Phase-reversed structures in superlattice of nonlinear materials

a r t i c l e i n f o We present detailed description of so-called phase-reversed structures that are characterized by two grating wave vectors allowing simultaneously phase-match two parametric three-wave processes. The novelty is that the structure is realized as a definite assembly of nonlinear segments leading to detailed description of cascaded three-photon processes with the parameters of realistic structured nonlinear materials of finite length. We apply these results for analysis of the quasi-phase-matching in production of both photon triplet and four-photon states in cascaded down-conversion. The received results are matched with the experimental data. Cascading processes in optical materials that involve several different second-order nonlinear interactions provide an efficient way to lower the critical power of optical parametric devices. The concept of multistep cascading brings new ideas into this field, leading to the possibility of an enhanced nonlinearity-induced phase shift, the simultaneous generation of higher-order harmonics, multicolor para-metric interaction, and difference-frequency generation, (see, [1] and references therein). Multistep parametric interactions and multi-step cascading are characterized by at least two different nearly phase-matching or quasi-phase-matching (QPM) parameters. QPM is an important technique in nonlinear optics and is widely used for various applications [1–3]. The width of the phase-matching curve depends on the type of the crystal, its length, and the phase-matching method. QPM not only makes efficient frequency conversion possible, but also enables diverse applications such as beam and pulse shaping, multi-harmonic generation, high harmonic generation and all-optical processing. Recently, it has been demonstrated that the quantum-computational gates, multimode quantum interference of photons and preparation of multi-photon entangled states also can be realized in QPM structures [4–7]. It is well known (see, for example [8,9] that multiple-wavelength quasi-phase matching can be achieved using two crystals for a two-step cascaded process where the first and second crystals are used to phase match only one of these processes. However, the same cascaded process can be also implemented using two successive gratings on a single crystal. Particularly, the multiple-peak frequency tripling and quadrupling was demonstrated using a single crystal by selecting a periodic structure that phase matches several processes simultaneously [10]. The main experimental disadvantages of the last scheme are its rather low efficiency that takes place due to the shorter length of the crystal that is used for each interaction and the fact that it is unidirectional, i.e., it operates only in one direction of propagation [8]. On the …