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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 12 — Jun. 17, 2013
  • pp: 14159–14168
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Plasmon-enhanced spectral changes in surface sum-frequency generation with polychromatic light

Luyu Wang, Franklin Che, Sergey A. Ponomarenko, and Zhizhang (David) Chen  »View Author Affiliations


Optics Express, Vol. 21, Issue 12, pp. 14159-14168 (2013)
http://dx.doi.org/10.1364/OE.21.014159


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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

The field of plasmonics has lately experienced a truly explosive growth [1

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

]. Much research in plasmonics has so far been focused on linear light-matter interaction modalities [2

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

, 3

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

], owning largely to the success of plasmonic-based sensors as a powerful tool for probing surfaces [4

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

, 5

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

]. However, resonantly enhanced local electric fields bring about pronounced enhancement of nonlinear responses of plasmonic materials as well [1

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

]. To date, several plasmon-enhanced nonlinear optical phenomena have been explored, including second-harmonic generation (SHG) from deterministic [6

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

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] .

], random [8

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

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] .

], and phase-matched [11

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] .

] nanostructured surfaces. While SHG can be realized with a quasi-monochromatic light source of a fundamental wave (FW), the sum-frequency generation (SFG) [12

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

, 13

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] .

] or difference-frequency generation (DFG) [14

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] .

] in plasmonic materials is more difficult to realize experimentally; this is because it requires two such sources with distinct carrier frequencies as, in general, does surface plasmon excitation by four-wave mixing [15

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

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] .

]. These second- and third-order nonlinear processes are surface sensitive at the molecular level, rendering them highly attractive for nonlinear microscopy. In fact, one such modality, the second-harmonic microscopy, has already been proposed and studied [17

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

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] .

].

Although the vast majority of work in plasmonics deals with quasi-monochromatic light, there has been growing interest in spectral signatures of plasmon enhanced electromagnetic fields. In particular, the 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] .

] and inhomogeneous–periodic or random [20

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] .

]–plasmonic nanostructures, probed with broadband light beams, has been recently examined. However, to the best of our knowledge, plasmon-enhanced 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.

In this work, we investigate the spectral behavior of the fundamental and sum-frequency waves in the surface SFG from a thin metal film with the polychromatic incident light. We assume that the source field is well collimated such that it can be treated as a plane wave. The wide bandwidth of the source makes it possible to realize SFG with a single source: any pair of monochromatic components within the source spectrum gives rise to a sum-frequency component through the surface SFG process. For symmetric source spectra, one would expect the SFG spectrum to peak at half the carrier wavelength of the source. We show, however, that at the incidence angle corresponding to light coupling to the surface plasmon, the reflected sum-frequency wave (SFW) spectrum gets blue-shifted from the expected maximum whereas the reflected FW has a spectral hole at the carrier frequency. We further demonstrate that the magnitude of the effect depends on the bandwidth of the source spectrum and the incidence angle: the shifts of SFW spectra become more pronounced as the source bandwidth increases, while at a certain angle a spectral switch is observed. Also, as the incidence angle deviates from the plasmon coupling angle, all spectral changes disappear. The appearance of large SFW shifts can serve as an unambiguous plasmon signature in nonlinear surface spectroscopy.

2. Theory

We consider fully spatially coherent incident light [21

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

, 22

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] .

], which we assume to behave as a plane wave. We examine the spectral behavior of fundamental and sum-frequency waves in the Kretschmann geometry [23

23. E. Kretschmann and H. Raether, “Radiative decay of non-radiative surface plasmons excited by light,” Z. Naturforsch. A 23, 2135–2136 (1968).

] illustrated in Fig. 1. A thin metal (gold) film is illuminated by a p-polarized polychromatic plane wave from glass (ε1 = 2.25) at the angle of incidence θi. The gold film has a thickness d and relative dielectric permittivity ε2(ω). The incident wave with the spectral amplitude A(ω) can be represented as
Ei(x,z,ω,θi)=A(ω)(k1zk1exkxk1ez)ei(kxx+k1zz),
(1)
where k1 = (kx, 0, k1z) and k1=ωμ0ε1; ex and ez are unit vectors in the x- and z-directions, respectively. The components of the wave vector k1 can be expressed as kx = k1 sinθi and k1z = k1 cosθi. 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

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] .

]
Si(ω)|Ei(x,z,ω,θi)|2=|A(ω)|2,
(2)
up to an immaterial proportionality constant.

Fig. 1 Illustrating the Kretschmann configuration.

The (multiply) reflected FW strikes the detector. Using the standard multiple-reflection Airy method it can be inferred that the reflected wave is
Er(x,z,ω,θi)=A(ω)(k1zk1exkxk1ez)r˜12(ω,θi)ei(kxxk1zz).
(3)
The reflected energy spectrum can then be written as
S(1)(ω,θi)|Er(x,z,ω,θi)|2|r˜12(ω,θi)|2Si(ω).
(4)
Here 12(ω, θi) is the double-interface Fresnel reflection coefficient for p-polarization given by [25

25. W. C. Chew, Waves and Fields in Inhomogeneous Media, II ed. (Institute of Electrical and Electronics Engineers, New York, 1995).

]
r˜12(ω,θi)=r12+r23ei2k2zd1+r12r23ei2k2zd,
(5)
where k2z=k22kx2.

Next, the FW gives rise to nonlinear polarizations on both interfaces of the film. In general, the i’th component (i = x, y, or z) of the sum-frequency polarization field can be written as [26

26. R. W. Boyd, Nonlinear Optics, II ed. (Academic, Boston, 2003).

]
Pi(r,ω3)=ε0jkdω12πχijk(2)(ω3;ω1,ω2)Ej(r,ω1)Ek(r,ω2),
(6)
where ω1 and ω2 are pump frequencies while ω3 = ω1 + ω2 represents the generated nonlinear frequency, and r = (x, y, z); χijk(2)(ω3;ω1,ω2) is the nonlinear susceptibility tensor of the sum-frequency generation (SFG) process. The subscripts denote the Cartesian field components tangential and normal to the interface, respectively. It was argued theoretically [27

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] .

] that at relatively large pump wavelengths (λ ≥ 690 nm for gold), the leading contribution to the nonlinear polarization comes from the diagonal surface component χS,zzz(2) of the second-order susceptibility tensor. This claim is supported with the available SHG experimental data [28

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 80, 233402–1–4 (2009).

,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] .

], and it has been recently employed in a surface DFG study [14

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] .

]. Hence, we will ignore the other contributions to 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).

It can be shown that the total FW field in the glass is simply a superposition of the incident and reflected waves in Eqs. (1) and (3), respectively. The normal component of the reflected electric field is then
E1z(x,z,ω,θi)=kxk1A(ω)eikxx[eik1zz+r˜12(ω,θi)eik1zz].
(7)
The field on the lower interface can be found by taking 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
E2z<(x,ω,θi)=kxk1ε1ε2A(ω)eikxx[1+r˜12(ω,θi)].
(8)
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
E2z(x,z,ω,θi)=kxk2A(ω)eikxxt121+r12r23ei2k2zd[eik2zz+r23ei2k2zdeik2zz].
(9)
At the upper interface z = d, we have
E2z>(x,ω,θi)=kxk2A(ω)eikxxR(ω,θi),
(10)
where
R(ω,θi)=t12(1+r23)eik2zd1+r12r23ei2k2zd.
(11)
On substituting from Eqs. (8) and (10) into Eq. (6), the polarization fields at the upper and lower interfaces read
P<(x,ω3,θi)=ezP0<(ω3,θi)eikx(ω3)x,
(12)
P>(x,ω3,θi)=ezP0>(ω3,θi)eikx(ω3)x,
(13)
where kx(ω3) = k1(ω3) sinθi, k1(ω3)=ω3μ0ε1, and we introduced
P0<(ω3,θi)=ε0ε12sin2θidω12πχS,zzz(2)<(ω3;ω1,ω2)×A(ω1)A(ω2)ε2(ω1)ε2(ω2)[1+r˜12(ω1,θi)][1+r˜12(ω2,θi)],
(14)
and
P0>(ω3,θi)=ε0ε1sin2θidω12πχS,zzz(2)>(ω3;ω1,ω2)×A(ω1)A(ω2)ε2(ω1)ε2(ω2)R(ω1,θi)R(ω2,θi).
(15)

These polarizations act as the sources of secondary upconverted SFW. The i’th Cartesian component of the resulting sum-frequency field is determined from Maxwell’s equations to be
Ei(r,ω)=(ω/c)2ε0jdrGij(r,r,ω)Pj(r,ω).
(16)
Here Gij(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] .

]
Gij(r,r,ω)=[δij+1k2ij]G0(r,r,ω),
(17)
where G0(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

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

]
G0(r,r,ω)=eik|rr|4π|rr|=i8π2dkxkzeikx(xx)+ikz(zz).
(18)
Note that the problem we study is two-dimensional implying that 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
Edown(2)<(x,z,ω3,θi)=iω3sinθi8π2ε0cε1P0<(ω3,θi)(ex+tanθiez)ei[kx(ω3)xk1z(ω3)z],
(19)
where k1(ω3) = kx(ω3)ex + k1z(ω3)ez. By the same token, the other contribution from P to the SF field, partially transmitted into the film and eventually reflected back to the lower half-space, is
Eup(2)<(x,z,ω3,θi)=iω3sinθi8π2ε0cε2(ω3)P0<(ω3,θi)(ex+tanθiez)×r23t21ei2k2z(ω3)d1+r12r23ei2k2z(ω3)dei[kx(ω3)xk1z(ω3)z].
(20)
The Fresnel coefficients here are all evaluated at the frequency ω3 = ω1 + ω2 while k2(ω3)=kx2(ω3)+k2z2(ω3).

The contribution to the reflected SFW from the nonlinear polarization field at the upper interface P> is determined as
E(2)>(x,z,ω3,θi)=iω3sinθi8π2ε0cε2(ω3)P0>(ω3,θi)(ex+tanθiez)×t21ei2k2z(ω3)d1+r12r23ei2k2z,ω3dei[kx(ω3)xk1z(ω3)z].
(21)
Finally, combining Eqs. (19)(21), the energy spectrum of the reflected SFW in the lower half-space is found to be
S(2)(ω3,θi)|Edown(2)<(x,z,ω3,θi)+Eup(2)<(x,z,ω3,θi)+E(2)>(x,z,ω3,θi)|2.
(22)

3. Results

We utilize Eqs. (4) and (22) to evaluate the spectra of FW and SFW at the detector. The laser source is assumed to be tunable, generating ultrashort pulses of duration ranging from 30 to 90 fs (FWHM). This translates to the bandwidth of approximately 3.33×1013 to 1.0×1014 s−1 assuming a Gaussian pulse profile; typical Ti-sapphire lasers generate femtosecond pulses in this temporal range [30

30. J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena, II ed. (Academic, Boston, 2006).

]. The carrier wavelength of the source spectrum is assumed to be λ0 = 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] .

]
ε2(ω)=1ωp2ω2+iΓω+ω˜p2ω02ω2iγω.
(23)
The parameters of the model are: plasma frequencies, ωp = 13.8 × 1015s−1 and ω̃p = 4.5 × 1015s−1; damping rates, = 1.075 × 1015s−1 and γ = 9 × 1014s−1; bound electron resonant frequency, ω0 = 4.187 × 1015s−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] .

]. The leading contribution reads
χS,zzz(2)(ω3;ω1,ω2)=a(ω1,ω2)[ε2(ω1)1][ε2(ω2)1]32π2nBe,
(24)
where nB is the equilibrium free-electron density in the bulk. The dimensionless parameter a(ω1, ω2) is essentially frequency-independent whenever the two pump frequencies ω1 and ω2 lie well below the volume plasma frequency ωp. In our case, Δω < 0.1ω0 and ω0/ωp ≈ 0.117, implying that any frequency within the source bandwidth is much smaller than ωp. Hence, we may safely treat a(ω1, ω2) as a constant. The evaluated χS,zzz(2)(ω3;ω1,ω2) is then of the order of 10−18 m2/V (10−12 cm2/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] .

].

The plasmon coupling angle is given by [3

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

]
θc(ω)=sin1ε2(ω)ε1[ε2(ω)+1].
(25)
In our case, θc(ω0) ≈ 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.

Fig. 2 Far-field energy spectra of (a) FW and (b) SFW around the plasmon coupling angle. The source pulse duration is tp = 90 fs.

To better illustrate spectral aspects of SFG in the system, we normalize the SFW spectrum of Fig. 2(b) to the corresponding maximum value for each θi 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 ε2 is evaluated at 2ω0 leading to θc(2)(2ω0)45.6°. As is seen in Fig. 3(c), which shows the SFW spectrum on an even larger scale, the spectrum is consistently centered at 581 nm for incidence angles ranging from 0 to 90°, except in the neighborhood of linear and nonlinear SPRs. As the incidence angle deviates a little from θc or θc(2), the magnitude of the corresponding spectral shift falls off precipitously.

Fig. 3 Normalized far-field SFW energy spectrum for different incident angle ranges. The source pulse duration is tp = 90 fs.

We can also show that the magnitude of discovered spectral changes is strongly influenced by the bandwidth of the source spectrum. To drive this point home, we display in Fig. 4 relative shifts of the mean fundamental (sum-frequency) wavelength relative to the (half) pump carrier wavelength as functions of the incidence angle for different pulse durations. It can be inferred from the figure that the shorter the pulse duration, the larger the spectral shift. More specifically, as we increase the source bandwidth, a sharp transition from blue to red in the vicinity of the plasmon coupling angle, seen in Fig. 3(a), transforms to a spectral dip. We observe such a spectral switch in Fig. 5(a) at θi = 42.47° for the input pulse of tp = 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

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

]. We note that for the incidence angles outside the immediate neighborhood of the switch angle, the SFW spectrum displays no anomalous features, remaining Gaussian-like. We stress that the appearance of extremely surface-sensitive features in the reflected SFW spectrum can provide for environmental sensing with unprecedented accuracy. Indeed, any tiny perturbation of the film surface, leading to the corresponding change in the refractive index, can cause a switch of the SFW spectrum. Although the principle has been previously employed in conventional linear plasmonic sensor configurations [3

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

5

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

], the use of 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.

Fig. 4 Relative shifts of mean fundamental (sum-frequency) wavelengths at different incident angles with respect to the (half) pump carrier wavelength for different source pulse durations. Insert shows relative spectral shifts for incidence angles in the vicinity of the plasmon coupling angle. Negative values indicate blue shifts.
Fig. 5 (a) Normalized far-field SFW energy spectrum in the vicinity of the plasmon coupling angle with an incident pulse duration of tp = 30 fs. (b) The SFW spectral switch.

4. Summary

To summarize, we theoretically explored the spectral behavior of surface-enhanced sum-frequency generation from a thin metal film produced with coherent ultrashort laser pulses. We have shown that while spectra of fundamental waves, reflected at the angle corresponding to surface plasmon excitation in the film, can have a hole at the carrier freqency, the resonantly enhanced sum-frequency waves display pronounced spectral shifts. Thus, excited surface plasmons leave characteristic signatures in the spectra of fundamental and sum-frequency waves. We have also revealed that the discovered spectral changes strongly depend on the incidence angle and the bandwidth of the source spectrum, as well as observed a spectral switch which is sensitive to the angle variations. Our results may open up new avenues in nonlinear spectroscopy, surface plasmon sensing, and surface morphology studies.

References and links

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] .

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] .

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. 29, 62–64 (2004) [CrossRef] [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] .

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] .

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] .

23.

E. Kretschmann and H. Raether, “Radiative decay of non-radiative surface plasmons excited by light,” Z. Naturforsch. A 23, 2135–2136 (1968).

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] .

25.

W. C. Chew, Waves and Fields in Inhomogeneous Media, II ed. (Institute of Electrical and Electronics Engineers, New York, 1995).

26.

R. W. Boyd, Nonlinear Optics, II ed. (Academic, Boston, 2003).

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] .

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 80, 233402–1–4 (2009).

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] .

30.

J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena, II ed. (Academic, Boston, 2006).

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] .

32.

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

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


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References

  1. M. I. Stockman, “Nanoplasmonics: past, present, and glimpse into future,” Opt. Express19, 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 B54, 3–15 (1999). [CrossRef]
  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]
  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.29, 62–64 (2004). [CrossRef] [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. B68, 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. B16, 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. B85, 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]
  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. Express20, 11466–11477 (2012). [CrossRef] [PubMed]
  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. A345, 10–12 (2005). [CrossRef]
  23. E. Kretschmann and H. Raether, “Radiative decay of non-radiative surface plasmons excited by light,” Z. Naturforsch. A23, 2135–2136 (1968).
  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]
  25. W. C. Chew, Waves and Fields in Inhomogeneous Media, II ed. (Institute of Electrical and Electronics Engineers, New York, 1995).
  26. R. W. Boyd, Nonlinear Optics, II ed. (Academic, Boston, 2003).
  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. B50, 17597–17605 (1994). [CrossRef]
  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. B80, 233402–1–4 (2009).
  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]
  30. J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena, II ed. (Academic, Boston, 2006).
  31. 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]
  32. S. A. Ponomarenko and E. Wolf, “Spectral anomalies in Fraunhofer diffraction,” Opt. Lett.27, 1211–1213 (2002). [CrossRef]

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