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Nonlinear properties of nanoscale antennas
Nano Today (2013) 8, 469—479
Available online at www.sciencedirect.com
ScienceDirect journal homepage: www.elsevier.com/locate/nanotoday
REVIEW
Nonlinear properties of nanoscale antennas Jae Yong Suh a, Teri W. Odom a,b,∗ a b
Department of Chemistry, Northwestern University, Evanston, IL 60208, USA Department of Materials Science and Engineering, Northwestern University, Evanston, IL 60208, USA
Received 10 March 2013 ; received in revised form 29 July 2013; accepted 30 August 2013 Available online 25 September 2013
KEYWORDS Nanoscale antennas; Localized surface plasmons; Nonlinear optical susceptibility; Plasmonic lasers
Summary Nanoscale antennas are optical devices that can facilitate the localization and transfer of electromagnetic (EM) energy at the nanometer length scale. In this review, we discuss nanoscale antennas based on coupled metal nanoparticles that exhibit strong optical nonlinear behavior. These distinct properties are a consequence of the large EM field concentration at the localized plasmon resonance frequency, which can enhance the local strength of lightmatter interactions. Specifically, we will highlight how optical nanoantennas can boost nonlinear processes, resonant energy transfer between surface plasmons and excitons, and lasing action in the presence of gain materials. © 2013 Elsevier Ltd. All rights reserved.
Introduction Wireless communication technology relies on the transfer of electromagnetic (EM) waves, and antennas are a key element that enables the reception and transmission of EM fields. In a dipole antenna, the free electrons in a metal wire oscillate via time-varying currents to transmit localized EM energy into the far-field. Similarly, for reception, EM fields drive the electrons in an antenna to oscillate and generate an electric current in the circuit load of the antenna. Antenna theory and their applications have mostly focused on the microwave and radio-frequency (RF) regime [1,2]. Nanoscale antennas are metal nanostructures that localize and radiate EM fields in the optical range with
∗ Corresponding author at: Department of Chemistry, Northwestern University, Evanston, IL 60208, USA. Tel.: +1 847 491 7674. E-mail addresses: [email protected] (J.Y. Suh), [email protected] (T.W. Odom).
operational frequencies in the visible to near-infrared. As the antenna size approaches nanoscale dimensions, RFantenna theory cannot be used to describe the behavior of optical antennas because of the intrinsic properties of metals at visible wavelengths [3—5]. At RF frequencies, charge oscillations in metals can be excited without a phase lag since the imaginary part of the conductivity is very low (i.e., metals can be treated as perfect electrical conductors). At optical frequencies, nanoscale antennas have large resistive losses with an increased phase offset [5]. Another difference is that RF antennas require transmission lines to couple the circuit load to the antenna. To maximize energy transfer from the incident radiation, the impedances of the load and the antenna must match [6]. An analogous situation of impedance matching exists in optical antennas supporting small gaps since the nano-capacitance can be tuned by the geometrical parameters of the nanoscale antennas [5]. Additionally, the relatively large penetration depth of light at optical frequencies compared to the size of a nanoantenna does not allow the simple RF antenna design
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470 (L = const . × free , where L is the antenna length and free is the wavelength in free space) to scale [7]. The operational wavelength of an optical antenna depends on the ratio of the free-space and plasma wavelengths (free /p ) as well as the geometrical parameters [8]. When the dimension of a metal nanoparticle (NP) is much smaller than the wavelength of incident light, the conduction electrons confined to the NP can oscillate in phase characterized by a localized surface plasmon (LSP) resonance [9]. At the LSP frequency, large local electric field concentration and enhanced light scattering occurs in addition to non-propagating near-field excitations without a cut-off wavelength [10]. The aim of this review is to highlight how nanoantennas with specific structural features—–especially those containing nanoscale gaps—–can produce unique nonlinear optical responses. We will first briefly describe nanofabrication approaches to produce these metal nanostructures and summarize their linear optical properties. We will then focus on how nanoantennas can enhance light-matter interactions via nonlinear and light-amplification processes. The intense local EM fields sustained by optical antennas with gaps not only plays a role in a variety of spectroscopic processes [11—13] but also enables large optical responses with small excitation powers [14]. Recent reviews on nanoantennas [5,15—17] have emphasized applications including plasmonic sensing [18—20], scanning near-field microscopy [21,22], and ultrafast [23] and nonlinear spectroscopy [24,25]; hence, these topics will not be emphasized here. Fig. 1 highlights a miniaturized version of an RF YagiUda antenna and nanoantennas that show nonlinear effects from highly localized fields in their gaps. These architectures summarize the key nanostructures in this review. In the Yagi-Uda optical antenna (Fig. 1a), five gold nanorods act as parasitic dipole elements that increase the directionality and emission of a single quantum dot attached to the feed element [26]. This nanoscale realization of conventional RF antennas is useful for designing and controlling emission from single-photon sources. Fig. 1b—f summarizes typical geometries of nanoantennas with small gaps: nanorod dimers and ‘‘bowtie’’ nanoparticles. These architectures support large local field enhancements and hence significant nonlinear effects related to material anharmonicity under strong, external electric fields [13,27—30]. Because of the increased nonlinear polarizability at the LSP resonance, multi-photon absorption or frequency-conversion processes can be observed [30—37]. Finally, besides using nanoantennas to direct the emission of emitters, strong localized fields can be exploited to enhance and manipulate the properties of semiconducting nanostructures and molecules [17,38,39].
Fabrication of nanoscale antennas The ability to control nanoscale structure has enabled new ways to probe enhanced light-matter interactions. Because fabrication accuracies for nanoantennas are typically less than 10 nm, serial tools such as electron beam lithography (EBL) or focused ion-beam (FIB) have been used to create planar structures. EBL is especially suited for prototyping and designing complex nanoscale structures (Fig. 1a).
J.Y. Suh, T.W. Odom Despite its flexibility and accuracy in prototype patterning, the throughput of EBL (10−10 m2 /s) is not amenable for large-scale production of nanoantennas in a cost-effective manner [40]. Typical EBL-patterned areas are less than 100 m × 100 m. FIB also shares similar disadvantages in terms of low throughput (10−13 m2 /s at high resolution) [41], although single-crystalline nanoantennas can be fabricated [15]. For studying quantum effects related to small inter-particle spacing, accurate control of critical dimensions as small as 1 nm is required [42,43]. Accessing a size regime well below 10 nm is challenging to achieve by direct lithographic methods, however, and additional fabrication techniques such as self-assembly [44,45], surface functionalization [46] or oxidation processes [47] have been pursued. In contrast, soft nanolithography techniques provide a scalable route to produce large-area (cm2 ) nanoscale patterns. This parallel fabrication approach enables opportunities to measure collective effects such as diffractive coupling between individual nanoantennas [48—51]. Soft lithography uses elastomeric molds or masks made from poly(dimethylsiloxane) (PDMS) as the pattern transfer element. These masks can be used to generate template patterns in photoresist by exposing with UV light in phaseshifting photolithography [52] or by molding with organic solvents using solvent-assisted nanoscale embossing [53]. Etching, deposition, and lift-off steps and/or followed by template stripping can then transfer the photoresist nanopatterns into arrays of nanoantennas [28,54].
Linear optical effects of nanoantennas A single metal nanosphere, which is the simplest structural component of a nanoantenna, can capture and re-radiate light. In the quasi-static approximation where the incident wavelength is much larger than the size of the nanoparticle, the scattering and absorption cross-section can be analytically calculated [55]. The dipole moment induced in an isolated nanosphere under an external electric field E0 is given by sphere = 3Vεd [(εm − εd )/(εm + 2εd )]E0 , where V is the particle volume, and εm and εd are the dielectric constants of the metal and surrounding medium [56]. The LSP resonance occurs when the denominator becomes zero, which determines the resonant wavelength. For a single nanosphere, the plasmon resonance is independent of the polarization direction of the incident plane wave. Compared to nanospheres, single nanorods exhibit reduced plasmon damping and an increased dephasing time [57]. The radiation efficiency in a nanorod antenna is highest when the polarization of the incident light is parallel to the long axis of the particle [57], similar to an RF antenna. Fig. 2 shows the extinction spectra of single and dimer nanorod antennas (arm length L = 100 nm, radius r = 20 nm) calculated by the boundary element method [58,59]. Coupling of two nanorods with a small gap leads to a red-shift of the plasmon resonance to longer wavelengths (Fig. 2a); the resonance peak approaches that of the single nanorod as the gap distance increases. The strongest near-field enhancement and the largest resonance shifts are achieved at the smallest gap sizes. Note that the extinction efficiency is about 50-fold lower when the polarization is perpendicular to the dimer axis (Fig. 2b), and only a
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Figure 1 Representative nanoscale antennas. (a) Yagi-Uda nanoantennas exhibit directional emission from a quantum dot (adapted from [26]). (b) Nanocluster antennas show two-photon photoelectron emission (adapted from [29]). (c) Bowtie nanoantennas array show third-harmonic generation (adapted from [30]). (d) Nanorod dimer antennas can generate super-continuum white light (adapted from [13]). (e) 2D bowtie nanoantennas can enhance the emission intensity of fluorescent molecules (adapted from [27]). (f) 3D bowtie nanoantennas can show plasmonic lasing (adapted from [108]). Scale bars for (b)—(f), 100 nm.
single nanorod resonance is present. In a coupled nanoantenna or dimer structure, energy hybridization can generate bonding (bright) and anti-bonding (dark) modes in the extinction spectrum [60—62]. This energy splitting is directly related to the structural symmetry of the antenna. In particular, an anti-bonding mode can be excited in an asymmetric dimer configuration in which the net dipole moment is nonzero [61,63,64]. The arm length L and gap distance () of gold nanorod dimers are the two major parameters that determine the position of the LSP resonance and wavelength of antenna operation. Fig. 3 indicates that a longitudinal LSP resonance in the visible range (<700 nm) requires arm lengths smaller than 100 nm [65]. Also, as depicted
by red circles and the isowavelength curve, different combinations of L and can result in the same far-field spectrum. For example, L = 70 nm, = 10 nm and L = 110 nm, = 80 nm both have a resonances at 730 nm. For the same L but different , the near-field intensity is higher with smaller gap distances, but the resonance moves to longer wavelengths. As an example, the LSP resonance redshifts from 730 nm with = 70— 850 nm with = 20 nm for a given arm length (L = 110 nm). Therefore, this trade-off between the near-field intensity and resonance location sets a simple design rule for dimer nanoantennas. To have strong near-field intensity at the resonance wavelength at visible wavelengths, the gap distance and antenna arm lengths should be as small as possible.
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Figure 3 Resonance positions of nanorod dimer antennas depend on arm length and gap size. (Top) Dark-field scattering image for combinations of different arm lengths L and gap widths . Red circles denote the maximum scattering intensity. Graph of calculated longitudinal LSP mode as a function of L and . Red open circles denote the spectral positions of the experimental maximum scattering intensity. Adapted from [65]. Figure 2 Polarization-dependent optical properties of nanorod dimer antennas. (a) Calculated longitudinal LSP resonances from a single nanorod (40 nm × 100 nm) and nanorod dimers with gap distances of 10 nm, 20 nm and 100 nm using the boundary element method. (b) Calculated transverse LSP resonances under polarization along the particle short axis.
Moreover, the local surface curvature of an antenna can significantly influence the near- and far-field spectrum [11]. Fig. 4a shows a scheme of a 3D bowtie nanoantenna in which the gold particles are ‘‘folded’’ along the dimer axis. The low-energy mode at 860 nm is the dipolar bonding mode whereas the strong high-energy resonance at 640 nm is a quadrupolar mode (Fig. 4b and c) [28]. The high surface curvature of the 3D bowtie antenna results in field-retardation [66] that can generate a quadrupolar charge distribution at the four corners of each particle. In 2D planar nanoantennas, the excitation efficiency for a quadrupolar mode is low [67]. Surprisingly, the far-field intensity of the quadrupolar mode from the folded 3D bowtie antenna is as high as the dipolar mode. When the polarization direction is perpendicular to the dimer axis, only one resonance at 780 nm is present due to the lack of near-field interactions across the gap (Fig. 4c). Finite-difference-time-domain (FDTD) calculations [28] of the optical transmission of the 3D bowtie nanoantenna show excellent agreement with the experimental spectra. The simulated local field intensity can be increased up to four orders of magnitude at the dipolar bonding mode compared
to incident field intensity (Fig. 4d). Similar to the nanorod dimer case in Fig. 2b, when the polarization is perpendicular to the dimer axis, only a single particle resonance is present (Fig. 4e). The high local field enhancements supported by the 3D bowties suggest that this structure can be used as an efficient resonator to generate high nonlinear effects.
Nonlinear plasmonic effects of nanoantennas The nonlinear optical responses of materials are inherently very small even under excitation fields of moderate intensity [68]. When metals are structured as a nanoantenna with a small gap, the highly localized EM fields in the near-field can induce strong nonlinear responses [69]. The polarization of a material from an external electric field can be − → − → linearly approximated as P ≈ ε0 (1) E , where (1) is the first-order optical susceptibility. Under high incident fields, the nth-order susceptibilities (n) have nonlinear contributions to the induced polarization [70]. Most materials have complex third-order optical (Kerr) nonlinearities, and noble metals have large third-order susceptibilities (gold thin film, (3) gold ∼10−8 esu) [71]. In a metal NP-dielectric composite material, the effective third-order susceptibility goes as the fourth power of the local field enhancement factor (3) (eff ∝ |Elocal /E0 |4 ), where Elocal is the electric field inside the metal NPs [72—74].
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Figure 4 3D bowtie nanoantennas exhibit polarization-dependent electric field localization. (a) Scheme of 3D bowtie nanoantenna. Experimental and simulated transmittance spectra when polarization is (b) along the bowtie axis and (c) perpendicular to the dimer axis. (d and e) FDTD-calculated field intensity maps at wavelengths corresponding to the LSP resonances in (b) and (c). Adapted from [28].
Multi-photon absorption and photoluminescence can also occur with high efficiency when the local field enhancement is resonantly involved in the nonlinear processes [75]. Two-photon absorption that leads to the transition of electrons from the d valence band to the sp conduction band is increased because of high local fields at LSP frequencies [76]. Therefore, enhanced two-photon absorption can increase the rate of two-photon photoluminescence (TPPL). For example, a 2D gold bowtie nanoantenna shows a clear 4 fourth-power (Elocal ) dependence of the local electric field in the TPPL signal when the gap distance is less than 30 nm (Fig. 5) [77]. Spectral analysis on gold dimer nanorod antennas has also shown that the TPPL maps match calculated 4 Elocal distributions [78]. The spatially-resolved TPPL signal of the gap was four times higher than that at the ends of the antenna arms. In addition, nanoantennas can also exhibit second- and third-harmonic generation (SHG and THG) signals, where the frequency of incident light is doubled (2ω) or tripled (3ω). Although metal NPs have symmetric atomic lattices, they can give rise to efficient SHG when the overall shape of the NPs is not symmetric, such as L-shaped NPs [79,80], T-shaped NPs [81], nano-cup structures [82] and split-ring resonators [83]. Symmetric shapes can also produce SHG depending on local field asymmetries [81], structural chirality [84] and multi-pole interferences [85]. In contrast, THG from nanoantennas is not constrained by a symmetry argument, and its intensity is directly related to the effective
third-order susceptibility (3) of the metal NPs. Intense THG associated with d-band transitions has been observed from gold bowtie nanoantennas [12] and can be correlated with linear optical properties [35]. For example, THG is
Figure 5 Local field enhancement depends on the fourthpower in 2D bowtie nanoantennas. Two-photon photoluminescence shows |E4 | dependence for gap distances <40 nm. Adapted from [77].
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Figure 6 THG generation is correlated to linear optical properties of bowtie nanoantennas. (Left) Extinction spectra from a single NP and bowtie nanoantennas with varying gap distances. As the gap deceased, the LSP resonance red-shifted into the wavelength range of laser excitation (gray). (Right) Intensity of corresponding THG is maximized with smaller gap sizes. Adapted from [30].
highest in nanorod antennas when the incident wavelength matches the LSP resonance wavelength (Fig. 6) [30]. The linear extinction and overall THG emission spectra of the bowtie nanoantennas can be fit by a single anharmonic oscillator. For smaller gap sizes (<20 nm), however, the larger near-fields in the gap contribute to the THG signal, which causes the results to deviate from the nonlinear oscillator model. Consequently, nanoantennas can enhance both THG and TPPL signals by increasing (3) at the LSP resonance. High nonlinearity supported by metal nanoantennas can also enhance the resolving power of near-field imaging or TPPL microscopy in the optical range [86,87]. Whereas TPPL microscopy images the relative intensity of the local (3) , z-scan transmission can directly
measure the complex (3) , where the imaginary part of the susceptibility is related to nonlinear absorption [88]. Via open-aperture z-scan measurements, nonlinear optical absorption by 3D gold bowtie nanoantennas was found to be extremely high (Im (3) = 10−4 esu) [28]. Slightly different values of the measured Im (3) were also observed depending on whether the bowtie was folded or flat; these nanoscale structural differences produced different local field strengths in the gap. In addition, saturable absorption, which is a non-parametric nonlinear process [68], was observed from the 3D bowtie nanoantennas under femtosecond (fs) excitation [28]. Gold NPs are known as good saturable absorbers with high Im (3) in the fs regime [89]. The intensity-dependent saturable absorption of the metal
Nonlinear properties of nanoscale antennas
Figure 7 Fourth-order nonlinearity from nanorod dimer antennas. (a and b) SEM images of a gold nanoantenna (L = 250 nm, = 20 nm). (c) Confocal image showing that WLSC is created in the gap region when incident laser pulses are vertically polarized. (d) Confocal image showing that WLSC disappears with horizontally polarized pulses because of the absence of near-field interactions. Average pump power is 100 W. Adapted from [13].
NPs thus enables nanoscale antennas to be used as potential Q-switching devices [90,91]. Even higher-order nonlinearities can be obtained from gap nanoantennas. White-light super-continuum (WLSC), which is described by a fourth-order optical nonlinearity, was observed in the gap of nanorod dimer antennas [13]. Similar to linear effects, the white-light intensity was controlled by the arm length L and was generated only when the polarization was parallel to the antenna axis (Fig. 7). This polarization-dependence again shows that strong nearfield enhancement across the gap is important for nonlinear effects. Second-order (TPPL) nonlinearity dominates at low power, but at higher incident power (>80 W), the output curve has a quartic dependence on the incident power, which confirms that the generation of WLSC is a fourth-order nonlinear process.
Nanoantenna-emitter systems Nanoantennas can control the quantum efficiency of emitters such as quantum dots and dye molecules through resonant energy transfer between the emitter and localized plasmons [27,38]. When an emitter is placed within the near-field region of a nanoscale antenna, the spontaneous emission (SE) rate can be enhanced by a factor of several hundred [92—94]. Fig. 8 depicts a scheme of energy transfer between a four-level electronic system and a metal NP. In describing gain media, a simple 4-level system is widely employed because population inversion can be readily achieved due to the relatively long lifetime of the transition from 2 to |1. External pumping can result in population in the upper levels of the first excited state. When the energy difference of the emitter (E2 − E1 ) is the same as the energy needed to excite LSPs in the metal NP (ωsp − |EF ), the resonant interaction can modify the total recombination rate. According to Fermi’s golden rule, the SE rate is proportional to the local density of states (LDOS) available for the decay of the emitter [95,96]. Because the plasmon field of the metal NP can increase the LDOS, the radiative recombination rate of excitons should also be enhanced.
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Figure 8 Scheme and energy diagram of the interaction between an emitter and a metal NP. A simple four-level system can represent a dye molecule whose energy can be transferred to a metal NP in close proximity through resonant energy transfer (ksp ). The absorbed energy can be dissipated by radiative and non-radiative decay channels.
The near-field coupling of emitters to nanoantennas can result in enhanced fluorescence, a phenomenon that can be described by the Purcell effect in the weak-coupling regime [97]. The Purcell effect is maximized when there is (1) maximum field confinement (small mode volume V) and (2) minimum cavity losses (high quality factor Q), where the ratio between Q and V is called the Purcell factor (F). Metal structures capable of high F also show characteristics of gap nanoantennas. As an example, 2D gold bowtie nanoantennas have been shown to increase the fluorescence intensity from a single near-infrared dye molecule (TPQDI) by a factor of more than 1000 (Fig. 9) [27]. With a gap = 80 nm, the fluorescence enhancement was equivalent to the case of single triangles since the near-field interaction between the bowtie arms was very weak. The enhancement, however, was maximized when < 20 nm, which is consistent with the high local field intensities as discussed earlier. The total decay lifetime ( F ) of TPQDI was reduced to <10 ps from 275 ps in the presence of the 2D bowties, evidence of the enhancement of radiative and non-radiative decay rates
Figure 9 2D bowtie nanoantennas increase the fluorescence intensity of single molecules. Scatter plot of fluorescence enhancement (fF ) from TPQDI single molecules. fF is increased by a factor of 1300 when the bowtie gap distance is less than 20 nm. Adapted from [27].
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Figure 10 Yagi-Uda nanoantennas can direct emission from single quantum dots. (a) Scanning confocal luminescence images of a reference (gold square, 60 nm × 60 nm), half-wave dipole nanorods, and Yagi-Uda nanoantennas, respectively. (b) Only the Yagi-Uda nanoantenna shows a unidirectional radiation distribution. Adapted from [26].
as a result of resonant coupling of single molecules to the nanoantenna [98]. Nanoantennas coupled to quantum emitters not only can enhance the fluorescence intensity but can also steer the direction of the emission. As described previously, miniaturized Yagi-Uda antennas rely on long-range, dipolar interactions between aligned metal nanorods to achieve directionality of light from a single quantum dot [26] or Raman molecules [99]. Fig. 10 shows that only the YagiUda arrangement of gold nanorods exhibited unidirectional emission in the angular radiation pattern, while control nanoantenna structures did not [26]. The arm lengths and inter-particle distances were chosen such that the LSP resonances from each nanorod had a slight phase-lag with respect to the feed element. High radiation efficiency was achieved because the quantum dot was positioned in the near-field region of the feed element in the antenna. Plasmonic nanoantennas can also be used to generate coherent light (i.e., lasing action) below the diffraction limit. Plasmonic lasing has been demonstrated in a variety of metal nanostructures, such as gold-coated InP/InGaAs/InP nanopillars [100], CdS nanowires and slabs [101,102], and InP nanodisks [103]. Stimulated emission is usually characterized by the onset of a narrowed emission peak over the underlying PL spectrum, where a single-mode lasing peak grows nonlinearly as the pump intensity increases with a kink at the threshold level [104]. A distinct feature of plasmonic lasing from metal nanocavities is the thresholdless behavior because of a high SE factor ˇ (the ratio between the SE rate of a single lasing mode and the total SE rate) [105]. Plasmonic cavities can exhibit high ˇ-factors through strong field confinement of a single mode while excluding competing emission factors [101]. High ˇ-factors account for a ‘‘smearing’’ of the threshold level; in contrast, ˇ-factors for conventional laser cavities are very small (<10−3 ) [106]. Experimentally, a coaxial Ag nanocavity with InGaAsP gain
medium clearly showed a thresholdless behavior in lasing at low-temperature provided that ˇ ∼ 1 [107]. As described previously, 3D gold bowtie nanoantennas have properties of excellent optical resonators that support well-defined EM hot spots. These high and localized fields can also be exploited for nanoscale lasing [108]. An example of an emitter that can couple with the LSP gap mode of 3D bowtie nanoantennas is the organic dye IR-140. Within a polymer matrix, the dye molecules can be positioned in the antenna gap region. When coupling occurs, the excited state energy from the dye can be non-radiatively transferred to create a localized plasmon mode. This additional coupling channel of the excited states in the presence of the 3D bowtie nanoantenna increases the SE rate of the dye molecules. The rate of exciton-plasmon coupling can be characterized by the fast decay component in timeresolved absorption spectra. The transient decay traces of the excited state absorption with and without the bowtie nanoantenna clearly show a lifetime reduction (1 ns to 13 ps) of the excited molecules (Fig. 11a), which is comparable to the case of 2D bowties [27]. The enhancement factor in the SE rate can be determined from the ratio of LSP coupling and radiative recombination rates (Fbowtie = kLSP /krad = 440), which is about two times higher than that of a single nanosphere (Fsphere = 250) [109]. The 3D bowtie resonators were found to lase in the presence of organic dye molecules. Above a certain threshold, a laser oscillation was observed at 873 nm with a narrowed linewidth (1.5 nm) from the bowtie resonators (Fig. 11b). The existence of a lasing threshold level indicates that even though the losses of this system are somewhat high (Q < 20), the stimulated emission rate was enhanced and exceeded the SE and non-radiative recombination rates (Fig. 11b, inset). This bowtie nanolaser is an example of how coherent light can be produced from high local EM fields in a sub-diffraction region from nanoantennas with gaps.
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Figure 11 3D bowtie antennas exhibit room-temperature lasing. (a) Femtosecond transient absorption traces reveal that IR140 shows fast decay components in the presence of 3D bowties under parallel and perpendicular pump polarizations relative to the nanoantenna axis (red and blue curves). (b) Lasing spectra as a function of pump energy for a 3D gold bowtie array (inset, periodicity = 1200 nm) with gain. Input—output light curves show threshold behavior. Adapted from [108].
Conclusions Nanoscale antennas can localize and concentrate EM fields into subwavelength volumes at their LSP frequencies. The large local field concentration supported by metal nanoantennas can induce strong optical nonlinearities, which makes them promising for nonlinear applications such as frequency conversion, four-wave mixing or Q-switching. Multi-photon absorption and second and third harmonic generation processes can also be greatly enhanced near the LSP resonance; however, an efficient design for nonlinear nanoantennas is still a challenge. Nanoantennas with gaps are also good optical resonators that can exhibit plasmonic
lasing from well-defined and localized EM fields in the gap region. Enhanced light-matter interactions at the nanoscale and coherent photon sources from optical nanoantennas will enable the development of optical and plasmonic devices that can be sensitive to a single quantum emitter. Further miniaturization of nanoscale antennas can ultimately access the regime where strong quantum effects exist, and hence ultrafast energy transfer processes can potentially be probed even at atomic length scales. Nanoscale antennas hold promise not only for nonlinear nano-optics applications but also for spectroscopies with detection resolution down to the single molecule level.
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Acknowledgements This work was supported by an Initiative for Sustainability and Energy at Northwestern (ISEN) Award (J.Y.S.) and the NSF-MRSEC program at the Materials Research Science and Engineering Center at Northwestern University (DMR1121262) (J.Y.S., T.W.O.).
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REVIEW
Nonlinear properties of nanoscale antennas Jae Yong Suh a, Teri W. Odom a,b,∗ a b
Department of Chemistry, Northwestern University, Evanston, IL 60208, USA Department of Materials Science and Engineering, Northwestern University, Evanston, IL 60208, USA
Received 10 March 2013 ; received in revised form 29 July 2013; accepted 30 August 2013 Available online 25 September 2013
KEYWORDS Nanoscale antennas; Localized surface plasmons; Nonlinear optical susceptibility; Plasmonic lasers
Summary Nanoscale antennas are optical devices that can facilitate the localization and transfer of electromagnetic (EM) energy at the nanometer length scale. In this review, we discuss nanoscale antennas based on coupled metal nanoparticles that exhibit strong optical nonlinear behavior. These distinct properties are a consequence of the large EM field concentration at the localized plasmon resonance frequency, which can enhance the local strength of lightmatter interactions. Specifically, we will highlight how optical nanoantennas can boost nonlinear processes, resonant energy transfer between surface plasmons and excitons, and lasing action in the presence of gain materials. © 2013 Elsevier Ltd. All rights reserved.
Introduction Wireless communication technology relies on the transfer of electromagnetic (EM) waves, and antennas are a key element that enables the reception and transmission of EM fields. In a dipole antenna, the free electrons in a metal wire oscillate via time-varying currents to transmit localized EM energy into the far-field. Similarly, for reception, EM fields drive the electrons in an antenna to oscillate and generate an electric current in the circuit load of the antenna. Antenna theory and their applications have mostly focused on the microwave and radio-frequency (RF) regime [1,2]. Nanoscale antennas are metal nanostructures that localize and radiate EM fields in the optical range with
∗ Corresponding author at: Department of Chemistry, Northwestern University, Evanston, IL 60208, USA. Tel.: +1 847 491 7674. E-mail addresses: [email protected] (J.Y. Suh), [email protected] (T.W. Odom).
operational frequencies in the visible to near-infrared. As the antenna size approaches nanoscale dimensions, RFantenna theory cannot be used to describe the behavior of optical antennas because of the intrinsic properties of metals at visible wavelengths [3—5]. At RF frequencies, charge oscillations in metals can be excited without a phase lag since the imaginary part of the conductivity is very low (i.e., metals can be treated as perfect electrical conductors). At optical frequencies, nanoscale antennas have large resistive losses with an increased phase offset [5]. Another difference is that RF antennas require transmission lines to couple the circuit load to the antenna. To maximize energy transfer from the incident radiation, the impedances of the load and the antenna must match [6]. An analogous situation of impedance matching exists in optical antennas supporting small gaps since the nano-capacitance can be tuned by the geometrical parameters of the nanoscale antennas [5]. Additionally, the relatively large penetration depth of light at optical frequencies compared to the size of a nanoantenna does not allow the simple RF antenna design
1748-0132/$ — see front matter © 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.nantod.2013.08.010
470 (L = const . × free , where L is the antenna length and free is the wavelength in free space) to scale [7]. The operational wavelength of an optical antenna depends on the ratio of the free-space and plasma wavelengths (free /p ) as well as the geometrical parameters [8]. When the dimension of a metal nanoparticle (NP) is much smaller than the wavelength of incident light, the conduction electrons confined to the NP can oscillate in phase characterized by a localized surface plasmon (LSP) resonance [9]. At the LSP frequency, large local electric field concentration and enhanced light scattering occurs in addition to non-propagating near-field excitations without a cut-off wavelength [10]. The aim of this review is to highlight how nanoantennas with specific structural features—–especially those containing nanoscale gaps—–can produce unique nonlinear optical responses. We will first briefly describe nanofabrication approaches to produce these metal nanostructures and summarize their linear optical properties. We will then focus on how nanoantennas can enhance light-matter interactions via nonlinear and light-amplification processes. The intense local EM fields sustained by optical antennas with gaps not only plays a role in a variety of spectroscopic processes [11—13] but also enables large optical responses with small excitation powers [14]. Recent reviews on nanoantennas [5,15—17] have emphasized applications including plasmonic sensing [18—20], scanning near-field microscopy [21,22], and ultrafast [23] and nonlinear spectroscopy [24,25]; hence, these topics will not be emphasized here. Fig. 1 highlights a miniaturized version of an RF YagiUda antenna and nanoantennas that show nonlinear effects from highly localized fields in their gaps. These architectures summarize the key nanostructures in this review. In the Yagi-Uda optical antenna (Fig. 1a), five gold nanorods act as parasitic dipole elements that increase the directionality and emission of a single quantum dot attached to the feed element [26]. This nanoscale realization of conventional RF antennas is useful for designing and controlling emission from single-photon sources. Fig. 1b—f summarizes typical geometries of nanoantennas with small gaps: nanorod dimers and ‘‘bowtie’’ nanoparticles. These architectures support large local field enhancements and hence significant nonlinear effects related to material anharmonicity under strong, external electric fields [13,27—30]. Because of the increased nonlinear polarizability at the LSP resonance, multi-photon absorption or frequency-conversion processes can be observed [30—37]. Finally, besides using nanoantennas to direct the emission of emitters, strong localized fields can be exploited to enhance and manipulate the properties of semiconducting nanostructures and molecules [17,38,39].
Fabrication of nanoscale antennas The ability to control nanoscale structure has enabled new ways to probe enhanced light-matter interactions. Because fabrication accuracies for nanoantennas are typically less than 10 nm, serial tools such as electron beam lithography (EBL) or focused ion-beam (FIB) have been used to create planar structures. EBL is especially suited for prototyping and designing complex nanoscale structures (Fig. 1a).
J.Y. Suh, T.W. Odom Despite its flexibility and accuracy in prototype patterning, the throughput of EBL (10−10 m2 /s) is not amenable for large-scale production of nanoantennas in a cost-effective manner [40]. Typical EBL-patterned areas are less than 100 m × 100 m. FIB also shares similar disadvantages in terms of low throughput (10−13 m2 /s at high resolution) [41], although single-crystalline nanoantennas can be fabricated [15]. For studying quantum effects related to small inter-particle spacing, accurate control of critical dimensions as small as 1 nm is required [42,43]. Accessing a size regime well below 10 nm is challenging to achieve by direct lithographic methods, however, and additional fabrication techniques such as self-assembly [44,45], surface functionalization [46] or oxidation processes [47] have been pursued. In contrast, soft nanolithography techniques provide a scalable route to produce large-area (cm2 ) nanoscale patterns. This parallel fabrication approach enables opportunities to measure collective effects such as diffractive coupling between individual nanoantennas [48—51]. Soft lithography uses elastomeric molds or masks made from poly(dimethylsiloxane) (PDMS) as the pattern transfer element. These masks can be used to generate template patterns in photoresist by exposing with UV light in phaseshifting photolithography [52] or by molding with organic solvents using solvent-assisted nanoscale embossing [53]. Etching, deposition, and lift-off steps and/or followed by template stripping can then transfer the photoresist nanopatterns into arrays of nanoantennas [28,54].
Linear optical effects of nanoantennas A single metal nanosphere, which is the simplest structural component of a nanoantenna, can capture and re-radiate light. In the quasi-static approximation where the incident wavelength is much larger than the size of the nanoparticle, the scattering and absorption cross-section can be analytically calculated [55]. The dipole moment induced in an isolated nanosphere under an external electric field E0 is given by sphere = 3Vεd [(εm − εd )/(εm + 2εd )]E0 , where V is the particle volume, and εm and εd are the dielectric constants of the metal and surrounding medium [56]. The LSP resonance occurs when the denominator becomes zero, which determines the resonant wavelength. For a single nanosphere, the plasmon resonance is independent of the polarization direction of the incident plane wave. Compared to nanospheres, single nanorods exhibit reduced plasmon damping and an increased dephasing time [57]. The radiation efficiency in a nanorod antenna is highest when the polarization of the incident light is parallel to the long axis of the particle [57], similar to an RF antenna. Fig. 2 shows the extinction spectra of single and dimer nanorod antennas (arm length L = 100 nm, radius r = 20 nm) calculated by the boundary element method [58,59]. Coupling of two nanorods with a small gap leads to a red-shift of the plasmon resonance to longer wavelengths (Fig. 2a); the resonance peak approaches that of the single nanorod as the gap distance increases. The strongest near-field enhancement and the largest resonance shifts are achieved at the smallest gap sizes. Note that the extinction efficiency is about 50-fold lower when the polarization is perpendicular to the dimer axis (Fig. 2b), and only a
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Figure 1 Representative nanoscale antennas. (a) Yagi-Uda nanoantennas exhibit directional emission from a quantum dot (adapted from [26]). (b) Nanocluster antennas show two-photon photoelectron emission (adapted from [29]). (c) Bowtie nanoantennas array show third-harmonic generation (adapted from [30]). (d) Nanorod dimer antennas can generate super-continuum white light (adapted from [13]). (e) 2D bowtie nanoantennas can enhance the emission intensity of fluorescent molecules (adapted from [27]). (f) 3D bowtie nanoantennas can show plasmonic lasing (adapted from [108]). Scale bars for (b)—(f), 100 nm.
single nanorod resonance is present. In a coupled nanoantenna or dimer structure, energy hybridization can generate bonding (bright) and anti-bonding (dark) modes in the extinction spectrum [60—62]. This energy splitting is directly related to the structural symmetry of the antenna. In particular, an anti-bonding mode can be excited in an asymmetric dimer configuration in which the net dipole moment is nonzero [61,63,64]. The arm length L and gap distance () of gold nanorod dimers are the two major parameters that determine the position of the LSP resonance and wavelength of antenna operation. Fig. 3 indicates that a longitudinal LSP resonance in the visible range (<700 nm) requires arm lengths smaller than 100 nm [65]. Also, as depicted
by red circles and the isowavelength curve, different combinations of L and can result in the same far-field spectrum. For example, L = 70 nm, = 10 nm and L = 110 nm, = 80 nm both have a resonances at 730 nm. For the same L but different , the near-field intensity is higher with smaller gap distances, but the resonance moves to longer wavelengths. As an example, the LSP resonance redshifts from 730 nm with = 70— 850 nm with = 20 nm for a given arm length (L = 110 nm). Therefore, this trade-off between the near-field intensity and resonance location sets a simple design rule for dimer nanoantennas. To have strong near-field intensity at the resonance wavelength at visible wavelengths, the gap distance and antenna arm lengths should be as small as possible.
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Figure 3 Resonance positions of nanorod dimer antennas depend on arm length and gap size. (Top) Dark-field scattering image for combinations of different arm lengths L and gap widths . Red circles denote the maximum scattering intensity. Graph of calculated longitudinal LSP mode as a function of L and . Red open circles denote the spectral positions of the experimental maximum scattering intensity. Adapted from [65]. Figure 2 Polarization-dependent optical properties of nanorod dimer antennas. (a) Calculated longitudinal LSP resonances from a single nanorod (40 nm × 100 nm) and nanorod dimers with gap distances of 10 nm, 20 nm and 100 nm using the boundary element method. (b) Calculated transverse LSP resonances under polarization along the particle short axis.
Moreover, the local surface curvature of an antenna can significantly influence the near- and far-field spectrum [11]. Fig. 4a shows a scheme of a 3D bowtie nanoantenna in which the gold particles are ‘‘folded’’ along the dimer axis. The low-energy mode at 860 nm is the dipolar bonding mode whereas the strong high-energy resonance at 640 nm is a quadrupolar mode (Fig. 4b and c) [28]. The high surface curvature of the 3D bowtie antenna results in field-retardation [66] that can generate a quadrupolar charge distribution at the four corners of each particle. In 2D planar nanoantennas, the excitation efficiency for a quadrupolar mode is low [67]. Surprisingly, the far-field intensity of the quadrupolar mode from the folded 3D bowtie antenna is as high as the dipolar mode. When the polarization direction is perpendicular to the dimer axis, only one resonance at 780 nm is present due to the lack of near-field interactions across the gap (Fig. 4c). Finite-difference-time-domain (FDTD) calculations [28] of the optical transmission of the 3D bowtie nanoantenna show excellent agreement with the experimental spectra. The simulated local field intensity can be increased up to four orders of magnitude at the dipolar bonding mode compared
to incident field intensity (Fig. 4d). Similar to the nanorod dimer case in Fig. 2b, when the polarization is perpendicular to the dimer axis, only a single particle resonance is present (Fig. 4e). The high local field enhancements supported by the 3D bowties suggest that this structure can be used as an efficient resonator to generate high nonlinear effects.
Nonlinear plasmonic effects of nanoantennas The nonlinear optical responses of materials are inherently very small even under excitation fields of moderate intensity [68]. When metals are structured as a nanoantenna with a small gap, the highly localized EM fields in the near-field can induce strong nonlinear responses [69]. The polarization of a material from an external electric field can be − → − → linearly approximated as P ≈ ε0 (1) E , where (1) is the first-order optical susceptibility. Under high incident fields, the nth-order susceptibilities (n) have nonlinear contributions to the induced polarization [70]. Most materials have complex third-order optical (Kerr) nonlinearities, and noble metals have large third-order susceptibilities (gold thin film, (3) gold ∼10−8 esu) [71]. In a metal NP-dielectric composite material, the effective third-order susceptibility goes as the fourth power of the local field enhancement factor (3) (eff ∝ |Elocal /E0 |4 ), where Elocal is the electric field inside the metal NPs [72—74].
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Figure 4 3D bowtie nanoantennas exhibit polarization-dependent electric field localization. (a) Scheme of 3D bowtie nanoantenna. Experimental and simulated transmittance spectra when polarization is (b) along the bowtie axis and (c) perpendicular to the dimer axis. (d and e) FDTD-calculated field intensity maps at wavelengths corresponding to the LSP resonances in (b) and (c). Adapted from [28].
Multi-photon absorption and photoluminescence can also occur with high efficiency when the local field enhancement is resonantly involved in the nonlinear processes [75]. Two-photon absorption that leads to the transition of electrons from the d valence band to the sp conduction band is increased because of high local fields at LSP frequencies [76]. Therefore, enhanced two-photon absorption can increase the rate of two-photon photoluminescence (TPPL). For example, a 2D gold bowtie nanoantenna shows a clear 4 fourth-power (Elocal ) dependence of the local electric field in the TPPL signal when the gap distance is less than 30 nm (Fig. 5) [77]. Spectral analysis on gold dimer nanorod antennas has also shown that the TPPL maps match calculated 4 Elocal distributions [78]. The spatially-resolved TPPL signal of the gap was four times higher than that at the ends of the antenna arms. In addition, nanoantennas can also exhibit second- and third-harmonic generation (SHG and THG) signals, where the frequency of incident light is doubled (2ω) or tripled (3ω). Although metal NPs have symmetric atomic lattices, they can give rise to efficient SHG when the overall shape of the NPs is not symmetric, such as L-shaped NPs [79,80], T-shaped NPs [81], nano-cup structures [82] and split-ring resonators [83]. Symmetric shapes can also produce SHG depending on local field asymmetries [81], structural chirality [84] and multi-pole interferences [85]. In contrast, THG from nanoantennas is not constrained by a symmetry argument, and its intensity is directly related to the effective
third-order susceptibility (3) of the metal NPs. Intense THG associated with d-band transitions has been observed from gold bowtie nanoantennas [12] and can be correlated with linear optical properties [35]. For example, THG is
Figure 5 Local field enhancement depends on the fourthpower in 2D bowtie nanoantennas. Two-photon photoluminescence shows |E4 | dependence for gap distances <40 nm. Adapted from [77].
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Figure 6 THG generation is correlated to linear optical properties of bowtie nanoantennas. (Left) Extinction spectra from a single NP and bowtie nanoantennas with varying gap distances. As the gap deceased, the LSP resonance red-shifted into the wavelength range of laser excitation (gray). (Right) Intensity of corresponding THG is maximized with smaller gap sizes. Adapted from [30].
highest in nanorod antennas when the incident wavelength matches the LSP resonance wavelength (Fig. 6) [30]. The linear extinction and overall THG emission spectra of the bowtie nanoantennas can be fit by a single anharmonic oscillator. For smaller gap sizes (<20 nm), however, the larger near-fields in the gap contribute to the THG signal, which causes the results to deviate from the nonlinear oscillator model. Consequently, nanoantennas can enhance both THG and TPPL signals by increasing (3) at the LSP resonance. High nonlinearity supported by metal nanoantennas can also enhance the resolving power of near-field imaging or TPPL microscopy in the optical range [86,87]. Whereas TPPL microscopy images the relative intensity of the local (3) , z-scan transmission can directly
measure the complex (3) , where the imaginary part of the susceptibility is related to nonlinear absorption [88]. Via open-aperture z-scan measurements, nonlinear optical absorption by 3D gold bowtie nanoantennas was found to be extremely high (Im (3) = 10−4 esu) [28]. Slightly different values of the measured Im (3) were also observed depending on whether the bowtie was folded or flat; these nanoscale structural differences produced different local field strengths in the gap. In addition, saturable absorption, which is a non-parametric nonlinear process [68], was observed from the 3D bowtie nanoantennas under femtosecond (fs) excitation [28]. Gold NPs are known as good saturable absorbers with high Im (3) in the fs regime [89]. The intensity-dependent saturable absorption of the metal
Nonlinear properties of nanoscale antennas
Figure 7 Fourth-order nonlinearity from nanorod dimer antennas. (a and b) SEM images of a gold nanoantenna (L = 250 nm, = 20 nm). (c) Confocal image showing that WLSC is created in the gap region when incident laser pulses are vertically polarized. (d) Confocal image showing that WLSC disappears with horizontally polarized pulses because of the absence of near-field interactions. Average pump power is 100 W. Adapted from [13].
NPs thus enables nanoscale antennas to be used as potential Q-switching devices [90,91]. Even higher-order nonlinearities can be obtained from gap nanoantennas. White-light super-continuum (WLSC), which is described by a fourth-order optical nonlinearity, was observed in the gap of nanorod dimer antennas [13]. Similar to linear effects, the white-light intensity was controlled by the arm length L and was generated only when the polarization was parallel to the antenna axis (Fig. 7). This polarization-dependence again shows that strong nearfield enhancement across the gap is important for nonlinear effects. Second-order (TPPL) nonlinearity dominates at low power, but at higher incident power (>80 W), the output curve has a quartic dependence on the incident power, which confirms that the generation of WLSC is a fourth-order nonlinear process.
Nanoantenna-emitter systems Nanoantennas can control the quantum efficiency of emitters such as quantum dots and dye molecules through resonant energy transfer between the emitter and localized plasmons [27,38]. When an emitter is placed within the near-field region of a nanoscale antenna, the spontaneous emission (SE) rate can be enhanced by a factor of several hundred [92—94]. Fig. 8 depicts a scheme of energy transfer between a four-level electronic system and a metal NP. In describing gain media, a simple 4-level system is widely employed because population inversion can be readily achieved due to the relatively long lifetime of the transition from 2 to |1. External pumping can result in population in the upper levels of the first excited state. When the energy difference of the emitter (E2 − E1 ) is the same as the energy needed to excite LSPs in the metal NP (ωsp − |EF ), the resonant interaction can modify the total recombination rate. According to Fermi’s golden rule, the SE rate is proportional to the local density of states (LDOS) available for the decay of the emitter [95,96]. Because the plasmon field of the metal NP can increase the LDOS, the radiative recombination rate of excitons should also be enhanced.
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Figure 8 Scheme and energy diagram of the interaction between an emitter and a metal NP. A simple four-level system can represent a dye molecule whose energy can be transferred to a metal NP in close proximity through resonant energy transfer (ksp ). The absorbed energy can be dissipated by radiative and non-radiative decay channels.
The near-field coupling of emitters to nanoantennas can result in enhanced fluorescence, a phenomenon that can be described by the Purcell effect in the weak-coupling regime [97]. The Purcell effect is maximized when there is (1) maximum field confinement (small mode volume V) and (2) minimum cavity losses (high quality factor Q), where the ratio between Q and V is called the Purcell factor (F). Metal structures capable of high F also show characteristics of gap nanoantennas. As an example, 2D gold bowtie nanoantennas have been shown to increase the fluorescence intensity from a single near-infrared dye molecule (TPQDI) by a factor of more than 1000 (Fig. 9) [27]. With a gap = 80 nm, the fluorescence enhancement was equivalent to the case of single triangles since the near-field interaction between the bowtie arms was very weak. The enhancement, however, was maximized when < 20 nm, which is consistent with the high local field intensities as discussed earlier. The total decay lifetime ( F ) of TPQDI was reduced to <10 ps from 275 ps in the presence of the 2D bowties, evidence of the enhancement of radiative and non-radiative decay rates
Figure 9 2D bowtie nanoantennas increase the fluorescence intensity of single molecules. Scatter plot of fluorescence enhancement (fF ) from TPQDI single molecules. fF is increased by a factor of 1300 when the bowtie gap distance is less than 20 nm. Adapted from [27].
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Figure 10 Yagi-Uda nanoantennas can direct emission from single quantum dots. (a) Scanning confocal luminescence images of a reference (gold square, 60 nm × 60 nm), half-wave dipole nanorods, and Yagi-Uda nanoantennas, respectively. (b) Only the Yagi-Uda nanoantenna shows a unidirectional radiation distribution. Adapted from [26].
as a result of resonant coupling of single molecules to the nanoantenna [98]. Nanoantennas coupled to quantum emitters not only can enhance the fluorescence intensity but can also steer the direction of the emission. As described previously, miniaturized Yagi-Uda antennas rely on long-range, dipolar interactions between aligned metal nanorods to achieve directionality of light from a single quantum dot [26] or Raman molecules [99]. Fig. 10 shows that only the YagiUda arrangement of gold nanorods exhibited unidirectional emission in the angular radiation pattern, while control nanoantenna structures did not [26]. The arm lengths and inter-particle distances were chosen such that the LSP resonances from each nanorod had a slight phase-lag with respect to the feed element. High radiation efficiency was achieved because the quantum dot was positioned in the near-field region of the feed element in the antenna. Plasmonic nanoantennas can also be used to generate coherent light (i.e., lasing action) below the diffraction limit. Plasmonic lasing has been demonstrated in a variety of metal nanostructures, such as gold-coated InP/InGaAs/InP nanopillars [100], CdS nanowires and slabs [101,102], and InP nanodisks [103]. Stimulated emission is usually characterized by the onset of a narrowed emission peak over the underlying PL spectrum, where a single-mode lasing peak grows nonlinearly as the pump intensity increases with a kink at the threshold level [104]. A distinct feature of plasmonic lasing from metal nanocavities is the thresholdless behavior because of a high SE factor ˇ (the ratio between the SE rate of a single lasing mode and the total SE rate) [105]. Plasmonic cavities can exhibit high ˇ-factors through strong field confinement of a single mode while excluding competing emission factors [101]. High ˇ-factors account for a ‘‘smearing’’ of the threshold level; in contrast, ˇ-factors for conventional laser cavities are very small (<10−3 ) [106]. Experimentally, a coaxial Ag nanocavity with InGaAsP gain
medium clearly showed a thresholdless behavior in lasing at low-temperature provided that ˇ ∼ 1 [107]. As described previously, 3D gold bowtie nanoantennas have properties of excellent optical resonators that support well-defined EM hot spots. These high and localized fields can also be exploited for nanoscale lasing [108]. An example of an emitter that can couple with the LSP gap mode of 3D bowtie nanoantennas is the organic dye IR-140. Within a polymer matrix, the dye molecules can be positioned in the antenna gap region. When coupling occurs, the excited state energy from the dye can be non-radiatively transferred to create a localized plasmon mode. This additional coupling channel of the excited states in the presence of the 3D bowtie nanoantenna increases the SE rate of the dye molecules. The rate of exciton-plasmon coupling can be characterized by the fast decay component in timeresolved absorption spectra. The transient decay traces of the excited state absorption with and without the bowtie nanoantenna clearly show a lifetime reduction (1 ns to 13 ps) of the excited molecules (Fig. 11a), which is comparable to the case of 2D bowties [27]. The enhancement factor in the SE rate can be determined from the ratio of LSP coupling and radiative recombination rates (Fbowtie = kLSP /krad = 440), which is about two times higher than that of a single nanosphere (Fsphere = 250) [109]. The 3D bowtie resonators were found to lase in the presence of organic dye molecules. Above a certain threshold, a laser oscillation was observed at 873 nm with a narrowed linewidth (1.5 nm) from the bowtie resonators (Fig. 11b). The existence of a lasing threshold level indicates that even though the losses of this system are somewhat high (Q < 20), the stimulated emission rate was enhanced and exceeded the SE and non-radiative recombination rates (Fig. 11b, inset). This bowtie nanolaser is an example of how coherent light can be produced from high local EM fields in a sub-diffraction region from nanoantennas with gaps.
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Figure 11 3D bowtie antennas exhibit room-temperature lasing. (a) Femtosecond transient absorption traces reveal that IR140 shows fast decay components in the presence of 3D bowties under parallel and perpendicular pump polarizations relative to the nanoantenna axis (red and blue curves). (b) Lasing spectra as a function of pump energy for a 3D gold bowtie array (inset, periodicity = 1200 nm) with gain. Input—output light curves show threshold behavior. Adapted from [108].
Conclusions Nanoscale antennas can localize and concentrate EM fields into subwavelength volumes at their LSP frequencies. The large local field concentration supported by metal nanoantennas can induce strong optical nonlinearities, which makes them promising for nonlinear applications such as frequency conversion, four-wave mixing or Q-switching. Multi-photon absorption and second and third harmonic generation processes can also be greatly enhanced near the LSP resonance; however, an efficient design for nonlinear nanoantennas is still a challenge. Nanoantennas with gaps are also good optical resonators that can exhibit plasmonic
lasing from well-defined and localized EM fields in the gap region. Enhanced light-matter interactions at the nanoscale and coherent photon sources from optical nanoantennas will enable the development of optical and plasmonic devices that can be sensitive to a single quantum emitter. Further miniaturization of nanoscale antennas can ultimately access the regime where strong quantum effects exist, and hence ultrafast energy transfer processes can potentially be probed even at atomic length scales. Nanoscale antennas hold promise not only for nonlinear nano-optics applications but also for spectroscopies with detection resolution down to the single molecule level.
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Acknowledgements This work was supported by an Initiative for Sustainability and Energy at Northwestern (ISEN) Award (J.Y.S.) and the NSF-MRSEC program at the Materials Research Science and Engineering Center at Northwestern University (DMR1121262) (J.Y.S., T.W.O.).
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