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Digital Holography and Three-Dimensional Imaging

Smart transmission matrix measurement of multimode fibers using digital holography and deep learning for confidential data transmission

Stefan Rothe, Qian Zhang, Dennis Pohle, Nektarios Koukourakis, J. Czarske

Published Jan 1, 2022• 0 citations
Publisher

Abstract

We present smart measurements of the transmission matrix of multimode fibers (MMF). The modal crosstalk of the MMF is exploited by authorized communication participants against an eavesdropper towards physical layer security.
DOI
10.1364/dh.2022.m2a.5

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Multimode fibers hold great promise to advance data rates in optical communications but come with the challenge to compensate for modal crosstalk and mode-dependent losses, resulting in strong distortions. The holographic measurement of the transmission matrix enables not only correcting distortions but also harnessing these effects for creating a confidential data connection between legitimate communication parties, Alice and Bob. The feasibility of this physical-layer-security-based approach is demonstrated experimentally for the first time on a multimode fiber link to which the eavesdropper Eve is physically coupled. Once the proper structured light field is launched at Alice's side, the message can be delivered to Bob, and, simultaneously, the decipherment for an illegitimate wiretapper Eve is destroyed. Within a real communication scenario, we implement wiretap codes and demonstrate confidentiality by quantifying the level of secrecy. Compared to an uncoded data transmission, the amount of securely exchanged data is enhanced by a factor of 538. The complex light transportation phenomena that have long been considered limiting and have restricted the widespread use of multimode fiber are exploited for opening new perspectives on information security in spatial multiplexing communication systems.
Holographic transmission matrix measurements of optical multimode fibre communication channels enable optical precoding on the transmitter-side exploiting the physical layer. This approach can achieve a crucial SNR advantage for legitimate communication participants over illegitamte ones, such as an eavesdropper. We present measurements on a 55-mode fibre channel including transmitter Alice and receiver Bob, to which an eavesdropper Eve is physically coupled. Alice performs a programmable optical precoding through an SLM based on singular value decomposition enabling space division multiplexing. Demonstration of confidential data transmission is based on measurements from both channels Alice/Bob and Alice/Eve, which are used for determining the achievable amount of securely exchanged data between Alice and Bob, i.e. secrecy rate. Results are shown on step-index fibres of up to 100 m length.
The light propagation through a multimode fiber is used to increase information security during data transmission without the need for cryptographic approaches. The use of an inverse precoding method in a multimode fiber-optic communication network is based on mode-dependent losses on the physical layer. This leads to an asymmetry between legitimate (Bob) and illegitimate (Eve) recipients of messages, resulting in significant SNR advantage for Bob. In combination with dynamic mode channel changes, there are defined hurdles for Eve to reconstruct a sent message even in a worst-case scenario in which she knows the channel completely. This is the first time that physical layer security has been investigated in a fiber optical network based on measured transmission matrices. The results show that messages can be sent securely using traditional communication techniques. The technology introduced is a step towards the development of cyber physical systems with increased security.
Secret keys play a critical role in secure data transmission, and an efficient secret key generation scheme will enhance the secure transmission rate. However, the secret key is a scarce resource for classical encryption schemes like the Rivest-Shamir-Adleman (RSA) cryptosystem and its counterpart in quantum applications, and we should extract it from all possible random sources to maximize the key rate. In this paper, we investigate the achievable rate of the secret key generation (SKG)-channel-model based on an actual measured multi-mode fiber (MMF) channel, where there is an additional public discussion channel between the legitimate parties, which the adversary can perfectly overhear. In particular, we measure the fiber transmission matrix by digital holography. Based on the real measurements, we show that for 55-mode MMF, we can achieve a positive secret key rate at 51.3 bit/channel use with mode-dependent loss (MDL) at 1 dB and transmit power at 20 dBm. This demonstrates the feasibility of SKG in MMF.
Optical multicore and multimode fibers (MCF/MMF) are promised to pace with the capacity crunch of back-bone networks by their spatial domain using space division multiplexing (SDM) [1]. Although multiple channels propagate within the same media in parallel, material inhomogenities and bendings induce inter- and intra-core crosstalk (XT), the compensation of which is crucial for long-haul SDM-fiber deployment [2]. In addition, the inherent XT provides random scattering to be exploited for physical layer security (PLS), either as physical un-clonable function (PUF) [3] or secret key generation (SKG) for end-to-end security [4], [5]. For both, SDM and PLS, the main challenge is to recover the spatial amplitude and phase contributions of each channel at the receiver-side in real-time, e.g. by digital signal processing (DSP). With increased number of SDM channels the computational effort in DSP-based channel diagonalization arises.
The ability to engineer the spatial wavefunction of photons has enabled a variety of quantum protocols for communication, sensing, and information processing. These protocols exploit the high dimensionality of structured light enabling the encodinng of multiple bits of information in a single photon, the measurement of small physical parameters, and the achievement of unprecedented levels of security in schemes for cryptography. Unfortunately, the potential of structured light has been restrained to free-space platforms in which the spatial profile of photons is preserved. Here, we make an important step forward to using structured light for fiber optical communication. We introduce a smart high-dimensional encryption protocol in which the propagation of spatial modes in multimode fibers is used as a natural mechanism for encryption. This provides a secure communication channel for data transmission. The information encoded in spatial modes is retrieved using artificial neural networks, which are trained from the intensity distributions of experimentally detected spatial modes. Our on-fiber communication platform allows us to use spatial modes of light for high-dimensional bit-by-bit and byte-by-byte encoding. This protocol enables one to recover messages and images with almost perfect accuracy. Our smart protocol for high-dimensional optical encryption in optical fibers has key implications for quantum technologies relying on structured fields of light, particularly those that are challenged by free-space propagation.