We now report measurements and comparative numerical results for the sample platform of and the imaging system of . Here, a 4.4 μm diameter BaTiO3 microsphere was embedded in solid PDMS, and a gold nanoparticle of diameter either 50 nm, 60 nm, 80 nm, or 100 nm was positioned in liquid PDMS 350 nm above the microsphere within its nanojet. An unpolarized broadband visible-light (λ
0 = 400 to 700 nm) plane wave illuminated the system, and the backscattered intensities were measured. Imaging results for this system are shown in
Fig. 5 Comparison of two experimental visible-light backscattering images: (a) isolated 4.4 μm diameter BaTiO3 microsphere in PDMS; (b) microsphere of (a) with a 100 nm gold nanoparticle located 350 nm above the microsphere within its nanojet. 5X magnification (more ...)
qualitatively illustrates the visible-light backscattering enhancement caused by a 100 nm gold nanoparticle located within the nanojet of the 4.4 μm diameter BaTiO3 microsphere embedded in PDMS. In , both images are normalized by the maximum intensity, 1669, of the central peak in , with the same gray scale used for both images and the background signal not removed. From , it is clear that the presence of the gold nanoparticle in the nanojet of the microsphere significantly enhanced the microsphere’s visibility. Otherwise, when isolated, the microsphere was barely visible above the background, as shown in . (Note that does not show the “rings” seen in because: (a) the intensity of the rings is very small relative to the central peak generated by the nanoparticle; and (b) the sharpness of the rings is reduced by the comparatively low value of NA = 0.12 used to obtain and vs. NA = 0.6 used to obtain .)
shows computational modeling results for the normalized backscattering intensity enhancement as a function of the NA for the experiment of . These results reveal that the enhancement factor initially rises as the NA is increased from zero. The enhancement factor reaches a maximum value of about 65 when the NA is approximately 0.075, corresponding to a scattering integration angle between 175° and 180°. Thereafter, the enhancement factor decreases rapidly. Note that the previously reported dimensionally scaled microwave measurements of backscattering enhancement [10
] used what amounted to be a zero-NA detection system.
Fig. 6 (a) Computationally modeled NA dependence of the backscattering intensity enhancement caused by a 100-nm gold nanoparticle for the broadband illumination case of . (b) Typical monochromatic scattering intensity of the microsphere vs. scattering (more ...)
The reason why the maximum backscattering enhancement occurs for a nonzero NA can be deduced by considering , which plots a typical monochromatic, ϕ-symmetric, scattering intensity pattern of the microsphere / nanoparticle system vs. the scattering angle θ. Here, we see that the scattering intensity oscillates as θ decreases from 180° (direct backscattering). For a nonzero collection angle defined by the NA of the objective, fields scattered at smaller angles than 180° are summed coherently to form an image in the image plane. Due to the angular oscillation of the scattered field, the total intensity for a nonzero NA has a maximum value at θ corresponding to the first peak in .
depicts the measured backscattering spectral responses of the 4.4 μm diameter BaTiO3 microsphere with and without the nearby perturbing 100 nm diameter gold nanoparticle for an imaging objective NA of 0.12. plots the spectral response of the backscattering intensity enhancements corresponding to the data of . We observe that the enhancement factor exhibits repetitive peaks similar to the numerical results shown in , although the heights of these peaks are smaller than the numerical ones. Background noise and the limited resolution of the spectrometer used in the measurements may have contributed to this difference. Despite this limitation, measured enhancement factors reached almost 24 dB at wavelengths between 600 and 700 nm. We note that these large enhancements reduce to about 17 dB when the spectral intensities are integrated.
Fig. 7 (a) Measured backscattering spectral responses of the 4.4 μm diameter BaTiO3 microsphere with and without the nearby perturbing 100 nm diameter gold nanoparticle for an objective NA = 0.12. (b) Spectral response of the backscattering enhancement (more ...)
depicts the dependence of the backscattering intensity enhancement upon the diameter of the gold nanoparticle in the nanojet. The upper blue dotted line with star marks shows the GMM-calculated backscattering intensities as a function of the gold nanoparticle size for free-space, λ
= 400 nm, plane-wave illumination of the 3.5 μm polystyrene microsphere / gold nanoparticle system reported in [8
]. In [8
], gold nanoparticles sized from 2 to 60 nm yielded the slope m
3.3, whereas m
5.1 was obtained for nanoparticles sized from 50 to 100 nm.
Measured and modeled backscattering intensity enhancements as a function of the gold nanoparticle diameter.
The two lower curves in are our experimental results (red dotted line with star marks) and our computational model results (blue dotted line with circle marks) for the backscattering enhancements obtained with the system of and for an objective NA of 0.12. The measured and modeled results agree well for gold nanoparticle sizes of 50, 60, 80, and 100 nm. Relative to the results in [8
], our measured slope m
4.5 is smaller, and the enhancement factor is reduced by 10 dB because of the averaging effect over the broadband illumination wavelengths that we used.
Despite our smaller measured backscattering enhancements relative to what Ref. [8
]. obtained theoretically for monochromatic illumination, shows that a gold nanoparticle as small as 50 nm can be readily detected using broadband visible light via the nanojet backscattering enhancement phenomenon. This size nanoparticle caused a measured 3:1 (200%) increase in the measured backscattering intensity of the adjacent 4.4 μm diameter microsphere when positioned within its nanojet.