Random Polarization Memory in Disordered Media

• Random polarization memory effect is a history-dependent phenomenon where disordered, mode-mixing systems retain a deterministic correlation to the input polarization.
• In multimode fibers, the effect manifests as a spatially random intensity speckle with local polarization states rotating synchronously with the input, as confirmed by Stokes polarimetry.
• This robust polarization retention offers opportunities for advanced imaging, sensing, and analysis of polarization dynamics in complex optical, scattering, and spintronic systems.

to=arxiv_search.search ુમળાયેલું 彩经彩票 code string='all:"random polarization memory effect" OR ti:"random polarization memory effect" OR abs:"random polarization memory effect"' max_results=10

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Random polarization memory effect denotes a class of history-dependent polarization phenomena in disordered or strongly mode-mixing systems where an apparently scrambled output retains a deterministic or recoverable relation to an earlier polarization state. In its most explicit arXiv usage, the term refers to multimode-fiber propagation in which the output exhibits a spatially random polarization speckle, yet each local polarization state rotates in a highly correlated way with the input polarization rotation (Arora et al., 6 Sep 2025). Closely related polarization-memory phenomena also arise in random scattering media, where circular polarization can retain helicity over many scattering events (Macdonald et al., 2015), and in disordered multiferroic or spintronic systems, where a previously written polarization state can persist through nominally nonpolar regimes because of phase coexistence, disorder, or slow magnetic reservoirs (De et al., 2015, Balanta et al., 2015).

1. Definition and conceptual boundaries

In the multimode-fiber literature, random polarization memory effect is the observation that linearly polarized light entering a strongly mode-mixing multimode fiber produces both a spatially random speckle intensity pattern and a spatially random distribution of polarization states at the output, while the local polarization state at each output point still rotates in a highly correlated way with the input polarization rotation (Arora et al., 6 Sep 2025). In the ideal case, each local polarization ellipse rigidly rotates by the same azimuthal angle as the input linear polarization. The effect is therefore a memory effect because the output retains memory of the input polarization in a deterministic way, even though the spatial distribution is randomized.

A central conceptual point is that “random” does not mean statistically uncorrelated in this usage. In the multimode-fiber case it refers to the random spatial structure of the polarization speckle, not to a loss of deterministic response (Arora et al., 6 Sep 2025). This distinguishes the phenomenon from conventional descriptions of polarization scrambling in multimode fibers, where input polarization is often treated as lost.

The broader optical literature uses “polarization memory” in a related but not identical sense. In multiple scattering, “polarization memory” or the random polarization memory effect refers to the partial preservation of some polarization states after many random scattering events in a disordered medium, with circular polarization being the canonical example in the Mie regime (Macdonald et al., 2015). In that context the memory is commonly discussed as the survival of helicity rather than as a pixel-wise rotation law.

Beyond wave optics, several papers describe phenomena that do not use the exact phrase but exhibit analogous history-dependent polarization retention in complex media. Mixed rare-earth manganites show a non-volatile, history-dependent polarization state that persists even when the material is heated well above the ferroelectric and magnetic ordering temperatures, in a regime described as nominally paraelectric and paramagnetic (De et al., 2015). Mn $\delta$-doped III–V heterostructures exhibit optically writable and optically readable spin-polarization memory through a disordered Mn ensemble (Balanta et al., 2015). These cases are best regarded as related polarization-memory phenomena rather than strict instances of the optical multimode-fiber definition.

2. Vector-wave formulation in random and mode-mixing media

The multimode-fiber realization is naturally formulated as a vectorial interference problem. In a step-index multimode fiber, the excitation field is decomposed into a basis of guided vector modes; each mode propagates along the fiber length and acquires a different phase, producing a seemingly random interference pattern at the output (Arora et al., 6 Sep 2025). The output polarization at each spatial point is described by spatially varying Stokes parameters,

$$\begin{aligned} S_0(x,y) &= |E_H(x,y)|^2 + |E_V(x,y)|^2,\ S_1(x,y) &= |E_H(x,y)|^2 - |E_V(x,y)|^2,\ S_2(x,y) &= 2\,\mathrm{Re}\!\left[E_H^*(x,y)E_V(x,y)\right],\ S_3(x,y) &= 2\,\mathrm{Im}\!\left[E_H(x,y)E_V^*(x,y)\right], \end{aligned}$$

with normalized Stokes vector

$$\mathbf{s}(x,y)=\frac{1}{S_0(x,y)}\left(S_1,S_2,S_3\right),$$

which corresponds to a point on the Poincaré sphere (Arora et al., 6 Sep 2025).

The mechanism is described in terms of the decomposition of the incident linear polarization into right- and left-circular components. Rotating the input linear polarization with a half-wave plate does not change the magnitudes of these circular components but changes their relative phase. The output can then be viewed as an interference of two fixed output patterns associated with the two circular components, with the half-wave plate controlling a global relative phase. Because this phase is global, all spatial points undergo the same phase sweep between the two circular components, and the local polarization states evolve synchronously on the Poincaré sphere (Arora et al., 6 Sep 2025).

An important theoretical contrast appears in general random-media transport. For electromagnetic propagation in random media with small fluctuations of electric permittivity, the field can be decomposed into transverse electric and transverse magnetic plane-wave modes with random amplitudes whose evolution is governed by a coupled system of stochastic differential equations in range (Borcea et al., 2015). In the long-range Markov limit, the theory yields scattering mean free paths for the decay of mean mode amplitudes and transport equations with polarization for the Wigner transform of the field. That framework quantifies the loss of coherence and the exchange of energy between polarization modes, thereby giving a rigorous description of how polarization is preserved, mixed, or forgotten in random media (Borcea et al., 2015). This suggests that random polarization memory can be viewed as a regime in which the polarization-dependent transport remains sufficiently structured that input–output polarization correlations survive strong spatial scrambling.

3. Multimode-fiber realization

The clearest direct observation of random polarization memory effect is reported in a 50 cm, round-core, step-index Thorlabs FG050LGA multimode fiber with core diameter $50~\mu\text{m}$, numerical aperture $0.22$, and a coherent He–Ne source coupled with a $40\times$ objective matched to the fiber NA (Arora et al., 6 Sep 2025). The input polarization is controlled by a polarizer and a half-wave plate, while the output facet is imaged onto a camera. Full polarization characterization is performed by Stokes polarimetry using six images $I_H, I_V, I_D, I_A, I_R, I_L$ for each half-wave-plate angle.

The output at a fixed input polarization is a random vector speckle: the intensity is highly structured and random, and the local polarization ellipses vary in orientation and handedness across the output facet (Arora et al., 6 Sep 2025). Yet when the half-wave plate is rotated, the intensity at individual output points observed through a linear analyzer shows strong periodic modulation, with a dominant frequency corresponding to $90^\circ$ half-wave-plate rotation. In the full Stokes measurement, the polarization state at each sampled output point rotates as the input polarization is rotated, and the amount of azimuthal rotation matches the change of input polarization azimuth (Arora et al., 6 Sep 2025).

The ideal and non-ideal cases are physically distinct. In an ideal non-birefringent multimode fiber, all local states rotate in the same direction and by the same amount as the input, while ellipticity and handedness are preserved. In a non-ideal birefringent fiber, additional retardation between orthogonal linear components causes more complex trajectories: some points rotate clockwise, others counterclockwise, and some points change ellipticity and handedness. Nevertheless, a one-to-one, monotonic relation between input azimuth and local output azimuth remains, so the polarization memory survives even in the presence of stress-induced birefringence and coiling (Arora et al., 6 Sep 2025).

This phenomenon is vectorial rather than intensity-domain memory. Without an analyzer, the intensity speckle remains essentially unchanged when the input polarization is rotated; the memory manifests in the local polarization state rather than in a bulk translation or rotation of the intensity pattern (Arora et al., 6 Sep 2025). That differentiates it from the amplitude-domain memory effects more commonly discussed in multimode-fiber and multiple-scattering optics.

4. Relation to polarization memory in random scattering media

In random scattering media, polarization memory is most prominently discussed for circular polarization. The relevant operational fact is that photon direction may already be randomized after about one transport length $l_t$, while the scattered light still carries a non-negligible degree of circular polarization (Macdonald et al., 2015). Circular polarization memory is therefore the tendency of an incident circularly polarized state to retain its handedness more strongly and over longer distances than linear polarization in suitable random media.

The analysis begins from the Stokes-vector scattering relation for a sphere, where the scattered degree of circular polarization for incident right-circularly polarized light is

$$\frac{V_s}{I_s}=\frac{S_{33}(\theta)}{S_{11}(\theta)}.$$

The single-scattering-averaged degree of circular polarization is then

$$\begin{aligned} S_0(x,y) &= |E_H(x,y)|^2 + |E_V(x,y)|^2,\ S_1(x,y) &= |E_H(x,y)|^2 - |E_V(x,y)|^2,\ S_2(x,y) &= 2\,\mathrm{Re}\!\left[E_H^*(x,y)E_V(x,y)\right],\ S_3(x,y) &= 2\,\mathrm{Im}\!\left[E_H(x,y)E_V^*(x,y)\right], \end{aligned}$$0

and the mean degree of circular polarization after $$\begin{aligned} S_0(x,y) &= |E_H(x,y)|^2 + |E_V(x,y)|^2,\ S_1(x,y) &= |E_H(x,y)|^2 - |E_V(x,y)|^2,\ S_2(x,y) &= 2\,\mathrm{Re}\!\left[E_H^*(x,y)E_V(x,y)\right],\ S_3(x,y) &= 2\,\mathrm{Im}\!\left[E_H(x,y)E_V^*(x,y)\right], \end{aligned}$$1 scattering events is modeled as

$$\begin{aligned} S_0(x,y) &= |E_H(x,y)|^2 + |E_V(x,y)|^2,\ S_1(x,y) &= |E_H(x,y)|^2 - |E_V(x,y)|^2,\ S_2(x,y) &= 2\,\mathrm{Re}\!\left[E_H^*(x,y)E_V(x,y)\right],\ S_3(x,y) &= 2\,\mathrm{Im}\!\left[E_H(x,y)E_V^*(x,y)\right], \end{aligned}$$2

where $$\begin{aligned} S_0(x,y) &= |E_H(x,y)|^2 + |E_V(x,y)|^2,\ S_1(x,y) &= |E_H(x,y)|^2 - |E_V(x,y)|^2,\ S_2(x,y) &= 2\,\mathrm{Re}\!\left[E_H^*(x,y)E_V(x,y)\right],\ S_3(x,y) &= 2\,\mathrm{Im}\!\left[E_H(x,y)E_V^*(x,y)\right], \end{aligned}$$3 is the helicity survival parameter (Macdonald et al., 2015).

This framework generalizes naturally to polydisperse media by averaging over the particle-size and refractive-index distribution: $$\begin{aligned} S_0(x,y) &= |E_H(x,y)|^2 + |E_V(x,y)|^2,\ S_1(x,y) &= |E_H(x,y)|^2 - |E_V(x,y)|^2,\ S_2(x,y) &= 2\,\mathrm{Re}\!\left[E_H^*(x,y)E_V(x,y)\right],\ S_3(x,y) &= 2\,\mathrm{Im}\!\left[E_H(x,y)E_V^*(x,y)\right], \end{aligned}$$4 The main conclusion is that circular polarization memory cannot be characterized solely by the anisotropy factor $$\begin{aligned} S_0(x,y) &= |E_H(x,y)|^2 + |E_V(x,y)|^2,\ S_1(x,y) &= |E_H(x,y)|^2 - |E_V(x,y)|^2,\ S_2(x,y) &= 2\,\mathrm{Re}\!\left[E_H^*(x,y)E_V(x,y)\right],\ S_3(x,y) &= 2\,\mathrm{Im}\!\left[E_H(x,y)E_V^*(x,y)\right], \end{aligned}$$5 or by $$\begin{aligned} S_0(x,y) &= |E_H(x,y)|^2 + |E_V(x,y)|^2,\ S_1(x,y) &= |E_H(x,y)|^2 - |E_V(x,y)|^2,\ S_2(x,y) &= 2\,\mathrm{Re}\!\left[E_H^*(x,y)E_V(x,y)\right],\ S_3(x,y) &= 2\,\mathrm{Im}\!\left[E_H(x,y)E_V^*(x,y)\right], \end{aligned}$$6; it depends on the full distribution of particle sizes and refractive indices because polarization memory is driven by the angular and polarization structure of scattering, not merely by the first angular moment (Macdonald et al., 2015).

The comparison with the multimode-fiber effect is conceptually useful. In scattering media, the memory variable is helicity survival under many random events, whereas in multimode fibers the memory variable is the synchronized local rotation of vector speckle under a global input-polarization change. In both cases, however, the system is random in its spatial or path structure while retaining a deterministic polarization correlation that would be missed by intensity-only inspection.

System	Randomized quantity	Memory variable
Multimode fiber	Spatial polarization speckle	Local polarization rotation with input azimuth
Polydisperse scattering medium	Photon directions and paths	Circular helicity survival $$\begin{aligned} S_0(x,y) &= |E_H(x,y)|^2 + |E_V(x,y)|^2,\ S_1(x,y) &= |E_H(x,y)|^2 - |E_V(x,y)|^2,\ S_2(x,y) &= 2\,\mathrm{Re}\!\left[E_H^*(x,y)E_V(x,y)\right],\ S_3(x,y) &= 2\,\mathrm{Im}\!\left[E_H(x,y)E_V^*(x,y)\right], \end{aligned}$$7
Random dielectric medium	Mode amplitudes and directions	TE/TM coherence and polarization transport

5. Condensed-matter and spin-memory analogues

Mixed rare-earth manganites $$\begin{aligned} S_0(x,y) &= |E_H(x,y)|^2 + |E_V(x,y)|^2,\ S_1(x,y) &= |E_H(x,y)|^2 - |E_V(x,y)|^2,\ S_2(x,y) &= 2\,\mathrm{Re}\!\left[E_H^*(x,y)E_V(x,y)\right],\ S_3(x,y) &= 2\,\mathrm{Im}\!\left[E_H(x,y)E_V^*(x,y)\right], \end{aligned}$$8Dy$$\begin{aligned} S_0(x,y) &= |E_H(x,y)|^2 + |E_V(x,y)|^2,\ S_1(x,y) &= |E_H(x,y)|^2 - |E_V(x,y)|^2,\ S_2(x,y) &= 2\,\mathrm{Re}\!\left[E_H^*(x,y)E_V(x,y)\right],\ S_3(x,y) &= 2\,\mathrm{Im}\!\left[E_H(x,y)E_V^*(x,y)\right], \end{aligned}$$9MnO$$\mathbf{s}(x,y)=\frac{1}{S_0(x,y)}\left(S_1,S_2,S_3\right),$$0 with $$\mathbf{s}(x,y)=\frac{1}{S_0(x,y)}\left(S_1,S_2,S_3\right),$$1 Eu or Gd exhibit a non-volatile ferroelectric memory effect even in the paraelectric and paramagnetic region, with memory persisting up to about $$\mathbf{s}(x,y)=\frac{1}{S_0(x,y)}\left(S_1,S_2,S_3\right),$$2 K and vanishing only when the ramping temperature reaches $$\mathbf{s}(x,y)=\frac{1}{S_0(x,y)}\left(S_1,S_2,S_3\right),$$3 K (De et al., 2015). The compounds show double pyrocurrent and dielectric peaks, assigned to competing $$\mathbf{s}(x,y)=\frac{1}{S_0(x,y)}\left(S_1,S_2,S_3\right),$$4 and $$\mathbf{s}(x,y)=\frac{1}{S_0(x,y)}\left(S_1,S_2,S_3\right),$$5 cycloidal spin orders, and the authors attribute the remarkable memory behavior to the coexistence of these cycloidal phases. The microscopic polarization mechanism is the inverse Dzyaloshinskii–Moriya relation

$$\mathbf{s}(x,y)=\frac{1}{S_0(x,y)}\left(S_1,S_2,S_3\right),$$6

so phase coexistence implies coexisting polarizations along distinct crystallographic directions (De et al., 2015). The paper does not use the phrase random polarization memory effect explicitly, but the reported phenomenology is described as history dependent, non-volatile, and likely stabilized by phase coexistence and disorder.

A related multiferroic example appears in single-crystal CuFeO$$\mathbf{s}(x,y)=\frac{1}{S_0(x,y)}\left(S_1,S_2,S_3\right),$$7, where a nonpolar collinear antiferromagnetic ground state at $$\mathbf{s}(x,y)=\frac{1}{S_0(x,y)}\left(S_1,S_2,S_3\right),$$8 T retains a strong memory of the polarization magnitude and direction written in the ferroelectric incommensurate phase (Beilsten-Edmands et al., 2016). Upon re-entering the ferroelectric phase without external bias, a net polarization of comparable magnitude to the initial polarization is recovered. The proposed microscopic origin is the existence of helical domain walls within the nonpolar collinear ground state, which retain the helicity of the polar phase for certain magnetothermal histories (Beilsten-Edmands et al., 2016). This is not a random polarization speckle phenomenon, but it is a rigorous example of polarization memory encoded in a disordered or domain-wall texture rather than in a static ferroelectric state.

Spintronic heterostructures provide another analogue. In Mn $$\mathbf{s}(x,y)=\frac{1}{S_0(x,y)}\left(S_1,S_2,S_3\right),$$9-doped InGaAs/GaAs structures, a pre-pulse with opposite circular polarization reduces the polarization degree of the quantum-well emission, demonstrating that Mn ions act as a spin-memory that can be optically controlled by the polarization of the photocreated carriers (Balanta et al., 2015). In related GaAs/InGaAs heterostructures with $50~\mu\text{m}$0 layers, the spin-memory effect consists in spin polarization of Mn atoms due to interaction with photogenerated spin-polarized holes, and the amplitude of the $50~\mu\text{m}$1-effect is most strongly affected by the concentration of resident electrons in the quantum well (Dorokhin et al., 2021). These systems are explicitly about spin-polarization memory rather than the optical vector-speckle effect, but they reinforce a common theme: a disordered or stochastic microscopic subsystem can preserve the sign of a previously written polarization and imprint it on a later optical readout.

6. Quantification, limitations, and open directions

The multimode-fiber observation is currently characterized primarily by local intensity modulation under an analyzer and by local trajectories on the Poincaré sphere reconstructed from Stokes polarimetry, rather than by a formal correlation function or a memory length (Arora et al., 6 Sep 2025). The paper explicitly leaves open the definition of a quantitative Stokes-correlation metric, the dependence on fiber length and mode count, and the role of bending, coherence, and bandwidth. This suggests that a mature theory of random polarization memory in fibers will likely require a polarization-resolved correlation formalism analogous to amplitude-domain memory-effect metrics.

In random media more broadly, the transport-theoretic description already provides the mathematical language for such a formalization. Scattering mean free paths quantify coherent decay, while matrix-valued transport equations describe polarization-dependent redistribution of energy among modes and directions (Borcea et al., 2015). A plausible implication is that random polarization memory should be strongest in regimes where spatial scrambling is substantial but the polarization transport has not yet relaxed to an effectively isotropic coherence matrix.

Experimentally, the immediate application space emphasized for the multimode-fiber effect is imaging and sensing. The effect provides an additional deterministic degree of freedom beyond amplitude-based memory effects and may support polarization-resolved imaging through multimode fibers, fiber-based sensing of birefringence and stress, and combinations with wavefront shaping or adaptive optics (Arora et al., 6 Sep 2025). In scattering media, circular polarization memory offers an alternate pathway toward recovering particle size distributions from diffusing circularly polarized light and helps explain why media with matched $50~\mu\text{m}$2 and $50~\mu\text{m}$3 can nonetheless differ strongly in polarization behavior (Macdonald et al., 2015).

Across optical, magnetic, and multiferroic realizations, the common scientific significance of random polarization memory is that polarization can remain encoded in systems whose spatial structure, domain structure, or scattering paths appear strongly scrambled. The detailed mechanism varies—from coherent interference of fixed circular-component patterns in multimode fibers, to helicity survival under Mie scattering, to phase coexistence or domain-wall helicity in multiferroics—but in each case the observed polarization is not simply erased by disorder. Instead, disorder coexists with a constrained, history-dependent polarization response that can be measured, and in some cases exploited, as a robust memory channel (Arora et al., 6 Sep 2025, Macdonald et al., 2015).