Towards polarization steganography

Abstract

We propose and experimentally demonstrate a polarization--based steganographic scheme using partially polarized vector beams. In our approach, the spatially dependent polarization structure of the optical field serves as the carrier through which the hidden information can be retrieved. By engineering a vector beam whose polarization states populate a prescribed region of the Poincaré sphere, specifically, the equatorial disk, we establish a nontrivial mapping between transverse spatial coordinates and polarization states. Information retrieval is achieved by applying a spatial mask derived from a parametric curve defined within this region of the Poincaré sphere, followed by spatially resolved polarization analysis. We demonstrate the selective reconstruction of various parametric shapes, including polygonal and smooth curves, confirming that the hidden patterns are retrieved through the combined use of spatial filtering and polarization--domain mapping. Our results establish partially polarized vector beams as a flexible and experimentally accessible platform for polarization--based information hiding.

Figures (7)

• Figure 1: (a)--(d) RGB Steganography. Three letters are encoded using distinct colors: A (blue), B (green), and C (red). (d) Spatial overlap of the three letters, which makes it difficult to isolate the individual information channels; however, applying a matching color filter reveals the corresponding letter. (e) Concept of polarization steganography. A suitable spatial filter (red key in the diagram) applied in the transverse $(x,y)$ plane of the field reveals the information embedded (“msg”) within the equatorial disk of the Poincaré sphere.
• Figure 2: (a) Far field intensity and (b) transverse phase, of a spherical source realization after propagation through a $q$--plate, computed from Eq. \ref{['eq:oam']} with parameters $\ell=1$, $f=15$ cm, $z=50$ cm, and $\lambda = 625$ nm. The numerical window has a side length of 2 mm.
• Figure 3: (a)--(d) Theoretical Stokes parameters $S_0, S_1, S_2, S_3$, respectively, and (e) their corresponding map to the Poincaré sphere. We used the following parameters: $\ell=1$, $a=3.75\times 10^{-4}$ m, $\lambda = 625$ nm, $f = 15$ cm, and $z = 24$ cm. The numerical window has a side length of 2 mm.
• Figure 4: Illustration of the spatial--polarization mapping. A suitable spatial filter applied in the $(x,y)$ plane translates into a predefined shape within the equatorial disk of the Poincaré sphere (left--hand panel). The red trajectory in the $(x,y)$ plane maps onto the blue curve in the $(s_1,s_2)$ plane. The right--hand panel depicts $S_0$, together with representative electric field trajectories, consistent with the corresponding polarization states.
• Figure 5: Schematic layout of experimental setup. LED, extended source; A1--A2, apertures; L1--L3, lenses; LP, linear polarizer; QP, $q$--plate; SM, spatial mask; Stokes, spatially resolved Stokes polarimetry.