys. Rev. Lett.37, 440–443 (1976). [CrossRef]
- S. Polomba and L. Novotny, “Nonlinear excitation of surface plasmon polaritons by four-wave mixing,” Phys. Rev. Lett.101, 056802–1–4 (2008). [PubMed]
- R. M. Corn and D. A. Higgins, “Optical second harmonic generation as a probe of surface chemistry,” Chem. Rev.94, 107–125 (1994). [CrossRef]
- J. Vydra and M. Eich, “Mapping of the lateral polar orientational distribution in second-order nonlinear thin films by scanning second-harmonic microscopy,” Appl. Phys. Lett.72, 275–277 (1998). [CrossRef]
- T.-H. Lan, Y.-K. Chyng, J. Li, and C.-H. Tien, “Plasmonic rainbow rings induced by white radial polarization,” Opt. Lett.37, 1205–1207 (2012). [CrossRef] [PubMed]
- Y. Nishijima, L. Roza, and S. Juodkazis, “Surface plasmon resonances in periodic and random patterns of gold nano-disks for broadband light harvesting,” Opt. Express20, 11466–11477 (2012). [CrossRef] [PubMed]
- L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, Cambridge, 1995). [CrossRef]
- S. A. Ponomarenko, H. Roychowdhury, and E. Wolf, “Physical significance of complete spatial coherence of optical fields,” Phys. Lett. A345, 10–12 (2005). [CrossRef]
- E. Kretschmann and H. Raether, “Radiative decay of non-radiative surface plasmons excited by light,” Z. Naturforsch. A23, 2135–2136 (1968).
- S. A. Ponomarenko, G. P. Agrawal, and E. Wolf, “Energy spectrum of nonstationary ensemble of pulses,” Opt. Lett.29, 394–396 (2004). [CrossRef] [PubMed]
- W. C. Chew, Waves and Fields in Inhomogeneous Media, II ed. (Institute of Electrical and Electronics Engineers, New York, 1995).
- R. W. Boyd, Nonlinear Optics, II ed. (Academic, Boston, 2003).
- W. Hübner, K. H. Bennemann, and K. Böhmer, “Theory for the nonlinear optical response of transition metals: Polarization dependence as a fingerprint of the electronic structure at surfaces and interfaces,” Phys. Rev. B50, 17597–17605 (1994). [CrossRef]
- F. X. Wang, F. J. Rodriguez, W. M. Albers, R. Ahorinta, J. E. Sipe, and M. Kauranen, “Surface and bulk contributions to the second-order nonlinear optical response of a gold film,” Phys. Rev. B80, 233402–1–4 (2009).
- D. Krause, C. W. Teplin, and C. T. Rogers, “Optical surface second harmonic measurements of isotropic thin-film metals: Gold, silver, copper, aluminum, and tantalum,” J. Appl. Phys.96, 3626–3634 (2004). [CrossRef]
- J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena, II ed. (Academic, Boston, 2006).
- J. A. Maytorena, W. L. Mochán, and B. S. Mendoza, “Hydrodynamic model of sum and difference frequency generation at metal surfaces,” Phys. Rev. B57, 2580–2585 (1998). [CrossRef]
- S. A. Ponomarenko and E. Wolf, “Spectral anomalies in Fraunhofer diffraction,” Opt. Lett.27, 1211–1213 (2002). [CrossRef]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.