Electromagnetic fields and forces in nanostructures
File(s)
Author(s)
Antonoyiannakis, Emmanuel (Manolis) Ioannou
Type
Thesis
Abstract
We have developed a general methodology for computing electromagnetic (EM)
fields and forces in matter, based on solving the macroscopic Maxwell's equations
numerically in real space and adopting the time-averaged Maxwell Stress Tensor
formalism. Our approach can be applied to both dielectric and metallic systems
characterised by a local frequency-dependent dielectric function, and in principle
to any size and geometry. In this study we are particularly interested in calculating
forces on nanostructures, induced by a beam of monochromatic light (such
as a laser) of frequency w. These forces are the direct analogue of Van der Waals
interactions at a single frequency: the presence of matter scatters the light and
alters the EM field, resulting in an energy-change that manifests itself as a force.
The motivation behind this particular direction is the facilitation of self-assembly
in colloidal systems with the aim of aiding the fabrication of photonic crystals.
In order to understand the main features of light-induced EM forces, as well
as to provide a testbed for our numerical methodology, we first solve (analytically
and numerically) for two homogeneous systems: a half-space and a slab. We find
that in passing from a low-e to a high-e medium, the light beam always attracts
the interface {i.e. the surface force is negative). The implication is that light will
generally induce an attraction between the surfaces of two liquids separated by a
layer of lower e. For attraction between solids there is a tougher requirement: the
total force must also be negative. When the EM field is that of a travelling wave
the total pressure is positive. In contrast, evanescent waves may cause the total
pressure to become attractive (negative). Thus by shining evanescent light in the
region between two solid bodies an attraction between them may be induced.
We then study numerically the influence of monochromatic light (a travelling
wave) on a crystal of dielectric spheres of GaP, concentrating on total forces
induced on each sphere and on the crystal as a whole. We identify three regimes
in the response of the system to radiation:
• At large wavelengths the crystal may be approximated by a homogeneous slab
with an effective permittivity eg//. The analytical results for reflectance and
forces apply.
• At wavelengths comparable to the lattice constant, multiple scattering effects
tune in: when lo is inside the photonic band gaps the reflectivity of a thick
crystalline slab rises to unity, the beam bounces off the crystal and there is a
maximum momentum exchange (and largest forces). Also, a multitude of force
orientations results when the Bragg conditions for multiple outgoing waves are
met.
• Much more interesting is the regime where the radiation couples to the E M
eigenmodes supported by isolated spheres (Mie resonances). These modes are
analogous to electronic orbitals and, like their electronic counterparts, can form
bonding and anti-bonding interactions between neighbouring spheres. By irradiating
the system with light at the bonding frequency an attractive interaction
is induced between the spheres. The photo-induced attraction is strong; for a
moderate /q ^ 3 x 10® W/m^ it surpasses all other interactions present (gravitational,
thermal and Van der Waals) by 1-2 orders of magnitude. These resonant
forces are sensitive to absorption, but, for GaP spheres in water (a common liquid
medium for colloids), their effect should still be clearly seen, even for a polydispersion
of a few percent. Thus we suggest that by judicious selection of bonding
states we can drive a system towards a desired structure, rather than rely on the
structure dictated by gravitational and Van der Waals forces. Apart from possible
applications in the fabrication of 3D photonic crystals, the resonant mechanism
leading to the bonding/anti-bonding effect may contribute to our understanding
of novel non-linear phenomena arising due to the application of laser light fields
in nanostructures.
fields and forces in matter, based on solving the macroscopic Maxwell's equations
numerically in real space and adopting the time-averaged Maxwell Stress Tensor
formalism. Our approach can be applied to both dielectric and metallic systems
characterised by a local frequency-dependent dielectric function, and in principle
to any size and geometry. In this study we are particularly interested in calculating
forces on nanostructures, induced by a beam of monochromatic light (such
as a laser) of frequency w. These forces are the direct analogue of Van der Waals
interactions at a single frequency: the presence of matter scatters the light and
alters the EM field, resulting in an energy-change that manifests itself as a force.
The motivation behind this particular direction is the facilitation of self-assembly
in colloidal systems with the aim of aiding the fabrication of photonic crystals.
In order to understand the main features of light-induced EM forces, as well
as to provide a testbed for our numerical methodology, we first solve (analytically
and numerically) for two homogeneous systems: a half-space and a slab. We find
that in passing from a low-e to a high-e medium, the light beam always attracts
the interface {i.e. the surface force is negative). The implication is that light will
generally induce an attraction between the surfaces of two liquids separated by a
layer of lower e. For attraction between solids there is a tougher requirement: the
total force must also be negative. When the EM field is that of a travelling wave
the total pressure is positive. In contrast, evanescent waves may cause the total
pressure to become attractive (negative). Thus by shining evanescent light in the
region between two solid bodies an attraction between them may be induced.
We then study numerically the influence of monochromatic light (a travelling
wave) on a crystal of dielectric spheres of GaP, concentrating on total forces
induced on each sphere and on the crystal as a whole. We identify three regimes
in the response of the system to radiation:
• At large wavelengths the crystal may be approximated by a homogeneous slab
with an effective permittivity eg//. The analytical results for reflectance and
forces apply.
• At wavelengths comparable to the lattice constant, multiple scattering effects
tune in: when lo is inside the photonic band gaps the reflectivity of a thick
crystalline slab rises to unity, the beam bounces off the crystal and there is a
maximum momentum exchange (and largest forces). Also, a multitude of force
orientations results when the Bragg conditions for multiple outgoing waves are
met.
• Much more interesting is the regime where the radiation couples to the E M
eigenmodes supported by isolated spheres (Mie resonances). These modes are
analogous to electronic orbitals and, like their electronic counterparts, can form
bonding and anti-bonding interactions between neighbouring spheres. By irradiating
the system with light at the bonding frequency an attractive interaction
is induced between the spheres. The photo-induced attraction is strong; for a
moderate /q ^ 3 x 10® W/m^ it surpasses all other interactions present (gravitational,
thermal and Van der Waals) by 1-2 orders of magnitude. These resonant
forces are sensitive to absorption, but, for GaP spheres in water (a common liquid
medium for colloids), their effect should still be clearly seen, even for a polydispersion
of a few percent. Thus we suggest that by judicious selection of bonding
states we can drive a system towards a desired structure, rather than rely on the
structure dictated by gravitational and Van der Waals forces. Apart from possible
applications in the fabrication of 3D photonic crystals, the resonant mechanism
leading to the bonding/anti-bonding effect may contribute to our understanding
of novel non-linear phenomena arising due to the application of laser light fields
in nanostructures.
Version
Open Access
Date Issued
1998-06
Date Awarded
1998
Copyright Statement
Attribution NoDerivatives 4.0 International Licence (CC BY-ND)
Advisor
Pendry, John
Sponsor
Imperial College London
Publisher Department
Physics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)
Author Permission
Permission granted