Acoustic self-induced transparency for transverse waves in a system with resonant and quasi-resonant transitions

Abstract

A theoretical analysis of acoustic self-induced transparency is presented for transverse elastic waves propagating perpendicular to an applied magnetic field through a crystal with spin-3/2 paramagnetic impurities. The interaction between an acoustic pulse and magnetic field is described by Maxwell-Bloch-type equations for a system with transitions inhomogeneously broadened because of a quadrupole Stark shift. If the pulse carrier frequency is resonant with one transition and quasi-resonant with another transition, then the evolution of a one-dimensional pulse is described by an integrable Konno-Kameyama-Sanuki (KKS) equation. The underlying physics of its soliton solution and the corresponding behavior of the medium are analyzed. Self-focusing and self-trapping conditions are found for a pulse of finite transverse size. In the latter regime, the pulse stretches along the propagation direction, transforming into a “hollow bullet,” while its transverse size remains constant.