Polarforming: Real-Time Polarization Control

• Polarforming is the technique to continuously control antenna polarization (linear, circular, elliptical) via tunable phase shifters for adaptive channel matching.
• It enables single-RF-chain operation by adjusting the polarization domain independently from spatial beamforming, achieving SNR gains up to 6.3 dB over fixed methods.
• Research challenges include accurate polarized CSI acquisition and mitigating hardware nonidealities, driving innovations in training schemes and low-complexity optimization.

Polarforming is a term with several domain-specific meanings, but its most formalized current use is in wireless communications, where it denotes the real-time shaping of an antenna’s polarization state—linear, circular, or general elliptical—via tunable phase shifters so that transmit and/or receive polarization matches, or deliberately mismatches, the instantaneous channel. In that setting, it is described as a “waveforming-in-the-polarization-domain” technique that equips each antenna with continuous control over polarization angle, ellipticity, and handedness while using only a single radio-frequency chain. Related literatures use the same term, or closely allied language, for the cold assembly of highly polar molecular clusters in helium nanodroplets, mechanically induced switching of polar metals via strain gradients, spontaneous orientation polarization in organic films, and the optimal-control formation of oriented polar molecules (Zhou et al., 2024, Zhou et al., 28 May 2025, Ding et al., 27 May 2025, Niman et al., 2019, Zabalo et al., 2020, Tanaka et al., 8 May 2025, Forlevesi et al., 15 Sep 2025).

1. Wireless polarforming as polarization-domain waveforming

In wireless communications, polarforming starts from the observation that the polarization of an electromagnetic wave is a two-degree-of-freedom quantity. In Jones form, a general polarization state can be written as

$$\mathbf{p}(\chi,\phi)= \begin{bmatrix} \cos\chi\ e^{j\phi}\sin\chi \end{bmatrix},$$

where $\chi\in[0,\pi/2]$ is the polarization angle and $\phi\in[0,2\pi)$ is the phase difference. Because realistic propagation paths include reflections, scatterers, antenna-interface imperfections, and other depolarizing effects, a wave transmitted in a nominal linear or circular state may arrive in a mixed polarization state. Polarforming treats this mismatch as a controllable impairment rather than a fixed loss source (Ding et al., 27 May 2025, Ding et al., 23 Jul 2025).

The concept is defined most explicitly for phase-shifter-based polarization-reconfigurable antennas (PS-PRAs). A PS-PRA shapes polarization in real time over the full $0$–$2\pi$ phase range, enabling continuous adaptation of the transmit and/or receive polarization to the channel. This directly distinguishes it from several adjacent antenna classes. Fixed-polarization antennas cannot adapt once fabricated; dual-polarized antennas require two RF chains; switchable polarization-reconfigurable antennas only toggle among a finite set of predefined polarizations; and polarization-agile antennas only rotate a linear polarization vector. The intended advantage of polarforming is therefore not merely reconfiguration, but continuous low-cost single-RF-chain adaptation over the full polarization manifold (Zhou et al., 28 May 2025).

A recurrent misconception is that polarforming is simply conventional analog beamforming expressed in a different basis. The literature treats the two operations as distinct. Conventional analog beamforming adjusts spatial phase across antenna elements while keeping polarization fixed; polarforming adjusts the polarization basis itself, aligning the antenna’s Jones vector with the dominant eigen-polarization of the channel. In narrowband models, the effective scalar channel is written as

$$h_{\mathsf{eff}}=\mathbf{p}_{\mathsf{rx}}^H\,\mathbf{H}\,\mathbf{p}_{\mathsf{tx}},$$

so the optimization variable is not only spatial phasing but also the transmit and receive polarization vectors (Zhou et al., 2024, Ding et al., 27 May 2025).

2. Antenna architectures and polarization synthesis

The canonical PS-PRA architecture comprises two orthogonally oriented antenna elements, usually denoted vertical and horizontal, with a single variable phase shifter inserted on one branch before combination into one RF chain. By controlling the phase difference between the two branches, the antenna can radiate or receive any desired linear, circular, or elliptical polarization. In the simplest equal-amplitude form, the polarforming vectors are written as

$$\mathbf{p}(\theta)=\frac{1}{\sqrt{2}} \begin{bmatrix} 1\ e^{j\theta} \end{bmatrix}, \qquad \mathbf{q}(\phi)=\frac{1}{\sqrt{2}} \begin{bmatrix} 1\ e^{j\phi} \end{bmatrix},$$

with $\theta,\phi\in[0,2\pi]$ for the transmit and receive phase shifts, respectively (Zhou et al., 28 May 2025, Zhou et al., 22 Jul 2025).

The wireless survey literature organizes PRA hardware into three polarforming dimensions. In 1D polarforming, a single-element antenna is mechanically rotated, so the controllable variable is the linear polarization angle. In 2D polarforming, two orthogonally polarized elements share one RF chain via a power divider and one phase shifter, allowing linear polarization at arbitrary angle, circular polarization, or elliptical polarization; a mechanical rotation stage can add a second degree of freedom. In 3D polarforming, three mutually orthogonal elements are fed from one RF chain by a $1\!:\!3$ splitter and two independent phase shifters, providing full coverage of the Poincaré sphere without mechanical motion (Ding et al., 27 May 2025).

The mathematical synthesis of these states is expressed through rotation and relative phase-shift operators. In Jones form,

$$R(\psi)= \begin{bmatrix} \cos\psi & -\sin\psi\ \sin\psi & \cos\psi \end{bmatrix}, \qquad P(\delta)=\operatorname{diag}\{1,e^{j\delta}\}.$$

Linear polarization at angle $\chi\in[0,\pi/2]$0 is obtained as $\chi\in[0,\pi/2]$1, whereas right-hand circular polarization appears as

$\chi\in[0,\pi/2]$2

This formalism makes explicit that polarforming is a controlled traversal of the Jones-state manifold rather than a fixed selection among a few presets (Ding et al., 27 May 2025).

A broader hardware model appears in polarized six-dimensional movable-antenna and integrated sensing-and-communication systems, where each orthogonal polarization feed is assigned both an attenuator and a phase shifter. In that setting, the polarforming vector uses complex coefficients from a discrete feasible set $\chi\in[0,\pi/2]$3, and polarforming refers to reconfigurable adjustment of both the complex amplitude and phase of the two orthogonal ports of a single-RF-chain dual-polarized antenna (Shao et al., 4 Jun 2025, Shao et al., 12 May 2025).

3. Channel models and optimization frameworks

For narrowband SISO links, the effective polarized channel is modeled as a bilinear form in the transmit and receive polarization vectors. One common expression is

$\chi\in[0,\pi/2]$4

where $\chi\in[0,\pi/2]$5 is the quasi-static polarized channel matrix. The corresponding instantaneous SNR is

$\chi\in[0,\pi/2]$6

Under this model, maximizing receive SNR is non-concave jointly in $\chi\in[0,\pi/2]$7, but the two scalar subproblems admit closed-form updates. Fixing $\chi\in[0,\pi/2]$8, the receive-side optimum is

$\chi\in[0,\pi/2]$9

and fixing $\phi\in[0,2\pi)$0, the transmit-side optimum is

$\phi\in[0,2\pi)$1

The resulting alternating optimization procedure is monotone and convergent because each step nondecreasingly improves the objective and the SNR is upper-bounded (Zhou et al., 28 May 2025).

For polarized MIMO links, the problem is cast as capacity maximization with joint optimization over transmit covariance and antenna polarization states. After polarforming, the effective channel is inserted into the standard log-det capacity expression, and water-filling over the singular values of the effective MIMO channel provides both the optimal power allocation and an upper bound when the phase shifts are further optimized. This places polarforming within the same optimization lineage as precoding and beamforming, but with polarization states appearing as additional design variables (Zhou et al., 2024).

Once the setting expands beyond single-user SISO, the optimization landscape becomes more heterogeneous. In secrecy-rate maximization, the beamforming subproblem admits a principal-eigenvector update, whereas the polarforming subproblem is rewritten as a unimodular quadratic fractional program, relaxed to a semidefinite program through $\phi\in[0,2\pi)$2, transformed by Charnes–Cooper, and solved with Gaussian randomization for rank-one recovery (Ding et al., 23 Jul 2025). In movable-antenna systems, the joint dependence of the channel on antenna positions and polarization phases leads to successive convex approximation, where non-concave cosine terms are replaced by concave quadratic surrogates and the updates reduce to quadratic programs (Zhou et al., 22 Jul 2025). In polarized 6D movable-antenna systems, weighted sum-rate maximization is addressed by a two-timescale decomposition: slow mechanical rotation from statistical CSI, fast electronic polarforming from instantaneous CSI, and a penalty-dual-decomposition/WMMSE inner loop whose complexity scales as $\phi\in[0,2\pi)$3 (Shao et al., 4 Jun 2025).

4. Reported performance and network-level uses

The baseline PS-PRA SISO study provides the clearest first-order performance picture. Under Rayleigh fading with inverse XPD $\phi\in[0,2\pi)$4, phase shifts in $\phi\in[0,2\pi)$5, convergence threshold $\phi\in[0,2\pi)$6, $\phi\in[0,2\pi)$7, and $\phi\in[0,2\pi)$8 Monte Carlo channel realizations, alternating optimization typically converges within 5–6 iterations. At a target rate $\phi\in[0,2\pi)$9 bps/Hz, end-to-end transmit-plus-receive polarforming reports SNR gains of $0$0 dB over SPRA, $0$1 dB over PAA, $0$2 dB over CPA, and $0$3 dB over LPA. Across $0$4–$0$5 dB average SNR, the performance gap remains nearly constant, indicating robustness against channel depolarization (Zhou et al., 28 May 2025).

The broader wireless-network perspective emphasizes that the utility of polarforming is not limited to point-to-point links. Proposed applications include integrated sensing and communication, space-air-ground integrated networks, reconfigurable environments, next-generation multiple access, physical-layer security, and machine-type communications. In the survey simulations with six transmit and six receive PRAs, 3D polarforming outperforms a tri-polarized-antenna system of the same physical aperture by up to $0$6–$0$7 at low–moderate SNR; 2D polarforming exceeds dual-RF-chain DPA in the low-SNR regime and approaches its multiplexing gain at high SNR; 1D polarforming yields $0$8–$0$9 dB gain over LPAs and CPAs; and when inverse-XPD is swept from $2\pi$0 dB to $2\pi$1 dB at SNR $2\pi$2 dB, fixed-polarization-antenna rates collapse by more than $2\pi$3 while polarforming remains within $2\pi$4 of the high-XPD ideal (Ding et al., 27 May 2025).

In secure communications, polarforming is used jointly with spatial beamforming to align the legitimate link and misalign the eavesdropper. For a $2\pi$5 PRA-equipped base station with $2\pi$6 and linearly polarized user and eavesdropper antennas, the reported secrecy-rate gain at $2\pi$7 dB is on the order of $2\pi$8–$2\pi$9 dB over fixed-circular-polarization or maximum-ratio-transmission baselines with circular polarization. The same study reports less than $$h_{\mathsf{eff}}=\mathbf{p}_{\mathsf{rx}}^H\,\mathbf{H}\,\mathbf{p}_{\mathsf{tx}},$$0 secrecy-rate loss when the normalized variance of eavesdropper-CSI error reaches $$h_{\mathsf{eff}}=\mathbf{p}_{\mathsf{rx}}^H\,\mathbf{H}\,\mathbf{p}_{\mathsf{tx}},$$1, and continued advantage even against a multi-antenna eavesdropper using MRC (Ding et al., 23 Jul 2025).

When polarforming is combined with mechanical reconfigurability, the problem changes from polarization-only matching to joint spatial-polarization adaptation. In movable-antenna SISO systems, the alternating SCA algorithm converges in about six outer iterations, movable antennas outperform fixed antennas across SNR, number of paths, and movement region size, and polarforming adds $$h_{\mathsf{eff}}=\mathbf{p}_{\mathsf{rx}}^H\,\mathbf{H}\,\mathbf{p}_{\mathsf{tx}},$$2–$$h_{\mathsf{eff}}=\mathbf{p}_{\mathsf{rx}}^H\,\mathbf{H}\,\mathbf{p}_{\mathsf{tx}},$$3 bps/Hz over fixed linear or circular polarization. In polarized 6D movable-antenna multiuser systems with $$h_{\mathsf{eff}}=\mathbf{p}_{\mathsf{rx}}^H\,\mathbf{H}\,\mathbf{p}_{\mathsf{tx}},$$4 P-6DMAs at $$h_{\mathsf{eff}}=\mathbf{p}_{\mathsf{rx}}^H\,\mathbf{H}\,\mathbf{p}_{\mathsf{tx}},$$5 GHz, the weighted sum-rate at $$h_{\mathsf{eff}}=\mathbf{p}_{\mathsf{rx}}^H\,\mathbf{H}\,\mathbf{p}_{\mathsf{tx}},$$6 dBm is approximately $$h_{\mathsf{eff}}=\mathbf{p}_{\mathsf{rx}}^H\,\mathbf{H}\,\mathbf{p}_{\mathsf{tx}},$$7 bit/s/Hz for the joint design, versus $$h_{\mathsf{eff}}=\mathbf{p}_{\mathsf{rx}}^H\,\mathbf{H}\,\mathbf{p}_{\mathsf{tx}},$$8 for polarforming-only, $$h_{\mathsf{eff}}=\mathbf{p}_{\mathsf{rx}}^H\,\mathbf{H}\,\mathbf{p}_{\mathsf{tx}},$$9 for rotation-only, and $$\mathbf{p}(\theta)=\frac{1}{\sqrt{2}} \begin{bmatrix} 1\ e^{j\theta} \end{bmatrix}, \qquad \mathbf{q}(\phi)=\frac{1}{\sqrt{2}} \begin{bmatrix} 1\ e^{j\phi} \end{bmatrix},$$0 for fixed parameters; with $$\mathbf{p}(\theta)=\frac{1}{\sqrt{2}} \begin{bmatrix} 1\ e^{j\theta} \end{bmatrix}, \qquad \mathbf{q}(\phi)=\frac{1}{\sqrt{2}} \begin{bmatrix} 1\ e^{j\phi} \end{bmatrix},$$1 bits each for amplitude and phase quantization, performance remains within $$\mathbf{p}(\theta)=\frac{1}{\sqrt{2}} \begin{bmatrix} 1\ e^{j\theta} \end{bmatrix}, \qquad \mathbf{q}(\phi)=\frac{1}{\sqrt{2}} \begin{bmatrix} 1\ e^{j\phi} \end{bmatrix},$$2 of the continuous-valued optimum (Zhou et al., 22 Jul 2025, Shao et al., 4 Jun 2025).

The ISAC literature extends the idea further by using polarization diversity not only for communication but also for localization. In the proposed two-timescale protocol, pilot-polarforming vectors create a PARAFAC-structured tensor whose stable LoS components are extracted by alternating least squares, followed by MUSIC-based direction estimation and least-squares distance recovery. Under the reported setup, localization MSE falls below $$\mathbf{p}(\theta)=\frac{1}{\sqrt{2}} \begin{bmatrix} 1\ e^{j\theta} \end{bmatrix}, \qquad \mathbf{q}(\phi)=\frac{1}{\sqrt{2}} \begin{bmatrix} 1\ e^{j\phi} \end{bmatrix},$$3 m for SNR above $$\mathbf{p}(\theta)=\frac{1}{\sqrt{2}} \begin{bmatrix} 1\ e^{j\theta} \end{bmatrix}, \qquad \mathbf{q}(\phi)=\frac{1}{\sqrt{2}} \begin{bmatrix} 1\ e^{j\phi} \end{bmatrix},$$4 dB, compared with more than $$\mathbf{p}(\theta)=\frac{1}{\sqrt{2}} \begin{bmatrix} 1\ e^{j\theta} \end{bmatrix}, \qquad \mathbf{q}(\phi)=\frac{1}{\sqrt{2}} \begin{bmatrix} 1\ e^{j\phi} \end{bmatrix},$$5 m for the benchmark, and joint placement-plus-polarforming achieves up to roughly $$\mathbf{p}(\theta)=\frac{1}{\sqrt{2}} \begin{bmatrix} 1\ e^{j\theta} \end{bmatrix}, \qquad \mathbf{q}(\phi)=\frac{1}{\sqrt{2}} \begin{bmatrix} 1\ e^{j\phi} \end{bmatrix},$$6 sum-rate gain over the baseline at $$\mathbf{p}(\theta)=\frac{1}{\sqrt{2}} \begin{bmatrix} 1\ e^{j\theta} \end{bmatrix}, \qquad \mathbf{q}(\phi)=\frac{1}{\sqrt{2}} \begin{bmatrix} 1\ e^{j\phi} \end{bmatrix},$$7 dBm (Shao et al., 12 May 2025).

5. Molecular and materials-science usages

Outside wireless communications, polarforming refers less to polarization matching and more to the formation, stabilization, or switching of polar configurations. In superfluid helium nanodroplets, polarforming denotes the cold-assembly process by which polar molecules steer one another through long-range dipole–dipole forces into metastable highly polar configurations that are then frozen by the $$\mathbf{p}(\theta)=\frac{1}{\sqrt{2}} \begin{bmatrix} 1\ e^{j\theta} \end{bmatrix}, \qquad \mathbf{q}(\phi)=\frac{1}{\sqrt{2}} \begin{bmatrix} 1\ e^{j\phi} \end{bmatrix},$$8 K helium environment. Its direct signature is electrostatic beam deflection. For an oriented dipole in a field gradient, $$\mathbf{p}(\theta)=\frac{1}{\sqrt{2}} \begin{bmatrix} 1\ e^{j\theta} \end{bmatrix}, \qquad \mathbf{q}(\phi)=\frac{1}{\sqrt{2}} \begin{bmatrix} 1\ e^{j\phi} \end{bmatrix},$$9, and a droplet traversing a deflection region of length $\theta,\phi\in[0,2\pi]$0 at velocity $\theta,\phi\in[0,2\pi]$1 acquires displacement $\theta,\phi\in[0,2\pi]$2. In DMSO clusters, the measured dipole moments were $\theta,\phi\in[0,2\pi]$3 D for the dimer and $\theta,\phi\in[0,2\pi]$4 D for the trimer, implying formation of polar metastable minima rather than only symmetric ground-state structures (Niman et al., 2019).

A related usage appears in polar metals, where the problem is not polarization matching but mechanical switching of a polar axis that cannot be reversed by an electric field because mobile carriers screen the field. In LiOsO$\theta,\phi\in[0,2\pi]$5, flexoelectricity couples strain gradients to the polar soft mode, and a first-principles Landau–Ginzburg–Devonshire Hamiltonian combined with real-space interatomic-force-constant summation yields a coercive bending radius

$\theta,\phi\in[0,2\pi]$6

For the $\theta,\phi\in[0,2\pi]$7 direction, $\theta,\phi\in[0,2\pi]$8 eV and $\theta,\phi\in[0,2\pi]$9 eV/Å, giving $1\!:\!3$0 Å. The reported comparison values are $1\!:\!3$1 Å for rhombohedral BaTiO$1\!:\!3$2 and $1\!:\!3$3 Å for its tetragonal phase (Zabalo et al., 2020).

In organic electronics, the relevant phenomenon is spontaneous orientation polarization in vacuum-deposited films. There the “polarforming” implication is the creation of built-in internal polar layers through asymmetric intermolecular interactions during film growth. In the parallel-dipole model, the surface-potential slope satisfies

$1\!:\!3$4

For the FDI-based molecules studied by Tanaka and co-workers, FDI-2FC5 produced $1\!:\!3$5 mV nm$1\!:\!3$6 and $1\!:\!3$7 under room-temperature deposition, while increasing the deposition rate improved $1\!:\!3$8 to $1\!:\!3$9 mV nm$$R(\psi)= \begin{bmatrix} \cos\psi & -\sin\psi\ \sin\psi & \cos\psi \end{bmatrix}, \qquad P(\delta)=\operatorname{diag}\{1,e^{j\delta}\}.$$0. In an $$R(\psi)= \begin{bmatrix} \cos\psi & -\sin\psi\ \sin\psi & \cos\psi \end{bmatrix}, \qquad P(\delta)=\operatorname{diag}\{1,e^{j\delta}\}.$$1 mol\% codeposition with the nonpolar host SF$$R(\psi)= \begin{bmatrix} \cos\psi & -\sin\psi\ \sin\psi & \cos\psi \end{bmatrix}, \qquad P(\delta)=\operatorname{diag}\{1,e^{j\delta}\}.$$2-TRZ, the orientation degree approached $$R(\psi)= \begin{bmatrix} \cos\psi & -\sin\psi\ \sin\psi & \cos\psi \end{bmatrix}, \qquad P(\delta)=\operatorname{diag}\{1,e^{j\delta}\}.$$3, and a $$R(\psi)= \begin{bmatrix} \cos\psi & -\sin\psi\ \sin\psi & \cos\psi \end{bmatrix}, \qquad P(\delta)=\operatorname{diag}\{1,e^{j\delta}\}.$$4 nm SOP interlayer in a hole-only device yielded large rectification with $$R(\psi)= \begin{bmatrix} \cos\psi & -\sin\psi\ \sin\psi & \cos\psi \end{bmatrix}, \qquad P(\delta)=\operatorname{diag}\{1,e^{j\delta}\}.$$5 at $$R(\psi)= \begin{bmatrix} \cos\psi & -\sin\psi\ \sin\psi & \cos\psi \end{bmatrix}, \qquad P(\delta)=\operatorname{diag}\{1,e^{j\delta}\}.$$6 V (Tanaka et al., 8 May 2025).

In optimal quantum control, a related “polarforming” strategy is the formation of oriented polar molecules from colliding atoms with a single shaped pulse. For the O + H rovibrational model, the control Hamiltonian is $$R(\psi)= \begin{bmatrix} \cos\psi & -\sin\psi\ \sin\psi & \cos\psi \end{bmatrix}, \qquad P(\delta)=\operatorname{diag}\{1,e^{j\delta}\}.$$7, and the target functional is the expectation of a bound-state-restricted orientation operator $$R(\psi)= \begin{bmatrix} \cos\psi & -\sin\psi\ \sin\psi & \cos\psi \end{bmatrix}, \qquad P(\delta)=\operatorname{diag}\{1,e^{j\delta}\}.$$8. The monotonically convergent TBQCP updates reshape the field to combine photoassociation, vibrational stabilization, and orientation. Reported outcomes include $$R(\psi)= \begin{bmatrix} \cos\psi & -\sin\psi\ \sin\psi & \cos\psi \end{bmatrix}, \qquad P(\delta)=\operatorname{diag}\{1,e^{j\delta}\}.$$9 for orientation alone, $\chi\in[0,\pi/2]$00 for photoassociation into $\chi\in[0,\pi/2]$01, and final orientation $\chi\in[0,\pi/2]$02 for the simultaneous photoassociation-plus-orientation objective (Forlevesi et al., 15 Sep 2025).

6. Limitations, misconceptions, and open problems

The wireless literature is explicit that polarforming should not be reduced to “rotating the antenna” or “doing beamforming in another coordinate system.” Phase-only PS-PRA designs can continuously generate linear, circular, and elliptical states, whereas polarization-agile antennas only rotate a linear polarization vector; similarly, dual- and tri-polarized arrays achieve multi-polarization capability by spending additional RF chains, whereas polarforming is motivated by single-RF-chain reconfigurability (Zhou et al., 28 May 2025, Ding et al., 27 May 2025).

The most immediate research bottleneck is polarized CSI acquisition. Many formulations assume full knowledge of the polarization-domain channel matrix $\chi\in[0,\pi/2]$03 or of all polarized links $\chi\in[0,\pi/2]$04, but practical systems must estimate this information from scalar observations under one RF chain per antenna. This affects point-to-point polarforming, secrecy design, and large-scale ISAC systems alike. The survey literature therefore identifies polarized channel estimation, new training schemes, and compressed-sensing approaches as central unresolved problems (Zhou et al., 28 May 2025, Ding et al., 27 May 2025, Ding et al., 23 Jul 2025).

Hardware nonidealities remain equally important. Finite phase-shifter resolution, insertion loss, mismatch between vertical and horizontal elements, mutual coupling, limited cross-polarization isolation, and quantized amplitude–phase control all degrade the ideal continuous-state model. In large arrays, the computational burden of repeated semidefinite programming or Gaussian randomization can also become prohibitive, motivating direct alternating updates and other low-complexity approximations. Wideband operation introduces frequency-dependent polarization response; dynamic channels require low-latency phase-shifter tuning and fast CSI feedback; and joint beamforming–polarforming across MIMO and multiuser settings is still an open problem, including integrated beam-and-polarization forming and hybrid architectures for massive-MIMO systems (Zhou et al., 28 May 2025, Ding et al., 23 Jul 2025, Shao et al., 4 Jun 2025).

Across the broader literature, the common thread is that polarity or polarization is treated as an active design variable rather than a passive material or channel attribute. In wireless systems that variable is the Jones state of an antenna; in helium droplets it is the metastable dipole configuration of a cluster; in polar metals it is the switchable polar axis; in organic films it is the oriented dipole density; and in quantum control it is the orientational expectation of a newly formed molecule. The term therefore names a family of techniques unified less by implementation than by the deliberate formation and control of polar order (Zhou et al., 2024, Niman et al., 2019, Zabalo et al., 2020, Tanaka et al., 8 May 2025, Forlevesi et al., 15 Sep 2025).