Exact solution for the interaction of two decaying quantized fields.

We show that the Markovian dynamics of two coupled harmonic oscillators may be analyzed using a Schrödinger equation and an effective non-Hermitian Hamiltonian. This may be achieved by a non-unitary transformation that involves superoperators; such transformation enables the removal of quantum jump superoperators, which allows us to rewrite the Lindblad master equation in terms of a von Neumann-like equation with an effective non-Hermitian Hamiltonian. This may be generalized to an arbitrary number of interacting fields. Finally, by applying an extra non-unitary transformation, we may diagonalize the effective non-Hermitian Hamiltonian to obtain the evolution of any input state in a fully quantum domain.

Kapitza-Dirac photonic lattices.

We show that the Kapitza-Dirac effect may be modeled by classical light propagation in photonic lattices having a square power law for the refraction index coefficient. The dynamics is shown to be fully soluble because both systems share the same time-independent Schrödinger equation: the angular Mathieu equation. We examine the trajectories of classical light propagating in such structures.

Generalized revival and splitting of an arbitrary optical field in GRIN media.

Assuming a non-paraxial propagation operator, we study the propagation of an electromagnetic field with an arbitrary initial condition in a quadratic GRIN medium. We show analytically that at certain specific periodic distances, the propagated field is given by the fractional Fourier transform of a superposition of the initial field and of a reflected version of it. We also prove that for particular wavelengths, there is a revival and a splitting of the initial field. We apply this results, first to an initial field given by a Bessel function and show that it splits into two generalized Bessel functions, and second, to an Airy function. In both cases our results are compared with the numerical ones.

Revival and splitting of a Gaussian beam in gradient index media.

The short range revival of an arbitrary monochromatic optical field, which propagates in a quadratic GRIN rod, is a well-known effect that is established assuming the first-order approximation of the propagation operator. We discuss the revival and multiple splitting of an off-axis Gaussian beam propagating to relatively long distances in a quadratic GRIN medium. These effects are obtained assuming the second-order approximation of the propagation operator in this medium.

Optical realization of quantum Kerr medium dynamics.

We use the propagation of a conveniently shaped Gaussian beam in a GRIN media to mimic a quantum cavity filled with a Kerr medium. This is attained by introducing a second-order correction to the paraxial propagation of the beam. An additional result is that a Gaussian beam propagating in GRIN media may split into two Gaussian beams, corresponding to the generation of superposition of coherent states (Schrödinger cat states) in the cavity filled with the Kerr medium.