This thesis investigates the world of optics at the sub-wavelength scale, with a focus on understanding the behaviour of singularities that can arise in the electromagnetic field when confined to two dimensions. Predominantly we have investigated random waves, which are the most generic form of wave patterns. By treating these singularities as if they are real particles, we make use of methods from statistical physics to investigate their behaviour, both their spatial correlations, as well as their temporal dynamics through time-resolved measurements. Finally we show that it is possible to measure both infrared and visible light simultaneously, while still retaining sensitivity to amplitude, phase and polarization for both colours.@en

In order to utilize the full potential of tailored flows of electromagnetic energy at the nanoscale, we need to understand its general behavior given by its generic representation of interfering random waves. For applications in on-chip photonics as well as particle trapping, it is important to discern between the topological features in the flow-field of the commonly investigated cases of fully vectorial light fields and their 2D equivalents. We demonstrate the distinct difference between these cases in both the allowed topology of the flow-field and the spatial distribution of its singularities, given by their pair correlation function g(r). Specifically, we show that a random field confined to a 2D plane has a divergence-free flow-field and exhibits a liquid-like correlation, whereas its freely propagating counterpart has no clear correlation and features a transverse flow-field with the full range of possible 2D topologies around its singularities.

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