Bistable light-driven π phase switching using a twisted nematic liquid crystal film Chun-Wei Chen,1,2 Cheng-Chang Li,1,2 Hung-Chang Jau,1 Chun-Hong Lee,1 Chun-Ta Wang,1 and Tsung-Hsien Lin1,* 1
Department of Photonics, National Sun Yat-Sen University, Kaohsiung, Taiwan 2 Contributed equally to this work *[email protected]
Abstract: A light-activated optical phase switch was developed, exploiting the conversion between left-handed and right-handed twisted nematic liquid crystals. Theoretical and experimental analyses revealed that the handedness inversion of the twisted nematic film altered the optical phase of the output waves by π. Herein, the competition between the helical twisting powers of the two reverse-handed chiral dopants determines the handedness of the twisted nematic film. The photo-responsibility and the bistability are attributed to the azobenzene chromophores in one of the chiral additives. ©2014 Optical Society of America OCIS codes: (120.5060) Phase modulation; (230.1150) All-optical devices; (230.3720) Liquidcrystal devices.
References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.
P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84(2), 268–298 (1996). Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzaka, Y. Kobayashi, and T. Hara, “High Efficiency Electrically-Addressable Phase-Only Spatial Light Modulator,” Opt. Rev. 6(4), 339–344 (1999). Y.-H. Lin, H. Ren, Y.-H. Wu, Y. Zhao, J. Fang, Z. Ge, and S.-T. Wu, “Polarization-independent liquid crystal phase modulator using a thin polymer-separated double-layered structure,” Opt. Express 13(22), 8746–8752 (2005). Y. Huang, C.-H. Wen, and S.-T. Wu, “Polarization-independent and submillisecond response phase modulators using a 90° twisted dual-frequency liquid crystal,” Appl. Phys. Lett. 89(2), 021103 (2006). J. Sun, Y. Chen, and S.-T. Wu, “Submillisecond-response and scattering-free infrared liquid crystal phase modulators,” Opt. Express 20(18), 20124–20129 (2012). X.-W. Lin, W. Hu, X.-K. Hu, X. Liang, Y. Chen, H.-Q. Cui, G. Zhu, J.-N. Li, V. Chigrinov, and Y.-Q. Lu, “Fast response dual-frequency liquid crystal switch with photo-patterned alignments,” Opt. Lett. 37(17), 3627–3629 (2012). Y.-T. Lin, H.-C. Jau, and T.-H. Lin, “Polarization-independent rapidly responding phase grating based on hybrid blue phase liquid crystal,” J. Appl. Phys. 113(6), 063103 (2013). I. Dozov, “26.1: Invited Paper: Bistable Liquid Crystal Technologies,” SID Symp. Dig. Tec. 34, 946–949 (2003). Y. W. Li and H. S. Kwok, “Bistable twisted-bend and twisted-nematic liquid crystal display,” Appl. Phys. Lett. 95(18), 181107 (2009). A. Y.-G. Fuh, J.-T. Chiang, Y.-S. Chien, C.-J. Chang, and H.-C. Lin, “Multistable Phase-Retardation Plate Based on Gelator-Doped Liquid Crystals,” Appl. Phys. Express 5(7), 072503 (2012). J. H. Park, C. J. Yu, J. Kim, S. Y. Chung, and S. D. Lee, “Concept of a liquid-crystal polarization beamsplitter based on binary phase gratings,” Appl. Phys. Lett. 83(10), 1918–1920 (2003). C. H. Gooch and H. A. Tarry, “The optical properties of twisted nematic liquid crystal structures with twist angles ≤90 degrees,” J. Phys. D Appl. Phys. 8(13), 1575–1584 (1975). N. Konforti, E. Marom, and S. T. Wu, “Phase-only modulation with twisted nematic liquid-crystal spatial light modulators,” Opt. Lett. 13(3), 251–253 (1988). U. A. Hrozhyk, S. V. Serak, N. V. Tabiryan, and T. J. Bunning, “Photoinduced Isotropic State of Cholesteric Liquid Crystals: Novel Dynamic Photonic Materials,” Adv. Mater. 19(20), 3244–3247 (2007). H.-C. Jau, K.-T. Cheng, T.-H. Lin, Y.-S. Lo, J.-Y. Chen, C.-W. Hsu, and A. Y.-G. Fuh, “Photo-rewritable flexible LCD using indium zinc oxide/polycarbonate substrates,” Appl. Opt. 50(2), 213–217 (2011).
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Received 31 Mar 2014; revised 4 May 2014; accepted 5 May 2014; published 12 May 2014 19 May 2014 | Vol. 22, No. 10 | DOI:10.1364/OE.22.012133 | OPTICS EXPRESS 12133
16. C.-T. Wang, Y.-C. Wu, and T.-H. Lin, “Photo-switchable bistable twisted nematic liquid crystal optical switch,” Opt. Express 21(4), 4361–4366 (2013). 17. C.-T. Wang, C.-W. Tseng, J.-H. Yu, Y.-C. Li, C.-H. Lee, H.-C. Jau, M.-C. Lee, Y.-J. Chen, and T.-H. Lin, “Optical bistability in a silicon nitride microring resonator with azo dye-doped liquid crystal as cladding material,” Opt. Express 21(9), 10989–10994 (2013). 18. X. J. Yu and H. S. Kwok, “Bistable bend-splay liquid crystal display,” Appl. Phys. Lett. 85(17), 3711–3713 (2004). 19. L. A. Parry-Jones and S. J. Elston, “Flexoelectric switching in a zenithally bistable nematic device,” J. Appl. Phys. 97(9), 093515 (2005). 20. D. H. Song, J. H. Lee, S. J. Lee, S.-i. Kim, S. Lim, S. T. Shin, J. C. Kim, and T.-H. Yoon, “Bistable switching of twist direction in a twisted-nematic liquid crystal cell,” Appl. Phys. Lett. 97(6), 063501 (2010). 21. S.-W. Ke, T.-H. Lin, and A. Y. G. Fuh, “Tunable grating based on stressed liquid crystal,” Opt. Express 16(3), 2062–2067 (2008). 22. S. P. Fletcher, F. Dumur, M. M. Pollard, and B. L. Feringa, “A Reversible, Unidirectional Molecular Rotary Motor Driven by Chemical Energy,” Science 310(5745), 80–82 (2005). 23. C.-H. Lee, C.-W. Wu, C.-W. Chen, H.-C. Jau, and T.-H. Lin, “Polarization-independent bistable light valve in blue phase liquid crystal filled photonic crystal fiber,” Appl. Opt. 52(20), 4849–4853 (2013). 24. P. Yeh and C. Gu, “Jones Matrix Method,” in Optics of liquid crystal displays (Wiley, New York, 1999), pp. 103–160. 25. J. Ma, Y. N. Li, T. White, A. Urbas, and Q. Li, “Light-driven nanoscale chiral molecular switch: reversible dynamic full range color phototuning,” Chem. Commun. (Camb.) 46(20), 3463–3465 (2010). 26. S.-W. Ko, S.-H. Huang, A. Y. G. Fuh, and T.-H. Lin, “Measurement of helical twisting power based on axially symmetrical photo-aligned dye-doped liquid crystal film,” Opt. Express 17(18), 15926–15931 (2009). 27. M. V. Vasnetsov, V. A. Pas’ko, and D. S. Kasyanyuk, “Observation of polarization conflict caused by geometrical phase in a twisted nematic liquid crystal cell,” Opt. Lett. 36(11), 2134–2136 (2011).
1. Introduction Phase-only modulation is adopted in various optical applications, including spatial light modulators, beam steering and optical cross-connect switches [1, 2]. Liquid crystalline materials are commonly used to develop phase modulators because of their extraordinarily large birefringence and susceptibility of director-axis reorientation by external stimuli. Nowadays, most effort in the field is made to speed up the response and achieve polarizationindependent modulation [3–7]. However, for long-term single-state applications, bi- or multistability is essential to reducing power consumption and preventing the effects of some instabilities of the power supply [8–10]; in addition, a phase shift of π is desirable. For instance, a phase difference of π maximizes the highest diffraction efficiency of a typical phase grating [11]. Therefore, in this letter, a bistable π phase switch has been designed to meet the two needs. The proposed device is generally based on a twisted nematic (TN) film that can be converted between reverse handedness states, levorotation and dextrorotation, by illuminating with visible light. TN-based modulators are attractive for their wavelength- and polarizationindependence when satisfying the Mauguin condition [12, 13]. Furthermore, their insensitivity to cell-gap variations reduces the required manufacturing accuracy. Photoswitchability arises from the addition of azobenzene molecules. Switches that can be operated by light [14–17] support easier device design, local addressing and tether-free control than those driven by an electric field [8, 18–20], mechanical stress [21], chemical reaction [22] or heat [23]. The following sections present the operating mechanism, a theoretical explanation of the procedures for fabricating and experimental results concerning such switches. 2. Theoretical description The proposed device can be optically switched between left-handed and right-handed twisted nematic states. To verify theoretically that this device can be employed as a zero-to-π phase modulator, the concept is tested using Jones calculus. The following concerns a TN film of thickness d, a total twist angle φ and a uniaxial liquid crystal with an ordinary refractive index no and an extraordinary refractive index ne. Treating the TN film as a stack of planar-aligned nematic layers with different azimuth angles yields the following Jones matrix [24],
#209308 - $15.00 USD (C) 2014 OSA
Received 31 Mar 2014; revised 4 May 2014; accepted 5 May 2014; published 12 May 2014 19 May 2014 | Vol. 22, No. 10 | DOI:10.1364/OE.22.012133 | OPTICS EXPRESS 12134
cos φ M = sin φ
Γ sin X cos X − i − sin φ 2 X cos φ sin X −φ X
sin X X Γ sin X cos X + i 2 X
φ
,
(1)
where Г is the phase retardation of the untwisted film, and X is a substitution term,
Γ=
2π
λ
⋅ d ⋅ ( ne − no ) =
2
2π
Γ ⋅ d ⋅ Δn ; X = φ 2 + . λ 2
(2)
When a horizontally polarized plane wave enters a + 90° TN film, the polarization state of the output wave can be written as the following Jones vector, sin X φ X E out ,+90° = M ⋅ E in = cos X − i Γ sin X 2 X
.
(3)
If the film satisfies the Mauguin condition (Δn·d ? λ), which is equivalent to φ = Г, then X is approximately a half of Г and the upper element of the vector is close to zero. The output polarization state at the point at which the waves leaves the film can be derived as, sin ( Γ / 2 ) φ 0 E out ,+90° = ( Γ / 2) = exp ( −iΓ / 2 ) 1 , cos ( Γ / 2 ) − i sin ( Γ / 2 )
(4)
which describes vertically polarized light whose phase is determined by film thickness, birefringence and probe wavelength. Now, if the film is flipped into the opposite handedness mode (−90°), the output polarization state will be transformed into,
0 E out ,−90° = exp ( −i Γ / 2 ) . −1
(5)
From the resulting Jones vectors, the output waves have the same polarization and amplitude but are “out of phase”, corresponding to a phase difference of π. To elucidate schematically the operation of the device, Fig. 1 simply illustrates π phase switching. When horizontally polarized light enters a 90° TN film, its polarization rotates along the liquid crystal director until the light is vertically polarized. If the TN film is left-handed, then at the output point “o”, the electric field ( E ) oscillation is assumed to begin from zero in the positive y direction [Fig. 1(a)]. On the contrary, if the film is right-handed, then the electric field points in the negative y direction [Fig. 1(b)]. As the device is converted from one state to the other, the phase is shifted by π. In terms of the twist angle, such π phase switching is not limited to a 90° TN. It can be set to any angle except 0° and other integral multiples of 180°.
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Received 31 Mar 2014; revised 4 May 2014; accepted 5 May 2014; published 12 May 2014 19 May 2014 | Vol. 22, No. 10 | DOI:10.1364/OE.22.012133 | OPTICS EXPRESS 12135
Fig. 1. Schematic π phase switching using an optically responsive twisted nematic film.
3. Device fabrication
To realize the above concept, a photo-responsive liquid crystal (PRLC), formulated by blending chiral agents, 0.1755 wt% R-811 (Merck) and 0.1245 wt% ChAD-3C-S (BEAM), into a nematic host E7 (Merck), was capillary-filled into a 12 μm-thick sandwich cell with two perpendicularly rubbed polyimide layers. Chiral additives were used to select the handedness of the whole TN film. R-811 is a static right-handed chiral dopant with a Helical Twisting Power (HTP) of ~10.8 μm−1; by contrast, ChAD-3C-S is a left-handed chiral bis(azobenzene) dye, whose HTP can be modulated by light [16, 25]. Doping ChAD-3C-S into E7 yielded an initial HTP value of −42.6 μm−1; that of the green light stationary state (λ = 532 nm) was −30.7 μm−1. Under irradiation by violet light (λ = 411 nm), the trans-cis isomerization reduced the chirality of the liquid crystal. Hence, the HTP dropped to almost nil, making it achiral nematic. Notably, both photo-stationary states were nonvolatile upon the removal of illumination. The concentrations of the chiral additives were consistent with the following conditions: Green Green PChAD = ( HTPChAD ⋅ CChAD ) −1 < ( HTPR-811 ⋅ CR-811 ) −1 = PR-811 ;
(6)
Violet Violet PChAD = ( HTPChAD ⋅ CChAD ) −1 > ( HTPR-811 ⋅ CR-811 ) −1 = PR-811 ;
(7)
Green Green PPRLC = ( HTPChAD ⋅ CChAD − HTPR-811 ⋅ CR-811 ) −1 > 4d ;
(8)
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Received 31 Mar 2014; revised 4 May 2014; accepted 5 May 2014; published 12 May 2014 19 May 2014 | Vol. 22, No. 10 | DOI:10.1364/OE.22.012133 | OPTICS EXPRESS 12136
Violet Violet PPRLC = ( HTPR-811 ⋅ CR-811 − HTPChAD ⋅ CChAD ) −1 > 4d ,
(9)
where P denotes the pitch length; C is the fraction of the chiral dopant and d represents the film thickness; the superscript identifies the color of the pump laser, while the subscript specifies which chiral agent(s) was/were contained. The former two terms ensure that the handedness can be converted. The nematic liquid crystal could not be twisted by more than 90° when the latter two requirements were fulfilled. 4. Experimental verification and discussion
Firstly, the TN film was examined under a polarizing optical microscope (POM) to confirm the general polarization rotation effect. Figure 2 indicates that, under crossed polarizers, both the left- and right-handed modes were highly see-through, whereas the light was almost completely blocked when the polarizer was parallel to the analyzer. The slight difference in transmittance was possibly attributable to the fact that the included angle between the two polarizers was not an exact right angle and the limitation on d·Δn/λ prevent the complete satisfaction of the Mauguin condition. The defect line reveals that the twist angle varied in an abrupt and discontinuous manner owing to the boundary conditions [26, 27]. This feature is of crucial importance for designing hitless switches in optical communications. With respect to the response of the device, the handedness inversion under exposure to violet light (λ = 411 nm, I = 30 mW/cm2) and green light (λ = 532 nm, I = 90 mW/cm2) took less than half a second. Since the trans-isomers are steadier than the cis-, the left-handed TN could last for weeks without any external stimuli; still, the right-handed state could be retained for at least two hours after ten minutes violet illumination. The response rate, stability and reliability of the optical switch are believed to be able to be further improved by lowering the HTP value of the azobenzene dopant to increase the dosage.
Fig. 2. POM images of (a) left-handed state, (b) transformation of states and (c) right-handed state under crossed and parallel polarizers.
Since a phase difference of π exists between the two TN modes, the phenomenon can be easily monitored by interferometry. The sample was set on one arm of the Mach-Zehnder interferometer; and, a half-wave plate was placed on the other to enable the polarization of the two probe beams in identical directions. Upon exposure to the green laser for a period of ten minutes, the TN film entered the left-handed photo-stationary state and exhibited line fringes, as displayed in Fig. 3(a). To switch it into the right-handed state, the film was subsequently irradiated by a violet laser. The original fringes were soon covered by an “inverse” interference pattern. Figure 3(b) demonstrates that the position of the new (converted) dark #209308 - $15.00 USD (C) 2014 OSA
Received 31 Mar 2014; revised 4 May 2014; accepted 5 May 2014; published 12 May 2014 19 May 2014 | Vol. 22, No. 10 | DOI:10.1364/OE.22.012133 | OPTICS EXPRESS 12137
fringes matched that of the former bright fringes because the phase differed by π. Within a second, the sample completely transitioned from the counterclockwise to the clockwise TN state, as presented in Fig. 3(c). Further illuminating the device with a green laser put it back into the left-handed state. Figure 3(d) compares the intensity distribution of the interference pattern in the right-handed mode to that of the levorotary TN. Evidently, the two TN states are perfectly out of phase with each other.
Fig. 3. Photographs of interference patterns at (a) left-handed state, (b) transformation of states and (c) right-handed state, corresponding to (d) intensity distribution in cross-section (axis x).
5. Conclusion
In summary, a bistable phase switch was realized using a handedness-invertible chiral nematic liquid crystal in the TN mode. By means of Jones calculus, it was revealed that the handedness inversion of the TN film leads to a phase shift of the output light by π. With the addition of a photosensitizing chiral dopant, the to and fro phase switching processes can be implemented by violet and green irradiations respectively. This method is advantageous as it offers noncontact control, nonvolatile switching and a fast response. When the boundary conditions of the sandwich cell are applied, the resultant phase shift is stepwise. This device is normally insensitive to wavelength, polarization and film thickness owing to the TN nature. Therefore, the design and fabrication of the device are simpler with regard to the electronicdriven TN switch [20]. Such a light-driven π phase switch is potentially effective for beam steering, digital switching and signal processing in optical systems, e.g. phase grating, interferometric optical switch and binary phase shift keying modulation system. Acknowledgment
The authors gratefully thank the National Science Council of Taiwan for financial support under Contract No. NSC100-2628-E-110-007-MY3. One of the authors, Chun-Wei Chen, would like to thank Cheng-Yu Wang and Shuo Zhao for fruitful discussions.
#209308 - $15.00 USD (C) 2014 OSA
Received 31 Mar 2014; revised 4 May 2014; accepted 5 May 2014; published 12 May 2014 19 May 2014 | Vol. 22, No. 10 | DOI:10.1364/OE.22.012133 | OPTICS EXPRESS 12138
Department of Photonics, National Sun Yat-Sen University, Kaohsiung, Taiwan 2 Contributed equally to this work *[email protected]
Abstract: A light-activated optical phase switch was developed, exploiting the conversion between left-handed and right-handed twisted nematic liquid crystals. Theoretical and experimental analyses revealed that the handedness inversion of the twisted nematic film altered the optical phase of the output waves by π. Herein, the competition between the helical twisting powers of the two reverse-handed chiral dopants determines the handedness of the twisted nematic film. The photo-responsibility and the bistability are attributed to the azobenzene chromophores in one of the chiral additives. ©2014 Optical Society of America OCIS codes: (120.5060) Phase modulation; (230.1150) All-optical devices; (230.3720) Liquidcrystal devices.
References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.
P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84(2), 268–298 (1996). Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzaka, Y. Kobayashi, and T. Hara, “High Efficiency Electrically-Addressable Phase-Only Spatial Light Modulator,” Opt. Rev. 6(4), 339–344 (1999). Y.-H. Lin, H. Ren, Y.-H. Wu, Y. Zhao, J. Fang, Z. Ge, and S.-T. Wu, “Polarization-independent liquid crystal phase modulator using a thin polymer-separated double-layered structure,” Opt. Express 13(22), 8746–8752 (2005). Y. Huang, C.-H. Wen, and S.-T. Wu, “Polarization-independent and submillisecond response phase modulators using a 90° twisted dual-frequency liquid crystal,” Appl. Phys. Lett. 89(2), 021103 (2006). J. Sun, Y. Chen, and S.-T. Wu, “Submillisecond-response and scattering-free infrared liquid crystal phase modulators,” Opt. Express 20(18), 20124–20129 (2012). X.-W. Lin, W. Hu, X.-K. Hu, X. Liang, Y. Chen, H.-Q. Cui, G. Zhu, J.-N. Li, V. Chigrinov, and Y.-Q. Lu, “Fast response dual-frequency liquid crystal switch with photo-patterned alignments,” Opt. Lett. 37(17), 3627–3629 (2012). Y.-T. Lin, H.-C. Jau, and T.-H. Lin, “Polarization-independent rapidly responding phase grating based on hybrid blue phase liquid crystal,” J. Appl. Phys. 113(6), 063103 (2013). I. Dozov, “26.1: Invited Paper: Bistable Liquid Crystal Technologies,” SID Symp. Dig. Tec. 34, 946–949 (2003). Y. W. Li and H. S. Kwok, “Bistable twisted-bend and twisted-nematic liquid crystal display,” Appl. Phys. Lett. 95(18), 181107 (2009). A. Y.-G. Fuh, J.-T. Chiang, Y.-S. Chien, C.-J. Chang, and H.-C. Lin, “Multistable Phase-Retardation Plate Based on Gelator-Doped Liquid Crystals,” Appl. Phys. Express 5(7), 072503 (2012). J. H. Park, C. J. Yu, J. Kim, S. Y. Chung, and S. D. Lee, “Concept of a liquid-crystal polarization beamsplitter based on binary phase gratings,” Appl. Phys. Lett. 83(10), 1918–1920 (2003). C. H. Gooch and H. A. Tarry, “The optical properties of twisted nematic liquid crystal structures with twist angles ≤90 degrees,” J. Phys. D Appl. Phys. 8(13), 1575–1584 (1975). N. Konforti, E. Marom, and S. T. Wu, “Phase-only modulation with twisted nematic liquid-crystal spatial light modulators,” Opt. Lett. 13(3), 251–253 (1988). U. A. Hrozhyk, S. V. Serak, N. V. Tabiryan, and T. J. Bunning, “Photoinduced Isotropic State of Cholesteric Liquid Crystals: Novel Dynamic Photonic Materials,” Adv. Mater. 19(20), 3244–3247 (2007). H.-C. Jau, K.-T. Cheng, T.-H. Lin, Y.-S. Lo, J.-Y. Chen, C.-W. Hsu, and A. Y.-G. Fuh, “Photo-rewritable flexible LCD using indium zinc oxide/polycarbonate substrates,” Appl. Opt. 50(2), 213–217 (2011).
#209308 - $15.00 USD (C) 2014 OSA
Received 31 Mar 2014; revised 4 May 2014; accepted 5 May 2014; published 12 May 2014 19 May 2014 | Vol. 22, No. 10 | DOI:10.1364/OE.22.012133 | OPTICS EXPRESS 12133
16. C.-T. Wang, Y.-C. Wu, and T.-H. Lin, “Photo-switchable bistable twisted nematic liquid crystal optical switch,” Opt. Express 21(4), 4361–4366 (2013). 17. C.-T. Wang, C.-W. Tseng, J.-H. Yu, Y.-C. Li, C.-H. Lee, H.-C. Jau, M.-C. Lee, Y.-J. Chen, and T.-H. Lin, “Optical bistability in a silicon nitride microring resonator with azo dye-doped liquid crystal as cladding material,” Opt. Express 21(9), 10989–10994 (2013). 18. X. J. Yu and H. S. Kwok, “Bistable bend-splay liquid crystal display,” Appl. Phys. Lett. 85(17), 3711–3713 (2004). 19. L. A. Parry-Jones and S. J. Elston, “Flexoelectric switching in a zenithally bistable nematic device,” J. Appl. Phys. 97(9), 093515 (2005). 20. D. H. Song, J. H. Lee, S. J. Lee, S.-i. Kim, S. Lim, S. T. Shin, J. C. Kim, and T.-H. Yoon, “Bistable switching of twist direction in a twisted-nematic liquid crystal cell,” Appl. Phys. Lett. 97(6), 063501 (2010). 21. S.-W. Ke, T.-H. Lin, and A. Y. G. Fuh, “Tunable grating based on stressed liquid crystal,” Opt. Express 16(3), 2062–2067 (2008). 22. S. P. Fletcher, F. Dumur, M. M. Pollard, and B. L. Feringa, “A Reversible, Unidirectional Molecular Rotary Motor Driven by Chemical Energy,” Science 310(5745), 80–82 (2005). 23. C.-H. Lee, C.-W. Wu, C.-W. Chen, H.-C. Jau, and T.-H. Lin, “Polarization-independent bistable light valve in blue phase liquid crystal filled photonic crystal fiber,” Appl. Opt. 52(20), 4849–4853 (2013). 24. P. Yeh and C. Gu, “Jones Matrix Method,” in Optics of liquid crystal displays (Wiley, New York, 1999), pp. 103–160. 25. J. Ma, Y. N. Li, T. White, A. Urbas, and Q. Li, “Light-driven nanoscale chiral molecular switch: reversible dynamic full range color phototuning,” Chem. Commun. (Camb.) 46(20), 3463–3465 (2010). 26. S.-W. Ko, S.-H. Huang, A. Y. G. Fuh, and T.-H. Lin, “Measurement of helical twisting power based on axially symmetrical photo-aligned dye-doped liquid crystal film,” Opt. Express 17(18), 15926–15931 (2009). 27. M. V. Vasnetsov, V. A. Pas’ko, and D. S. Kasyanyuk, “Observation of polarization conflict caused by geometrical phase in a twisted nematic liquid crystal cell,” Opt. Lett. 36(11), 2134–2136 (2011).
1. Introduction Phase-only modulation is adopted in various optical applications, including spatial light modulators, beam steering and optical cross-connect switches [1, 2]. Liquid crystalline materials are commonly used to develop phase modulators because of their extraordinarily large birefringence and susceptibility of director-axis reorientation by external stimuli. Nowadays, most effort in the field is made to speed up the response and achieve polarizationindependent modulation [3–7]. However, for long-term single-state applications, bi- or multistability is essential to reducing power consumption and preventing the effects of some instabilities of the power supply [8–10]; in addition, a phase shift of π is desirable. For instance, a phase difference of π maximizes the highest diffraction efficiency of a typical phase grating [11]. Therefore, in this letter, a bistable π phase switch has been designed to meet the two needs. The proposed device is generally based on a twisted nematic (TN) film that can be converted between reverse handedness states, levorotation and dextrorotation, by illuminating with visible light. TN-based modulators are attractive for their wavelength- and polarizationindependence when satisfying the Mauguin condition [12, 13]. Furthermore, their insensitivity to cell-gap variations reduces the required manufacturing accuracy. Photoswitchability arises from the addition of azobenzene molecules. Switches that can be operated by light [14–17] support easier device design, local addressing and tether-free control than those driven by an electric field [8, 18–20], mechanical stress [21], chemical reaction [22] or heat [23]. The following sections present the operating mechanism, a theoretical explanation of the procedures for fabricating and experimental results concerning such switches. 2. Theoretical description The proposed device can be optically switched between left-handed and right-handed twisted nematic states. To verify theoretically that this device can be employed as a zero-to-π phase modulator, the concept is tested using Jones calculus. The following concerns a TN film of thickness d, a total twist angle φ and a uniaxial liquid crystal with an ordinary refractive index no and an extraordinary refractive index ne. Treating the TN film as a stack of planar-aligned nematic layers with different azimuth angles yields the following Jones matrix [24],
#209308 - $15.00 USD (C) 2014 OSA
Received 31 Mar 2014; revised 4 May 2014; accepted 5 May 2014; published 12 May 2014 19 May 2014 | Vol. 22, No. 10 | DOI:10.1364/OE.22.012133 | OPTICS EXPRESS 12134
cos φ M = sin φ
Γ sin X cos X − i − sin φ 2 X cos φ sin X −φ X
sin X X Γ sin X cos X + i 2 X
φ
,
(1)
where Г is the phase retardation of the untwisted film, and X is a substitution term,
Γ=
2π
λ
⋅ d ⋅ ( ne − no ) =
2
2π
Γ ⋅ d ⋅ Δn ; X = φ 2 + . λ 2
(2)
When a horizontally polarized plane wave enters a + 90° TN film, the polarization state of the output wave can be written as the following Jones vector, sin X φ X E out ,+90° = M ⋅ E in = cos X − i Γ sin X 2 X
.
(3)
If the film satisfies the Mauguin condition (Δn·d ? λ), which is equivalent to φ = Г, then X is approximately a half of Г and the upper element of the vector is close to zero. The output polarization state at the point at which the waves leaves the film can be derived as, sin ( Γ / 2 ) φ 0 E out ,+90° = ( Γ / 2) = exp ( −iΓ / 2 ) 1 , cos ( Γ / 2 ) − i sin ( Γ / 2 )
(4)
which describes vertically polarized light whose phase is determined by film thickness, birefringence and probe wavelength. Now, if the film is flipped into the opposite handedness mode (−90°), the output polarization state will be transformed into,
0 E out ,−90° = exp ( −i Γ / 2 ) . −1
(5)
From the resulting Jones vectors, the output waves have the same polarization and amplitude but are “out of phase”, corresponding to a phase difference of π. To elucidate schematically the operation of the device, Fig. 1 simply illustrates π phase switching. When horizontally polarized light enters a 90° TN film, its polarization rotates along the liquid crystal director until the light is vertically polarized. If the TN film is left-handed, then at the output point “o”, the electric field ( E ) oscillation is assumed to begin from zero in the positive y direction [Fig. 1(a)]. On the contrary, if the film is right-handed, then the electric field points in the negative y direction [Fig. 1(b)]. As the device is converted from one state to the other, the phase is shifted by π. In terms of the twist angle, such π phase switching is not limited to a 90° TN. It can be set to any angle except 0° and other integral multiples of 180°.
#209308 - $15.00 USD (C) 2014 OSA
Received 31 Mar 2014; revised 4 May 2014; accepted 5 May 2014; published 12 May 2014 19 May 2014 | Vol. 22, No. 10 | DOI:10.1364/OE.22.012133 | OPTICS EXPRESS 12135
Fig. 1. Schematic π phase switching using an optically responsive twisted nematic film.
3. Device fabrication
To realize the above concept, a photo-responsive liquid crystal (PRLC), formulated by blending chiral agents, 0.1755 wt% R-811 (Merck) and 0.1245 wt% ChAD-3C-S (BEAM), into a nematic host E7 (Merck), was capillary-filled into a 12 μm-thick sandwich cell with two perpendicularly rubbed polyimide layers. Chiral additives were used to select the handedness of the whole TN film. R-811 is a static right-handed chiral dopant with a Helical Twisting Power (HTP) of ~10.8 μm−1; by contrast, ChAD-3C-S is a left-handed chiral bis(azobenzene) dye, whose HTP can be modulated by light [16, 25]. Doping ChAD-3C-S into E7 yielded an initial HTP value of −42.6 μm−1; that of the green light stationary state (λ = 532 nm) was −30.7 μm−1. Under irradiation by violet light (λ = 411 nm), the trans-cis isomerization reduced the chirality of the liquid crystal. Hence, the HTP dropped to almost nil, making it achiral nematic. Notably, both photo-stationary states were nonvolatile upon the removal of illumination. The concentrations of the chiral additives were consistent with the following conditions: Green Green PChAD = ( HTPChAD ⋅ CChAD ) −1 < ( HTPR-811 ⋅ CR-811 ) −1 = PR-811 ;
(6)
Violet Violet PChAD = ( HTPChAD ⋅ CChAD ) −1 > ( HTPR-811 ⋅ CR-811 ) −1 = PR-811 ;
(7)
Green Green PPRLC = ( HTPChAD ⋅ CChAD − HTPR-811 ⋅ CR-811 ) −1 > 4d ;
(8)
#209308 - $15.00 USD (C) 2014 OSA
Received 31 Mar 2014; revised 4 May 2014; accepted 5 May 2014; published 12 May 2014 19 May 2014 | Vol. 22, No. 10 | DOI:10.1364/OE.22.012133 | OPTICS EXPRESS 12136
Violet Violet PPRLC = ( HTPR-811 ⋅ CR-811 − HTPChAD ⋅ CChAD ) −1 > 4d ,
(9)
where P denotes the pitch length; C is the fraction of the chiral dopant and d represents the film thickness; the superscript identifies the color of the pump laser, while the subscript specifies which chiral agent(s) was/were contained. The former two terms ensure that the handedness can be converted. The nematic liquid crystal could not be twisted by more than 90° when the latter two requirements were fulfilled. 4. Experimental verification and discussion
Firstly, the TN film was examined under a polarizing optical microscope (POM) to confirm the general polarization rotation effect. Figure 2 indicates that, under crossed polarizers, both the left- and right-handed modes were highly see-through, whereas the light was almost completely blocked when the polarizer was parallel to the analyzer. The slight difference in transmittance was possibly attributable to the fact that the included angle between the two polarizers was not an exact right angle and the limitation on d·Δn/λ prevent the complete satisfaction of the Mauguin condition. The defect line reveals that the twist angle varied in an abrupt and discontinuous manner owing to the boundary conditions [26, 27]. This feature is of crucial importance for designing hitless switches in optical communications. With respect to the response of the device, the handedness inversion under exposure to violet light (λ = 411 nm, I = 30 mW/cm2) and green light (λ = 532 nm, I = 90 mW/cm2) took less than half a second. Since the trans-isomers are steadier than the cis-, the left-handed TN could last for weeks without any external stimuli; still, the right-handed state could be retained for at least two hours after ten minutes violet illumination. The response rate, stability and reliability of the optical switch are believed to be able to be further improved by lowering the HTP value of the azobenzene dopant to increase the dosage.
Fig. 2. POM images of (a) left-handed state, (b) transformation of states and (c) right-handed state under crossed and parallel polarizers.
Since a phase difference of π exists between the two TN modes, the phenomenon can be easily monitored by interferometry. The sample was set on one arm of the Mach-Zehnder interferometer; and, a half-wave plate was placed on the other to enable the polarization of the two probe beams in identical directions. Upon exposure to the green laser for a period of ten minutes, the TN film entered the left-handed photo-stationary state and exhibited line fringes, as displayed in Fig. 3(a). To switch it into the right-handed state, the film was subsequently irradiated by a violet laser. The original fringes were soon covered by an “inverse” interference pattern. Figure 3(b) demonstrates that the position of the new (converted) dark #209308 - $15.00 USD (C) 2014 OSA
Received 31 Mar 2014; revised 4 May 2014; accepted 5 May 2014; published 12 May 2014 19 May 2014 | Vol. 22, No. 10 | DOI:10.1364/OE.22.012133 | OPTICS EXPRESS 12137
fringes matched that of the former bright fringes because the phase differed by π. Within a second, the sample completely transitioned from the counterclockwise to the clockwise TN state, as presented in Fig. 3(c). Further illuminating the device with a green laser put it back into the left-handed state. Figure 3(d) compares the intensity distribution of the interference pattern in the right-handed mode to that of the levorotary TN. Evidently, the two TN states are perfectly out of phase with each other.
Fig. 3. Photographs of interference patterns at (a) left-handed state, (b) transformation of states and (c) right-handed state, corresponding to (d) intensity distribution in cross-section (axis x).
5. Conclusion
In summary, a bistable phase switch was realized using a handedness-invertible chiral nematic liquid crystal in the TN mode. By means of Jones calculus, it was revealed that the handedness inversion of the TN film leads to a phase shift of the output light by π. With the addition of a photosensitizing chiral dopant, the to and fro phase switching processes can be implemented by violet and green irradiations respectively. This method is advantageous as it offers noncontact control, nonvolatile switching and a fast response. When the boundary conditions of the sandwich cell are applied, the resultant phase shift is stepwise. This device is normally insensitive to wavelength, polarization and film thickness owing to the TN nature. Therefore, the design and fabrication of the device are simpler with regard to the electronicdriven TN switch [20]. Such a light-driven π phase switch is potentially effective for beam steering, digital switching and signal processing in optical systems, e.g. phase grating, interferometric optical switch and binary phase shift keying modulation system. Acknowledgment
The authors gratefully thank the National Science Council of Taiwan for financial support under Contract No. NSC100-2628-E-110-007-MY3. One of the authors, Chun-Wei Chen, would like to thank Cheng-Yu Wang and Shuo Zhao for fruitful discussions.
#209308 - $15.00 USD (C) 2014 OSA
Received 31 Mar 2014; revised 4 May 2014; accepted 5 May 2014; published 12 May 2014 19 May 2014 | Vol. 22, No. 10 | DOI:10.1364/OE.22.012133 | OPTICS EXPRESS 12138
