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Liquid crystal phase modulators are emerging as a new technological advancement, since they can be used for a wide range of applications. To improve their performance, polymer stabilized blue phase liquid crystal (PS-BPLC) phase modulators with fast response time and accurate phase profile become a necessary. Here, we proposed a facile PS-BPLC phase modulator to achieve particularly low voltage and high resolution. By employing a specific external compact optical system setup, the driving voltage is reduced to 26.09V to obtain 2π phase change at the wavelength of 532 nm. An accurate numerical modeling is also conducted to provide a systematic investigation of the fringing electric field effect to the performance of high resolution PS-BPLC phase modulator. The wavefront distortion caused by the fringing electric field can be automatically compensated to generate accurate phase profile for fast response liquid crystal phase modulator. This work provides a new protocol to realize liquid crystal on silicon based fast response and high resolution phase modulator.
© 2015 Optical Society of America
1. Introduction
Liquid crystal phase modulator is one of the most extensive used phase modulation devices in the field of polarization pattern beam generator, computer generated holography, adaptive optics, beam steering and optical correction [1–6]. For these applications, at least 2π phase change, fast response and low operation voltage are the major requirements [7]. To achieve continuously variable phase control, nematic liquid crystals (LCs) are extensive used, but suffered from relatively slow switching speeds, i.e. slow response time, inherently due to their viscoelasticity. To reduce response time, various LC materials such as ferroelectric liquid crystals (FLCs), dual frequency liquid crystals (DFLCs), polymer dispersed liquid crystals (PDLCs) and polymer network liquid crystals (PNLCs) have been proposed [8–13]. Each material has its own pros and cons. For example, FLCs show sub-millisecond response time, but it is difficult to obtain continuous phase-only modulation because of its bi-stability. DFLCs can greatly improve the decay time by using an electric field to reorient the LC molecules, but its crossover frequency is quite sensitive to the temperature and the control of DFLCs is notoriously difficult. In spite of fast response, PDLC phase modulators suffered from very small phase change to refrain from scattering state. Similarly, PNLCs scatter light strongly in the visible region because of voltage-induced micron-sized multi-domain structures. Moreover, fringing electric field, produced between two adjacent electrodes applied with different voltages causing unwanted transverse electric field, can also greatly degrade the performance of phase modulator. This drawback is mainly from the minimized electrodes which is approximate to or even smaller than the cell gap to obtain high spatial resolution [14–17]. Consequently, new protocols enabling low driving voltage, fast response time and high accurate phase profile design would be advantageous.
Polymer stabilized blue phase liquid crystals (PS-BPLCs) exhibit attractive features such as sub-millisecond response time, no need for surface alignment layer, large optical Kerr effect and the ability to perform multilevel phase modulation, making it a promising candidate for fast response liquid crystal phase modulator [18–20]. Nevertheless, few reports focus on PS-BPLC based phase modulators. Recently, one approach made by R.M. Hyman et al utilized blue phase liquid crystal (BPLC) over silicon device to obtain polarization-independent phase modulation [21]. This BPLC phase modulator working on reflective mode offers both high speed switching and input polarization state insensitive. However, it requires about 128V to obtain 1.8π phase change and the effect of fringing electric field is not compensated which will certainly affect the polarization properties of the device.
Herein, we propose a single high-resolution reflective mode PS-BPLC phase modulator with compact optical system to generate 2π phase change with low driving voltage, sub-millisecond response time and suppressed fringing electric field effect. An accurate numerical modeling is provided to analyze the fringing electric field effect in the high resolution reflective mode PS-BPLC phase modulator. Evaluation method is also proposed to evaluate the non-uniformity quantitatively of the phase profile. This work provides a new protocol to generate accurate phase profile for fast response liquid crystal phase modulator.
The paper is organized as follows. After Introduction, Section 2 describes the optical architecture and the working principle of this system. Then, results and discussion in Section 3 is divided into three parts. Firstly, the PS-BPLC material parameter is obtained by experimental fitting and the optimized cell gap for our phase modulator is calculated. Secondly, the fringing electric field effect in a high resolution reflective BPLC spatial light modulator is studied by accurate numerical modeling and evaluation method is proposed to evaluate the performance of the phase profile. Thirdly, the general design issues which affect the fringing electric field such as applied voltage, electrode size, and the gap between two adjacent electrodes are investigated. Finally, the conclusions of this work are presented in Section 4.
2. Compact optical system architecture and principle
BPLCs are photonic crystals with a symmetric structure that is optically isotropic when no electric field is applied. The birefringence is induced by the electric-field-induced orientation of polar molecules according to the Kerr effect [20]. For a high resolution BPLC phase modulator, the fringing electric field between two adjacent electrodes producing transverse electric field which makes the device polarization dependent. Thus, we proposed a facile PS-BPLC phase modulator to automatically compensate the effect of the fringing electric field and lower driving voltage as well. The schematic diagram of the PS-BPLC phase modulator with the external compact optical setup is as shown in Fig. 1 . A collimated linearly polarized laser beam oriented at 0 degrees i.e. parallel to the page plane is launch onto the system. A beam-splitter (BS1) divides the incident light into two parts and preserves the polarization. The transmitted beam is blocked by the light barrier (LB) while the reflected one is directed onto left-half of the high resolution BPLC phase modulator, which is used to modulate the phase of the incident light with the applied voltage between Al electrode and ITO electrode. The beam is then reflected back to BS1 and the transmitted part passes through a half-wave plate (HWP) oriented with a relative angle of 45 degree to rotate the polarization state 90 degree. Then the polarized beam perpendicular to the page plane passes through an optical system containing two prisms and a second beam-splitter (BS2) to the other half of the high resolution BPLC phase modulator to gain another phase modulation for the other polarization state. Thus, the total phase delay for this proposed structure is doubled compared to a traditional reflective mode BPLC phase modulator and it contains both the phase delay accumulated by ordinary refractive index no and extraordinary refractive index ne.
Fig. 1 Scheme of the optical setup of the PS-BPLC phase modulator. HWP indicate half-wave plate; BS1 and BS2 are beam splitters; P1 and P2 are prisms and LB indicates a light barrier to block light.
The voltage applied to the corresponding electrodes of the left-half PS-BPLC phase modulator and the right-half one is the same. Therefore, the total phase delay (ψ) of the incident light under the electric field E passing through this system is governed by:
Where λ means the wavelength of the incident light, d is the cell gap, no and neff are the ordinary and effective extraordinary refractive indices which can be calculated as Eq. (2)-(4) show according to extended Kerr model and refractive index theory of anisotropy crystal [22,23].
Where niso is refractive index when no voltage is applied, ne is the extraordinary refractive index of the LC composite, Δnsat and Es represent the saturated induced birefringence and the saturation electric field, respectively, θ is the angle between incident light and optical axis of crystal.
Though the intensity of the light is reduced, the optical path is doubled compared with a traditional reflective mode LC phase modulator. Thus, the driving voltage can be significantly lowered which will enable PS-BPLC to be integrated with a high resolution liquid-crystal-on-silicon (LCoS) phase modulator. Moreover, the unwanted phase deviation caused by the fringing electric field can be automatically compensated in this proposed optical system which will be presented in details in the following sections.
3. Results and discussion
3.1 Experiment results of PS-BPLC materials
To obtain the simulation parameters of PS-BPLC materials, we prepared a vertical field switching (VFS) PS-BPLC sample [24]. The cell gap thickness is measured to be 4.89μm. The BPLC precursor consists of 88.77 wt.% liquid crystal host HBG980000 (HCCH) with 3.25 wt.% chiral dopant R5011 (HCCH), 4.53 wt.% di-functional reactive monomer RM257 (HCCH) and 3.44 wt.% LA (HCCH). The precursor appears blue phase between 59.6 °C and 63.7 °C during the cooling process and is cured with 30 mW/cm2 UV light (365 nm) at 60.5 °C for 15min.
The electro-optic properties of the VFS cell is measured using the experimental setup reported previously [25]. The sample is driven by a 1 kHz square-wave voltage at room temperature. During the measurement, the operation frequency and temperature remain constant as they have notable impact on the Kerr constant for some BPLC materials [26]. Figure 2 depicts the measured results and the simulation results through fitting with Eq. (2)–(3). We obtain Δnsat = 0.1566 and Es = 6.535 V/μm, the Kerr constant K = Δnsat/(λEs2) = 6.89nm/V2 for the wavelength of 532nm. The cell gap influence on Von to obtain 2π phase change for our optical system neglecting the fringing electric field effect is also calculated as showed in Fig. 3 . A thinner cell gap results in a stronger electric field so that the induced birefringence is larger, which in turn lowers Von. However, as d continually decreases the accumulated phase delay would be smaller. Eventually, Von will increases as the cell gap gets too thin [19,27]. So the optimized cell gap to obtain the lowest Von for our compact optical PS-BPLC phase modulator is 3.575μm for the wavelength of 532nm.
3.2 Evaluation method of fringing electric field effect
For a high resolution PS-BPLC phase modulator, the fringing electric field between two adjacent electrodes applied with different voltages producing transverse electric field which makes the device polarization dependent. Thus, the real phase profile would deviate from the desired phase profile especially in the region of the gap between two adjacent electrodes which significantly degrade the performance of the device. Thus, the characteristics of the PS-BPLC phase modulator under the effect of fringing electric field is studied by accurate numerical modeling.
The first step toward evaluating the fringing electric field effect of our proposed modulator is to determine the driving voltage for the desired phase change relative to the phase delay with no applied voltage by using a one-dimensional configuration simulation which neglecting the fringing electric field effect. The applied voltage values are shown in Table 1 where a total 2π phase change is divided into 8 greyscales.
Table 1. The determined applied voltage vs. phase change.
Unlike a traditional nematic LC phase modulator, the fringing electric field effect on the LC director distribution caused by the left-side pixel and the right-side pixel is different because of the existence of pretilted angle [6]. For a BPLC phase modulator, there is no need of surface alignment layer and no pretilted angle exist. Thus, the phase profile under the fringing electric field effect caused by left-side pixel and that caused by right-side pixel are symmetrical. Therefore, the phase profile of our proposed architecture which considering the fringing electric field effect is then carried out as shown in Fig. 4 . The electrode size is set to be 4μm, the gap between two adjacent electrodes is 0.5μm, so the electrode space w defined as the distance contained one electrode and half width of the gap is 4.25μm. The voltage applied to the electrode is 0V i.e. greyscale 0 and the adjacent electrode is applied with greyscale 7. O-mode phase profile plotted as blue line in Fig. 4 presents the phase delay properties above the electrode space w only considering the phase delay accumulated by ordinary refractive index no (in the case that the polarization of the incident light is perpendicular to the transverse electric field induced by the fringing electric field) while the E-mode phase profile only considering the phase delay accumulated by extraordinary refractive index ne. The desired phase profile means the ideal phase profile over the electrode space w when no fringing electric field existed. Obviously, it is found that the PS-BPLC phase modulator is polarization dependent due to the effect of fringing electric field. The discreteness of driving electrodes in PS-BPLC phase modulator causes phase trough in the region between two adjacent electrodes for the O-mode light while it causes phase crest for the E-mode light. By utilizing the optical setup as shown in Fig. 1, the phase performance of the modulator can be greatly improved since the proposed architecture accumulates both no and ne phase delay to automatically compensated the phase deviation caused by the fringing electric field as the pink line shown in Fig. 4.
Fig. 4 The phase profile of O-mode light, E-mode light and proposed structure under the effect of fringing electric field.
We define evaluation function Mψ and affected region ratio MΛ to evaluate the performance of the PS-BPLC phase modulator. The evaluation function Mψ as Eq. (5) presents is used to evaluate the non-uniformity quantitatively of the phase profile, where ψ(x(i)) is the discrete distribution of phase delay in the X axial direction and is the average phase delay value. Nx is the number of discrete points along the X axis. σ(ψ(x)) is the standard error [28].
We consider it is acceptable when the wavefront distortion is within the range of 1/5λ (i.e. grey region, see Fig. 4). Thus the affected region ratio MΛ (i.e. MΛ = Λ/w) is defined as the proportion of the affected region (i.e. Λ, see Fig. 4) where the phase deviation beyond the range of 1/5λ to the electrode space w. The smaller of the function value Mψ, the more uniform of the phase delay distribution, so is the value of MΛ.
3.3 The effect of general design issues on the modulator performance
The general design issues such as grayscale difference, electrode size, and the gap between two adjacent electrodes have significant impact on the forming of transverse electric field which determining the modulator performance. Figure 5 depicts the effect of greyscale difference on the modulator performance. The electrode size is 4μm, the gap between two adjacent electrodes is 0.5μm. The electrode is applied with greyscale 0 and the voltage applied to the adjacent electrode is varied from greyscale 0 to greyscale 7. It is clearly shown that for the E-mode and O-mode light phase profile, the evaluation function value Mψ and the affected region ration MΛ greatly increase with the increase of greyscale difference as a larger transverse electric field is generated between the adjacent electrodes for a larger voltage difference. Whereas, the evaluation function value Mψ decreased 6 times for the maximum greyscale difference and the greyscale difference has little effect on Mψ for our proposed structure, which means we can obtain a uniform phase profile by using our proposed optical systems. Moreover, for all the greyscale difference, the wavefront distortion is within the region of 1/5λ which means the proposed structure is suitable for realizing precise phase profile control.
Fig. 5 The effect of greyscale difference between two adjacent electrodes on the modulator performance. (a) The effect of greyscale difference on Mψ. (b) The effect of greyscale difference on MΛ.
The effect of electrode size which determining the spatial resolution is also studied as shown in Fig. 6 . The electrode size is set to be from 1.5μm to 8μm while keeping the gap between two adjacent electrodes 0.5μm. The voltages applied to the electrode and the adjacent electrode are greyscale 0 and greyscale 7, respectively. As the electrode size becomes smaller, the corresponding uniformity quantitatively of the phase profiles for the E-mode and O-mode light get worse as shown in Fig. 6(a). The affected region ratio dramatically increase while the width of the electrode is smaller than 4μm which makes it difficult to realize high resolution phase modulation for the E-mode and O-mode light. For our proposed structure, the wavefront distortion caused by the fringing electric field is automatically compensated leading to sufficiently good performance for our high resolution PS-BPLC phase modulator.
Fig. 6 The effect of electrode size on the modulator performance. (a) The effect of electrode size on Mψ. (b) The effect of electrode size on MΛ.
Figure 7 presents the influence of the gap between two adjacent electrodes. We keep the electrode size 4μm, and varied the gap distance from 0.1μm to 2μm. The greyscales for the two electrodes are still greyscale 0 and greyscale 7. From the simulation results, it is clearly shown that the width of the gap between two adjacent electrodes has small impact on the performance of phase profile. Though a larger gap between the electrodes would decreases the transverse electric field to obtain a more uniform phase profile, the small aperture opening ratio still sacrifices the total performance of the devices. It is noteworthy that our proposed structure greatly improves the performance of the BPLC phase modulator by automatically compensating the phase deviation caused by the fringing electric field.
Fig. 7 The effect of the gap between two adjacent electrodes on the modulator performance. (a) The effect of the gap between two adjacent electrodes on Mψ. (b) The effect of the gap between two adjacent electrodes on MΛ.
4. Conclusion
A PS-BPLC phase modulator with external compact optical system setup is described in this paper. Besides of the ability to obtain 2π phase change at a particularly low driving voltage (26.09V) by doubled optical path at the wavelength of 532nm, this architecture can also automatically compensate the phase deviation caused by the fringing electric field which reduce the evaluation function value Mψ 6 times and restrict wavefront distortion within the range of 1/5λ. The PS-BPLC phase modulator is polarization dependent due to fringing electric field effect according to accurate numerical modeling. A larger voltage difference and smaller electrode size would induce larger phase deviation, while the gap between two adjacent electrodes has small effect on the performance of phase modulator. Utilizing PS-BPLC with larger Kerr constant and larger Δns, the driving voltage for our proposed architecture can be further reduced to meet the requirements of high resolution LCoS.
Acknowledgments
This work is sponsored by the National Basic Research Program of China (973 program) under grant no. 2013CB328803 and 2013CB328804, the National High Technology Research and Development Program of China under grant no. 2012AA03A302 and 2013AA011004, and the Fundamental Research Funds for the Central Universities, Foundation Research Grant of Southeast University and the Postgraduate Research and Innovation Program (CXZZ13_0097).
References and links
1. X. Zheng, A. Lizana, A. Peinado, C. Ramirez, J. L. Martinez, A. Marquez, I. Moreno, and J. Campos, “Compact LCOS-SLM based polarization pattern beam generator,” J. Lightwave Technol. 33(10), 2047–2055 (2015).
2. A. Georgiou, J. Christmas, J. Moore, A. Jeziorska-Chapman, A. Davey, N. Collings, and W. A. Crossland, “Liquid crystal over silicon device characteristics for holographic projection of high-definition television images,” Appl. Opt. 47(26), 4793–4803 (2008). [CrossRef] [PubMed]
3. Q. Mu, Z. Cao, L. Hu, D. Li, and L. Xuan, “An adaptive optics imaging system based on a high-resolution liquid crystal on silicon device,” Opt. Express 14(18), 8013–8018 (2006). [CrossRef] [PubMed]
4. P. McManamon and W. Thompson, “Phased array of phased arrays (PAPA) laser systems architecture,” Fiber Integr. Opt. 22(2), 79–88 (2003). [CrossRef]
5. F. Feng, I. H. White, and T. D. Wilkinson, “Free space communications with beam steering a two-electrode tapered laser diode using liquid-crystal SLM,” J. Lightwave Technol. 31(12), 2001–2007 (2013). [CrossRef]
6. X. Wang, B. Wang, P. J. Bos, P. F. McManamon, J. J. Pouch, F. A. Miranda, and J. E. Anderson, “Modeling and performance limits of a large aperture high-resolution wavefront control system based on a liquid crystal spatial light modulator,” Opt. Eng. 46(4), 044001 (2007). [CrossRef]
7. P. F. McManamon, P. J. Bos, M. J. Escuti, J. Heikenfeld, S. Serati, H. Xie, and E. A. Watson, “A review of phased array steering for narrow-band electrooptical systems,” Proc. IEEE 97(6), 1078–1096 (2009). [CrossRef]
8. T. D. Wilkinson, C. D. Henderson, D. G. Leyva, and W. A. Crossland, “Phase modulation with the next generation of liquid crystal over silicon technology,” J. Mater. Chem. 16(33), 3359–3365 (2006). [CrossRef]
9. T. D. Wilkinson, W. A. Crossland, and A. B. Davey, “Applications of ferroelectric liquid crystal LCOS devices,” Ferroelectrics 278(1), 227–232 (2002). [CrossRef]
10. Y. Huang, C. Wen, and S. Wu, “Polarization-independent and submillisecond response phase modulators using a 90 twisted dual-frequency liquid crystal,” Appl. Phys. Lett. 89(2), 021103 (2006). [CrossRef]
11. H. Ren, Y. Lin, Y. Fan, and S. Wu, “Polarization-independent phase modulation using a polymer-dispersed liquid crystal,” Appl. Phys. Lett. 86(14), 141110 (2005). [CrossRef]
12. J. Sun, S. Wu, and Y. Haseba, “A low voltage submillisecond-response polymer network liquid crystal spatial light modulator,” Appl. Phys. Lett. 104(2), 023305 (2014). [CrossRef]
13. F. Peng, H. Chen, S. Tripathi, R. J. Twieg, and S. Wu, “Fast-response infrared phase modulator based on polymer network liquid crystal,” Opt. Mater. Express 5(2), 265 (2015). [CrossRef]
14. X. Wang, B. Wang, P. J. Bos, P. F. McManamon, J. J. Pouch, F. A. Miranda, and J. E. Anderson, “Modeling and design of an optimized liquid-crystal optical phased array,” J. Appl. Phys. 98(7), 073101 (2005). [CrossRef]
15. B. Apter, U. Efron, and E. Bahat-Treidel, “On the fringing-field effect in liquid-crystal beam-steering devices,” Appl. Opt. 43(1), 11–19 (2004). [CrossRef] [PubMed]
16. L. Xu, L. Wu, J. Zhang, and X. Liu, “Effect of phase valley on diffraction efficiency of liquid crystal optical phased array,” Proc. SPIE 7133, 71333L (2008).
17. K. Fan-Chiang, S. Wu, and S. Chen, “Fringing-field effects on high-resolution liquid crystal microdisplays,” J. Disp. Technol. 1(2), 304–313 (2005). [CrossRef]
18. H. Kikuchi, M. Yokota, Y. Hisakado, H. Yang, and T. Kajiyama, “Polymer-stabilized liquid crystal blue phases,” Nat. Mater. 1(1), 64–68 (2002). [CrossRef] [PubMed]
19. Y. Chen, D. Xu, S. Wu, S. Yamamoto, and Y. Haseba, “A low voltage and submillisecond-response polymer-stabilized blue phase liquid crystal,” Appl. Phys. Lett. 102(14), 141116 (2013). [CrossRef]
20. Y. Haseba, H. Kikuchi, T. Nagamura, and T. Kajiyama, “Large Electro‐optic Kerr Effect in Nanostructured Chiral Liquid‐Crystal Composites over a Wide Temperature Range,” Adv. Mater. 17(19), 2311–2315 (2005). [CrossRef]
21. R. M. Hyman, A. Lorenz, S. M. Morris, and T. D. Wilkinson, “Polarization-independent phase modulation using a blue-phase liquid crystal over silicon device,” Appl. Opt. 53(29), 6925–6929 (2014). [CrossRef] [PubMed]
22. J. Yan, H. Cheng, S. Gauza, Y. Li, M. Jiao, L. Rao, and S. Wu, “Extended Kerr effect of polymer-stabilized blue-phase liquid crystals,” Appl. Phys. Lett. 96(7), 071105 (2010). [CrossRef]
23. D. Xu, Y. Chen, Y. Liu, and S. T. Wu, “Refraction effect in an in-plane-switching blue phase liquid crystal cell,” Opt. Express 21(21), 24721–24735 (2013). [PubMed]
24. H. Cheng, J. Yan, T. Ishinabe, and S. Wu, “Vertical field switching for blue-phase liquid crystal devices,” Appl. Phys. Lett. 98(26), 261102 (2011). [CrossRef]
25. J. Yan, Y. Chen, S. Wu, S. Liu, K. Cheng, and J. Shiu, “Dynamic response of a polymer-stabilized blue-phase liquid crystal,” J. Appl. Phys. 111(6), 063103 (2012). [CrossRef]
26. F. Peng, Y. Chen, J. Yuan, H. Chen, S. Wu, and Y. Haseba, “Low temperature and high frequency effects on polymer-stabilized blue phase liquid crystals with large dielectric anisotropy,” J. Mater. Chem. C. 2, 3597–3601 (2014).
27. H. Cheng, J. Yan, T. Ishinabe, N. Sugiura, C. Liu, T. Huang, C. Tsai, C. Lin, and S. Wu, “Blue-phase liquid crystal displays with vertical field switching,” J. Disp. Technol. 8(2), 98–103 (2012). [CrossRef]
28. L. Xu, J. Zhang, and L. Wu, “Numerical modeling for liquid crystal optical phased array and its phase delay characteristic,” Proc. SPIE 6352, 635225 (2006).
