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arXiv:2104.13022 · Optics Express

Geometric phase with full-wedge and half-wedge rotation in nonlinear frequency conversion

Feiyan Zhao, Jiantao Lü, Hexiang He, Yangui Zhou, Shenhe Fu, Yongyao Li

Published Jun 18, 2021• 22 citations
arXivHTMLPDF

Abstract

nonlinear crystal rotate along a closed path, geometric phase will be generated in the signal and idler waves that participate in the nonlinear frequency conversion. In this paper, we study two rotation schemes, full-wedge rotation and half-wedge rotation, of the QPM parameters in the process of fully nonlinear three-wave mixing. These two schemes can effectively suppress the uncertainty in creating the geometric phase in the nonlinear frequency conversion process when the intensity of the pump is depleted. The finding of this paper provides an avenue toward constant control of the geometric phase in nonlinear optics applications and quantum information processing.

DOI
10.1364/oe.428485

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nonlinear crystal rotate along a closed path, geometric phase will be generated in the signal and idler waves that participate in the nonlinear frequency conversion. In this paper, we study two rotation schemes, full-wedge rotation and half-wedge rotation, of the QPM parameters in the process of fully nonlinear three-wave mixing. These two schemes can effectively suppress the uncertainty in creating the geometric phase in the nonlinear frequency conversion process when the intensity of the pump is depleted. The finding of this paper provides an avenue toward constant control of the geometric phase in nonlinear optics applications and quantum information processing.
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, Δ, 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 Δ 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.
The application of the adiabatic geometric phase (AGP) to nonlinear frequency conversion may help to develop new types of all-optical devices, which leads to all-optical modulation of the phase front of one wave by the intensity of other waves. In this paper, we develop the canonical Hamilton equation and a corresponding geometric representation for two schemes of four-wave mixing (FWM) processes (ω1 + ω2 = ω3 + ω4 and ω1 + ω2 + ω3 = ω4), which can precisely describe and calculate the AGP controlled by the quasi-phase matching technique. The AGPs of the idler (ω1) and signal (ω4) waves for these two schemes of FWM are studied systematically when the two pump waves (ω2 and ω3) are in either the undepleted or in the depleted pump cases, respectively. The analysis reveals that the proposed methods for calculating the AGP are universal in both cases. We expect that the analysis of AGP in FWM processes can be applied to all-optically shaping or encoding of ultrafast light pulse.
The geometric phase is a common phenomenon in a variety of physical systems, with significant applications in optics. We report the first experimental demonstration of the adiabatic geometric phase in nonlinear frequency conversion, wherein the coupling between the signal and idler frequencies constitutes the intrinsic two-level dynamics of the system. We observe a variety of effects associated with the geometric phase, including the adiabatic broadening of bandwidth, asymmetric transmission for opposite propagation directions, conjugation of the phase for orthogonal eigenstates, and the nonreciprocity associated with the pump field bias. Our work paves the way towards all-optically controlled geometric phase elements for wavefront shaping, isolation, guiding, and quantum optical applications, harnessing spectral and spatial correlations.
A comprehensive study of two simultaneous three wave mixing processes, a second harmonic generation followed by difference frequency generation, under nonlinear stimulated Raman adiabatic passage (STIRAP) is presented. An input pump is up-converted to its second harmonic, which then gets down-converted to a signal and idler pair with frequencies lying very close to the input pump in such a manner that complete conversion from the pump to the signal and idler takes place without exciting the second harmonic under counterintuitive adiabatic passage. This process involves nonlinear STIRAP with a nonlinear dark state similar to atomic population transfers, and we bring an analogy from atomic systems to our nonlinear dynamics to linearize the problem and analytically obtain the adiabaticity condition required for complete conversion. We also show that the nonlinear STIRAP mechanism results in a large bandwidth of about 380 nm with almost complete conversion of the pump to the signal and idler.
Back conversion is an intrinsic phenomenon in nonlinear frequency down-conversion processes. However, the physical reason for its occurrence is not well understood. Here, we theoretically reveal that back conversion is the result of a π-phase jump associated with the depletion of one interacting wave. By suppressing the idler phase jump through a deliberate crystal absorption, the back conversion can be inhabited, thus enhancing the conversion efficiency from the pump to the signal. The results presented in this Letter will further the understanding of nonlinear parametric processes and pave the way toward the design of highly efficient down-conversion systems.
Quasi-phase-matching (QPM) technique has been successfully applied in nonlinear optics, such as optical frequency conversion. Recently, remarkable advances have been made in the QPM generation and manipulation of photon entanglement. In this paper, we review the current progresses in the QPM engineering of entangled photons, which are finished mainly by our group. By the design of concurrent QPM processes insides a single nonlinear optical crystal, the spectrum of entangled photons can be extended or shaped on demand, also the spatial entanglement can be transformed by transverse inhomogeneity of domain modulation, resulting in new applications in path-entanglement, quantum Talbot effects, quantum imaging etc. Combined with waveguide structures and the electro-optic effect, the entangled photons can be generated, then guided and phase-controlled within a single QPM crystal chip. QPM devices can act as a key ingredient in integrated quantum information processing.