Two-photon Luminance of Out-of-plane Nanorods

Small metal particles exhibit complex optical and physical properties. Their small sizes (< 100 nm) cause strong confinement of the electrons, giving rise to fascinating effects not observed in the bulk material. The most striking phenomenon encountered in metal nanoparticles are electromagnetic resonances due to the collective oscillation of the conduction electrons. These so called localized surface plasmon resonances (SPR) induce a strong interaction with light, and the wavelength at which this resonance occurs depends on the local environment, shape, size and orientation of the particle [129-131].

The role of a nanorod is a perfect light absorber which can be used to indicate the orientation of a nanorod. Figure 6.7 shows the experiment results of polarization

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dependence luminance intensity. The gold nanorods were synthesized by the seeded method having the aspect ratio ~ 4 which have a maximum extinction at the wavelength of 780 nm.

By focusing linearly polarized light onto the nanorod with a 1.4 NA objective, the nanorod is able to generate a two-photon luminance (TPL). The strength of its luminance depends on relationship between the orientation of nanorod and the polarization distribution at the focus. The maximum luminance would be generated when the polarization axis of illumination beam is parallel to the longitudinal axis of nanorod. In contrast, there is no luminance as the polarization is perpendicular to the longitudinal axis of nanorod, as shown in Fig. 6.7(a). By controlling the polarization angle of linear polarized light through a half-wave plate, one can plot its intensity variation versus the rotation of incident polarization, as shown in Fig. 6.7(b). The strength of TPL is polarization angle dependence and exhibits a relation which is directly proportional to the four square of cosine theta multiplied by electric field (𝜃) ∝ (E cos 𝜃)⁴. The orientation angle of an in-plane nanorod could be determine by this dipolar cosine fits.

Fig. 6. 7 Imaging gold nanorods. (a) Schematic diagram of the link between polarization and the intensity of TPL. (b) Polarized TPL versus angle, with dipolar cosine fits.

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However, this method is only suitable for detecting in-plane nanorods and some of out-of-plane nanorods with small title angle. Most of standing nanorods cannot be detected due to the weak projection from out-of-plane to in-plane. In this case, an axial polarization at the focus is needed for handling standing nanorods. By means of pupil polarization engineering, one can create an axial polarization at the focus. Figure 6.8 shows the field distribution of TPL excited by different state of polarized illumination under the strong focusing condition (NA = 1.4, = 780 nm). By using linear polarized light to determine the orientation of nanorods, one should take at least three images by rotating the polarization cover 0, 45 and 90 degrees. In contrast, azimuthal polarization provides a better route providing fast detection based on a single shot. This is because the field distribution of its focus is spatially varied in polarization and rotational symmetry in amplitude. As a result, one can observe a pair of lobes rather than a perfect donut shape on its TPL. This pair of lobes is central symmetry along the axis of zero intensity which is the degeneration of original donut shape. This null axis is parallel to the longitudinal axis of nanorods. Based on this link we can easily determine the orientation of nanorods without the need of rotating polarization angle.

Fig. 6. 8 Field distribution of TPL excited by different state of polarized illumination under the strong focusing condition (NA = 1.4, = 780 nm). The

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orientation of nanorod is in-plane and parallel to (a) x-axis and (b) y-axis, and (c) out-of-plane which is parallel to z-axis, the image width of TPL is 3 m.

In addition, radially polarized illumination provides not only fast examination for in-plane nanorods but also additional link for standing nanorods due to its unique longitudinal component along axial direction based on the strong focusing. Generally speaking, radial polarization is a perfect illumination source for orientation detection which provides an entire response cover every orthogonal axis.

The size of a gold nanorod is significantly smaller compared to the size of focused spot.

Therefore its luminance scanning image pattern resembles the point spread function of a focused beam. In experimental, we fix the position of objective lens and move the scanning stage of the nanorods sample. All of the excited TPL were collected by a high sensitivity PMT.

In addition, a notch filter placed in front of PMT for blocking the strong reflectance of excitation light source. Figure 6.9 shows experimental results of TPL of godnanorods which is

Fig. 6. 9 Experimental results of TPL of godnanorods. The raster scanning image of TPL of nanorods which is generated by (a) azimuthal polarization and (b) radial polarization. Dashed line encircle of mark #1 to #3 highlight the field distribution of TPL of nanorods and their individual schematic diagrams are shown in (f) to (h), respectively. The field distribution of focus is calculated under the condition of NA

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=1.4, annular illumination of = 0.4, and = 780 nm for (c) azimuthal polarization and (d)-(e) radial polarization.

generated by (a) azimuthally and (b) radially polarized illumination. The same as our prediction, the field distribution of TPL image only exhibits a pair of lobes with different orientated angle which is depending on the orientation of nanorods. In the case of radially polarized illumination, a bright circle spot is also revealed which implies the existence of standing nanorods. Also, we can observed that the brightness of TPL of #2 is dimmer than that of #3. This is because the annular illumination purified the strength of longitudinal of a radially polarized focus. In the case of = 0.4, the ratio of peak intensity for them are IX,AP : IX,RP : IZ,RP = 0.6 : 0.25 : 1. This means the focus of radial polarization is not a pure longitudinal component; we still can observe the existence of transverse component which is not negligible. Figure 6.10 give us a strong evidence to support our theoretical prediction that we mentioned above. Before that, we have to dress a brief introduction on the excitation dynamics of small metal particles, in which the photon energy of a short laser pulse is converted to thermal energy and acoustic vibrations.