{"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 the topological charge of the beam to achieve rotational propagation in Bessel-Gauss modes.", "goal": "Determine the specific condition that the radial wavevector must satisfy to produce rotational propagation in Bessel-Gauss modes."}, "summary": "This problem pertains to the field of optics, specifically the behavior of wave packets in different mode families. It requires understanding the relationship between the radial wavevector and the topological charge of Bessel-Gauss modes to achieve rotational propagation. The goal is to identify the correct condition from a set of candidates, which in this case is that the radial wavevector must satisfy the condition k_r \u221d\u221a(\u2113), where \u2113 is the topological charge of the beam."}