[Paper Review] How to build the optical inverse of a multimode fibre

Unė G. Būtaitė, Hlib Kupianskyi+2 more|arXiv (Cornell University)|Apr 6, 2022

Random lasers and scattering media66 references7 citations

TL;DR

This paper proposes a passive, diffractive optical inverter—designed via inverse design—that simultaneously unscrambles all spatial modes in a multimode fibre (MMF) in a single shot, enabling wide-field and super-resolution imaging through MMFs. The inverter, composed of a cascade of optimized phase masks, acts as a complementary scattering medium that reverses the MMF's transmission matrix, preserving phase and coherence, and outperforms electronic neural networks in unscrambling incoherent light with minimal resolution loss.

ABSTRACT

When light propagates through a multimode optical fibre (MMF), the spatial information it carries is scrambled. Wavefront shaping can undo this scrambling, typically one spatial mode at a time - enabling deployment of MMFs as ultra-thin micro-endoscopes. In this work we go beyond serial wavefront shaping by showing how to simultaneously unscramble all spatial modes emerging from an MMF in parallel. We introduce a passive multiple-scattering element - crafted through the process of inverse design - that is complementary to an MMF and undoes its optical effects. This optical inverter makes possible both single-shot wide-field imaging and super-resolution imaging through MMFs. Our design consists of a cascade of diffractive elements, and can be understood from the perspective of both multi-plane light conversion, and as a physically inspired deep diffractive neural network. This physical architecture can outperform state-of-the-art electronic neural networks tasked with unscrambling light, as it preserves the phase and coherence information of the optical signals flowing through it. Here we demonstrate our MMF inversion concept through numerical simulations, and efficiently sort and unscramble up to ~400 step-index fibre modes, reforming incoherent images of scenes at arbitrary distances from the distal fibre facet. We also describe how our optical inverter can dynamically adapt to see through flexible fibres with a range of experimentally realistic TMs - made possible by moulding optical memory effects into the structure of our design. Although complex, our inversion scheme is based on current fabrication technology so could be realised in the near future. Beyond imaging through scattering media, these concepts open up a range of new avenues for optical multiplexing, communications and computation in the realms of classical and quantum photonics.

Motivation & Objective

• To overcome the limitations of serial wavefront shaping in multimode fibres, which restricts imaging to scanning or sequential mode unscrambling.
• To enable single-shot, wide-field imaging and super-resolution microscopy at the distal end of a multimode fibre.
• To develop a passive optical system that inverts the transmission matrix of an MMF without requiring real-time measurements or electronic feedback.
• To preserve phase and coherence of optical signals, enabling potential applications in quantum imaging and quantum communication.
• To demonstrate dynamic adaptability of the optical inverter to varying fibre transfer matrices through a reconfigurable phase mask.

Proposed method

• The optical inverter is designed using inverse design to create a cascade of 29 diffractive phase masks separated by free-space propagation, forming a multi-plane light conversion (MPLC) structure.
• The system is structured into three functional modules: a mode sorting module, a phase correction module, and a mode combining module, inspired by physical principles rather than purely data-driven optimization.
• The design is trained using the fibre's spatial modes as the optimal basis, ensuring efficient representation of any image transmitted through the MMF.
• The inverter's transfer function is engineered to be the inverse of the MMF's transmission matrix, such that the combined system acts as an identity operator convolved with the diffraction-limited point spread function.
• The design incorporates optical memory effects by integrating a single reconfigurable phase mask, allowing dynamic adaptation to different fibre transfer matrices.
• The system is modeled as a physically inspired deep diffractive neural network, with performance benchmarked against electronic neural networks trained on intensity-only data.

Experimental results

Research questions

• RQ1 Can a passive, all-optical system be designed to simultaneously unscramble all spatial modes in a multimode fibre in a single shot?
• RQ2 How can inverse design be used to create a diffractive optical element that acts as the exact inverse of a multimode fibre's transmission matrix?
• RQ3 To what extent can such an optical inverter outperform electronic neural networks in unscrambling incoherent optical signals while preserving phase and coherence?
• RQ4 Can the optical inverter be dynamically reconfigured to adapt to different multimode fibres or varying transmission matrices?
• RQ5 What are the limits of spectral bandwidth and imaging distance for such an optical inversion system?

Key findings

• The optical inverter successfully unscrambles up to approximately 400 step-index fibre modes in numerical simulations, enabling the reformation of incoherent images at arbitrary distances beyond the fibre's distal facet.
• The system achieves single-shot wide-field imaging through the MMF, overcoming the frame-rate and scanning limitations of conventional wavefront shaping.
• The inverter preserves the phase and coherence of optical signals, enabling potential applications in quantum imaging and quantum communication where entanglement must be maintained.
• The design outperforms electronic neural networks trained on intensity-only data, particularly in unscrambling incoherent light with minimal resolution degradation.
• The integration of a reconfigurable phase mask allows the inverter to dynamically adapt to a range of experimentally realistic transmission matrices, enabling operation with flexible or variable fibres.
• The system's performance is rooted in its physical architecture as a multi-plane light converter, which enables high-fidelity image reconstruction without iterative computation.