Complex Functions, Multipoles and Light Polarization in a Ferrocell

Ferrofluid is a magnetic fluid that undergoes structural changes when subjected to a magnetic field, with the formation of arrays of nanoparticles aligned with the field. Using polarized light passing through the ferrofluid, we can observe the formation of light patterns for different magnetic field configurations. Using a device known as a Ferrocell, we present a study relating magnetic fields and complex functions. Our main issue here is to know what the relationship is between fundamental multipole expressions and light polarization patterns obtained with the ferrofluid. We have applied multipole fields to the Ferrocell, observed the light patterns, and compared them with multipoles of complex functions. We interpreted other luminous polarization patterns as the sum of these fundamental multipoles.