Abstract

We show the opportunity of fabricating axially symmetric waveplates fine tuned to a desired wavelength. High quality waveplates are obtained using liquid crystal polymer layers on photoaligning substrates extending their functional range from UV to IR wavelengths. We characterize the effect of the waveplate on laser beams showing formation of a doughnut beam with over 240 times attenuation of intensity on the axis. We pay attention that the power density is strongly reduced on the doughnut ring as well and use this opportunity for taking charge coupled devices (CCDs) out of a deep saturation regime. Strong deformation of the beam profile is observed when the vortex axis is shifted towards the periferies of the beam. We demonstrate feasibility of using this phenomenon for shaping the profile of light beams with a set of waveplates.

© OSA

1. Introduction

Continuous modulation of optical axis orientation with high spatial resolution, an opportunity uniquely provided by liquid crystals (LCs) [1,2], can be used for producing axially symmetric waveplates [35]. Such waveplates present a valuable photonics tool for beam shaping [68], imaging [9,10], laser material processing [11], spectral filtering [12] and for optical tweezer applications [13,14]. Structural continuity and simple fabrication are substantial advantages of LC-based axial waveplates that, in addition, provide external control opportunities [15,16]. We have shown here also the possibility of attaining the condition for producing doughnut beams for UV, visible and IR wavelengths.

LC polarization converters were studied earlier combining substrates with different orienting conditions such as planar and axial [2,1719]. Spectrally broadband radiation (white light) was used for demonstrating polarization converting properties of LC cells of different configurations. The feasibility of fabricating LC-cells with two axially symmetric substrates using dye-doped LCs is shown in [20].

The axial waveplates output a doughnut beam if the half-waveplate condition is met. The output wave is hard to characterize quantitatively in order to introduce adjustments and optimize the waveplate for a given wavelength. Due to the difficulty of tuning the LC cell to the desired half-waveplate condition, the LC axial waveplates studied in [3] could not be used for creating the doughnut beam without additional phase elements in the path of the beam. This difficulty applies to LC polymer (LCP) waveplates as well [4].

In the present paper, we have employed a photoalignment technique for fabricating both radially and azimuthally oriented LCP films and have directly demonstrated and characterized their capability for producing doughnut beams for UV-IR wavelengths. The performance of radial and azimuthal waveplates was qualitatively similar, and we discuss here in detail the results related to radial waveplates only. An important advantage of LCP axial waveplates is the feasibility of producing homogeneous large area films, fine tuning the retardation conditions, and stacking LCP layers for operation at long wavelengths.

2. Fabrication

A He-Cd laser of λ=325 nm wavelength and 50 mW power was used in this study. The 2.4 mm diameter beam at the output of the laser was expanded 25 times, and a homogeneous distributed radiation intensity fixed at 10 mW/cm2 in the central part of the beam was selected with a 1” aperture diaphragm. A narrow strip of the beam was further selected with the aid of a mask with a 500 µm wide linear aperture. A cylindrical lens of 50 mm focal length focused the strip onto a glass substrate treated with photoalignment layer. The width of the linearly shaped beam on the substrate was 200 µm.

Glass substrates of 25×25 mm area and 1 mm thickness were spin-coated for a period of 60 s at 3000 rpm with linear photopolymerizable polymer (LPP) ROP-108 provided by ROLIC Technologies. This material produces planar orientation condition for the LCP along the polarization of the laser beam. According to material specifications, the process described above results in a uniform LPP film thickness of ~50 nm. The residual solvent from the alignment layer was removed by heating the substrate at 100°C for 10 min.

Photoalignment was performed with the substrate rotating in the laser strip. The laser beam was polarized either along, or perpendicular to the strip resulting in radially or azimuthally aligning boundary conditions, respectively. Tests showed that reliable high quality photoalignment can be obtained at 100 rpm rotation speed and 1 hour exposure time. The waveplate fabrication process is accomplished by spin-coating the LCP on top of the LPP and polymerizing it.

3. Tuning

The thickness of the LCP layer, for the given optical anisotropy, determines the optimum condition for generation of a doughnut beam – the half-waveplate condition. It is difficult to blindly tune the axial waveplate to a given wavelength. No techniques were known so far for fine tuning an axial waveplate, and probably that was the reason that no axial waveplates have been produced before for different wavelengths corresponding to important classes of lasers.

In order to determine the conditions for obtaining an axial waveplate optimized for a given wavelength, we used the data obtained by us for cycloidal optical axis gratings (OAGs) that are essentially waveplates with transversely periodic modulation of their optical axis [21]. The peak diffraction wavelength of OAGs, or “diffractive waveplates (DWs)”, determined by the same half-waveplate condition, can easily be obtained by taking their spectra. Since the diffracted light does not reach the input of the spectrometer, it is registered as absorption. Thus, the peak diffraction wavelength, hence the retardation of DWs, can easily be obtained as a function of the spin coating conditions for any given LCP. Such spectra are much harder to obtain, if possible at all, for axial waveplates due to the smallness of the doughnut size compared to the size of the spectrometer light beam.

The dependence of the peak diffraction wavelength of DWs as a function of spin coating speed and the number of LCP layers are presented in our papers [21,22] for LCP ROF 5102 (ROLIC Technologies) and we use them in the current study. According to those data, this LCP coated at 1000 rpm for 60 s results in a waveplate at λ=458 nm wavelength. The procedure of using ROF 5102 includes drying the substrate for 5 min and polymerizing under a nitrogen atmosphere for 10 min using unpolarized UV light of 365 nm wavelength and 15 mW/cm2 power density.

4. Characterization

The output of an axial waveplate with topological charge m=2 between crossed polarizers illuminated with white light is shown in Fig. 1(a). The half-wave condition for that waveplate is met for λ=458 nm wavelength, and laser beam of a different wavelength is generally deformed when propagating through such a waveplate without forming a doughnut profile. The patterns obtained for an input linear polarized He-Ne laser beam of λ=633 nm wavelength are shown in Fig. 1(b)-1(d).

A spiral phase profile was directly observed with the axial waveplate in a Mach-Zender interferometeric setup. A quarter-waveplate was inserted in one of the arms of the interferometer to produce a circularly polarized beam incident on the axial waveplate. As expected, the interference pattern exhibits bifurcation for a plane wave reference beam propagating at a small angle (5 degrees) with respect to the probe beam, Fig. 2(a), 2(b). A double spiral interference pattern is revealed for the reference beam with a spherical wave front obtained with the help of a lens (35 mm in our setup), Fig. 2(c), 2(d). In both geometries, the interference patterns are typical for beams with the helical mode of m=± 2 [2,3]. Reversing the sign of circular polarization of the beam at the input of the axial waveplate reverses the sign of corresponding interference patterns, Fig. 2.

 

Fig. 1. (a) Axial waveplate between crossed polarizers illuminated with a white light. Photos of a He-Ne laser beam, λ=633 nm, propagated through an axial waveplate with half-waveplate condition at 458 nm. Photos are taken with no polarizers in the optical path (b), and between parallel (c) and orthogonal polarizers (d).

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Fig. 2. The patterns obtained for a circular polarized beam of a He-Ne laser propagated through a double-layer LCP axial waveplate as a result of interference with a reference plane wave, (a) and (b), and a reference beam of a spherical phase profile, (c) and (d). The patterns (a) and (c) switch to (b) and (d), respectively, when changing the sign of circular polarization.

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Figure 3 shows a series of photos of doughnut beams obtained for axial waveplates designed for UV (325 nm), visible (458 nm and 633 nm), and IR (1064 nm) wavelengths. The photos for UV and IR laser beams are obtained using fluorescent screens.

 

Fig. 3. The columns correspond to images of linear polarized laser beams of different wavelengths propagated through axial waveplates with no polarizers in the optical path (1st column) and between parallel (2nd column) and perpendicular polarizers (3rd column). (a)-(c) He-Cd laser beam propagated through an axial waveplate with half-wave condition at the wavelength λ=325 nm; (d)-(f) Ar+ laser beam, λ=458 nm, half-wave condition at 458 nm; (g)-(i) He-Ne laser beam and a double layer axial waveplate with half-wave condition at 633 nm; (j)-(l) IR laser beam, λ=1064 nm, and a three layer axial waveplate with half-wave condition at 1000 nm.

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The half-waveplate condition for 325 nm wavelength was obtained by coating the LCP at 4500 rpm for 60 s while, as mentioned above, it requires 1000 rpm for 60 s for 458 nm wavelength. The half-waveplate condition for the red wavelength was achieved by coating a second LCP layer on top of the first one under similar process conditions (1000 rpm rotation for 60 s), Fig. 3(g)-3(i). A three layer system allowed obtaining an axial waveplate outputting a doughnut beam for the 1064 nm wavelength, Fig. 3(j)-3(l). As evidenced by images obtained with a polarizer, the polarization of the doughnut beam continuously rotates around the axis of the beam making a 4π angle corresponding to an optical vortex of charge m=2.

We have further studied the intensity profile of a He-Ne beam emerging from the axial waveplate designed for 633 nm wavelength to obtain quantitative characteristics of the energy redistribution that occurs in the process of the laser beam reshaping from Gaussian to doughnut. Figure 4(a) shows the corresponding one-dimensional graphical profiles. The profiles of the laser beam captured by a CCD beam profiler at a fixed sensitivity level without and with the axial waveplate in the path of the beam are shown as inserts to Fig. 4(a).

 

Fig. 4. (a) One-dimensional intensity profiles of a He-Ne laser beam obtained without and with the axial waveplate. (b) 2-D and 3-D profiles of the doughnut beam obtained for a highly saturating gaussian beam; (c) 2-D and 3-D profiles of the beam at a power level saturating a CCD; (d) demonstrating the capability of the axial waveplate to remove the saturation of the CCD camera.

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Direct measurement of the on-axis power density with and without the axial waveplate showed that the intensity at the center of the doughnut beam is reduced by more than 245 times compared to the Gaussian beam. The power of the beam measured through a pinhole with a 1 mm aperture decreased from 50 µW down to 0.2 µW as a result of inserting the axial waveplate into the beam. Let us stress that the plate itself did not have losses other than regular Fresnel reflection. Strong attenuation of intensity at the center of the doughnut beam produced by the axial waveplate under discussion is well demonstrated by the beam profile obtained under conditions of strong saturation of the CCD, Fig. 4(b).

Intensity distribution in a doughnut beam is described by a complex function rather difficult for qualitative analysis [2325]. Figure 4(a) shows, however, that it can be well approximated by a Gaussian profile with its peak shifted with respect to the center of the beam in a polar coordinate system,

I=Ide(rrd)2wd2

Equation (1) does indeed provide a good fit of experimental data points for the shift radius rd=837 µm and beam width wd=564 µm for particular experimental conditions. The smallness of the error, χ 2~2·10-5, is apparently a result of the circumstance that the deviation from the actual beam profile is most pronounced on the axis of the beam where the intensity is small. Equation (1) fails to provide good evaluation of the minimum intensity obtained in the middle of the doughnut, but it is not a concern for many applications. The width of the doughnut ring wd is smaller compared to that of the Gaussian input beam w=714 µm. The peak intensity in the doughnut beam Id can thus be related to the peak intensity of the original Gaussian beam IG by a simple function

IGId=πrdwd[1+erf(rdwd)]+e(rdwd)2

For experimental parameter values, rd/wd=1.5, Eq. (2) predicts 5.3 times decrease of the peak power density which is close to the measured value of 6.1. Thus, placing the axial waveplate in front of a CCD results in the removal of saturation caused by a laser beam as shown in Fig. 4(c) and 4(d). The width of the doughnut increases with increasing helical mode number and higher attenuation ratios are feasible.

The axial waveplate has dramatic effect on the beam profile even if it is misaligned with respect to the axis of the incident beam or is arranged at the peripheries of the beam. Figure 5 shows transformations in the beam profile when the vortex is moved from one edge of the beam to the other. This phenomenon could be used for shaping the profile of light beams. Generally, more than one vortex waveplate would be required for efficient control with the beam profile.

This is demonstrated in Fig. 6 with a Gaussian beam of a He-Ne laser, 1.2 mm in beam diameter, for a system of two vortex waveplates. The waveplates were arranged 2 mm from each other. The beam maintains a Gaussian profile when the axes of both vortex waveplates coincided with the axis of the laser beam. No doughnut beam profile is generated in this case. The series of photos in Fig. 6 correspond to moving the centers of the waveplates symmetrically away from the axis of the beam in opposite directions. The Gaussian profile of the beam is transformed into an elliptical shape, and the effect of the waveplates is apparent even when the waveplates are moved as far away as 1 mm from the beam axis (2 mm distance between the axes of the waveplates).

 

Fig. 5. The effect of an axial waveplate on the profile of a He-Ne laser beam for different ratios of the separation distance between the axes of the waveplate and beam to the radius of the beam d/w: (a) >2; (b) 1; (c) 0.25; (d) 0; (e) -0.25; (f) -1; (g) -0.75; (h) <-2. The sign of the ratio refers to having the vortex on the opposite sides of the beam.

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Fig. 6. Beam shaping with axial waveplates. The profiles are obtained for a Gaussian He-Ne laser beam by shifting the centers of two radial waveplates positioned at 2 mm distance from each other with respect to the beam axis. The shifts are equal for both waveplates but are of opposite signs.

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5. Waveplate arrays

This technique was used for creating arrays of waveplates as shown in Fig. 7. Such arrays can become useful tools for imaging, spatial filtering, beam forming applications making possible, for example, ‘optical “multi-tweezers” ’. Each vortex in those arrays was recorded at 40 rpm rotation speed with 20 min exposure to the He-Cd laser beam of 500 µm in width and 8 mm in length for 3×3 array and 5 mm in length for 5×5 array. Photos are taken between polarizers.

 

Fig. 7. 3×3 and 5×5 vortex arrays with single, (a) and (c), and double LCP layers, (b) and (d). The arrays (a), (c) and (b), (d) are designed for 458 nm and 633 nm wavelengths, correspondingly.

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6. Conclusions

Summarizing, liquid crystal polymer films allow production of high quality axial waveplates with continuous rotation of optical axis. The fabrication technology is rather robust: the quality and functionality of the waveplates are not compromised even when using inexpensive glass substrates not meeting optical window requirements on surface quality. The characteristics of these films can be fine tuned for different wavelengths from UV to IR. The intensity at the center of the beam propagated through an axial waveplate is dramatically reduced, over 240 times in our case, allowing the creation of deep wells of intensity distribution with steep edges. The peak intensity in the ring of the doughnut beam is also reduced remarkably, by a factor of 6 in our case.

Direct writing as used in this paper is rather time consuming and restrictive on the number of vortices that can be obtained in an array, and requires high precision mechanical motion for obtaining high quality vortices. Recently we have demonstrated that optical axis gratings can be produced in a process of printing from a master grating [22]. Similar principle was tested for obtaining axial waveplates using a radial polarization converter instead of a master grating. The polarization converter was made with a LC cell between two substrates, one inducing a planar, and the second one inducing radial orientation pattern similar to those discussed in [17,19]. The state of light polarization at the output of the converter is linear with radial symmetry. It produces radially symmetric photoalignment pattern when using LPP ROP-108, and azimuthally symmetric photoalignment pattern for azobenzene based photoalignment materials of PAADB series (Beam Engineering). Detailed description of the technique for replication of axial waveplates will be presented elsewhere.

This document has been approved for public release. US Army Natick RD&E Center PAO# U09-165.

References and links

1. R. Yamaguchi, T. Nose, and S. Sato, “Liquid crystal polarizers with axially symmetrical properties,” Jpn. J. Appl. Phys. 28(Part 1), 1730–1731 (1989). [CrossRef]  

2. M. Stalder and M. Schadt, “Linearly polarized light with axial symmetry generated by liquid-crystal polarization converters,” Opt. Lett. 21(23), 1948–1950 (1996). [CrossRef]  

3. L. Marrucci, C. Manzo, and D. Paparo, “Pancharatnam-Berry phase optical elements for wave front shaping in the visible domain: Switchable helical mode generation,” Appl. Phys. Lett. 88, 221102 (1–3) (2006). [CrossRef]  

4. S. C. McEldowney, D. M. Shemo, R. A. Chipman, and P. K. Smith, “Creating vortex retarders using photoaligned liquid crystal polymers,” Opt. Lett. 33(2), 134–136 (2008). [CrossRef]  

5. H. Choi, J.H Woo, and J.W. Wu, “Holographic inscription of helical wavefronts in a liquid crystal polarization grating,” Appl. Phys. Lett. 91, 141112 (1–3) (2007).

6. R. Bhandari, “Polarization of light and topological phases,” Phys. Rep. 282(1), 1–64 (1997). [CrossRef]  

7. Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, “Space-variant Pancharatnam-Berry phase optical elements with computer-generated subwavelength gratings,” Opt. Lett. 27(13), 1141–1143 (2002). [CrossRef]  

8. A. Jesacher, A. Schwaighofer, S. Fürhapter, C. Maurer, S. Bernet, and M. Ritsch-Marte, “Schwaighofer, S. Fuerhapter, C. Maurer, S. Bernet, and M. Ritsch-Marte, “Wavefront correction of spatial light modulators using an optical vortex image,” Opt. Express 15(9), 5801–5808 (2007). [CrossRef]  

9. G. A. Swartzlander Jr., , “Peering into darkness with a vortex spatial filter,” Opt. Lett. 26(8), 497–499 (2001). [CrossRef]  

10. S. Bernet, A. Jesacher, S. Fuerhapter, C. Maurer, and M. Ritsch-Marte, “Quantitative imaging of complex samples by spiral phase contrast microscopy,” Opt. Express 14(9), 3792–3805 (2006). [CrossRef]  

11. A. V. Nesterov and V. G. Niziev, “Laser beams with axially symmetric polarization,” Phys. D: Appl. Phys. 33(15), 1817–1822 (2000). [CrossRef]  

12. J. H. Lee, H. R. Kim, and S. D. Lee, “Polarization-insensitive wavelength selection in an axially symmetric liquid-crystal Fabry-Perot filter,” Appl. Phys. Lett. 75(6), 859–861 (1999). [CrossRef]  

13. G. Sinclair, P. Jordan, J. Courtial, M. Padgett, J. Cooper, and Z. J. Laczik, “Assembly of 3-dimensional structures using programmable holographic optical tweezers,” Opt. Express 12(22), 5475–5480 (2004). [CrossRef]  

14. S. C. Chapin, V. Germain, and E. R. Dufresne, “Automated trapping, assembly, and sorting with holographic optical tweezers,” Opt. Express 14(26), 13095–13100 (2006). [CrossRef]  

15. D. Ganic, X. Gan, M. Gu, M. Hain, S. Somalingam, S. Stankovic, and T. Tschudi, “Generation of doughnut laser beams by use of a liquid-crystal cell with a conversion efficiency near 100%,” Opt. Lett. 27(15), 1351–1353 (2002). [CrossRef]  

16. Q. Wang, X. W. Sun, P. Shum, and X. J. Yin, “Dynamic switching of optical vortices with dynamic gamma-correction liquid crystal spiral phase plate,” Opt. Express 13(25), 10285–10291 (2005). [CrossRef]  

17. H. Ren, Y.-H. Lin, and S.-T. Wu, “Linear to axial or radial polarization conversion using a liquid crystal gel,” Appl. Phys. Lett. 89, 051114 (1–3) (2006). [CrossRef]  

18. S. Masuda, T. Nose, R. Yamaguchi, and S. Sato, “Polarization converting devices using a UV curable liquid crystal,” Proc. SPIE 2873, 301–304 (1996).

19. Y. Y. Tzeng, S.-W. Ke, C.-L. Ting, A. Y.-G. Fuh, and T.-H. Lin, “Axially symmetric polarization converters based on photo-aligned liquid crystal films,” Opt. Express 16(6), 3768–3775 (2008). [CrossRef]  

20. S.-W. Ko, Y.-Y. Tzeng, C.-L. Ting, A. Y.-G. Fuh, and T.-H. Lin, “Axially symmetric liquid crystal devices based on double-side photo-alignment,” Opt. Express 16(24), 19643–19648 (2008). [CrossRef]  

21. S. R. Nersisyan, N. V. Tabiryan, D. M. Steeves, and B. R. Kimball “Optical axis gratings in liquid crystals and their use for polarization insensitive optical switching,” J. NonlinearOpt. Phys. Mater. 18(01), 1–47 (2009). [CrossRef]  

22. S. R. Nersisyan, N. V. Tabiryan, D. M. Steeves, and B. R. Kimball, “Reproduction of polarization gratings,” Appl. Opt. (Submitted to).

23. V. V. Kotlyar, A. A. Kovalev, R. V. Skidanov, S. N. Khonina, O. Yu. Moiseev, and V. A. Soifer, “Simple optical vortices formed by a spiral phase plate,” J. Opt. Technol. 74, 686–693 (2007). [CrossRef]  

24. J. F. Nye and M. V. Berry, ““Dislocations in wave trains,” Proc. Roy. Soc. London, Ser,” A 336 , 165–190 (1974).

25. N. B. Baranova, B. Ya, and A. V. Zel’dovich, “Mamayev, N.F. Pilipetskii, and V. V. Shkukov, “Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment),” JETP Lett. 33, 195–199 (1981).

References

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  1. R. Yamaguchi, T. Nose, and S. Sato, “Liquid crystal polarizers with axially symmetrical properties,” Jpn. J. Appl. Phys. 28(Part 1), 1730–1731 (1989).
    [CrossRef]
  2. M. Stalder and M. Schadt, “Linearly polarized light with axial symmetry generated by liquid-crystal polarization converters,” Opt. Lett. 21(23), 1948–1950 (1996).
    [CrossRef]
  3. L. Marrucci, C. Manzo, and D. Paparo, “Pancharatnam-Berry phase optical elements for wave front shaping in the visible domain: Switchable helical mode generation,” Appl. Phys. Lett. 88, 221102 (1–3) (2006).
    [CrossRef]
  4. S. C. McEldowney, D. M. Shemo, R. A. Chipman, and P. K. Smith, “Creating vortex retarders using photoaligned liquid crystal polymers,” Opt. Lett. 33(2), 134–136 (2008).
    [CrossRef]
  5. H. Choi, J. H. Woo and J. W. Wu, “Holographic inscription of helical wavefronts in a liquid crystal polarization grating,” Appl. Phys. Lett. 91, 141112 (1–3) (2007).
  6. R. Bhandari, “Polarization of light and topological phases,” Phys. Rep. 282(1), 1–64 (1997).
    [CrossRef]
  7. Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, “Space-variant Pancharatnam-Berry phase optical elements with computer-generated subwavelength gratings,” Opt. Lett. 27(13), 1141–1143 (2002).
    [CrossRef]
  8. A. Jesacher, A. Schwaighofer, S. Fürhapter, C. Maurer, S. Bernet, and M. Ritsch-Marte, “Schwaighofer, S. Fuerhapter, C. Maurer, S. Bernet, and M. Ritsch-Marte, “Wavefront correction of spatial light modulators using an optical vortex image,” Opt. Express 15(9), 5801–5808 (2007).
    [CrossRef]
  9. G. A. Swartzlander., “Peering into darkness with a vortex spatial filter,” Opt. Lett. 26(8), 497–499 (2001).
    [CrossRef]
  10. S. Bernet, A. Jesacher, S. Fuerhapter, C. Maurer, and M. Ritsch-Marte, “Quantitative imaging of complex samples by spiral phase contrast microscopy,” Opt. Express 14(9), 3792–3805 (2006).
    [CrossRef]
  11. A. V. Nesterov and V. G. Niziev, “Laser beams with axially symmetric polarization,” Phys. D: Appl. Phys. 33(15), 1817–1822 (2000).
    [CrossRef]
  12. J. H. Lee, H. R. Kim, and S. D. Lee, “Polarization-insensitive wavelength selection in an axially symmetric liquid-crystal Fabry-Perot filter,” Appl. Phys. Lett. 75(6), 859–861 (1999).
    [CrossRef]
  13. G. Sinclair, P. Jordan, J. Courtial, M. Padgett, J. Cooper, and Z. J. Laczik, “Assembly of 3-dimensional structures using programmable holographic optical tweezers,” Opt. Express 12(22), 5475–5480 (2004).
    [CrossRef]
  14. S. C. Chapin, V. Germain, and E. R. Dufresne, “Automated trapping, assembly, and sorting with holographic optical tweezers,” Opt. Express 14(26), 13095–13100 (2006).
    [CrossRef]
  15. D. Ganic, X. Gan, M. Gu, M. Hain, S. Somalingam, S. Stankovic, and T. Tschudi, “Generation of doughnut laser beams by use of a liquid-crystal cell with a conversion efficiency near 100%,” Opt. Lett. 27(15), 1351–1353 (2002).
    [CrossRef]
  16. Q. Wang, X. W. Sun, P. Shum, and X. J. Yin, “Dynamic switching of optical vortices with dynamic gamma-correction liquid crystal spiral phase plate,” Opt. Express 13(25), 10285–10291 (2005).
    [CrossRef]
  17. H. Ren, Y.-H. Lin and S.-T. Wu, “Linear to axial or radial polarization conversion using a liquid crystal gel,” Appl. Phys. Lett. 89, 051114 (1–3) (2006).
    [CrossRef]
  18. S. Masuda, T. Nose, R. Yamaguchi, and S. Sato, “Polarization converting devices using a UV curable liquid crystal,” Proc. SPIE 2873, 301–304 (1996).
  19. Y. Y. Tzeng, S.-W. Ke, C.-L. Ting, A. Y.-G. Fuh, and T.-H. Lin, “Axially symmetric polarization converters based on photo-aligned liquid crystal films,” Opt. Express 16(6), 3768–3775 (2008).
    [CrossRef]
  20. S.-W. Ko, Y.-Y. Tzeng, C.-L. Ting, A. Y.-G. Fuh, and T.-H. Lin, “Axially symmetric liquid crystal devices based on double-side photo-alignment,” Opt. Express 16(24), 19643–19648 (2008).
    [CrossRef]
  21. S. R. Nersisyan, N. V. Tabiryan, D. M. Steeves, and B. R. Kimball, “Optical axis gratings in liquid crystals and their use for polarization insensitive optical switching,” J. Nonlinear Opt. Phys. Mater. 18(01), 1–47 (2009).
    [CrossRef]
  22. S. R. Nersisyan, N. V. Tabiryan, D. M. Steeves, and B. R. Kimball, “Reproduction of polarization gratings,” Appl. Opt. (Submitted to).
  23. V. V. Kotlyar, A. A. Kovalev, R. V. Skidanov, S. N. Khonina, O. Yu. Moiseev, and V. A. Soifer, “Simple optical vortices formed by a spiral phase plate,” J. Opt. Technol. 74, 686–693 (2007).
    [CrossRef]
  24. J. F. Nye and M. V. Berry, ““Dislocations in wave trains,” Proc. Roy. Soc. London, Ser,” A 336, 165–190 (1974).
  25. N. B. Baranova, B. Ya, and A. V. Zel’dovich, “Mamayev, N. F. Pilipetskii, and V. V. Shkukov, “Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment),” JETP Lett. 33, 195–199 (1981).

2009

S. R. Nersisyan, N. V. Tabiryan, D. M. Steeves, and B. R. Kimball, “Optical axis gratings in liquid crystals and their use for polarization insensitive optical switching,” J. Nonlinear Opt. Phys. Mater. 18(01), 1–47 (2009).
[CrossRef]

2008

2007

2006

2005

2004

2002

2001

2000

A. V. Nesterov and V. G. Niziev, “Laser beams with axially symmetric polarization,” Phys. D: Appl. Phys. 33(15), 1817–1822 (2000).
[CrossRef]

1999

J. H. Lee, H. R. Kim, and S. D. Lee, “Polarization-insensitive wavelength selection in an axially symmetric liquid-crystal Fabry-Perot filter,” Appl. Phys. Lett. 75(6), 859–861 (1999).
[CrossRef]

1997

R. Bhandari, “Polarization of light and topological phases,” Phys. Rep. 282(1), 1–64 (1997).
[CrossRef]

1996

M. Stalder and M. Schadt, “Linearly polarized light with axial symmetry generated by liquid-crystal polarization converters,” Opt. Lett. 21(23), 1948–1950 (1996).
[CrossRef]

S. Masuda, T. Nose, R. Yamaguchi, and S. Sato, “Polarization converting devices using a UV curable liquid crystal,” Proc. SPIE 2873, 301–304 (1996).

1989

R. Yamaguchi, T. Nose, and S. Sato, “Liquid crystal polarizers with axially symmetrical properties,” Jpn. J. Appl. Phys. 28(Part 1), 1730–1731 (1989).
[CrossRef]

1981

N. B. Baranova, B. Ya, and A. V. Zel’dovich, “Mamayev, N. F. Pilipetskii, and V. V. Shkukov, “Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment),” JETP Lett. 33, 195–199 (1981).

1974

J. F. Nye and M. V. Berry, ““Dislocations in wave trains,” Proc. Roy. Soc. London, Ser,” A 336, 165–190 (1974).

Baranova, N. B.

N. B. Baranova, B. Ya, and A. V. Zel’dovich, “Mamayev, N. F. Pilipetskii, and V. V. Shkukov, “Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment),” JETP Lett. 33, 195–199 (1981).

Bernet, S.

Berry, M. V.

J. F. Nye and M. V. Berry, ““Dislocations in wave trains,” Proc. Roy. Soc. London, Ser,” A 336, 165–190 (1974).

Bhandari, R.

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Fuh, A. Y.-G.

Fürhapter, S.

Gan, X.

Ganic, D.

Germain, V.

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Hain, M.

Hasman, E.

Jesacher, A.

Jordan, P.

Ke, S.-W.

Khonina, S. N.

Kim, H. R.

J. H. Lee, H. R. Kim, and S. D. Lee, “Polarization-insensitive wavelength selection in an axially symmetric liquid-crystal Fabry-Perot filter,” Appl. Phys. Lett. 75(6), 859–861 (1999).
[CrossRef]

Kimball, B. R.

S. R. Nersisyan, N. V. Tabiryan, D. M. Steeves, and B. R. Kimball, “Optical axis gratings in liquid crystals and their use for polarization insensitive optical switching,” J. Nonlinear Opt. Phys. Mater. 18(01), 1–47 (2009).
[CrossRef]

S. R. Nersisyan, N. V. Tabiryan, D. M. Steeves, and B. R. Kimball, “Reproduction of polarization gratings,” Appl. Opt. (Submitted to).

Kleiner, V.

Ko, S.-W.

Kotlyar, V. V.

Kovalev, A. A.

Laczik, Z. J.

Lee, J. H.

J. H. Lee, H. R. Kim, and S. D. Lee, “Polarization-insensitive wavelength selection in an axially symmetric liquid-crystal Fabry-Perot filter,” Appl. Phys. Lett. 75(6), 859–861 (1999).
[CrossRef]

Lee, S. D.

J. H. Lee, H. R. Kim, and S. D. Lee, “Polarization-insensitive wavelength selection in an axially symmetric liquid-crystal Fabry-Perot filter,” Appl. Phys. Lett. 75(6), 859–861 (1999).
[CrossRef]

Lin, T.-H.

Masuda, S.

S. Masuda, T. Nose, R. Yamaguchi, and S. Sato, “Polarization converting devices using a UV curable liquid crystal,” Proc. SPIE 2873, 301–304 (1996).

Maurer, C.

McEldowney, S. C.

Moiseev, O. Yu.

Nersisyan, S. R.

S. R. Nersisyan, N. V. Tabiryan, D. M. Steeves, and B. R. Kimball, “Optical axis gratings in liquid crystals and their use for polarization insensitive optical switching,” J. Nonlinear Opt. Phys. Mater. 18(01), 1–47 (2009).
[CrossRef]

S. R. Nersisyan, N. V. Tabiryan, D. M. Steeves, and B. R. Kimball, “Reproduction of polarization gratings,” Appl. Opt. (Submitted to).

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A. V. Nesterov and V. G. Niziev, “Laser beams with axially symmetric polarization,” Phys. D: Appl. Phys. 33(15), 1817–1822 (2000).
[CrossRef]

Niziev, V. G.

A. V. Nesterov and V. G. Niziev, “Laser beams with axially symmetric polarization,” Phys. D: Appl. Phys. 33(15), 1817–1822 (2000).
[CrossRef]

Nose, T.

S. Masuda, T. Nose, R. Yamaguchi, and S. Sato, “Polarization converting devices using a UV curable liquid crystal,” Proc. SPIE 2873, 301–304 (1996).

R. Yamaguchi, T. Nose, and S. Sato, “Liquid crystal polarizers with axially symmetrical properties,” Jpn. J. Appl. Phys. 28(Part 1), 1730–1731 (1989).
[CrossRef]

Nye, J. F.

J. F. Nye and M. V. Berry, ““Dislocations in wave trains,” Proc. Roy. Soc. London, Ser,” A 336, 165–190 (1974).

Padgett, M.

Ritsch-Marte, M.

Sato, S.

S. Masuda, T. Nose, R. Yamaguchi, and S. Sato, “Polarization converting devices using a UV curable liquid crystal,” Proc. SPIE 2873, 301–304 (1996).

R. Yamaguchi, T. Nose, and S. Sato, “Liquid crystal polarizers with axially symmetrical properties,” Jpn. J. Appl. Phys. 28(Part 1), 1730–1731 (1989).
[CrossRef]

Schadt, M.

Schwaighofer, A.

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Shum, P.

Sinclair, G.

Skidanov, R. V.

Smith, P. K.

Soifer, V. A.

Somalingam, S.

Stalder, M.

Stankovic, S.

Steeves, D. M.

S. R. Nersisyan, N. V. Tabiryan, D. M. Steeves, and B. R. Kimball, “Optical axis gratings in liquid crystals and their use for polarization insensitive optical switching,” J. Nonlinear Opt. Phys. Mater. 18(01), 1–47 (2009).
[CrossRef]

S. R. Nersisyan, N. V. Tabiryan, D. M. Steeves, and B. R. Kimball, “Reproduction of polarization gratings,” Appl. Opt. (Submitted to).

Sun, X. W.

Swartzlander, G. A.

Tabiryan, N. V.

S. R. Nersisyan, N. V. Tabiryan, D. M. Steeves, and B. R. Kimball, “Optical axis gratings in liquid crystals and their use for polarization insensitive optical switching,” J. Nonlinear Opt. Phys. Mater. 18(01), 1–47 (2009).
[CrossRef]

S. R. Nersisyan, N. V. Tabiryan, D. M. Steeves, and B. R. Kimball, “Reproduction of polarization gratings,” Appl. Opt. (Submitted to).

Ting, C.-L.

Tschudi, T.

Tzeng, Y. Y.

Tzeng, Y.-Y.

Wang, Q.

Ya, B.

N. B. Baranova, B. Ya, and A. V. Zel’dovich, “Mamayev, N. F. Pilipetskii, and V. V. Shkukov, “Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment),” JETP Lett. 33, 195–199 (1981).

Yamaguchi, R.

S. Masuda, T. Nose, R. Yamaguchi, and S. Sato, “Polarization converting devices using a UV curable liquid crystal,” Proc. SPIE 2873, 301–304 (1996).

R. Yamaguchi, T. Nose, and S. Sato, “Liquid crystal polarizers with axially symmetrical properties,” Jpn. J. Appl. Phys. 28(Part 1), 1730–1731 (1989).
[CrossRef]

Yin, X. J.

Zel’dovich, A. V.

N. B. Baranova, B. Ya, and A. V. Zel’dovich, “Mamayev, N. F. Pilipetskii, and V. V. Shkukov, “Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment),” JETP Lett. 33, 195–199 (1981).

A

J. F. Nye and M. V. Berry, ““Dislocations in wave trains,” Proc. Roy. Soc. London, Ser,” A 336, 165–190 (1974).

Appl. Opt.

S. R. Nersisyan, N. V. Tabiryan, D. M. Steeves, and B. R. Kimball, “Reproduction of polarization gratings,” Appl. Opt. (Submitted to).

Appl. Phys. Lett.

J. H. Lee, H. R. Kim, and S. D. Lee, “Polarization-insensitive wavelength selection in an axially symmetric liquid-crystal Fabry-Perot filter,” Appl. Phys. Lett. 75(6), 859–861 (1999).
[CrossRef]

J. Nonlinear Opt. Phys. Mater.

S. R. Nersisyan, N. V. Tabiryan, D. M. Steeves, and B. R. Kimball, “Optical axis gratings in liquid crystals and their use for polarization insensitive optical switching,” J. Nonlinear Opt. Phys. Mater. 18(01), 1–47 (2009).
[CrossRef]

J. Opt. Technol.

JETP Lett.

N. B. Baranova, B. Ya, and A. V. Zel’dovich, “Mamayev, N. F. Pilipetskii, and V. V. Shkukov, “Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment),” JETP Lett. 33, 195–199 (1981).

Jpn. J. Appl. Phys.

R. Yamaguchi, T. Nose, and S. Sato, “Liquid crystal polarizers with axially symmetrical properties,” Jpn. J. Appl. Phys. 28(Part 1), 1730–1731 (1989).
[CrossRef]

Opt. Express

A. Jesacher, A. Schwaighofer, S. Fürhapter, C. Maurer, S. Bernet, and M. Ritsch-Marte, “Schwaighofer, S. Fuerhapter, C. Maurer, S. Bernet, and M. Ritsch-Marte, “Wavefront correction of spatial light modulators using an optical vortex image,” Opt. Express 15(9), 5801–5808 (2007).
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G. Sinclair, P. Jordan, J. Courtial, M. Padgett, J. Cooper, and Z. J. Laczik, “Assembly of 3-dimensional structures using programmable holographic optical tweezers,” Opt. Express 12(22), 5475–5480 (2004).
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S. Bernet, A. Jesacher, S. Fuerhapter, C. Maurer, and M. Ritsch-Marte, “Quantitative imaging of complex samples by spiral phase contrast microscopy,” Opt. Express 14(9), 3792–3805 (2006).
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Q. Wang, X. W. Sun, P. Shum, and X. J. Yin, “Dynamic switching of optical vortices with dynamic gamma-correction liquid crystal spiral phase plate,” Opt. Express 13(25), 10285–10291 (2005).
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Y. Y. Tzeng, S.-W. Ke, C.-L. Ting, A. Y.-G. Fuh, and T.-H. Lin, “Axially symmetric polarization converters based on photo-aligned liquid crystal films,” Opt. Express 16(6), 3768–3775 (2008).
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S.-W. Ko, Y.-Y. Tzeng, C.-L. Ting, A. Y.-G. Fuh, and T.-H. Lin, “Axially symmetric liquid crystal devices based on double-side photo-alignment,” Opt. Express 16(24), 19643–19648 (2008).
[CrossRef]

Opt. Lett.

Phys. D: Appl. Phys.

A. V. Nesterov and V. G. Niziev, “Laser beams with axially symmetric polarization,” Phys. D: Appl. Phys. 33(15), 1817–1822 (2000).
[CrossRef]

Phys. Rep.

R. Bhandari, “Polarization of light and topological phases,” Phys. Rep. 282(1), 1–64 (1997).
[CrossRef]

Proc. SPIE

S. Masuda, T. Nose, R. Yamaguchi, and S. Sato, “Polarization converting devices using a UV curable liquid crystal,” Proc. SPIE 2873, 301–304 (1996).

Other

H. Choi, J. H. Woo and J. W. Wu, “Holographic inscription of helical wavefronts in a liquid crystal polarization grating,” Appl. Phys. Lett. 91, 141112 (1–3) (2007).

L. Marrucci, C. Manzo, and D. Paparo, “Pancharatnam-Berry phase optical elements for wave front shaping in the visible domain: Switchable helical mode generation,” Appl. Phys. Lett. 88, 221102 (1–3) (2006).
[CrossRef]

H. Ren, Y.-H. Lin and S.-T. Wu, “Linear to axial or radial polarization conversion using a liquid crystal gel,” Appl. Phys. Lett. 89, 051114 (1–3) (2006).
[CrossRef]

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Figures (7)

Fig. 1.
Fig. 1.

(a) Axial waveplate between crossed polarizers illuminated with a white light. Photos of a He-Ne laser beam, λ=633 nm, propagated through an axial waveplate with half-waveplate condition at 458 nm. Photos are taken with no polarizers in the optical path (b), and between parallel (c) and orthogonal polarizers (d).

Fig. 2.
Fig. 2.

The patterns obtained for a circular polarized beam of a He-Ne laser propagated through a double-layer LCP axial waveplate as a result of interference with a reference plane wave, (a) and (b), and a reference beam of a spherical phase profile, (c) and (d). The patterns (a) and (c) switch to (b) and (d), respectively, when changing the sign of circular polarization.

Fig. 3.
Fig. 3.

The columns correspond to images of linear polarized laser beams of different wavelengths propagated through axial waveplates with no polarizers in the optical path (1st column) and between parallel (2nd column) and perpendicular polarizers (3rd column). (a)-(c) He-Cd laser beam propagated through an axial waveplate with half-wave condition at the wavelength λ=325 nm; (d)-(f) Ar+ laser beam, λ=458 nm, half-wave condition at 458 nm; (g)-(i) He-Ne laser beam and a double layer axial waveplate with half-wave condition at 633 nm; (j)-(l) IR laser beam, λ=1064 nm, and a three layer axial waveplate with half-wave condition at 1000 nm.

Fig. 4.
Fig. 4.

(a) One-dimensional intensity profiles of a He-Ne laser beam obtained without and with the axial waveplate. (b) 2-D and 3-D profiles of the doughnut beam obtained for a highly saturating gaussian beam; (c) 2-D and 3-D profiles of the beam at a power level saturating a CCD; (d) demonstrating the capability of the axial waveplate to remove the saturation of the CCD camera.

Fig. 5.
Fig. 5.

The effect of an axial waveplate on the profile of a He-Ne laser beam for different ratios of the separation distance between the axes of the waveplate and beam to the radius of the beam d/w: (a) >2; (b) 1; (c) 0.25; (d) 0; (e) -0.25; (f) -1; (g) -0.75; (h) <-2. The sign of the ratio refers to having the vortex on the opposite sides of the beam.

Fig. 6.
Fig. 6.

Beam shaping with axial waveplates. The profiles are obtained for a Gaussian He-Ne laser beam by shifting the centers of two radial waveplates positioned at 2 mm distance from each other with respect to the beam axis. The shifts are equal for both waveplates but are of opposite signs.

Fig. 7.
Fig. 7.

3×3 and 5×5 vortex arrays with single, (a) and (c), and double LCP layers, (b) and (d). The arrays (a), (c) and (b), (d) are designed for 458 nm and 633 nm wavelengths, correspondingly.

Equations (2)

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I=Ide(rrd)2wd2
IGId=πrdwd[1+erf(rdwd)]+e(rdwd)2

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