Whether in art or physics, two dimensions are better than one.udAnd in this context, we consider the spatial shaping of opticaludfields and atomic polarisations.ududThis work begins with a comprehensive review of how toudaccurately and arbitrarily modulate transverse beam profilesudusing six different methods. The methods are presented in theudcontext of a general complex input beam and the shaping andudmeasuring of the input beam with a single SLM is discussed anduddemonstrated.udA simple setup is then considered that allows for the rapidudswitching between arbitrary profiles, using only a single holo-udgraphic component and an acousto-optical modulator (AOM). Inudthis setup, a switching speed of approximately 10 kHz is demon-udstrated explicitly, limited by the current detection system, butudwhere speeds of up to 20 MHz are estimated to be possible.udThe following discussion then concentrates on the spatialudstructure of atoms, reviewing the conceptual tools needed toudmeasure and interpret an atomic cloud in the presence of a mag-udnetic field from fundamental concerns, both in theory and inudpractice: assuming a classical light field and a quantum atomicudsystem. The specific implementation of both a magneto-opticaludtrap and a holographically-shaped dynamic dark SpOT follows.ududThe crux of the work then concerns how polarisation-structuredudlight can be used to create spatial patterns of transparency (spa-udtial EIT) within an atomic cloud. Beginning with a review of EITudin general, with particular focus on an F = 1 → F = 0 transition,udthe spatial modulation of absorption, dispersion, polarisationudrotation and change in ellipticity is predicted for systems in theudpresence of a transverse magnetic field. The depth of this mag-udnetic field dependency is then explored in some detail, where theudrelationship between observed patterns and applied magneticudfield suggests the possibility of a visual magnetometer. The finaludsection then considers how linearly polarised light and a q-plateudwas used to demonstrate spatially dependent transparency in audreal atomic cloud.
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