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Structures for thermal tweezers. Nanoparticles on the surface of a thin metal film deposited onto a dielectric substrate. The arrows represent two laser pulses producing an interference pattern and the periodic temperature modulation on the surface of the film. (a) The pulses are incident onto the free surface of the film. (b) The interfering pulses are incident through the dielectric substrate (the temperature modulation at the free surface of the film is produced primarily due to heat conduction through the thin film).
Probability density functions averaged over the final positions of 50 000 independent particles/molecules within the square on the surface. (half the wavelength for a He–Ne laser), , , , , (Refs. 15–18). (a) for different evolution times: (1) , (2) , (3) , (4) , (5) . (b) , (1) , (2) , (3) , (4) ; the thick solid curve is obtained using 100 000 independent particles and corresponds to the steady-state probability density at (two-dimensional bulk thermophoresis). Dashed horizontal lines represent the steady-state maximal probability densities in the cold regions for (a) and (b) .
Time evolution of the probability density in the cold (the upper curves) and hot (the lower curves) regions at different temperature modulations : (solid), (dotted), and (dash and dotted); the other parameters are the same as for Fig. 2(a). The error bars on the upper curves (concentration maxima) show the typical standard errors of the mean for the calculated points. Curve fitting was done assuming exponential dependencies.
Super-resolution technique in thermal tweezers. (a) The probability density function identical to curve 1 in Fig. 2(a) (no super-resolution). (b) resulting from applying thermal tweezers to the uniform distribution of 50 000 noninteracting particles (in the square with the periodic boundary conditions) at , , , , , , (Refs. 15–18), and the evolution time . (c) obtained from the particle distribution in (b) by shifting the temperature modulation pattern by and allowing the system to evolve for another . (d) obtained from the particle distribution in (c) by making , further shifting the temperature modulation by [so that the hot regions coincide with every second maximuma in (c)], and allowing the system to evolve for .
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