Saturable and reverse saturable scattering were discovered in isolated plasmonic particles and adopted as a novel non-bleaching contrast method in super-resolution microscopy. Here the experimental procedures of detecting and extracting nonlinear scattering are explained in detail, as well as how to enhance resolution with the aid of saturated excitation microscopy.
Plasmonics, which are based on the collective oscillation of electrons due to light excitation, involve strongly enhanced local electric fields and thus have potential applications in nonlinear optics, which requires extraordinary optical intensity. One of the most studied nonlinearities in plasmonics is nonlinear absorption, including saturation and reverse saturation behaviors. Although scattering and absorption in nanoparticles are closely correlated by the Mie theory, there has been no report of nonlinearities in plasmonic scattering until very recently.
Last year, not only saturation, but also reverse saturation of scattering in an isolated plasmonic particle was demonstrated for the first time. The results showed that saturable scattering exhibits clear wavelength dependence, which seems to be directly linked to the localized surface plasmon resonance (LSPR). Combined with the intensity-dependent measurements, the results suggest the possibility of a common mechanism underlying the nonlinear behaviors of scattering and absorption. These nonlinearities of scattering from a single gold nanosphere (GNS) are widely applicable, including in super-resolution microscopy and optical switches.
In this paper, it is described in detail how to measure nonlinearity of scattering in a single GNP and how to employ the super-resolution technique to enhance the optical imaging resolution based on saturable scattering. This discovery features the first super-resolution microscopy based on nonlinear scattering, which is a novel non-bleaching contrast method that can achieve a resolution as low as l/8 and will potentially be useful in biomedicine and material studies.
The study of plasmonics has attracted great interest due to its applications in many different fields1-4. One of the most investigated fields in plasmonics is surface plasmonics, in which the collective oscillation of conduction electrons couples with an external electromagnetic wave at an interface between a metal and dielectric. Surface plasmonics has been explored for its potential applications in subwavelength optics, biophotonics, and microscopy5,6. The strong field enhancement in the ultra-small volume of metallic nanoparticles due to localized surface plasmon resonance (LSPR) has attracted extensive attention, not only because of its exceptional sensitivity to particle sizes, particle shapes, and the dielectric properties of the surrounding medium7-10, but also because of its ability to boost inherently weak nonlinear optical effects11. The exceptional sensitivity of LSPR is valuable for bio-sensing and near-field imaging techniques12,13. On the other hand, the enhanced nonlinearity of plasmonic structures can be utilized in photonic integrated circuits in applications such as optical switching and all-optical signal processing14,15. It is well known that the plasmonic absorption is linearly proportional to the excitation intensity at low intensity levels. When the excitation is strong enough, the absorption reaches saturation. Intriguingly, at higher intensities, the absorption increases again. These nonlinear effects are called saturable absorption (SA)15-17 and reverse saturable absorption (RSA)18, respectively.
It is known that due to the LSPR, scattering is particularly strong in plasmonic structures. Based on fundamental electromagnetics, the response of scattering versus incident intensity should be linear. However, in nanoparticles, scattering and absorption are closely linked via the Mie theory, and both can be expressed in terms of real and imaginary parts of the dielectric constant. Under the assumption that a single GNS behaves as a dipole under light illumination, the scattering coefficient (Qsca) and absorption coefficient (Qabs) from a single plasmonic nanoparticle according to the Mie theory can be expressed as19
where x is 2πa/λ, a is the radius of the sphere, and m2 is εm/εd. Here, εm and εd correspond to the dielectric constants of the metal and of the surrounding dielectrics, respectively. Since the form of the scattering coefficient is similar to that of the absorption coefficient, it is therefore expected to observe saturable scattering in a single plasmonic nanoparticle20.
Recently, nonlinear saturable scattering in an isolated plasmonic particle was demonstrated for the first time21. It is remarkable that at deep saturation, the scattering intensity in fact decreased slightly when the excitation intensity increased. Even more remarkably, when the excitation intensity continued increasing after the scattering became saturated, the scattering intensity rose again, showing the effect of reverse saturable scattering20. Wavelength- and size-dependent studies have shown a strong relationship between LSPR and nonlinear scattering21. The intensity and wavelength dependences of plasmonic scattering are very similar to those of absorption, suggesting a common mechanism underlying these nonlinear behaviors.
In terms of applications, it is well known that nonlinearity helps to improve optical microscopy resolution. In 2007, saturated excitation (SAX) microscopy was proposed, which can enhance resolution by extracting the saturated signal via a temporal sinusoidal modulation of the excitation beam22. SAX microscopy is based on the concept that, for a laser focal spot, the intensity is stronger at the center than at the periphery. If the signal (either fluorescence or scattering) exhibits saturation behavior, the saturation must start from the center, while the linear response remains at the periphery. Therefore, if there is a method to extract only the saturated part, it will leave only the central part while rejecting the peripheral part, thus effectively enhancing the spatial resolution. In principle, there is no lower resolution limit in SAX microscopy, as long as deep saturation is reached and there is no sample damage due to the intense illumination.
It has been shown that the resolution of fluorescence imaging can be significantly enhanced by utilizing the SAX technique. However, fluorescence suffers from the photobleaching effect. Combining the discovery of scattering nonlinearity and the concept of SAX, super-resolution microscopy based on scattering can be realized21. Compared to conventional super-resolution microscopies, the scattering-based technique provides a novel non-bleaching contrast method. In this paper, a step-by-step description is given to outline the procedures required to obtain and extract the nonlinearity of plasmonic scattering. Methods of identifying scattering nonlinearities introduced by changing the incident intensity are described. More details will be provided to unravel how these nonlinearities affect images of single nanoparticles and how spatial resolution can be enhanced accordingly by the SAX technique.
1. GNS Sample Preparation
2. Alignment of Home-built Confocal Microscope
3. Characterization of Scattering Nonlinearity
4. Measurement of a Scattering Spectrum of a Single Gold Nanosphere
5. Alignment of SAX Microscope
Figure 6 shows the measured spectrum from an 80 nm GNS. A calculated curve based on the Mie theory is given in the same plot, showing excellent agreement. The LSPR peak is around 580 nm. In the following experiment, the laser wavelength was 532 nm, which was chosen as it is located inside the plasmonic band to enhance optical scattering with plasmonic effect and enable scattering saturation21.
Figure 7 presents scattering images of a single gold nanoparticle at different excitation intensities, and the bottom row provides the line profile of each particle to highlight the nonlinearity. The image size is 600 nm × 600 nm, and the pixel size is 13.8 nm. The acquisition speed was 234,000 pixels per second in the normal xy imaging mode. Each image was averaged over five acquisitions to enhance the signal to noise ratio.
When the excitation intensity is lower than 1.5 × 106 W/cm2, the scattering is linearly dependent on the excitation intensity, so the resulting image of a single nanoparticle resembles the PSF of the excitation beam, with a standard Gaussian profile. However, when the excitation intensity increases to 1.7 × 106 W/cm2, not only clear flattening at the top of the PSF is observed, but also widening of the FWHM, indicating saturation. Very interestingly, at slightly higher intensities, the central intensity becomes lower than the peripheral, resulting in a donut-shaped PSF. Then, as the excitation intensity continues to increase, the scattering intensity increases again, revealing reverse saturation and resulting in a new peak in the center of the PSF.
By plotting the central intensities of the PSFs at different excitation intensities, the scattering intensity dependence is obtained, as shown by the dots in Figure 8. This curve clearly reveals the trends of saturation and reverse saturation behaviors. As expected, it looks very similar to the intensity dependence of nonlinear absorption15-17. Following the typical method of analyzing nonlinear absorption, a polynomial function was used to fit the nonlinear scattering result. However, different from most nonlinear absorption studies, in which third-order nonlinearity is sufficient to model the results, here fifth-order nonlinearity was required to better fit the scattering curve.
As mentioned in section 5, the harmonic frequency components can be experimentally extracted by a lock-in amplifier, and the results are given in Figure 9A. On the other hand, the harmonic components can be calculated from Figure 8. First, use a polynomial function , where I is excitation intensity, to fit Figure 8, so we have the fitting parameters α, β, γ…. We can then express the excitation intensity as a temporally modulated function I(t) = I0(1+cos(2πfmt))/2, where t is time, fm is the modulation frequency, and I0 is the maximum excitation intensity. By substituting I(t) into S(I), and make a Fourier transform to convert the resultant S(I(t)) into frequency domain, we have the following equation composed of multiple delta functions (δ):
The coefficient of each delta function (A0, A1, A2, etc.) represents the amplitude of the SAX signal at the corresponding harmonic frequency. These coefficients, which correspond to the SAX signal strengths at different harmonics, can be written as functions of the fitting parameters α, β, γ…:
The calculation results are shown in Figure 9B. The experimental and calculation plots agree closely, especially in the following two aspects.
First, the curves of 2fm and 3fm are not smooth, showing dips at specific intensities along the curves. In both figures, there are three dips in the 2fm curves, while two dips are seen in the 3fm curves. Second, the slopes are different with different excitation intensities. When the excitation intensity is not high, the slopes of 1fm, 2fm, and 3fm are 1, 2, and 3, respectively. However, after each dip, the slopes of the corresponding nonlinear curves become larger.
With the dips and slope variations, unconventional PSFs are anticipated if the nonlinear components are extracted via the SAX technique, when the excitation intensity increases across the dips. Figure 10A shows the SAX image examples of the 1fm, 2fm, and 3fm frequency components at different excitation intensities. In the first row, the excitation intensity is 0.7 MW/cm2, which is sufficient to induce the nonlinear components, but the amplitude is relatively weak. At this intensity level, the slope of the 2fm signal is 2, and it is 3 for the 3fm signal, as shown in Figure 9A. If the excitation intensity increases to the level of the first dip of the 2fm signal, the SAX images of the 2fm signal become donut shaped, as shown in the second row in Figure 10A. Both the 1fm and 3fm images remain solid, while the FWHM of the 3fm PSF is significantly smaller than that of the 1fm signal, manifesting remarkable resolution enhancement. From the signal profile at the rightmost panel of the same row, the FWHM of the 2fm donut ring is about 110 nm. On the other hand, the third row of Figure 10A shows that when the excitation intensity increases to the first dip of the 3fm signal, only the 3fm image becomes donut shaped, with a 65 nm ring width. At this intensity, remarkable resolution enhancement is found when comparing the 2fm signal to the 1fm one.
Figures 10B and 10C show the calculated PSFs of the 2fm and 3fm signals, respectively, at the corresponding intensities that result in the donut shapes. The calculations were based on the polynomial fitting curve in Figure 9B. The calculated curves well reproduce the features of the experimental PSFs in the rightmost panels in Figure 10A, confirming again the suitability of a fifth-order polynomial fit for the nonlinear scattering.
Figure 1. SEM image of GNSs. By performing the preparation processes described in the first part of the protocol, sufficiently separated GNSs are observed. With more than 100 nm between GNSs, their LSPR effects are not coupled to each other. Scale bar: 100 nm. Please click here to view a larger version of this figure.
Figure 2. (A) Setup of home-built confocal microscope24. (B) xy image with GNSs at focus. 2(c): xz image of PSF with correct alignment. There are two laser sources for this system. One is a 532 nm continuous-wave laser, and the other is a pulsed super-continuum laser. When measuring the scattering signals, a 532 nm continuous-wave laser was used as the source and a PMT as the detector (with a laser line filter inserted). To measure the spectrum, a super-continuum laser was adopted as the laser source and a spectrometer as the detector. The selected laser is sent through a set of neutral density filters to control the excitation intensity. A 50/50 beamsplitter guides the laser into the scanning microscope and allows half of the backward-scattering signals into the PM T or the spectrometer, which is selected by a flipping mirror. In the scanning system, there are two galvano mirrors that form vertical and horizontal raster scanning in the focal plane of an objective. The backward scattering is collected by the same objective and converted into electrical signals by the detectors. The signals are synchronized with the confocal scanning system to form images. The PI stage was used to acquire the xz image by moving the GNSs axially. Please click here to view a larger version of this figure.
Figure 3. Setup of SAX microscopy. Most components are the same as those obtained from a confocal microscope (red rectangle), but sinusoidal modulation was added to the excitation laser beam. Blue rectangle shows modulator setup. First, the excitation laser was divided into two beams and separately sent through two AOMs to produce high-frequency modulations with slightly different frequencies. Then, the two modulated beams were combined to produce sinusoidal modulation at the beat frequency between the two AOMs. Please click here to view a larger version of this figure.
Figure 4. Modulation of combined beams after AOMs measured by oscilloscope. Y1 and Y2 indicate maximum (52.1 mW) and minimum (1.2 mW) values of modulation intensity, respectively. Y2 should be zero to achieve perfect modulation. Current modulation frequency was 10 kHz. Please click here to view a larger version of this figure.
Figure 5. Linearity test of detection system. By placing a cover glass at the focal plane, the reflection of the excitation laser from the glass/air interface was used to check the linearity of the detection system. The signal output versus excitation intensity shows linearity below a readout value of 1-V. Furthermore, the noise level is well below 10-4 V, so the system provides a dynamic range of at least 104. Please click here to view a larger version of this figure.
Figure 6. Scattering spectrum of 80 nm GNS. Red dots indicate experimental measurements, and black line represents calculation from Mie theory. Please click here to view a larger version of this figure.
Figure 7. Scattering images of GNS from linear to reverse saturation. Top row shows backscattering images, and bottom row gives signal profiles of selected nanoparticle at various excitation intensities. Transition from linearity to saturation to reverse saturation is clearly observed. Please click here to view a larger version of this figure.
Figure 8. Scattering intensity versus excitation intensity from single GNS. Blue dots correspond to scattering intensities at center of PSF at different excitation intensities, showing very nonlinear responses, including saturation and reverse saturation. Red curve indicates fit curve based on fifth-order polynomial function. (Images reproduced from Ref. 25.) Please click here to view a larger version of this figure.
Figure 9. Intensity dependences of SAX signals according to (A) experiment and (B) calculation. (A) SAX signals were extracted by lock-in amplifier, and each experimental data point was averaged over four 80 nm GNSs. Dotted lines indicate slopes of SAX signals25. (B) Following protocol 5, SAX signals were calculated based on fifth-order polynomial fit in Figure 8. (Images reproduced from Ref. 25) Please click here to view a larger version of this figure.
Figure 10. SAX images at different excitation intensities. (A) Experimentally observed 1fm, 2fm, and 3fm SAX images at different excitation intensities. Pixel size is 20 nm, and each image size is 750 nm × 750 nm. Intensity profiles of donuts at 2fm and 3fm are plotted in rightmost panels. (B) Calculated image profile of 2fm image at 0.75 MW/cm2. (C) Calculated image profile of 3fm image at 1.1 MW/cm2. (Images reproduced from Ref. 25.) Please click here to view a larger version of this figure.
In the protocol, there are several critical steps. First, when preparing the samples, the density of nanoparticles should not be too high, to avoid plasmonic coupling among particles. If two or more particles are very close to each other, the coupling results in the LSPR wavelength shifting toward longer wavelengths, thus significantly reducing the nonlinearity. However, this imaging technique actually maps the distribution of plasmonic modes, instead of the particles themselves. Therefore, it is expected that with an appropriate excitation wavelength, the coupled plasmonic modes can also show strong scattering nonlinearity and can be imaged with enhanced resolution. Second, it is very important to produce pure sinusoidal modulation within the excitation beam, thus motivating the use of beating between the two AOMs. Since resolution enhancement relies on extracting nonlinear parts (harmonic frequency components) of the scattering signal modulation, if nonlinear distortion is present in the excitation modulation, then extraction will be more difficult. In addition, in the current scheme, an interferometer setup is used to produce the beating modulation, so the alignment of the two beams in the interferometer is also critical to achieve as large of a modulation depth as possible. Third, it is very important to ensure that the signal nonlinearity does not arise from the detection system (which includes the detector, amplifier, A/D converter, and computer I/O). Therefore, special attention is necessary to guarantee that the detection system is working within the dynamic range. The dynamic range is defined as the region of detection system linearity, that is, from the noise level to detector saturation. In the current case, the detected voltage signal is linear below 1 V, and the noise level is below 10-4 V. Therefore, the system provides a dynamic range of at least 104. To ensure that the signal nonlinearity originates from the gold nanoparticle itself, not from the detection system, it is necessary to maintain the readout value within the dynamic range. The fourth critical factor is the mechanical stability of the sample. During the nonlinearity characterization, it is essential that the nanoparticles remain in the same focal plane. Axial drift of the nanoparticle or the sample stage would severely affect the accuracy of the nonlinearity assessment. Therefore, when working with nanoparticles, it is important to find particles that do not easily move around under light excitation. On the other hand, it is also possible to work with samples grown from lithography. In this case, microscopic stage stability is the main limiting factor. There are stages with position feedback control that can greatly enhance the stability. Alternatively, since stage movement is typically very slow (e.g., 1 µm in 10 min), it is helpful to acquire a xyz 3D image stack, such as 10 images with 100 nm axial separation between adjacent images, at each different intensity value. Then during the analysis stage, the brightest image out of each stack should be chosen as the representative image at that intensity.
In principle, the resolution of saturation-based techniques, which include SAX and saturated structured-illumination microscopy (SSIM)26, exhibits no lower limit as long as high-order nonlinearity (high harmonic frequency components) can be achieved. Nevertheless, in practice, the resolution is limited by the signal-to-noise ratio (SNR), especially when extracting higher-order harmonic demodulation components. There are a few strategies that can enhance the SNR. For example, it has been shown that the modulation frequency severely affects the SNR27. It is also possible to enhance the SNR by calculating the intensity difference between non-saturated and saturated signals to extract only the saturated signal (manuscript in preparation).
Now we make a brief comparison of the current technique to others on two aspects: contrast and resolution. As mentioned, the contrast of our images reflects the plasmonic mode distribution, or equivalently the nonlinear plasmonic local density of state (LDOS). It is well known that electron energy loss spectroscopy (EELS) or two-photon photoluminescence (TPPL) can also be used to probe the LDOS. Compared to EELS, our optical imaging method allows the potential of mapping LDOS of metal nanospheres in biological samples. Compared to TPPL, our technique provides superior resolution. On the other hand, compared to other existing methods that achieve resolution beyond the diffraction limit, the main achievement of this work is the development of a novel non-bleaching contrast method for super-resolution microscopy. Most of the previous far-field super-resolution techniques have relied on nonlinearities of fluorophores, including their on/off switching28-30, or by saturation of fluorescence emission22,26,31. However, fluorescence exhibits an intrinsic problem of photo-bleaching, especially under strong light illumination. This study demonstrated that saturable scattering of GNSs is a promising method of super-resolution microscopy since there is no bleaching issue21. Compared with previous studies of SAX microscopy utilizing fluorescence, the resolution enhancement with saturable scattering was much higher in this investigation, possibly due to the higher-order nonlinearity22. In addition, other than SAX microscopy, there is another super-resolution technique based on saturation: SSIM26. SSIM exploits spatial modulation of fringes to extract the nonlinear signals, while SAX microscopy utilizes temporal modulation. With the saturation property of this non-bleaching scattering, it is therefore expected that this discovery can be combined with SSIM to improve the spatial resolution under wide-field illumination.
In future applications, this plasmonic SAX technique will be useful not only to resolve resonance-mode distributions and dynamics in plasmonic circuits, but also to enhance the resolution of biological tissue imaging. Similar resolution enhancement has been demonstrated with other plasmonic materials such as silver (unpublished), as well as non-plasmonic materials, such as silicon32. In the super-resolution imaging field, SAX microscopy has advantages in several respects. Compared to stochastic optical reconstruction microscopy (STORM) and photo-activated localization microscopy (PALM), SAX microscopy has a faster scanning speed of only a few seconds per image. Compared to stimulated emission depletion (STED) microscopy, only one laser is required for SAX microscopy, significantly reducing the optical complexity. Compared to SSIM, the resolution of SAX is simultaneously improved in both the lateral and axial directions. In addition, to achieve a sufficient imaging depth, random scattering along the beam path of excitation or collection is critical. For wide-field techniques like STORM, PALM, and SSIM, images are captured with a camera, which is highly susceptible to random scattering of emitted fluorescence photons in tissues. For point-scan techniques like STED and SAX, the fluorescence signals are collected by a point detector, so they are more robust against tissue scattering. Nevertheless, STED requires a phase plate to create a donut beam profile at the focus, and the phase information may be deteriorated during beam propagation in tissues. Therefore, SAX microscopy should be the best among these modalities for deep tissue super-resolution imaging.
The authors have nothing to disclose.
This work is supported by Ministry of Science and Technology under NSC-101-2923-M-002-001-MY3 and NSC-102-2112-M-002-018-MY3. This research is 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.
microscope body | Olympus, Japan | BX-51 | |
objective lens | Olympus, Japan | UPlanSapo, 100X, NA 1.4 | |
80-nm gold colloid | BBI Solutions, UK | EM.GC80 | |
supercontinuum laser | Fianium, United Kingdom | SC400-2-PP | |
broadband dielectric mirrors | Thorlabs, USA | BB1-E02 | |
field emission SEM | JEOL, Japan | JSM-6330F | optional |
spectrometer | Andor Technology, UK | Shamrock 163 | |
charge-coupled device | Andor Technology, UK | iDus DV420A-OE | |
acousto-optic modulators | IntraAction Corp., USA | AOM-402AF1 | |
lock-in amplifier | Stanford Research Systems, USA | SR-830 | |
MAS-coated slide glass | Matsunami Glass, Japan, | S9215 |