Deformation enduring conveyance of structured light through multimode waveguides and its exploitation for flexible hair-thin endoscopes

Abstract

The remarkable advancements in our capacity to synthesise structured light have facilitated the generation of any desired optical landscapes and even controlling the spatial distribution of light propagating through optically complex media such as multimode fibres. The availability of precisely defined structured light at the extremity of an exceedingly narrow and flexible cable holds the potential to stimulate a diverse range of highly sought-after applications, encompassing rapid communication, quantum computing, and, notably, imaging. What we lack in reaching these aspirations is the resilience of such light transport to deformations of the waveguide. Although recent theoretical investigations have delineated the attributes of ideal multimode fibres capable of deformation-enduring conveyance of structured light, tangible fibres possessing this indispensable trait to a practical extent remain elusive. Our study takes a deep dive into the precision of commercially available multimode fibres with the highest probability of demonstrating the phenomenon. We identified minuscule imperfections in their refractive index distribution, examined how these affect light transport when the fibre is deformed, and studied their implications for imaging applications. Our investigation has confirmed that these imperfections are indeed responsible for the undesirable alterations introduced into the output structured light fields during bending. Finally, as an alternative to standard graded-index fibres, manufactured by drawing silica-based preforms, we present narrow multimode waveguides in which the refractive-index profile has been established by ion exchange. These waveguides indeed exhibit previously unseen resilience of structured light transport even under severe deformation conditions and aptly fulfil the requirements of imaging applications.

Figures (3)

• Figure 1: Qualitative illustration of bending resilience. ( A) Bending tool translating and reorienting the distal end imposing adiabatic curvature along the used fibre. ( B) Range of adiabatic fibre layouts used. ( C) Scene recorded by SI fibre. The central part is obtained by combining narrow middle sectors (5 pixels wide) of images obtained as the fibre was bend across the full range of the bending tool. Half-moon parts at the left and the right are taken from the first and the last recorded image respectively. ( D) Scene recorded by the best performing commercially available graded-index fibres of our selection and the best roll orientation, with the lowest and the highest information capacity ($\mathrm{GI_{S}^{1}}$ and $\mathrm{GI_{L}^{2}}$). ( E) Scene recorded by DECStL waveguide for its full information capacity. Roll orientation played no observable role.
• Figure 2: Imaging performance bending resilience modelling for aberrated fibres.$\mathrm{GI_{M}^{2}}$ is used as model case for all data shown in this figure. ( A) Interferogram of fibre placed perpendicularly with respect to the object wave direction. ( B) Computer tomography-based reconstruction of refractive index difference from that of the cladding material. ( C) Isolated aberration after paraboloid dependence has been subtracted. ( D) Aberration after low-pass filtering by projection onto 300 lowest Zernike polynomials. ( E) PIMs of perfect parabolic fibre. Solid line indicates their order considered in deformation operators below. ( F to H) DOs for straight fibre (unitary matrix) and two cases bent fibre (distal yaw of 90°) for different roll orientations. For better clarity the basis in these examples has been reduced to 320 PIMs of the lowest order (largest propagation constants), where the strongest effects of bending appear. ( I and J) Diagonal components of complete DOs organised into mode pyramids (as in D) for two different roll orientations and gradually increasing distal end yaw. ( K to M) Examples of far-field foci formed through deformations of F to H, considering the fibre was calibrated at the straight layout. ( N to P) Simulated raster-scanning-based imaging of single-spatial-frequency gratings for corresponding deformations. ( Q) Contrast transfer function evolution under the influence of bending. Values of contrast were averaged over the field of view and four different orientations of the grating's fringes. The red contour signifies the resolution limiting 9% frequency (analogous to Rayleigh criterion). ( R) 9% frequency and total information capacity dependence on the distal end yaw for several different roll orientations of the fibre.
• Figure 3: Experimental assessment of imaging performance resilience to bending and its comparison to theoretical prediction.$\mathrm{GI_{M}^{2}}$ is used as model case for results shown in panels A to C. ( A) Illustration of experimental settings and procedure. ( B and C) Raw images of Ronchi targets obtained for straight and bent (90° distal yaw) fibre layouts respectively. ( D) Normalised contrast transfer function evolution under the influence of bending. The red contour signifies the resolution limiting 9% frequency. ( E) Modelled decline of total information capacity (number of resolvable features) under the influence of bending for four fibres which our model could handle. Shaded intervals signify spread obtained for different roll orientations. ( F) Corresponding experimental results for the same fibre selection as in E, with additional fibres of higher capacity and the step-index type. ( G) Equivalent measurements on DECStL waveguide with information capacity of the initial layout manipulated by aperturing the input signals.