(Invited) In Situ Accurate Analysis of Colloidal Nanoparticles via Four Wave Mixing
Authors: Gordon Reuven 
Published: February 2020

Four-wave mixing (FWM) is used to measure the vibrational modes of nanoparticles in solution. The vibrations give information about the particle size, material properties and shape. This method has been used for in-situ monitoring of the growth of nanoparticles with high accuracy, as confirmed by electron microscopy analysis. We observe a threshold in the FWM signal which we believe is from a cavity forming around the nanoparticles that reduces viscous damping. We have observed this effect in molecular dynamics simulations as well.
Here we report a highly accurate method for the analysis of colloidal nanoparticles by means of four wave mixing (FWM). Other optical methods exist to analyse nanoparticles in solution, such as extinction and dynamic light scattering. Extinction is widely used in plasmonic nanoparticle analysis; however, it is not very sensitive to particle size, even though it is quite sensitive to particle shape. For accurate sizing and shape characterization, usually transmission electron microscopy is used as an alternative measure.
Previously we developed an optical tweezer method to measure individual nanoparticles, including proteins and DNA [1,2]. This method interfered two lasers at the trapping site to create a beat signal with high frequency that excited the vibration modes of the trapped nanoparticle. The vibration resonance was measured indirectly via increased motion of the trapped nanoparticle. We developed the FWM technique to analyse many nanoparticles in solution, instead of individually.
In FWM, two laser beams are interfered with a slight frequency difference (in the 10 GHz – 10 THz range). The setup is based on an early degenerate FWM configuration [3]. This drives oscillations in the nanoparticles via electrostriction. When the oscillation frequency matches a natural vibration resonance of the nanoparticles, extremely strong FWM is observed by scattering of a third beam off of a dynamic grating induced by the electrostriction force.
The vibration resonances allow for accurate sizing and size distribution information. For example, 2 nm gold nanoparticles give a resonance at 1.5 THz. The resonance frequencies allow for precise determination of nanoparticle size and shape, as has been verified by electron microscopy measurements. We have also demonstrated that this method can be used for in-situ growth characterization of nanoparticles [4]. Furthermore, complex shaped materials (nanoprisms, octahedrons, nanorods) can be analysed with this technique, giving insight into their size and shape [5, 6].
The observed four wave mixing signal is extremely strong and it shows a turn-on threshold [7, 8]. We have ruled out a stimulated threshold here, and so we believe that this strong response is really the result of a sudden reduction in damping from the water environment, akin to cavitation. We have used molecular dynamics simulations to test this hypothesis, and found that they also produce a threshold.
In conclusion, we have demonstrated a method for characterizing nanoparticles in situ via electrostriction. This approach is highly accurate and may be used as an alternative to electron microscopy, dynamic light scattering and extinction measurements. We are also intrigued at the cavitation effect that allows for such a strong signal even with weakly focussed continuous wave diode lasers and we believe this effect will allow for a new class of strong nonlinear optical materials.

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