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arXiv:1706.04297 · Optica

Demonstration of an optical-coherence converter

Chukwuemeka Okoro, H. Esat Kondakci, Ayman F. Abouraddy, Kimani C. Toussaint

Published Aug 28, 2017• 31 citations
arXivHTMLPDF

Abstract

Studying the coherence of an optical field is typically compartmentalized with respect to its different optical degrees of freedom (DoFs) -- spatial, temporal, and polarization. Although this traditional approach succeeds when the DoFs are uncoupled, it fails at capturing key features of the field's coherence if the DOFs are indeed correlated -- a situation that arises often. By viewing coherence as a `resource' that can be shared among the DoFs, it becomes possible to convert the entropy associated with the fluctuations in one DoF to another DoF that is initially fluctuation-free. Here, we verify experimentally that coherence can indeed be reversibly exchanged -- without loss of energy -- between polarization and the spatial DoF of a partially coherent field. Starting from a linearly polarized spatially incoherent field -- one that produces no spatial interference fringes -- we obtain a spatially coherent field that is unpolarized. By reallocating the entropy to polarization, the field becomes invariant with regards to the action of a polarization scrambler, thus suggesting a strategy for avoiding the deleterious effects of a randomizing system on a DoF of the optical field.

DOI
10.1364/optica.4.001052

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Studying the coherence of an optical field is typically compartmentalized with respect to its different optical degrees of freedom (DoFs) -- spatial, temporal, and polarization. Although this traditional approach succeeds when the DoFs are uncoupled, it fails at capturing key features of the field's coherence if the DOFs are indeed correlated -- a situation that arises often. By viewing coherence as a `resource' that can be shared among the DoFs, it becomes possible to convert the entropy associated with the fluctuations in one DoF to another DoF that is initially fluctuation-free. Here, we verify experimentally that coherence can indeed be reversibly exchanged -- without loss of energy -- between polarization and the spatial DoF of a partially coherent field. Starting from a linearly polarized spatially incoherent field -- one that produces no spatial interference fringes -- we obtain a spatially coherent field that is unpolarized. By reallocating the entropy to polarization, the field becomes invariant with regards to the action of a polarization scrambler, thus suggesting a strategy for avoiding the deleterious effects of a randomizing system on a DoF of the optical field.
The entropy associated with an optical field quantifies the field fluctuations and thus its coherence. Any binary optical degree-of-freedom (DoF) - such as polarization or the field at a pair of points in space - can each carry up to one bit of entropy. We demonstrate here that entropy can be reversibly swapped between different DoFs, such that coherence is converted back and forth between them without loss of energy. Specifically, starting with a spatially coherent but unpolarized field carrying one bit of entropy, we unitarily convert the coherence from the spatial DoF to polarization to produce a spatially incoherent but polarized field by swapping the entropy between the two DoFs. Next, we implement the inverse unitary operator, thus converting the coherence back to yield once again a spatially coherent yet unpolarized field. We exploit the intermediate stage between the two coherence conversions - where the spatial coherence has been converted to the polarization DoF - to verify that the field has become immune to the deleterious impact of spatial phase scrambling. Maximizing the spatial entropy protects the spatial DoF by preventing it from taking on any additional fluctuations. After the second coherence conversion, spatial coherence is readily retrieved, and the effect of spatial phase scrambling circumvented.
Optical coherence is a well-established branch of physical optics in which the statistical properties of fluctuating optical fields are described in terms of correlation functions over continuous spatial and temporal degrees of freedom (DoFs). Nevertheless, in any practical setting, only discrete DoFs are ever accessible. In these scenarios, the modes are fixed, stable, and deterministic, and partial coherence arises from random relative complex amplitudes, a configuration we refer to as 'structured coherence'. Advances in structured coherence have recently unveiled new conceptual ground in optical communications and information processing in which partial coherence may be preferable to full coherence, which we call a 'coherence advantage'. We formulate structured coherence in terms of coherence matrices to investigate these recent theoretical and experimental breakthroughs. We first review optical fields characterized by a binary DoF via 2x2 Hermitian coherence matrices and introduce key concepts that take on new significance for larger-dimensional modal sets. Next, we examine the structured coherence of two binary DoFs, which can be described by 4x4 coherence matrices. We introduce the concept of coherence rank, entropy swapping, and optical cross-purity. In the perspective outlined here, coherence is viewed as a 'resource', which can be exchanged between DoFs, concentrated into a DoF or into particular modes, or spread over the DoFs. We then examine larger-dimensional modal sets, which allow for more versatile applications in optical information processing. The formulation presented here lends itself particularly to the manipulation of partial optical coherence in integrated photonic platforms, thereby opening myriad avenues for novel fundamental investigations of structured coherence and exploiting the coherence advantage in optical communications and information processing.
In optical communications, logical bits (0 and 1) encoded in light’s degrees-of-freedom (DoFs) are confounded in scattering channels. This scattering may affect a single DoF, e.g., a rotation in polarization, or DoFs may be coupled, e.g., polarization may be coupled to spatial modes, leading to a bit error in both scenarios. Adaptive techniques that probe the channel may be used to prescribe an optical field with properties that counteract the scattering. However, these techniques are ineffective if the channel changes stochastically bit-to-bit. In this work, we utilize partially coherent light to circumvent the deleterious effects of a channel that rapidly and randomly scatters one or two DoFs, including operations that couple DoFs. Partially coherent fields in which two DoFs are relevant can be described by a 4×4 coherence matrix, the rank of which (the coherence-rank) is invariant to unitary channels. In our experiments, we use channels that stochastically change bit-to-bit, unitarily scattering the polarization and spatial DoFs leading to scrambled information transfer when bits are encoded in just one of these DoFs. The scattering from these channels is subverted when data is encoded in the coherence-rank. These results offer a new method of using partially coherent light for optical communications through scrambling channels.