We present new lenses – waveplate lenses created in liquid crystal and liquid crystal polymer materials. Using an electrically-switchable liquid-crystal half-wave retarder we realized switching between focused and defocused beams by the waveplate lens. A combination of two such lenses allowed the collimation of a laser beam as well as the change of focal length of optical system.
© 2015 Optical Society of America
Lenses are commonly made by shaping an optical material such as glass. The weight of such lenses increases strongly with diameter making them very expensive and prohibitively heavy for applications requiring large area. Also the quality of a lens typically decreases with increasing size. Diffractive lenses such as Fresnel lenses are relatively thin, however, the structural discontinuity adds to aberrations [1, 2]. Uses of holographic lenses are limited by the compromise of efficiency and dispersion . Liquid crystal lenses have been developed intensively due to their capability to provide electrically-controllable focal length [4–16], however, those are thick, aberrational, and are limited in f-number.
Thus, there is a need for switchable and non-switchable lenses that could be obtained in the form of thin film structurally continuous coatings on a variety of substrates.
We developed continuous thin film, ~1 μm thick, waveplate lenses, which can switch between concave and convex positions by control of light polarization sign. Lenses of various sizes, various focal lengths, from micrometers to meters, various parabolic structures, cylindrical, spherical of axicon configurations, for a wide wavelength range were created. Combinations of waveplate lenses with liquid crystal (LC) retarders allowed electrical switching between collimated and focused/defocused beams as well as control of focal length.
In this work, we describe some preliminary descriptions of the methods for producing the complex, high spatial frequency patterns that are required to provide lens action with focal characteristics required for applications. These focal characteristics include operating wavelength range, diffraction efficiency, focal length, and f-number. In subsequent publications, we will provide further detail on general methods for producing diffractive waveplates with nearly arbitrary optical axis patterns.
2. Waveplate lens concept
Thin film cycloidal waveplate gratings were recorded by cycloidal distribution of beam polarization in one direction in liquid crystal materials [17–25]. Here we report two dimensional structures having parabolic distribution of orientation of director of liquid crystal molecules. Pattern of optical axis orientation demonstrating waveplate lenses (WLs) performing the same optical function as a refractive lens with spherical surfaces is shown in Fig. 1(a). The waveplate lenses are fabricated using photoalignment of a liquid crystal or liquid crystal polymer (LCP). The polarization pattern of radiation used for photoalignment is obtained by propagating the light through an optical system comprising a shape-variant nonlinear spatial light polarization modulator [Fig. 1(b)]. Recording cycloidal orienting conditions on a substrate coated with a photoaligning material film (PAAD) is shown in Fig. 1(c).
The theoretical upper limit on diffraction efficiency for WLs of the type described here is 100%, as it is with waveplate gratings with cycloidal distribution previously reported. By suitable axial structuring of the optical axis orientation, high efficiency over a wide spectral band can be, and has been, achieved in both cycloidal patterned waveplates and in WL devices. A typical spectral bandwidth of Δλ/λ0 = 0.56 is possible with the appropriate axial structure of the optical axis orientation . Here Δλ is the spectral bandwidth over which >99% diffraction efficiency is achieved, and λ0 is the wavelength at the center of the operating wavelength band.
To create waveplate lenses in liquid crystals materials, the thickness of LC layer L and its birefringence Δn must be such that the half-wave phase retardation condition LΔn = λ/2 is met, where λ is the operating wavelength. Somewhat more complex axial structure is required for cases in which broadband operation is required .
3. Experiment and results
3.1. Waveplate lens fabrication
The polarization modulation patterns were recorded on PAAD series photoalignment material layers (BEAM Co.). The PAAD layer is created on a glass substrate by spin-coating, for example, a solution of PAAD-72(1%)/DMF at a speed 3000 rpm during 30 s. Then, the PAAD layer was exposed to the laser beam at wavelength corresponding to the absorption band of the PAAD material. The peak absorption of PAAD-72 occurs at a wavelength of 424 nm. A He-Cd laser operated at wavelength 442 nm and Argon ion laser operated at one of the several of the wavelengths of which such lasers are capable (457 am, 488 nm and 514 nm) were used for exposure. At intensity of laser beams 15 mW/cm2 was used. The exposure time was 5 min for wavelength 442 nm and 10 min for wavelength 488 nm. He-Ne laser beam at wavelength 633 nm was used for probing. Having thus created the required alignment conditions, the PAAD coated substrate was coated with a layer of liquid crystal monomer solution RLCS-7 (BEAM Co.) followed by photopolymerization with unpolarized UV light at 365 nm wavelength and intensity 90 mW/cm2 with an exposure time of 5 min. The layer of RLCS-7 was spin-coated on the PAAD-72 layer at a rotational speed of 3000 rpm for 1 min. The thickness of the polymer layer allowed creation of a half-wave phase retardation condition at 633 nm wavelength.
Alternatively, photoaligned substrates were used for making liquid crystal cells. Nematic liquid crystal (NLC) cells consisted of two glass substrates coated with PAAD material and exposed to Argon ion laser beam to create orientation distribution of LC molecules in the cell. Thickness of the cells was chosen to create half-wave retardation condition at wavelengths of 532 or 633 nm. Low birefringence BEAM Co. liquid crystal material R-237 (Δn = 0.057) was filled in the gap between substrates.
3.2. Waveplate lenses equivalent to refractive lenses with spherical surfaces
In the discussion below, reference will be made to the period of the optical axis pattern at the edge of the lens. In this context, the period is defined as the distance over which the optical axis orientation angle changes by 180°. For circular WLs, the period is nominally infinite at the center of the lens and decreases monotonically from the center to the edge. Therefore, the period is smallest at the edge. The period of the optical pattern at the edge of the lens is a useful parameter in characterizing the lens for a variety of reasons, one of which is that in the paraxial approximation, the f-number is related to the period Λ at the edge by f-number = Λ/2λ where λ is the operating wavelength.
Figure 2(a) shows a waveplate lens of 18-mm diameter in thin LCP film. Figures 2(b) and 2(c) demonstrate structure of WL between crossed polarizers. Focal length of the lens was 320 mm at wavelength 633 nm. Spacing period on the edge was 22 μm.
Phase profile across the lens in accordance to distance between rings, which was calculated from photomicrographs of the lens between crossed polarizers, is shown in Fig. 2(d). A lens of 7-mm diameter and focal length F = 460 mm was used. Number of rings corresponded to optical phase shift equal to 45π. Fitting of data with parabolic function demonstrates high symmetry and good agreement between the calculated optical phase and the parabolic phase model.
Lenses of different focal length were recorded by simply changing the size of the polarization modulation pattern projected onto the photoalignment layer. Figure 3 shows pattern of lenslets of 4-mm diameter with focal length of 41 mm. Spacing period on the edge was 11 μm. Expanded laser beam passed through lens array was focused on a screen, Fig. 3(b). Relationship between paraxial focal length F, grating period Λ on the edge, wavelength λ and lens diameter D can be calculated taking into account diffraction condition for grating period on the edge of the lens: F = ΛD/2λ. We also recorded lenses with smaller spacing period Λ = 3.6 μm with focal length F = 5.7 mm.
A probe beam was created by expanding the linearly-polarized output of a He-Ne laser with a beam expander consisting of conventional lenses L1 and L2. The polarization of the light at the input to the mask in Fig. 4(a) was switched from right-hand circular polarization (RHCP) to left-hand circular polarization (LHCP) by rotating the quarter-wave plate (QWP). The probe beam passed through a triangular aperture and then was focused or defocused with waveplate lens, Fig. 4(a).
Figure 4(b) shows photos of projections of this triangular aperture with a waveplate lens for different polarization states. Photos (1) – (3) of Fig. 4(b) were taken behind the lens before focus, photos (4) – (6) were taken at the focus of the lens (F = 190 mm), and the photos (7) – (9) taken far from the focus. The photos (1), (4), (7) of Fig. 4(b) correspond to linear polarized (LP) or unpolarized incident beam, the photos (2), (5), (8) correspond to RHCP incident beam, and the photos (3), (6), (9) correspond to LHCP beam. Two images corresponded to lenses with positive and negative focal lengths were observed simultaneously for linear polarized laser beam. When laser beam was RHCP, waveplate lens had a positive focal length, as if it were a convex (CX) refractive lens, and therefore converged the collimated input beam. When laser beam was LHCP, the waveplate lens was switched to having a negative focal length, as if it were a concave (CV) refractive lens, thus diverging the collimated input beam. Focal length of lens was switched between FCX = 190 mm and FCV = −190 mm by switching the circular polarization of the probe beam. The sign of the focal length of the waveplate lens was changed from positive to negative for the same RHCP laser beam, when the lens was turned from face side to back side, Figs. 4(c) and 4(d).
Figure 5 shows images of an eye chart observed without any WL lens in the optical path, and with a WL lens and circular polarizer in the optical path. The size of the image at the camera is decreased when the light is RHCP, Fig. 5(b), and increased when the light is LHCP, Fig. 5(c). This is because the signs of the focal lengths of the WL are opposite for the two circular polarizations.
For a WP designed for high efficiency in the red region of the spectrum, Fig. 6 demonstrates that the half-wave phase retardation condition was satisfied exactly for a red wavelength, but not for a blue wavelength. For the blue wavelength, the deviation of the optical retardation from the half-wave condition results in some leakage of undiffracted light through the lens. For the red wavelength, nearly 100% of the light is diffracted, so the red light is nearly all focused in Fig. 6(b), and nearly all defocused in Fig. 6(c).
3.3. Optics of two waveplate lenses
Two waveplate lenses of the same aperture diameter and the same focal length were tested with a collimated input probe red laser beam, with test results shown in Fig. 7. The axial location of the screen on which the beam was projected was adjusted with only WL1 in place, with the circular polarization at the input set such that the focal length of WL1 was positive, and with the screen at the focal point of the lens. In case A the waveplate patterns of the two lenses were facing the same way with axial spacing small compared with the focal length, Fig. 7(a). If the input circular polarization was set such that the focal length of lens WL1 was positive, then the focal length of lens WL2 was negative taking into account that the waveplate lens changes the handedness of circular polarization due to the half wave of optical retardation introduced by lens WL1. For this case, the focal length of WL2 for any given polarization is the inverse of the focal length of lens WL1, so the combination of the two lenses has essentially no effect on the beam, which remains collimated at the output of the lens pair regardless of the polarization of the input beam.
In case B the same two waveplate lenses were arranged such that the waveplate patterns on the two lenses were facing in opposite directions, Fig. 7(b). For this arrangement, the focal lengths of the two lenses were the same for a given input beam. For case B, the absolute value of the focal length of the combination of the two lenses was one-half the focal length of each of the lenses separately. For the input circular polarization for which the focal lengths were both positive, the focal length of each lens separately was 480 mm, and the focal length of the two lenses together with negligible axial spacing was 240 mm.
It is possible to arrange two WL lenses such that light of any polarization is brought to focus at the same point, as illustrated in Fig. 8.
Expressions for the lens spacing s and the back focus distance d such that light of either polarization is brought to the same focus are as follows:
3.4. Electrical switching between focused and defocused states
3.4.1. Switching of single WL
The focusing conditions can be controlled by using electrically controlled phase retardation plates to modulate the polarization state and distribution in the input light. Rotation of quarter-wave plate allowed switching between right- and left-handed circular polarized laser beams that resulted in switching the sign of the focal length of any WL lens.
We used NLC retarder of thickness L = 1.9 μm to create electrically controlled half-wave plate. NLC cell was filled with nematic liquid crystal 6CHBT (from AWAT, Poland). NLC retarder had a retardation of one half wave in its initial state for red wavelength (633 nm). If initially the input circular polarization was set such that the focal length of the WL was negative, the LC retarder switched the sign of the focal length from negative to positive. An AC voltage of amplitude 10 V at a frequency of 1kHz was used to switch the sign of the focal length, Figs. 9(a)-9(c).
If the input circular polarization was adjusted so the WL lens focal length was positive and LC retarder was set, waveplate lens focal length was switched to negative. The sign of the lens focal length was switched with the application of 10 V, Figs. 9(d)-9(f).
Another LC retarder of thickness L = 10 μm was used for multiple switching between positive and negative WL focal length. LC oriented axis was aligned at angle 45° to initial linear beam polarization. Quarter-wave plate was absent in this set-up. Focal length of the waveplate lens was positive or negative for several voltages, Figs. 9(g) and 9(h).
3.4.2. Switching of two WLs
Switching between collimated and focused beam was achieved with two waveplate lenses and 1.9 μm thick LC retarder between them. Figure 10(a) shows this combined optical system. Initially lens WL1 had a positive focal length for LHCP light, and lens WL2 had a negative focal length for such light. Both lenses had a focal length of 240 mm. When LC retarder was set between lenses, WL2 was switched to a negative focal length and the combination of the two lenses collimated the laser beam. When an AC voltage of 10 V (frequency of 1 kHz) was applied, WL2 was switched to a positive focal length and both lenses together focused the laser beam at a distance of 240 mm. Photos in Figs. 10(b)-10(d) demonstrate this effect.
Thin NLC lens with substrates coated with WLs was used also as optical switching element, Figs. 10(e)-10(g). When voltage was not applied to the substrate, laser beam was focused (e) or defocused (f). When voltage was applied to the substrate, two waveplate lenses collimated laser beam (g).
3.5. Printing WLs
We used original WL1 to print waveplate lens on another PAAD coated substrate. Original WL and PAAD coated substrate were set in the same holder as close as possible to each other. Printed waveplate lens had focal length a factor of two shorter than that of the original lens. Images of laser beam, passed triangular mask for original and printed WLs are shown in Fig. 11. Distance between WL and screen was 320 mm, which corresponded to focal length of original lens.
3.6. Cylindrical waveplate lenses
Parabolic cylindrical patterns in LCP were recorded as well, Fig. 12. Focusing and defocusing of Argon laser beam by cylindrical lens with focal length F = 510 mm at wavelength 514 nm is shown in Figs. 12(c)-12(d). We include this data here to highlight the fact that this new technology allows the fabrication of a wide variety of diffractive waveplates with complex optical axis patterns, not limited to the radial parabolic dependence of grating period characteristic of lenses in the paraxial approximation. On the contrary, any two-dimensional pattern is now achievable, limited only by such factors as a lower limit on grating period.
The recent development of precise methods for creating photoalignment layers with nearly arbitrary spatial patterns now allows the fabrication of a new generation of optical devices consisting of a micron-thick layers of anisotropic optical material such as liquid crystal polymers with spatially-patterned optical axis orientation. The diffraction efficiency of such components has been demonstrated to be near 100% for a single polarization of light. Such layers can be formed on a variety of substrates. We have demonstrated such techniques by fabricating and testing waveplate lenses and lens arrays, and we have demonstrated electrical switching of the sign of the focal length of such lenses by means of a switchable half-wave plate. We have also demonstrated that a suitably designed pair of waveplate lenses can focus light of any polarization to the same point.
This new type of lens is expected to have many applications in optics and photonics, for example as an alternative to other types of diffractive lens coatings. The switchable versions of these lenses could be used for such applications as digital control of laser beam divergence and laser focal distance.
The work was supported by funding from US Army Natick Soldier Research, Development and Engineering Center. We thank Dr. S. Nersisyan and Dr. H. Xianyu for assistance with LCP coating.
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