Studying the conversion between transverse light modes via four-wave mixing in a heated rubidium vapor, we demonstrate and explain a transfer between azimuthal and radial mode numbers. They relate to orthogonal modal dimensions, which one would not normally expect to interact. While angular momentum conservation in this nonlinear process dictates the selection rules for the angular mode number, the role of the radial mode number is more esoteric. We demonstrate systematically that the Gouy phase is the key to understanding this conversion, leading to strikingly different conversion behavior in the thick- and thin-medium regimes. Our experimental investigation of the transition between these regimes bridges the gap between previous experiments in atomic thick media and work in nonlinear crystals. Our work sets a clear starting point to explore the thick-medium regime, allowing efficient radial-to-azimuthal and radial-to-radial mode conversion.

中文翻译：

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四波混频中的Gouy相匹配角和径向模式转换

通过在加热的vapor蒸气中通过四波混合研究横向光模之间的转换，我们证明并解释了方位模数与径向模数之间的转换。它们与正交模态尺寸有关，通常不会期望相互作用。尽管此非线性过程中的角动量守恒规定了角模数的选择规则，但径向模数的作用更加深奥。我们系统地证明，Gouy阶段是理解此转换的关键，从而导致在厚中型和薄中型方案中出现显着不同的转换行为。我们对这些状态之间的过渡进行的实验研究弥合了先前在原子厚介质中的实验与在非线性晶体中的工作之间的鸿沟。