Full characterization of spin-orbit coupled photons via spatial-Stokes measurement

Bao-Sen Shi; Bing-Shi Yu; Carmelo Rosales-Guzman; Hai-Jun Wu; Hao-Ran Yang; Wei Gao; Zhi-Han Zhu

arxiv: 1907.04035 · v1 · pith:ONAVJVLUnew · submitted 2019-07-09 · ⚛️ physics.optics

Full characterization of spin-orbit coupled photons via spatial-Stokes measurement

Bing-Shi Yu , Hai-Jun Wu , Hao-Ran Yang , Wei Gao , Carmelo Rosales-Guzman , Bao-Sen Shi , Zhi-Han Zhu This is my paper

Pith reviewed 2026-05-25 00:24 UTC · model grok-4.3

classification ⚛️ physics.optics

keywords spin-orbit couplingstructured lightspatial-Stokes measurementphoton wavefunctionpolarizationgeometric phaseoptical characterizationquantum state measurement

0 comments

The pith

Spatial-Stokes measurement determines the full wavefunction of spin-orbit coupled photons by directly extracting spatial amplitudes and phases.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that spin-orbit coupled photon states can be fully characterized using spatial-Stokes measurements. This extracts the two complex spatial probability amplitudes for spin-dependent modes and their relative phase directly. By skipping the wavefront-flattening operations of standard tomography, the method captures the actual photon structure without distortion. Researchers care because accurate wavefunction records support better development of structured-light sources and devices that use these states.

Core claim

Determination of photonic SOC states via spatial-Stokes measurement allows two spatial complex probability amplitudes of spin-dependent spatial modes within SOC states and their relative intramode phase to be measured directly. By avoiding wavefront-flattening operations, the apparatus records photons' realistic SOC structure completely, resulting in a more accurate and precise determination of the wavefunction. This provides a simple and general approach for in-situ measuring of photonic SOC states.

What carries the argument

Spatial-Stokes measurement, which uses polarization-resolved spatial intensity patterns to extract the two complex amplitudes and their intramode phase.

If this is right

Enables in-situ measurement of photonic SOC states during experiments.
Allows characterization of the quality of SOC light sources.
Allows characterization of associated geometric-phase devices.
Supplies a simpler toolkit than full quantum-state tomography for these states.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The method could support real-time monitoring of SOC states in operating optical systems.
It might extend to characterization of other spatially structured light fields that carry polarization coupling.
Higher accuracy could improve precision in experiments that rely on the geometric phase of these photons.

Load-bearing premise

Spatial-Stokes measurement can directly extract the two spatial complex probability amplitudes and their intramode phase for spin-dependent modes while preserving the true SOC structure without additional operations.

What would settle it

Compare wavefunctions of the same SOC state extracted via spatial-Stokes versus standard tomography on an identical input; the spatial-Stokes result should show no flattening-induced deviation from the known structure.

Figures

Figures reproduced from arXiv: 1907.04035 by Bao-Sen Shi, Bing-Shi Yu, Carmelo Rosales-Guzman, Hai-Jun Wu, Hao-Ran Yang, Wei Gao, Zhi-Han Zhu.

**Figure 2.** Figure 2: (d) indicate the measured states are not pure for the predefined HOSP; while the smaller error bars in the fidelity shown in Fig [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. (a) [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

read the original abstract

Characterization and analysis of spin-orbit coupled (SOC) states, as a measurement problem, play a vital role in research on the modern optics and photonics based on structured light. Here, we demonstrate determination of photonic SOC states via spatial-Stokes measurement, in which two spatial complex probability amplitudes of spin-dependent spatial modes within SOC states and their relative (intramode) phase can be measured directly. Compared with the standard quantum-state tomography, by avoiding wavefront-flattening operations, the apparatus can completely record photons' realistic SOC structure, leading to a more accurate and precise determination of wavefunction. This simple and general approach for SOC state determination can provide a powerful toolkit for in-situ measuring photonic SOC state, characterizing the quality of SOC light source and associated geometric-phase devices.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Spatial-Stokes recovers |a(r)|, |b(r)| and arg(a)-arg(b) but leaves the common phase arg(a)+arg(b) undetermined, so the full-wavefunction claim does not hold.

read the letter

The paper's main move is to treat spatial-Stokes parameters as a direct route to the two complex amplitudes in a spin-orbit coupled beam and their intramode phase, without the usual wavefront-flattening step. That framing is new enough compared with the tomography references in the abstract, and the setup looks simpler on paper. If the goal is only to get the intensity profiles and the relative phase between the right- and left-circular components, the approach could be useful for quick checks on structured-light sources or geometric-phase elements. The abstract is clear that this is the intended use case. What the work does well is spell out an apparatus that records the four Stokes images in one go and then extracts those three real functions from them. That part is straightforward and could save time in a lab that already has the right polarization optics. The soft spot is exactly the one the stress-test flags. Standard Stokes analysis on E = a(r)|R> + b(r)|L> yields S0, S1, S2, S3 that fix |a|, |b| and the difference phase, but supply nothing about the sum phase. The full complex wavefunction is therefore still missing an arbitrary real function θ(r). The claim that the method “completely record[s] photons’ realistic SOC structure” and gives “determination of wavefunction” therefore does not follow from the measurement. No data, error bars, or side-by-side comparison with tomography appear in the abstract, so the accuracy advantage also cannot be checked. This is the sort of paper that belongs in a specialized optics journal if the authors either restrict the claim to the three measurable functions or show how the missing phase is recovered by some other means. A reader who already works on SOC beams might pick up the setup idea and try it, but anyone who needs the complete field will still reach for interferometry. I would send it to referees so the phase issue can be settled in review rather than desk-rejecting it outright.

Referee Report

1 major / 2 minor

Summary. The paper claims to introduce spatial-Stokes measurement as a method for full characterization of spin-orbit coupled (SOC) photonic states. It asserts that the technique directly extracts the two spatial complex probability amplitudes of spin-dependent modes along with their relative (intramode) phase, and that by avoiding wavefront-flattening operations required in standard quantum-state tomography, it records the realistic SOC structure more accurately and precisely, yielding a complete wavefunction determination. The approach is positioned as a simple, general toolkit for in-situ SOC state measurement and device characterization.

Significance. If the central measurement claim holds without the phase gap identified below, the method could offer a practical alternative to tomography for structured-light experiments, potentially improving accuracy in characterizing SOC sources and geometric-phase elements. The avoidance of flattening operations is a clear practical advantage if the extracted quantities suffice for the intended applications.

major comments (1)

[Abstract] Abstract: The assertion that the method determines the 'two spatial complex probability amplitudes ... and their relative (intramode) phase' and thereby achieves 'complete record[ing of] photons’ realistic SOC structure' and 'determination of wavefunction' is not supported by the standard Stokes analysis. For a field E = a(r)|R⟩ + b(r)|L⟩, the four Stokes parameters recover only |a(r)|, |b(r)|, and φ(r) = arg(a) − arg(b); the common phase θ(r) = [arg(a) + arg(b)]/2 remains inaccessible. This leaves the full complex wavefunction undetermined up to an arbitrary real-valued spatial function θ(r), directly contradicting the 'full characterization' and 'more accurate ... determination of wavefunction' claims.

minor comments (2)

The manuscript should explicitly state whether the common phase θ(r) is considered irrelevant for the targeted applications or whether an auxiliary measurement is proposed to recover it.
Clarify the precise definition of 'spatial complex probability amplitudes' versus the relative phase that is actually extracted, to avoid ambiguity with full complex amplitudes.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful review and for identifying an important point of precision in our claims. We respond to the major comment below.

read point-by-point responses

Referee: [Abstract] Abstract: The assertion that the method determines the 'two spatial complex probability amplitudes ... and their relative (intramode) phase' and thereby achieves 'complete record[ing of] photons’ realistic SOC structure' and 'determination of wavefunction' is not supported by the standard Stokes analysis. For a field E = a(r)|R⟩ + b(r)|L⟩, the four Stokes parameters recover only |a(r)|, |b(r)|, and φ(r) = arg(a) − arg(b); the common phase θ(r) = [arg(a) + arg(b)]/2 remains inaccessible. This leaves the full complex wavefunction undetermined up to an arbitrary real-valued spatial function θ(r), directly contradicting the 'full characterization' and 'more accurate ... determination of wavefunction' claims.

Authors: We agree that standard spatial-Stokes analysis recovers |a(r)|, |b(r)| and the relative phase φ(r) = arg(a) − arg(b), but leaves the common phase θ(r) undetermined. Our abstract already qualifies the phase as 'relative (intramode)', yet the phrasing 'complete record of photons’ realistic SOC structure' and 'determination of wavefunction' can be read as implying access to θ(r). We will revise the abstract to state explicitly the three quantities obtained and to qualify the characterization accordingly, while retaining the practical advantage of avoiding wavefront flattening. This revision will be incorporated. revision: yes

Circularity Check

0 steps flagged

No circularity; experimental measurement technique is self-contained

full rationale

The manuscript presents an experimental method using spatial-Stokes parameters to characterize SOC photon states. No derivations, equations, or predictions are shown that reduce by construction to fitted inputs, self-citations, or ansatzes. The comparison to quantum-state tomography and avoidance of wavefront-flattening is framed as a physical apparatus choice, not a mathematical reduction. The work contains no load-bearing self-referential steps; any limitations on phase recovery are matters of experimental completeness rather than circular logic.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only; no equations, data fits, or modeling details are given, so no free parameters, axioms, or invented entities can be identified.

pith-pipeline@v0.9.0 · 5677 in / 1034 out tokens · 32704 ms · 2026-05-25T00:24:03.456410+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

36 extracted references · 36 canonical work pages

[1]

K. Y. Bliokh, F. J. Rodriguez-Fortuno, F. Nori, et al. Spin-orbit interactions of light. Nat. Photon. 9, 796, (2015)

work page 2015
[2]

Aiello, F

A. Aiello, F. Tö ppel, C. Marquardt, E. Giacobino, and G. Leuchs. Quantum-like nonseparable structures in optical beams. New J. Phys. 17, 043024 (2015)

work page 2015
[3]

C. V. S. Borges, M. Hor -Meyll, J. A. O. Huguenin, and A. Z. Khoury. Bell-like inequality for the spin -orbit separability of a laser beam. Phys. Rev. A 82, 033833 (2010)

work page 2010
[4]

J. Chen, C. -H Wan, and Q. -W. Zhan. Vectorial optical ﬁelds: recent advances and future prospects. Sci. Bull. 63, 54 (2018)

work page 2018
[5]

Cylindrical vector beams: from mathematical concepts to applications

Zhan Q. Cylindrical vector beams: from mathematical concepts to applications. Adv. Opt. Photon. 1,1 (2009)

work page 2009
[6]

Rubinsztein-Dunlop, et al

H. Rubinsztein-Dunlop, et al. Roadmap on structured light. J. Opt. 19, 013001 (2017)

work page 2017
[7]

Rosales-Guzmá n, B

C. Rosales-Guzmá n, B. Ndagano and A. Forbes. A review of complex vector light fields and their applications. J. Opt. 20, 123001 (2018)

work page 2018
[8]

R. Chen, K. Agarwal, C. J. R. Sheppard, and X. Chen, Imaging using cylindrical vector beams in a high -numerical-aperture microscopy system. Optics lett. 38, 3111-4 (2013)

work page 2013
[9]

L. Du, A. Yang, A. V. Zayats, X. Yuan. Deep -subwavelength features of photonic skyrmions in a confined electromagnetic field with orbital angular momentum. Nat. Phys. 2019: 1

work page 2019
[10]

D’Ambrosio, et al

V. D’Ambrosio, et al. Complete experimental toolbox for alignment-free quantum communication. Nat. Commun. 3:961 (2012)

work page 2012
[11]

Vallone, et al

G. Vallone, et al. Free -Space Quantum Key Distribution by Rotation-Invariant Twisted Photons, Phys. Rev. Lett. 113, 060503 (2014)

work page 2014
[12]

D’Ambrosio, et al

V. D’Ambrosio, et al. Entangled vector vortex beams. Phys. Rev. A 94, 030304(R) (2016)

work page 2016
[13]

Berg-Johansen, F

S. Berg-Johansen, F. Tö ppel, B. Stiller, P. Banzer, M. Ornigotti, E. Giacobino, G. Leuchs, A. Aiello, and C. Marquardt, Classically entangled optical beams for high -speed kinematic sensing. Optica 2, 864-868 (2015)

work page 2015
[14]

Naidoo, et al., Con trolled generation of higher -order Poincare sphere beams from a laser

D. Naidoo, et al., Con trolled generation of higher -order Poincare sphere beams from a laser. Nat. Photon. 10, 327-332 (2016)

work page 2016
[15]

Slussarenko, A

S. Slussarenko, A. Alberucci, C. P. Jisha, B. Piccirillo, E. Santamato, G. Assanto, L. Marrucci. Guiding light via geometric phases. Nat. Photon. 10, 571-575 (2016)

work page 2016
[16]

Cardano, L

F. Cardano, L. Marrucci. Spin -orbit photonics. Nat. Photon. 9, 776 (2015)

work page 2015
[17]

Chen, et al

P. Chen, et al. Digitalizing Self‐Assembled Chiral Superstructures for Optical Vortex Processing. Adv. Mater. 30(10), 1705865 (2018)

work page 2018
[18]

Vieira, R

J. Vieira, R. M. G. M. Trines, E. P. Alves, R. A. Fonseca, J. T. Mendonç a, R. Bingham, P. Norreys, and L. O. Silva . Amplification and generation of ultra -intense twisted laser pulses via stimulated Raman scattering. Nat. Commun. 7, 10371 (2016)

work page 2016
[19]

H.-J. Wu, Z. -Y. Zhou, W. Gao, B. -S. Shi, and Z.-H. Zhu. Dynamic tomography of the spin -orbit coupling in nonlinear optics. Phys. Rev. A 99, 023830 (2019)

work page 2019
[20]

Milione, H

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, Higher - Order Poincar´ e Sphere, Stokes Parameters, and the Angular Momentum of Light. Phys. Rev. Lett. 107, 053601 (2011). 6

work page 2011
[21]

Milione, S

G. Milione, S. Evans, D. A. Nolan, and R. R. Alfano, Higher Order Pancharatnam-Berry Phase and the Angular Momentum of Light. Phys. Rev. Lett. 108, 190401 (2012)

work page 2012
[22]

L. J. Pereira, A. Z. Khoury, K. Dechoum. Quantum and classical separability of spin–orbit laser modes. Phys. Rev. A 90, 053842 (2014)

work page 2014
[23]

McLaren, T

M. McLaren, T. Konrad, and A. Forbes, Measuring the non - separability of vector vortex beams Phys. Rev. A 92, 023833 (2015)

work page 2015
[24]

Ndagano, H

B. Ndagano, H. Sroor, M. McLaren, C. R. Guzmá n, and A. Forbes. A beam quality measure for vector beams. Opt. Lett. 41, 3407-3410 (2016)

work page 2016
[25]

Pinheiro da Silva, D

B. Pinheiro da Silva, D. S. Tasca, E. F. Galvã o , and A. Z. Khoury. Astigmatic tomography of orbital -angular-momentum superpositions. Phys. Rev. A 99, 043820 (2019)

work page 2019
[26]

Qassim, F

H. Qassim, F. M. Miatto, J. P. Torres, M. J. Padgett, E. Karimi, and R. W. Boyd. Limitations to the determination of a Laguerre– Gauss spectrum via projective, phase-flattening measurement. J. Opt. Soc. Am. B 31, A20 (2014)

work page 2014
[27]

S., Sutherland, B., Patel, A., Stewart, C

Lundeen, J. S., Sutherland, B., Patel, A., Stewart, C. & Bamber, C. Nature 474, 188–191 (2011)

work page 2011
[28]

Salvail, M

Jeff Z. Salvail, M. Agnew, A. S. Johnson, E. Bolduc, J. Leach, & R. W. Boy d. Full characterization of polarization states of light via direct measurement. Nat. Photon. 7, 316–321 (2013)

work page 2013
[29]

Malik, M. et al. Direct measurement of a 27 -dimensional orbital-angular-momentum state vector. Nat. Commun. 5: 3115 (2014)

work page 2014
[30]

J. S. Lundeen and C . Bamber. Procedure for Direct Measurement of General Quantum States Using Weak Measurement. Phys. Rev. Lett. 108, 070402 (2012)

work page 2012
[31]

G. S. Thekkadath, L. Giner, Y. Chalich, M. J. Horton, J. Banker, and J. S. Lundeen. Direct Measurement of the Density Matrix of a Quantum System. Phys. Rev. Lett. 117, 120401 (2016)

work page 2016
[32]

Kim, Y. et al. Direct quantum process tomography via measuring sequential weak values of incompatible observables. Nat. Commun. 9, 192 (2018)

work page 2018
[33]

Fridman, M

M. Fridman, M. Nixon, E. Grinvald , N. Davidson, and A. Friesem, Real-time measurement of space-variant polarizations, Opt. Express 18, 10805-10812 (2010)

work page 2010
[34]

Basis independent tomography of complex vectorial light ﬁelds by Stokes projections

Adam Selyem et al. Basis independent tomography of complex vectorial light ﬁelds by Stokes projections. arXiv: 1902.07988v1

work page arXiv 1902
[35]

Zhou, Z.-H

Z.-Y. Zhou, Z.-H. Zhu, S.-L. Liu, Y.-H Li, S. Shi, D. -S. Ding, L.-X. Chen, W. Gao, G.-C. Guo, and B.-S. Shi, Quantum twisted double-slits experiments: confirming wavefunctions’ physical reality. Sci. Bull. 62,1185 (2017)

work page 2017
[36]

Karimi, G

E. Karimi, G. Zito, B. Piccirillo, L. Marrucci, and E. Santamato. Hypergeometric-Gaussian modes. Opt. Lett. 32, 3053 (2007)

work page 2007

[1] [1]

K. Y. Bliokh, F. J. Rodriguez-Fortuno, F. Nori, et al. Spin-orbit interactions of light. Nat. Photon. 9, 796, (2015)

work page 2015

[2] [2]

Aiello, F

A. Aiello, F. Tö ppel, C. Marquardt, E. Giacobino, and G. Leuchs. Quantum-like nonseparable structures in optical beams. New J. Phys. 17, 043024 (2015)

work page 2015

[3] [3]

C. V. S. Borges, M. Hor -Meyll, J. A. O. Huguenin, and A. Z. Khoury. Bell-like inequality for the spin -orbit separability of a laser beam. Phys. Rev. A 82, 033833 (2010)

work page 2010

[4] [4]

J. Chen, C. -H Wan, and Q. -W. Zhan. Vectorial optical ﬁelds: recent advances and future prospects. Sci. Bull. 63, 54 (2018)

work page 2018

[5] [5]

Cylindrical vector beams: from mathematical concepts to applications

Zhan Q. Cylindrical vector beams: from mathematical concepts to applications. Adv. Opt. Photon. 1,1 (2009)

work page 2009

[6] [6]

Rubinsztein-Dunlop, et al

H. Rubinsztein-Dunlop, et al. Roadmap on structured light. J. Opt. 19, 013001 (2017)

work page 2017

[7] [7]

Rosales-Guzmá n, B

C. Rosales-Guzmá n, B. Ndagano and A. Forbes. A review of complex vector light fields and their applications. J. Opt. 20, 123001 (2018)

work page 2018

[8] [8]

R. Chen, K. Agarwal, C. J. R. Sheppard, and X. Chen, Imaging using cylindrical vector beams in a high -numerical-aperture microscopy system. Optics lett. 38, 3111-4 (2013)

work page 2013

[9] [9]

L. Du, A. Yang, A. V. Zayats, X. Yuan. Deep -subwavelength features of photonic skyrmions in a confined electromagnetic field with orbital angular momentum. Nat. Phys. 2019: 1

work page 2019

[10] [10]

D’Ambrosio, et al

V. D’Ambrosio, et al. Complete experimental toolbox for alignment-free quantum communication. Nat. Commun. 3:961 (2012)

work page 2012

[11] [11]

Vallone, et al

G. Vallone, et al. Free -Space Quantum Key Distribution by Rotation-Invariant Twisted Photons, Phys. Rev. Lett. 113, 060503 (2014)

work page 2014

[12] [12]

D’Ambrosio, et al

V. D’Ambrosio, et al. Entangled vector vortex beams. Phys. Rev. A 94, 030304(R) (2016)

work page 2016

[13] [13]

Berg-Johansen, F

S. Berg-Johansen, F. Tö ppel, B. Stiller, P. Banzer, M. Ornigotti, E. Giacobino, G. Leuchs, A. Aiello, and C. Marquardt, Classically entangled optical beams for high -speed kinematic sensing. Optica 2, 864-868 (2015)

work page 2015

[14] [14]

Naidoo, et al., Con trolled generation of higher -order Poincare sphere beams from a laser

D. Naidoo, et al., Con trolled generation of higher -order Poincare sphere beams from a laser. Nat. Photon. 10, 327-332 (2016)

work page 2016

[15] [15]

Slussarenko, A

S. Slussarenko, A. Alberucci, C. P. Jisha, B. Piccirillo, E. Santamato, G. Assanto, L. Marrucci. Guiding light via geometric phases. Nat. Photon. 10, 571-575 (2016)

work page 2016

[16] [16]

Cardano, L

F. Cardano, L. Marrucci. Spin -orbit photonics. Nat. Photon. 9, 776 (2015)

work page 2015

[17] [17]

Chen, et al

P. Chen, et al. Digitalizing Self‐Assembled Chiral Superstructures for Optical Vortex Processing. Adv. Mater. 30(10), 1705865 (2018)

work page 2018

[18] [18]

Vieira, R

J. Vieira, R. M. G. M. Trines, E. P. Alves, R. A. Fonseca, J. T. Mendonç a, R. Bingham, P. Norreys, and L. O. Silva . Amplification and generation of ultra -intense twisted laser pulses via stimulated Raman scattering. Nat. Commun. 7, 10371 (2016)

work page 2016

[19] [19]

H.-J. Wu, Z. -Y. Zhou, W. Gao, B. -S. Shi, and Z.-H. Zhu. Dynamic tomography of the spin -orbit coupling in nonlinear optics. Phys. Rev. A 99, 023830 (2019)

work page 2019

[20] [20]

Milione, H

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, Higher - Order Poincar´ e Sphere, Stokes Parameters, and the Angular Momentum of Light. Phys. Rev. Lett. 107, 053601 (2011). 6

work page 2011

[21] [21]

Milione, S

G. Milione, S. Evans, D. A. Nolan, and R. R. Alfano, Higher Order Pancharatnam-Berry Phase and the Angular Momentum of Light. Phys. Rev. Lett. 108, 190401 (2012)

work page 2012

[22] [22]

L. J. Pereira, A. Z. Khoury, K. Dechoum. Quantum and classical separability of spin–orbit laser modes. Phys. Rev. A 90, 053842 (2014)

work page 2014

[23] [23]

McLaren, T

M. McLaren, T. Konrad, and A. Forbes, Measuring the non - separability of vector vortex beams Phys. Rev. A 92, 023833 (2015)

work page 2015

[24] [24]

Ndagano, H

B. Ndagano, H. Sroor, M. McLaren, C. R. Guzmá n, and A. Forbes. A beam quality measure for vector beams. Opt. Lett. 41, 3407-3410 (2016)

work page 2016

[25] [25]

Pinheiro da Silva, D

B. Pinheiro da Silva, D. S. Tasca, E. F. Galvã o , and A. Z. Khoury. Astigmatic tomography of orbital -angular-momentum superpositions. Phys. Rev. A 99, 043820 (2019)

work page 2019

[26] [26]

Qassim, F

H. Qassim, F. M. Miatto, J. P. Torres, M. J. Padgett, E. Karimi, and R. W. Boyd. Limitations to the determination of a Laguerre– Gauss spectrum via projective, phase-flattening measurement. J. Opt. Soc. Am. B 31, A20 (2014)

work page 2014

[27] [27]

S., Sutherland, B., Patel, A., Stewart, C

Lundeen, J. S., Sutherland, B., Patel, A., Stewart, C. & Bamber, C. Nature 474, 188–191 (2011)

work page 2011

[28] [28]

Salvail, M

Jeff Z. Salvail, M. Agnew, A. S. Johnson, E. Bolduc, J. Leach, & R. W. Boy d. Full characterization of polarization states of light via direct measurement. Nat. Photon. 7, 316–321 (2013)

work page 2013

[29] [29]

Malik, M. et al. Direct measurement of a 27 -dimensional orbital-angular-momentum state vector. Nat. Commun. 5: 3115 (2014)

work page 2014

[30] [30]

J. S. Lundeen and C . Bamber. Procedure for Direct Measurement of General Quantum States Using Weak Measurement. Phys. Rev. Lett. 108, 070402 (2012)

work page 2012

[31] [31]

G. S. Thekkadath, L. Giner, Y. Chalich, M. J. Horton, J. Banker, and J. S. Lundeen. Direct Measurement of the Density Matrix of a Quantum System. Phys. Rev. Lett. 117, 120401 (2016)

work page 2016

[32] [32]

Kim, Y. et al. Direct quantum process tomography via measuring sequential weak values of incompatible observables. Nat. Commun. 9, 192 (2018)

work page 2018

[33] [33]

Fridman, M

M. Fridman, M. Nixon, E. Grinvald , N. Davidson, and A. Friesem, Real-time measurement of space-variant polarizations, Opt. Express 18, 10805-10812 (2010)

work page 2010

[34] [34]

Basis independent tomography of complex vectorial light ﬁelds by Stokes projections

Adam Selyem et al. Basis independent tomography of complex vectorial light ﬁelds by Stokes projections. arXiv: 1902.07988v1

work page arXiv 1902

[35] [35]

Zhou, Z.-H

Z.-Y. Zhou, Z.-H. Zhu, S.-L. Liu, Y.-H Li, S. Shi, D. -S. Ding, L.-X. Chen, W. Gao, G.-C. Guo, and B.-S. Shi, Quantum twisted double-slits experiments: confirming wavefunctions’ physical reality. Sci. Bull. 62,1185 (2017)

work page 2017

[36] [36]

Karimi, G

E. Karimi, G. Zito, B. Piccirillo, L. Marrucci, and E. Santamato. Hypergeometric-Gaussian modes. Opt. Lett. 32, 3053 (2007)

work page 2007