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From Cartesian to polar: a new POLICRYPS geometry for realizing circular optical diffraction gratings Domenico Alj, Roberto Caputo,* and Cesare Umeton Department of Physics and Centre of Excellence for Innovative Functional Materials University of Calabria and CNR-IPCF UOS, Cosenza- 87036, Arcavacata di Rende (CS), Italy *Corresponding author: [email protected] Received August 13, 2014; revised September 27, 2014; accepted September 28, 2014; posted September 29, 2014 (Doc. ID 220989); published October 22, 2014 We report on the realization of a liquid crystal (LC)-based optical diffraction grating showing a polar symmetry of the director alignment. This has been obtained as a natural evolution of the POLICRYPS technique, which enables the realization of highly efficient, switchable, planar diffraction gratings. Performances exhibited in the Cartesian geometry are extended to the polar one by exploiting the spherical aberration produced by simple optical elements. This enables producing the required highly stable polar pattern that allows fabricating a circular optical diffraction grating. Results are promising for their possible application in fields in which a rotational structure of the optical beam is needed. © 2014 Optical Society of America OCIS codes: (090.1970) Diffractive optics; (130.0250) Optoelectronics; (160.3710) Liquid crystals; (310.6845) Thin film devices and applications. http://dx.doi.org/10.1364/OL.39.006201
The possibility of shaping matter by using light is very fascinating. After many years from the first experiments by Margerum et al. [1] for realizing microstructures in polymeric composite materials, the topic is still quite up-to-date. In those experiments, the 1D fringe pattern produced by two interfering laser beams was replicated in a polymer-dispersed-liquid-crystal (PDLC) material to obtain a particular diffraction grating, afterward referred to as HPDLCs [2]. Performances exhibited by HPDLCs were due to the presence of LC droplets encapsulated in the polymeric matrix, which allowed the electric tunability of the optical properties of samples. Despite the extreme variety of structures enabled by that technology (periodic and aperiodic, dimensionality 1D, 2D, and 3D) [3–5] and the high optical performance in terms of diffraction efficiency [6], the success of the HPDLC paradigm was dumped by some intrinsic drawbacks when exploited as transmission diffraction grating. Indeed, if the droplet size is comparable to the wavelength of the impinging light, samples become strongly scattering. To improve their performance, the LC droplet average size was reduced to almost the nanoscale: this allowed low scattering losses and higher diffraction efficiencies. Some new issues, however, appeared: the smaller the size of droplets, the higher the required switching voltages, a circumstance that, in fact, limited the possibility of developing commercial elements [7]. The introduction of POLICRYPS technology [8,9] represented a satisfactory solution of HPDLC drawbacks, since the new system was still tunable, but free of droplets. A homogeneous, well-aligned, LC phase, confined between polymeric slices and not inside droplets, enabled low scattering losses, low switching voltages, and fast response times. Applications proved soon to be not limited to diffraction gratings, but opened a horizon of new devices, designed and realized in the last years, ranging from tunable optical switches, phase modulators [10–12], lasing systems and displays [13–16], to metamaterials [17] and bio-applications [18], whose working principle is always based on the possibility of controlling the birefringence of the system. At present, however, emerging applications in 0146-9592/14/216201-04$15.00/0
optics, like optical manipulation and beam shaping, demand not only, and not much, an active control of the birefringence of the system, but mainly, the capability to locally shape the orientation of its optical axis. A planar slab of uniaxial birefringent medium, able to induce a π phase retardation across the slab (λ∕2 plate), and exhibiting an inhomogeneous orientation of the fast optical axis, lying parallel to the slab plane (indicated in literature as “q-plate”), produces on an impinging wave the interesting effect that not only it emerges circularly polarized (as it would occur with any λ∕2 plate) but, it also acquires a phase factor expilφ (with l 2q integer), i.e., it is transformed into a “helical” wave [19]. In this framework, POLICRYPS technology can assume an interesting role. Since, within a POLICRYPS, the LC director is aligned perpendicularly to the polymeric slices [20], by properly shaping the polymeric structure of the sample, it is possible to locally achieve a particular orientation of its optical axis. De Sio et al. have recently explored the intriguing possibility of realizing curved POLICRYPS structures by replicating the pattern produced by a Fresnel lens in a photosensitive material. It turns out that, in their case, the sample is ring-shaped, and its center presents a circular area of about 1 mm diameter where the LC director is radially oriented [21]. The study is appealing for the possibility to electrically switch the central spot of the sample; this, on the other hand, exhibits a highly irregular distance between its rings, with a lowest value of ≈100 μm, that prevents its exploitation as circular optical diffraction grating. In the present Letter, we show a simple, single-beam, and cost-effective way to commute from the standard Cartesian geometry of the POLICRYPS structure to a polar one with a high-quality morphology. The interest of such a structure is at least two-fold. First of all, it behaves as a circular diffraction grating working in the visible range; to our knowledge, this is the first time that such a result is realized by exploiting holographic means. Moreover, the intrinsic LC director orientation exhibited in all the rings of the sample represents a promising opportunity for realizing optical q-plates and related © 2014 Optical Society of America
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Fig. 1. Optical setup for the visible curing of polar POLICRYPS optical diffraction gratings. Laser, CW solid-state laser; P, Polarizing beam splitter; HWP, λ∕2 plate; OBJ, microscope objective (10×); L1 , L2 , spherical lenses. The sample is put in a hot-stage to control its temperature. In the inset: sketch of the spherical aberration the laser beam undergoes passing through the lens L1 and the ring pattern imaged on a plane perpendicular to the optical axis of the system.
applications. Following some recent preliminary results [22], fabrication of the polar POLICRYPS grating has been performed by exploiting the setup reported in Fig. 1. Power and polarization of the curing beam, from a green laser source, (“Verdi” by Coherent, λ 532 nm), are controlled by a λ∕2 plate and a polarizing beamsplitter. The beam is tightly focused by a microscope objective (10×) to an almost point source of coherent light that, imaged by the lens L1, experiences a spherical aberration. In the longitudinal spherical aberration (LSA) image-space of the lens, a centrosymmetric diffraction pattern is produced, whose center is located on the optical axis of the system (Fig. 1, inset). The produced pattern consists of very closely spaced concentric rings with a typical spacing that can range from few to tens of micrometers, depending on the specific values of involved geometrical parameters. Due to spherical aberration, light rays coming from L1 are not all focused in the same point; marginal rays (passing through the lens in its extreme outer parts) focus closest to the lens, while rays passing through the lens center focus at the most distant point from the lens. The region between these two focal points (Fig. 1, inset) is called LSA region. The presence of a ring pattern is understood by considering that, on a given plane (perpendicular to the optical axis) in the LSA region, light beams come from different annular regions of the lens; therefore, depending on their different optical paths, beams have different converging wavefronts, which may constructively or destructively interfere, thus producing bright and dark rings. A model, based on the diffraction theory of converging waves in presence of spherical aberration, allows to predict the pattern fringe spacing anywhere in the LSA region. The radial distance from the center of the pattern to the nth ring null point is calculated as ρn βn z∕ka, where βn is the nth root of the Bessel function J 0 kaρn ∕z [23], k the wavevector of the impinging light, z the distance, along the optical axis, from lens L1 to the plane containing the considered ring pattern, and a is the radius of the illuminated circular area on the lens surface.
The obtained pattern is focused on the sample surface by the lens L2 , and used to cure a photosensitive mixture. Noteworthy, the size of the pattern can be controlled by properly choosing the focusing power of L2 ; at the same time, periodicity and number of rings can be varied by acting on lens diameter, lens-to-source distance, and viewing conditions. This ample flexibility in the choice of involved geometric parameters makes the proposed technique quite straightforward and easy to implement. Moreover, being the used elements easily available in every optics lab, the technique results also cost-effective. Samples are assembled by putting two glass substrates at a controlled distance (10 μm), to form a cell that is, later on, filled in by capillarity with a photosensitive syrup; this is made of the pre-polymer system NOA61 (70–72% wt, by Norland), the nematic liquid crystal (NLC) E7 (28–30% wt, by Merck) and the photo-initiator Irgacure 784 (1–2% wt, by BASF Resins). The choice of the mixture composition is the result of a study performed to extend the use of the POLICRYPS technology also to systems exploiting visible-light curing [24]. For the fabrication of all samples used in this work, the standard POLICRYPS protocol is followed [8]. Three samples with different number of rings and average pitch values (Λa ≈ 100 μm, Λb ≈ 25 μm, Λc ≈ 5 μm, Fig. 2) have been realized by slightly modifying the setup of Fig. 1, using optical elements (objective, L1 and L2 ) with different magnifications and focal distances, and/or by changing their relative distance. Micrographs of the obtained morphologies (taken between crossed polarizers at the polarized optical microscope, POM) are shown in Fig. 2. A whole view [Fig. 2(a)] of the sample with the largest pitch (Λa ≈ 100 μm) shows a Maltese cross that confirms a uniform (radial or circular) alignment of the LC component in all the circles of the structure. Indeed, between crossed polarizers, a system with a good radial/circular alignment of the LC director exhibits a very high contrast between the bright areas (around the 45° direction where the maximum of intensity is expected) and the dark ones, which are along the polarizer and analyzer directions [11]. In Figs. 2(b) and 2(c), two angular portions of the samples with smaller pitches are reported. A comparison of the three micrographs shows the best LC alignment in the sample with the smallest pitch (Λc ≈ 5 μm). The reason lies in the dynamics of the curing process. According to a previously implemented model [25], a continuous of curing regimes exists, which range from poor to perfect phase separation conditions. In fact, the resulting morphology of the photo-cured structure is affected by the interplay between reactions of polymerization and a mass diffusion process that takes place during curing, and depends, in a quite complex way, on the values assumed by two control parameters: G, related to the curing intensity I, and B, related to the ratio between the diffusion parameter (which depends on temperature T) and Λ2 . Since in our experiments we have fixed both T ≈ 75°C and I (≈1.2 mW∕cm2 ), the only varying parameter is Λ, whose different values determine switching between different curing regimes, that means different realized morphologies. If Λ is small enough, [Λc ≈ 5 μm, Fig. 2(c)], B is quite large, and an almost complete phase separation between polymer and LC components occurs, which produces the best example
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Fig. 2. Micrographs (taken at the POM between crossed polarizers) of the morphologies obtained by exploiting the optical setup in Fig. 1; (a)–(c) polar POLICRYPS structures with different number of rings and pitches, (d) polar POLICRYPS structures obtained by slightly misaligning the setup in Fig. 1, and (e) magnification of the central area of the structure of Fig. 2(d).
of polar POLICRYPS structure. By increasing Λ [Λb ≈ 25 μm, Fig. 2(b)], the resulting decrease of B determines a curing condition that crosses the narrow border between POLICRYPS and HPDLC regimes, and the LC component almost completely nucleates in droplets encapsulated in a polymeric matrix. A further smaller B value (Λa ≈ 100 μm) corresponds to a regime that probably lies in the POLICRYPS region, but very close to the border with the HPDLC area. Figure 2(a) shows, indeed, a morphology that represents an intermediate result between (b) and (c). Looking at the micrograph along the diagonals, a bright region is observed, which indicates that a given amount of well aligned LC has created a separated phase between two consecutive rings. However, a complete phase separation did not occur and a quite large amount of LC remained trapped in droplets in the polymeric rings, which appear, therefore, differently colored. It is worth noting, however, that once the value of the period Λ has been fixed, the resulting morphology is always the same, turning out to be very reproducible. In particular, the morphology of the grating of interest for optical applications [pitch Λc ≈ 5 μm, part (c)] always consists, in all the samples we have fabricated, of rings of pure polymer alternated to rings of pure and well aligned LC. As for the geometry (radial or circular) of the director alignment, available optical techniques are not reliable enough to investigate this aspect, and we believe that a Raman analysis, already performed for Cartesian POLICRYPS gratings [20], would be needed. We underline, however, that the typical LC homeotropic alignment between polymer slices, which is the fingerprint of Cartesian POLICRYPS structures, is due to the interaction of polymeric thiolene systems with LC molecules; in presence of a polar geometry, the same chemical interaction should ensure a radial alignment of the LC director. Indeed, a particular note is due on the micrograph in Fig. 2(d) and its magnification [Fig. 2(e)]. This 2D structure is a replica of the Moiré pattern [23], due to a slight misalignment of L1 and L2 . Even if much more complex than a simple ring pattern,
this structure shows a very nice (radial) LC alignment. Interestingly, the director orientation is visible from the magnification of an area close to the center of symmetry of the structure [Fig. 2(e)]; notwithstanding the complex distribution of the polymer branches, the director tends to orient perpendicularly to the polymeric slices as in Cartesian POLICRYPS structures. Where the optical properties of our samples are concerned, they produce a far-field diffraction pattern given by a series of concentric rings. If this pattern is observed at a distance z from the sample [Fig. 3(a)], the radius r m of the mth ring, as deduced from Bragg’s formula, is derivable from mλ ; Λ p 2 z∕ r m z2 tgθm
(1)
where θm is the diffraction angle of the mth order while λ and Λ are the wavelength of the probe beam and the fringe spacing of the circular structure, respectively. In Fig. 3(b), we show the circular diffraction pattern produced by the sample with Λc ≈ 5 μm, when it is acted on, at normal incidence, by a green laser probe (≈10 μW, solid state laser); the screen is put at z 1 m from the sample. Almost equally spaced diffraction rings are located at a distance r m m5.5 mm 25% from
Fig. 3. (a) Sketch of the diffraction pattern produced by a circular diffraction grating when illuminated with coherent light and (b) picture of the diffraction pattern produced by the polar POLICRYPS probed with green laser light.
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the center, against the predicted value r th m m5.33 mm [Eq. (1)], where the integer m refers to the mth ring. We observe that the intensity of the different diffracted orders decreases by increasing the number of the order. However, as a difference from the Cartesian case, measuring the diffraction efficiency of a given order is now more difficult, the light being diffracted in a ring and no more in a point. An estimate of the first-order diffraction efficiency (performed by means of geometric considerations) has given a value of about 20%. An electro-optical characterization of our samples is actually ongoing and will be the argument of a further publication. However, both energetic considerations and switching values reported for curved POLICRYPS structures of bigger dimensions [21] bring us to predict that quite high values are needed to reorient the LC director in our polar POLICRYPS structures. In conclusion, a simple method for fabricating circular optical diffraction gratings has been developed. The produced diffractive pattern is made of concentric bright rings whose radius can be calculated by using Bragg’s equation. The technique offers freedom in the choice of the fringe spacing, and values in the range 5–100 μm have been achieved. The optical setup for realizing the utilized polar POLICRYPS structures is made of readily available optical elements without need of any customdesigned optical items. Modification of distances between optical elements, or their substitution with other ones with different focal length, can allow controlling the number of annular apertures and their periodicity. Morphology of obtained structures largely depends, however, on their pitch; thus, in case a particular application of polar POLICRYPS has to be designed, the best morphological result, for a given pitch, will correspond to a careful choice of all involved curing parameters. Reported results may extend the large range of applications already demonstrated for Cartesian POLICRYPS. Raman analysis to determine the director orientation in LC rings and measurement of light polarization at different positions around the rings of the diffracted pattern is already going on and represents part of an extensive optical and electro-optical characterization of the new structures. The authors would like to acknowledge the contribution of the COST Action IC1208. www.ic1208.com References 1. J. D. Margerum, A. M. Lackner, E. Ramos, G. W. Smith, N. A. Vaz, J. L. Kohler, and C. R. Allison, “Polymer dispersed
2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22.
23. 24. 25.
liquid crystal film devices,” U.S. patent 5,096,282 (March 17, 1992, filed 1990). A. Y.-G. Fuh, C.-Y. Huang, M.-S. Tsai, J.-M. Chen, and L.-C. Chien, Jpn. J. Appl. Phys. 35, 630 (1996). M. Date, Y. Takeuchi, K. Tanaka, and K. Kato, J. Soc. Inf. Disp. 7, 17 (1999). M. J. Escuti, J. Qi, and G. P. Crawford, Appl. Phys. Lett. 83, 1331 (2003). X. Sun, X. Tao, T. Ye, P. Xue, and Y.-S. Szeto, Appl. Phys. B 87, 267 (2007). R. L. Sutherland, V. P. Tondiglia, L. V. Natarajan, P. F. Lloyd, and T. J. Bunning, Proc. SPIE 7050, 705003 (2008). D. E. Lucchetta, R. Karapinar, A. Manni, and F. Simoni, J. Appl. Phys. 91, 6060 (2002). R. Caputo, L. De Sio, A. V. Sukhov, A. Veltri, and C. Umeton, Opt. Lett. 29, 1261 (2004). R. Caputo, A. V. Sukhov, C. Umeton, and A. Veltri, J. Opt. Soc. Am. B 21, 1939 (2004). L. De Sio, A. Veltri, C. Umeton, S. Serak, and N. Tabiryan, Appl. Phys. Lett. 93, 181115 (2008). L. De Sio, N. Tabiryan, R. Caputo, A. Veltri, and C. Umeton, Opt. Express 16, 7619 (2008). R. Caputo, I. Trebisacce, L. De Sio, and C. Umeton, Opt. Express 18, 5776 (2010). G. Strangi, V. Barna, R. Caputo, A. De Luca, C. Versace, N. Scaramuzza, C. Umeton, and R. Bartolino, Phys. Rev. Lett. 94, 063903 (2005). R. Caputo, L. De Sio, A. Veltri, C. Umeton, and A. V. Sukhov, J. Disp. Tech 2, 38 (2006). L. De Sio, A. Veltri, R. Caputo, A. De Luca, G. Strangi, R. Bartolino, and C. Umeton, Riv. Nuovo Cimento 35, 575 (2012). L. De Sio, A. Veltri, R. Caputo, A. De Luca, G. Strangi, R. Bartolino, and C. Umeton, Liq. Cryst. Rev. 1, 2 (2013). L. De Sio, R. Caputo, U. Cataldi, and C. Umeton, J. Mater. Chem. 21, 18967 (2011). L. De Sio, P. D’Aquila, E. Brunelli, G. Strangi, D. Bellizzi, G. Passarino, C. Umeton, and R. Bartolino, Langmuir 29, 3398 (2013). L. Marrucci, C. Manzo, and D. Paparo, Phys. Rev. Lett. 96, 163905 (2006). M. Castriota, A. Fasanella, E. Cazzanelli, L. De Sio, R. Caputo, and C. Umeton, Opt. Express 19, 10494 (2011). L. De Sio, N. Tabiryan, and T. Bunning, Appl. Phys. Lett. 104, 221112 (2014). D. Alj, R. Caputo, and C. Umeton, “From Cartesian to radial: a new way of writing POLICRYPS,” in Work Group Meeting, COST Action IC 1208, Santarem, Portugal, March 20–21, 2014. R. B. Gwynn and D. A. Christensen, Appl. Opt. 32, 1210 (1993). M. Infusino, A. Ferraro, A. De Luca, R. Caputo, and C. Umeton, J. Opt. Soc. Am. B 29, 3170 (2012). A. Veltri, R. Caputo, C. Umeton, and A. V. Sukhov, Appl. Phys. Lett. 84, 3492 (2004).
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From Cartesian to polar: a new POLICRYPS geometry for realizing circular optical diffraction gratings Domenico Alj, Roberto Caputo,* and Cesare Umeton Department of Physics and Centre of Excellence for Innovative Functional Materials University of Calabria and CNR-IPCF UOS, Cosenza- 87036, Arcavacata di Rende (CS), Italy *Corresponding author: [email protected] Received August 13, 2014; revised September 27, 2014; accepted September 28, 2014; posted September 29, 2014 (Doc. ID 220989); published October 22, 2014 We report on the realization of a liquid crystal (LC)-based optical diffraction grating showing a polar symmetry of the director alignment. This has been obtained as a natural evolution of the POLICRYPS technique, which enables the realization of highly efficient, switchable, planar diffraction gratings. Performances exhibited in the Cartesian geometry are extended to the polar one by exploiting the spherical aberration produced by simple optical elements. This enables producing the required highly stable polar pattern that allows fabricating a circular optical diffraction grating. Results are promising for their possible application in fields in which a rotational structure of the optical beam is needed. © 2014 Optical Society of America OCIS codes: (090.1970) Diffractive optics; (130.0250) Optoelectronics; (160.3710) Liquid crystals; (310.6845) Thin film devices and applications. http://dx.doi.org/10.1364/OL.39.006201
The possibility of shaping matter by using light is very fascinating. After many years from the first experiments by Margerum et al. [1] for realizing microstructures in polymeric composite materials, the topic is still quite up-to-date. In those experiments, the 1D fringe pattern produced by two interfering laser beams was replicated in a polymer-dispersed-liquid-crystal (PDLC) material to obtain a particular diffraction grating, afterward referred to as HPDLCs [2]. Performances exhibited by HPDLCs were due to the presence of LC droplets encapsulated in the polymeric matrix, which allowed the electric tunability of the optical properties of samples. Despite the extreme variety of structures enabled by that technology (periodic and aperiodic, dimensionality 1D, 2D, and 3D) [3–5] and the high optical performance in terms of diffraction efficiency [6], the success of the HPDLC paradigm was dumped by some intrinsic drawbacks when exploited as transmission diffraction grating. Indeed, if the droplet size is comparable to the wavelength of the impinging light, samples become strongly scattering. To improve their performance, the LC droplet average size was reduced to almost the nanoscale: this allowed low scattering losses and higher diffraction efficiencies. Some new issues, however, appeared: the smaller the size of droplets, the higher the required switching voltages, a circumstance that, in fact, limited the possibility of developing commercial elements [7]. The introduction of POLICRYPS technology [8,9] represented a satisfactory solution of HPDLC drawbacks, since the new system was still tunable, but free of droplets. A homogeneous, well-aligned, LC phase, confined between polymeric slices and not inside droplets, enabled low scattering losses, low switching voltages, and fast response times. Applications proved soon to be not limited to diffraction gratings, but opened a horizon of new devices, designed and realized in the last years, ranging from tunable optical switches, phase modulators [10–12], lasing systems and displays [13–16], to metamaterials [17] and bio-applications [18], whose working principle is always based on the possibility of controlling the birefringence of the system. At present, however, emerging applications in 0146-9592/14/216201-04$15.00/0
optics, like optical manipulation and beam shaping, demand not only, and not much, an active control of the birefringence of the system, but mainly, the capability to locally shape the orientation of its optical axis. A planar slab of uniaxial birefringent medium, able to induce a π phase retardation across the slab (λ∕2 plate), and exhibiting an inhomogeneous orientation of the fast optical axis, lying parallel to the slab plane (indicated in literature as “q-plate”), produces on an impinging wave the interesting effect that not only it emerges circularly polarized (as it would occur with any λ∕2 plate) but, it also acquires a phase factor expilφ (with l 2q integer), i.e., it is transformed into a “helical” wave [19]. In this framework, POLICRYPS technology can assume an interesting role. Since, within a POLICRYPS, the LC director is aligned perpendicularly to the polymeric slices [20], by properly shaping the polymeric structure of the sample, it is possible to locally achieve a particular orientation of its optical axis. De Sio et al. have recently explored the intriguing possibility of realizing curved POLICRYPS structures by replicating the pattern produced by a Fresnel lens in a photosensitive material. It turns out that, in their case, the sample is ring-shaped, and its center presents a circular area of about 1 mm diameter where the LC director is radially oriented [21]. The study is appealing for the possibility to electrically switch the central spot of the sample; this, on the other hand, exhibits a highly irregular distance between its rings, with a lowest value of ≈100 μm, that prevents its exploitation as circular optical diffraction grating. In the present Letter, we show a simple, single-beam, and cost-effective way to commute from the standard Cartesian geometry of the POLICRYPS structure to a polar one with a high-quality morphology. The interest of such a structure is at least two-fold. First of all, it behaves as a circular diffraction grating working in the visible range; to our knowledge, this is the first time that such a result is realized by exploiting holographic means. Moreover, the intrinsic LC director orientation exhibited in all the rings of the sample represents a promising opportunity for realizing optical q-plates and related © 2014 Optical Society of America
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Fig. 1. Optical setup for the visible curing of polar POLICRYPS optical diffraction gratings. Laser, CW solid-state laser; P, Polarizing beam splitter; HWP, λ∕2 plate; OBJ, microscope objective (10×); L1 , L2 , spherical lenses. The sample is put in a hot-stage to control its temperature. In the inset: sketch of the spherical aberration the laser beam undergoes passing through the lens L1 and the ring pattern imaged on a plane perpendicular to the optical axis of the system.
applications. Following some recent preliminary results [22], fabrication of the polar POLICRYPS grating has been performed by exploiting the setup reported in Fig. 1. Power and polarization of the curing beam, from a green laser source, (“Verdi” by Coherent, λ 532 nm), are controlled by a λ∕2 plate and a polarizing beamsplitter. The beam is tightly focused by a microscope objective (10×) to an almost point source of coherent light that, imaged by the lens L1, experiences a spherical aberration. In the longitudinal spherical aberration (LSA) image-space of the lens, a centrosymmetric diffraction pattern is produced, whose center is located on the optical axis of the system (Fig. 1, inset). The produced pattern consists of very closely spaced concentric rings with a typical spacing that can range from few to tens of micrometers, depending on the specific values of involved geometrical parameters. Due to spherical aberration, light rays coming from L1 are not all focused in the same point; marginal rays (passing through the lens in its extreme outer parts) focus closest to the lens, while rays passing through the lens center focus at the most distant point from the lens. The region between these two focal points (Fig. 1, inset) is called LSA region. The presence of a ring pattern is understood by considering that, on a given plane (perpendicular to the optical axis) in the LSA region, light beams come from different annular regions of the lens; therefore, depending on their different optical paths, beams have different converging wavefronts, which may constructively or destructively interfere, thus producing bright and dark rings. A model, based on the diffraction theory of converging waves in presence of spherical aberration, allows to predict the pattern fringe spacing anywhere in the LSA region. The radial distance from the center of the pattern to the nth ring null point is calculated as ρn βn z∕ka, where βn is the nth root of the Bessel function J 0 kaρn ∕z [23], k the wavevector of the impinging light, z the distance, along the optical axis, from lens L1 to the plane containing the considered ring pattern, and a is the radius of the illuminated circular area on the lens surface.
The obtained pattern is focused on the sample surface by the lens L2 , and used to cure a photosensitive mixture. Noteworthy, the size of the pattern can be controlled by properly choosing the focusing power of L2 ; at the same time, periodicity and number of rings can be varied by acting on lens diameter, lens-to-source distance, and viewing conditions. This ample flexibility in the choice of involved geometric parameters makes the proposed technique quite straightforward and easy to implement. Moreover, being the used elements easily available in every optics lab, the technique results also cost-effective. Samples are assembled by putting two glass substrates at a controlled distance (10 μm), to form a cell that is, later on, filled in by capillarity with a photosensitive syrup; this is made of the pre-polymer system NOA61 (70–72% wt, by Norland), the nematic liquid crystal (NLC) E7 (28–30% wt, by Merck) and the photo-initiator Irgacure 784 (1–2% wt, by BASF Resins). The choice of the mixture composition is the result of a study performed to extend the use of the POLICRYPS technology also to systems exploiting visible-light curing [24]. For the fabrication of all samples used in this work, the standard POLICRYPS protocol is followed [8]. Three samples with different number of rings and average pitch values (Λa ≈ 100 μm, Λb ≈ 25 μm, Λc ≈ 5 μm, Fig. 2) have been realized by slightly modifying the setup of Fig. 1, using optical elements (objective, L1 and L2 ) with different magnifications and focal distances, and/or by changing their relative distance. Micrographs of the obtained morphologies (taken between crossed polarizers at the polarized optical microscope, POM) are shown in Fig. 2. A whole view [Fig. 2(a)] of the sample with the largest pitch (Λa ≈ 100 μm) shows a Maltese cross that confirms a uniform (radial or circular) alignment of the LC component in all the circles of the structure. Indeed, between crossed polarizers, a system with a good radial/circular alignment of the LC director exhibits a very high contrast between the bright areas (around the 45° direction where the maximum of intensity is expected) and the dark ones, which are along the polarizer and analyzer directions [11]. In Figs. 2(b) and 2(c), two angular portions of the samples with smaller pitches are reported. A comparison of the three micrographs shows the best LC alignment in the sample with the smallest pitch (Λc ≈ 5 μm). The reason lies in the dynamics of the curing process. According to a previously implemented model [25], a continuous of curing regimes exists, which range from poor to perfect phase separation conditions. In fact, the resulting morphology of the photo-cured structure is affected by the interplay between reactions of polymerization and a mass diffusion process that takes place during curing, and depends, in a quite complex way, on the values assumed by two control parameters: G, related to the curing intensity I, and B, related to the ratio between the diffusion parameter (which depends on temperature T) and Λ2 . Since in our experiments we have fixed both T ≈ 75°C and I (≈1.2 mW∕cm2 ), the only varying parameter is Λ, whose different values determine switching between different curing regimes, that means different realized morphologies. If Λ is small enough, [Λc ≈ 5 μm, Fig. 2(c)], B is quite large, and an almost complete phase separation between polymer and LC components occurs, which produces the best example
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Fig. 2. Micrographs (taken at the POM between crossed polarizers) of the morphologies obtained by exploiting the optical setup in Fig. 1; (a)–(c) polar POLICRYPS structures with different number of rings and pitches, (d) polar POLICRYPS structures obtained by slightly misaligning the setup in Fig. 1, and (e) magnification of the central area of the structure of Fig. 2(d).
of polar POLICRYPS structure. By increasing Λ [Λb ≈ 25 μm, Fig. 2(b)], the resulting decrease of B determines a curing condition that crosses the narrow border between POLICRYPS and HPDLC regimes, and the LC component almost completely nucleates in droplets encapsulated in a polymeric matrix. A further smaller B value (Λa ≈ 100 μm) corresponds to a regime that probably lies in the POLICRYPS region, but very close to the border with the HPDLC area. Figure 2(a) shows, indeed, a morphology that represents an intermediate result between (b) and (c). Looking at the micrograph along the diagonals, a bright region is observed, which indicates that a given amount of well aligned LC has created a separated phase between two consecutive rings. However, a complete phase separation did not occur and a quite large amount of LC remained trapped in droplets in the polymeric rings, which appear, therefore, differently colored. It is worth noting, however, that once the value of the period Λ has been fixed, the resulting morphology is always the same, turning out to be very reproducible. In particular, the morphology of the grating of interest for optical applications [pitch Λc ≈ 5 μm, part (c)] always consists, in all the samples we have fabricated, of rings of pure polymer alternated to rings of pure and well aligned LC. As for the geometry (radial or circular) of the director alignment, available optical techniques are not reliable enough to investigate this aspect, and we believe that a Raman analysis, already performed for Cartesian POLICRYPS gratings [20], would be needed. We underline, however, that the typical LC homeotropic alignment between polymer slices, which is the fingerprint of Cartesian POLICRYPS structures, is due to the interaction of polymeric thiolene systems with LC molecules; in presence of a polar geometry, the same chemical interaction should ensure a radial alignment of the LC director. Indeed, a particular note is due on the micrograph in Fig. 2(d) and its magnification [Fig. 2(e)]. This 2D structure is a replica of the Moiré pattern [23], due to a slight misalignment of L1 and L2 . Even if much more complex than a simple ring pattern,
this structure shows a very nice (radial) LC alignment. Interestingly, the director orientation is visible from the magnification of an area close to the center of symmetry of the structure [Fig. 2(e)]; notwithstanding the complex distribution of the polymer branches, the director tends to orient perpendicularly to the polymeric slices as in Cartesian POLICRYPS structures. Where the optical properties of our samples are concerned, they produce a far-field diffraction pattern given by a series of concentric rings. If this pattern is observed at a distance z from the sample [Fig. 3(a)], the radius r m of the mth ring, as deduced from Bragg’s formula, is derivable from mλ ; Λ p 2 z∕ r m z2 tgθm
(1)
where θm is the diffraction angle of the mth order while λ and Λ are the wavelength of the probe beam and the fringe spacing of the circular structure, respectively. In Fig. 3(b), we show the circular diffraction pattern produced by the sample with Λc ≈ 5 μm, when it is acted on, at normal incidence, by a green laser probe (≈10 μW, solid state laser); the screen is put at z 1 m from the sample. Almost equally spaced diffraction rings are located at a distance r m m5.5 mm 25% from
Fig. 3. (a) Sketch of the diffraction pattern produced by a circular diffraction grating when illuminated with coherent light and (b) picture of the diffraction pattern produced by the polar POLICRYPS probed with green laser light.
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the center, against the predicted value r th m m5.33 mm [Eq. (1)], where the integer m refers to the mth ring. We observe that the intensity of the different diffracted orders decreases by increasing the number of the order. However, as a difference from the Cartesian case, measuring the diffraction efficiency of a given order is now more difficult, the light being diffracted in a ring and no more in a point. An estimate of the first-order diffraction efficiency (performed by means of geometric considerations) has given a value of about 20%. An electro-optical characterization of our samples is actually ongoing and will be the argument of a further publication. However, both energetic considerations and switching values reported for curved POLICRYPS structures of bigger dimensions [21] bring us to predict that quite high values are needed to reorient the LC director in our polar POLICRYPS structures. In conclusion, a simple method for fabricating circular optical diffraction gratings has been developed. The produced diffractive pattern is made of concentric bright rings whose radius can be calculated by using Bragg’s equation. The technique offers freedom in the choice of the fringe spacing, and values in the range 5–100 μm have been achieved. The optical setup for realizing the utilized polar POLICRYPS structures is made of readily available optical elements without need of any customdesigned optical items. Modification of distances between optical elements, or their substitution with other ones with different focal length, can allow controlling the number of annular apertures and their periodicity. Morphology of obtained structures largely depends, however, on their pitch; thus, in case a particular application of polar POLICRYPS has to be designed, the best morphological result, for a given pitch, will correspond to a careful choice of all involved curing parameters. Reported results may extend the large range of applications already demonstrated for Cartesian POLICRYPS. Raman analysis to determine the director orientation in LC rings and measurement of light polarization at different positions around the rings of the diffracted pattern is already going on and represents part of an extensive optical and electro-optical characterization of the new structures. The authors would like to acknowledge the contribution of the COST Action IC1208. www.ic1208.com References 1. J. D. Margerum, A. M. Lackner, E. Ramos, G. W. Smith, N. A. Vaz, J. L. Kohler, and C. R. Allison, “Polymer dispersed
2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22.
23. 24. 25.
liquid crystal film devices,” U.S. patent 5,096,282 (March 17, 1992, filed 1990). A. Y.-G. Fuh, C.-Y. Huang, M.-S. Tsai, J.-M. Chen, and L.-C. Chien, Jpn. J. Appl. Phys. 35, 630 (1996). M. Date, Y. Takeuchi, K. Tanaka, and K. Kato, J. Soc. Inf. Disp. 7, 17 (1999). M. J. Escuti, J. Qi, and G. P. Crawford, Appl. Phys. Lett. 83, 1331 (2003). X. Sun, X. Tao, T. Ye, P. Xue, and Y.-S. Szeto, Appl. Phys. B 87, 267 (2007). R. L. Sutherland, V. P. Tondiglia, L. V. Natarajan, P. F. Lloyd, and T. J. Bunning, Proc. SPIE 7050, 705003 (2008). D. E. Lucchetta, R. Karapinar, A. Manni, and F. Simoni, J. Appl. Phys. 91, 6060 (2002). R. Caputo, L. De Sio, A. V. Sukhov, A. Veltri, and C. Umeton, Opt. Lett. 29, 1261 (2004). R. Caputo, A. V. Sukhov, C. Umeton, and A. Veltri, J. Opt. Soc. Am. B 21, 1939 (2004). L. De Sio, A. Veltri, C. Umeton, S. Serak, and N. Tabiryan, Appl. Phys. Lett. 93, 181115 (2008). L. De Sio, N. Tabiryan, R. Caputo, A. Veltri, and C. Umeton, Opt. Express 16, 7619 (2008). R. Caputo, I. Trebisacce, L. De Sio, and C. Umeton, Opt. Express 18, 5776 (2010). G. Strangi, V. Barna, R. Caputo, A. De Luca, C. Versace, N. Scaramuzza, C. Umeton, and R. Bartolino, Phys. Rev. Lett. 94, 063903 (2005). R. Caputo, L. De Sio, A. Veltri, C. Umeton, and A. V. Sukhov, J. Disp. Tech 2, 38 (2006). L. De Sio, A. Veltri, R. Caputo, A. De Luca, G. Strangi, R. Bartolino, and C. Umeton, Riv. Nuovo Cimento 35, 575 (2012). L. De Sio, A. Veltri, R. Caputo, A. De Luca, G. Strangi, R. Bartolino, and C. Umeton, Liq. Cryst. Rev. 1, 2 (2013). L. De Sio, R. Caputo, U. Cataldi, and C. Umeton, J. Mater. Chem. 21, 18967 (2011). L. De Sio, P. D’Aquila, E. Brunelli, G. Strangi, D. Bellizzi, G. Passarino, C. Umeton, and R. Bartolino, Langmuir 29, 3398 (2013). L. Marrucci, C. Manzo, and D. Paparo, Phys. Rev. Lett. 96, 163905 (2006). M. Castriota, A. Fasanella, E. Cazzanelli, L. De Sio, R. Caputo, and C. Umeton, Opt. Express 19, 10494 (2011). L. De Sio, N. Tabiryan, and T. Bunning, Appl. Phys. Lett. 104, 221112 (2014). D. Alj, R. Caputo, and C. Umeton, “From Cartesian to radial: a new way of writing POLICRYPS,” in Work Group Meeting, COST Action IC 1208, Santarem, Portugal, March 20–21, 2014. R. B. Gwynn and D. A. Christensen, Appl. Opt. 32, 1210 (1993). M. Infusino, A. Ferraro, A. De Luca, R. Caputo, and C. Umeton, J. Opt. Soc. Am. B 29, 3170 (2012). A. Veltri, R. Caputo, C. Umeton, and A. V. Sukhov, Appl. Phys. Lett. 84, 3492 (2004).
