Intensity-preserving self-similar beams

Non-diffracting beams, propagating with unchanged transverse profiles and intensity, have been extensively studied in past decades. More recently, self-similar beams with scaling transverse profiles during propagation were proposed as a generalization of non-diffracting beams. Here, we present a type of beam that can be regarded as an intermediate mode between traditional self-similar beams and non-diffracting beams. During propagation, such beams feature a strict self-similar transverse profile and the intensity remains unchanged. Thus, we name these beams the “perfect self-similar beams”. Our work reveals a class of previously unnoticed beam modes that hold both main characteristics of self-similar beams and non-diffracting beams, which conceptually expands the study of free-space beams with special propagation properties.