Fototransducción

The structure of this thesis is separated approximately between three mainly theoretical chapters followed by four mainly experimental chapters.

The next two chapters concentrate on calculating the optical forces that act on the particles. The second chapter is devoted purely to a derivation of these optical forces analytically where the importance of both the polarisability of the particle and the intensity profile of the field are stressed. Both the Mie theory and Rayleigh theory are derived (the Rayleigh theory being an approximation to the more complex Mie theory). The thirdchapter investigates this intensity profile by analysing the fields of modes in an optical channel waveguide. This chapter is used to theoretically predict the charac- teristics of a waveguide that can then be used to design optimised waveguides.

The fourth chapter investigates the non-optical forces on the particles. These are the gravitational and buoyancy force, Brownian motion and a Stokes’ drag force, the DLVO theory that encompasses the van der Waals force and the double-layer force, and a force predicted by modelling of the temperature profile caused by absorption of the laser radiation. It then brings these forces together with the optical forces and discusses the relevance of each of them.

Thefifthchapter concentrates on the fabrication and characterisation of the waveguides used. It describes results from both K+and Cs+ion-exchanged waveguides in a range of substrates. It includes the characterisation of the composition of the substrates, effective index measurements, modal cut-off wavelengths and modal sizes.

Thesixth chapter discusses in detail the experimental apparatus and programs used to analyse and record the data. It also shows a range of results for particles being trapped along straight waveguides.

Theseventhchapter uses waveguides fabricated in the shape of a Y-junction and shows how these can be used to sort both gold and latex particles.

The eighthchapter introduces a counter-propagating wave and shows how this can be used to control the position of latex particles axially along the waveguide.

Finally in the ninth chapter the conclusions from the thesis are given and suggestions of future work in the area are put forward.

Throughout this thesis there are a small number of conventions that are used to make the reading of the thesis more fluent. Firstly when a particle size is referred to it should be taken to be referring to a spherical particle with the value being the particle diameter. Where the terms transverse, lateral and axial are used these refer to the dimensions normal to the substrate, in the plane of the substrate and normal to the waveguide and along the axis of the waveguide, respectively.

This project largely involves quantifying the motion of particles and it was felt that great benefit and understanding could be achieved for the reader by the use of animated

ROM is enclosed inside the back cover of this thesis. The reader is directed to the supplementary material section for details on how to access and use these movies. In all cases in the text a figure of the first frame is shown and it is made clear that there is a movie available for viewing.

Theory of Optical Forces on a

Particle

2.1

Introduction

To aid the understanding of how to improve the trapping and propulsion of particles this chapter studies the theory involved in the interaction of light and spherical particles. There are three potential analytical methods for analysing optical trapping forces on a particle. These are Rayleigh theory, Mie theory and a ray optics approach. The theory that should be applied depends upon the size of the particle [70].

The factor that determines which theory should be used for a certain particle is called the size parameter,χ, and is given as:

χ= 2πaNm

λ (2.1)

where a is the radius of the particle, N_m is the refractive index of the surrounding medium and λis the wavelength of light in a vacuum.

Although Mie theory is theoretically accurate for all size parameters it is unsuited to very small or very large particles. For particles much larger than the wavelength of light it is generally better to use the ray optics approach. This is because the Mie series uses a sum of an infinite series. This may be approximated by fewer terms, where the number of terms required increases with χ. If the number of terms is very large this can lead to small rounding errors introduced mounting up. For very small particles the Rayleigh theory can be used. This assumes a dipole is induced in the particle and is thus both conceptually and computationally much simpler. A guideline for the size range applicable to each theory is that for a¿ λ

Nm the Rayleigh theory may be used, for

a>20λ, geometrical theory can be used [71] and Mie theory should be used for particles between these approximate limits.

This chapter discusses both the Rayleigh and Mie theories. Although the particles used in this project would mainly fall into the size regime for which the Mie theory is the most suited, the Rayleigh theory is simpler, more intuitive and much less computationally demanding. The ray optics method is omitted as it would only be applicable to particles larger than those used in the project.

In the first section the Mie theory is derived for a plane wave and results for gold and latex particles are shown that give exact results for this case. The method to extend this to an evanescent wave is briefly outlined. An approximation to Mie theory is used to obtain the Rayleigh theory and the two are then compared to highlight the size limitations of the Rayleigh theory. The Rayleigh theory is derived by a more intuitive method and the importance of the polarisability of a particle is discussed. The form of the evanescent wave is applied to the theory to obtain expressions for the optical Rayleigh forces upon a particle in an evanescent wave. Values are estimated and used to demonstrate the trends and relative size of these forces.