Clarifying the origin of third-harmonic generation from film-coupled nanostripes

Xiaojun Liu; Stéphane Larouche; Patrick Bowen; David R. Smith

doi:10.1364/OE.23.019565

1. Introduction

The collective oscillations of conduction electrons in metal nanostructures give rise to plasmonic resonances at optical frequencies. These resonances, which are typically accompanied by large enhancement and localization of electromagnetic fields, have been exploited in many nonlinear processes [1–4]. Various plasmonic structures, including films, nanoparticles, and optical-antennas, have been investigated for second-harmonic generation (SHG) [5–8], third-harmonic generation (THG) [9–15], four-wave-mixing (FWM) [16–21], and high harmonic generation [22–24]. Coupled plasmonic nanostructures are of particular interest, as when such nanostructures are positioned in close proximity to each other, the hybridization of the plasmonic resonances can lead to extremely large localized fields between the nanostructures. The gaps between metal nanostructures, often referred to as “hot spots,” have the potential to dramatically boost the nonlinear response of embedded materials that interact with the strongly enhanced fields. The optical properties of many coupled geometries, such as gap-antennas [11, 12], bowties [10, 14, 22], and film-coupled nanostripes [15], have been investigated for their scattering and field enhancement characteristics. The nonlinear properties of metals have also drawn considerable interest, due to their large inherent third-order nonlinear susceptibilities. While metals suffer from optical losses, the third-order nonlinear responses of metal nanostructures can be enhanced by the local fields near hot spots, raising the prospect of achieving high nonlinear efficiencies with nanoscale metallic structures.

Since the strongly enhanced fields in a hybrid nanostructure—consisting of both metallic and dielectric components—interact with the metal as well as with any integrated dielectric materials, the nonlinearities of the metal and the dielectrics can both contribute to the nonlinear signal [25–27]. This situation makes the origin of the nonlinear response from hybrid plasmonic structures ambiguous. When a nonlinear dielectric material with large nonlinear susceptibility, such as TiO2 or ITO, is integrated into the hot spot of a plasmonic nanostructure, large enhancement of the nonlinear response can be obtained. In this case, the nonlinearity from the dielectric component dominates the signal, while the nonlinearity from the metal can be neglected. However, if we are interested in isolating the enhancement associated with the intrinsic nonlinear response of the metallic nanostructure (for example, when investigating the influence of the geometries of plasmonic structures), the observed signal will necessarily include the contribution of the embedded dielectric material, which may overwhelm the contribution of the metal. In recent theoretical studies, the nonlinear optical response of metals has proven an intriguing topic, since a rich variety of nonlinear phenomena are expected from the response of conduction electrons [28].

Motivating our present study is a recent experiment in which the THG from film-coupled gold nanostripes separated from a gold film by an Al₂O₃ spacer was measured. It was found that the THG from the Al₂O₃ spacer could be comparable to that from the gold, even though the third order susceptibility of the Al₂O₃ is at least four orders of magnitude smaller [15]. It was thus not possible to independently identify the contribution from the metallic component versus that from the dielectric component, though a large enhancement of the THG was observed.

In this paper, we propose a method to identify the origin of the THG from isolated film-coupled nanostripes. Film-coupled nanostripes have recently attracted significant interest, not only because of their potential in amplifying the nonlinear response of materials, but also because their gap sizes are easily controllable down to the sub-nanometer scale, where quantum effects may become significant. By considering the THG from each nonlinear source separately in numerical simulations, we investigate the far field radiation pattern of each nonlinear source respectively, and show that their far field radiation patterns are distinguishable due to the fundamental difference in their radiation properties. We also find a simple relation that connects the total THG and the THG from each individual nonlinear source. To illustrate the underlying mechanism, we divide our analysis into two steps. First, we only consider the THG before it couples to the film-coupled nanostripe, whose field distribution is directly related to that of the third-order nonlinear polarization. Second, we take into account the film-coupled nanostripe and study the coupling between the THG and the structure. Finally, we demonstrate the generality of our method by investigating film-coupled nanostripes over a wider range of parameters.

2. Geometry and method

The geometry used in this study is shown in Fig. 1 (a). A 30 nm-thick gold stripe lies on top of a 100 nm-thick, infinitely wide, gold film coated with an aluminum oxide (Al₂O₃) layer. This geometry results in a coupled plasmonic structure that behaves like a two-dimensional optical patch antenna, where a cavity resonator is defined between the stripe and film in the Al₂O₃ gap. When the system is excited at resonance and normal incidence by a TM-polarized wave, with the electric field oriented along the width of the stripe, most of the incident energy is coupled to the system and a close-to-zero reflectance can be observed [29, 30]. The electromagnetic field in the gap region is localized and enhanced by the cavity effect: confined gap plasmons propagate along the width and are reflected at the edges. As a result, a maximum in the magnetic field is created at the center of the gap region and a maximum in the electric field is created at either edge of the gap region (Figs. 1(b) and 1(c)). The electric fields in the stripe and the film are horizontal and anti-parallel to each other. The resonance frequency of this structure is determined by the stripe width, W, the gap size, g, the optical properties of the Al₂O₃ spacer layer and those of the gold [31]. In numerical simulations, we choose the refractive index of the Al₂O₃ to be 1.45, which was determined by ellipsometry measurements previously reported [15]. The permittivity of the gold stripes (evaporated gold) and the ultra-flat gold film (template-stripped gold) were taken from empirical data [32]. The substrate of the structure is assumed to be optical epoxy, which is a material commonly used in the fabrication of ultra-flat, template-stripped gold films. By choosing the stripe width W to be 115 nm and the gap spacing to be 3 nm, we are able to tune the resonance wavelength to 1.55 µm. Note that the resonance discussed above is the fundamental resonance of the film-coupled nanostripe. This structure also supports higher order resonances, where the confined plasmons propagating along the gap have multiple nodes, as shown in Figs. 1(d) and 1(e). The resonance wavelength of the first-order gap plasmon mode for the considered structure (W = 115 nm, g = 3 nm) is around 720 nm, and the second-order gap plasmon mode is around 600 nm. As we are going to show in the following text, while the fundamental resonance ensures the enhancement of nonlinear signal by strongly localizing the pumping field in nonlinear materials, these higher order resonances are beneficial as they facilitate the radiation of the nonlinear signal through coupling.

Fig. 1 (a) Geometry of the film-coupled nanostripe. EV gold: evaporated gold; TS gold: template-stripped gold. (b) and (c) Magnetic and electric field distributions at the fundamental resonance of the system (1.55 μm); arrows represent the direction of magnetic and electric fields. (d) and (e) Magnetic and electric field distributions at a higher-order resonance at 720 nm.

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The third-harmonic fields were computed using COMSOL Multiphysics, a finite-element based solver, under the undepleted pump approximation. The fields at the pumping wavelength (1.55 µm) were used as the source term for computing the response at THG. Both the gold and the Al₂O₃ spacer layer are treated as isotropic nonlinear materials, whose third-order nonlinear polarizations are expressed as

Ρ (r) = \frac{1}{4} ε_{0} χ^{(3)} [Ε (r) \cdot Ε (r)] Ε (r) .

The

χ^{(3)}

of the gold and of the amorphous Al₂O₃ spacer layer are unknown. In previous work, a value for the susceptibility of

χ_{}^{(3)} (Au) = 2.45 \times 10^{- 19} {(m / V)}^{2}

was used as an approximation, which was an orientational average of the

χ^{(3)}

tensor of the polycrystalline gold film [33]. The

χ^{(3)}

of the amorphous Al₂O₃ spacer layer was found to be

2.3 \times 10^{- 23} {(m / V)}^{2}

by fitting simulation results with experimental measurements [15]. This value was relatively reasonable when compared to the

χ^{(3)} (~ 10^{- 22} m^{2} / V^{2})

of crystalline Al₂O₃, and the

χ^{(3)}

estimated from a single atomic oscillator model [34]. Here, to make our discussion general, instead of assigning specific values to

χ_{}^{(3)} (Au)

and

χ_{}^{(3)} ({Al}_{2} O_{3})

, we focus on the ratio between

χ_{}^{(3)} (Au)

and

χ_{}^{(3)} ({Al}_{2} O_{3})

. We maintain the bulk nonlinearity of gold in simulation, but ignore any possible surface nonlinearity. In order to study the THG arising from different nonlinear sources, we performed separate THG simulations, taking into account the nonlinear contribution from the Al₂O₃ spacer layer, the gold stripe, and the gold film, respectively. The far-field radiation of each nonlinear source is calculated as a function of radiation angle in COMSOL Multiphysics, where

Ε_{f a r} = \lim_{r \to \infty} r Ε_{s c a} .

To avoid the influence of the near-field, we choose our simulation domain to be much larger than the pumping wavelength.

To describe the THG enhancement by the film-coupled nanostripe, we define a THG enhancement factor of the form

η (θ) = \frac{| Ε_{f a r} (3 ω, θ) |}{χ^{(3)} {| Ε_{0}^{} (ω) |}^{3}},

where

| Ε_{0}^{} (ω) |

is the amplitude of the pumping field at normal incidence,

| Ε_{far} (3 ω, θ) |

is the amplitude of the THG far field measured at

θ

, and

χ_{}^{(3)}

is the third order nonlinear susceptibility of the component (e.g., gold, dielectric) of interest.

η (θ)

depends neither on the field amplitude at the pumping frequency, nor the specific values of the source nonlinearities,

χ_{}^{(3)} (Au)

or

χ_{}^{(3)} ({Al}_{2} O_{3})

. That is,

η (θ)

presents the overall THG enhancement of the system, rather than the THG from a specific bulk

χ_{}^{(3)}

pumped by certain amount of energy.

3. Results and discussion

For nonlinear enhancement, the nanostructure plays a dual role as a coupler for the incident field, and an antenna for the harmonic field. In this section, we probe in detail the behavior of the nanostripe structure, providing a potential path for future optimization of nonlinear nanostructures.

First, consider the case that only the Al₂O₃ spacer, the gold stripe, or the gold film has nonlinear optical properties. Figures 2(a)–2(c) shows the THG enhancement factor as a function of radiation angle for the THG generated from the Al₂O₃ spacer layer, the gold stripe, and the gold film, respectively. The patterns of the three THG enhancement factors are completely different. The enhancement factors for the THG from the gold stripe and the gold film are more omnidirectional, while that from the Al₂O₃ spacer layer is more directional. This difference in the shape of the enhancement factor indicates different enhancement mechanisms for the three nonlinear sources. The total THG that includes all the nonlinear contributions is found empirically to be approximately

Ε_{far}^{THG} (total) \approx χ_{}^{(3)} (Au) [η (stripe) - η (film) + χ_{}^{(3)} ({Al}_{2} O_{3}) / χ_{}^{(3)} (Au) η (spacer)] Ε_{0}^{3} .

This equation indicates that the THG contribution from the spacer layer and that from the stripe interfere constructively, while that from the gold film interferes destructively with the previous two. Equation (4) also indicates that the far field radiation pattern of the total THG completely depends on the enhancement factor of each of the nonlinear sources and their relative weights. In other words, the ratio between the

χ_{}^{(3)} (Au)

and

χ_{}^{(3)} ({Al}_{2} O_{3})

, and the enhancement factor of each nonlinear source are the only factors that influence the shape of the far field radiation pattern of the total THG. To demonstrate this idea and the validity of Eq. (4), we numerically and analytically calculated the total THG using different ratios of the third-order susceptibilities between the Al₂O₃ spacer and the gold. Figures 2(d)–2(f) show the total THG normalized by

χ_{}^{(3)} (Au)

and

Ε_{0}^{}

for

χ_{}^{(3)} ({Al}_{2} O_{3}) / χ_{}^{(3)} (Au) = 0,^{} 0.5 \times 10^{- 4}

and

5 \times 10^{- 4}

, respectively. The red circles represent simulated data, while the black curves are calculated by inserting the simulated THG enhancement factors into Eq. (4). All the data in Figs. 2(d)–2(f) are normalized by

χ_{}^{(3)} (Au)

and

Ε_{0}^{}

, which are constants and do not influence the results. When the nonlinear responses are only from the gold, that is,

χ_{}^{(3)} ({Al}_{2} O_{3}) / χ_{}^{(3)} (Au) = 0

, the radiation pattern of the total THG is similar to the shape of

η (stripe)

. This is caused by the destructive interference between the THG signal from the gold stripe and the gold film, where the influence of the film is small when compared to that of the stripe. When

χ_{}^{(3)} ({Al}_{2} O_{3}) / χ_{}^{(3)} (Au) = 0.5 \times 10^{- 4}

, the enhancement from the gold and Al₂O₃ spacer are comparable to each other. As a result, an intermediate far field radiation pattern is seen between the shape of

η (stripe)

and

η (spacer)

, as shown in Fig. 2(e). For

χ_{}^{(3)} ({Al}_{2} O_{3}) / χ_{}^{(3)} (Au) = 5 \times 10^{- 4}

, the signal from the spacer layer dominates, resulting in a pattern similar to that of the

η (spacer)

.

Fig. 2 (a)–(c) THG enhancement factor for the THG from the Al₂O₃ spacer, the gold stripe and the gold film, respectively. (d)–(f) Total THG enhancement factor evolving with the ratio of the third-order susceptibilities between the Al₂O₃ spacer and the gold; (curve) calculated from Eq. (4); (circles) simulated data. (d) ratio = 0; (e) ratio = 5 × 10⁻⁵; (f) ratio = 5 × 10⁻⁴.

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These results highlight two important observations. Firstly, even though the $χ^{(3)}$ of the Al₂O₃ spacer layer is four orders of magnitude smaller than that of the gold, the THG from the spacer may dominate over the THG from the gold. This is not only due to the large field enhancement in the gap, but also the different enhancement mechanism. Secondly, by investigating the far field radiation of the total THG as a function of the radiation angle, we can infer which nonlinear source dominates. This will be helpful for experiments where it is often difficult to determine the source of the nonlinear signal.

To understand the enhancement mechanism for each nonlinear source, we divide our analysis into three steps. First, we consider the THG before it couples to the film-coupled nanostripe, whose field distribution is directly related to the distribution of the third-order nonlinear polarization $Ρ^{nl}$ . In the following text, we call the distribution of the THG considered in this step as the far-field radiation of the $Ρ^{nl}$ to distinguish it from the actual THG radiated from the structure. In the numerical simulations, we use the field distribution of the film-coupled nanostripe at the pumping wavelength as the source to compute the THG response, but assume that there is no structure present at the THG wavelength. We do this by setting the optical properties of all materials at 3ω to be those of vacuum.

Figures 3(a), 3(e) and 3(i) show the near-field distributions of the $Ρ^{nl}$ considering that only the Al₂O₃ spacer layer, the gold stripe, or the gold film are nonlinear, respectively. For clarity, we only show the norms of magnetic near fields. The film-coupled nanostripe supports a resonance at the pumping wavelength (Figs. 1(b) and 1(c)), such that the $Ρ^{nl}$ generated by nonlinearity within the Al₂O₃ spacer layer resembles an electric quadrupole mode, with electric field perpendicular to the film (Fig. 3(a)). The corresponding far field radiation consists of two lobes in the horizontal direction, as plotted in Fig. 3(d) in red. By contrast, for nonlinearity in the gold stripe or the gold film, the pumping fields penetrating into the gold are along the stripe width and the film (Fig. 1(c)). As a result, the far-field radiation patterns of $Ρ^{nl} (stripe)$ and $Ρ^{nl} (film)$ are similar to planar electric dipoles, as shown in Figs. 3(e) and 3(i). The corresponding far field radiation patterns are omnidirectional, in agreement with the typical radiation pattern of electric dipoles. Note that there is a π difference in phase between the far-field radiations of $Ρ^{nl} (stripe)$ and $Ρ^{nl} (film)$ , which is caused by the opposite electric fields in the gold stripe and the gold film at the pumping frequency (Fig. 1(c)). This phase difference ultimately causes the THG from the gold stripe and the gold film to destructively interfere in the far-field.

Fig. 3 (a)–(c) Near field distributions of the THG generated from the Al₂O₃ spacer, (a) radiating in vacuum, (b) being reflected by a gold film, (c) being coupled to the film-coupled nanostripe. (d) Far field radiation patterns of the THG generated from the Al₂O₃ spacer radiating in vacuum (red), being reflected by a gold film (black), being coupled to the full structure (blue). (e)–(g) Near field distributions of the THG generated from the gold stripe, (e) radiating in vacuum, (f) being reflected by a gold film, (g) being coupled to the film-coupled nanostripe. (h) Far field radiation patterns of the THG generated from the gold stripe radiating in vacuum (red), being reflected by a gold film, being coupled to the full structure (blue). (i) – (k) Near field distributions of the THG generated from the gold film, (i) radiating in vacuum, (j) being reflected by a gold film, (k) being coupled to the film-coupled nanostripe. (l) Far field radiation patterns of the THG generated from the gold film radiating in vacuum (red), being reflected by a gold film (black), being coupled to the full structure (blue).

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To distinguish the influence of the gold film and that of the nanostripe, we now consider that the gold film is present at the third harmonic frequency, but that the optical properties of the spacer and the stripe are still those of vacuum. For the case where the spacer layer is nonlinear with an equivalent quadrupole source distribution, the THG is completely suppressed due to the interaction between its radiation and the reflection of the gold film (black curve in Fig. 3(d)). For nonlinearities in the gold stripe or the gold film, whose equivalent electric dipoles are parallel to the gold film, the reflection by the gold film enhances the far field by a factor of about four (black curves in Figs. 3(h) and 3(l)).

Finally, we consider how the THG in the first step couples to the entire nanostructure by setting the optical properties of all materials at 3ω to their actual values. The THG far-field generated by the nonlinearity in the gap is now normal to the surface, rather than in the plane of the surface, as shown by the blue curve in Fig. 3(d). This change is caused by the coupling between the THG generated in the gap and the higher-order gap plasmon modes supported by the structure at $λ / 3$ . When examining the near field, nodes are found in the magnetic field distribution of the THG, indicating the presence of gap plasmon modes (Fig. 3(c)). By comparing the far field radiation patterns in Fig. 3(d), we find that, because of the coupling between the THG field and the higher-order gap plasmon modes, the THG originating from the spacer layer has been enhanced. For THG originating from the gold, the equivalent electric dipoles either couple to the gap plasmon modes supported by the film-coupled nanostripe or the radiation modes. On the contrary, the near-field distributions of $Ρ^{nl} (stripe)$ and $Ρ^{nl} (film)$ only have a large overlap with the fundamental gap plasmon mode whose resonance is at 1.55µm. However, the THG wavelength is far from 1.55µm and the coupling is so weak that it can be neglected. For this reason, the stripe behaves as a simple scatterer and the film as a mirror, which leads to the coupling of the THG directly to radiation modes, without the intermediary of the gap plasmon mode. By examining the far-field radiation patterns in Figs. 3(h) and 3(l), we notice that the radiation originating from the gold stripe and the gold film is suppressed by the nanostripe. The THG radiation from the gold film, corresponding to electric dipoles embedded in gold, experiences larger losses in all three conditions. Note that the phase relation between the THG from the stripe and the film is not changed by the coupling, leading to the destructive interference between the THG from the stripe and the film. The nonlinear sources, their equivalent dipole sources and how they couple to the nanostructure at the THG wavelength are summarized in Table 1.

Table 1. Nonlinear sources and their equivalent dipole sources

View Table

4. Generality

In this section, we demonstrate the generality of our results by using film-coupled nanostripes of different dimensions. To eliminate any changes in the THG due to the material dispersion, we fix the resonance wavelength at 1.55µm by varying the gap size (g) and stripe width (W) simultaneously. For gap size g = 1nm, 2nm, 3nm, 4nm, 5nm, 6nm, 7nm, 8nm, 9nm, and 10nm, the corresponding stripe widths are 65nm, 94nm, 115nm, 131nm, 145nm, 157nm, 167nm, 177nm, 185nm and 193nm.

In Fig. 4(a), we plot the THG enhancement factor for THG from the Al₂O₃ spacer, the gold stripe and the gold film as a function of gap size, at a radiation angle of 90 degrees. For all nonlinear sources, two factors having opposite effects come into play. As the gap size increases, the field enhancement in the gap region decreases, while more nonlinear material (gold or Al₂O₃) is included within the gap region due to the increase of the stripe width. For the nonlinear spacer, the former factor predominantly influences the THG, while for the gold, the latter factor is more influential. As a result, $η (spacer)$ reaches its maximum at 2nm and decreases afterward with increasing the gap size, while $η (stripe)$ and $η (film)$ increase all the way to g = 10nm.

Fig. 4 (a) and (b) The THG enhancement factor for THG from the Al₂O₃ spacer, the gold stripe and the gold film as a function of gap size, at radiation angles of 90 degree (a) and 45 degree (b). Red: η(spacer); blue: η(stripe); η(film). (c) and (d) The total THG enhancement factor evolving with the ratio of the third-order susceptibilities between the Al₂O₃ spacer and the gold, at radiation angles of 90 degrees (c) and 45 degrees (d); (stars) calculated data from Eq. (4); (lines) simulated data.

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Figure 4(b) shows the three THG enhancement factors at a radiation angle of 45 degrees. By comparing Figs. 4(a) and 4(b), we notice that although the trends at 45 degrees are similar to those at 90 degrees, $η (spacer)$ decreases more than $η (stripe)$ and $η (film)$ . This provides evidence that the THG radiated from the Al₂O₃ spacer is more directional than that radiated from the gold. To demonstrate the validity of Eq. (4) for film-coupled nanostripes of different dimensions, we numerically and analytically calculated the total THG evolving with the ratio between the third-order susceptibilities of the gold and the Al₂O₃ spacer at radiation angles of 90 degrees and 45 degrees, as shown in Figs. 4(c) and 4(d). When the THG signal from the Al₂O₃ spacer dominates, that is, $χ_{}^{(3)} ({Al}_{2} O_{3}) / χ_{}^{(3)} (Au) = 5 \times 10^{- 4}$ , the trend is exactly the same as that of the THG enhancement factor $η (spacer)$ . When the THG signal from the Al₂O₃ spacer is comparable to ( $χ_{}^{(3)} ({Al}_{2} O_{3}) / χ_{}^{(3)} (Au) = 0.5 \times 10^{- 4}$ ) or smaller than that from the gold ( $χ_{}^{(3)} ({Al}_{2} O_{3}) / χ_{}^{(3)} (Au) = 0$ ), the trend follows the THG enhancement factor $η (gold)$ . In resolving the THG from different nonlinear sources in the film-coupled nanostripes, as the THG enhancement factor of different nonlinear sources are inherent to the plasmonic structure and can be determined using numerical simulations, the ratio between the third-order susceptibilities of the gold and the Al₂O₃ spacer can be determined by fitting Eq. (4) with the measured THG curve.

5. Conclusion

In conclusion, we propose a method to determine the origin of the THG from a single nanostripe coupled to infinitely large film. By considering the THG from each nonlinear source separately, the near- and far- fields of the THG radiating from different nonlinear sources are distinguishable due to the fundamental difference in their radiation properties. The THG signal from the gold film and the gold stripe destructively interfere with each other, and the THG signal from the gold is suppressed by the structure itself. However, due to different coupling schemes, the structure enhances the THG signal generated from the Al₂O₃ spacer and facilitates its radiation. The total nonlinear radiation pattern is the sum of the far-fields of all the nonlinear sources, which is determined by the ratio between the third-order susceptibilities of the dielectric and the metal. We find that, even though the third-order susceptibility of the gold is four orders larger than that of the Al₂O₃ spacer, it is still possible for the THG generated by the spacer to dominate.

Since the THG is a superposition of the contributions from all the nonlinear sources, the THG from each nonlinear source in our structure can be identified in two ways. First, as the THG far-field radiation patterns from different nonlinear sources are distinguishable, the dominating nonlinear source can be determined by measuring the far-field radiation pattern of the THG. Second, by fixing the resonant frequency while varying the structure geometry, the THG enhancement factor of each nonlinear source has a specific trend that is inherent to the plasmonic structure. This trend can be determined using numerical simulations to investigate other nonlinear hybrid plasmonic structures. By fitting the measured total THG with Eq. (4), the ratio between the third-order susceptibilities of the metal and the dielectric can be determined.

Our method can be applied to analyze the origin of the nonlinear signal associated with other hybrid plasmonic structures, such as film-coupled nanospheres. However, our method fails to identify the origin of nonlinear response in periodic structures, whose nonlinear radiation patterns are mostly uniform and indistinguishable in the far-field. A different approach has been developed to address the periodic structures, which will be presented in a future work.

Acknowledgements

This work was supported by the Air Force Office of Scientific Research (AFOSR, Grant No. FA9550-12-1-0491).

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Nonlinear sources	Equivalent dipole sources
Nonlinear sources	Pumping wavelength	$Ρ^{nl}$	Strongly couple to gap plasmon modes?	Strongly couple to radiation modes?
Al₂O₃ spacer layer	Magnetic dipole	Multipole	Yes	No
Gold stripe	Electric dipole	Electric dipole	No	Yes
Gold film	Electric dipole	Electric dipole	No	Yes

Clarifying the origin of third-harmonic generation from film-coupled nanostripes

Abstract

1. Introduction

2. Geometry and method

3. Results and discussion

4. Generality

5. Conclusion

Acknowledgements

References and links

Cited By

Figures (4)

Tables (1)

Equations (4)

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