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If the fundamental wave is tuned to 1018.5 nm and illuminated on the NB’s center, SHG is only found at the excitation point (fig. 6.2b) and no observable SHG is detected at the edges (L and R).

Figure 6.2 A) SEM image of CdS NB. θ described the angle of incidence with respect the the edge of the NB. The scale bar is 10 μm. B) SHG observed from center of NB at point C, no waveguiding is observed at the edges. C) Fundamental wave incident at point L and SHG observe at both point L and waveguided to point R.

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However, if the fundamental wave is moved toward to one of edges or boundaries, for example the L-edge in fig. 6.2c, the SHG signal is observed at both the L-edge and the opposite edge (R-edge). If the fundamental wave is moved to the R-edge, SHG is also seen at the L-edge. We attribute this phenomenon to edge-scattering of the fundamental wave, that is, the fundamental wave can be strongly scattered and coupled into the NB waveguide through the edge of the NB and further excite SHG. The fundamental wave then propagates along the waveguide and meanwhile excites the SHG signal that co- propagates along the waveguide and finally exits from the other edge (R-edge). Because of edge-scattering, the SHG signal is observed to radiate orthogonal to the scattering edges (fig. 6.3). This is why directional SHG occurs in very small NBs or NWs.

However, we must consider the possibility that the light observed at the R-edge in figure 6.2c is not waveguided fundamental and SHG light, rather it may be caused by multiphoton absorption induced photoluminescence (PL) or the SHG signal that is excited at the L-edge and then scattered to the R-edge through the waveguide or free space. In order to rule out these possibilities, we fixed the excitation laser (fundamental wave) at the L-edge and detected the light emission at the L-edge (our naming convention

Figure 6.3 A-C) Optical images of directional edge scattering of SHG off different edges of a CdS NB.

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is to call this L-L) and R-edge (L-R) at the different excitation wavelengths, 980 nm, 1011nm and 1018.5 nm (fig. 6.4). At the excitation wavelength of 980 nm, the SHG signal is observed at ~490 nm and two photon absorption (TPA) induced PL is centered at ~503 nm at the L-edge (fig. 6.4a). At the R-edge, we observe two features, an unchanged SHG peak wavelength (~490 nm) and red-shifted PL with the central peak at ~512.8 nm.

Due to the high absorption coefficient in CdS near 490 nm (above the band gap), the SHG signal excited at the L-edge attenuates with the absorption coefficient of 15.4 /m18 while propagating along the waveguide (6.2-um-long) and precludes significant SHG at the R-edge (further verified below by polarization dependent in-coupling efficiency).

Figure 6.4 A) Measured spectrum from fundamental wave at 980 nm when the fundamental is at position L and SHG is measured at L (L-L) and when the fundamental is at position L and SHG is measured at R (L-R). The spectrum shows a strong two photon photoluminescence (PL) and SHG peak at L-L and a red-shifted PL peak and a weaker SHG peak at L-R. This indicates that PL is waveguided due to band edge absorption and that fundamental is also waveguided and excites PL at the R edge, otherwise it would be absorbed. B) Measured spectrum from fundamental wave at 1011 nm for position L-L and L-R. The spectrum at L-L shows one peak, much narrower that the PL peak in A, indicating it is just SHG. The L-R spectrum shows two peaks, which indicates that there SHG is being coupled to a cavity mode. C) Measured spectrum from fundamental wave at 1018.5 nm for position L-L and L-R. The spectrum for L-L shows a SHG peak with a clear shoulder, indicating the presence of a cavity mode. The spectrum at L-R shows a slightly red-shifted and narrower peak which is the SHG being completely coupled to the cavity mode.

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Since the absorption coefficient of CdS dramatically drops from above to below the band gap19, the short spectral side of PL is more absorptive than the long side, and exhibits faster damping when propagating along the waveguide, consequently leading to significant red-shifted PL20, which rules out the possibility that light emitted from the L- edge is scattered toward to the R-edge through the free space otherwise we would not observe red shifting. The unchanged peak wavelength of SHG was also indicative of the fundamental light waveguiding inside the NB and exciting SHG at the R edge. When the excitation wavelength is tuned at 1011 nm, only SHG signal with the spectral width of ~4 nm is observed at the L-edge, compared to the R-edge where the light emission red-shifts and splits (fig. 6.4b). Since the light emission at two edges exhibits the same polarization properties (discussed later) and the red-shifted peak is narrower than red-shifted PL at the R-edge (fig. 6.4a), the light emission at the R-edge can only be SHG. The peak splitting is due to waveguide mode cavities in this spectral region. Figure 6.4c shows the detected light emissions at the L-edge and R-edge when FW is tuned at 1018.5 nm. Compared with the red-shifted PL (512.5 nm) at the R-edge at 980 nm in figure 6.4a, the detected signal at the R-edge at 1018.5 nm in figure 6.4c is much narrower and peaks at ~510.8 nm, which indicates that it is only SHG. Clearly at 1018.5 nm, the SHG signal at the R- edge is narrower and red-shifts in contrast to the L-edge, and also matches the slight spectral shoulder (~510.8 nm) at the L-edge. This may result from the dramatic change in the absorption coefficient near the band gap and modulation of the waveguide mode cavity. It can be concluded that the SHG signal observed at the R-edge is generated and modulated in the NB waveguide where the fundamental wave propagates concurrently.

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