  Integrated optical devices are expected to play a promising role in the field
of quantum information science and technology. In this paper, we propose a
scheme for the generation of nondegenerate, copolarised, modal, and path-
entangled photons using a directional coupler and an asymmetric Y-coupler
geometry in type 0 phase-matched domain engineered lithium niobate(LN)
waveguide. The nonlinearity in LN is tailored in such a way that quasi phase
matching conditions for two different spontaneous parametric down conversion
processes are obeyed simultaneously, leading to a modal and path-entangled
state at the output. Assuming typical values of various parameters, we show,
through numerical simulations, that an almost maximally entangled state is
achievable over a wide range of waveguide parameters. For the degenerate case,
the scheme gives a NOON state for N = 2. The generated entangled photon pairs
should have potential applications in quantum information schemes and also in
quantum metrology. By appropriate domain engineering and component designing,
the idea can be further extended to generate hyperentangled and two-photon
multipath-entangled states, which may have further applications in quantum
computation protocols.
