Structured light in complex channels

Abstract

The renewed interest in studying the relationship between the atmosphere and structured light can be, in part, attributed to the promise of free space optical (FSO) communication networks. These channels have been suggested as a mech- anism for bringing high speed internet connections to difficult-to-reach areas, overcoming the cost and hassle of traditional fibre optic connections. However, propagating structured light fields through complex media like the Earth’s at- mosphere introduces a new suite of problems. Understanding the interaction between optical fields and a turbulent atmosphere has therefore become a highly topical research field, and forms the focus of this dissertation.

A cursory introduction to structured light is presented in Chapter 1. The different families of beams studied in this dissertation are obtained from the Helmholtz equation and we describe the propagation of these beams using scalar diffraction theory. Next, the angular spectrum method of propagation is pre- sented as it is used for numerical simulations throughout this dissertation. Fi- nally, we explain how structured light fields can carry orbital angular momentum (OAM). This property of light is studied extensively in Chapter 4.

Chapter 2 discusses the experimental techniques and equipment used to shape light, simulate turbulence and take measurements. We illustrate how light is con- trolled in the laboratory through the implementation of holograms displayed on liquid crystal spatial light modulators and digital micromirror devices and pro- vide the procedure for generating these holograms. We then show how carefully chosen holograms are used to evaluate an inner product of two optical states to obtain a modal decomposition of a desired field.

Chapter 3 explains characteristics and statistics of atmospheric turbulence. Using these statistics and physical insight, we introduce the thin phase screen approximation to modelling weak turbulence and discuss the different methods used to generate these screens. We then extend this model to strong turbulence using the split-step method and the chapter concludes by discussing how the strength of these phase screens is calibrated in a laboratory setting.

Chapters 4 and 5 present novel research. The atmosphere is famous for causing distortions in the OAM spectrum of structured light beams. Chapter 4 recasts this effect as a transfer of OAM between the beam and the atmosphere by viewing the atmosphere as a store of OAM. Such a perspective allows us to resolve the debate on the effects of turbulence on structured light. We show that the spread in OAM of structured light beams caused by turbulent effects is symmetric about and independent of the beam’s initial OAM. Further, the spectrum finds a maximum value at the initial OAM. We show that the beam’s size determines a field’s behaviour in turbulence and not its OAM by considering Laguerre-Gaussian and perfect vortex modes.

Chapter 5 writes the turbulent channel as a linear operator and finds its corre- sponding eigenvectors, termed ‘eigenmodes’. These beams are invariant as they propagate through a turbulence atmosphere. The chapter explains important nu- merical details such as sampling constraints and we verify the robustness of the eigenmodes experimentally. When considering many realisations of turbulence, we show that it is better to use the ‘usual’ vacuum modes in communication studies as turbulence has a zero average effect on structured light fields.