The dispersion relation on the Kerr constant (K) of a polymer-stabilized isotropic phase (PSIP) liquid-crystal (LC) composite is investigated. Our experimental results show that K decreases as the wavelength (lambda) increases. The single-band birefringence dispersion model is used to fit the lambda K values of the PSIP LC composite. Very good agreement between the experiment and physical model is obtained

Jiao, Meizi

Wu, Shin-Tson

Yan, Jin

English

University of Central Florida (UCF): STARS (Showcase of Text, Archives, Research & Scholarship)

University of Central Florida STARS Faculty Bibliography 2010s Faculty Bibliography 1-1-2011 Dispersion relation on the Kerr constant of a polymer-stabilized optically isotropic liquid crystal Meizi Jiao University of Central Florida Jin Yan University of Central Florida Shin-Tson Wu University of Central Florida Find similar works at: https://stars.library.ucf.edu/facultybib2010 University of Central Florida Libraries http://library.ucf.edu This Article is brought to you for free and open access by the Faculty Bibliography at STARS. It has been accepted for inclusion in Faculty Bibliography 2010s by an authorized administrator of STARS. For more information, please contact STARS@ucf.edu. Recommended Citation Jiao, Meizi; Yan, Jin; and Wu, Shin-Tson, "Dispersion relation on the Kerr constant of a polymer-stabilized optically isotropic liquid crystal" (2011). Faculty Bibliography 2010s. 1435. https://stars.library.ucf.edu/facultybib2010/1435 PHYSICAL REVIEW E 83, 041706 (2011)Dispersion relation on the Kerr constant of a polymer-stabilized optically isotropic liquid crystalMeizi Jiao, Jin Yan, and Shin-Tson WuCollege of Optics and Photonics, University of Central Florida, Orlando, Florida 32816, USA(Received 15 December 2010; published 11 April 2011)The dispersion relation on the Kerr constant (K) of a polymer-stabilized isotropic phase (PSIP) liquid-crystal(LC) composite is investigated. Our experimental results show that K decreases as the wavelength (λ) increases.The single-band birefringence dispersion model is used to fit the λK values of the PSIP LC composite. Very goodagreement between the experiment and physical model is obtained.DOI: 10.1103/PhysRevE.83.041706 PACS number(s): 61.30.−v, 42.55.−fI. INTRODUCTIONThe Kerr effect is a second-order electro-optic (EO) effect[1]; it has been studied extensively in gases and liquids, suchas benzene, CS2, CCl4, water, nitrotoluene, and nitrobenzene[2–4]. In a Kerr medium, the electric-field-induced birefrin-gence is proportional to the electric field (E) asnind = λKE2, (1)where λ is the wavelength and K is the Kerr constant [1].Several high-speed (∼ns) EO modulators based on Kerr mediahave been demonstrated. However, the required operatingvoltage is quite high (∼kV) because the Kerr constant is fairlysmall (∼10−12 m/V2).Recently, polymer-stabilized blue-phase liquid crystals(PSBP LCs) have been developed [5–8]. The correspondingKerr constant of these PSBP LC composites is ∼3–4 ordersof magnitude larger than that of isotropic liquids becauseof the short-range interaction of LC molecules. As a result,the operating voltage is significantly reduced [9,10]. PSBPexhibits some revolutionary features as compared to con-ventional nematic liquid crystals in the following aspects:(1) the isotropic dark state, which leads to wide and symmetricviewing angle, (2) a submillisecond gray-to-gray responsetime [11], which enables color sequential displays with tripledoptical efficiency and resolution density, (3) no need for align-ment layers, and (4) insensitivity to the cell gap, provided thatin-plane switching (IPS) electrodes are employed. Therefore,PSBP liquid crystals are attractive for high-speed photonicsand display applications [12,13]. In the PSBP precursor,the blue phase temperature range is widened (7–9 ◦C) ascompared to the pure blue phase range of the LC-chiral mixture(1–2 ◦C), but it is still relatively narrow. The UV curing processcould take place either in a blue phase or in an isotropicphase to extend the temperature range. In the latter case,the LC composite is called the polymer-stabilized isotropicphase (PSIP). From a macroscopic viewpoint, both PSBP andPSIP LC composites are optically isotropic in the voltage-offstate due to self-assembly nanosized lattice structures [14].Therefore, the EO effects of PSBP and PSIP can be describedby the Kerr effect.However, Eq. (1) has raised some confusion: (1) Willthe induced birefringence keep on increasing as the electricfield increases? (2) Will the induced birefringence increasewith the wavelength because K is called a “constant”? Thefirst confusion has been clarified recently, and an “extendedKerr effect” [15] has been developed to correctly predict thesaturation phenomenon in the high-field region of a PSBPliquid crystal. Regarding the second question, some scatteredexperimental data and theories can be found in literaturefor isotropic liquids and gases [3,4], but, to the best of ourknowledge, the implicit dispersion relation of the Kerr constantfor PSIP has not been explored.In this paper, we report the dispersion relation on theKerr constant of a PSIP LC composite. Our experimentalresults show that the Kerr constant decreases gradually as thewavelength increases. We fit the measured Kerr constant with asingle-band birefringence dispersion model [16,17] and obtainexcellent agreement. This information clearly answers theabove-mentioned second possible confusion and, moreover,it is useful for designing a PSIP LC device for photonicsand display applications by taking wavelength dispersion intoconsideration.II. EXPERIMENTFigure 1 shows the experimental setup for measuring the EOproperties of a PSIP LC composite with different wavelengths.A narrowband interference color filter was placed in frontof the white light source for selecting the wavelength. Inour experiment, five color filters with transmission peaksat λ ∼ 450, 500, 550, 633, and 660 nm and bandwidths∼±5 nm were used and their corresponding voltage-dependenttransmittance (V-T) curves measured. In our experiment, an acvoltage with 1-kHz square-wave frequency was applied. Sincethe white light source has an evident divergence angle, a groupof lenses were used to collimate the light. In Fig. 1, we use onelens to represent this collimating lens group. A collimated lightcan travel a long distance without much divergence. Finally, afocusing lens was used to collect the transmitted light into aphotodiode detector.The PSIP LC used in this experiment comprised a 56 wt%nematic LC host MLC-14200 (Merck, n = 0.17, ε = 30,clearing point Tc = 94 ◦C), 29 wt% chiral dopants (24% CB15and 5% ZLI-4572, Merck), and 15 wt% monomers (6% RM-257 and 9% EHA). The LC-monomer mixture was injectedinto an IPS cell with an electrode width ∼10 μm, electrodegap ∼10 μm, and cell gap ∼7.5 μm. The cell was curedby an UV lamp (λ ∼ 365 nm) at 70 ◦C, which was wellabove the isotropic temperature of the LC-monomer mixture.The LC cell was sandwiched between two crossed polarizerswith the striped electrodes oriented at 45◦ with respect to thepolarizer’s transmission axis. We measured the V-T curves atroom temperature (∼23 ◦C) under different wavelengths.041706-11539-3755/2011/83(4)/041706(4) ©2011 American Physical SocietyMEIZI JIAO, JIN YAN, AND SHIN-TSON WU PHYSICAL REVIEW E 83, 041706 (2011)WhitelightsourceColorfilterCollimatinglensPolarizer LC SampleAnalyzer FocusinglensDetectorFIG. 1. (Color online) Experimental setup for measuring the V-Tcurves of a polymer-stabilized isotropic LC composite at differentwavelengths.Figure 2 shows the measured V-T curves of the LC compos-ite at five wavelengths. From left to right, the correspondingwavelengths are 450, 500, 550, 633, and 660 nm. Because theluminous flux of each wavelength is different, we normalizethe transmittance of each wavelength to its own peak value.The operating voltage is lower at a shorter wavelength fortwo reasons: (1) The induced phase retardation is inverselyproportional to the wavelength, thus a shorter wavelengthwill exhibit a larger phase retardation under the same drivingvoltage; and (2) under normal dispersion conditions theinduced birefringence decreases as the wavelength increases.Considering these two factors, the on-state voltage is lower fora shorter wavelength.III. PHYSICAL MODELS AND DISCUSSIONSTo study the detailed dispersion relation of the PSIP LCcomposite, we carried out simulations to fit the experimentaldata shown in Fig. 2. First, we calculated the electric-fielddistribution in our IPS cell at voltage-on states using a finite-element method [18]. Then for each wavelength we used thefollowing extended Kerr effect model [15,19] to calculate theinduced birefringence based on the electric-field distribution:n = nsat{1 − exp[−(EEs)2]}, (2)where nsat is the saturated induced birefringence and Es is thesaturation electric field. Afterward, we used the extended Jones0 50 100 150 2000.00.20.40.60.81.0Normalized TransmittanceVoltage (V)FIG. 2. (Color online) Measured (dots) and fitted (lines) V-Tcurves of the PSIP LC cell at different wavelengths. From left toright, the corresponding wavelengths are 450, 500, 550, 633, and660 nm.TABLE I. Fitting results of the saturated birefringence (nsat),saturation electric field (Es), and Kerr constant of the PSIP LCcomposite at the corresponding wavelengths.λ (nm) nsat Es (V/μm) K (nm/V2)450 0.0730 6.8 3.51500 0.0695 6.8 3.01550 0.0670 6.8 2.63633 0.0635 6.8 2.17660 0.0630 6.8 2.06matrix method [20,21] to calculate the averaged transmittance.The extended Kerr effect model [Eq. (2)] clearly explains theconvergence phenomenon observed in the high-field region.The fitting results with Eq. (2) are shown in Fig. 2, inwhich dots represent experimental data and solid lines arefitting curves. They overlap with each other very well at eachwavelength. There are two fitting parameters, nsat and Es .The fitting results at each wavelength are listed in Table I.It is interesting to note that the fitting results of Esare the same for all the wavelengths studied. Because ata given temperature and voltage the LC director reorien-tation profile is determined by the balanced elastic andelectric torques, the LC director distribution will not beaffected by the wavelength. However, the V-T curves willbe different for different wavelengths because the inducedbirefringence (nsat) does depend on the wavelength, as shownin Table I. Moreover, the phase retardation varies with thewavelength.The lower part of Fig. 3 shows the wavelength-dependentnsat for the PSIP LC composite; here squares stand for theexperimental data listed in Table I and the solid line representsthe fitting curve with the following single-band birefringencedispersion model [15,16]:nsat = G λ2λ∗2λ2 − λ∗2λλ∗−−−→ Gλ∗2, (3)300 400 500 600 700 8000.050.060.070.080.090.100.120.140.160.180.200.22Δn satWavelength (nm)ΔnhostLC  hostLC composite FIG. 3. (Color online) Dispersion relations of the saturatedinduced birefringence of the PSIP LC composite (filled squares) andits nematic LC host MLC-14200 (open circles). Solid lines are fittingcurves.041706-2DISPERSION RELATION ON THE KERR CONSTANT OF A . . . PHYSICAL REVIEW E 83, 041706 (2011)where λ∗ is the average resonant wavelength of the LCcomposite and G is a proportionality constant. For a conjugatedLC compound, the two π → π∗ electronic transitionsusually occur in the UV region [22] and G decreases asthe temperature increases according to the order parameterS = (1 − T/Tc)β ; here the exponent β is a material constant[23]. For a multicomponent LC mixture, there will be severaldifferent π →π∗ electronic transition wavelengths, dependingon the conjugation length of the individual compound. Inthe off-resonance region, the single-band model treats theseπ → π∗ transition wavelengths as an average wavelength λ∗.This model works equally well for both single-compound andeutectic mixtures [24]. Similar to nematic LCs, the dispersionof the PSIP LC composite also follows the single-bandbirefringence dispersion model well. Through fittings, we findλ∗ ∼ 216 nm and G ∼ 1.205 × 10−6 nm−2.To correlate the dispersion property of the LC compositewith the LC host, we also measured the birefringence disper-sion of the LC host (MLC-14200) using an Abbe refractometer.The measured data are included in the upper part of Fig. 3,where the solid (blue) line is the fitting curve based on Eq. (3)with λ∗ ∼ 218 nm and G ∼ 3.047 × 10−6 nm−2. The twoobtained λ∗ values agree with each other to within 1%. This isnot surprising because the dispersion of the PSIP LC compositeis primarily determined by the LC host employed. On theother hand, the decreased G value of the polymer-stabilizedoptically isotropic LC composite mainly originates from thedecreased LC concentration. In our PSIP LC composite, the LCconcentration is only ∼56 wt% and the rest are chiral dopantsand photocurable monomers. Thus, the expected decrease inbirefringence is ∼44%, but the obtained G value is decreasedby ∼60%. This excessive ∼16% reduction could be attributedto two unaccounted factors: (1) The LC composite has alower clearing temperature than its host, and (2) some LCmolecules could be trapped by the polymer networks duringpolymerization process. The lower clearing point leads to adecreased order parameter while the trapped LC moleculesare hardly reoriented by the applied electric field.From Fig. 3, the nsat of the PSIP LC composite decreasesas the wavelength increases. When the wavelength is muchlonger than the resonant wavelength, i.e., λ  λ∗, the inducedbirefringence gradually saturates to a plateau (Gλ∗2) accordingto Eq. (3). When a PSIP LC composite is used in theinfrared region (say, λ > 1 μm), the induced birefringencewill reach a saturation level, similar to nematic liquidcrystals.In the low electric-field region (E  Es), the extended Kerreffect [Eq. (2)] is reduced to conventional Kerr effect [Eq. (1)].With Taylor’s expansion, the Kerr constant is expressed as [15]K = nsat/λE2s . (4)As shown in Table I, the obtained Kerr constant decreasesgradually with wavelength. Based on Eq. (4), we derive thedispersion relation of Kerr constant as follows:K = Gλλ∗2E2s (λ2 − λ∗2)= Aλλ∗2λ2 − λ∗2 , (5)where A = G/E2s is a proportionality constant. In Fig. 4, wefitted the Kerr constant data with Eq. (5) using λ∗ ∼ 216 nm400 500 600 700 80012345Kerr ConstantK(10-9 m/V2 )Wavelength (nm)FIG. 4. (Color online) Measured Kerr constant (squares) and thefitting results (solid line) of the PSIP LC composite at differentwavelengths.and A ∼ 0.0262 nm−1. The well-fitted data clearly demonstratethe implicit wavelength dependency of the Kerr constant.In the low-field region, the conventional Kerr effect is validandλK is a coefficient for calculating the induced birefringenceunder a given electric field. From Eqs. (3) and (4), the termλK has the same dispersion relation as nsat, which can bedescribed well by the single-band model. Therefore, to takethe implicit wavelength dependency of the Kerr constant intoconsideration, it would be clearer to rewrite the conventionalKerr equation asnind = Ko(λ,T )E2, (6)where Ko = λK (in units of m2/V2) is the modified Kerr coef-ficient representing the Kerr effect at a given wavelength andtemperature. Apparently, Ko decreases with the wavelengthand temperature according to the single-band model. Thetemperature-dependent Kerr constant K is indeed followingthe order parameter, as validated experimentally [25]. In thehigh-field region, the conventional Kerr effect is no longervalid so that the extended Kerr effect [Eq. (2)] has to beused.IV. CONCLUSIONSThe dispersion relation of a polymer-stabilized opticallyisotropic LC composite is investigated. The experimentalresults of λK follow the same dispersion trend as its nematichost LC, and can be described well by the single-bandbirefringence dispersion model. For display and photonicapplications, the wavelength-dependent Kerr constant has tobe taken into consideration.ACKNOWLEDGMENTThe authors are indebted to the Industrial TechnologyResearch Institute (Taiwan) for financial support.041706-3MEIZI JIAO, JIN YAN, AND SHIN-TSON WU PHYSICAL REVIEW E 83, 041706 (2011)[1] J. Kerr, Philos. Mag. 50, 337 (1875).[2] T. H. Havelock, Phys. Rev. 28, 136 (1909).[3] J. W. Beams, Rev. Mod. Phys. 4, 133 (1932).[4] A. Yariv and P. Yeh, Optical Waves in Crystal: Propagation andControl of Laser Retardation (Wiley, New York, 2002).[5] H. Kikuchi, M. Yokota, Y. Hisakado, H. Yang, and T. Kajiyama,Nat. Mater. 1, 64 (2002).[6] Y. Haseba, H. Kikuchi, T. Nagamura, and T. Kajiyama, Adv.Mater. 17, 2311 (2005).[7] Z. Ge, S. Gauza, M. Jiao, H. Xianyu, and S. T. Wu, Appl. Phys.Lett. 94, 101104 (2009).[8] L. Rao, J. Yan, S. T. Wu, S. Yamamoto, and Y. Haseba, Appl.Phys. Lett. 98, 081109 (2011).[9] L. Rao, Z. Ge, S. T. Wu, and S. H. Lee, Appl. Phys. Lett. 95,231101 (2009).[10] M. Jiao, Y. Li, and S. T. Wu, Appl. Phys. Lett. 96, 011102 (2010).[11] K. M. Chen, S. Gauza, H. Xianyu, and S. T. Wu, J. Disp. Technol.6, 49 (2010).[12] Y. H. Lin, H. S. Chen, H. C. Lin, Y. S. Tsou,H. K. Hsu, and W. Y. Li, Appl. Phys. Lett. 96, 113505(2010).[13] H. Y. Liu, C. T. Wang, C. Y. Hsu, T. H. Lin, and J. H. Liu, Appl.Phys. Lett. 96, 121103 (2010).[14] S. Meiboom, J. P. Sethna, P. W. Anderson, and W. F. Brinkman,Phys. Rev. Lett. 46, 1216 (1981).[15] J. Yan, H. C. Cheng, S. Gauza, Y. Li, M. Jiao, L. Rao, and S. T.Wu, Appl. Phys. Lett. 96, 071105 (2010).[16] S. T. Wu, Phys. Rev. A 33, 1270 (1986).[17] S. T. Wu, C. S. Wu, M. Warenghem, and M. Ismaili, Opt. Eng.32, 1775 (1993).[18] J. Jin, The Finite Element Method in Electromagnetics, 2nd ed.(Wiley-IEEE, New York, 2002).[19] J. Yan, M. Jiao, L. Rao, and S. T. Wu, Opt. Express 18, 11450(2010).[20] A. Lien, Appl. Phys. Lett. 57, 2767 (1990).[21] Z. Ge, X. Zhu, T. X. Wu, and S. T. Wu, J. Opt. Soc. Am. A 22,966 (2005).[22] S. T. Wu, E. Ramos, and U. Finkenzeller, J. Appl. Phys. 68, 78(1990).[23] I. Haller, Prog. Solid State Chem. 10, 103 (1975).[24] J. Li and S. T. Wu, J. Appl. Phys. 96, 170 (2004).[25] L. Rao, J. Yan, and S. T. Wu, J. Soc. Inf. Disp. 18, 954 (2010).041706-4

Dispersion relation on the Kerr constant of a polymer-stabilized optically isotropic liquid crystal

https://stars.library.ucf.edu/cgi/viewcontent.cgi?article=2434&amp;context=facultybib2010

Dispersion relation on the Kerr constant of a polymer-stabilized optically isotropic liquid crystal

Abstract

Similar works

Full text

Available Versions

University of Central Florida (UCF): STARS (Showcase of Text, Archives, Research & Scholarship)