Efficient parametric generation in a nonlinear photonic crystal pumped by a dual beam

Abstract

We investigate parametric down-conversion in a hexagonally poled nonlinear photonic crystal, pumped by a dual pump with a transverse modulation that matches the periodicity of the χ (2) nonlinear grating. A peculiar feature of this resonant configuration is that the two pumps simultaneously generate photon pairs over an entire branch of modes, via quasi-phasematching with both fundamental vectors of the reciprocal lattice of the nonlinearity. The parametric gain of these modes depends thus coherently on the sum of the two pump amplitudes and can be controlled by varying their relative intensities and phases. We find that a significant enhancement of the source conversion efficiency, comparable to that of one-dimensionally poled crystals, can be achieved by a dual symmetric pump. We also show how the four-mode coupling arising among shared modes at resonance can be tailored by changing the dual pump parameters.Considering e.g. inversion domains shaped as discs of radius R = 0.28Λ (Fig. 2(a)), one has d 01 = d 10 = 0.32d e f f [22], d e f f denoting the effective nonlinear susceptibility of the χ (2) material.

Multipartite spatial entanglement generated by concurrent nonlinear processes

“…1c: here the intensity pattern created by the interference of the two pump modes superimposes to the static pattern of the periodic poling. The four possible combinations of the pump modes with the grating vectors G 1 and G 2 drive four concurrent processes which create four families of intersecting cones [19,22]. A specially important configuration is reached at spatial resonance, when the periodicity of the pump pattern matches that of the poling pattern, and two of the four processes degenerate into a single one, whose parametric gain is controlled by the coherent sum of the two pump amplitudes 19,22].…”

“…This work stems from some recent publications [17][18][19][20][21][22], which showed the possibility of generating a multipartite coupling -the prerequisite for multiparty entanglement -among separate spatial modes copropagating in the same beam, by properly engineered parametric processes. The present work will not deal with the physics of the optical sources, extensively described in Refs.…”

“…The present work will not deal with the physics of the optical sources, extensively described in Refs. [17][18][19][20][21][22], but will focus on the characterization and possibly on the quantification of the multipartite entanglement thereby produced. Figure 1 summarizes the optical schemes that will be considered, along with the states generated by each of them.…”

“…The third example is a mixture of the other two, corresponding to a nonlinear photonic crystal pumped by two noncollinear optical modes. In this case, four nonlinear processes coexist in the same medium, and under particular resonance conditions give rise to the square coupling in the graph c2) [19,22].…”

Engineering multipartite entangled states in doubly pumped parametric down-conversion processes

“…The use of a spatially structured pump with a T EM 01 modal profile, to produce peculiar spatial correlation between twin photons was also explored in [13]. More recently, a scheme for engineering the quantum and classical properties of parametric generation by dual pumping a 2D nonlinear photonic crystal was proposed by some of us [14,15]. Several four-wave mixing schemes, exploiting the χ (3) nonlinearity, with dual spatial pump modes have been recently studied and experimentally realized [16,17].…”