Study of Light Polarization by Ferrofluid Film Using Jones Calculus

Abstract

We studied the polarized light patterns obtained using a thin film of ferrofluid subjected to an applied magnetic field. We obtained patterns of polarized light with magnetic field configurations between parallel plates, monopolar, tetrapolar, and hexapolar, and studied how polarized light varies for different intensities and orientations of the applied magnetic field. Using the Jones calculus, we explored the key optical properties of this system and how these properties relate to the applied magnetic field. We have observed general aspects of polarized light obtained by transmission in a Ferrocell using polariscopes and analyzing the resulting Jones vector, such as the formation and rotation of dark bands known as isogyres. We suggest that in a thin film of ferrofluid as in a Ferrocell, two effects occur. The primary effect is dichroism, which is more sensitive to the component of the magnetic field in the direction parallel to the film plane. The secondary effect is the birefringence that can be observed by analyzing the circular polarization of light. Birefringence is related to the thin film thickness of ferrofluid.

Complex Functions, Multipoles and Light Polarization in a Ferrocell

“…In Figure 5b the field is oriented at 45 • in relation to the analyzer, and the light passes with the maximum intensity for this configuration between the two magnetic poles that are in parallel. Thus, the luminous intensity for the case of the internal magnetic dipole basically depends on the orientation of the parallel lines of the dipole in relation to the analyzer orientation axis, as already discussed in the Malus law case [12,13].…”

“…As the orientation of the particles and the polarization of light depend on the intensity of the magnetic field, this gray region at the bottom of the plot in Figure 3 is placed to emphasize that this limiting region of the polarization pattern can vary, but even so, we have an average curve that defines the luminous profile. Each curve represents one of the six magnet arrangements that give different magnetic field intensities that create the magneto-optical lobe patterns ranging from 1300 G up to 2250 G. In order to simulate the amplitudes of the light patterns, we have used Mueller m trices [12][13][14], with values associated with poles given by the numbers lp and mp. A mat representing the association of vector fields with the angle θ is shown below: With this matrix, we can represent the superposition of two magnetic fields, with t number of lp and mp related to different types of multipoles with different intensities the magnetic field given by the proportionality factor k. For example, considering t Stokes vector of a horizontal linear polarized light being operated by the matrix M, taki In order to simulate the amplitudes of the light patterns, we have used Mueller matrices [12][13][14], with values associated with poles given by the numbers lp and mp.…”

“…With this matrix, we can represent the superposition of two magnetic fields, with the number of lp and mp related to different types of multipoles with different intensities of the magnetic field given by the proportionality factor k. For example, considering the Stokes vector of a horizontal linear polarized light being operated by the matrix M, taking the following values for a dipolar field (lp = 0.5) and adding it to a sextupolar field (mp = 2), we will have the intensity graph in polar coordinates for different values of k from 0 to1 as shown in Figure 4c. Figure 4a represents the intensity parameter of the Stokes vector related to a dipole, and Figure 4b represents the intensity parameter of the Stokes vector related to a sextupole; the combination of these two intensities is shown in Figure 4c for different values of the parameter k. In the literature related to this type of system [12][13][14], we can find in more detail the application of the Jones calculus and the Mueller matrices to analyze the formation of magneto-optical light patterns obtained with a Ferrocell. In this work, we consider two-dimensional fields because we study thin films of ferrofluid.…”

Exploring the Polarization of Light in Ferrofluids with Mueller Matrices

“…Furthermore, in regions where the magnetic field has a weak intensity (less than 200 gauss), the grating does not form and light is not transmitted, resulting in the dark parts around the pattern. In our previous paper involving Jones vectors [9], we have considered the electric field of the light expressed as two-component vector with 0 ≤ λ ≤ 1; in the following, κ is an amplitude parameter [16]:…”

“…Magnetochemistry 2022, 8, x FOR PEER REVIEW 3 of 1 transmitted, resulting in the dark parts around the pattern. In our previous paper in volving Jones vectors [9], we have considered the electric field of the light expressed a two-component vector with0 ≤ 𝜆 ≤ 1;in the following, 𝜅 is an amplitude parameter [16] |𝐸〉…”