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Register a new userWhat is Nonreciprocity? Part II
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This paper is the second part of a two-part paper on emph{Electromagnetic (EM) Nonreciprocity (NR)}. Part~I has defined NR, pointed out that linear NR is a stronger form of NR than nonlinear (NL) NR, explained EM Time-Reversal (TR) Symmetry (TRS) Breaking (TRS-B), described linear Time-Invariant (TI) NR media, generalized the Lorentz reciprocity theorem for NR, and provided a physical interpretation of the resulting Onsager-Casimir relations~cite{Caloz_AWPL_NR_I_2018}. This part first explains the TR specificity of lossy and open systems. Next, it proposes an extended version of the S-parameters for emph{all NR} systems. Then, it presents the fundamentals of linear-TI (LTI) NR, linear Time-Variant (LTV) Space-Time (ST) modulated NR and NL NR systems. Finally, it addresses confusions between with systems.
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This paper aims at providing a global perspective on electromagnetic nonreciprocity and clarifying confusions that arose in the recent developments of the field. It provides a general definition of nonreciprocity and classifies nonreciprocal systems according to their linear time-invariant (LTI), linear time-variant (LTV) or nonlinear nonreciprocal natures. The theory of nonlinear systems is established on the foundation of the concepts of time reversal, time-reversal symmetry, time-reversal symmetry breaking and related Onsager- Casimir relations. Special attention is given to LTI systems, as the most common nonreciprocal systems, for which a generalized form of the Lorentz reciprocity theorem is derived. The delicate issue of loss in nonreciprocal systems is demystified and the so-called thermodynamics paradox is resolved from energy conservation considerations. The fundamental characteristics and applications of LTI, LTV and nonlinear nonreciprocal systems are overviewed with the help of pedagogical examples. Finally, asymmetric structures with fallacious nonreciprocal appearances are debunked.
Electromagnetically-induced-transparency (EIT) and Autler-Townes splitting (ATS) are two prominent examples of coherent interactions between optical fields and multilevel atoms. They have been observed in various physical systems involving atoms, molecules, meta-structures and plasmons. In recent years, there has been an increasing interest in the implementations of all-optical analogues of EIT and ATS via the interacting resonant modes of one or more optical microcavities. Despite the differences in their underlying physics, both EIT and ATS are quantified by the appearance of a transparency window in the absorption or transmission spectrum, which often leads to a confusion about its origin. While in EIT the transparency window is a result of Fano interference among different transition pathways, in ATS it is the result of strong field-driven interactions leading to the splitting of energy levels. Being able to tell objectively whether a transparency window observed in the spectrum is due to EIT or ATS is crucial for clarifying the physics involved and for practical applications. Here we report a systematic study of the pathways leading to EIT, Fano, and ATS, in systems of two coupled whispering-gallery-mode (WGM) microtoroidal resonators. Moreover, we report for the first time the application of the Akaike Information Criterion discerning between all-optical analogues of EIT and ATS, and clarifying the transition between them.
Tellurite glass fibers with embedded nanodiamond are attractive materials for quantum photonics applications. Reducing the loss of these fibers in the 600-800 nm wavelength range of nanodiamond fluorescence is essential to exploit the unique properties of nanodiamond in the new hybrid material. The first part of this study reported the origin of loss in nanodiamond-doped glass and impact of glass fabrication conditions. Here, we report the fabrication of nanodiamond-doped tellurite fibers with significantly reduced loss in the visible through further understanding of the impact of glass fabrication conditions on the interaction of the glass melt with the embedded nanodiamond. We fabricated tellurite fibers containing nanodiamond in concentrations up to 0.7 ppm-weight, while reducing the loss by more than an order of magnitude down to 10 dB/m at 600-800 nm.
Breaking Lorentz reciprocity was believed to be a prerequisite for nonreciprocal transmissions of light fields, so the possibility of nonreciprocity by linear optical systems was mostly ignored. We put forward a structure of three mutually coupled microcavities or optical fiber rings to realize optical nonreciprocity. Although its couplings with the fields from two different input ports are constantly equal, such system transmits them nonreciprocally either under the saturation of an optical gain in one of the cavities or with the asymmetric couplings of the circulating fields in different cavities. The structure made up of optical fiber rings can perform nonreciprocal transmissions as a time-independent linear system without breaking Lorentz reciprocity. Optical isolation for inputs simultaneously from two different ports and even approximate optical isolator operations are implementable with the structure.
General acceptance of a mathematical proposition $P$ as a theorem requires convincing evidence that a proof of $P$ exists. But what constitutes convincing evidence? I will argue that, given the types of evidence that are currently accepted as convincing, it is inconsistent to deny similar acceptance to the evidence provided for the existence of proofs by certain randomized computations.
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