Abstract

We report the phenomenon of ultra-enhanced backscattering of visible light by nanoparticles facilitated by the 3-D photonic nanojet – a sub-diffraction light beam appearing at the shadow side of a plane-wave-illuminated dielectric microsphere. Our rigorous numerical simulations show that backscattering intensity of nanoparticles can be enhanced up to eight orders of magnitude when locating in the nanojet. As a result, the enhanced backscattering from a nanoparticle with diameter on the order of 10 nm is well above the background signal generated by the dielectric microsphere itself. We also report that nanojet-enhanced backscattering is extremely sensitive to the size of the nanoparticle, permitting in principle resolving sub-nanometer size differences using visible light. Finally, we show how the position of a nanoparticle could be determined with subdiffractional accuracy by recording the angular distribution of the backscattered light. These properties of photonic nanojets promise to make this phenomenon a useful tool for optically detecting, differentiating, and sorting nanoparticles.

© 2005 Optical Society of America

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References

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Appl. Opt.

Appl. Phys. A

M. Mosbacher, H. J. Munzer, J. Zimmermann, J. Solis, J. Boneberg, and P. Leiderer, "Optical field enhancement effects in laser-assisted particle removal," Appl. Phys. A 72, 41-44 (2001).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

V. Backman, V. Gopal, M. Kalashnikov, K. Badizadegan, R. Gurjar, A. Wax, I. Georgakoudi, M. Mueller, C. W. Boone, R. R. Dasari, and M. S. Feld, "Measuring cellular structure at submicrometer scale with light scattering spectroscopy," IEEE J. Sel. Top. Quantum Electron. 7, 887-893 (2001).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. B

P.B. Johnson, R.W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

Phys. Rev. E

Y. L. Xu and R. T. Wang, "Electromagnetic scattering by an aggregate of spheres: Theoretical and experimental study of the amplitude scattering matrix," Phys. Rev. E 58, 3931-3948 (1998).
[CrossRef]

Radio Sci.

C. Liang and Y. T. Lo, "Scattering by 2 Spheres," Radio Sci. 2, 1481-& (1967).

Other

<a href= "http://www.astro.ufl.edu/~xu/">http://www.astro.ufl.edu/~xu/</a.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

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Figures (6)

Fig. 1.
Fig. 1.

Photonic nanojets generated by illuminating dielectric spheres (nµ=1.59) with a λ=400nm, x̂ - polarized, - propagating incident plane wave in vacuum. The near-field intensity distributions are calculated with Eq. (2). (a) Sphere diameter D=1µm. (b) D=2µm. (c) D=3.5µm. (d) D=8µm.

Fig. 2.
Fig. 2.

The backscattering enhancement factor E for a gold nanoparticle placed in the photonic nanojet elevates by orders of magnitude as the nanoparticle size drops below 60 nm. The nanojet is generated by illuminating the n µ =1.59, D=3.5µmdielectric microsphere with plane wave of λ=400 nm. The gold nanoparticles are assumed to have refractive index n ν =1.47-j1.95.

Fig. 3.
Fig. 3.

The normalized backscattering intensity perturbation, defined as ΔI ν ≡δI/I µ , lies within the range of -35 dB to +15 dB relative to the backscattering intensity of the microsphere for nanoparticles diameters of 2–60 nm. This is within the dynamic range of available optical instruments, implying that nanoparticles as small as a few atoms across could be detected with visible light.

Fig. 4.
Fig. 4.

Simulation of a 20-nm gold nanoparticle moving through a photonic nanojet while the backscattering signal is recorded. (a) Geometry. (b) Normalized backscattering intensity (relative to by the dielectric microsphere alone) as a function of the position of the nanoparticle. We see that the nanoparticle generates a 40% jump in the recorded backscattering signal at its peak response.

Fig. 5.
Fig. 5.

High sensitivity of the nanoparticle backscattering signal (recorded with configuration shown in Fig. 4 (a)) relative to a nm-size variations of the nanoparticle. These signal perturbations are well within the measurement dynamic range of available laboratory instrumentation.

Fig. 6.
Fig. 6.

Angular maps (dB scale) of the normalized co-polarized backscattering intensity perturbation for four positions of a 20-nm gold nanoparticle relative to the center of the nanojet shown in Fig. 4 (a). (a) y=-150 nm. (b) y=-100 nm. (c) y=-50 nm. (d) y=0. We see that a nanoparticle displacement of only 50 nm from the nanojet center is sufficient to noticeably break the symmetry of the angular pattern. Such maps could be used to locate the nanoparticle with subdiffractional precision.

Equations (4)

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E inc ( r ) = n = 1 i n { ( 2 n + 1 ) [ n ( n + 1 ) ] } [ M o ln ( 1 ) ( r ) i N e ln ( 1 ) ( r ) ]
E scat ( r ) = n = 1 i n { ( 2 n + 1 ) [ n ( n + 1 ) ] } [ i a n N e ln ( 3 ) ( r ) b n M o ln ( 3 ) ( r ) ]
E δ I I ν = ( I μ + ν I μ ) I ν
Δ I N δ I I μ = ( I μ + ν I μ ) I μ ,

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