Radial Polarization

Variable spiral plate (VSP) for vortex beam generation

Linear entrance can be transformed in all
kinds of Polarization distributions

Planar wave with circular Polarization
is transformed in a helical wave

Alignment of the liquid crystal within a Spiral-plate with topological charge of 2

The variable spiral plate (VSP) is a passive liquid crystal optical element that is capable to modify a simple laser beam into a vortex beam, radial polarized beam having orital momentum (L=1 or L=2). The VSP is a perfectly transparent optical element without scattering or diffracted ligh losses (apart from the absorption losses of the material). The conversion from homogenous linear polarized beam to, for example, radial, azimuthal (or also lemon, spiral or star distribution) can simply be obtained by placing the VSP in the optical path of your laser beam. The different output Polarization patterns can be obtained by simply changing the bias applied on the Q-plate the VSP.

Capable to generate many different circular symmetric and continuous Polarization distributions by simply changing the bias or input Polarization
One element works for all wavelengths from 400 to 1500nm
Works for all types of laser also femto-second pulsed lasers
Capable to generate Orbital momentum and helical beams
Capable to generate radial & azimuthal Polarization distribution
No loss, no scattering, no diffraction, no segments

Orbital momentum or helical wavefront generation-spiral phase plate (SPP)

One interesting application of the VSP is the transformation of a planar wavefront with circular (left or right) Polarization into a beam with an optical vortex (with an undefined phase in the center of the beam). Such a beam carries an orbital momentum (OAM) and has a helical wavefront as shown in the picture below. The retardation of the Q-plate is controlled by an AC bias and can be adjusted to any wanted value between 50-1500nm. As an additional feature, the orbital momentum can switched on and off (within 100ms) simply by changing the bias on the q plate. Notice

Radial and azimuthal Polarization

As the ARCoptix radial Polarization converter product (link), the VSP (with topology q = 0.5) is capable to transform a linear input Polarization into a radial or an azimuthal Polarization (depending of the input Polarization). The same Q-plate can be adapted to any wavelength by simply adjusting an AC voltage (0-5V) that is applied on the VSP.

Spiral Phase

The variable spiral plate can produce from a simple gaussian beam with a spiral phase. To proove this, we create a well-known Mac-Zehnder interferometer setup coupled to a CDD camera to record the interference pattern at the output of the interferometer. By tilting the two beams of the interferometer, we obtain regular interference fringes (as shown in picture) and by introducing a spiral plate (with half wave retardation), we obtain a phase dislocation (pitchfork hologram). Again, if the VSP retardation is tuned (via an electric bias) to full wave retardation, the dislocation disappear as in pictures below.

An interesting recent article published in applied sciences decribed in details the possibilities of the arcoptix S-plate. Here is the link to the article: LINK

VSP switched off-
no disclocation

VSP switched on-
disclocation shows spiral phase

Q=0,5 (OM=1) between crossed polarizers
Radial Polarization

Q=1 (OM=2) between crossed polarizers

Notice that the spiral plate is similar to our radial Polarization converter product. The principal difference between this product is that with the spiral plate, one can obtain either a spiral or a radial Polarization and with the Polarization converter one obtains always the radial Polarization and the spiral phase at the same time. The differences between the spiral plate and the ARCoptix Polarization converter are summarised in the table below.
By looking at the comparaison in the table, it seems clear that the VSP has many advantages compared to the Polarization converter. Also, the VSP does not have the PI phase step in the middle of the aperture, which makes the device simpler to adjust and beam quality will be better. It is also important to note that Polarization is a proven device that has already been used by many scientists with full satisfaction. The VSP is a new product that does not have reference for the moment. Notice that for optimal quality it is recommended to use a beam size of at least 5mm in diameter. Results obtained with a beam size below 2-3 mm may suffer from inperfection dues fundamental LC manufactring limitatios in the center of the cell.

Features	Polarization Converter	Variable spiral plate
Technology	Alignment of LC nematic with rubbing	Alignment LC nematic with polymers aligned with pol. UV light
Topological charge	not relevant	Q=+/- 0.5 standard Q=1 on demand
Minimal Beam Size	2 mm	5 mm
Orbital Momentum	OM= +/- 1	OM= +/- 1 on demand +/- 2
Wavelength range	400-1700nm	400-1700nm
Broadband wavelength illumination	Yes possible	Max wavelength width 100nm
Generation of various singularities	Fix singularity	Singularity can varied with input Polarization and phase retardance
Radial or azimuthal Polarization	Yes	Yes
Spiral phase	No	Yes (with circular pol.)
Pi phase step	Yes need to be compensate with phase compensator	No phase step
Electrical driving	Yes USB LC driver recommended	Yes USB LC driver recommended

Principle

Alignment of the liquid crystal within a
spiral-plate with topological charge of q=1

The spiral plate is a nematic liquid crystal cell composed of two polymer aligned substrates with a liquid crystal layer in between. The local alignment of the LC in the spiral plate can be structured to any desired pattern during its fabrication. Indeed, the alignment direction imprinted on the polymer layer is parallel to the Polarization of the UV light during the polymerization process. By playing on the Polarization of the incoming UV light, all kinds of alignment patterns of the liquid crystal, and hence of the optical axis, can be obtained. In the schematic, it is shown how the different alignment patterns of the Q-plates are realized. By playing on the rotation speed of the mask and the polarizer, all kinds of circular symmetric alignment patterns can be obtained. A more detailed description of a similar fabrication process can be found in the references (Publication tab).

Notice that the process is a continuous process and there is no creation of alignment step. The UV alignment process creates a smooth and continuous variation of the local alignment of the LC (or optical axis).

Also, we want to point out here that the same photo-alignment techniques used to make this Q-plates would, in principle, allow to create almost every Polarization distribution. For the moment, we have focused our effort on Polarization distribution with a circular symmetric distribution that permits to generate easily (by simply placing the Q-plate in the optical path of the beam) vector vortex beams with different topological charges. But we are open to every customer suggestion or demand for new ideas of useful birefringent patterns.

Variable Spiral Plate Specs

Features	Spiral Plate
wavelength range	400-1700 nm
Phase retardance	electrically adjustable (0-5V AC)
Available topological charges (fixed during manufacturing)	q=0,5 standard q=1 and higher on demand
Orbital momentum	+/- 1
Maximal Beam Size	10 mm
Minimal Beam Size	5 mm
Active area	12 mm diameter
Transmission	better than 85% (in the VIS)
Retarder material	Nematic Liquid-Crystal
Substrate material	Glass bk7
Local extinction ratio (input Intensity/ouput intensity) when placed between crossed polarizers for radial Polarization configuration	~100 @ 633nm
Output intensity homogeneity	< 1/100 RMS variation
Temperature range	15° - 35°
Save operating limit	300 W/cm2 CW 100 mJ/cm2 10 ns, 450-1500 nm 50 W/cm2 CW, below 450nm
Total size of the housing	6 cm x 4 cm x 1.5 cm

Applications

Doughnut focal point (or reduced size focal spot)

As the Polarization converter from ARCoptix, the Q-plate is capable to produce doughnut shaped focal point that is useful for many applications. the topological charge of the beam (that is defined by the spiral plate at fabrication) can produce doughnut focal point of different sizes (The higher the topological charge, the larger the ring is).

Orbital momentum

When a Polarization converter is used in combination with a polarizer, a device results that can be used as Polarization axis finder (PAF). Watching the PAF, a dark segment appears when the entrance Polarization is linear. The orientation of the dark segment gives the direction of the Polarization.

Inspection of birefringent materials: When placing a brefrigent material between two PAFs (two polarizers with two Polarization converters), one can analyze the birefringent properties of the sample in one glimpse (characteristic interference colors and main axis). Neither the sample nor the polarizers have to be rotated.

Helical wavefront

The spiral plate generate beams with a helical wavefron or orbital momentum. Such beams are capabale, for example, to make spinning particles. Also it could be used for telecom applications.

Strong Electric field in the Z direction (or longitudinal field)

For some application like atomic force microscopy (AFM) it is omportant to a have a strong electric field in the Z direction. Such fields can be obtain when focusing a radial polarized beam that is produced wiht the S-plate for example.

Two photon microscopy, STED, plasmon surface resonance

Focusing LG beams of different topological charges permit to generate all sorts of intensity and Polarization patterns in the focal point having interesting properties for STED, two photon microscopy or plasmon surface resonance. The possibility to vary the phase retardance of the spiral plate and to make different topological charges offers a widevariety of interesting configurations.

Driver (optional)

The variable spiral plate can be driven with a standard laboratory function generators but it can also be driven the USB ARCoptix LC Driver. The Variable spiral plate is provided with a Lemo connector compatible with the USB LC driver.
The Arcoptix LC (Liquid Crystal) driver is a USB computer controlled electrical power supply optimized for driving the Polarization converter. The phase retardance of the variable Q-plate can be adjusted by tuning the bias on its two electrodes. The retardance can so be adjusted to the used laser wavelength.
The Variable spiral plate is provided with a Lemo connector compatible with the USB LC driver.

The LC driver has two independent outputs (Lemo connectors). They are controlled via a simple windows compatible software. The output has a variable square amplitude with polarity inversion and a frequency of 1.6 KHz. This guarantees a homogenous variation of the LC layer inside the cell. An external trigger input can be provided on demand.

Publication

The variable spiral plate has been discovered a few years ago. Here are some references using the variable spiral plate produced by ARCoptix (apart the 3 first articles where cells have been made directely by the scientists). In the papers below, the VSP is denoted as Q-plate:

L. Marrucci, C. Manzo, and D. Paparo, “Optical Spin-to-Orbital Angular Momentum Conversion in Inhomogeneous Anisotropic Media,” Phys. Rev. Lett. 96, 163905 (2006). NOT Arcoptix device
S. Slussarenko, A. Murauski, T. Du, V. Chigrinov, L. Marrucci, and E. Santamato, “Tunable liquid crystal q-plates with arbitrary topological charge,” Opt. Express 19, 4085-4090 (2011).NOT Arcoptix device
F. Cardano, E. Karimi, S. Slussarenko, L. Marrucci, C. de Lisio, and E. Santamato, “Polarization pattern of vector vortex beams generated by q-plates with different topological charges,” Appl. Opt. 51, C1–C6 (2012).NOT Arcoptix device
Quiceno-Moreno, Julio & Marco, David & Sanchez-Lopez, Maria & Solarte, Efrain & Moreno, Ignacio. (2020). Analysis of Hybrid Vector Beams Generated with a Detuned Q-Plate. Applied Sciences. 10. 3427. 10.3390/app10103427.
David Marco, María del Mar Sánchez-López, Pascuala García-Martínez, and Ignacio Moreno, "Using birefringence colors to evaluate a tunable liquid-crystal q-plate," J. Opt. Soc. Am. B 36, D34-D41 (2019)
Quiceno-Moreno, Julio & Marco, David & Sanchez-Lopez, Maria & Solarte, Efrain & Moreno, Ignacio. (2020). Analysis of Hybrid Vector Beams Generated with a Detuned Q-Plate. Applied Sciences. 10. 3427. 10.3390/app10103427.
Maria del Mar Sanchez_lopez, & al. , Extending the use of commercial Q-plates for the generation of high-order and hybrid vector beams,Proceedings Volume 10744, Laser Beam Shaping XVIII; 1074407 (2018)