Localisation and disorder in the design of 2D photonic crystal devices

Photonic crystals are meta-materials that can inhibit the propagation of light in all directions for specific wavelength ranges. Material or structural defects can be introduced into the crystal to cause localised modes, providing the ability to mould the flow of light on the wavelength scale and allowing the development of miniaturised, integrated photonic devices. For this reason, photonic crystals will likely be key building blocks for future micro-optical and communication technology. In this paper, we examine the Bloch mode modelling of 2D photonic crystal structures with application to the analysis of photonic crystal waveguides and their susceptibility to disorder, which provides a framework for studying fabrication tolerances in realistic devices

Diffusion and anomalous diffusion of light in two-dimensional photonic crystals

The transport properties of electromagnetic waves in disordered, finite, two-dimensional photonic crystals composed of circular cylinders are considered. Transport parameters such as the transport and scattering mean free paths and the transport velocity are calculated, for the case where the electromagnetic radiation has its electric field along the cylinder axes. The range of the parameters in which the diffusion process can take place is specified. It is shown that the transport velocity [Formula presented] can be as much as [Formula presented] times less than its free space value, while just outside the cluster [Formula presented] can be 0.3c. The effects of weak and strong disorders on the transport velocity are investigated. Different regimes of the wave transport—ordered propagation, diffusion, and anomalous diffusion—are demonstrated, and it is inferred that Anderson localization is incipient in the latter regime. Exact numerical calculations from the Helmholtz equation are shown to be in good agreement with the diffusion approximation. © 2003 The American Physical Society

Conductance of photons and Anderson localization of light

Conductance properties of photons in disordered two-dimensional photonic crystals is calculated using exact multipole expansions technique. The Landauers two-terminal formula is used to calculate average of the conductance, its variance and the probability density distribution

Building a Practical Natural Laminar Flow Design Capability

A preliminary natural laminar flow (NLF) design method that has been developed and applied to supersonic and transonic wings with moderate-to-high leading-edge sweeps at flight Reynolds numbers is further extended and evaluated in this paper. The modular design approach uses a knowledge-based design module linked with different flow solvers and boundary layer stability analysis methods to provide a multifidelity capability for NLF analysis and design. An assessment of the effects of different options for stability analysis is included using pressures and geometry from an NLF wing designed for the Common Research Model (CRM). Several extensions to the design module are described, including multiple new approaches to design for controlling attachment line contamination and transition. Finally, a modification to the NLF design algorithm that allows independent control of Tollmien-Schlichting (TS) and cross flow (CF) modes is proposed. A preliminary evaluation of the TS-only option applied to the design of an NLF nacelle for the CRM is performed that includes the use of a low-fidelity stability analysis directly in the design module

Modernizing Language in the California Government Claims Act to Enable Consistent Enforcement of Statutory Sovereign Immunity

Ideally, sovereign immunity provisions should (1) protect public officials from undue interference with discharge of their duties and (2) hold accountable public officials who act unlawfully. Analytical frameworks and statutes at both the federal and state levels often fail to fulfill these objectives. Federal courts are guided by statutes and objectives that are indirectly relevant to state courts. As a result, states are left to address independently how to address clams of sovereign immunity when plaintiffs file suits alleging torts by public entities and employees. In California, when plaintiffs sue public employees or entities in civil court, the California Government Claims Act (GCA) determines whether defenses of sovereign immunity may preclude liability. However, the statutory language of the GCA mirrors the common law language in force at the time the GCA was enacted. This language has led to inconsistent interpretations of California’s sovereign immunity statutes. This Comment argues (1) that the GCA\u27s use of common law language can frustrate the ability of courts to establish a consistent understanding of which tortious actions may be protected by immunity from charges of either intentional or negligent misconduct; and (2) that a lack of legislative guidance frustrates the ability of courts to determine whether certain state actions are either discretionary acts protected by absolute immunity or mandatory duties protected by qualified immunity. Further, modernizing language throughout the GCA would ensure more consistent enforcement of statutory sovereign immunity. Part I of this Comment outlines the history of the doctrine of sovereign immunity and summarizes the public policy arguments for and against its continuation. Part II provides an overview of the GCA\u27s architecture and how judicial interpretations have shaped its implementation. Part III analyzes statutory language and recommends amendments

Biometric Data Collection: Market Necessity or Unconstitutional Overkill?

Congress should pass, and the President should sign into law, the National Biometric Information Privacy Act of 2020 (National BIPA). Introduced by Senators Jeff Merkley (D-OR) and Bernie Sanders (I-VT), this bill limits the ability of private entities to collect biometric data and requires them to ensure the privacy and security of data they do collect. Unlike most federal regulatory legislation, it also provides for a private right of action through which individuals can seek meaningful remedies. Critics argue that the bill will deprive consumers of online shopping services and convenient digital security, and that employers and retailers may retaliate by requiring consent for biometric data collection as a condition of service or employment. Supporters argue that the status quo has already defaulted to mandatory consent, and that without legislation, citizens who value their privacy are left without a remedy. Biometric data collection provides relatively negligible benefits in commercial and employment contexts. Conversely, unregulated collection erodes civil liberties and violates the fundamental right to privacy. On balance, the risks far outweigh the benefits

The Classical and Maximin Versions of the Two-Envelope Paradox

The Two-Envelope Paradox is classically presented as a problem in decision theory that turns on the use of probabilities in calculating expected utilities. I formulate a Maximin Version of the paradox, one that is decision-theoretic but omits considerations of probability. I investigate the source of the error in this new argument, and apply the insights thereby gained to the analysis of the classical version