Robust Geometric Phase of Bloch Sphere Deformation in Quasiphase Matched Structures

We consider the adiabatic geometric phase (AGP) in the sum frequency generation process under the undepleted pump approximation. The Bloch sphere is stretched or compressed by adjusting the modulation wave vector, Delta, which is one of the control parameters of quasiphase matching (QPM). In this paper, two kinds of parametric rotation schemes on the sphere are studied: elliptical rotation and elliptical wedge rotation. We find that the AGP generated in the elliptical rotation is related to the length of the Delta axis of the ellipse, but there is a certain point where the AGP is independent, while the AGP in the elliptical wedge rotation shows great stability and does not depend on the shape of the ellipsoid. The results further demonstrate the superior flexibility of the wedge scheme, which helps to suppress the uncertainty in the generation of AGPs.