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Liquid crystal polarization gratings exhibit high diffraction efficiency (~ 100%) in thin material layers comparable to the radiation wavelength. We demonstrate that they can be combined for polarization-insensitive imaging and optical switching applications. A pair of closely spaced, parallel oriented, cycloidal polarization gratings is capable of canceling the diffractive property of an individual grating. As a result, the phase of the beam is not distorted, and holographic images can be formed through them. An anti-parallel arrangement results in a broader effective diffraction band and doubles the diffraction angle. Broadband diffraction spanning from 480 nm to beyond 900 nm wavelengths has been obtained for a pair of gratings with 500 nm and 633 nm peak diffraction wavelengths. Liquid crystal polymer cycloidal gratings were used in the study showing 98% diffraction efficiency over a large area, and allowed for the use of laser beams expanded to 25 mm. The characteristics of combined cycloidal gratings were tested with laser beams at both UV and red wavelengths.
©2009 Optical Society of America
1. Introduction
High transmission is a key requirement for most electro-optical and nonlinear optical systems. However, materials possessing the highest electro-optical and nonlinear optical constants are liquid crystalline and, due to their strong birefringence, their optical properties are polarization selective. Polarizers are therefore an essential component of liquid crystal (LC) based optical modulators, absorbing more than half of the beam energy and reducing the transmission to levels unacceptable for some applications. For nonlinear optical applications, reduced light energy levels that reach the nonlinear optical material, due to losses at the input polarizer, result in lower sensitivity of the optical system. This is a particularly substantial drawback when there are no focal planes in the path of the light beam.
Combining the unique light modulating capabilities of LCs with a polarization insensitive functionality is a very attractive task. In some cases, two LC cells can be combined with their optical axes perpendicular to each other to obtain polarization insensitive phase modulation [1,2]. Such an approach does not provide a solution when high contrast switching of the transmission state is required. As an alternative, techniques for converting unpolarized light into polarized light with high efficiency have been suggested for improving transmission and switching characteristics of LC displays [3–5].
A breakthrough approach for polarization insensitive LC display applications based on polarization gratings has been disclosed [6–8]. Such gratings are characterized by 100% diffraction efficiency for the 0th order beam (transmitted beam) independent of the polarization state of the incident radiation [9]. Electrically switching a LC polarization grating to a homeotropic orientation would eliminate the diffraction, resulting in 100% transmission, Fig. 1. This concept is presently being intensely explored for electro-optical switching applications including LC displays [10–14].
Fig. 1. (a) A polarization grating diffracting an incident unpolarized beam into ±1st order beam. (b) Transformation of the grating into a homeotropic aligned LC cell due to electro-optical or nonlinear optical processes switches off the diffraction and restores normal propagation of the incident beam.
Switching between a “cycloidal” and a homeotropic orientation of LC molecules can also be induced by a laser beam using surface command layers [15–17]. Changing boundary conditions affect the grating properties within time scales determined by the LC cell thickness (~ 1 ms for a 1 μm thick layer) and do not take advantage of typically orders of magnitude higher speed of optically induced molecular processes. Polarization gratings based on nonlinear optical materials, particularly azobenzene LCs (azo LCs) [18,19], may offer more opportunities for optically controlled diffraction. Optical anisotropy of azo LCs can be efficiently controlled and even eliminated by low power light beams thus changing the spectrum or ultimately switching the diffraction of polarization gratings.
In the present paper, we pay attention to a system of polarization gratings and demonstrate the feasibility of combining them for polarization-insensitive imaging and optical switching applications.
2. Opportunities provided by LC polarization gratings
Figure 2 shows the alignment of LC molecules in cycloidal polarization gratings [20,21]. The LC orientation rotates in a transverse direction (x-axis) in the grating plane. The possibility of two rotation signs, α = ±(2π/Λ)x (where Λ is the rotation period) results in two types of cycloidal gratings. Since a grating of one sign is transformed into another by 180° rotation around the normal to the grating plane as well as around the grating axis, the geometrical configuration of a cycloidal grating can conveniently be designated by a “momentum” vector m = (q×n) in the grating plane (with q being the grating vector and n − the normal to the grating plane). The sign of the vector m determines the specifics of the diffractive properties of gratings for different signs of circular polarized beams, as shown in Fig. 2 for a number of basic geometries.
Fig. 2. Schematic presentation of cycloidal polarization gratings of opposite signs of the “momentum” vector m. The gratings are in the (x,y) plane. The orientation of LC molecules changes periodically along the x-axis by rotating the molecules in the grating plane as shown by circled vectors. Solid black and open arrows represent right and left circular polarized beams, correspondingly. The subscripts indicate the sign of propagation/diffraction angle.
Figure 3 illustrates the diffractive properties of a system of two cycloidal gratings. An unpolarized beam incident at the first grating is split into two circularly polarized beams of opposite sign at its output. In the case where the gratings have the same sign or orientation, each of these beams further diffracts on the second grating restoring the propagation direction of the incident light; however, the beams undergo a transverse shift of the opposite sign. The magnitude of the shift ∆x depends on the distance between the gratings ∆z; decreasing with decreasing separation between them: ∆x = 2∆ztanα, where α is the diffraction angle. Note that even for a rather large diffraction angle, α ~ 45°, the thinness of the gratings allows for the reduction of the distance between the diffracted beams to ~ 1 μm, resulting in negligibly small (for imaging purposes) separation between them.
Fig. 3. Diffraction cancellation in a system of two cycloidal gratings of the same sign: black and white arrows correspond to right and left circular polarization components in the incident unpolarized light; ∆x is the shift between the beams of opposite polarization states at the output of the grating system; ∆z is the distance between the gratings.
Thus, two cycloidal polarization gratings, each about 1 μm-thick, can be paired in a manner that they form a transparent planar optical window. No image blurring, no dispersive coloring, and no multiple images affect viewing through such a system of polarization gratings. Note that any combination of conventional phase gratings would distort images due to dispersion, multiple diffraction orders, light scattering, and high angular and wavelength selectivity. If one of the cycloidal gratings in such a pair is made of electrically or optically switchable material and its diffractive property is switched off with the aid of electric fields or light beams, the remaining grating in the pair would diffract the unpolarized incident light into ±1 diffraction orders, Fig. 4. High diffraction efficiency of cycloidal gratings over a wide spectral and angular range enables switching between the “normally” transmissive and diffractive states over a wide spectral band and wide range of viewing angles.
Fig. 4. Schematic of the diffraction switching concept using a pair of “cycloidal” gratings: (a) the gratings are combined in such a way that the second grating restores the propagation direction of the beam diffracted on the first grating; (b) the diffractive property of one of the gratings is switched off, and the remaining grating diffracts the incident beam away from the sensor.
Below we present the results of a study of the diffraction properties of a pair of cycloidal gratings at UV and visible wavelengths. We show the feasibility of imaging through such gratings without distortions for a diffraction canceling configuration where both gratings are parallel oriented. We also show a considerable broadening effect of the diffraction spectrum when the gratings are combined in an anti-parallel orientation. The latter situation was studied in details in a recent paper [22] by producing two overlaying gratings separated by a chiral layer to optimize for achromatic diffraction [23].
3. Experimental
3.1. Fabrication and characterization of the cycloidal gratings
LC polymer cycloidal gratings used in these tests were fabricated with the aid of a photoalignment technique [17,23,24]. The photoalignment layer, ROP-108, was spin-coated onto glass substrates at 3000 rpm for 60 s followed by baking in an oven at 100°C for 10 min to evaporate the residual solvent. It was then illuminated for 10 min with a cycloidal polarization pattern obtained by interfering He-Cd laser beams of 325 nm wavelength. The substrates were further spin-coated with LC prepolymer (LCP) ROF-5102/30CP (Rolic) at 1000 rpm for 60 s, and polymerized in a nitrogen atmosphere with unpolarized UV light (λ = 365 nm) for 10 min. A single grating layer thus obtained exhibits a peak diffraction wavelength at 400 nm. Adding the second LCP layer in a similar process shifts the peak wavelength to 633 nm. Gratings with a peak diffraction wavelength in the UV, 320 nm, were obtained with higher spin coating speeds, 5000 rpm, with all other conditions being the same.
3.2. Diffraction cancellation
The diffraction patterns for UV beams produced with different combinations of single-layer cycloidal gratings are shown in Fig. 5. A parallel combination of gratings results in the overlap of the diffracted beams, whereas anti-parallel gratings double the diffraction angle.
Fig. 5. Demonstration of diffractive properties of a single and a pair of cycloidal gratings of 325 nm peak diffraction wavelength. The gratings are marked with plus/minus signs on their surfaces. An anti-parallel pair of gratings doubles the diffraction angle. The diffraction is cancelled for light propagation through a parallel grating pair.
The distance between the diffracted beams increases with increasing distance between the gratings in a linear fashion for relatively large distances, Fig. 6. The angle between the gratings is as important as the distance between them for a good overlap of the diffracted beams. Angular misalignment results in out-of-plane separation between the diffracted beams. In Fig. 7 we show the diffraction patterns obtained when rotating one of the gratings around a normal to the grating plane. The separation reaches a maximum at 180° rotation, corresponding to reversal of the sign of the grating momentum vector.
Fig. 6. (a) Separation between the beams of a linearly polarized He-Cd laser (λ = 325 nm) diffracted by a pair of parallel cycloidal gratings as a function of distance between the gratings. (b) Photos correspond to different distances. Photos were captured at 45 cm from the input grating. The beam spot size is 25 mm.
Fig. 7. (a) Separation between the beams of a linearly polarized He-Cd laser (λ = 325 nm) diffracted by a pair of parallel cycloidal gratings as a function of the angle between the gratings. (b) Photos correspond to different angles.
Similar results were obtained for a He-Ne laser beam. Figures 8 and 9 correspond to a beam expanded to 25 mm in diameter. In order to qualitatively demonstrate the change in the intensity of the transmitted beam when removing one of the gratings, we show in Fig. 10 the diffraction patterns for a single and paired gratings obtained with higher power density beams that saturated the CCD. The gratings exhibited high diffraction efficiency, 98% for unpolarized incident light, over practically the entire area of the 1 inch diameter spot. The transmission of the grating pair in a diffraction canceling configuration was 97 %. Removing one of the gratings resulted in a decrease of over 600 times in the power of the transmitted beam due to diffraction at the second grating.
Fig. 8. Diffraction patterns of a linearly poralized He-Ne laser beam for (a) single grating; (b) pair of parallel gratings; (c) pair of anti-parallel gratings.
Fig. 9. Diffraction patterns of a He-Ne laser beam for a pair of polymer gratings at different angles of rotation of the first grating with respect to the second one.
Fig. 10. Diffraction photos (a) for a single grating and (b) for a grating pair in a diffraction canceling configuration using a laser beam. The high power density saturated the CCD to reveal all diffracted beams.
4. Spectra of a pair of cycloidal gratings
Cycloidal gratings can be characterized by their transmission spectra, as obtained with a fiber optic spectrometer. Since the diffracted light does not fully enter the light collecting fiber of the spectrometer, and the LCP is transparent from UV to near IR wavelengths, lower transmission regions observed in their spectra correspond to higher diffraction efficiency. Figure 11 shows the spectra for different combinations of two gratings for which the peak diffraction wavelength is 633 nm. Note that the spectra of both gratings are practically identical. The transmission is high in a spectral band of over 60 nm in the diffraction-canceling geometry corresponding to less than 2% diffraction efficiency. The transmission is low; hence, high diffraction efficiency is obtained, when the orientation vectors of the gratings are anti-parallel.
Fig. 11. Transmission spectra of single gratings with 633 nm peak diffraction wavelength and the grating pair at different configurations: 1 and 2 single gratings of opposite signs; 3 pair of parallel gratings; 4 pair of anti-parallel gratings.
Spectra of combined gratings of different peak wavelengths are shown in Figs. 12 and 13. Substantial diffraction canceling for a grating pair of 450 nm and 633 nm peak wavelengths is achieved at around 550 nm. Gratings of 500 nm and 633 nm peak diffraction wavelengths result in good cancellation at around 500 nm wavelength.
Fig. 12. Transmission spectra of a single grating with 450 nm peak wavelength (1) and its combination with a grating of 633 nm peak wavelength at different configurations: 2, parallel; 3, anti-parallel.
Fig. 13. Transmission spectra of a single grating with 500 nm peak wavelength (1) and its combination with a grating of 633 nm peak wavelength at different configurations: 2, parallel; 3, anti-parallel.
Figures 11–13 reveal considerable broadening of the spectral range of high diffraction efficiency (low transmission) for anti-parallel grating pairs. For the case of two gratings with peak diffraction wavelength of the individual gratings at 633 nm, the spectral range of diffraction is broadened to 240 nm, with higher than 98% efficiency, Fig. 11. An anti-parallel combination, consisting of a grating pair with 633 nm and 500 nm peak wavelengths, results in a high diffraction region (~ 95%) extending from 480 nm to beyond 900 nm, Fig. 13.
5. Summary
Images obtained through a pair of cycloidal gratings at different combination conditions are shown in Fig. 14 and Fig. 15. No coloring or blurring of the image is observed for the diffraction canceling condition. Figure 15 corresponds to an image obtained when propagating a laser beam through a holographic phase plate. Perfect overlap of the two diffraction patterns proves that in the geometry of diffraction canceling no distortions are introduced in the phase of the beam as well.
Fig. 14. Photos of an image taken through a pair of cycloidal gratings (a) at different alignment conditions and (b) at different distance between parallel gratings.
Fig. 15. Diffraction of a red beam of a laser pointer propagated through a holographic phase plate. Photos are taken for different angles between parallel gratings.
Thus, in the present paper, we showed that two high efficiency diffraction gratings can be combined to cancel the diffraction, just as a complementary pair of plano-concave and planoconvex lenses or two rectangular prisms can be combined into a planar optical window that does not affect the beam propagated through them. Unlike those optical components, the gratings under discussion are only micrometers in thickness and can readily be made switchable electrically and optically. Holographic polymer-dispersed-LCs [25,26] and so-called “swinging nematics” [27,28] also provide the opportunity of electrical or optical switching for an unpolarized light, however, high diffraction efficiency obtained in a thin layer of polarization grating is characterized by wider spectral and angular diffraction bandwidth. The opportunity of obtaining high diffraction efficiency in thin films is particularly valuable for optically controlled systems since the spectra of nonlinear optical or photosensitive materials typically possess with strong absorption bands. While this is not an issue for electro-optical processes, it may present a substantial drawback for applications in high power light beams [29].
Combined polarization gratings can be used for a variety of optical modulation purposes, including electro-optical and nonlinear optical switching and spectral tuning, beam steering, phase and polarization modulation. The switching and diffractive properties of the system discussed in this paper can be optimized or further enhanced for specific applications by complex combinations of polarization gratings and their pairs. Studies detailing the exploration of such opportunities will be reported elsewhere.
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