Nonlinear optical interactions are of fundamental significance for advanced photonic applications, but usually the nonlinearity magnitude is insufficient. Here we review recent progresses to boost the optical nonlinearity of metal or semiconductor nanostructures via the combination of Mie resonance and coupled photothermal/thermo-optical effects. In plasmonic and silicon nanoparticles, the effective photothermal nonlinear index n2 is enhanced by 103 and 105 times over that of bulk, respectively. The large nonlinearities enable applications of not only all-optical switch, but also super-resolution imaging based on suppression of scattering, saturation (sub-linearity) and reverse saturation (super-linearity).
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Nonlinear optical effect is essential in various photonic applications such as optical switching, wavelength conversion, and ultrashort pulse generation [1–4]. In the field of optical microscopy, several super-resolution techniques are developed by exploiting the nonlinear light-material interaction between illumination light and contrast probes [5–7]. However, because the nonlinear optical effect is intrinsically weak, high laser powers are typically required for the excitation, resulting in potential sample damage. Therefore, it is highly desirable to improve the efficiency of nonlinear optical effects.
Plasmonic effect is one well-known approach to significantly enhance optical nonlinearities [1,8,9]. Through surface plasmon resonance (SPR), the collective oscillation of conductive electrons on the metal structure couples with the excitation light and produces a strong local electric field, leading to immensely enhanced nonlinearity, as demonstrated by second harmonic generation [10,11] and four-wave mixing .
Another approach to induce strong nonlinear optical effect is through non-instantaneous light-matter interactions, including intraband transition, interband transition, hot electrons, and hot lattice [13,14]. Pump-probe spectroscopy has been extensively applied to investigate these ultrafast interactions in metallic nanostructures, such as single layer films [15,16], bilayer films , nanospheres  and nanorods . These studies focus on nonlinear optical responses on the picosecond time scale, where carrier generation and relaxation dynamics dominate. By measuring the absorption cross-section of these materials in spatial modulation spectroscopy, the density of excited carriers can be precisely calculated, and the nonlinearity of the optical response is quantified [17,20]. On the other hand, there are nonlinear nanophotonics studies using nanosecond pulses , where the hot lattice shall play a major role. In this review, we mainly address hot lattice induced nonlinear responses excited via continuous-wave lasers.
Typically, non-instantaneous nonlinearity is characterized by the variation of refractive index n = n0+n2I, where n0 is the linear refractive index, I is the intensity of incident light and n2 is the nonlinear refractive index coefficient. The nonlinear index n2 of bulk gold ranges from 10−7 µm2/mW (intraband) to 10−3 µm2/mW (hot lattice) . Although the hot lattice nonlinearity, i.e., photothermal nonlinearity, is much larger than the instantaneous Kerr nonlinearity (effective n2 ∼ 10−7 µm2/mW), the meaning of 10−3 µm2/mW is that to achieve index modulation of 50%, i.e., n0 = n2I, the excitation intensity needs to be on the order of 103 mW/µm2. Therefore, considerable efforts to enhance the nonlinear optical effect have been demonstrated, e.g., the uses of waveguide structures to accumulate nonlinear response along with beam propagation . In the past few years, we have shown that by combining plasmonic field enhancement with photothermal/thermo-optical interactions, the nonlinear optical response of a metallic nanostructure can reach n2 of ∼1 µm2/mW, which is three orders of magnitude higher than that of bulk, and allows operation with a low-power continuous-wave laser in a single nanoparticle. Note that n2 is not an inherent parameter of the material because the value of n2 may change depending on the measurement system and material structures. The reason we adopt n2 here is to provide a convenient magnitude comparison of nonlinear responses between bulk and nanostructures.
Before we dive into the nonlinearity review, the readers should be aware that the photothermal effect does not necessarily induce nonlinear optical responses. It is well known that “linear” photothermal effect of metallic nanoparticles has been utilized for high sensitivity optical imaging , biological treatment, and various other applications . One particular emphasis is photothermal microscopies, including thermal lens imaging , photothermal interference contrast imaging , and photothermal heterodyne imaging [26–28], construct the image contrast by detecting the photothermally induced refractive index variation of the medium surrounding the nanoparticle. Photothermal microscopy techniques are capable of detecting a single nanoparticle with size as small as 5 nm , and study molecular dynamics such as the membrane proteins with unprecedented precision and speed by using small nanoparticles as imaging probes [30–32].
Another important application field of the linear photothermal effect is optical thermometry with metallic nanoparticles. For example, the measurement of anti-Stokes emission spectrum from a metallic nanoparticle helps to determine its absolute temperature in a direct way [33–36]. Other methods take more indirect approaches of either detecting the thermal lens effect surrounding the hot nanoparticle [37–39], or observing the thermally induced fluorescence property variation, such as depolarization, from fluorescence molecules around the nanoparticle. [40–42].
In the following, we review recent advances in characterizing photothermal “nonlinearity” of plasmonic nanostructures, including different materials (gold, silver) and geometries (sphere, rod, shell, bowtie). The nonlinearity is identified through the power dependences of scattering on excitation intensities. Typically, the nonlinear power dependences are acquired either by increasing laser irradiation gradually or by retrieving from the signal distribution of the nanoparticle image. The latter method is denoted as “x-scan”, i.e., laser scanning microscopy, which is useful to quantify nonlinear scattering and absorption [43,44]. Similar to z-scan , a focused Gaussian beam is required, but different from z-scan, the focused beam scans laterally across a single nanoparticle, which is much smaller than the focal spot. When there is no nonlinear response, a scanning image with Gaussian distribution is expected (in z-scan, it is constant transmission). When nonlinearity takes place, the image intensity distribution profile deviates from the Gaussian profile, and the deviation directly facilitates the nonlinear coefficient characterization.
In Section 2, we present the mechanism of the photothermal/thermo-optical nonlinearity of plasmonic particles. In Section 2.1 and 2.2, two application examples will be given. The first one is high-efficiency all-optical switching, which is a long-standing goal in the field of nonlinear optics. The second one is super-resolution microscopy, which is much less considered in typical nonlinear optics literature, and we hope to stimulate more interesting applications from our efforts. In addition to plasmonics, in Section 3, we introduce our recent discovery of giant photothermal nonlinearity in silicon nanostructures, featuring five orders of magnitude enhancement over silicon bulk photothermal nonlinearity, as well as the corresponding applications. Section 4 offers discussion of overall potentials and limitations of photothermal/thermo-optical nonlinearity in future applications.
2. Photothermal nonlinearity of plasmonic scattering
It is well known that plasmonic nanoparticles display saturable and reverse saturable absorption [46–48]. In 2014, it was discovered that scattering intensity from a plasmonic nanoparticle exhibits saturation behavior [49,50]. The effect can be illustrated by considering the scattering cross-section of a plasmonic nanoparticle, based on quasi-static approximation of the classical Mie theory, as below:
Experimentally, Figs. 2(a) and 2(b) show that scattering intensity from the single gold nanoparticle significantly reduces as the temperature increases via the irradiation of CW laser and heating of a hot plate, respectively , confirming the photothermal nature of the saturation behavior. Figure 2(c) presents saturation of scattering (SS) from a single gold nanosphere, with three excitation wavelengths. The 532 nm one is close to the SPR peak (∼580 nm), and the required excitation intensity to induce SS is the lowest. The 671 nm one is located at the tail of the broad SPR band, so SS is still observable. Nevertheless, the 405 nm is outside the SPR band, and no saturation is found even at high intensity, manifesting the strong correlation between SS and localized SPR.
To account for the photothermal/thermo-optical effect, a self-consistent model is developed , via solving Maxwell and heat equations iteratively with experimentally measured temperature-dependent permittivity of metal [53,57]. More recently, by relaxing the quasi-static approximation with a purely numerical approach, the theory approaches better quantitative agreement with experimental results as shown in Fig. 1(b) . Through considering the host medium heating, it improves the agreement between the theory and the experimental result. One useful approach is the effective medium technique at nanoscale heating, as manifested in a pioneer study . In this linear photothermal study, they consider the effective dielectric constant as the ratio of volume-averaged electric displacement to volume-averaged electric field. This should be included in future theoretical explorations.
The nonlinearity of plasmonic scattering is observed not only for a gold nanosphere but also for various materials and structures. The photothermal effects of particles with non-spherical shapes and of different materials may be studied with the aforementioned numerical approach . Figure 2(d-f) respectively show ubiquitous nonlinear scatterings from silver nanosphere, gold nanorod, and gold nano-bowtie . The red lines in the figures represent linear extrapolation of scattering at low excitation intensity (Se), and the value ΔS denotes the difference between the experimental data and Se at high excitation intensity. The nonlinear deviation ratio (NDR) is defined as ΔS/Se, and it serves as an intuitive indication of the nonlinear magnitude. As the excitation intensity increases, the NDRs of each nanostructure show negative values, reaching at least 50%, indicating strong SS. Interestingly, in Figs. 2(d) and 2(e), at high excitation intensities, we found reverse saturation of scattering (RSS), which may directly modulate the scattering images in x-scan (Section 2.2.3). In the subsections below, we present photonic applications, including all-optical switching and various super-resolution imaging, based on SS and RSS .
2.1 Application 1: all-optical switching
We utilized the SS of plasmonic nanoparticles to realize all-optical switching of scattering response from plasmonic nanoparticles. When SS is induced, the nanoparticle scattering intensity does not increase with growing illumination photons, creating an effective “off-state”. The photothermal suppression of scattering is valid within the whole SPR spectrum, as shown in Figs. 2(a) and 1(b). This inspires us to use two simultaneous illumination wavelengths, as shown in Fig. 3: one (λ=543 nm) induces scattering, and the other (λ=592 nm) suppresses scattering, to achieve all-optical switching in a single gold nanoparticle.
In Fig. 3(a), when the intensity of the 592 nm beam is low, i.e., in the linear regime (blue region), the scattering of the 543 nm beam is not affected by the irradiation of the 592 nm beam, as expected. Interestingly, when the 592 nm beam is strong enough to induce SS of the nanoparticle (green region), the scattering intensity of the 543 nm beam drops quickly as the 592 nm beam intensity increases. Figure 3(b) shows that the all-optical modulation depth is up to 90%, and is fully reversible and repeatable.
2.2 Application 2: super-resolution imaging
2.2.1 Plasmonic SAX microscopy
By exploiting SS of plasmonic nanoparticles in Fig. 2, we developed plasmonic saturated excitation (p-SAX) microscopy to improve the spatial resolution beyond the diffraction limit [49,59,60], featuring the first super-resolution imaging based on (plasmonic) scattering. In a laser scanning microscope, the illumination focal spot exhibits a Gaussian intensity distribution and thus the center of the focal spot should reach SS before the peripheral [6,61]. The underlying principle of resolution improvement by SAX microscopy is to distinguish between the saturated and linear signals via temporally modulating the excitation intensity, and demodulating the scattering signal at harmonic frequencies . Figure 4(a) shows the SEM image and p-SAX images of gold nanospheres reconstructed by the scattering signals demodulated at fm, 2fm and 3fm, manifesting the improvement of the spatial resolution (highlighted by the arrow) down to λ/8 of excitation wavelength in the image reconstructed by nonlinear signal. The arrowheads indicate aggregated particles whose SPR wavelength may shift toward long wavelength, and 2fm/3fm signal of the 532 nm scattering vanishes, i.e., diminishing nonlinear response. In Fig. 4(b), with a large (aggregated) structure, p-SAX helps to identify localized hot spots with improved resolution, as shown in Fig. 4(b).
One advantage of p-SAX microscopy is the potential to achieve super-resolution imaging in deep tissue. A long-standing challenge in microscopy is the trade-off between spatial resolution and imaging depth [62–64], in particular most super-resolution tools only allow thin cell observations, not thick tissues. SAX microscopy improves spatial resolution via temporal modulation and demodulation, which is less affected by tissue scattering and aberration. It was demonstrated that visible p-SAX microscopy enhances spatial resolution by three folds in biological tissues throughout a 200 µm objective working distance . To further extend the penetration depth, we developed near-infrared p-SAX microscopy based on nonlinear scatterings from gold nanoshells and gold nanorods, providing both contrast and resolution enhancement over 400 µm depth in a tissue phantom, as shown in Figure 4(c) .
2.2.2 Suppression of scattering imaging (SUSI)
In Section 2.1, we discussed the all-optical switching application of the nonlinear plasmonic scattering. It is well known that all-optical switching of fluorescence enables super-resolution imaging via stimulated emission depletion (STED) microscopy, which uses a donut beam to suppress spontaneous fluorescence emission . Based on a similar concept and setup, we developed suppression of scattering imaging (SUSI) to achieve super-resolution with scattering . Figure 5(a) and 5(b) show the scattering image of gold nanospheres obtained by using conventional confocal microscopy and SUSI, respectively. As indicated by white arrows in the images, two adjacent gold nanospheres are only distinguishable with SUSI in Fig. 5(b). Figure 5(c) shows that the resolution can be further enhanced via deconvolution.
Numerous studies have adopted plasmonic nanoparticles as imaging and biosensing contrast probes for biomedical applications, offering flexible spectral tunability, high signal contrast, non-bleaching, and good biocompatibility . The SUSI approach provides an opportunity to break the diffraction limit in cell/tissue imaging with plasmonic nanoprobes. Figure 5(d) and 5(e) are respectively conventional confocal microscopy and SUSI images of a tumor cell (Human Osteosarcoma MG-63) stained with gold nanospheres, demonstrating the improvement of spatial resolution in SUSI .
2.2.3 RSS and super-linearity
In Fig. 2, we have shown that plasmonic scattering of a silver nanosphere and a gold nanorod exhibit RSS. Figure 6(a) presents RSS (the red region) of a gold nanosphere, which has super-linear power dependency that leads to super-resolution capability without additional temporal or spatial modulation [50,70]. In a laser scanning setup, the scattering images of a single nanoparticle show dramatic change due to these nonlinear power dependencies, as illustrated in Fig. 6. Figure 6(b) shows that when the scattering intensity linearly responds to excitation intensity, the signal distribution of the nanoparticle image corresponds to a Gaussian function. In Fig. 6(c), by increasing excitation intensity into the saturation regime (green region in Fig. 6(a)), the image distorts at the center, where the SS starts, resulting in a larger image FWHM than that of Fig. 6(b). Interestingly, near the particle center, deep SS induces side lobes with 40 nm width, which is much smaller than the size of the diffraction limited focal spot (∼200 nm). Figure 6(d) shows that at high excitation intensity, scattering displays super-linear power dependency through RSS, leading to significant FWHM reduction to 100 nm, demonstrating the potential for straightforward super-resolution imaging.
3. Photothermal nonlinearity of silicon nanoparticle
In addition to plasmonics, high index dielectric nanomaterials attract lots of interest due to their diverse electromagnetic Mie resonances. Among various materials, silicon receives particular attention because of its natural abundance and its compatibility with modern industrial production lines. However, compared to metals, the nonlinearity of silicon is smaller (Kerr n2 ∼ 10−9 µm2/mW , photothermal n2 ∼ 10−6 µm2/mW ). Following the discussion in Section 2, Mie resonance may significantly enhance the photothermal nonlinear response through self-induced thermo-optical effect. Since Mie-resonance-enhanced absorption induces temperature rising, temperature rising affects permittivity, and permittivity change in turn causes resonance shift and absorption efficiency variation, it is necessary to develop a recursive analytical model to quantify the local temperature and the absorption/scattering spectra, as shown schematically in Fig. 7 .
Recently, systematic studies were carried out on the photothermal nonlinearity of silicon nanostructures, and discovered a giant nonlinear refractive index n2 ∼ 0.1 µm2/mW, as shown in Fig. 8, featuring five orders of magnitude enhancement over that of bulk silicon . Figure 8 shows the real and imaginary parts of refractive indices under different laser excitation intensities of silicon nanoblocks with different widths. Note that the dependences of refractive indices on excitation intensity are strongly size dependent, thus the usage of the effective photothermal nonlinear index n2 must take into account this structural dependency.
The photothermal nonlinearities of silicon nanoblocks with 100-200 nm width and 150 nm height are summarized in Fig. 9. Figure 9(a)–9(c) presents various optical nonlinear behaviors, including saturation (sub-linear), reverse saturation (super-linear), and deep saturation (negative slope), respectively, in silicon nanoblocks with different sizes (all excited at 561 nm). The insets show the signal distribution of the nanoparticle image under low and high excitation intensities. NDRs of scattering intensity are calculated by using the same definition in Section 2.
Figure 9(d)–9(f) are corresponding simulations based on iterative calculations with Maxwell and heat equations, similar to what we mentioned in Section 2. Exceptionally well correspondences are found between experiments and simulations, manifesting that the underlying mechanism can be fully explained by the spectral red-shift of the Mie resonance (see insets) due to photothermally rising refractive index. That is, if the excitation wavelength is at the blue side of a resonance peak, the scattering exhibits SS (Fig. 9(d) and (f)). On the other hand, if the excitation is at the red side of a peak, the scattering dependency becomes super-linear (Fig. 9(e)).
3.1 Application 1: all-optical switch
Similar to the plasmonic all-optical switch in Section 2.1, the saturation behaviors of a single silicon nanoblock allow efficient all-optical switching based on scattering . Figure 10(a) presents that the 543 nm scattering from a silicon nanoblock is efficiently controlled via a 592 nm suppression beam, showing modulation depth as high as 90%, and full repeatability. Compared to conventional resonant structures, such as microring resonator or photonic crystal [74,75], the Mie-resonant all-optical switches made of plasmonic and silicon both provide greatly reduced footprint, on the order of 0.001µm3.
Conventionally, thermo-optical nonlinearity is not preferred in optical modulation applications due to the slow heat dissipation at milli- to microsecond scale . In this work, by reducing the size of silicon structure to the nanoscale, the lifetime of optical switching reduces down to nanoseconds. Figure 10(b) shows the temporal response of the silicon all-optical switch, either measured by pump-probe microscopy (black line) or calculated from the photothermal simulation (color dots). Both the experiment and the simulation manifest that the photothermal relaxation time of silicon nanoblock is about 1 nanosecond, featuring the potential for GHz operation.
3.2 Application 2: super-resolution imaging
3.2.1 SAX microscopy
The nonlinear scattering responses of silicon nanostructures are also applicable to super-resolution imaging. Similar to Section 2.2 of plasmonics, one strategy is to combine SS and SAX microscopy. Figure 11(a) and 11(b) show scattering SAX images of a single silicon nanoblock, reconstructed by the signals demodulated at fm, and 2fm. The image size of a silicon nanoblock reduces 2.3-fold in Fig. 11(b) compared to Fig. 11(a), as quantitatively depicted in Fig. 11(c).
Based on the idea of SUSI, Xiangping Li’s group performed super-resolution imaging of silicon nanodiscs by suppressing scattering signals with a donut beam . The donut beam contains azimuthally polarized light, which is capable of efficiently heating up the nanodisk through magnetic dipole resonantly enhanced absorption to suppress the scattering. Figure 12(a) shows the SEM and the scattering images of the silicon nanodisk array, demonstrating better and better resolution obtained at growing intensities of the azimuthally polarized donut beam. Figure 12(b) characterizes the FWHM reduction of silicon SUSI, featuring values down to ∼50 nm.
3.2.3 RSS via anapole
As mentioned in Section 2.2.3, the super-linearity with RSS creates a sharp peak in the center, and itself may lead to resolution enhancement. In the case of silicon, which may exhibit anapole resonance that has diminishing scattering, the RSS can be particularly evident, as shown in Fig. 13(a) . Here a silicon nanodisk with 200 nm diameter and 50 nm thickness is excited with a 532 nm laser, which is located at the red side of the anapole resonance. At low laser intensity, the scattering is linearly proportional to excitation. With increasing laser intensity, the nanodisk resonance shifts into anapole, i.e., deep saturation with scattering drops to nearly zero (SS in Fig. 13(a)), and subsequently into bright mode again, leading to sharp RSS.
Figure 13(b)–13(d) show the laser scanning scattering images of a single silicon nanodisk, in the state of linear, RSS, and SS, respectively. As we expected, SS creates a scattering zero in the image center and RSS produces a sharp peak in the center, but the latter is surrounded by a donut of linear scattering with comparable scattering strength. Borrowing the idea from differential SAX microscopy , Fig. 13(e) presents that the localization precision can be enhanced to ∼40 nm through subtracting Fig. 13(d) from Fig. 13(c), offering an interesting potential for super-resolution imaging of silicon nanostructures.
4. Discussion and summary
In this review, we introduce our recent studies on the photothermal nonlinearity of scattering response from plasmonic and silicon nanostructures. We first review the photothermal nonlinearity that occurred in various kinds of plasmonic material and geometries in Section 2. The combination of the field enhancement by plasmonics and photothermal effect offers giant nonlinearity with n2 approaching ∼1 µm2/mW, leading to potential applications in all-optical switching and super-resolution imaging, as we demonstrated in Section 2.1 and 2.2, respectively.
One concern in the plasmonic nonlinear response is that metal nanoparticles, in particular the non-spherical ones such as the nanorods, might be prone to thermal surface melting and reshaping under intense illumination, and in turn significantly affect the optical properties [80,81]. Currently, there is no direct evidence to ensure no surface reshaping during the nonlinear scattering responses of non-spherical gold nanostructures (Fig. 2(e) and 2(f)). However, the reversibility and the repeatability of the nonlinear scattering in gold nanorod has been experimentally confirmed , implying that irreversible damage is not induced. A better morphology characterization through electron microscopy before and after illumination shall be considered in the future. In addition, nano-thermometry based on the measurement of anti-Stokes emission  should be an effective method to investigate the temperature rise of the gold nanorod, offering quantitative evaluation of not only photothermal effect, but also the potential of surface reshaping. Recent review by Hashimoto et al. provides a summary of previous studies of nanoparticle reshaping using pulse lasers and shows the required laser power threshold . However, particle reshaping induced by continuous-wave lasers has not been enough studied and remains as a future work.
In Section 3, we present the photothermal nonlinearity of silicon nanoparticles. With the aid of Mie resonance and photothermal nonlinearity, silicon nanostructures exhibit nonlinearity with a comparable magnitude to that of plasmonic materials. In a similar manner to the plasmonic nanostructure, it was demonstrated that the nonlinearities of silicon nanostructures are capable of achieving optical switching and various super-resolution microscopy modalities.
The thermo-optical nonlinearities of both plasmonic and silicon nanostructures are enhanced significantly by Mie resonance. However, the Q-factor of typical Mie-resonance is only on the order of 10, which determines the slope in saturation and reverse saturation in the scattering intensity curves (Figs. 2 and 9). It is envisioned that if high-Q resonant nanostructures are adopted, the effective optical nonlinearity can be further enhanced. For example, symmetry-broken nanostructures may provide Q-factor well above 1000 , which could lead to two orders of magnitude enhancement on nonlinear scattering responses, as well as the all-optical switch efficiency.
Although both nonlinear scatterings from metal and silicon nanoparticles are based on the photothermal effect, the dominant factors that affect the nonlinearity could be different. For metal nanoparticles, the SPR peak exhibits mainly amplitude reduction, along with little spectral shift under intense laser illumination (Fig. 2(a) and 2(b)). Therefore, the excited electromagnetic multipole composition keeps the same, implying that the directionality of its scattering remains unchanged. On the other hand, for silicon nanoparticles, the scattering spectrum experienced both amplitude change and spectral red-shift (Fig. 7(d-f) insets), thus the excited multipole composition changes as excitation intensity increases. Therefore, the directionality of scattering waves from the silicon nanoparticle varies at elevated temperature and the nonlinearity of detected scattering intensity is affected by the collection optics.
Another important factor accounting for the nonlinear scattering is the polarization of incident/scattering light. Manipulating the multipole resonances inside the nanostructures by excitation field profile has been a rigorous topic in the field of nanophotonics. For example, tightly focused cylindrical vector beams have the capability to selectively excite electric/magnetic multipoles owing to their unique field profiles [84,85]. Most of the studies introduced in this review focused on non-polarized detection methods. Based on the vectorial scattering behavior of the multipoles, polarization dependent detection may be introduced to tailor the nonlinear signals in the future.
The local intensity of the excitation source may also influence the scattering nonlinearity. In most cases, the full-width-at-half-maximum of the excitation field is much larger than the particle size and there is no intensity gradient sensed by the nanostructure. However, it is possible that when the full-width-at-half-maximum of the excitation field is comparable to nanostructure’s size, the intensity gradient inside the focus affects the scattering behavior owing to the strong field confinement caused by Mie resonance. We expect future studies to unravel the local intensity interactions.
In addition, the optical interference between nanoparticle scattering and the reflection from the substrate shall be considered as another influential factor for signal measurement. In most of the experiments shown in this review, the interface reflection from glass substrate was eliminated by immersing the nanoparticle in index matching oil, and therefore the effect of interference is negligible. On the other hand, it is well known that efficient use of the interference effect enables high sensitivity detection of small scatterers, as demonstrated in interferometric scattering (iSCAT) microscopy [86,87]. More studies would be necessary to further explore how the interference can affect the measurement of nonlinear scattering when observing the nanoparticles under air or water ambiances.
The photothermal/thermo-optical nonlinearities enable several kinds of super-resolution techniques that are capable of reducing imaging FWHM and improving spatial resolution in scattering mapping of plasmonic and silicon nanostructures. These reversible and contactless techniques are expected to facilitate label-free inspections of plasmonic and silicon nano-devices. For example, Fig. 4(b) shows that p-SAX microscopy observes the hotspot regions with highly enhanced near-field intensity in aggregated gold nanoparticles. Figure 12 and 13 present that SUSI and super-linear subtraction resolve a closely packed silicon nanodisk array. In the future, we anticipate that SAX microscopy may similarly resolve the hotspots in complicated silicon nanostructures, i.e., visualizing near-field intensity distribution through far-field imaging. In addition, one most straightforward method to achieve super-resolution imaging is super-linear excitation emission (SEE) microscopy, which has been demonstrated with fluorescence emission . We have shown that the scattering of both plasmonic (Fig. 2(d)–2(f) and 6(a)) and silicon (Fig. 5(b) and 5(e)) nanoparticles exhibit super-linearity, and will combine SEE to improve resolution without the need of image post-processing.
However, practical application of these super-resolution techniques to biological imaging, especially in living specimens, is still a challenging task particularly because of the heat generation from nanoparticle probes. According to experimental  and theoretical  results, when gold nanosphere scattering saturates, the temperature rise is estimated to be at least over 50 °C, which may induce thermal damage on not only the biological molecules nearby the nanoparticles, but also the surface coating of nanoparticles, such as protein-ligand and polymer. Having said that, in a tissue imaging environment, it is vital to keep in mind that the temperature rise of a surrounding medium shall be significantly lower than that of the nanoparticle itself because the thermal conductivity of the biological tissues is much lower than that of a metallic nanoparticle, and the thermal load might not be as high as expected. To further reduce heat generation from nanoprobes, one potential future direction is to improve the resonance quality factor of the scattering spectrum through engineering the dielectric nanoprobe structure and the material . As we discussed in Section 3, the nonlinear scattering from the dielectric nanoparticle is caused by the photothermal/thermo-optical shift of the scattering spectrum. Therefore, with higher quality factor of the scattering spectrum, the required spectral shift, i.e., temperature rise, to induce the nonlinearity of scattering should become lower.
An interesting consideration is the wavelength dependences of the nonlinear strength, as well as the resulting super-resolution capability. As shown in Fig. 2(c), careful wavelength selection is important to obtain optimized nonlinearity. In most of our results, we used 532 nm or 561 nm to excite the gold plasmonic and silicon nanostructures. It is well known that the resonant wavelengths shift with sizes and geometries, and silicon displays a plethora of electric and magnetic multipole resonances. Therefore, we propose that by combining our techniques with a broadband source, such as a super-continuum laser, it is possible to explore nonlinear response and super-resolution observation with various nanostructures, even under the condition of unknown structure and materials.
With this perspective in mind, one important question to solve before practical applications is to understand the fundamental mechanism of scattering-based and photothermal/thermo-optical nonlinear image formation. As shown in Figs. 4(a), 10(a), and 11(e), the super-resolution image sizes can be much smaller than the physical sizes of the nanostructures. In the case of incoherent imaging, such as fluorescence microscopy, the images correspond to the convolution between an intensity point spread function of the microscope and an object, and thus the image never becomes smaller than the size of the object. Nevertheless, in coherent imaging using scattering signals, the image cannot be calculated by intensity convolution, but needs field convolution (amplitude + phase) to take into account the interference effect. The complex image formation due to the coherent nature of scattering signals can be one probable reason to produce images smaller than the physical morphology of the sample.
Another possible explanation is the spatial modulation of scattering cross-section due to the photothermal/thermo-optical nonlinear effect. In a laser-scanning setup, the nanoparticle temperature rise is strongly dependent on the position of the scanning laser spot. Note that in most of our studies, the laser focus spot is larger than the nanoparticle diameters. When the laser focus scans across the nanoparticle, the nanoparticle temperature starts to increase as the focus edge touches the nanoparticle edge, reaches highest temperature as the focal spot aligns with the nanoparticle center, and decreases as the focus moves away to the other edge of the nanoparticle. The temperature variation shall change material refractive index, and result in a modified scattering cross-section. That is, the coupled photothermal and thermo-optical effects are determined by the scanning position, thus leading to scanning-dependent scattering cross-section, similar to the idea of a nonlocal heating effect [89,90]. In this case, the image brightness is more strongly related to the mechanism of nonlinear scattering, such as absorption and local field confinement, rather than the structure of the sample. Therefore, the simple convolution idea in the conventional laser scanning microscopy may no longer be feasible. Further studies are necessary to quantify the nonlinear mechanism and resolution enhancement during laser scanning image formation.
One more unsolved issue, which is worthy of pointing out, is the mechanism behind the RSS of plasmonic nanostructure (note that RSS of silicon nanoparticles is well explained via red shift of Mie resonance at elevated temperature ). The change of scattering intensity from the gold nanoparticle under heating, shown in Figs. 2(a) and 2(b), is a direct proof that the photothermal effect is the dominant mechanism in nonlinear scattering from the gold nanoparticle. However, the simplistic photothermal model used so far is not sufficient to explain the RSS shown in Fig. 6(a). Specifically, the excitation intensity to induce the RSS of the scattering/absorption (e.g., 1.5- 2 MW/cm2 for the gold nanosphere of r=40 nm) is much higher than the excitation level in the current theoretical studies . A quantitative agreement from numerical simulation thus probably requires taking into account the slight metal surface melting or size reduction of the nanoparticle under strong excitation. In principle, plasmonic resonance is sensitive to surface modification, and thus the effect may be studied by developing a new system that can acquire full plasmonic scattering spectra when increasing excitation intensity gradually.
Ministry of Science and Technology, Taiwan (MOST 109-2112-M-002-026-MY3, 110-2119-M-002-010-MBK, 110-2321-B-002-012); The Featured Areas Research Center Program (NTHU and NTU-110L8809) within the framework of the Higher Education Sprout Project co-funded by the MOST and the Ministry of Education, Taiwan (MOE); Japan Society for the Promotion of Science (Core-to-Core Program); National Key Research and Development Program of China (2018YFB1107200); Guangdong Science and Technology Department (2016ZT06D081).
The authors declare no conflicts of interest
Data underlying the results presented in this paper may be obtained from the authors upon reasonable request.
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