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The reorientation inversion of liquid crystal molecules in azo-dye-doped liquid crystal (ADDLC) films irradiated by biphotonic (green and red light) lasers is studied using the self-phase-modulation method. The results show that the induced change of refractive index (∆n) in an ADDLC cell illuminated with a fixed intensity of green light increases with the red-light intensity. Notably, the value of ∆n is initially negative, and becomes positive when the intensity of the red laser is increasing. It is due to the fact that an extra positive torque is exerted on the LCs, which is produced by cis-isomers upon absorbing red light to compensate the negative torque induced by the excitation of the green light.
©2011 Optical Society of America
1. Introduction
The molecular reorientation in the dye-doped nematic liquid crystal cell (DDNLC) has attracted much interest because of its potential applications in display, optical storage, image processing, optical limiting, tunable lenses, and optical devices. For the liquid crystal (LC) (with dielectric anisotropy ∆ε>0) cell doped with an anthraquinone (AQ) dye after being illuminated suitable laser light, the LC molecules are reoriented to the direction parallel to the optical field [1,2]. The reason is that the irradiation of the laser beam establishes the electric dipole inside the excited-state AQ-dye molecules, and which then provides an extra torque to align LC molecules parallel to the optical field. This torque is called a positive torque, because the reorientation direction of LC molecules under such a torque is the same as that under the photo-induced torque. Unlike AQ dye molecules, azo dye molecules have a variation in molecular structures after absorbing suitable optical energy. The transformation of the molecular structure of an azo dye is called photoisomerization. The two isomers are trans and cis. The dye-induced torque in an azo-dye-doped nematic liquid crystal (ADDLC) cell is dependent on the structure of the chosen dye molecules, the category of the liquid crystal, as well as the wavelength, the polarization, and the intensity of the exciting light [3–7]. However, the interaction between the azo dyes and the LCs is not well-understood [8]. Janossy et al. present a model, in which the trans- and the cis-isomers are considered to be different dye dopants, and contribute a negative (ηt) and a positive enhancement (ηc) of the dye-induced torque, respectively [5–7]. The negative and positive torques from trans- and cis-isomers, which reorient LC molecules perpendicular and parallel to the polarization of the pump laser, respectively, can cancel each other.
For some azo dyes, the cis-isomers exhibit a new n-π* absorption in the long wavelength region, which is not within the absorption spectrum of the trans-isomers [9–11]. Immediately after the cis-isomers absorb the optical energy in the long wavelength region, they are photoisomerizated back to the trans-isomers. The trans→cis and cis→trans photoisomerizations, which are induced simultaneously by two wavelengths of photons, is called the biphotonic effect. Notably, the transition of the cis→trans photoisomerization upon the absorption of the biphotonic light beams is much faster than that upon the absorption of one laser light. When an ADDLC cell is irradiated by biphotonic lasers under a proper intensity ratio of the lasers, the molecular reorientation of LCs tends to remain in their initial direction [11,12].
In this paper, the photo-induced reorientation of liquid crystals in ADDLC films was studied by observing the diffraction patterns resulted from self-phase modulation (SPM). The SPM results indicate that the induced change of refractive index (∆n) in an ADDLC cell illuminated by biphotonic lasers rises from a negative to a positive with the increasing IR. The reason is due to the fact that the red light provides an extra positive torque in the ADDLC film, and which increases with the red-light intensity. This study proves a further understanding in the biphotonic-induced molecular reorientation of liquid crystals doped with azo dyes.
2. Experiments
In this experiment, the nematic LC and the azo-dye used are BL009 and D2 (all from Aldrich), respectively. The ordinary and extraordinary refractive indices of BL009 are no = 1.5266 and ne = 1.8181, respectively. D2 was doped into the LC host at a concentration of ~0.5 wt%. The clear temperature of LC BL009 is ~108 °C. The homogeneous mixture was injected into an empty cell, which was made from two indium-tin-oxide (ITO)-coated pieces of glass, separated by 50 μm-thick spacers to form a sample. Each piece of ITO glass was coated with surfactant N, N-dimethyl-N-octadecyl-3-aminopropyl trimethoxysilyl chloride (DMOAP) to promote homeotropical alignment. The homeotropical alignment of the cell was verified using a conoscopic technique.
The self-phase-modulation (SPM) method is used to study the reorientation inversion of liquid crystal molecules in azo-dye-doped liquid crystal (ADDLC) films. It is a very convenient method, which does not need complex mathematic calculations and setups. Figure 1 shows the experimental setup. A linearly polarized continuous-wave (CW) diode-pumped solid state (DPSS) laser (wavelength λ = 532 nm) is focused by a lens with a focal length of 5 cm, and then is used to irradiate the sample at an incident angle of ~45°. The exciting green DPSS laser beam is an E-wave. A screen was placed ~14.5 cm behind the sample to observe the SPM diffraction rings. When required, another CW Ar+-Kr+ laser, which emits red light at λ = 649 nm, is applied to the rear of the sample at an angle of ~5°, as presented in Fig. 1. The red Ar+-Kr+ laser is p-polarized. The radius of the red beam on the sample is larger than that of the green beam, so that the spot of green beam can be covered completely.
Fig. 1 Experimental setup; DPSS: diode pumped solid-state laser, P: polarizer, L1: 5 cm convex lens, L2: 3 cm convex lens, NDF: neutral density filter.
3. Theory
Azo-dyes are usually stable as trans-isomers in the dark. Excitation resonantly transforms their structures from the trans- to the cis-isomers. The absorption spectra of azo-dye (D2) doped LC sample in the dark and when irradiated by one green light with intensity ~10 mW/cm2 for 5 min were reported in Ref [11]. The trans-isomers of D2 do not absorb red light. After they are excited by green light, the trans-isomers are photoisomerized to become the cis-isomers. The cis-isomers are isomerized immediately back to the trans-isomers after absorbing red light. The fraction of cis-isomers, X, in the biphotonic experiment can be described by
where σit,G, σic,G, and σic,R are the absorption cross sections of the trans- and cis-isomers, respectively, for green (G) and red (R) light with i being the polarization. Φtc and Φct are the quantum efficiencies of the trans-to-cis and the cis-to-trans transitions, respectively. hν are hν' are the photon energies of green and red light, respectively. IiG and IiR are the intensities of green and red lasers with the i polarization, respectively. τ is the thermal relaxation time from the cis- back to the trans-state, which is related to the environmental temperature and the intensities of the lasers.Therefore, the fraction of cis-isomers in the steady state, Xeq, is given by
with the saturation intensity of green lightand the characteristic intensity of red lightwhere the saturation cis fraction isConsidering that the trans- and the cis-isomers are different dye dopants, which contribute a negative and a positive torque, respectively [5–7], the dye-induced torque in the biphotonic experiment can be presented as
where C 1 and C 2 are the coefficients of the dye-induced torques resulted form absorbing the photon energies of the green and red light, respectively. These coefficients are related to the absorption coefficient of the sample, the transmission coefficient at the input face, and the material parameters of the liquid crystals [13]. ηt and ηc are the enhancement factor of the dye-induced torque contributed by the trans- and the cis-isomers, respectively, which are negative and positive. β 1 and β 2 are the incident angles of the green and red lasers, respectively. The dye-induced torque produced by the cis isomers upon absorbing red light is a positive torque, and is given byNotably, from Eqs. (2) and (7), it is known that a high red-light intensity results in a low cis/trans concentration ratio, and however gives rise to a large Γdye,R.
When the sample is irradiated by green laser only, the dye-induced torque is
withwhere the cis fraction is X = XiS/(1 + IiS/IiG). η is the amplification factor of dye-induced torque resulted from absorbing the green-laser light. η increases linearly with X from a negative to a positive for azo dyes with |ηt|<|ηc| [6]. When IiG = IiS, the cis fraction is a half of the saturation cis fraction. The DO3 dye with 0.2 wt% doped into liquid crystals has the saturation intensity IS = 1.3 mW/cm2 for the laser with λ = 488 nm [5].4. Results and discussions
Figure 2 shows the photographs of the SPM diffraction rings of the ADDLC film that was irradiated by a p-polarized DPSS laser with IG = 0.3~1.8 W/cm2. Self-phase modulation results from that the excitation laser induces the change of the refractive index of the sample, which influences the phase of the excitation laser itself, and thus generates a diffraction ring pattern in the far field [14–16]. The results shown in Fig. 2 presents that the number of SPM diffraction rings, N, increases with IG to a maximum N = 12 at IG = 0.7 W/cm2, then decreases to zero at IG = 1.1 W/cm2, and increases again to a saturated N = 5 at IG = 1.8 W/cm2. Media 1 shows the dynamic variation of diffraction rings when IG increases. Notably, N = 0 means that the director of LC molecules is in the original orientation. Accordingly, the results shown in Fig. 2 present a reorientation inversion of LC molecules with the increase of IG.
Fig. 2 Photographs of self-phase-modulation diffraction patterns of an ADDLC film illuminated with various intensities of pump green laser light. Media 1 shows the dynamic variation of diffraction rings when IG increases.
From the known N, the magnitude of induced change of refractive index |∆n| can be estimated [14–16]. As shown in Fig. 1, the green laser is incident onto the sample obliquely in this experiment. Notably, the liquid crystals doped with azo dyes D2 tend to be reoriented to the direction perpendicular to the polarization of the exciting laser with low intensity [11], which means that ∆n is negative in the low IG region. Figure 3 plots the variation of ∆n of the ADDLC cell with IG. The reason can be understood by referring to Eq. (8), which shows that the dye-induced torque is related to the square of IG. Therefore, for azo dyes with |ηt|<|ηc|, there should exist a negative extreme value of ∆n in the low IG region, and then ∆n increases from the negative value to a positive value through zero with the increasing IG, as shown in Fig. 3. The extreme value of ∆n was observed to be −0.9028 at IG = 0.7 W/cm2. When IG is 1.1 W/cm2, ∆n is zero corresponding to the dye-induced torque being zero. It means that the torques contributed from trans- and cis-isomers cancel each other completely. In the region IG = 1.1~1.8 W/cm2, ∆n becomes positive and increases with IG, where the LC molecules tend to be reoriented with their long axes parallel to the polarization of the green laser. When IG is above 1.3 W/cm2, a saturation phenomenon of molecular reorientation of LCs is observed.
Fig. 3 Variation of the induced change of refractive index for the ADDLC cell with the intensity of green light.
Similar experiments were performed in a pure LC (BL009) cell and in an azo-dye-doped LC cell with the application of an external AC (1 kHz) voltage ~30V. The results show that the no diffraction rings were observed for these two films in the region IG = 0.3~1.3 W/cm2. These results indicate that the contribution of the optical field-induced reorientation and the thermal effect to the number of SPM diffraction rings can be neglected.
Figures 4(a)-(f) present the SPM diffraction patterns of ADDLC film illuminated with a fixed green light intensity IG = 0.7 W/cm2 and with various red-light intensities. The two lasers were p-polarized (Fig. 1). Clearly, N decreases when the red-light intensity (IR) rises, reaching zero at IR = 4.4 W/cm2, and then increasing with IR. Figure 5 presents that the variation of ∆n with IR from the results shown in Fig. 4(a)-(f). Such a variation of ∆n in the biphotonic experiment is due to the fact that an extra positive torque is produced by cis-isomers absorbing red light (Eq. (6)) to compensate the negative torque produced by the green laser. The higher the intensity of red light is, the higher the extra positive torque (Γdye,R) is (see Eq. (7)). Because the dye-induced torque in an ADDLC sample illuminated solely with IG = 0.7 W/cm2 is negative, the total dye-induced torque and ∆n increase from negative values to positive values with the growth of IR, as shown in Fig. 5.
Fig. 4 Photographs of steady-state SPM patterns of an ADDLC film (a)-(f) illuminated with a fixed green-light intensity IG = 0.7 W/cm2, but with various red-light intensities; (g)-(i) applied green light, red light and an external AC (1 kHz) voltage ~30V simultaneously.
Fig. 5 The variation of ∆n in the ADDLC film illuminated with a fixed green light intensity IG = 0.7 W/cm2 and various intensities of red light.
When IR is below 4.4 W/cm2, LC molecules in an ADDLC cell are reoriented towards back to their initial orientation from the direction pushed by the negative torque induced by the illumination of the green laser with IG = 0.7 W/cm2. Thus, N decreases with the increase of IR, as shown in Figs. 4(a)-(b). When IR reaches 4.4 W/cm2, LC molecules are back to their original orientation, because the negative torque induced by azo dyes absorbing green light (Γdye,G) is completely offset by the positive torque Γdye,R. Hence, no diffraction ring was observed in the screen, as presented in Fig. 4(c). In the region with IR being above 4.4 W/cm2, |Γdye,R| is larger than |Γdye,G|. The overall torque becomes positive and increases with IR. Hence, N increases with IR , as shown in Figs. 4(d)-(f). Besides, no diffraction ring was observed in the ADDLC film illuminated with 0.7 W/cm2 IG and various IR under the application of an AC (1 kHz) external voltage ~30 V, as shown in Figs. 4(g)-(i). It means that the contribution of the thermal effect to the number of diffraction rings can be ignored.
The biphotonic effect of the ADDLC film in the intensity interval IG = 1.1~1.8 W/cm2 (refer to Fig. 2) was also investigated by examining the SPM diffraction rings. The experimental results indicate that N can always be enhanced by red light when the input IG is 1.1~1.8 W/cm2. Figure 6 presents the photographs of the SPM diffraction rings of an ADDLC film illuminated with IG~1.15 W/cm2 only, and simultaneously illuminated with IR~3 W/cm2. The reason is that the torque in the sample illuminated with IG = 1.1~1.8 W/cm2 only is positive (see above), and red light can produce a positive Γdye,R to enhance the number of SPM diffraction rings. In this case, the thermal effect was also verified to be negligible, because the diffraction rings disappeared when an AC (1 kHz) external voltage of ~30 V was applied.
Fig. 6 Photographs of steady-state SPM patterns of an ADDLC film illuminated (a) with IG~1.15 W/cm2 only and (b) simultaneously illuminated with IR~3 W/cm2.
To investigate the biphotonic effect in the ADDLC film further, experiments with the applications of green and red light (IG and IR) that result in no SPM diffraction ring were performed. No diffraction ring means that the director of LC molecules remains unchanged with the balance of the negative and positive torques, respectively produced by the green and red lasers. Figure 7 presents the result. It shows that IR required to offset completely Γdye,G increases with the growth of IG. The experimental results are also consistent with the result of Eq. (6).
Fig. 7 The relation between green light intensity and red light intensity that results in no diffraction ring.
5. Conclusion
In the present study, the molecular reorientation in an ADDLC film irradiated solely by green laser and by biphotonic (green and red) lasers is studied by the SPM method. The number of SPM diffraction rings of an ADDLC film under the sole illumination of a green pump laser increases with IG, then decreases almost to zero, and finally rises again with the increase of IG. The reason is that the dye-induced torque is related to the square of IG. Further, the biphotonic results present that the value of ∆n in an ADDLC cell irradiated by both the green and red lasers increases with the red-light intensity IR. It is due to the fact that an extra positive torque is produced by cis-isomers absorbing red light, and increases with IR. The contributions of the optical field-induced reorientation and thermal effect are verified to be negligible in the present case.
Acknowledgments
The authors would like to thank the National Science Council of the Republic of China (Taiwan) for financially supporting this research under the Grant No. NSC 98-2112-M-006-011-MY3. Additionally, this work is partially supported by Advanced Optoelectronic Technology Center.
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