Quantization of coupled modes propagation in integrated optical waveguides

Solving the quantum master equation of coupled harmonic oscillators with Lie-algebra methods

“…with the bosonic mode operatorsâ k ,â † k , the energy σ k of the kth mode, and the coupling κ k between modes k and k + 1. Such a Hamiltonian is often encountered, for example, when modelling light propagation in photonic waveguides [17,18].…”

“…Let us start with the right ground state and its defining equations given by Eq. (18). Because the right action of the superoperators P ± i , Q ± i are known by the definitions of the underlying superoperators L ± i , R ± i , the right ground state and all states |α, β constructed from it can straightforwardly be calculated once the ground state itself is found.…”

Guided-wave electron optics for the integration of nanophotonic devices with nanoelectronic devices

“…Moreover, this result would play a relevant role in a second quantization, like in the case of the vector light modes. 11 In short Equations (8,9) are the spinor-electron mode wave equations, where the SU and SD are nondegenerate unlike of the electron optics based on the Schrödinger equation; 1-5 moreover, the non-relativistic limit is obtained when the terms S ↓ (η) and S ↑ (η) can be neglected, that is, an usual scalar electron wave equation is obtained for SU and SD modes; however, under relativistic conditions the above terms will induce important effects on both the phase and momentum of the spinor-electron modes, and even we must stress that although these terms S ↓ (η) and S ↑ (η) are small, for typical values of the parameters of electron waveguides at their present technology, their contribution to the phase of the spinor modes is not negligible. 8 Likewise, it is interesting to indicate that Equations (8,9) can be regarded as analogous to the TE and TM wave equations for vector light optics in dielectric guides, 9 and the standard vector wave equations for TE and TM modes can be easily rewritten with the same structure that equations (8,9).…”

“…It is important to indicate that these different values of shifting phases can be also increased by applying a normal static electric field F , that is, the wellknown Rashba effect, which, in our case, can be formalized within the rigorous Dirac theory by means of the following formal change (which is usually introduced within the Pauli's approximated theory): (∂V /∂η) → (∂V /∂η) + F , which must be inserted into equations (10,11); the resultanting Dirac equation allows to calculate the Rashba effect in a fully relativistic way.…”

Active and Quantum Integrated Photonic Elements by Ion Exchange in Glass

“…The use of quantum light states in integrated optical devices allows to develop different on-chip applications in quantum optical communications and in other fields such as quantum photonic simulations [196] and quantum photonic sensing [218]. Rigorous theories of linear and nonlinear quantum spatial propagation states in integrated waveguides can be used [219][220][221][222], which allows us to study and design linear and nonlinear quantum integrated optical elements. Moreover, we consider three types of quantum states of a great interest for proofs of concept as the coherent states, the single photon states and the biphoton states.…”