Ultraslow Kuznetsov-Ma solitons and Ahkmediev breathers in a cold three-state medium exposed to nanosecond optical pulses

Wanwan Wang,Dandan Cheng,Yanlin Ye,Shihua Chen,Lili Bu,Fabio Baronio

doi:10.1364/osac.422914

Abstract

We investigate the formation of the Kuznetsov-Ma solitons and Ahkmediev breathers in a cold Λ-type three-level atomic system that interacts with a probe field of nanosecond pulse duration and a strong continuous-wave driving field via an electromagnetically induced transparency process. Within the framework of the Hirota equation, exact explicit analytical solutions of these breathers are obtained, showing different amplitude and oscillatory characteristics. Numerical simulations confirm the stability of both types of breathers against non-integrable perturbations that are caused by the nonvanishing decay rates of atomic states. We show that both breathers thus generated can propagate at a quite low group velocity.

Highlights

The breathers on a finite background have attracted increasing attention in many fields including hydrodynamics and optics [1,2], due to their intimate connection to the formation of extreme rogue wave events [3,4]
We investigate the formation of the Kuznetsov-Ma solitons and Ahkmediev breathers in a cold Λ-type three-level atomic system that interacts with a probe field of nanosecond pulse duration and a strong continuous-wave driving field via an electromagnetically induced transparency process
We investigated the formation of the KM solitons and Ahkmediev breather (AB) in a cold three-level atomic medium, within the framework of the Hirota equation that has comprised the third-order dispersion and self-steepening effects seen by nanosecond probe pulses

Summary

Introduction

The breathers on a finite background have attracted increasing attention in many fields including hydrodynamics and optics [1,2], due to their intimate connection to the formation of extreme rogue wave events [3,4]. Vg = 1/K1′ gives the group velocity of the probe field In this regard, Eq (8) becomes an analog of the (3+1)D complex Ginzburg-Landau equation [38], comprising the spectral filtering and the nonlinearity denoted gain by γby′′.KH2′′o, wtheevtehri,ridn-oarvdeerryspshecotrrtadl icsotarnreccetiaonndbcyoKns3′i′d, ethreinlgintehaart loss by α, ∆2 ≫ γ2 and ∆3 ≫ γ3, which is accessible by typical alkali atoms, these extra effects resulting from the imaginary parts of the coefficients will become insignificant and can be neglected. Which depends on the coupling strength (κ), the input power of the coupling beam (∝ |Ωc|2), and the one- and two-photon detunings (∆2,3) It suggests that, for obtaining a significantly low group velocity, sufficiently small one- and two-photon detunings yet still predominating over the decay rates, along with a moderately weak control field, are favorable. This is a trade-off process, whose outcome is unavailable with the conventional perfectly resonant EIT scheme under weak driving conditions, in which exceptionally low light speeds can be observed [25,26]

Dynamics of KM solitons and ABs and numerical simulations

Conclusion