Dynamics of Light Localization via Coherent Control: The Interplay of Transmission, Absorption and Disorder in Photonic Crystals

Abstract

This study investigates the interplay between structural disorder, absorption, and Lyapunov exponent dynamics to exploit localization phenomena in photonic crystals with engineered defect layers. We generate disorder by introducing random refractive index variations in one of the bilayers, while the application of a control field to $Λ$-type atoms within a central defect layer enables dynamic tuning of the effective refractive index of crystal. We have employed traditional transfer matrix method to demonstrate transmission, Lyapunov exponents and absorption in the crystal. Through coherent control, we dynamically tune absorption, revealing sharp contrasts in band gap and band edge regions. while Lyapunov exponents, quantifying localization lengths, exhibit a consistent scaling across both band gap and band edge frequencies, and this behavior remains robust even in the presence of disorder. Hence, distinct localization mechanisms emerge at bandgap and band-edge frequencies. Bandgap localization arises from optical mode confinement and resonant alignment of atomic transitions with the probe field while band edge localization stems from a synergy of loss-difference-induced trapping and Anderson like disorder effects. Notably, while disorder weakens confinement localization in the band gap, it actually strengthens localization at the band edges. These results deepen the understanding of light-matter coupling in disordered photonic systems and provide a framework for designing reconfigurable optical devices with tailored localization properties.