We theoretically examine the transport properties of non-ideal optical fibres with high numerical aperture. Using a simple spectral method, we derive the modes in perturbed or non-ideal fibres from the numerically evaluated modes of circularly symmetric fibres. We then consider the propagation through the fibre of Gaussian spots, projected onto the distal fibre end. The incident spots are of uniform, arbitrary polarization and positioned at any point on the fibre facet. We then evaluate the effect of propagation through the fibre in terms of various indices. In particular, we consider the motion of the centre of energy, the average polarization state and the average spin and orbital angular momentum. The study includes both step index and graded index optical fibres with symmetric and chiral deformations. We observe a fundamental difference between propagation in step index and graded index optical fibres: in the latter case, the centre of energy converges to the fibre axis as the light propagated along the fibre and in the former it moves erratically about the transverse plane. In addition, we find that circular polarization states are preserved for cylindrically symmetric fibres, of arbitrarily high numerical aperture. However, this property is destroyed by relatively weak deformations of the fibre.
Progress in the domain of complex photonics enabled a new generation of minimally invasive, high-resolution endoscopes by substitution of the Fourier-based image relays with a holographic control of light propagating through apparently randomizing multimode optical waveguides. This form of endo-microscopy became recently a very attractive way to provide minimally invasive insight into hard-to-access locations within living objects.
Here, we review our fundamental and technological progression in this domain and introduce several applications of this concept in bio-medically relevant environments.
By taking advantage of the cylindrical symmetry of the fibre and the known distribution of the refractive index, we show how to simplify measurement of the transmission matrix of such fibres and correct for the influences of bending deformations.
Our newest addition is the employment of Graded-index fibres, which, based on our numerical model, and first experimental verifications, allow for much simpler compensation of bending deformation when compared to step-index fibres.
Lastly we show the development and exploitation of highly specialized fiber probes for optical manipulation. We show that light control through these fibres allows sufficiently tight focusing for confinement and manipulation of large particle arrays, and their positioning with nanometric precision.
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