In this Letter, we study the Brownian motion of a particle in a speckle pattern and, in particular, we derive the characteristic timescale τ of such motion, which is universal as it depends only on the universal properties of speckle light fields 3, 21, 22. (e) Brownian particle mean square displacements as a function of 〈F〉 (purple lines) and their deviation from Einstein's free diffusion law (black line). The dashed line represents the theoretical normalized autocorrelation function of the speckle pattern intensity. (d) Normalized autocorrelation function of the force field produced by the speckle pattern according to our theoretical model (solid line) and in the simulated speckle pattern (circles). The trajectories (green solid lines) show progressive confinement of a polystyrene bead (R = 250 nm, n p = 1.59) in water ( n m = 1.33, η = 0.001 Ns/m 2, T = 300 K) as a function of the increasing speckle intensity corresponding to an average force on the particle of (a) 〈F〉 = 10 fN (〈I〉 = 13 mW/μm 2), (b) 〈F〉 = 50 fN (〈I〉 = 65 mW/μm 2), (c) 〈F〉 = 200 fN (〈I〉 = 260 mW/μm 2). (a–c) The background represents a speckle pattern generated by a circular aperture (λ = 1064 nm, speckle grain 490 nm) the white scale bar corresponds to 2 μm. Subdiffusion in a static speckle pattern. For example, in non-equilibrium statistical physics, the dynamics of a Brownian particle in a moving periodic potential can be described as a straightforward generalization of the dynamics of a Brownian particle in static not out-of-equilibrium potentials, while this is no longer the case for random potentials for which a full out-of-equilibrium description is still required 20. It is not a priori obvious that the same phenomena that have been observed with periodic potentials can also arise with random potentials, as the statistical properties of random potentials fundamentally differ from those of periodic potentials. In fact, similar and even more complex effects have been extensively studied using periodic potentials rather than random potentials: these studies include the observation of giant diffusion induced by an oscillating periodic potential 13 and the demonstration of guiding and sorting particles using either moving periodic potentials 14, 15, 16 or static periodic potentials in microfluidic flows 17, 18, 19. However, apart from these previous studies, there is little understanding of the interaction of Brownian motion with random light potentials and the intrinsic randomness of speckle patterns is largely considered a nuisance to be minimized for most purposes, e.g., in optical manipulation 11, 12. Earlier experimental works showed the possibility of trapping particles in high-intensity speckle light fields 6, 7, 8, 9, the simplest optical manipulation task and the emergence of superdiffusion in an active media constituted by a dense solution of microparticles that generates a time-varying speckle field 10. This latter example is particularly suited to work as a model system because its parameters (e.g., particle size and material, illumination light) are easily controllable and its dynamics are easily accessible by standard optical microscopy techniques 5. ![]() Another example of this kind of phenomena is given by the motion of a Brownian particle in a random optical potential generated by a speckle pattern, i.e., the random light field resulting from complex light scattering in optically complex media, such as biological tissues, turbid liquids and rough surfaces (see background in Figure 1a–c) 3, 4. Examples range from the nanoscopic world of molecules undergoing anomalous diffusion within the cytoplasm of a cell 1 to the Brownian motion of stars within galaxies 2. Various phenomena rely on particles performing stochastic motion in random potentials.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |