Light-matter interactions have been attracting researchers for ages, as these interactions provide a noninvasive way to probe the material properties and to rapidly detect variations over time. At low intensity, light and matter interact linearly, but the interaction becomes nonlinear at enough high intensity. Although the prediction of nonlinear interactions appeared in the early 20th century , , various experimental demonstrations, including optical harmonics in scattering, multiphoton absorption, and the saturation of emission, have been boosted up after the invention of lasers in 1960 , . These successful experiments led to the rapidly growing research field of nonlinear optics, and a major part focused towards the applications on biology and medicine.
Nowadays, optical nonlinearity is a subject of widespread studies in the photonics community. Nonlinear phenomena provide unique functionalities such as frequency expansion, high harmonic generations, self-focusing, ultra-short pulse control, ultra-fast switching, and all-optical signal processing , . However, the optical nonlinearities originate from the material properties of the interacting media and in general are inherently weak. There has been a long quest to improve the efficiency of nonlinear optical processes, and several methods have been proposed/verified, such as by reducing the speed of light , , by constructing a resonant cavity , by quasi-phase matching with periodic structures , by elongating the interaction length (fiber) , , by introducing a magnetic field , , and by local field enhancement . The last effect is related to plasmonics and is the main topic of this review.
Plasmon arises from the collective and coherent oscillation of free electrons in plasma or conduction electrons in metal at optical frequency when excited by light , . The field enhancement in general is achieved only in proximity to the plasmonic materials. When the collective oscillation occurs at a surface, such as a metal-dielectric interface, and propagates along the surface, it is called surface plasmon polariton (SPP) . When metals are brought down to nanometer scale, their sizes become comparable to the mean free path of their conduction band electrons (40–50 nm in gold). At this situation, the nanoparticle exhibits intense interaction with incoming light due to localized surface plasmon (LSP) , . With appropriate wavelength of incoming light, these localized surface electrons oscillate resonantly, giving rise to the opportunity for controlling light confinement on the nanoscale. The intense electromagnetic interactions associated with these surface plasmon resonance (SPR) nanoparticles depend strongly on the dimension, orientation, and material properties.
SPR on a metallic surface can boost optical nonlinearities in many ways. The coupling of light to SPR can result in extraordinarily strong local electromagnetic fields , , significantly enhancing optical nonlinear processes of the surrounding materials. Surface-enhanced Raman scattering (SERS) is a prime example of such effect, where SPP excitations at rough or engineered metal surfaces can enhance the inherently weak Raman process by several orders of magnitude, allowing even single-molecule detection , , . Surface plasmon enhancement over thin metallic film can also be used to improve multiphoton fluorescence signals . However, using metal films as the nonlinearity enhancer is typically limited to sample surfaces, so it is very difficult to obtain information from the interior of cells and tissues.
Noble metal nanoparticles, on the contrary, can easily be engulfed by cells or can flow through blood vessels. Evidently, nanoparticle-assisted LSP enhancement of both incoherent and coherent nonlinear processes, including multiphoton fluorescence , second harmonic generation (SHG) , , hyper-Raman scattering , and third harmonic generation (THG) , have been demonstrated. In a pioneering work, researchers have demonstrated that the presence of gold nanoparticles at cell membranes can simultaneously enhance SHG and quench two-photon fluorescence from nearby dye molecules , . Additionally, metallic nanoparticles have less toxicity than quantum dots, making them more biocompatible.
Other than enhancing nonlinear signals from surrounding materials, metal nanostructures are also capable of generating inherent nonlinear optical processes, including SHG , , multiphoton photoluminescence (PL) , THG , , four-wave mixing (FWM) , and excited-state absorption (ESA) . Nanoparticles with different shapes, such as nanorods, exhibit different SPR wavelength bands with varying geometrical parameters and thus allow imaging applications requiring long wavelength for deep penetration. For example, PL from gold nanorods with varying aspect ratios  and SHG from plasmonic nanomaterials of various shapes and arrangements have been studied extensively , , , , .
In this mini-review, we discuss the nonlinear processes accompanying plasmonic nanostructures, with an emphasis of imaging applications toward biological cells and tissues either in vivo or in vitro. In Section 2, we start by briefly reviewing the SPR-enhanced nonlinear processes. In Section 3, nonlinear optical interactions that are enhanced by plasmonics are discussed. In Section 4, inherent nonlinear optical signals from plasmonic nanostructures themselves are reviewed. In Section 5, we describe our recent work about the nonlinear saturation of plasmonic scattering from nanoparticles and the possibilities to enhance far-field imaging resolution. In Section 6, a brief summary and outlook for the future directions is given.
Although nonlinearities of plasmonic nanoparticle have many novel applications in photonics, such as lasing , all-optical switching , , and soliton generation , , they are not within the scope of this review, whose emphasis is on imaging-related techniques. An excellent review of nonlinear plasmonic can be found in Ref. . In addition, plasmonic nanoparticles are also well known to enhance linear optical processes such as single-photon fluorescence and linear absorption and scattering. In this review, we occasionally mention linear plasmonic interaction in comparison to nonlinear interactions, but the main focus is the latter.
2 Basic principles of nonlinear processes
Nonlinear optical processes arise due to nonlinear interactions of light and matter. As a wide field of research, it contains a broad spectrum of phenomena, such as optical frequency conversion, optical solitons, phase conjugation, and Raman scattering. It is important to note that the linearity of the optical signal with respect to its dependence on incoming light intensity I should not be confused with the linearity of the light-matter interaction . For example, both single-photon fluorescence and spontaneous Raman emission are linearly related to the incoming light intensity, as shown by Eq. (1):(1)
where Iem is emission intensity and Iex is excitation intensity. However, the light-matter interaction of the former is linear, whereas spontaneous Raman scattering is a nonlinear interaction between photon (optical field w1) and phonon (vibrational energy wv), as shown in Figure 1A, and hence is included in our discussion.
On the contrary, conventional nonlinear optical phenomena are “nonlinear” in the sense that they occur when the response of a material system to an applied optical intensity depends in a nonlinear manner upon the incoming light intensity. When the incoming intensity is low, the molecular dipole oscillates linearly with incoming electric field, creating linear polarization in the material. However, when the incoming intensity is high enough, the dipole oscillation becomes anharmonic, thus creating new radiation frequencies. The nonlinearity can be quantitatively expressed by expansion of the anharmonicity as power series of incident field intensity, as outlined in Eq. (2).(2)
where Iex is the applied field intensity and α, β, and γ are linear, second-order nonlinear, and third-order nonlinear coefficients, respectively. It is the linear coefficient that controls the linear optical response, such as absorption, reflection, spontaneous emission, and scattering in a weak field. For strong field intensity, the higher-order coefficients in Eq. (2) need to be considered. Higher-order terms contain components of sums and differences of the incident light frequencies and give rise to radiation at new frequencies, such as SHG and THG.
For second-order nonlinear interactions, SHG, hyper-Rayleigh scattering (HRS), sum, and difference-frequency generation are examples . As shown in Figure 1A, SHG involves the transition of the interacting molecules to a higher-energy virtual state by annihilating two incident photons and generating a new photon at twice frequency of them. Because SHG is only allowed with non-centrosymmetric materials, it provides a structural contrast mechanism for nonlinear microscopy .
HRS is a second-order nonlinear phenomenon, similar to SHG, coherently generating new photons with frequency doubled that of incident photons. Nevertheless, unlike SHG, HRS is allowed in isotropic medium dispersed with very small scatterers, and the summation of HRS intensity from scatterers is incoherent . HRS has been extensively used for chemical sensing , . Heinz and his group were the first to demonstrate formally that incoherent second-harmonic scattering (i.e. HRS) from spherical plasmonic nanoparticles can be explained based on Mie theory .
For third-order nonlinear interactions, we start from FWM. In FWM, three incident photons simultaneously interacting with the material dipole, are annihilated, and generate a new photon whose frequency is a linear combination of the incident photon frequencies. When the frequencies of the incident photons are the same, one of the degenerate processes is called THG, where the energy of the three incident photons adds up together to create an emission photon at tripled frequency, as shown in Figure 1A. Due to the Gouy phase shift, THG is generally observed only at interface or surface, making it a powerful tool for probing physical or chemical properties at the interface , . With its third-order power dependency, THG is more confined to the focal point than SHG, so it provides exceptional signal-to-background ratio when applied to an optical section in multiphoton imaging. Furthermore, when the frequencies of the incident photons are not the same, many different FWM configurations exist, and in this review, we mention coherent anti-Stokes Raman scattering (CARS) and stimulated Raman scattering (SRS) , , . The magnitude of FWM signal strongly depends on the resonance conditions of both incident and induced frequencies. In CARS and SRS, two beams with a frequency difference equal to a vibrational transition energy are used to resonantly and coherently excite the vibration, significantly enhancing the weak Raman interaction and allowing much more rapid detection , , . In addition, compared to Raman scattering, these coherent Raman techniques provide optical sectioning, as their emission intensity depends nonlinearly with incident intensity. There is another type of nonlinear Raman phenomena called hyper-Raman scattering, in which the emitted frequency is Raman shifted relative to the second harmonic of the incident frequency , , .
As we mentioned earlier, in the 1930s, Dr. Goeppert-Mayer predicted the first nonlinear interaction, which is two-photon absorption. Different from harmonic generations, in two-photon absorption, a molecule transits to a real excited electronic state by simultaneously absorbing two photons. The subsequent luminescence emission due to relaxation is thus called two-photon luminescence (2PL) . Different from harmonic generations, where resonance (real transition) is not necessary, and different from Raman scattering, where the vibrational state is probed, 2PL provides the information of electronic transition structure of the composition materials. On the contrary, similar to harmonic generations, where two- and three-photon interactions exist, there is also three-photon luminescence (3PL), where a molecule is excited by absorbing three photons simultaneously. Similar to THG, 3PL provides better optical sectioning capability due to its high nonlinearity , .
Other than the simultaneous absorption of multiple photons, another possible nonlinear interaction is to absorb two or three photons sequentially. The process is termed as ESA, in which a pump beam excites molecules into a first excited state and a time-delayed probe beam excites them into a higher excited state by a secondary absorption process. Similar to previous nonlinear processes, ESA provides intrinsic optical sectioning capability . Figure 1 schematically summarizes the second- and third-order nonlinear electronic transitions that we address in this review.
The nonlinear interactions of matter and light can be enhanced by various approaches as mentioned in Section 1. Among them, surface plasmon-enhanced nonlinear processes are relatively simple to implement, and the enhancement efficiency is remarkably high. The enhancement of nonlinear effects in the presence of plasmonic structures may occur in two different ways. First, near the metal-dielectric interface, the energy of photon can be efficiently coupled into either SPPs or LSPs , both of which provide significant increased energy density due to the strong confinement. It is the physical mechanism of the field enhancement generally associated with plasmonic resonance. The resulting strong field locally enhances the nonlinear response whether it is the nonlinearity of a material adjacent to the metal (enhanced response) or the inherent nonlinearity of the metal itself (inherent response). The former is the topic of Section 3, and the latter is discussed in Section 4.
Second, the refractive index (RI) of the metal itself or the surrounding dielectric can vary nonlinearly with respect to incident intensity. Because the plasmonic resonance, including both SPP and LSP, are very sensitive to the RI variation, such intensity-dependent RI causes significantly modified plasmonic properties. The corresponding nonlinearity enhancement is described in Section 5. Figure 1B1 and B2 schematically describes the two different nonlinearity enhancement approaches.
3 Plasmonics-enhanced nonlinear processes
The efficiency of nonlinear processes can be increased substantially by plasmonic effect. As mentioned earlier, the coupling of light to coherent oscillation of surface electron of SPP or LSP can result in strong local electromagnetic fields and thus considerably enhance existing nonlinear optical processes. In this section, we focus on nonlinear optical interactions that are already present in the host materials but are relatively weak. These nonlinearities are “enhanced” via the presence of plasmonic nanostructures. Below, we describe the enhancement of various far-field emissions, including multiphoton fluorescence, harmonic generations, Raman scattering, and near-field enhancement with the aid of metallic tips.
3.1 Enhancement of far-field harmonic generations
Surface-enhanced SHG was first detected from rough silver surfaces . From subsequent SHG enhancement experiments on metal-island films and lithographic nanostructures, the role of localized SPR was identified to be the underlying mechanism .
Plasmonic nanoparticles, which provide localized field enhancement, are also useful in enhancing harmonic generation signals. Weak SHG from biomolecules have been enhanced by metal nanoparticles , , , leading to widespread applications in biological imaging. For example, metal nanoparticle antibody complexes are directed to specific sites on a cell membrane that has been labeled with a chiral, dipolar, membrane-anchoring dye. Such complexes provide gigantically enhanced nonlinear signals, potentially useful to structural and physiological imaging (Figure 3B) , . The same group soon demonstrated functional cellular imaging based on the measurement of membrane potential around a single molecule by plasmonically enhanced SHG from gold nanoparticles .
Besides SHG, surface-enhanced THG has also been observed, with a detailed discussion of nanostructure symmetry effects . Yelin et al. have reported not only enhanced THG signals but also two-photon autofluorescence by noble metal nanoparticles attached to cellular organelles and membranes when illuminated by laser in resonance with their plasmon frequency (Figure 3B2 and D1) . We have previously studied the molecular imaging of cancer cells using enhanced THG from silver nanoparticles conjugated with Her2 (Figure 3B1) . Her2 is a transmembrane receptor protein for epidermal growth factors and can be used as predictor for the unfavorable growth behavior of cells. Using nanoparticles as exogenous THG contrast agents, this technique allows us to identify aggressive cancer cells with high molecular specificity. Additionally, we also have demonstrated silver nanoparticle-enhanced THG imaging of collagen fibers and muscle I-band in muscle tissue slices as described in Figure 3C .
Other than SHG and THG, the enhancement of FWM, which is a third-order nonlinear optical interaction, by propagating SPPs was demonstrated recently . In that report, it was emphasized on achieving highly directional, coherent, and frequency/angle tunable FWM radiation using local field enhancement at nanostructured surfaces. Their results show the potential for wavelength selection in imaging techniques such as dark-field microscopy. Furthermore, arrays of bowtie antennas were reported to enhance high harmonic generation up to the 17th harmonics and several other nonlinear processes , . Basically, the plasmonic nanostructures serve as a nanolens to increase local field strength and can be employed in conjunction with all nonlinear microscopy modalities, including fluorescence and coherent or incoherent Raman scattering, as shown in the following sections.
3.2 Enhancement of far-field multiphoton fluorescence
The first plasmonically enhanced two-photon fluorescence was demonstrated by Kano and Kawata in 1996 , where a 90-fold enhancement in total-internal-reflection two-photon fluorescence by SPR was found. As mentioned earlier, plasmonic nanoparticle-enhanced two-photon autofluorescence from cellular organelles was applied to image cells (Figure 3D1) . They are the pioneers who combined SPR field enhancement and nonlinear optical emissions to enhance the contrast of biological imaging. A similar SPR-enhanced two-photon total-internal-reflection fluorescence was recently adopted to image living monkey kidney fibroblast cell membranes transfected with enhanced green fluorescent protein (EGFP; Figure 3D2) .
3.3 Enhancement of far-field Raman scattering
Raman scattering is a very useful technique in chemical spectroscopy and label-free imaging applications. The major advantage of Raman scattering is that it provides intrinsic molecular information from vibrational states. However, the main difficulty of incoherent Raman scattering detection is its extremely small cross-section (~10-30 cm-2), especially along with the common presence of a strong fluorescence background. Plasmonic nanostructures, with greatly enhanced local field, can introduce substantial signal enhancement for adjacent molecules and make Raman imaging a more practical technique. The enhancement of Raman signal by a plasmonic surface has given rise to a whole new field of research known as SERS , .
It was first discovered in the 1970s, where 10–14 orders of magnitude higher signal than that of spontaneous Raman spectroscopy was found , . Since then, SERS has been extensively used in molecular sensing and imaging both in vitro and in vivo , , , . SERS is actually sensitive enough to detect even a single biological molecule without labeling , , . There are several geometries to obtain active “surfaces” for SERS, such as the surface of a thin metal film , patterned surfaces with nanometer-sized roughness , , metal-coated tip of an atomic force microscopy (AFM) probe , , or nanoparticles , , , .
SERS using metal thin surfaces or surfaces with nanometer-sized roughness are useful in sensing biomolecules. Metal-coated AFM probe and solid metal tips are advantageous in SERS imaging with high resolution. However, both flat surfaces and tip probes are used only to image at the surface. On the contrary, nanoparticles have the ability not only to target cell membrane but also to penetrate through it or get endocytose in intracellular vacuoles. SERS has been reportedly used in imaging cells by targeting cell surfaces with Raman-active molecules conjugated with metal nanoparticles  and also to detect cancer cell markers, such as Her2, at cell surface . It has also been used in intracellular imaging of live cell cytosol using gold nanoparticle conjugated with SERS reporter .
Recently, one of the authors has demonstrated an useful protocol for dynamic SERS imaging equipped with a slit-scanning excitation and nanoparticle-tracking system . Using a single gold nanoparticle engulfed by a vacuole, which travels through the cytosol, this technique allows SERS detection with high spatial and temporal resolution inside a living cell to probe local molecular information. Figure 3E1 shows the electron microscopy image of a macrophage cell with a nanoparticle inside a vacuole. High-speed, high-resolution SERS microspectroscopic imaging with 3D molecular mapping provides insights of organelle transport, membrane protein diffusion, nuclear membrane entry, and rearrangement of cellular cytoskeleton, as shown in Figure 3E2, without chemically or genetically modifying the Raman-active molecules , .
It is known that the weak scattering efficiency of spontaneous Raman scattering can also be enhanced by coherent excitation based on nonlinear optical interactions, such as hyper-Raman scattering , CARS , , and SRS . By combining SPR field enhancement, the signal intensity of these nonlinear Raman processes can be further improved. For example, Golab et al. have reported an experimental as well as theoretical study of hyper-Raman spectrum of pyridine adsorbed onto roughened silver electrodes. They argued that surface-enhanced hyper-Raman scattering is more sensitive to adsorbate orientation than SERS . Recently, an array of spherical nanocavities in a gold film was used to improve the signal magnitude of CARS spectroscopy by 105, and the sensitivity of this surface-enhanced CARS is 1000 times better than SERS .
In most examples above, the plasmonic enhancement occurs around metal nanostructures that are either fixed or randomly flowing. It is highly desirable to have a fixed plasmonic structure but with controllable movement. This can be achieved by combining near-field scanning system and a sharp metal tip, as we will discuss in the next section.
3.4 Enhancement by a metallic tip at near field
Scanning probe microscopies such as AFM  and near-field scanning optical microscopy (NSOM)  have emerged as very useful imaging techniques that provide resolution far beyond the optical diffraction limit. In conventional NSOM, the exceptional high resolution is accomplished by collecting light with a very small aperture in the near-field regime, which is a few tens of nanometers from sample surface. The aperture is typically formed by a tapered fiber tip. However, the tapered design, as well as the shrinked sampling volume, considerably reduces the overall signal strength. An alternative approach is to replace the fiber tip with a metallic tip that can provide efficient coupling between the local field enhancement from the tip and far-field detection , , . The technique is commonly named as tip-enhanced NSOM.
Tip-enhanced NSOM has been applied to almost every optical contrast agents, both linear and nonlinear. In one of the pioneering nonlinear works, Xie’s group have demonstrated polarization-dependent tip-enhanced two-photon excited near-field fluorescence imaging using a gold nanotip and a mode-locked Ti:sapphire laser . They imaged photosynthetic membrane fragments from algae with spatial resolutions on the order of 20 nm, as shown in Figure 2F1. Compared to single-photon far-field fluorescence imaging, the combination of near-field and 2PL provides not only greatly enhanced resolution and fluorescence emission but also the reduction of photobleaching. Later on, many other researchers adopted metallic tip-enhanced NSOM for various contrasts, including fluorescence, Raman scattering, and SHG , , , , , , , .
In another pioneering and interesting study, a gold nanoparticle is trapped and controlled by a laser beam to be an imaging probe . By scanning such a trapped gold particle over the sample surface, the enhanced 2PL imaging of fluorescence beads is demonstrated along with single-photon fluorescence imaging of DNA . Nevertheless, although the fluorescence enhancement near a metallic tip or nanoparticle is attractive, it should be noted that the requirement of long exposure time in near-field imaging might potentially photobleach the fluorescence.
On the contrary, Raman signal does not suffer from bleach. Raman scattering at near field has attracted a lot of attention with applications toward sensing and imaging. Kawata and his group have done extensive work in plasmon-enhanced near field Raman imaging/detection , , , . They have demonstrated that, using aperture-less metal tips, near-field Raman and multiphoton fluorescence imaging of biomolecules can be simultaneously achieved . Later, tip enhancement is further combined with CARS to capture high-resolution images of double-stranded DNA as demonstrated in Figure 2F2 . In an excellent review, various aspects and application of plasmon-enhanced near-field nanoimaging are comprehensively discussed .
4 Inherent nonlinear effects of plasmonic nanostructures
Different from what we have described in the previous sections, where plasmonic fields enhance the nonlinearities of adjacent materials, the plasmonic nanostructures themselves also provide inherent nonlinear interactions with light. Such nonlinear behaviors, especially from nanoparticles, can also be used as contrast agencies for optical microscopy in biology.
At this point, we should clarify the difference between inherent and enhanced nonlinear interactions. For example, in Ref. , SHG is observed from silver nanoparticles embedded in silica glass. Because silica is a centrosymmetric material, SHG should be forbidden in the material. Thus, the effect of silver nanoparticles is not to enhance an existing weak SHG source but to generate SHG on their own. As another example, it is known that, due to the Gouy phase shift, THG cancels out in bulk materials and is only observable at interfaces . Therefore, if a metal nanoparticle is placed on a surface, where (weak) THG is allowed, the resulting (strong) THG signal should mostly originate from enhancement . However, if a nanoparticle is immersed in bulk liquid, where THG should be zero, then the emitted THG is more likely to be inherent . In this section, we review the recent progress of various nonlinear optical processes generated inherently by plasmonic nanomaterials and their potential biological imaging applications.
4.1 Inherent harmonic generations
SHG is a nonlinear effect that arises due to light interaction with non-centrosymmetric materials. In the field of microscopy, intrinsic SHG is known to provide structural contrasts in the crystallized biological materials, such as starch granules , , collagen , , , and skeletal muscles , . As discussed in Section 3.1, metallic nanostructures, owing to their SPR, are known to enhance the SHG of the surrounding materials , , , . However, if plasmonic nanostructures break the centrosymmetry by themselves, they exhibit inherent SHG. For example, SHG signal, in transmission mode, from thin layers of ellipsoidal silver nanoparticles embedded in silica glass was detected . Following that, the second harmonic optical response from single silver nanoparticle was reported (Figure 3A1) . Gold nanospheres embedded in dielectric matrix such as gelatin were also reported to generate polarization-dependent SHG signal (Figure 3A2) .
The SHG signal strength is highly dependent on the orientation of plasmon oscillation versus excitation light polarization, so SHG can be used as a very sensitive probe to the subtle shape asymmetry of plasmonic nanoparticles . In fact, the SHG dependency of material symmetry and the nanostructure shape open up a series of technique development of in situ ultrasensitive nonlinear optical characterization, including the detection of very slight deviations from perfectly symmetric shapes ,  as well as minute surface roughness , . Because SHG can point out defects that linear responses cannot, it is attractive in some specific nanoparticle geometries such as the nonlinear optical characterization of gold nanotips by incident beams with azimuthal and radial polarizations . Based on the structural sensitivity, SHG is capable to provide useful information during the chemical synthesis of plasmonic nanoparticles , , , . From the same principle but in a completely different context, SHG emission from plasmonic nanoparticles also finds application in laser beam characterization, which is a crucial parameter for laser microscopy and imaging , .
Regarding biological applications, it has been demonstrated that SHG from plasmonic nanostructures can be used to sensitively detect biological and chemical toxins , . In an excellent review, details about the nonlinear optical response from metal nanoparticles and their applications in sensing biomolecules and other chemicals were discussed elaborately . SHG, as well as HRS, from individual plasmonic nanospheres has been used to diagnose single-base-mismatch DNA hybridization , to detect Alzheimer’s disease biomarkers , and to probe heavy metal ions . HRS from gold nanorods are used to selectively detect and identify Escherichia coli bacteria . Also, HRS from oval-shaped nanoparticles are used to detect breast cancer cells .
There are two remarks for inherent plasmonic SHG as biosensors. The first one is that, although in these literatures no imaging example is provided, these particles are functionalized toward the targeted chemical/biological molecules and are straightforward to molecular imaging applications. The second is that the molecular sensitivity of plasmonic SHG might not be as good as SERS, as illustrated by the comparative studies , .
Plasmonic nanoparticle have also been reported to exhibit inherent THG signal. THG signals from individual 40 nm gold nanoparticles are first discovered in 2005 (Figure 3B1), enabling the potential for single biomolecule detection and tracking . In that work, a pulsed laser with a center wavelength at 1500 nm is used, so the THG signals peak at 500 nm, matching the plasmonic band of the gold nanoparticles. In 2009, inherent THG from silver nanoparticles, as well as from silicon nanowires, is reported (Figure 3B2) . The authors claimed that THG from silver is less stable than silicon and adopted the later as an imaging contrast for deep-tissue intravital microscopy. However, to the best of our knowledge, inherent plasmonic THG in biological applications is awaiting to be explored.
4.2 Inherent PL emission
Metal nanoparticles are known to have inherent PL , . Mooradian was the first to report the experimental detection of single-photon excited PL from noble metals in 1969 , where PL was observed as the background noise in SERS. The luminescence of metal results from several steps of complex interband electronic transitions , . Metal nanostructures attract particular interests because of their promising emission properties in terms of outstanding photostability under continuous irradiation, no blinking effects, and the benefit of good biocompatibility. Additionally, metal nanoparticles are advantageous with the ability to tailor the absorption band by modifying the particle geometry (nanospheres, nanoshells, nanorods, nanostars) for specific applications. Both single-photon and multiphoton PL of metal nanoparticles have been shown to correlate strongly with their plasmon resonances , , , , and they have both been applied to biological imaging.
One interesting example of single-photon PL is to image cancer cells using gold nanoparticles as fluorescent probes engulfed via the endocytic pathways . Due to the exceptional photostability of plasmonic nanoparticles, when the cellular autofluorescence is bleached by strong laser illumination, the nanoparticle PL is unaffected, thus avoiding crosstalk between them.
It is well known that, compared to single-photon confocal techniques, the incorporation of multiphoton imaging techniques provides additional advantages of improved cell viability ,  and deep tissue imaging capabilities . Boyd et al. have first demonstrated enhanced 2PL emission efficiency from a rough metal surface with respect to a flat one . The mechanism of 2PL in the nanoparticles can be explained by the same electronic transition processes as in surfaces . In general, 2PL is much weaker than single-photon luminescence. However, the weak 2PL signal gets amplified substantially in plasmonic material due to the resonant coupling of the incident light wavelength with localized SPR .
In terms of biological applications, plasmonically resonant 2PL from gold nanorods are particularly attractive, because their longitudinal plasmon modes can be tuned to be resonant at near-infrared (NIR), where the absorption of water and most biological molecules is minimized. Wang et al. have reported 60-fold brighter 2PL from gold nanorods than the two-photon fluorescence from a single rhodamine molecule. They have successfully demonstrated the use of 2PL to monitor the flow of individual nanorods through mouse ear blood vessels in vivo . They have also argued that nanoparticles with a variety of shapes, including nanosphere, nanorods, nanoshells, and nanocages, can be internalized in macrophages for the in vivo monitoring of their dynamics in atherosclerosis and cancer , .
Recently, sophisticated 2PL correlation spectroscopic detection was adopted to detect gold nanoparticles dispersed in water and flowing through a microfluidic channel that mimics the mammalian blood capillaries . Other than nanorods, 2PL from gold nanoshells is as bright as their nanorods counterparts, also tunable by particle geometry, and has been reported for imaging subcutaneous tumor in vivo (Figure 3C1) . Very recently, multimodal gold nanostars for 2PL, SERS, X-ray computed tomography, and photothermal therapy of tumor have been reported. 2PL from the nanostars was used to monitor nanoparticle distribution at the cellular level inside a tumor .
To distinguish the 2PL of a metal nanoparticle from cellular autofluorescence, one possible way is to bleach the latter, as we mentioned earlier. An interesting possibility is to adopt luminescence lifetime measurement, because, compared to cellular autofluorescence or dye molecule fluorescence, gold nanoparticles have much shorter PL lifetime. Figure 3D presents the two-photon intensity (Figure 3D1) and fluorescence lifetime (Figure 3D2) images of lymphoma cells labeled with gold nanoparticles (yellow color) and H258 dye (blue-green color) at the membrane and the nuclear region, respectively , manifesting their clear distinction in lifetime domain.
With the exceptionally strong resonance nature of SPR, not only 2PL but also 3PL from metal nanoparticles were reported , . Bright 3PL from gold and silver alloy nanocage were reported for in vivo liver cell imaging with negligible photothermal toxicity and thus excellent cell viability . It is known that higher-order nonlinear signal is better for deep tissue imaging because of not only long excitation wavelength but also the background reduction , . Because the three-photon emission of fluorophores is typically weak, plasmonic particles may be an alternative candidate for three-photon deep tissue imaging. The idea is nicely demonstrated in a very recent paper, where 3D reconstructed intravital in vivo 3PL imaging of gold nanorod-stained mouse brain blood vessels is presented. High-contrast images are obtained as deep as 600 mm, as shown in Figure 3C2 .
Gold nanorods were also reported as probes for selectively imaging live cells with ESA microscopy . Unlike 2PL/3PL microscopy, where contrast comes from luminescence emission, in ESA microscopy, contrast originates from the variation of absorption (loss of transmission). To efficiently decouple weak absorption variation from huge transmission signals, two laser beams along with lock-in detection are generally required for ESA microscopy. The advantage of this relatively complicated set-up is the significantly enhanced sensitivity toward nonfluorescent nanostructures. In the cited work, the location of gold nanorods in cells can be distinguished even under the presence of a strong fluorescence background. Plasmonic nanostructures, including noble metal and graphene, are known to exhibit a large ESA effect or a transient absorption in a more general sense , . A noteworthy recent demonstration adopted the saturation of transient absorption in graphene to enhance spatial resolution beyond the diffraction limit without the need of fluorescence . Besides, ESA has been used to image nonplasmonic nanomaterials, such as carbon nanotube and nanodiamond . Although the technique is still in its infancy, it already shows great potential for future biological applications with plasmonic or nonplasmonic nanostructures.
4.3 Near-field imaging by inherent nonlinear emissions
As mentioned in Section 3.4, NSOM is a field where nonlinear plasmonics has extensive applications. Based on the “lightning rod” effect and due to plasmon resonance, immense near fields are generated at the apex of a sharp metal tip, which is able to initiate inherent nonlinear optical process . Here, we focus on inherent nonlinear signals from the NSOM tip. It is found that, when a sharp gold tip is excited with 780 nm femtosecond pulses, nonlinear inherent PL, as well as SHG, is generated , . The inherent emission spans across the visible and NIR regions, forming a highly confined white-light continuum source and exhibiting potential for multispectral imaging for near-field applications.
The same group later expands the concept. They investigated the nonlinear optical properties of gold nanoparticle dimer, which exhibits large field enhancement at its junction , . Using two ultrafast lasers at different wavelengths, multiple inherent second- and third-order nonlinearities are induced, including SHG, sum frequency generation, and FWM, significantly expanding the functional wavelength ranges of the plasmonic NSOM. Figure 3E displays the near-field fluorescence imaging of monodispersed red fluorescent particles, of size 40 nm, with this dimer probe technique along with topographic fluorescence image.
Very recently, the inherent linear PL, 2PL, and SHG from gold nanotips are used to achieve background-free nonlinear hyperspectral imaging for gold nanostructures, with resolution down to 30 nm . They have demonstrated a very nice correlation between the tip-sample coupling and sample topography, as shown in Figure 3F1 and F2.
Such tip-generated inherent signals may find applications toward the nonlinear near-field high-resolution imaging of biomolecules. From the above discussion, some of the plasmonic tips have been used in biology, whereas some are not yet. There is still a lot of room left for researchers to explore in this field.
5 Inherent nonlinearity of SPR scattering
In this section, we introduce a very different inherent nonlinearity: saturation and reverse saturation of SPR scattering from a single nanoparticle and its applications toward the resolution enhancement of optical microscopy. The linear scattering of metal nanoparticles, which can be derived from the Mie theory, has been extensively used for biological applications, such as the detection, imaging, or treatment of cancer cells , , , , . However, the resolutions of these applications, which all belong to far-field optical imaging, are limited by diffraction. Recently, several groundbreaking ideas revolutionized this field with greatly enhanced resolution, which was recognized by the Nobel Prize of Chemistry in 2014. These ideas overcome the diffraction barrier by the switching , ,  or saturation , ,  of fluorescence. However, these super resolution techniques are all based on the nonlinear responses of fluorophores under intense laser irradiation, and existing fluorescence molecules quickly bleach under intense laser irradiation. It puts a stringent constraint to fluorophore selections ,  and requests more robust contrast agents , . Therefore, it is highly desirable to search for a novel contrast agent that does not bleach.
One of the most appealing candidates is the extraordinarily strong scattering from SPR structures. Nevertheless, the nonlinearity of scattering from a single particle has not been observed until very recently , . Our group has demonstrated that scattering signal from even a single gold nanoparticle can be saturated by an intense laser light when the wavelength matches the SPR band of the nanoparticle. The saturated and unsaturated part of the point spread function (PSF) of the nanoparticle can be distinguished to achieve resolution beyond the diffraction limit , . The inherent nonlinearity of the gold nanoparticle can be described by the variation of RI with incident intensity:(3)
where n is the total RI, no is the linear RI of the particle, and n2 is nonlinear RI due to field enhancement condition. By assuming that the scattering signal comes from the real part index mismatch Dn between the metallic nanoparticle and the surrounding medium, it is straightforward to express the linear and nonlinear scattering coefficients in terms of linear and nonlinear index mismatch. Apparently, when n2 is negative, the saturation of scattering occurs.
When the signals saturate, we adopt saturated excitation (SAX) microscopy to enhance the spatial resolution . The principle of SAX microscopy is that, for a laser focal spot, the intensity is stronger at the center than at the periphery. Thus, the saturation should start from the center, whereas the periphery remains unsaturated, as described schematically in Figure 4A. By extracting only the saturated part (i.e. only the central part is left while rejecting the peripheral part), the spatial resolution is effectively enhanced. In SAX implementation, temporal modulation is added onto the excitation source. The scattering signal from the periphery follows the modulation frequency linearly, whereas that from the center does not due to saturation (Figure 4A, right). Transforming the signal into frequency domain, the linear signal in the periphery exhibits only one peak at modulation frequency, but the nonlinear (saturated) signal in the center results in harmonic components. By selectively collecting higher harmonic signals with a lock-in amplifier, and forming an image by scanning the laser beam across the sample, Figure 4B demonstrates resolution enhancement based on scattering from individual gold nanoparticles. Figure 4B1 to B3 corresponds to scattering images constructed by detecting 1fm, 2fm, and 3fm signals, respectively. A white arrow indicates two closely packed nanoparticles that cannot be resolved in Figure 4B1 but can be clearly distinguished with higher harmonic components. The line profiles of single-particle PSFs are given in Figure 4B4, showing a quantitative reduction of full-width at half-maximum (FWHM) to λ/8, which is much smaller than the diffraction limit.
Without SAX set-up, from the confocal PSFs of well-separated gold nanoparticles with increasing excitation intensity, we find that the inherent nonlinearity of scattering exhibits not only saturation but also reverse saturation, as shown in Figure 4C. In Figure 4C1, when the excitation intensity is low, a very nice Gaussian profile is observed, manifesting the linear response. In Figure 4C2, at high intensity, saturation occurs, so the scattering intensity at the center part becomes weaker than in the periphery. Very interestingly, in Figure 4C3, at higher intensity, scattering at the center dramatically increases, resulting in a narrow peak with FWHM on the order of 100 nm. The scattering versus excitation intensity dependence is drawn in Figure 4C4, showing complicated nonlinear behavior. Although the nonlinearity can be quantitatively expressed by a polynomial expansion similar to Eq. (2) , the underlying mechanism is still under investigation . Because the scattering of nanoparticles has been adopted as a contrast agent for biological imaging, our finding of resolution enhancement based on single-particle scattering paves the way toward subdiffraction limit and long-term observation of biological samples.
Nonlinear plasmonics is a young subject and its applications toward bioimaging is still at an early stage. In this mini-review, we have covered the recent progress of plasmonics in nonlinear optical microscopy and their potential biological applications. The intention is to encourage interdisplinary understanding and collaborations. We have addressed the advancement of imaging modalities, including SHG/THG, 2PL/3PL, and incoherent/coherent Raman scattering that are amalgamated with plasmonics, as well as novel subdiffraction limit imaging techniques based on the saturation of plasmonic scattering.
There are two aspects of nonlinear plasmonics, one is the enhancer of nonlinear phenomena within nonplasmonic materials and the other is the inherent nonlinear generator. For the former case, plasmonic field enhancements expedite all the nonlinear processes, allowing the detection of extremely weak nonlinear signals from cell surfaces and interiors. For example, in Section 3.1, two-photon autofluorescence signals from cells and tissues are enhanced by plasmonic particles. On the contrary, based on inherent nonlinearities, plasmonic particles may serve as multipurpose contrast agents. For example, both gold and silver nanoparticles exhibit multiphoton luminescence and SHG/THG. Recently, gold-coated iron nanoparticles are also reported to play dual roles as plasmonic nanoheater and magnetic resonance imaging (MRI) contrasting agent simultaneously .
Different geometries of nanostructures have been used for nonlinear plasmonic imaging. Plasmonic metal films were used to enhance nonlinear effects, such as Raman scattering, for molecular sensing. Films are useful for large-scale biological investigation, relatively noninvasive for cells, and relatively easy for sample preparation. Additionally, metal films with arranged nanostructures are reported to provide controllable inherent SHG nonlinear property . However, nonlinear enhancement occurs throughout films, with low spatial selectivity. In addition, the enhancement is limited to sample surface, making it difficult for intracellular imaging.
Using metal tips as scanning probes, significant localized field enhancement at the tip can be achieved. Plasmonic tip-enhanced NSOM provides exceptional high resolution down to a few nanometers and is a rapidly growing field in biological imaging. However, near-field phenomena are also restricted to topographic imaging at the surface, and the speed is typically much slower than cellular dynamics. At present, active researches in this field focus on several directions such as optimizing the optical antenna probe in terms of size, gain, directivity, ease of fabrication, reproducibility, etc., and at the same time increasing the pool of probe options. Within our review, we mentioned that several inherent nonlinear processes from plasmonic tips exhibit potential but are yet to be used in high-resolution biological applications. In the future, the unison of plasmonic effect with other scanning probe as well as time-resolved optical techniques will further advance tip-enhanced NSOM with respect to a wide range of applicability, signal enhancement, and spatial resolution.
Compared to films and tips, metal nanoparticles provide a unique advantage of imaging deeper than surface in a cell or tissue. Because of their small dimensions that allow endocytosis, metal nanoparticles are applicable for intracellular or even in vivo observation. The PL emission efficiency of plasmonic nanoparticles is much larger compared to fluorescent molecules, and their toxicity towards cells is much less compared to quantum dots. Hence, nanoparticles can fill the niche of contrast agent between fluorophores and quantum dots. On the contrary, nanoparticles also exhibit their own limitations. Similar to all external labeling, using nanoparticles as contrast agents may interfere with cellular or molecular functions. Compared to fluorescence molecules, nanoparticles are relatively large, so the interference might be stronger. Additionally, during the chemical fabrication of nanoparticles, it is difficult to maintain the size/shape uniformity, leading to varying resonance conditions, which in turn results in inefficient signal enhancement.
Different from PL, only virtual transitions are involved during harmonic generation processes, so the potential heat generation is less and the signal is more stable. One of the future directions is higher harmonic generation signal from gold and silver nanoparticles, which are waiting to be incorporated into the biological imaging domain. As a three-photon phenomenon, plasmonic THG has a huge potential for deep tissue in vivo imaging with minimum background. The tunability of plasmonic band by varying the sizes and shapes of nanoparticles provides a wide spectrum of application possibilities with both luminescence and harmonic generation modalities.
In this review, we have mentioned many different plasmonic nanostructures that have been applied in biology, whereas some are yet to be explored. In terms of materials, although we mainly discussed gold and silver nanostructures as the plasmonic filed enhancer, there are several other potential candidates as evaluated in an excellent review , such as platinum , copper , aluminum , gold- and silver-coated iron , , and graphene, which recently has also emerged as a promising candidate due to its unique electronic properties . On the contrary, some nonlinear optical interactions, such as sum frequency generation, which is very useful to probe non-centrosymmetric structures or molecular vibrational states , have not been combined with plasmonics for imaging. In the future, there are still plenty of opportunities to play with nonlinear plasmonic effects and their applications in biology.
This study was supported by the National Science Council grants NSC-101-2923-M-002-001-MY3 and NSC 102-2112-M-002-018-MY3. This research was also supported by the Japan Society for the Promotion of Science (JSPS) through the “Funding Program for Next Generation World-Leading Researchers (NEXT Program)”, initiated by the Council for Science and Technology Policy (CSTP) and JSPS Asian CORE Program.
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