Optical pulling force (OPF) can make a nanoparticle (NP) move against the propagation direction of the incident light. Long-distance optical pulling is highly desired for nano-object manipulation, but its realization remains challenging. We propose an NP-in-cavity structure that can be pulled by a single plane wave to travel long distances when the spherical cavity wrapping the NP has a refractive index lower than the medium. An electromagnetic multipole analysis shows that NPs made of many common materials can receive the OPF inside a lower index cavity. Using a silica-Au core-shell NP that is encapsulated by a plasmonic nanobubble, we experimentally demonstrate that a single laser can pull the Au NP-in-nanobubble structure for ~0.1 mm. These results may lead to practical applications that can use the optical pulling of NP, such as optically driven nanostructure assembly and nanoswimmers.
The critical behavior of the Yvon-Born-Green integral equation for fluids is analyzed by a moment expansion which yields a nonlinear differential equation accurately describing the long-range correlations. Phase plane analyses show that for dimensions d^4 a critical point is characterized by 17 = 4 -d wither) -1 negative for large distances, r, in contrast to normal expectations. For d>4 the differential equation allows ig(r)-1] >0 and 77 = 0 or 4 -d. The compressibility never diverges if d = l.PACS numbers: 05.70.JkRecently, Green, Luks, Lee, and Kozak 1 have reported theoretical values for the critical exponents j3, y, and 6 for a fluid derived from numerical solutions of the Yvon-Born-Green (YBG) equation, 2 ' 3 which utilizes the Kirkwood superposition approximation. 2 ' 3 The values reported, e.g., y-1.24±0.04, are surprisingly close to those believed to be correct for three-dimensional systems with a scalar order parameter. This naturally leads to the speculation that the YBG equation might yield an essentially correct description of the critical region of a fluid which would directly utilize the intermolecular interaction potential, ?(?), and be free of the approximations, on the one hand, of a discrete lattice structure as in Ising models or, on the other hand, of a field-theoretic momentum cutoff and an unbounded continuously varying local order parameter as in the Landau-Ginsburg-Wilson models. It is to be noted, however, that the value of the critical-point decay exponent 77 was not determined numerically in the studies reported in Ref. 1, primarily because convergence problems in the calculations made it difficult to obtain reliable numerical solutions with correlation lengths, I, exceeding about 67? 0 , where R 0 de-, notes the finite range of the hard-core-plussquare-well potential considered. 4 This situation makes it particularly desirable to investigate by analytic means the nature of those solutions of the YBG equation which have the smooth, slowly decaying behavior believed characteristic of the true correlation functions in the critical region. To this end we introduce here a systematic expansion procedure 5 which leads to the approximation of the YBG equation for distances r
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