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Table of Contents
                            Declaration of Authorship
	Motivation and aims
	Structure of the Thesis
Theoretical methods
	Electromagnetism in a nutshell
		Maxwell equations
		The Green dyadic function
	Permittivity and polarizability
		Drude and Lorentz permittivity
		Electric polarizability
		Scattering, absorption and extinction cross sections
	Optical forces
		Optical force on a dipolar particle
		Optical interaction between nanoparticles
			The force between two particles
			The force between several particles
	Forces due to random light illumination
		The field-field correlation functions
		The two-particle force
Arrested dimer's diffusion in Optical Lattices
	SIBA forces on a dimer in an Optical Lattice
		Analytical approach
	Dimer's diffusion
		Dimer's Brownian diffusion
		Langevin dynamics simulations in an optical lattice
Many-particle dynamics in optical lattices
	Pair-wise interactions
	Three-particle interactions
		Three particles illuminated by a plane wave
		Three particles in an optical lattice
	Interplay between optical forces and hydrodynamics
		Optical interactions among particles
Dipolar interactions in random electromagnetic fields
	Electric fields and optical forces
	The nonabsorbing case
		The kR  limit (no absorption)
		Short distance expansions (no absorption)
	The absorption case
		The  kR limit (absorption)
		Short distance expansions (absorption)
Effects due to absorption: "Mock" gravity and nonconservativity
	The full-range  FR-2  interaction
		The case of gold and silver
	Nonreciprocity and nonconservativity under RLI
		The force on the center of mass
Conclusiones (Spanish)
The Green dyadic function
The Coupled Dipole Approximation
Document Text Contents
Page 1



Light induced interactions between
nanoparticles in complex fields


Prof. Juan José SÁENZ

Prof. Manuel Ignacio MARQUÉS

A thesis submitted in fulfillment of the requirements
for the degree of Doctor of Philosophy

in the

MoLE Group
Departmento de Física de la Materia Condensada


June 26, 2017

Page 73

4.2. Three-particle interactions 45



FIGURE 4.5: Forces along the z-axis when particles 1, 2, 3
are located at (x, y) = (100, 250)nm. (A) Comparision
of two- and three-particle forces on particle 3. It can be
seen that, for this configuration, three particle contribu-
tions are almost negligible. (B) Sum of the z-component of
the forces on particles 1, 2, 3. Net forces are exerted on the

center of mass of the system of three particles.

Page 74

46 Chapter 4. Many-particle dynamics in optical lattices

and applied electromagnetic field for every particle are identical. Then,
the z-component of the pair-wise force on the center of mass of the system
of particles would identically vanish.

The contribution of three-particle forces have not been depicted in the
xy-plane since, except for very small separations, the forces produced by
the optical vortex field are larger than the optical interaction forces be-
tween NPs. The behavior along the z-axis studied for (x, y) = (100, 250)nm
is similar in any other point of the xy-plane, with the exception of the
points analogous to (x, y) = (λ/2, λ/2), where the z-component of the
force vanishes.

4.3 Interplay between optical forces and hydrodynam-

Emergent phenomena in the scope of self-driven particles were modeled
by Vicsek et al. (Vicsek et al., 1995). In this work, the authors proposed
that collective behavior of an ensemble of particles requires individuality,
connectivity and external injection of energy. On one hand, direct energy
conversion is a characteristic feature of optical forces when applied to res-
onant nanoparticles. At resonance, scattering forces on nanoparticles are
mainly associated to radiation pressure, which enables the system to take
energy from the environment and convert it into direct motion of the par-
ticles. On the other hand, hydrodynamic interactions among these active
nanoparticles show the kind of many-particle features that produces the
required connectivity, being capable to provoke the emergent collective
motion that is going to be the objective of this study.

In this section we present the study of one particular realization of
these collective phenomena, within the field of optical forces in colloidal
nanoparticles connected by hydrodynamic interactions, and will discuss
specifically the role of the optical interaction between the nanoparticles in
the system. This work has been done in collaboration with Prof. Rafael
Delgado-Buscalioni and Dr. Marc Meléndez, from the Department of The-
oretical Condensed Matter Physics at Universidad Autónoma de Madrid,
who implemented the Brownian hydrodynamic interactions and carried
out the numerical simulations and analysis. A detailed discussion on the
statistical and hydrodynamic aspects of this study can be found in Refer-
ence (Delgado-Buscalioni et al., 2017).

In the numerical simulations of the system formed by the fluid and
the ensemble of particles, optofluidic dynamics were numerically solved.
The robustness of the results were verified by considering two different

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