Invisibility and PT Symmetry: A Simple Geometrical Viewpoint

We give a simplified account of the properties of the transfer matrix for a complex one-dimensional potential, paying special attention to the particular instance of unidirectional invisibility. In appropriate variables, invisible potentials appear as performing null rotations, which lead to the helicity-gauge symmetry of massless particles. In hyperbolic geometry, this can be interpreted, via M\"{o}bius transformations, as parallel displacements, a geometric action that has no Euclidean analogy.Comment: 13 pages. No figure. Accepted for publication in Symmetr

The many facets of the Fabry-Perot

We address the response, both in amplitude and intensity, of a Fabry-Perot from a variety of viewpoints. These complementary pictures conspire to achieve a comprehensive and consistent theory of the operation of this system.Comment: 15 pages, 9 figure

The transfer matrix: a geometrical perspective

We present a comprehensive and self-contained discussion of the use of the transfer matrix to study propagation in one-dimensional lossless systems, including a variety of examples, such as superlattices, photonic crystals, and optical resonators. In all these cases, the transfer matrix has the same algebraic properties as the Lorentz group in a (2+1)-dimensional spacetime, as well as the group of unimodular real matrices underlying the structure of the abcd law, which explains many subtle details. We elaborate on the geometrical interpretation of the transfer-matrix action as a mapping on the unit disk and apply a simple trace criterion to classify the systems into three types with very different geometrical and physical properties. This approach is applied to some practical examples and, in particular, an alternative framework to deal with periodic (and quasiperiodic) systems is proposed.Comment: 50 pages, 24 figure

Comparing omnidirectional reflection from periodic and quasiperiodic one-dimensional photonic crystals

We determine the range of thicknesses and refractive indices for which omnidirectional reflection from quasiperiodic multilayers occurs. By resorting to the notion of area under the transmittance curve, we assess in a systematic way the performance of the different quasiperiodic Fibonacci multilayers.Comment: 5 pages, 4 color figures. Comments welcome

Efficient, Low Pressure Ratio Propulsor for Gas Turbine Engines

A gas turbine engine includes a spool, a turbine coupled to drive the spool, and a propulsor that is coupled to be driven by the turbine through the spool. A gear assembly is coupled between the propulsor and the spool such that rotation of the turbine drives the propulsor at a different speed than the spool. The propulsor includes a hub and a row of propulsor blades that extends from the hub. The row includes no more than 20 of the propulsor blades

Efficient, Low Pressure Ratio Propulsor for Gas Turbine Engines

A gas turbine engine includes a bypass flow passage that has an inlet and defines a bypass ratio in a range of approximately 8.5 to 13.5. A fan is arranged within the bypass flow passage. A first turbine is a 5-stage turbine and is coupled with a first shaft, which is coupled with the fan. A first compressor is coupled with the first shaft and is a 3-stage compressor. A second turbine is coupled with a second shaft and is a 2-stage turbine. The fan includes a row of fan blades that extend from a hub. The row includes a number (N) of the fan blades, a solidity value (R) at tips of the fab blades, and a ratio of N/R that is from 14 to 16