Vector Beam Polarization State Spectrum Analyzer

These results show a generalization to vector beams of the technique previously used with scalar vortex beams, which is now widely used as a mode sorter in vortex based communication systems.

“These results thus show a generalization to vector beams of the technique previously used with scalar vortex beams11, which is now widely used as a mode sorter in vortex based communication systems4, 9.”

• cites [11] Moreno, I., Davis, J. A., Pascoguin, B. M. L., Mitry, M. J. & Cottrell, D. M. Vortex sensing diffraction gratings. Opt. Lett. 34, 2927–2929 (2009). sourceNot checked — no full text of the source
• cites [4] Lei, T. et al. Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings. Light: Sci. & Appl. 4, e257 (2015). sourcePartly supported

  The Results and Discussion (p. 5) describe a Dammann optical vortex grating that separates OAM channels for detection, supporting its use as a mode sorter in vortex-based communications. The paper demonstrates and proposes this use, but does not establish that the technique is already widely used. (LLM, conf=0.82)

  Experimental — accuracy not yet measured
• cites [9] Huang, H. et al. Mode division multiplexing using an orbital angular momentum mode sorter and MIMO-DSP over a graded-index few-mode optical fibre. Sci. Rep. 5, 14931 (2015). sourceSupported

The grating designs provide diffraction efficiencies much higher than others have obtained.

“We note that our grating designs provide diffraction efficiencies using this procedure are much higher than others have obtained28.”

• cites [28] Fu, S., Zhang, S., Wang, T. & Gao, C. Rectilinear lattices of polarization vortices with various spatial polarization distributions. Opt. Express 24, 18486–18491 (2016). sourceCould not verify

  The Results and discussions section says the paper’s holograms cannot reach 100% diffraction efficiency in theory, but gives no efficiency value or comparison establishing that the citing authors’ designs are much higher. Searches for comparative efficiencies and the claimed wording found no supporting passage in our copy; no page number is available. (LLM, conf=0.74)

  Experimental — accuracy not yet measured

The combined diffractive element consists of two orthogonal grating structures.

“In our approach, we create a combined diffractive element that consists of two orthogonal grating structures.”

The polarization diffraction grating in the vertical diffracted orders gives each order a different polarization state on the zero-order Poincaré sphere.

“In addition, we combine this with a previously reported polarization diffraction grating17 in the vertical diffracted orders where each order has a different polarization state on the zero-order Poincaré sphere.”

• cites [17] Davis, J. A. et al. Diffraction gratings generating orders with selective states of polarization. Opt. Express 24, 907–917 (2016). sourceNot checked yet

  Checked before — its earlier verdict is held back until a new check runs.

Each of the six q-plate channels is split in the vertical direction into six polarization channels at the cardinal points of the corresponding higher-order Poincaré sphere.

“and each is split in the vertical direction into the six polarization channels at the cardinal points of the corresponding higher-order Poincaré sphere.”

• AssumptionRests on an assumption: The polarization state of a vector beam can be determined by projections onto the six cardinal points of the appropriate Poincaré sphere.

The phase grating design generates six equally intense diffraction orders k = ±1, ±2, ±3 in the horizontal direction.

“We followed this procedure to design a grating, diffracting in the horizontal direction, that generates six equally intense diffraction orders k = ± 1, ±2, ±3.”

• Also stated in: § Encoding harmonic q-plate gratings · plain

  “The grating design provides equal energy onto the six target diffraction orders.”

The vector beam diffraction grating simultaneously creates 6 different vector beams with different charges in the horizontal diffracted orders.

“Using our approach for generating q-plates27, we make a vector beam diffraction grating that simultaneously creates 6 different vector beams with different charges in the horizontal diffracted orders.”

• cites [27] Moreno, I., Sánchez-López, M. M., Badham, K., Davis, J. A. & Cottrell, D. M. Generation of integer and fractional vector beams with q-plates encoded onto a spatial light modulator. Opt. Lett. 41, 1305–1308 (2016). sourceNot checked — no full text of the source

The system has the ability to generate six different polarization states in parallel at the six different vertically diffracted target orders.

“These results show the ability to generate six different polarization states in parallel at the six different vertically diffracted target orders.”

With input polarization selected linear and vertical, the first k = 1 diffraction order reproduces the first order radial polarized beam.

“In this case, since the input polarization is selected linear and vertical, the first k = 1 diffraction order reproduces the first order radial polarized beam.”

The pattern in Fig. 4 shows single-shot parallel generation of all six cardinal vector beams of the higher order Poincaré spheres of topological charges l = ±1, l = ±2, and l = ±3.

“Therefore, this pattern in Fig. 4 shows the single-shot parallel generation of all six cardinal vector beams of the higher order Poincaré spheres of topological charges ℓ = ± 1, ℓ = ± 2, and ℓ = ± 3.”

Each diffraction order k = ±1, ±2, ±3 encodes a different q-plate M kq with a charge given by the relation 2q = kl.

“Note that each diffraction order k = ± 1, ±2, ±3 encodes a different q-plate M kq with a charge given by the relation 2q = kℓ.”

The two-dimensional grating generates an array of 6 × 6 diffraction orders, each one with a different vector beam.

“The two dimensional grating generates an array of 6 × 6 diffraction orders, each one with a different vector beam.”

The doughnut beam focalizations have dark centers increasing with the absolute value of k.

“shows doughnut beam focalizations with dark centers increasing with the absolute value of k.”

The experimental results show effective generation of the six target diffraction orders k = ±1, ±2, ±3.

“The column named “No Anal” refers to the case when no analyzer is placed before the detector, and shows the effective generation of the six target diffraction orders k = ± 1, ±2, ±3.”

The experimental results confirm the polarization grating design.

“The experimental results in Fig. 3 confirm this design.”

The red arrow indicates the position of the diffraction order corresponding to the orthogonal polarization state, which shows a null intensity.

“This order is indicated with a yellow arrow, while the red arrow indicates the position of the diffraction order corresponding to the orthogonal polarization state, which shows a null intensity.”

The experimental results demonstrate successful generation of an array of 6 × 6 vector beams.

“In spite of this limited resolution, the experimental results in Fig. 4 demonstrate the successful generation of an array of 6 × 6 vector beams.”

The two-dimensional polarization diffraction grating generates six different q-plate channels with topological charges from −3 to +3 in the horizontal direction.

“As a result, a two-dimensional polarization diffraction grating is formed that generates six different q-plate channels with topological charges from −3 to +3 in the horizontal direction”

• Also stated in: § Encoding harmonic q-plate gratings · plain

  “Note that each diffraction order k = ± 1, ±2, ±3 encodes a different q-plate M kq with a charge given by the relation 2q = kℓ.”

The difference in the sign of the charge can be noticed in the opposite sense that the lobes rotate with the equivalent input polarization.

“The difference in the sign of the charge can be noticed in the opposite sense that the lobes rotate with the equivalent input polarization (see for instance in the second row, the first 3 patterns rotate counterclockwise relative to the first row while the next 3 patterns rotate in the clockwise direction.”

These results demonstrate the experimental realization of a vector beam polarization diffraction grating capable of generating, in a single shot, an array of vector beams with different topological charges and different states of polarization.

“These results demonstrate the experimental realization of a vector beam polarization diffraction grating capable to generate, in a single shot, an array of vector beams with different topological charges and different states of polarization.”

We have demonstrated complete control over the polarization states for each order.

“First, we have demonstrated complete control over the polarization states for each order.”

The 36 vector beams are generated with encoded q-plate devices with values q = ±1/2, q = ±1, and q = ±3/2 along horizontal orders, each illuminated with the six input cardinal polarizations along vertical orders.

“As a result, we generate the 36 vector beams, generated with encoded q-plate devices with values q = ± 1/2, q = ± 1, and q = ± 3/2 (along orders diffracted horizontally), each one as illuminated with the six input cardinal polarizations (along orders diffracted vertically).”

36 different channels are generated in parallel.

“Consequently, 36 different channels are generated in parallel.”

Combining the multiple q-plate grating diffracting horizontally with the polarization grating diffracting vertically generates an array of 6 × 6 diffraction orders.

“In this section we combine the two gratings presented in the previous subsections: we combine the multiple q-plate grating diffracting in the horizontal direction, with the polarization grating diffracting in the vertical direction. As a consequence, we can generate an array of 6 × 6 diffraction orders.”

The total diffraction efficiency of the phase grating design exceeds 90%.

“The total diffraction efficiency of the phase grating design exceeds 90%.”

• Also stated in: § Polarization grating design · hedged

  “Although the total diffraction efficiencies of the phase gratings reach about 90%”

The same system, acting in a reverse sense, can be used as a vector beam analyzer to detect the charge and polarization of an incoming arbitrary vector beam.

“Let us remark that the same system, acting in a reverse sense, can be used also as a vector beam analyzer, useful to detect the charge and polarization of an incoming arbitrary vector beam.”

• AssumptionRests on an assumption: The polarization state of a vector beam can be determined by projections onto the six cardinal points of the appropriate Poincaré sphere.

The vector beam spectrum analyzer allows performing single shot multiple higher-order polarimetric measurements.

“Thus the vector beam spectrum analyzer allows performing single shot multiple higher-order polarimetric measurements.”

A given q-plate generates different output vector beams of the same charge for different input polarizations.

“Note that a given q-plate generates different output vector beams of the same charge for different input polarizations25.”

• cites [25] Davis, J. A. et al. Analysis of a segmented q-plate tunable retarder for the generation of first-order vector beams. Appl. Opt. 54, 9583–9590 (2015). sourceNot checked — no full text of the source

This kind of approach generalizes to vector beams previous techniques for scalar vortex beam detection, now widely used in orbital angular momentum based communication systems.

“This kind of approach generalizes to vector beams previous techniques for scalar vortex beam detection, now widely used in orbital angular momentum based communication systems.”

The detector array does not have sufficient resolution to accurately measure the strengths of the delta functions.

“Our detector array does not have sufficient resolution to accurately measure the strengths of the delta functions.”

If the incoming vector beam is generated with another q-plate, the phenomena can be regarded as a subtraction of the generating and detecting q-plate.

“If the incoming vector beam is generated with another q-plate, the phenomena can be regarded as a subtraction of the generating and detecting q-plate34.”

• cites [34] Delaney, S., Sánchez-López, M. M., Moreno, I. & Davis, J. A. Arithmetic with q-plates. Appl. Opt. 56, 596–600 (2017). sourceNot checked — no full text of the source

The vector beams are produced by the encoded q-plate devices that the embedded spiral phases effectively generate in each diffraction order.

“These vector beams are produced by the encoded q-plate devices that the embedded spiral phases effectively generate in each diffraction order.”

The system can be used as a vector beam polarization state spectrum analyzer, where both the topological charge and the state of polarization of an input vector beam can be simultaneously determined in a single experiment.

“Finally, we show that this system can be used as a vector beam polarization state spectrum analyzer, where both the topological charge and the state of polarization of an input vector beam can be simultaneously determined in a single experiment.”

• Also stated in: § Introduction · plain

  “Let us remark that the same system, acting in a reverse sense, can be used also as a vector beam analyzer, useful to detect the charge and polarization of an incoming arbitrary vector beam.”

• AssumptionRests on an assumption: The polarization state of a vector beam can be determined by projections onto the six cardinal points of the appropriate Poincaré sphere.

Inserting the q-plate in between two half-wave plates results in an equivalent q-plate with negative value.

“This is accomplished by inserting the q-plate in between two half-wave plates, what results in an equivalent q-plate with negative value34.”

• cites [34] Delaney, S., Sánchez-López, M. M., Moreno, I. & Davis, J. A. Arithmetic with q-plates. Appl. Opt. 56, 596–600 (2017). sourceNot checked — no full text of the source

The same diffraction grating can be used to detect an input vector beam in a similar manner as a vortex diffraction grating can detect a scalar vortex beam.

“The same diffraction grating demonstrated above can be used to detect an input vector beam in a similar manner as a vortex diffraction grating can detect a scalar vortex beam11.”

• cites [11] Moreno, I., Davis, J. A., Pascoguin, B. M. L., Mitry, M. J. & Cottrell, D. M. Vortex sensing diffraction gratings. Opt. Lett. 34, 2927–2929 (2009). sourceNot checked — no full text of the source

A vector beam polarization state spectrum analyzer based on the combination of a polarization diffraction grating (PDG) and an encoded harmonic q-plate grating (QPG) is demonstrated as a proof of concept.

“We present a proof of concept for a vector beam polarization state spectrum analyzer based on the combination of a polarization diffraction grating (PDG) and an encoded harmonic q-plate grating (QPG).”

The experimental system can encode q-plates with arbitrary integer and fractional q values.

“This system was demonstrated in ref. 27 to generate q-plates, with arbitrary integer and fractional q values.”

• cites ref. 27Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

The relative intensities of the six different delta functions appearing along the vertical direction corresponding to the detected topological charge are a direct measurement of the generalized Stokes parameters of the input vector beam.

“Note that, in fact, the relative intensities of the six different delta functions appearing along the vertical direction corresponding to the detected topological charge are a direct measurement of the generalized Stokes parameters of the input vector beam.”

This approach generalizes to vector beams the mode sensing technique that has been used for years in multichannel correlators and in modal wavefront sensors, and recently also for the orbital angular momentum density of light.

“This approach therefore generalizes to vector beams the mode sensing technique that has been used for years in multichannel correlators35 and in modal wavefront sensors36, and recently also for the orbital angular momentum density of light37.”

• cites [35] Davis, J. A., Day, T., Lilly, R. A. & Liu, H.-K. Multichannel optical correlator/convolver utilizing the magneto-optic spatial light modulator. Appl. Opt. 26, 2479–2483 (1987). sourceNot checked — no full text of the source
• cites [36] Neil, M. M. A., Booth, M. J. & Wilson, T. Closed-loop aberration correction by use of a modal Zernike wave-front sensor. Opt. Lett. 35, 1083–1085 (2000). sourceNot checked — no full text of the source
• cites [37] Schulze, C., Dudley, A., Flamm, D., Duparré, M. & Forbes, A. Measurement of the orbital angular momentum density of light by modal decomposition. New J. Phys. 15, 073025 (2013). sourceNot checked yet

  Checked before — its earlier verdict is held back until a new check runs.

Since the final HWP is not incorporated in the system, the polarization of the uniformly polarized output beam obtained when the charges match is defined simply by the input state E0.

“Also note that, since we are not incorporating the final HWP in the system in Fig. 1, the final HWP term in Eq. (13) can be omitted and the polarization of the uniformly polarized output beam obtained when the charges match is defined simply by the input state E 0.”