We report on lenses that operate over the visible wavelength band from 450 nm to beyond 700 nm, and other lenses that operate over a wide region in the near-infrared from 650 nm to beyond 1000 nm. Lenses were recorded in liquid crystal polymer layers only a few micrometers thick, using laser-based photoalignment and UV photopolymerization. Waveplate lenses allowed focusing and defocusing laser beams depending on the sign of the circularity of laser beam polarization. Diffraction efficiency of recorded waveplate lenses was up to 90% and contrast ratio was up to 500:1.
© 2016 Optical Society of America
Polarization gratings, often fabricated in the form of a liquid crystal polymer (LCP) film, have been developed to the point where they are a well-known and useful type of diffractive element [1–3]. While it has been known for some time (see, for example [3,4],) that it is in principle possible to fabricate thin-film diffractive waveplate (DW) devices with a wide variety of patterns, much of the available literature relates to linear cycloidal patterns [1–14], in which the optical axis orientation varies linearly along one Cartesian coordinate in the plane of the patterned anisotropic thin-film layer; or in vector vortex patterns [15–17], in which the optical axis orientation angle is linear in the azimuthal angle about a singularity point in the plane of the device. Recently, BEAM Co [18–22]. and others [23–25] have developed waveplate lenses with radially-symmetric optical axis patterns, with optical axis orientation that varies quadratically with distance from a central point. This type of optical axis pattern results in a lensing effect on light transmitted through the thin-film DW device. This recent work has also demonstrated the feasibility of electrically switching the lensing action on or off, or switching the sign of the focal length for a given circular polarization [21,22].
For the simplest type of diffractive waveplate devices, the optical axis orientation within the few micrometer thickness of the film has no axial dependence. For even this simplest type of device, the diffraction efficiency η is high over a relatively broad range of wavelengths, and depends on wavelength as follows : η = sin2(πLΔn/λ). Here L is the axial thickness of the film, Δn = (ne - no) is the anisotropy of the material comprising the film, ne and no are the extraordinary and ordinary indices of refraction of this film, respectively, and λ is the wavelength. From this equation, it can be shown that the wavelength range Δλ over which the diffraction efficiency satisfies η > ηmin for this simplest type of DW device is well approximated as follows for values of ηmin near 100%: Δλ ≈λ0(1 − ηmin)1/2. Here λ0 is defined to be that wavelength at which the half-wave condition is met. That is, for λ = λ0, . For example, if the film thickness L and the anisotropy Δn are adjusted such that the half-wave condition is met at wavelength λ0 = 550 nm (i.e. at the center of the visible wavelength band), and if a minimum diffraction efficiency of ηmin = 95% is acceptable, then the operating bandwidth Δλ is greater than 150 nm (neglecting small effects such as the variation of the indices of refraction with wavelength). That is, the efficiency for even the simplest DW grating can be greater than 95% over at least half the 400 nm to 700 nm band of visible wavelengths.
In some applications, it is desirable that the bandwidth be even greater than is provided by the simple DW device structure described above. It is possible to achieve higher diffraction efficiencies over a broader operating bandwidth than is indicated by the equations above if the optical axis orientation is given an appropriate spatial dependence along the axial direction, i.e. along the coordinate perpendicular to the plane of the thin-film DW coating. The idea of stacking multiple discrete waveplates with certain angles between their optical axes in order to broaden the bandwidth over which a certain retardation is obtained was introduced by Pancharatnam . This concept for broadening the bandwidth of waveplates was extended to multi-layer LCP films , to twisted nematic liquid crystal (LC) cells , and to multilayer LCP devices with a double-twist structure, in which the optical axis orientation varies continuously along the axial direction . Optical films employing such double-twist axial structures to achieve wider optical bandwidths than described by the equations above have been fabricated and optical performance has been reported for cycloidal diffractive waveplates  and vector vortex waveplates [15,17]. Here we report the application of this technique for broadening the optical bandwidth of waveplate lenses.
2. Experiment and results: broadband diffraction
The polarization modulation patterns were recorded in photoalignment material PAAD-72 (BEAM Co.) Some optical characteristics of this material are illustrated in Fig. 1.
As illustrated in Fig. 1(a), PAAD-72 absorbs in the visible wavelength range. It can be photoaligned with laser light in the blue or green regions of the spectrum. The thickness of the PAAD layer used for photoalignment is generally less than 100 nm, so the residue of such material in the finished LCP device does not have any significant impact on optical efficiency.
Figure 1(b) illustrates the dynamic photoalignment response of this material. In this figure, the optical transmission of linearly polarized argon ion laser light at a wavelength of 488 nm through a 10 μm thick LC cell between polarizers is shown. One cell boundary consists of a polyvinyl alcohol (PVA) film aligned by rubbing, and the other cell boundary consists of PAAD-72 deposited on a glass substrate. The PAAD layer was created by spin-coating a 1% solution of this photoalignment material in dimethylformamide (DMF) solvent at a rotation speed 3000 rpm for 30 s. The PAAD layer was initially photoaligned parallel to the PVA alignment direction, such that the E7 liquid crystal was planar aligned. The cell was then placed between parallel polarizers, and the transmission of argon ion laser light (wavelength λ = 488 nm) through the assembly of polarizers and LC cell was measured as a function of time as shown in Fig. 1(b). For this dynamic optical transmission measurement, the laser light was incident on the PAAD side of the cell. The planar alignment of the cell [indicated by inset (1) of Fig. 1(b)] was initially aligned to the polarizers, but was then dynamically converted to 90° twist alignment [indicated by inset (2) of Fig. 1(b)] during the exposure. This resulted in reduction of the optical transmission through the assembly from near unity to near zero. The power density of the photoalignment beam was 2.2 W/cm2 with a beam diameter of 0.7 mm. The results shown in Fig. 1(b) demonstrate that for the noted alignment beam power density, the alignment layer can be re-aligned in only a few seconds. Other measurements indicate that the degree of alignment or re-alignment with photoalignment materials such as PAAD-72 is primarily determined by the total dosage, i.e. the energy density of the alignment exposure, over a wide range of exposure power density. With PAAD-72, a total dosage of ~1 J/cm2 at λ = 488 nm is sufficient to align or re-align the material, over a wide range of exposure power densities. An exposure dosage of 1 J/cm2 is somewhat greater than BEAM Co.’s recommended dosage for PAAD-72 at this wavelength  and is sufficient to assure complete photoalignment.
2.2 Lens recording
We recorded the photoalignment pattern for some waveplate lenses using a collimated argon ion laser beam approximately one inch in diameter, with a wavelength of 488 nm, using PAAD-72 photoalignment material. The alignment pattern required to fabricate an achromatic waveplate lens is the same as the alignment pattern required to fabricate the corresponding chromatic waveplate lens [21,22]. The polarization pattern of radiation used for photoalignment for one of the lenses of diameter 25 mm is shown in Fig. 2. Beam power density for photoalignment was 14 mW/cm2.
After recording the photoalignment pattern for each lens, a layer of liquid crystal monomer solution RLCS-7 (BEAM Co.) was spin-coated over the the PAAD layer. The rotation speed was adjusted so that the thickness of the final polymer layer would be one half wave of retardation at a wavelength of 633 nm. In this way, we produced a waveplate lens optimized for a wavelength of 633 nm by spin-coating a single layer of monomer at a rotational speed of 3000 rpm on the PAAD-72 photoalignment layer. Time of spin-coating was 1 minute and the monomer was cured with unpolarized UV light at 365 nm wavelength and an intensity of 15 mW/cm2 with an exposure time of 5 minutes.
Achromatic waveplate lenses were created for visible wavelengths using the methods previously described in [15,17,29,30]. The layer thickness required for a center design wavelength of 633 nm was created using two liquid crystal polymers of opposite chirality: RLCS-7/RH-VIS and RLCS-7/LH-VIS. The first polymer layer was spin coated from solution RLCS-7/RH-VIS with a speed of 1100 rpm, then the second layer was spin coated from a solution RLCS-7/LH-VIS with the same speed.
Achromatic DW lenses optimized for the near-IR spectral range were fabricated using four LCP layers, a method previously used to fabricate DW vector vortex gratings optimized for this wavelength region . The first and second layers were spin coated from a solution RLCS-7/RH-NIR with a speed of 1200 rpm. The third and fourth layers were spin coated from a solution RLCS-7/LH-NIR at the same rotation speed.
Figure 3 shows photographs of an achromatic LCP waveplate lens with a diameter of 20 mm and a focal length of 410 mm (at wavelength = 488 nm) between two linear polarizers.
2.3 Optical characterization of waveplate lenses
Spectra of chromatic LCP waveplate lenses (no axial variation of optical axis orientation) and achromatic LCP waveplate lenses (with double twist axial structure of optical axis orientation) are compared in Fig. 4(a). Zero-order (undiffracted) transmission spectra were measured with Ocean Optics spectrometer model USB-4000, with waveplate lenses placed between circular polarizers. Spectrum for the chromatic waveplate lens corresponds to the half-wave retardation condition being met (minimal transmission) at a wavelength of 633 nm. The achromatic waveplate lens had minimal transmission in a wide spectral range, from 475 to 700 nm.
It has been shown previously that the zero-order leakage through a pair of chromatic anti-symmetric cycloidal gratings is low over a broader wavelength band than is the case for a single cycloidal grating . The zero-order leakage at any given wavelength for two anti-symmetric gratings in succession is the product of the leakages of each of the two gratings, so for example, if the leakage through each grating is 10%, the leakage through two gratings in succession would be 1%. We have observed this same phenomenon in pairs of anti-symmetric waveplate lenses, as illustrated in Fig. 4(b). According to this figure, the observed width of the wavelength band over which the zero-order leakage is less than 1% is 6 times greater for the pair of anti-symmetric waveplate lenses than for the single waveplate lens.
The zero-order leakage obtained with two distinctly different types of broadband waveplate lenses are shown in Fig. 4(a) and 4(b). The data of Fig. 4(a) is for a single “achromatic” lens with the double-twist axial structure of the optical axis orientation for which broadband operation was previously demonstrated in cycloidal  and vector vortex [15,17] devices. The data of Fig. 4(b) is for two “chromatic” lenses in succession with no axial structure in the optical axis orientation, previously described for cycloidal devices . The choice of which of these devices to use in applications requiring a broader bandwidth than is obtainable with a single “chromatic” waveplate lens is complex, depending on many factors. In general, in applications in which low zero-order leakage is a primary requirement, two “chromatic” waveplate lenses may be the simplest and most cost-effective approach. In applications in which high efficiency in the diffracted component is of primary importance, a single “achromatic” waveplate lens is likely to be the best choice.
Properties of chromatic and achromatic waveplate lenses, with retardation optimized for high first-order diffraction efficiency at 633 nm, were compared using various probe beams, including a collimated white light source, an expanded and collimated HeNe laser beam at a wavelength of 633 nm, and expanded/collimated argon ion laser beams at wavelengths of 457, 488 and 514 nm. The comparison is illustrated in Fig. 5. The probe beams passed through the waveplate lens and were focused or defocused onto a diffusely-reflecting screen, depending on circularity of the incident beam polarization. The polarization of the probe beams was switched from right-hand circular polarization (RHCP) to left-hand circular polarization (LHCP) by rotating a quarter-wave plate (QWP).
Photos in column (a) of Fig. 5 show only the incident probe beam on the screen, without any lens in place. Photos in columns (b) and (d) are with an RHCP incident beam, and photos in columns (c) and (e) are with an LHCP incident beam. For columns (b) and (c), a chromatic LCP lens was placed in the beam. For columns (d) and (e), an achromatic lens with the same focal length was placed in the beam.
In columns (b) through (e) of Fig. 5, the zero-order leakage through the lens produces a round laser spot with essentially the same diameter as the spot shown in column (a) without any lens in place. The screen was placed near the focal point of the lenses for 633 nm wavelength. The first-order diffracted beams from the lenses produce spots larger than the incident beam for the defocused component, and smaller than the incident beam for the focused component.
When the laser beam was RHCP, the waveplate lenses had a positive focal length, as if they were convex (CX) refractive lenses, and therefore converged the collimated input beam. When the laser beam was LHCP, waveplate lenses were switched to having a negative focal length, as if they were concave (CV) refractive lenses, therefore diverging the collimated input beam. Focal length of the lens was switched from F + = 316 mm to F - = −316 mm (at λ = 633 nm) by switching the circular polarization of the probe beam.
The relationship between paraxial focal length F, grating period Λ at the edge of the lens, wavelength λ and lens diameter D can be calculated taking into account the Bragg diffraction condition: F = ΛD/2λ. For a waveplate lens of diameter D = 20 mm and grating period Λ = 20 μm at the edge of the lens, Fig. 6 shows the measured and calculated dependence of focal length on wavelength.
The diffraction efficiency of the achromatic LCP waveplate lens used for the measurements of Fig. 5 and Fig. 6 was measured at 633, 514, 488 and 457 nm wavelengths. The waveplate lens was probed with a small-diameter collimated laser beam incident near the edge of the lens. After passing through the edge of the lens, the beam was incident on a diffusely-scattering screen, and the screen was photographed as shown in Fig. 7. For RHCP incident light the beam was focused, and for LHCP incident light the beam was defocused.
By using an aperture, the focused beam shown in Fig. 7 was selected, and its power was measured, as illustrated in Fig. 8. The optical power at the input to the lens was also measured, and the ratio of transmitted optical power to the input optical power was computed for each of the four noted wavelengths, as a function of the angular setting of the QWP through which the incident beam was transmitted. This QWP was rotated from −45°, at which the transmitted light was RHCP, to + 45°, at which the transmitted light was LHCP.
Values of maximum and minimum transmission over angle measured as described above and their ratio, referred to here as contrast ratio, and the transmission of the zeroth order beam are listed in Table 1 for the same achromatic LCP waveplate lens.
Transmission decrease for blue wavelengths indicated in Fig. 8 was due to absorption by photoalignment material. At 633 nm wavelength, the total optical loss of 9% through the waveplate lens is likely dominated by Fresnel reflection losses at the input and output surfaces of the lens. Contrast ratio was lower for green wavelength 514 nm than for wavelength 488 nm due to slightly greater zero-order leakage at green wavelengths. This effect may be attributable to deviation of the twist angle (i.e. the total axial variation of azimuthal orientation of the optical axis in each of the two layers of the LCP coating) from the optimal twist angle of 70°. The sensitivity of zero-order leakage to the twist angle in the LCP coating is illustrated in Fig. 9. This figure shows both measured leakage through an LCP lens, and modeled leakage for two different assumed twist angles. The model is based on the methods of reference  and accounts for the measured dispersion of the birefringence of the LCP. As shown in this figure, even a 2° deviation of the twist angle in the as-built LCP coating from the target angle is predicted to result in a significant change in the dependence of leakage on wavelength, which would be expected to result in variations in the contrast that are not monotonically dependent on wavelength, as is the case with the data reported in Table 1.
Figure 10 shows photos of an achromatic LCP waveplate lens with a diameter of 12 mm, optimized for operation in the near IR spectral region, and also shows the measured zero-order leakage as a function of wavelength for this lens. The grating period on the edge of this lens was 52 µm. The focal length at a wavelength of 785 nm was measured to be 397 mm. As indicated in Fig. 10(e), the measured zero-order leakage for this lens was below 2% over a wavelength range of at least 650 nm to 1000 nm immediately after fabrication. However, Fig. 10(e) shows that this leakage increased for by a few percent over a period of 26 months after fabrication. It is possible that such changes with time in the optical properties of LCP materials may be due to incomplete polymerization.
The research in flat lenses has been active for many years now for numerous applications. Apart from a large variety of liquid crystal based lenses exploring conventional phase modulation, see for example a sampling of references [32–35] and references therein, there have been many recent approaches based on advanced technologies and materials [36–43]. None of those technologies offer the opportunity of inexpensive fabrication and has the scaling up capabilities of diffractive waveplate lens technology discussed here.
Thus the promise of diffractive waveplate devices with complex patterns is being fulfilled as the required materials and methods mature. We had previously fabricated achromatic waveplate cycloidal and vector vortex gratings, and in this work we have described the extension of this technology to waveplate lenses. The main value of having available the new techniques reported here is that these new techniques make it possible to employ waveplate lenses in applications requiring broader spectral coverage than can be achieved with waveplate lenses having the structures reported previously. These advancements bring closer the day when such lenses will be considered a superior alternative in some applications to approaches employing conventional mirrors and lenses. In other future advancements, it seems certain that this technology will enable applications that would have been considered impossible to implement using such conventional components.
This work was supported by the US Army Natick Soldier Research, Development and Engineering Center and the NASA Innovative Advanced Concepts (NIAC) program office. We thank E. Serabyn, U. Hrozhyk, H. Xianyu, and L. Wickboldt for discussions and assistance.
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