An explicit formula is given for the quantity of entanglement in the output state of a beam splitter, given the squeezed vacuum states input in each mode. For the general Gaussian states input, the necessary and sufficient condition for the inseparability of the output state from a beam splitter is given.

By directing the input light into a particular mode it is possible to obtain as output all of the input light for a beam splitter that is 50% absorbing. This effect is also responsible for nonlinear quantum interference when two photons are incident on the beam splitter.

Some of the key components are demonstrated to make three-dimensional (3-D) optical integrated circuits possible using polymers. Fabrication techniques of shadow reactive ion etching, shadow photolithography, and gray-level photolithography to produce complex 3-D integrated optic structures are demonstrated. Vertical waveguide bends exhibit excess losses of <0.3 dB, and vertical power splitters...

The self-imaging property of a homogeneous multi-moded planar optical waveguide has been applied in the design optical couplers based on multimode Interference (MMI). Based on this design, the optical wavelength and dimensions tolerance for MMI-3dB couplers are investigated analytically. They are shown to be inversely proportional to the multimode section width. Among Symmetrical, paired, and g...

Current experimental realizations of the quantum anomalous Hall phase in both electronic and photonic systems have been limited to a Chern number of one. In photonics, this corresponds to a single-mode one-way edge waveguide. Here, we predict quantum anomalous Hall phases in photonic crystals with large Chern numbers of 2, 3, and 4. These new topological phases were found by simultaneously gapp...