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Reciprocity is fundamental to light transport and is a concept that holds also in rather complex systems. Yet, reciprocity can be switched off even in linear, isotropic and passive media by setting the material structure into motion. In highly dispersive multilayers this leads to a fairly large forwardbackward asymmetry in the pulse transmission. Moreover, in multilevel systems, this transport phenomenon can be all-optically enhanced. For atomic multilayer structures made of three-level cold 87 Rb atoms, for instance, forward-backward transmission contrast around 95% can be obtained already at atomic speeds in the meter per second range. The scheme we illustrate may open up avenues for optical isolation that were not previously accessible.PACS numbers: 42.50. Wk, 42.70.Qs, 42.50.Gy, 37.10.Vz Much attention has been devoted to the development of advanced materials and composite systems to achieve optical functionalities not readily available in natural media. Such optical metamaterials can be engineered to stretch the rules that govern light propagation and lightmatter interaction, potentially seeding a new paradigm in all-optical, optoelectronic and optomechanical devices. Photonic crystals and negatively refracting media are prominent instances of man-made systems the optical properties of which can be tailored to a great extent. Nevertheless, some tasks are more difficult than others. Already in the familiar process of linear reflection and transmission of light [1] it is in general hard to achieve non-reciprocity. In particular, multilayer photonic structures made with linear isotropic media with dissipation and/or gain may exhibit reflection non-reciprocity, i.e., an unbalance between the forward and backward reflectivities. There are even cases in which one of them can be made negligible and the other one can increase without limit with the sample thickness [2]; this occurs in the so called P T -symmetric media which exhibit a variety of peculiar optical properties [3,4]. Yet, it is not possible to achieve a non-reciprocal transmissivity in such linear and passive systems. Transmission reciprocity is almost ubiquitous in optics [1,5].Non-reciprocal transmission is however rather desirable for information processing and crucial to the development of optical-based functional components in photonics. In much the same way in which electrical nonreciprocity has been realized through diodes, devising an optical diode is challenging, even in theory. Ideally, an optical diode would allow total light transmission over a bundle of wavelengths in one direction, providing total isolation in the reverse direction. Previous * s.horsley@exeter.ac.uk work on non-reciprocal transmission has been based on either magneto-optical effects [6][7][8] or non linear processes [9,10]. Other mechanisms have also been explored [11][12][13] and realized experimentally [14], including more involved diode designs based on two-dimensional square-lattice photonic crystals [15] or non-symmetric photonic crystal gratings exhibiting anomal...

We study a double-cavity optomechanical system in which a movable mirror with perfect reflection is inserted between two fixed mirrors with partial transmission. This optomechanical system is driven from both fixed end mirrors in a symmetric scheme by two strong coupling fields and two weak probe fields. We find that three interesting phenomena: coherent perfect absorption (CPA), coherent perfect transmission (CPT), and coherent perfect synthesis (CPS) can be attained within different parameter regimes. That is, we can make two input probe fields totally absorbed by the movable mirror without yielding any energy output from either end mirror (CPA); make an input probe field transmitted from one end mirror to the other end mirror without suffering any energy loss in the two cavities (CPT); make two input probe fields synthesized into one output probe field after undergoing either a perfect transmission or a perfect reflection (CPS). These interesting phenomena originate from the efficient hybrid coupling of optical and mechanical modes and may be all-optically controlled to realize novel photonic devices in quantum information networks.

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