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We introduce the notion of comparison of the criticality of two nodes in a coherent system, and devlop a monotonicity property of the reliability function under component pairwise rearrangement. We use this property to find the optimal component arrangement. Worked examples illustrate the methods proposed.

dielectric materials on a 2D material followed by postfabrication of PICs with lithography methods. [19][20][21][22] The layer transfer process of 2D materials on prefabricated PICs has the potential disadvantage of introducing strain and possible distortion of the 2D lattice if the strong van der Waals attraction between the 2D material and the dielectric surface produces conformal coverage over the sharp waveguide ridge corners, leading to reduced electron mobility, more phonon scattering centers, and possible degradation of device performance. While it is possible to planarize optical waveguides by additional processing involving deposition of low-refractive-index dielectrics followed by chemical-mechanical polishing, [6,8,13,23,24] such processes will reduce the optical overlap with the 2D material. For growing and patterning thin-film dielectric materials on 2D materials, the properties of both the thin-film dielectrics and 2D materials are usually affected adversely. [25][26][27][28] For example, the excellent properties of 2D materials can be destroyed by high-energy ions during the material growth process. Although some fabrication techniques for integrating 2D materials with dielectric materials like polymers [29] and chalcogenide glass [22] produce negligible effects on the material properties, they cannot universally be applied to many other types of dielectrics on 2D materials. In addition, few 2D materials can be grown on single-crystal materials with excellent optical properties. Therefore, a generic approach for integrating any types of 2D materials with any types of singlecrystal dielectrics is highly desired.The concept of "bound states in the continuum (BICs)" was first proposed by von Neumann and Wigner in 1929 with the mathematical construction of a 3D potential which can support perfectly confined states in a continuous band. [30] The radiation loss of these confined states can be eliminated by engineering their destructive interference with the continuous modes. [31][32][33][34][35][36][37][38][39] Harnessing BICs in PICs allows for low-loss light guidance and routing with a low-refractive-index waveguide on a high-refractive-index substrate. The light guided by the low-refractive-index waveguide can be confined to a region of the high-refractive-index substrate below the low-refractive-index waveguide. [40] Because the substrate is naturally flat, transferring a 2D material onto the high-refractive-index Integration of 2D materials on dielectric planar optical waveguides can make available new functionalities from the 2D materials' enhanced optoelectronic properties, such as nonlinearity, light emission, modulation, photodetection, and saturable absorption. However, the conventional integration schemes involving either the transfer of 2D materials onto prepatterned nonplanarized topology of photonic integrated circuits (PICs) or the growth and patterning of dielectric materials on 2D materials can degrade the properties of either the dielectric or the 2D material. Here, a fundamentally new ...

Majority systems are encountered in both decision theory and reliability theory. In decision theory for example a jury or committee employing a majority rule will make the ‘correct' decision if a majority of the individuals do so. In reliability theory some coherent systems function if and only if a majority of the components work properly. In this paper results concerning the reliability of majority systems are developed which are applicable in both areas. Two models incorporating dependence between individuals or components in majority systems are introduced, and various monotonicity results for their reliability functions are established. Comparisons are also made between direct (or simple) and indirect majority systems.

Photonic bound states in the continuum (BICs) have been exploited in various systems and found numerous applications. Here, we investigate high-order BICs and apply BICs on an integrated photonic platform to high-dimensional optical communication. A four-channel TM mode (de)multiplexer using different orders of BICs on an etchless lithium niobate (LiNbO 3) platform where waveguides are constructed by a low-refractive-index material on a highrefractive-index substrate is demonstrated. Low propagation loss of the TM modes in different orders and phase-matching conditions for efficient excitation of the high-order TM modes are simultaneously achieved. A chip consisting of four-channel mode (de)multiplexers was fabricated and measured with data transmission at 40 Gbps/channel. All the channels have insertion loss <4.0 dB and crosstalk <−9.5 dB in a 70-nm wavelength band. Therefore, the demonstrated mode (de)multiplexing and high-dimensional communication on LiNbO 3 platform can meet the increasing demand for high capacity in on-chip optical communication.