{"knowledge_schema": {"broad_category": "Physics \u2192 Optics \u2192 Wave Propagation", "refinement": "This problem focuses on the conditions required for rotational propagation of Bessel-Gauss modes in optical systems.", "specific_scope": "The task involves identifying the correct relationship between the radial wavevector and parameters such as the Rayleigh range and topological charge that influence the behavior of Bessel-Gauss modes.", "goal": "Determine the specific condition that the radial wavevector must satisfy to achieve rotational propagation in Bessel-Gauss modes."}, "summary": "This problem is centered on understanding the conditions necessary for rotational propagation in Bessel-Gauss modes, a type of optical wave packet. The goal is to identify the correct relationship between the radial wavevector and key parameters like the Rayleigh range and topological charge. By analyzing the provided candidates, students will learn to apply concepts from optics to determine the necessary conditions for achieving the desired wave propagation characteristics."}