A Langevin Model-Based Magneto-Optic Response SuperParamagnetic Nanoparticles Recorded with a Michelson Interferometer Setup
Syed Azer Reza, Maarij Syed
TL;DR
The paper develops a Langevin-model-based description of the magneto-optic Faraday rotation in superparamagnetic nanoparticles under an applied AC field and analyzes its detection with a Michelson interferometer. It derives the detected irradiance expressions, showing that the interferometer configuration yields both odd and even harmonics in the FR-induced signal. In the linear–FR limit, Jacobi–Anger expansions reveal a spectrum with harmonics at $\Omega$, $3\Omega$, $5\Omega$, etc., while in the nonlinear case a truncated expansion $\theta(t) \approx \frac{\kappa_1}{2}\sin(\Omega t) + \frac{\kappa_3}{2}\sin^3(\Omega t)$ leads to higher harmonics up to $4\Omega$ and compact expressions using $A_1$ and $A_3$. The results provide a practical method to quantify FR nonlinearities and potentially diagnose aggregation-related scattering in SPN suspensions.
Abstract
In this paper, we provide expressions for the detected optical irradiance for magneto-optic characterization of superparamagnetic nanoparticles (SPNs) in solution imparting Faraday rotation (FR) to an optical beam passing through the sample solution. For our analysis, we assume a Langevin model for SPN samples and show the presence of odd and even harmonics for SPN samples characterized with a Michelson interferometer. This optical geometry is potentially useful in understanding nonlinear SPN FR behavior as a result of particle aggregation-based scattering effects.