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[M. W. Matthès et al., Optica, 6 (2019)]

Performing linear operations using optical devices is a crucial building block in many fields ranging from telecommunications to optical analogue computation and machine learning. For many of these applications, key requirements are robustness to fabrication inaccuracies, reconfigurability and scalability. Traditionally, the conformation or the structure of the medium is optimized in order to perform a given desired operation. Since the advent of wavefront shaping, we know that the complexity of a given operation can be shifted toward the engineering of the wavefront, allowing, for example, to use any random medium as a lens.

In [M. W. Matthès et al., Optica, 6 (2019)], we propose to use this approach to use complex optical media such as multimode fibers or scattering media as a computational platform driven by wavefront shaping to perform analogue linear operations. Given a large random transmission matrix representing the light propagation in such a medium, we can extract any desired smaller linear operator by finding suitable input and output projectors. We demonstrate this concept by finding input wavefronts using a Spatial Light Modulator that cause the complex medium to act as a desired complex-valued linear operator on the optical field.

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I recently published a two-part tutorial on how to find the modes of an arbitrary multimode fiber without or with bending. Based on this tutorial, I published a (still experimental) version of a Python module to find the modes of multimode fibers and calculate their transmission matrix: pyMMF. The goal of this module is not to compete with commercial solutions in term of precision but to provide a way to easily simulate realistic fiber systems. To validate the approach, I use step-index multimode fibers as a benchmark test as the dispersion relation is analytically known (see my tutorial here) and for which the Linearly Polarized (LP) mode approximation yields good results. I focus my attention here on the precision of the numerically found propagation constants.

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We saw in the first part of the tutorial that the profiles and the propagation constants of the propagation modes of a straight multimode fiber can easily be avulated for an arbitrary index profile by inverting a large but sparse matrix. Under some approximations [1], a portion of fiber with a fixed radius of curvature satisfies a similar problem that can be solved with the same numerical tools, as we illustrate with the PyMMF Python module [2]. Moreover, when the modes are known for the straight fiber, the modes for a fixed radius can be approximate by inverting a square matrix of size the number of propagating modes [1]. It allows fast computation of the modes for different radii of curvature.

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Under the weakly guided approximation, analytical solutions for the mode profiles of step index (SI) and graded index (GRIN) multimode fibers (MMF) can be found [1]. It also gives a semi-analytical solution for the dispersion relation in SI MMFs, and, by adding stronger approximations, an analytical solution for the parabolic profile GRIN MMFs [2] (note that those approximations do fail for lower order modes). An arbitrary index profile requires numerical simulations to estimate the mode profiles and the corresponding propagation constants of the modes. I present in this tutorial how to numerically estimate the scalar solution for the profiles and propagation constants of guides modes in multimode circular waveguide with arbitrary index profile and in presence of bending. I released a beta version of the Python module pyMMF based on such approach [3]. It relies on expressing the transverse Helmholtz equation as an eigenvalue problem. Solutions are found by finding the eigenvectors of a large but spare matrix representing the equation on the discretized space.

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We published previously a tutorial presenting a technique to calibrate spatial light modulators (SLMs). The approach was based on measuring the interference between two paths that have been reflected off two different regions of the SLM. This technique is always valid but requires aligning a mask, using a lens and capturing and treating images of interference patterns. Nowadays, most phase only SLMs based on liquid crystals use linearly aligned nematic crystals. Unlike twisted nematic liquid crystals, they allow phase only modulation on one polarization while not affecting the orthogonal polarization. This feature can be used to simplify the calibration setup to characterize the SLM with a common path interferometer, not requiring a precise alignment [1]. Furthermore, it only needs a photo-detector, compared to a digital camera in the previously presented approach. This is convenient to measure the inevitable phase fluctuations of an SLM, usually around a 100 to 400 Hz frequency. In this document, we briefly describe the principle of the characterization scheme as presented in [2] and show typical results of the calibration and the phase fluctuations.

Written by Paul Balondrade and Sébastien M. Popoff

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We seek applications from suitably qualified candidates who will focus on the development of optical systems for the measurement and manipulation of the spatial, spectral and temporal properties of light in multimode optical fibre. The position is funded under an Australian Research Council (ARC), Discovery Project in collaboration with the University of Southampton and industrial partners Nokia (Bell Labs, US) and Finisar Australia.

Examples of previous work in this area available here : https://www.youtube.com/user/joelacarpenter

Duration: 2-3 years