A compound represented by the General Formula (I) as defined herein, in which, in the General Formula (I), P.sup.1 and P.sup.2 each independently represent a hydrogen atom, —CN, —NCS, or a polymerizable group, Sp.sup.1 and Sp.sup.2 each independently represent a single bond or a divalent linking group as defined herein, Z.sup.1, Z.sup.2 and Z.sup.3 each independently represent a particular linking group as defined herein, X.sup.1 and X.sup.2 each independently represent a single bond or —S as defined herein, k represents an integer of 2 to 4, m and n each independently represent an integer of 0 to 3 as defined herein, A.sup.1, A.sup.2, A.sup.3, and A.sup.4 each independently represent a particular group as defined herein is provided.

The optical device can comprise a substrate having a first face opposite a second face, a thickness between the first face and the second face, the first face and the second face being planar, the first face being parallel the second face, the substrate being transparent to an electromagnetic radiation in a given spectrum; a planar polarization-dichroic focusing lens covering the first face, the lens having a first focusing power for a first polarization of the electromagnetic radiation and a second focusing power for a second polarization of the electromagnetic radiation, the second focusing power being different from the first focusing power; and a planar polarization-dichroic mirror covering the second face, the mirror being reflective to the first polarization and transparent to the second polarization.

A waveguide apparatus, comprises: disposed in at least one layer: an input coupler; a first fold grating; a second fold grating; an output coupler; and a source of light optically coupled to the waveguide providing at least first and second polarizations of the light and at least one wavelength. The input coupler is configured to cause the first polarization light to travel along a first total internal reflection (TIR) path and the second polarization light to travel along a second TIR path.

An optical waveguide device includes first and second waveguides formed parallel to each other. The first waveguide includes a first rib and a first slab. The first slab is formed in a region between the first rib and the second waveguide. The second waveguide includes a second rib, a second slab and a third slab. The second rib is provided between the second slab and the third slab. The first and second slabs are integrally formed. At one end of the optical waveguide device, a first effective refractive index that indicates an effective refractive index of a TEi mode in the first waveguide is higher than a second effective refractive index that indicates an effective refractive index of a TEj mode in the second waveguide. At another end, the first effective refractive index is lower than the second effective refractive index.

An optical device for polarizing light including a polarization altering element operatively coupled to a light path associated with the first light coupling device and the second light coupling device is described. The optical device may further include a first waveguide portion including a first layer having parallel plane surfaces with the first waveguide portion having a first light coupling device. The optical device may also include a second waveguide portion including a second layer having parallel plane surfaces with the second waveguide portion having a second light coupling device.

A light-guide optical element (LOE) includes a transparent substrate having two parallel major external surfaces for guiding light within the substrate by total internal reflection (TIR). Mutually parallel internal surfaces within the LOE are provided with a structural polarizer which is transparent to light polarized parallel to a primary polarization transmission axis, and is partially or fully reflective to light polarized perpendicular to the primary polarization transmission axis. By suitable orientation of the polarization axis of successive internal surfaces together with the polarization mixing properties of TIR and/or use of birefringent materials, it is possible to achieve the desired proportion of coupling-out of the image illumination from each successive facet.

A system for transmission of optical data signals has first optical processing circuitry for receiving a plurality of digital signals and applying at least one of a Hermite-Gaussian function, a Laguerre-Gaussian function or an Ince-Gaussian function to each of the received plurality of digital signals. The first optical processing circuitry also combines each of the at least one of the Hermite-Gaussian function, the Laguerre-Gaussian function or the Ince-Gaussian function applied plurality of digital signals into a single carrier signal. An optical transmitter transmits the single carrier signal. An optical receiver receives the transmitted single carrier signal. Second optical processing circuitry separates the at least one of the Hermite-Gaussian function, the Laguerre-Gaussian function or the Ince-Gaussian function applied digital signals of the single carries signal into separate signals and removes the at least one of the Hermite-Gaussian function, the Laguerre-Gaussian function or the Ince-Gaussian function applied to each of the plurality of digital signals. An elliptical core fiber transmits the single carrier signal from the optical transmitter to the optical receiver. The elliptical core fiber includes an elliptical core have a major axis and a minor axis.

A system for integrated power combiners is disclosed and may include receiving optical signals in input optical waveguides and phase-modulating the signals to configure a phase offset between signals received at a first optical coupler, where the first optical coupler may generate output signals having substantially equal optical powers. Output signals of the first optical coupler may be phase-modulated to configure a phase offset between signals received at a second optical coupler, which may generate an output signal having an optical power of essentially zero and a second output signal having a maximized optical power. Optical signals received by the input optical waveguides may be generated utilizing a polarization-splitting grating coupler to enable polarization-insensitive combining of optical signals. Optical power may be monitored using optical detectors. The monitoring of optical power may be used to determine a desired phase offset between the signals received at the first optical coupler.

An optical system includes a silicon (Si) substrate, a buried oxide (BOX) layer formed on the substrate, a silicon nitride (SiN) layer formed above the BOX layer, and a SiN waveguide formed in the SiN layer. In some embodiments, the optical system may additionally include an interposer waveguide adiabatically coupled to the SiN waveguide to form a SiN-interposer adiabatic coupler that includes at least the tapered section of the SiN waveguide, the optical system further including at least one of: a cavity formed in the Si substrate at least beneath the SiN-interposer adiabatic coupler or an oxide overlay formed between a top of a SiN core of the SiN waveguide and a bottom of the interposer waveguide. Alternatively or additionally, the optical system may additionally include a multimode Si—SiN adiabatic coupler that includes a SiN taper of a SiN waveguide and a Si taper of a Si waveguide.

A photonic integrated circuit comprises an input interface adapted for receiving an optical input signal and splitting it into two distinct polarization modes and furthermore adapted for rotating the polarization of one of the modes for providing the splitted signals in a common polarization mode. The PIC also comprises a combiner adapted for combining the first mode signal and the second mode signal into a combined signal and a decohering means adapted for transforming at least one of the first mode signal and the second mode signal such that the first mode signal and the second mode signal are received by the combiner in a mutually incoherent state. A processing component for receiving and processing said combined signal is also comprised.