Phase matching in three-dimensional nonlinear photonic crystals

Abstract

The coupled-wave equations of three-wave interactions are generalized into three dimensions. The reciprocal lattice vectors ͑RLVs͒ of three-dimensional ͑3D͒ nonlinear photonic crystals ͑NPCs͒ which show some unique properties are analyzed in detail as compared to those in one-and two-dimensional cases. It is proposed as an example that the cross-distributing conical harmonic beams can be obtained from the 3D NPC by intentionally using the proper RLVs. Some other possible applications are suggested at the end of discussion.

Pattern formation of second harmonic conical waves in a nonlinear medium with extended defect structure

“…However, SHG is not restricted to the collinear interactions; non-collinear schemes can be realized as well. Though the noncollinear geometries are not suitable for efficient frequency doubling, scientists have taken great interests in their physics and applications on material characterization [2][3][4][5][6][7][8][9][10][11][12][13].…”

“…Several kinds of non-collinear parametric interactions have been recently demonstrated, such as a conical third-harmonic emission generated in an isotropic material [2], a hollow beam generated by the frequency difference in a periodically poled LiNbO 3 crystal [7], and a conical SH beam discovered in a two-dimensional (2D) hexagonally poled LiTaO 3 crystal [8]. Studies have shown that the conical SH beams can be generated from nonlinear media with different order photonic structures through the quasi-phase-matching technique [7][8][9][10][11][12]. However, it is not necessary to work with order photonic structures; the conical SH patterns can even be produced in a disordered nonlinear crystal [4].…”

Dynamics of a particle confined in a two-dimensional dilating and deforming domain

“…In the original picture (with moving walls), the average energy of the system is given by E(t) = ψ| H |ψ , so that in the picture with static walls such average energy is given by the mean value, over the state |φ , of the operator U HU † = H 1 + H 3 in Eq. (19), from which we have to cancel the deformation terms, hence obtaining U HU † = H 1 .…”

“…For example, in the field of cavity quantum electrodynamics appeared a study of the implications of small displacements of the mirrors on the dynamics of an atom interacting with the cavity modes [18]. On the other hand, cooling techniques of trapped particles based upon exploitation of expanding boxes have been proposed [19]. Furthermore, the study of two particles in a box with moving boundaries has been recently presented, and the relevant results suggest the idea of an effective interaction between the particles induced by their common interaction with the moving walls [20].…”

Controllable polarization coupled dual-focused second-harmonic generations in a two-dimensional optical superlattice

“…During the first 10 years after the 2D and 3D OSLs were proposed, most work focused on periodic or quasi-periodic structures [4][5][6]. Recently, studies on aperiodic OSLs implementing multiple operations on one chip and reinvestigating classical principles in nonlinear optics have become hot topics; this includes such topics as second-harmonic generation (SHG) lenses and nonlinear wave shaping [7][8][9][10][11][12].…”