Orbital Angular Momentum Filters

• Orbital-angular-momentum filters are devices that map OAM-labeled inputs to measurable outputs using phase masks, angular sorters, and reciprocal designs.
• They encompass multiple modalities such as direct spatial sorters, matched phase filters, and symmetry-enforced comb filters, each with specific performance trade-offs.
• Applications span free-space optics, integrated photonics, electron and neutron microscopy, and quantum measurements, optimizing resolution, throughput, and crosstalk.

Searching arXiv for recent and foundational papers on orbital-angular-momentum filters. arXiv search query: "orbital angular momentum filter angular lens spiral phase plate q-filter sorter multiplexer" Orbital-angular-momentum (OAM) filters are devices, phase masks, scattering media, or measurement architectures that selectively transmit, reject, spatially separate, or otherwise analyze wave components according to orbital angular momentum. In the optical paraxial setting, this usually means discrimination by the azimuthal index $\ell$ in fields of the form $E(r,\phi)\propto e^{i\ell\phi}$; in electron, neutron, and transport settings it can also mean selection by OAM sign, OAM orientation, or correlated spin–orbital channels. Across platforms, the common objective is to convert OAM information into a directly measurable observable such as angular position, on-axis intensity, output port, absorption asymmetry, radial profile, or channel-resolved transmission (Sahu et al., 2017, Hakimi et al., 25 Feb 2025, Jach et al., 2021, DOnofrio et al., 15 Feb 2025).

1. Definition and classification

A useful operational definition is that an OAM filter implements a mapping from an OAM-labelled input space to a measurable output space in which different OAM components become distinguishable. In optics, this may be a spatial mapping of $\ell$ to angle or to detector position; in reciprocal integrated photonics it may be mode-selective coupling into a specific emitter; in matter-wave systems it may be projective selection by diffraction or by polarization-dependent absorption; in electronic transport it may be unequal transmission into $m=+1$ and $m=-1$ channels, quantified by an orbital polarization $P_L=(T_{+1}-T_{-1})/(T_{+1}+T_{-1})$ (Sahu et al., 2017, Zhang et al., 2020, Jach et al., 2021, DOnofrio et al., 15 Feb 2025).

The literature represented here spans several distinct filtering modalities. Some are direct sorters, such as the angular lens, which transforms different OAM modes into localized spots at separated angular positions on a transverse plane (Sahu et al., 2017). Some are matched filters, such as inverse spiral phase plates, which convert a selected OAM state into a near-Gaussian beam for preferential collection while leaving mismatched states doughnut-like (Hakimi et al., 25 Feb 2025). Others are symmetry filters: rotationally symmetric superpositions transmit only $\ell$ that are integer multiples of $N$, and chiral motifs bias one handedness (Yang et al., 2017). A further class uses spin–orbit coupling or polarization-sensitive interactions, including the electron q-filter and the polarized $^3$He neutron analyzer (Karimi et al., 2012, Jach et al., 2021). In solid-state transport, OAM filtering can be realized in centrosymmetric systems if the mirror and twofold rotational symmetries that flip the target orbital moment are broken by inversion-even orbital couplings (DOnofrio et al., 15 Feb 2025).

Class	Filtering mechanism	Representative paper
Angular sorter	$\ell \rightarrow$ angular position on a ring	(Sahu et al., 2017)
Matched phase filter	inverse-SPP + propagation + pinhole or SMF	(Hakimi et al., 25 Feb 2025)
Symmetry comb	only $E(r,\phi)\propto e^{i\ell\phi}$0 survive	(Yang et al., 2017)
Integrated reciprocal filter	mode-selective coupling into tuned emitters	(Zhang et al., 2020)
Spin–orbit / absorption analyzer	polarization-dependent OAM signatures	(Karimi et al., 2012, Jach et al., 2021)
Centrosymmetric transport filter	$E(r,\phi)\propto e^{i\ell\phi}$1 via orbital couplings	(DOnofrio et al., 15 Feb 2025)

This classification suggests that “filter” is broader than “sorter.” Some implementations produce a full spatially resolved OAM spectrum, while others realize one-channel projective detection or channel-selective transmission.

2. Phase-only optical filters and direct spatial sorting

A particularly compact optical implementation is the angular lens, a single phase-only optical element with transmission

$E(r,\phi)\propto e^{i\ell\phi}$2

Here the $E(r,\phi)\propto e^{i\ell\phi}$3 term is the angular analogue of a quadratic phase, and the $E(r,\phi)\propto e^{i\ell\phi}$4 term acts as an axicon that radially concentrates the output onto an ultranarrow ring (Sahu et al., 2017). For constant-intensity OAM inputs

$E(r,\phi)\propto e^{i\ell\phi}$5

the reported stationary-phase estimate gives the approximate mapping

$E(r,\phi)\propto e^{i\ell\phi}$6

so the lens sorts OAM by angular position around the annulus (Sahu et al., 2017).

The measured resolution of this device depends on $E(r,\phi)\propto e^{i\ell\phi}$7, $E(r,\phi)\propto e^{i\ell\phi}$8, propagation distance $E(r,\phi)\propto e^{i\ell\phi}$9, and aperture diameter $\ell$0. For constant-intensity OAM modes at $\ell$1 cm and $\ell$2 mm, with the criterion that the valley-to-peak ratio between adjacent spots is $\ell$3, the reported resolutions were: $\ell$4, $\ell$5 with resolvable $\ell$6; $\ell$7, $\ell$8 with resolvable $\ell$9; and $m=+1$0, $m=+1$1 with resolvable $m=+1$2 (Sahu et al., 2017). For Laguerre–Gaussian modes with $m=+1$3 at $m=+1$4 cm, the reported resolutions were $m=+1$5, $m=+1$6, and $m=+1$7 for $m=+1$8, $m=+1$9, and $m=-1$0, respectively (Sahu et al., 2017).

The same paper reports a 19-mode crosstalk test with $m=-1$1 and $m=-1$2, using angular bins defined by pixels at least $m=-1$3 of the maximum intensity in the theoretical pattern. The experimental average crosstalk was $m=-1$4, compared with a theoretical average crosstalk of $m=-1$5 (Sahu et al., 2017). A significant feature is the exact scaling law for constant-intensity OAM inputs,

$m=-1$6

if $m=-1$7, $m=-1$8, and $m=-1$9, with $P_L=(T_{+1}-T_{-1})/(T_{+1}+T_{-1})$0 fixed. In that sense, $P_L=(T_{+1}-T_{-1})/(T_{+1}+T_{-1})$1 plays a role akin to focal length (Sahu et al., 2017).

A different optical matched-filter architecture uses an inverse spiral phase plate. An SPP of charge $P_L=(T_{+1}-T_{-1})/(T_{+1}+T_{-1})$2 multiplies the field by $P_L=(T_{+1}-T_{-1})/(T_{+1}+T_{-1})$3, mapping $P_L=(T_{+1}-T_{-1})/(T_{+1}+T_{-1})$4. If the incident mode has $P_L=(T_{+1}-T_{-1})/(T_{+1}+T_{-1})$5, the output has $P_L=(T_{+1}-T_{-1})/(T_{+1}+T_{-1})$6 and acquires strong on-axis intensity; if $P_L=(T_{+1}-T_{-1})/(T_{+1}+T_{-1})$7, the residual $P_L=(T_{+1}-T_{-1})/(T_{+1}+T_{-1})$8 preserves a doughnut-like profile, which is then rejected by a finite aperture or by coupling to the single-mode fiber fundamental mode (Hakimi et al., 25 Feb 2025). The paper defines crosstalk and signal-to-interference ratio as

$P_L=(T_{+1}-T_{-1})/(T_{+1}+T_{-1})$9

and emphasizes that SIR improves as the normalized aperture parameter $\ell$0 decreases, although the collected signal power also vanishes if the aperture is made too small (Hakimi et al., 25 Feb 2025). The same analysis shows that larger $\ell$1 gives substantially lower crosstalk at fixed $\ell$2 (Hakimi et al., 25 Feb 2025).

A related aperture-limited perspective appears in the study of Gaussian-vortex beams passing through a Fourier-plane circular low-pass filter in a 4f system. There the OAM filter is the spatial-frequency cutoff

$\ell$3

and the primary ring radius at the image plane satisfies the Bessel-root condition

$\ell$4

Experimentally, the calibration was reported as $\ell$5, close to the linear fit $\ell$6 over $\ell$7 (Husband et al., 23 Oct 2025). This establishes a distinct sense in which limited apertures act as OAM filters: they truncate the high transverse spatial frequencies needed to sustain steep azimuthal phase gradients, thereby inflating the vortex core, reshaping radial content, and reducing target-mode purity. The measured purity in the target $\ell$8 channel was reported as $\ell$9–$N$0 for $N$1 (Husband et al., 23 Oct 2025).

3. Symmetry-based filtering and reciprocal integrated implementations

A more abstract filtering principle is provided by rotationally symmetric superpositions of chiral states. If one superposes $N$2 rotated copies of a field,

$N$3

then the finite geometric sum enforces

$N$4

so only $N$5 survive (Yang et al., 2017). In the paper’s formulation, the mask transmission itself can be expanded as

$N$6

and $N$7-fold rotational symmetry implies $N$8 unless $N$9 (Yang et al., 2017). Chirality then breaks the $^3$0 degeneracy, favoring one handedness. The resulting structure acts as a discrete angular-momentum comb filter, transmitting $^3$1 and suppressing all other OAM components (Yang et al., 2017).

The implementation studied in that work uses binary amplitude chiral sieve masks, including logarithmic, Archimedean, and Fermat spiral motifs, and applies the principle to electron vortex beams. The reported fivefold achiral mask produces an OAM spectrum containing $^3$2, whereas a fivefold chiral mask strongly selects $^3$3 (Yang et al., 2017). For a larger compact sieve in a JEOL 2200FS TEM at $^3$4 kV, the observed three-ring pattern was associated with total phase windings $^3$5, $^3$6, and $^3$7; the central vortex was confirmed by astigmatic transformation into a pattern with $^3$8 dark stripes (Yang et al., 2017). The paper does not tabulate absolute efficiencies or numerical purities, but it defines mode purity in the standard way,

$^3$9

At the integrated-photonics end of the spectrum, the large-scale reconfigurable OAM mode multiplexer functions as an OAM filter by reciprocity. The device uses 10 concentric Q-shaped silicon waveguides with sidewall second-order Bragg gratings and localized resistive metallic heaters. The emitted topological charge of the $\ell \rightarrow$0-th emitter is tuned according to

$\ell \rightarrow$1

and coupling from the opposite bus flips the sign, $\ell \rightarrow$2 (Zhang et al., 2020). Because the out-coupling grating is reciprocal, an incident free-space OAM mode couples efficiently into the $\ell \rightarrow$3-th emitter only when its azimuthal phase matches the tuned $\ell \rightarrow$4, so each emitter acts as a narrow OAM “pass” filter (Zhang et al., 2020).

The demonstrated device integrates 10 emitters with radii $\ell \rightarrow$5–$\ell \rightarrow$6m in $\ell \rightarrow$7m steps, has an active diameter of approximately $\ell \rightarrow$8 mm, and is packaged in a $\ell \rightarrow$9 mm $E(r,\phi)\propto e^{i\ell\phi}$00 $E(r,\phi)\propto e^{i\ell\phi}$01 mm ceramic carrier (Zhang et al., 2020). Measured modal purity of the emitted beams was $E(r,\phi)\propto e^{i\ell\phi}$02–$E(r,\phi)\propto e^{i\ell\phi}$03 for $E(r,\phi)\propto e^{i\ell\phi}$04, and the criterion of at least $E(r,\phi)\propto e^{i\ell\phi}$05 dB crosstalk suppression to neighboring $E(r,\phi)\propto e^{i\ell\phi}$06 was satisfied over a $E(r,\phi)\propto e^{i\ell\phi}$07 nm wavelength window per emitter (Zhang et al., 2020). The device supports 10 independently tunable OAM orders per side, or up to 20 OAM channels using both buses, and 16 wavelength channels with 30 GHz spacing over $E(r,\phi)\propto e^{i\ell\phi}$08 nm (Zhang et al., 2020). Reconfiguration with thermal overdrive yielded a $E(r,\phi)\propto e^{i\ell\phi}$09 ns fall time for $E(r,\phi)\propto e^{i\ell\phi}$10, with approximately $E(r,\phi)\propto e^{i\ell\phi}$11s recovery without overdrive; sub-$E(r,\phi)\propto e^{i\ell\phi}$12 ns was projected with stronger excitation pulses (Zhang et al., 2020). In communication tests, the reported OSNR penalty was $E(r,\phi)\propto e^{i\ell\phi}$13 dB for OOK at BER $E(r,\phi)\propto e^{i\ell\phi}$14 and $E(r,\phi)\propto e^{i\ell\phi}$15 dB at the 16-QAM FEC limit for all nine simultaneously active beams, with an aggregate throughput of $E(r,\phi)\propto e^{i\ell\phi}$16 Tb/s at 28 Gbaud 16-QAM (Zhang et al., 2020).

These examples represent two different meanings of symmetry in OAM filtering. In the chiral-sieve case, symmetry directly determines the allowed OAM harmonics. In the integrated reciprocal filter, symmetry is engineered into a tunable emitter geometry whose reciprocal coupling selects a desired azimuthal phase.

4. Matter-wave filters: electrons and neutrons

For electrons, one route to OAM filtering uses a space-variant Wien filter, or q-filter. The electron dynamics are described by Pauli’s equation in crossed transverse electric and magnetic fields, with the Wien condition

$E(r,\phi)\propto e^{i\ell\phi}$17

for the selected velocity, so the Lorentz deflection is canceled while spin manipulation proceeds (Karimi et al., 2012). The magnetic-field orientation varies azimuthally as

$E(r,\phi)\propto e^{i\ell\phi}$18

and under a tuned half-turn spin rotation $E(r,\phi)\propto e^{i\ell\phi}$19 the spinor acquires a geometric phase $E(r,\phi)\propto e^{i\ell\phi}$20, which imprints an OAM vortex with $E(r,\phi)\propto e^{i\ell\phi}$21 (Karimi et al., 2012). The transfer rule is

$E(r,\phi)\propto e^{i\ell\phi}$22

$E(r,\phi)\propto e^{i\ell\phi}$23

A fraction $E(r,\phi)\propto e^{i\ell\phi}$24 flips spin and changes OAM by $E(r,\phi)\propto e^{i\ell\phi}$25, and for a tuned device $E(r,\phi)\propto e^{i\ell\phi}$26 (Karimi et al., 2012).

This spin–OAM correlation enables a four-element spin filter for an initially unpolarized beam. The proposed sequence is: OAM preparation, tuned q-filter with $E(r,\phi)\propto e^{i\ell\phi}$27, free-space or imaging propagation to the far field, and a circular iris that transmits the on-axis $E(r,\phi)\propto e^{i\ell\phi}$28 component while rejecting the doughnut-like $E(r,\phi)\propto e^{i\ell\phi}$29 component (Karimi et al., 2012). For the quantitative example with $E(r,\phi)\propto e^{i\ell\phi}$30 and iris radius equal to the Gaussian beam waist $E(r,\phi)\propto e^{i\ell\phi}$31, the reported transmission was approximately $E(r,\phi)\propto e^{i\ell\phi}$32 and the polarization degree approximately $E(r,\phi)\propto e^{i\ell\phi}$33, excluding losses in the OAM element (Karimi et al., 2012). The same mechanism can also act as an OAM generator or sorter, since selection is by far-field radial profile rather than by direct Stern–Gerlach splitting (Karimi et al., 2012).

A distinct matter-wave analyzer is the polarized $E(r,\phi)\propto e^{i\ell\phi}$34He cell for intrinsic neutron OAM. In the standard $E(r,\phi)\propto e^{i\ell\phi}$35 thermal-neutron case, the capture cross section is

$E(r,\phi)\propto e^{i\ell\phi}$36

with $E(r,\phi)\propto e^{i\ell\phi}$37 b at 25 meV, and absorption occurs exclusively via the singlet $E(r,\phi)\propto e^{i\ell\phi}$38 channel (Jach et al., 2021). For intrinsic $E(r,\phi)\propto e^{i\ell\phi}$39 neutron OAM, three independent polarizations enter: neutron spin $E(r,\phi)\propto e^{i\ell\phi}$40, $E(r,\phi)\propto e^{i\ell\phi}$41He nuclear polarization $E(r,\phi)\propto e^{i\ell\phi}$42, and OAM polarization $E(r,\phi)\propto e^{i\ell\phi}$43 with $E(r,\phi)\propto e^{i\ell\phi}$44. The accessible compound states are odd parity, $E(r,\phi)\propto e^{i\ell\phi}$45, and the relative absorption cross sections contain the pairwise products $E(r,\phi)\propto e^{i\ell\phi}$46, $E(r,\phi)\propto e^{i\ell\phi}$47, and $E(r,\phi)\propto e^{i\ell\phi}$48 (Jach et al., 2021). For example,

$E(r,\phi)\propto e^{i\ell\phi}$49

The presence of the $E(r,\phi)\propto e^{i\ell\phi}$50 and $E(r,\phi)\propto e^{i\ell\phi}$51 terms is absent in the $E(r,\phi)\propto e^{i\ell\phi}$52 case and therefore constitutes a definitive OAM signature (Jach et al., 2021).

The paper proposes two OAM-sensitive measurement modes: transmission asymmetries under controlled flips of $E(r,\phi)\propto e^{i\ell\phi}$53, $E(r,\phi)\propto e^{i\ell\phi}$54, and $E(r,\phi)\propto e^{i\ell\phi}$55, and capture-product detection comparing the charged $E(r,\phi)\propto e^{i\ell\phi}$56H branch with neutron reemission from odd-parity channels (Jach et al., 2021). It gives a concrete example with $E(r,\phi)\propto e^{i\ell\phi}$57, $E(r,\phi)\propto e^{i\ell\phi}$58, and $E(r,\phi)\propto e^{i\ell\phi}$59, for which the ratio of $E(r,\phi)\propto e^{i\ell\phi}$60 between $E(r,\phi)\propto e^{i\ell\phi}$61 and $E(r,\phi)\propto e^{i\ell\phi}$62 can exceed $E(r,\phi)\propto e^{i\ell\phi}$63, modulo $E(r,\phi)\propto e^{i\ell\phi}$64 (Jach et al., 2021). This is not a spatial sorter but a polarization-sensitive OAM analyzer: OAM is detected by its unique nuclear absorption signatures.

5. Generalized sorting and optimal measurement in electron microscopy

The generalized electron OAM sorter studied for molecular discrimination treats OAM filtering as a quantum measurement problem. In cylindrical coordinates, the OAM operator is

$E(r,\phi)\propto e^{i\ell\phi}$65

and an OAM eigenstate has the form $E(r,\phi)\propto e^{i\ell\phi}$66 (Troiani et al., 2020). The canonical sorter uses a log–polar transform,

$E(r,\phi)\propto e^{i\ell\phi}$67

so that $E(r,\phi)\propto e^{i\ell\phi}$68 becomes a plane wave in $E(r,\phi)\propto e^{i\ell\phi}$69, and a subsequent Fourier transform maps the tilt into a position shift $E(r,\phi)\propto e^{i\ell\phi}$70 (Troiani et al., 2020). The generalized architecture adds a cylindrical lens and a third phase element that phase-flattens the residual, $E(r,\phi)\propto e^{i\ell\phi}$71-dependent radial phase within each OAM channel. In the ideal limit, this realizes a projector

$E(r,\phi)\propto e^{i\ell\phi}$72

that is, a matched filter in the $E(r,\phi)\propto e^{i\ell\phi}$73-subspace (Troiani et al., 2020).

The optimization target is the single-electron success probability

$E(r,\phi)\propto e^{i\ell\phi}$74

bounded by the Helstrom limit. For dephased mixtures decomposed into OAM–radial subspaces, the reported optimum is

$E(r,\phi)\propto e^{i\ell\phi}$75

(Troiani et al., 2020). The generalized sorter is designed to approximate this optimum by a correlated OAM–radial measurement.

For the protein pairs considered, the reported overlaps and performance figures were: Pa vs Pb with $E(r,\phi)\propto e^{i\ell\phi}$76, $E(r,\phi)\propto e^{i\ell\phi}$77, $E(r,\phi)\propto e^{i\ell\phi}$78, best real-space $E(r,\phi)\propto e^{i\ell\phi}$79, and generalized OAM sorter $E(r,\phi)\propto e^{i\ell\phi}$80; Pa vs Pc with $E(r,\phi)\propto e^{i\ell\phi}$81, $E(r,\phi)\propto e^{i\ell\phi}$82, $E(r,\phi)\propto e^{i\ell\phi}$83, $E(r,\phi)\propto e^{i\ell\phi}$84, and $E(r,\phi)\propto e^{i\ell\phi}$85; and Pb vs Pc with $E(r,\phi)\propto e^{i\ell\phi}$86, $E(r,\phi)\propto e^{i\ell\phi}$87, $E(r,\phi)\propto e^{i\ell\phi}$88, $E(r,\phi)\propto e^{i\ell\phi}$89, and $E(r,\phi)\propto e^{i\ell\phi}$90 (Troiani et al., 2020). At target success thresholds $E(r,\phi)\propto e^{i\ell\phi}$91 and $E(r,\phi)\propto e^{i\ell\phi}$92, the required electron counts for Pa vs Pc were reported as $E(r,\phi)\propto e^{i\ell\phi}$93 versus $E(r,\phi)\propto e^{i\ell\phi}$94, corresponding to OAM doses of approximately $E(r,\phi)\propto e^{i\ell\phi}$95 (Troiani et al., 2020). The paper attributes the gain to the fact that the sorter is not merely measuring $E(r,\phi)\propto e^{i\ell\phi}$96; it is performing per-channel radial matched filtering, which is near-optimal for the stated discrimination task (Troiani et al., 2020).

This example broadens the notion of an OAM filter beyond spectral analysis. The filter is an OAM-conditional measurement basis, optimized for a downstream inference problem rather than for mode demultiplexing alone.

6. Transport filters, symmetry constraints, and recurring design trade-offs

A transport-theoretic version of OAM filtering appears in centrosymmetric systems with multi-orbital manifolds. In that setting, filtering means unequal transmission into $E(r,\phi)\propto e^{i\ell\phi}$97 and $E(r,\phi)\propto e^{i\ell\phi}$98 channels, $E(r,\phi)\propto e^{i\ell\phi}$99, producing a finite orbital polarization $\ell$00; when atomic spin–orbit coupling is present, this also yields a spin polarization $\ell$01 through $\ell$02 (DOnofrio et al., 15 Feb 2025). The central symmetry result is that OAM filtering along axis $\ell$03 requires breaking the mirror and $\ell$04-rotation operations whose axes are perpendicular to $\ell$05, while inversion $\ell$06 may remain intact (DOnofrio et al., 15 Feb 2025). In the minimal model, the region-II Hamiltonian contains inversion-even orbital couplings

$\ell$07

with cyclic permutations for $\ell$08, and a general coupling vector $\ell$09 controlling which mirror and rotational symmetries are broken (DOnofrio et al., 15 Feb 2025). For a single-component case $\ell$10, incoming $\ell$11 or $\ell$12 states are mixed and produce finite $\ell$13 in transmission, whereas an incoming $\ell$14 state remains OAM-neutral (DOnofrio et al., 15 Feb 2025). With SOC included as $\ell$15, the same setup yields simultaneous $\ell$16 and $\ell$17 filtering for spin-unpolarized injection (DOnofrio et al., 15 Feb 2025).

Across the platforms represented here, several recurring trade-offs appear. In the angular lens, smaller $\ell$18 increases angular separation per unit $\ell$19 but reduces the highest $\ell$20 that yields a localized spot; larger $\ell$21 increases dynamic range at the expense of resolution (Sahu et al., 2017). In inverse-SPP detection, smaller normalized aperture parameter $\ell$22 improves SIR but reduces collected power (Hakimi et al., 25 Feb 2025). In Fourier-plane low-pass filtering of Gaussian-vortex beams, smaller aperture diameter $\ell$23 increases the core radius $\ell$24 yet increases the near-field “uniformity distance” according to the empirical law $\ell$25 (Husband et al., 23 Oct 2025). In the integrated multiplexer, per-emitter passband is limited to approximately $\ell$26 nm, while thermal tuning provides sub-microsecond reconfiguration but incurs finite vertical emission efficiency of approximately $\ell$27 (Zhang et al., 2020). In the q-filter and the centrosymmetric transport filter, strong selectivity relies on tuning spin–orbit or orbital-coupling parameters without detuning the desired conversion fraction or symmetry pattern (Karimi et al., 2012, DOnofrio et al., 15 Feb 2025).

Several misconceptions are explicitly corrected by the literature. OAM filtering is not restricted to free-space optics: it is realized in silicon photonics, electron optics, neutron absorption, and centrosymmetric transport (Zhang et al., 2020, Karimi et al., 2012, Jach et al., 2021, DOnofrio et al., 15 Feb 2025). It is not identical to simple position sorting: it can take the form of a matched filter, an optimal POVM, or a polarization-dependent absorption analyzer (Hakimi et al., 25 Feb 2025, Troiani et al., 2020, Jach et al., 2021). It also does not require inversion symmetry breaking in all settings; orbital moment filtering in centrosymmetric systems is possible if the relevant mirror and rotational symmetries are broken by inversion-even orbital couplings (DOnofrio et al., 15 Feb 2025).

Taken together, these results define OAM filters as a family of mode-selective transducers. The transduction can be geometric, reciprocal, interferometric, absorptive, symmetry-enforced, or transport-mediated, but in every case the device converts the orbital degree of freedom into a more accessible observable while balancing resolution, crosstalk, throughput, fabrication complexity, and robustness.