Measurement of Scattering Nonlinearities from a Single Plasmonic Nanoparticle

Summary

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.

Abstract

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.

Introduction

The study of plasmonics has attracted great interest due to its applications in many different fields^1-4. 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 microscopy^5,6. 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 medium^7-10, 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 techniques^12,13. 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 processing^14,15. 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 (Q_sca) and absorption coefficient (Q_abs) 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 ε_m/ε_d. Here, ε_m and ε_d 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.

Protocol

1. GNS Sample Preparation

1. Before preparing the sample, sonicate 1 ml GNS colloid solution for at least 15 min at about 40 kHz to prevent particle aggregation, which may cause the LSPR peak to shift.
2. Drop 100-200 µl of GNS colloid onto a slide glass with commercial magnesium aluminum silicate (MAS) coating to fix the GNSs.
3. After at least 1 min, remove the extra colloid by flushing with distilled water. The waiting time depends on the required distribution density of the GNSs. Typically, 1-3 min results in a suitable density that enables the particles to be easily identified since most of them are isolated from each other. Significant aggregation may occur if the waiting time is too long.
4. Dry the sample by purging with nitrogen gas.
5. (Optional) To map the GNSs on the glass with high resolution, perform scanning electron microscopy (SEM) at this stage²³. An example image is provided in Figure 1, showing the characteristic density of GNSs. Use a field emission SEM to acquire the image. Once oil is added onto the sample (next step), it will be difficult to remove the oil and observe the sample with SEM.
6. Add a drop of oil with the same refractive index onto the sample to cover the GNSs and to eliminate the strong reflection from the glass substrate.
7. Place a cover glass on top of the sample and seal it with nail polish.
8. Wait at least 5 min until the nail polish dries. The sample is ready now.

2. Alignment of Home-built Confocal Microscope

1. See Figure 2 for the scheme of setup. Align the white light illumination path of the microscope body itself. Turn on the halogen light source of the microscope, and follow the microscope manufacturer’s manual to achieve the Köhler illumination condition. Ensure that the white halogen light beams are nearly parallel at the back of aperture of the objective, partially reflected by the 50/50 beamsplitter, and then propagate toward the laser.
2. Turn on the galvano mirrors to ensure that they remain at the correct initial position, that is, at the center of the scanning range.
3. Place at least two targets, made by a thin sheet of paper with concentric rings on it, along the halogen light path, and align them with the halogen beam.
4. To perform imaging, select the 532 nm laser. To perform spectroscopy measurements, select the super-continuum laser. During the alignment, the power of the lasers should be less than 10 μW at the back aperture of the objective to avoid nonlinearity. Then, collimate the incident laser beam opposite to the outgoing halogen beam with the aid of the two targets. When this process is complete, the coarse alignment of the laser beam has been achieved.
5. Align the laser beam through the center of the back aperture of the objective lens. Typically, use an oil-immersion objective. Add a drop of oil between the oil-immersion objective lens and the GNS sample. Use a photomultiplier tube (PMT) as the detector to collect the scattering signals of the GNSs.
6. Place a 20-µm-diameter pinhole in front of the PMT to block out-of-focus scattering signals. Turn on the galvano mirrors and PMT (via home-built software), adjust the pinhole position and height of the sample stage to maximize the backscattering signals of the GNSs, and then observe an individual GNS on a computer screen. A sample xy image of the GNSs with correct alignment is shown in Figure 2B.
7. Slightly change the height of the sample stage to check the concentricity of the focus. If it is not concentric, adjust the beam with the two mirrors in front of the scanner until the center of the GNS remains at the same position while the height of the sample stage is changed. Make sure that the xz image of the PSF is similar to Figure 2C to ensure correct beam alignment. Process these two images with low-pass and Gaussian smooth filters.

3. Characterization of Scattering Nonlinearity

1. At low excitation intensity (less than 10⁴ W/cm²), acquire an image of gold nanoparticles by following protocol 2.6.
2. Open the image in ImageJ (or any other image analysis software). Draw a line across one of the GNSs in the image (see Figure 2B), and use Analysis -> Plot profile of the ImageJ tools to retrieve the scattering intensity profile. Fit the profile of the chosen PSF by a Gaussian function:
   
   where y is the PMT readout value, y₀ is the background value (if any), A is the peak amplitude, w is the width, x is the spatial coordinate, and x_c is the center coordinate of the Gaussian function. The FWHM of the corresponding PSF is (½ln2)w. Based on the numerical aperture (NA) of the objective, the theoretical FWHM of the confocal PSF can be estimated to be approximately 0.43l/NA, where l is the excitation wavelength. Compare these two numbers to check the alignment of the imaging system.
3. Increase the excitation intensity by manually changing the neutral density (ND) filter in Figure 2A, and record the backscattering images at each intensity level. Take the value of the scattering signal from the center of each GNS at different excitation intensities, and plot the curve of scattering signals versus excitation intensities. Check the linearity of the first few points, which should exhibit a linear relationship when the excitation intensity is adequately low. Draw a line based on linear fitting of the first few points. If the scattering intensities of the subsequent points drop below this linear trend, saturation has occurred.
4. After observing saturable scattering, gradually decrease the intensity below the saturation threshold, and image the same GNSs again to ensure the reversibility of the nonlinear behaviors.

4. Measurement of a Scattering Spectrum of a Single Gold Nanosphere

1. To measure the backscattering spectrum from a single GNS, use the super-continuum laser as the laser source. The initial wavelength of the laser ranges from 450 nm to 1,750 nm. To remove the excess infrared power that might cause damage to the sample and the optical components, place one or two mirrors right after the super-continuum laser to reflect the visible light, and use beam dumps to collect the excess infrared light.
2. Follow the alignment procedures in Section 2 to direct the super-continuum laser into the laser scanning confocal microscope. Use a broadband 50/50 BS to ensure spectral coverage across the whole visible range.
3. Acquire an image of the GNSs on glass. Locate a single GNS in the image, and fix the focus of the incident broadband light on the particle.
4. Use a flipping mirror in front of the PMT to direct the backscattering signal toward the spectrometer, which is equipped with a charge-coupled device, and then take a spectrum of the selected single GNS. Be careful that the spectrum here is a mixture of GNS scattering and background due to reflections from other surfaces.
5. Switch back to the PMT detector, and take another image to confirm that the particle position has not changed. Then, shift the focus to a point at which no particle is present. Switch back to the spectrometer, and take one more spectrum, which represents the background.
6. Subtract the background spectrum from step 4.5 from the spectrum from step 4.4 to obtain a clear backscattering spectrum of a single GNS.

5. Alignment of SAX Microscope

1. See Figure 3 for the scheme of the SAX microscope, where an ideal sinusoidal temporal modulation is obtained from the beat frequency between two acousto-optic modulators (AOMs). First, adjust the beam size of the laser to meet the requirement of the subsequent AOMs. Split the 532 nm laser light into two beams by using a 50/50 beam splitter.
2. Guide the two beams through the two AOMs, with one beam passing through each AOM. The modulating frequencies of the two AOMs must be different. For example, one may be at 40.000 MHz and the other at 40.010 MHz, yielding a difference frequency of 10 kHz. This difference frequency will be the fundamental modulation frequency f_m for the SAX signals.
3. Take the first-order diffracted beams from both AOMs, and combine the two beams by using another 50/50 beam splitter. Adjust the mirrors after the AOMs to collimate the two beams.
4. Add a photodetector that is connected to an oscilloscope to monitor the temporal modulation. Split a small portion of the laser with a slide glass, and send it to the photodetector, as shown in Figure 3. With correct modulation and beam overlapping, observe sinusoidal intensity modulation at the main frequency f_m, similar to that of the waveform shown in Figure 4.
   Note: The background of the modulation needs to be as low as possible to achieve the maximum modulation depth. In addition, use the Fourier analysis function of the oscilloscope to check that the harmonic distortion of the modulation is diminishing. To achieve successful SAX implementation, ensure a perfect sinusoidal excitation intensity modulation with minimized initial nonlinearity.
5. Disconnect the electric output of the photodetector from the oscilloscope and connect to the reference input of a lock-in amplifier.
6. As shown in Figure 3, align the laser beam into the confocal system following the previous protocols. Here, connect the electric output of the PMT to the lock-in amplifier as the signal input.
7. Use a blank cover glass as the sample, and check the linearity of the electric detection system by gradually increasing the excitation power,, as shown in Figure 5, where the detector is linear below a readout value of 1-V. In all subsequent measurements, take care to restrain the readout to below this value.
8. Set the output of the lock-in amplifier to export the absolute magnitude of the voltage signal. By changing the harmonic component setting at the reference channel, obtain the amplitudes of the SAX signals, A₁, A₂, and so on.
9. Export the linear and nonlinear signals from the lock-in amplifier to a data acquisition card, which also receives the driving voltage signals of the raster scanning galvano mirrors. With the aid of a customized Labview program, synchronize the signals of the lock-in amplifier and the galvano mirrors to form an image.
10. To optimize the signal-to-noise ratio in the images, select appropriately the pixel acquisition and integration times of the lock-in amplifier. For example, when the main modulation frequency f_m of the excitation is 10 kHz, that is, when the period is 100 µsec, set the integration time of the lock-in amplifier to be at least three times longer than the period. Adding the time of the galvano mirror movement, the acquisition speed is set at 1,500 pixels per second in the SAX imaging mode.

Results

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 nan...

Discussion

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 ap...

Materials

List of materials used in this article

Name	Company	Catalog Number	Comments
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