Abstract: A method for displaying a source node having connections to contained nodes and linked nodes peripherally within and around the source node to which they are connected, computing a focus position for each of the contained and linked nodes; displaying a first contained node at an inclusion start angle, and displaying a first linked node at an adjacency start angle. Focus positions are calculated for a first contained node and a first linked node based on the start angles, a direction of rotation, either clockwise or counterclockwise, and the number of contained and linked nodes connected to the source node.

Abstract: A user interface with parameters that can be adjusted to display only a few nodes, in order to facilitate exploration, or many nodes simultaneously, in order to facilitate an user's understanding of a graph of nodes of information. The user interface provides for exploring a collection of connected objects simultaneously from the hierarchical and the relational points of view, and increases exposure to related information while maintaining context. Parameters can be adjusted to increase or decrease the extent of the relational context.

Abstract: A user interface is animated and configurable to optimize, facilitate and simplify displaying on a display device and exploring via user input a hierarchy of information accessible by an electronic device.

Abstract: A liquid crystal optical processor is configured in various applications, including a liquid crystal optical switch, polarization independent variable optical attenuator, wavelength selector switch, optical multiplexer and demultiplexer, tunable filter and flexible optical add drop multiplexer. The optical processor is generally configured to include a deposited metal gasket moisture barrier bonding two opposing substrates each having a spacer layer to accurately control cell gap thickness. The optical processor may be temperature insensative and be configured in one or more pixel configurations. The optical processor may include integrated subwavelength optical gratings. It may also include an integrated thermal sensor and heater deposition layer sandwiched between or deposited on at least one or both opposing substrates.

Abstract: A polarization independent optical device is provided wherein the device has two optical paths that include one or more birefringent crystals, a electrically controllable rotator, and a fixed waveplate. The device may operate as a switch, attenuator, coupler, or polarization mode dispersion compensator. The device may also include several folded path embodiments, a multifunctional embodiment, and a temperature insensitive embodiment.