An electrically controllable plasmonic enhanced coherent random lasing from the dye-doped nematic liquid crystal containing Au nanoparticles is demonstrated. To achieve the optimal control of the RL properties, the polarization of the pump light should be parallel to the rubbing direction of the cells. The lasing output intensity is direction-dependent and the substantial output distributes in an angle range of 0°~30° deviating from the direction of the pump stripe. The coherent feedback associated with the coherent random lasing mainly originates from the cooperative effect of the enhanced localized electric field in the vicinity of Au nanoparticles and the multiple scattering caused by the fluctuations of the liquid crystal director and local dielectric tensor.
© 2016 Optical Society of America
In recent years, random lasers have received enormous interest in research for their potential applications in the fields of display device, environment lighting and medical diagnostics . Random lasers have many advantages over conventional lasers, such as omni-directional emission, flexible shape and low fabrication cost , and they have been studied in many disordered or partially ordered materials, including semiconductor nanostructures [2–5], polymer films [6, 7], human tissues  and liquid crystals (LCs) [3, 9–14]. The nematic liquid crystal (NLC) has drawn much attention because the refractive index and the dielectric tensor of the NLC can be controlled by external thermal, electric or optic fields. The random lasing (RL) from the amplifying disordered dielectric material which was realized by infiltrating liquid crystal and laser dye inside sintered glass powders was observed by Wiersma in 2001 . Later, the coherent RL from the dye-doped NLC was reported and the corresponding mechanism was explained by Strangi [9, 16–18]. Afterwards, the optically and electrically controllable random lasers based on the dye-doped NLC were studied [19, 20]. In these works, the LC cells with thickness greater than 100 μm are usually used, because the emitted light cannot be confined in the thin cells for a long time to make the gain larger than the loss . In order to increase the scattering strength, Lee et al. introduced BiTiO3 nanoparticles (NPs) in the dye-doped NLC (DDNLC) and obtained a low threshold RL from the sample cell with low thickness of 23 μm .
Metal NPs are promising materials towards applications in random lasers because of their much larger scattering cross sections than dielectric NPs and the localized electric field enhancement in the vicinity of the surface of NPs due to the localized surface plasmon resonance (LSPR) [22–27]. In 2005, Dice et al. firstly reported the surface plasmon-enhanced incoherent random laser by introducing the silver (Ag) nanopowder in the Rhodamine 6G solution . 4 years later, Meng et al. reported the coherent RL in the weakly scattering polymer films containing the Ag NPs of ~50 nm in diameter . Hu fabricated a plasmonic polymer fiber laser based on the laser dye and gold (Au) NPs . Ziegler studied the RL from the thin film containing Rh6G and Au NPs with different shapes . Currently, Zhai observed a low threshold RL from an ultrathin plasmonic random laser consisting of a free-standing polymer membrane embedded with Ag NPs . In these works, the plasmonic RL in dye solutions and polymer films have been intensively investigated. However, the plasmonic enhanced RL in LCs is not studied in depth.
In this work, we investigate the electrically controllable plasmonic enhanced coherent RL from the dye-doped NLC containing the Au NPs (NPDDNLC) in the thin cells and study the roles of the Au NPs and the NLC in the formation of the RL. By analyzing the emission spectra and the lasing thresholds of the NPDDNLC and the dye-doped Au NP ethanol solution, we find that the enhancement of the localized electric field in the vicinity of Au NPs due to the LSPR is more effective in improving the lasing efficiency than the enhancement of the scattering strength of the medium. Furthermore, the multiple scattering of the NLC is also important in the formation of the low threshold RL. We observe that the thickness of the LC cells affects the RL properties. The threshold of the RL gradually decreases when the cell thickness increases from 10 μm to 26 μm. The lasing properties can be controlled by applying the direct current (DC) electric field on the LC cells. The lasing output intensity remains high and stable with 38 (a.u.) from 0.0 V/μm to 0.6 V/μm, then reduces sharply when the electric field is greater than 0.5 V/μm, and finally gains stability when the electric field is larger than 1.5 V/μm. The electrically controllable RL is achieved by changing the orientation of the NLC and dye molecules, thereby changing the absorption and the spontaneous emission of the dye. The lasing output intensity is direction-dependent. The considerable output distributed in an angle range of 0°~30° deviating from the direction of the pump stripe. The direction-dependent RL is mainly attributed to the fact that the fluorescence output intensity is different in different directions.
2. Sample preparation and experimental setup
The materials used in this experiment are the NLC P0616A (refractive indices ne = 1.72 and △n = 0.19 at 20 °C and 589 nm, dielectric constants ε⊥ = 5.2 and △ε = 11.5 at 20 °C and 1 kHz), the laser dyes DCM (from Exciton), and the ethanol solution of Au NPs of 50 nm in diameter. The number density of the Au NPs is ρ = 7.908 × 1011 / ml. We fabricated three kinds of samples with same 0.5 wt% laser dye: (1) the dye-doped NLC with addition of Au NPs, (2) the dye-doped NLC without addition of Au NPs and (3) the dye-doped Au NP ethanol solution. The dye-doped NLC with addition of Au NPs was obtained as follows. The NLC and the laser dye were mixed at the weight ratio of 99.5%:0.5%. The mixture was heated to the clearing point and stirred for one hour, and then was cooled to room temperature. The Au NP ethanol solution was added to the DDNLC solution with a volume ratio of 1:8, and the ultrasonic dispersion process in room temperature was applied to guarantee the dispersal of Au NPs and the volatilization of the ethanol. The number density of the NPs was 9.885 × 1010 / ml. In the dye-doped NLC without Au NPs, the Au NP ethanol solution adding step was not performed. In the dye-doped Au NP ethanol solution containing no NLC, the primary Au NP ethanol solution was diluted 8 times to get the same concentration of the Au NPs as the first kind of sample. The samples used in this study are listed in Table 1. In the experiment, the empty LC cells of 10 μm, 17 μm and 26 μm in thickness were used. The LC cells were fabricated by two polyvinyl alcohol (PVA) coated indium-tin-oxide coated (ITO) glass slides. The two glass slides were pre-rubbed in anti-parallel directions.
The experimental setup for measuring the emission spectra is shown in Fig. 1. A 532 nm laser beam, derived from a Q-switched Nd:YAG laser with pulse duration of 8 ns and a repetition rate of 10 Hz is used as the pump light. The pump laser is separated into two sub-beams when it passes through the NBS. One beam is monitored by the energy meter and the other sub-beam is used as the excitation beam. The excitation beam propagates along the z-axis, and is focused by a cylindrical lens (with focal length of 10 cm) to form an excited stripe on the cell (with width of 0.3 mm and length of 1 cm). The stripe and the polarization of the excitation beam are parallel to the rubbing direction (along the x-axis) of the cell. A fiber-optic probe is placed such that it faced one edge of the cell. The output lasing emission is collected by a spectrometer with a spectral resolution of 0.11 nm and is monitored in real time by a computer. An external DC voltage is applied on the cell using a DC regulated power supply.
3. Results and discussion
Figure 2(a) depicts the evolution of the emission spectra as a function of the pump energy from Sample 1 in the cell of 10 μm in thickness. As the pump energy increases from 9.71 μJ/pulse to 225.80 μJ/pulse, the intensity of the emission light increases gradually without narrowing. Figure 2(b) shows the output intensity and the full width at half maximum (FWHM) of the emission spectra versus the pump energy. In Fig. 2(b), the emission intensity gradually increases with the pump energy, nevertheless, no obvious knee point is observed. The FWHM of the spectra is larger than 13 nm, which illustrates that the observed light is the amplified spontaneous emission. The results in Figs. 2(a) and 2(b) demonstrate that although the fluctuations of the NLC director and the local dielectric tensor will cause the multiple scattering as the light passes the NLC , the scattering strength in cells with a thin thickness is weak , and the RL cannot occur because the loss is larger than the gain.
Figure 2(c) shows the emission spectra versus the pump energy from the DDNLC containing Au NPs in the cell of 10 μm in thickness and Fig. 2(d) illustrates the typical threshold behavior. At low pump energy, the spectra consist of a single broad spontaneous emission light with a bandwidth of ~36 nm. Upon increasing the pump energy to ~6.60 μJ/pulse, the discrete sharp peaks in the wavelength range of 603-617 nm emerge above the spontaneous emission, implying the generation of the RL. The FWHM of these peaks is about 0.3 nm, which is ~120 times lower than the bandwidth of the spontaneous emission. The corresponding Q factor, determined by λ/∆λ, is over 2000. The intensity of the peaks enhances rapidly when the pump energy further increases. The lasing threshold is about 6.60 μJ/pulse, as shown in Fig. 2(d).
We can only observe the amplified spontaneous emission from the DDNLC in absence of the Au NPs, but we can achieve the low threshold RL from the DDNLC when it has the Au NPs. It indicates that the Au NPs play an important role in the formation of the RL. Au NPs enhance the lasing efficiency via two main mechanisms [23, 30]: (1) Enhancement of the localized electric field in the vicinity of the Au NPs due to the LSPR. (2) Enhancement of the scattering strength of the medium. In order to determine which of these two mechanisms is more effective in enhancing the lasing efficiency in our experiment, we calculate the scattering mean free path of the Au NPs in Sample 2. The scattering mean free path ls can be estimated via the formula ls = 1/ρδs, where ρ and δs are the number density and the scattering cross section of the Au NPs. In Sample 2, the number density of the Au NPs is 9.885 × 1010/ml, and the scattering cross section is 1.51 × 10−11 cm2 at λ = 610 nm in NLC P0616A calculated by the Discrete Dipole Approximation method [31–33]. Thus, ls is obtained to be ~0.67 cm, which is 6.7 × 102 times larger than the thickness of the cell (10 μm). It demonstrates that in Sample 2, the scattering effect provided by the Au NPs is weak due do the low density of Au NPs. Therefore, the enhanced localized electric field effect is more effective in enhancing the lasing properties in our experiment.
To illustrate that the enhanced localized electric field is the major mechanism for the enhanced lasing properties further and to learn the effect of the NLC on the RL, we study the lasing properties of the dye-doped Au NPs ethanol solution (Sample 3). The scattering mean free path of Au NPs in Sample 3 is the same as that in Sample 2. Figure 2(e) shows the evolution of the emission spectra from Sample 3 in the cell of 10 μm in thickness and Fig. 2(f) depicts the corresponding peak intensity and the FWHM versus the pump energy. The RL can be observed from Sample 3, but the threshold is quite high. The lasing threshold is ~89.30 μJ/pulse, which is about 13.3 times larger than the lasing threshold of Sample 2 in the cell of same thickness. It indicates that the multiple scattering provided by the Au NPs is weak, and the scattering from the fluctuations of the LC director and local dielectric tensor in Sample 2 is important in reducing the lasing threshold. The lasing peaks are at the wavelength range of 622-640 nm. Compared with the emission band of Sample 2, the emission band of Sample 3 is red-shifted about 21 nm. According to the experimental results in Fig. 2, we can safely draw a conclusion that the enhancement in lasing by the Au NPs is the enhanced localized electric field, and the fluctuations of the LC molecules play an important role in the low threshold RL.
The mechanism of the formation of the low threshold RL in the NPDDNLC is shown in Fig. 3. The pump light and the emission from the dye can be localized around the Au NPs due to the LSPR, leading to the increased absorption by the dye and the enhanced fluorescence amplification. Local resonances induced by the Au NPs can create spatially localized modes. The fluctuations of the LC director and local dielectric tensor and the Au NPs can cause light scattering. The light waves associated with the spatially localized modes undergo multiple scattering and some of them may have a longer dwelling time in the LC cell. When the gain becomes larger than the loss, the RL will be engendered.
We study the effect of the cell thickness on the lasing properties. Figure 4(a) shows the emission spectra from Sample 2 in the cells of 10 μm, 17 μm and 26 μm in thickness with fixed pump energy (8.39 μJ/pulse). The lasing intensity increases gradually as the cell thickness increases from 10 μm to 26 μm. Figure 4(b) summarizes the evolution of the emission intensity versus the pump energy from Sample 2 in different cells. The lasing thresholds of Sample 2 in the cells of 10 μm, 17 μm and 26 μm in thickness are about 6.70 μJ/pulse, 4.65 μJ/pulse and 3.90 μJ/pulse respectively. We find that the threshold of the RL decreases with the increase of the cell thickness. This is because the number of dye molecules is larger and the emitted light has a longer dwelling time in the thick cells.
The RL emission from the DDNLC containing Au NPs can be controlled by applying the DC electric field. Figure 5(a) shows the emission spectra at different electric fields from Sample 2 in the cell of 10 μm in thickness and the inset summarizes the variation of the peak intensity versus the electric field. The pump energy is fixed at 17.87 μJ/pulse and the polarization of the pump light is set to be parallel to the rubbing direction (along the x-axis). Clearly, the intensity of the RL peaks can be controlled to change from a high value (~38 a.u.) to a low value (~5 a.u.). The lasing output intensity undergoes three main phases when the electric field increases from 0 V/μm to 2.1 V/μm. At first, the output shows stable and high intensity when the electric field is lower than 0.6 V/μm. The output intensity sharply reduces in second phase when the electric field increases gradually from 0.6 V/μm to 1.5 V/μm. Finally, when the applied electric field increases further from 1.5 V/μm value, the lasing output exhibits stability again with lower intensity. The electrically controllable RL is mainly caused by the reorientation of the LC director, followed by the reorientation of the dye molecule’s long axis . The absorption intensity of the dye is related to the size of the intersection angle between the polarization of the pump light and the long axis of the dye molecule. The dye molecule absorbs much more light for the optical field polarization parallel to its long axis than for the optical field polarization perpendicular to its long axis . When the electric field is absent or weak, the NLC director and the long axis of the dye molecule are along the rubbing direction. The fluorescence intensity is largest because the long axis of the dye molecule is parallel to the polarization of the pump light. As the electric field becomes larger than a typical value, the LC director will rotate a certain angle along the electric field (z direction) and the dye molecules will rotate with the LC molecules due to the gust-host effect. This makes the long axis of the dye molecule no longer parallel to the polarization of the pump light, leading to the decrease of the fluorescence intensity. The fluorescence intensity will decrease to the minimum when the long axis of the dye molecule is eventually perpendicular to the polarization of the pump light. With further increase in the electric field, the dye molecules do not rotate anymore and the fluorescence intensity keeps relatively stable.
To achieve the optimal control of the lasing properties, the polarization of the pump light should be parallel to the rubbing direction (see Fig. 5(a)). If we set the polarization of the pump light perpendicular to the rubbing direction, the applied electric field has little effect on the lasing output, as shown in Fig. 5(b). In the experiment of Fig. 5(b), the polarization of the pump light is set to be parallel to the y-axis. We can see that the emission intensity has no significant change when the applied electric field increases from 0 V/μm to 2.1 V/μm. As the electric field applies on the cell, the rotation of the LC and dye molecules occurs in the x-z plane. The polarization of the pump light is always perpendicular to the long axis of the dye molecules. Therefore, the fluorescence intensity does not change with the increase of the applied electric field. As a contrast, the emission characteristics of the DCM doped Au ethanol solution (Sample 3) as a function of the applied electric field are examined, as shown in Fig. 5(c). The pump energy is fixed at 38.80 μJ/pulse. The emission intensity of the RL does not decrease as the electric field increases from the 0 V/μm to 2.1 V/μm. This is because the absence of the LC makes the long axes of the DCM molecules in Sample 3 do not rotate with the electric field, the emission intensity does not change when the electric field is applied.
Although the NPDDNLC does not contain any external cavities, we find that the RL output intensity is direction-dependent. Figure 6(a) depicts the schematic diagram of the lasing output at different θ. θ is defined as the angle between the receiving direction of the RL and the rubbing direction of the cells. The lasing output intensity of Sample 2 in the cell of 10 μm in thickness at different angles is shown in Fig. 6(b). Clearly, the emission intensity decreases quickly with the increase of the θ. The output light is strongly confined in an angle range of 0°~30° from the direction of the stripe. For instance, the emission intensity at θ = 45° is about 20% compared with that at θ = 0°. There are two possible reasons to explain the direction-dependency of the RL emission. (1) The alignment of the dye and NLC molecules makes the fluorescence intensity along the stripe stronger than that perpendicular to the stripe. (2) The stripe length of the pump light (~1 cm) is much longer than the stripe width (~17 μm) and the penetration length (10 μm), so the optical gain along the long axis of the stripe is much larger than the other directions. In order to identify which of these two reasons gives rise to the direction-dependent emission, we study the variation of the output intensity with the angle θ from the dye-doped Au ethanol solution (Sample 3), as presented in Fig. 6(c). In Sample 3, the dye molecules are randomly distributed due to the absence of the NLC, so the fluorescence output does not have any preferred directions. It can be observed in Fig. 6(c) that the output intensity undergoes a little change as the angle increases from 0° to 60°. Nevertheless, with further increase in the angle θ, the output intensity begins to decrease. The result demonstrates that the decrease of the output intensity in Fig. 6(b) is mainly caused by the reason (1) mentioned above when the angle θ is less than 60°. The reason (2) comes into play in the decrease of the emission intensity as the angle increases further from 60°.
In conclusion, we have observed the plasmonic enhanced coherent RL from the DDNLC containing Au NPs in the thin LC cells. We analyze the effects of the Au NPs and the NLC in the formation of the RL. The enhanced action of the Au NPs on the RL is mainly achieved through the enhancement of the localized electric field in the vicinity of the Au NPs and the fluctuations of the director and the local dielectric tensor of the NLC provide the multiple scattering for the formation of low threshold RL. The thresholds of the RL decrease with the increase of the thickness of the cells. We realize the electrically controllable RL in the NPDDNLC. The output intensity undergoes a pattern of stability, then reduction, and finally stability when the applied electric field increases from 0 V/μm to 2.1 V/μm. Manipulation of the coherent RL is achieved by changing the direction of the LC director and the dye molecule’s long axis, thereby changing the absorption and the fluorescence emission of the dye. In order to achieve the optimal control of the RL, we should set the polarization of the pump light parallel to the rubbing direction of the cells. If the polarization is set to be perpendicular to the rubbing direction, the applied electric field will have little effect on the lasing output. In addition, the emission intensity of the RL is direction-dependent. The lasing output is confined in an angle range of 0°~30° deviating from the direction of the pump stripe. This deviation is due to the fact that the fluorescence emission intensity and the optical gain intensity are unequal in different collecting directions.
National Natural Science Foundation of China (NSFC) (11474021).
References and links
1. D. S. Wiersma, “The physics and applications of random lasers,” Nat. Phys. 4(5), 359–367 (2008). [CrossRef]
2. H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seelig, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82(11), 2278–2281 (1999). [CrossRef]
3. L. W. Li, L. Wang, and L. G. Deng, “Low threshold random lasing in DDPDLCs, DDPDLC@ZnO nanoparticles and dye solution@ZnO nanoparticle capillaries,” Laser Phys. Lett. 11(2), 025201 (2014). [CrossRef]
4. T. M. Sun, C. S. Wang, C. S. Liao, S. Y. Lin, P. Perumal, C. W. Chiang, and Y. F. Chen, “Stretchable Random Lasers with Tunable Coherent Loops,” ACS Nano 9(12), 12436–12441 (2015). [CrossRef] [PubMed]
5. T. Nakamura, B. P. Tiwari, and S. Adachi, “Control of random lasing in ZnO/Al2O3 nanopowders,” Appl. Phys. Lett. 99(23), 231105 (2011). [CrossRef]
6. X. G. Meng, K. Fujita, S. Murai, and K. Tanaka, “Coherent random lasers in weakly scattering polymer films containing silver nanoparticles,” Phys. Rev. A 79(5), 053817 (2009). [CrossRef]
7. A. Consoli, D. Mariano da Silva, N. U. Wetter, and C. López, “Large area resonant feedback random lasers based on dye-doped biopolymer films,” Opt. Express 23(23), 29954–29963 (2015). [CrossRef] [PubMed]
8. R. C. Polson and Z. V. Vardeny, “Random lasing in human tissues,” Appl. Phys. Lett. 85(7), 1289–1291 (2004). [CrossRef]
9. G. Strangi, S. Ferjani, V. Barna, A. De Luca, C. Versace, N. Scaramuzza, and R. Bartolino, “Random lasing and weak localization of light in dye-doped nematic liquid crystals,” Opt. Express 14(17), 7737–7744 (2006). [CrossRef] [PubMed]
11. J.-L. Zhu, W.-H. Li, Y. Sun, J.-G. Lu, X.-L. Song, C.-Y. Chen, Z. Zhang, and Y. Su, “Random laser emission in a sphere-phase liquid crystal,” Appl. Phys. Lett. 106(19), 191903 (2015). [CrossRef]
12. D. S. Wiersma and S. Cavalieri, “Temperature-controlled random laser action in liquid crystal infiltrated systems,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(5), 056612 (2002). [CrossRef] [PubMed]
13. L. Wang, M. Wang, M. C. Yang, L. J. Shi, H. Yang, and L. G. Deng, “Bichromatic coherent random lasing from dye-doped polymer stabilized blue phase liquid crystals controlled by pump light polarization,” Chin. Phys. B (to be published).
14. R. N. Wu, J. Wu, X. J. Wu, and Q. Dai, “Temperature-tunable lasing in negative dielectric chiral nematic liquid crystal,” Chin. Phys. B 24(5), 054211 (2015). [CrossRef]
17. S. Ferjani, L. Sorriso-Valvo, A. De Luca, V. Barna, R. De Marco, and G. Strangi, “Statistical analysis of random lasing emission properties in nematic liquid crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(1), 011707 (2008). [CrossRef] [PubMed]
19. C. R. Lee, J. D. Lin, B. Y. Huang, T. S. Mo, and S. Y. Huang, “All-optically controllable random laser based on a dye-doped liquid crystal added with a photoisomerizable dye,” Opt. Express 18(25), 25896–25905 (2010). [CrossRef] [PubMed]
20. C. R. Lee, J. D. Lin, B. Y. Huang, S. H. Lin, T. S. Mo, S. Y. Huang, C. T. Kuo, and H. C. Yeh, “Electrically controllable liquid crystal random lasers below the Fréedericksz transition threshold,” Opt. Express 19(3), 2391–2400 (2011). [CrossRef] [PubMed]
21. C. R. Lee, S. H. Lin, J. W. Guo, J. D. Lin, H. L. Lin, Y. C. Zheng, C. L. Ma, C. T. Horng, H. Y. Sun, and S. Y. Huang, “Electrically and thermally controllable nanoparticle random laser in a well-aligned dye-doped liquid crystal cell,” Opt. Mater. Express 5(6), 1469–1481 (2015). [CrossRef]
23. S. Ning, Z. Wu, H. Dong, L. Ma, B. Jiao, L. Ding, L. Ding, and F. Zhang, “The enhanced random lasing from dye-doped polymer films with different-sized silver nanoparticles,” Org. Electron. 30, 165–170 (2016). [CrossRef]
24. G. D. Dice, S. Mujumdar, and A. Y. Elezzabi, “Plasmonically enhanced diffusive and subdiffusive metal nanoparticle-dye random laser,” Appl. Phys. Lett. 86(13), 131105 (2005). [CrossRef]
25. X. Meng, K. Fujita, S. Murai, T. Matoba, and K. Tanaka, “Plasmonically controlled lasing resonance with metallic-dielectric core-shell nanoparticles,” Nano Lett. 11(3), 1374–1378 (2011). [CrossRef] [PubMed]
26. L. W. Li and L. G. Deng, “Random lasers in dye-doped polymer-dispersed liquid crystals containing silver nanoparticles,” Physica B 407(24), 4826–4830 (2012). [CrossRef]
27. C. Wang and L. G. Deng, “Electrically controlled plasmonic lasing resonances with silver nanoparticles embedded in amplifying nematic liquid crystals,” Laser Phys. Lett. 11(11), 115814 (2014). [CrossRef]
28. Z. Hu, Y. Liang, P. Gao, H. Jiang, J. Chen, S. Jiang, and K. Xie, “Random lasing from dye doped polymer optical fiber containing gold nanoparticles,” J. Opt. 17(12), 125403 (2015). [CrossRef]
30. W. Z. W. Ismail, T. P. Vo, E. M. Goldys, and J. M. Dawes, “Plasmonic enhancement of Rhodamine dye random lasers,” Laser Phys. 25(8), 085001 (2015). [CrossRef]
31. B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333(2), 848–872 (1988). [CrossRef]
32. B. T. Draine and P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11(4), 1491–1499 (1994). [CrossRef]
33. B. T. Draine and P. J. Flatau, “User Guide for the Discrete Dipole Approximation Code DDSCAT 7.3,” (2013).
34. I.-C. Khoo, Liquid Crystals: Physical Properties and Nonlinear Optical Phenomena (John Wiley & Sons, Inc., 1995).