# Fast-Response Liquid Crystals for 6G Optical Communications

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Material Characterizations

_{m}) and clearing temperature (T

_{c}). From Table 1, these two materials show a wide nematic range to meet the requirements for LCoS applications in 6G communications. The dielectric constants were measured with a multifrequency LCR meter, HP-4274. Both mixtures have a reasonably large dielectric constant (Δε > 15), which helps to lower the threshold voltage. According to the measured free relaxation response time of the test cell [20], the viscoelastic constant γ

_{1}/K

_{11}of each mixture can be extracted. For comparison, we also include the properties of a Merck high birefringence LC material, BL038 [21], as shown in Table 1. From Table 1, we can see that these two materials exhibit high Δn, large dielectric constants, and relatively low viscoelastic constants.

#### 2.1. Birefringence

_{c}(unit: K) is the clearing temperature of the LC (measured by DSC), Δn

_{0}represents the extrapolated birefringence when T = 0 K, and exponent β is a material parameter. The values of both Δn

_{0}and β can be obtained by fitting the experimental data with Equation (1), whose results are listed in Table 2.

#### 2.2. Viscoelastic Constant

_{1}/K

_{11}is also an important parameter affecting the LCoS response time. We measured γ

_{1}/K

_{11}through the transient decay time of an LC cell. The obtained results are plotted in Figure 5, where dots and triangles are the measured results, and solid lines are the fitting results using the following equation [24]:

_{a}is the activation energy, and k

_{B}is the Boltzmann constant. Here, A and E

_{a}are fitting parameters, whose values are also included in Table 2.

#### 2.3. Figure of Merit

_{1}/K

_{11}. From the figure, we can see that as the temperature increases, FoM increases first, reaching a peak, and then declines sharply as the temperature approaches T

_{c}. The reason the FOM shows such a tendency is that both Δn and γ

_{1}/K

_{11}decrease but at different rates as the temperature initially increases. In Figure 3, Δn decreases slowly as the temperature gradually increases, but the decreasing rate becomes more pronounced as the temperature approaches T

_{c}. However, γ

_{1}/K

_{11}shows an opposite trend, i.e., it decreases rapidly in the beginning and then gradually saturates as the temperature gets closer to T

_{c}. Detailed mechanisms have been explained in Ref. [24].

#### 2.4. Voltage-Dependent Phase Change

_{2π}= 5 V), and the intended operation temperature and wavelength. In the experiment, for convenience we measured the voltage-dependent transmittance (V–T) curves of these two materials using transmission-type LC cells at λ = 1550 nm and then converted to the voltage-dependent phase (V–Φ) curves depicted by red lines in Figure 7. Since the operating temperature of a working LCoS device could vary from 40 to 60 °C due to the thermal effects from the backplane driving circuits and the employed light source, we measured the electro-optic effects at 40, 50, and 60 °C for LCM-1107 (Figure 7a–c) and LCM-2018 (Figure 7d–f), respectively. From the measured results (red lines) shown in Figure 7, when the applied voltage is 5 V, the phase change is more than 2π, which means we can use a thinner cell gap (optimal cell gap) to achieve the desired V

_{2π}= 5 V at each temperature. Due to the limited available cell gaps in our lab, we extrapolated the V–Φ curve to the corresponding optimal cell gap as shown by the blue lines in Figure 7. The optimal cell gaps and the extrapolated V–Φ curves are obtained according to the phase retardation equation δ = 2πdΔn/λ. Since the cell gap is thinner, the response time is faster, as will be discussed quantitatively later.

#### 2.5. Response Time

_{1}and V

_{2}) depends on the viscoelastic constant, LC cell gap, threshold voltage, and operating voltages, which are described in the following equations [25]:

_{0}is the free relaxation time, V

_{th}is the threshold voltage, V

_{1}and V

_{2}are the low and high gray-level voltages, respectively. Based on the previous studies [17,26], the average gray-to-gray rise and decay time is approximately equal to the sum of free relaxation time (V

_{1}= 0) and turn-on time (V

_{2}= 8th gray level). Therefore, in our experiment we set V

_{1}= 0 and V

_{2}= V

_{2π}and just measured the rise time and decay time between gray levels 1 and 8 for each test cell without the need of measuring all the gray-to-gray transition times.

_{2π}= 5 V and λ = 1550 nm. Results are shown in Table 3 for LCM-1107 and Table 4 for LCM-2018. Next, we converted the measured results to the corresponding reflection-type cell, which is four times faster than that of a transmissive cell because its cell gap is one-half of the transmissive one. Furthermore, in each scenario we also need to convert the response time to the corresponding optimal cell gap with V

_{2π}= 5 V, as the blue lines depict in Figure 7. Under optimal conditions, the cell gap is thinner and the value of V

_{2π}increases to 5 V, which contributes to a faster rise time, as Equation (4) indicates. On the other hand, a thinner cell gap also helps to improve the decay time according to Equations (5) and (6). Therefore, the total response time is reduced significantly by using an optimal cell gap, and the extrapolated results are shown in Table 3 for LCM-1107 and Table 4 for LCM-2018. From Table 3, LCM-1107 has a total response time of 6 ms at 50 °C. On the other hand, LCM-2018 has an even higher birefringence than LCM-1107. Thus, a thinner cell gap can be used, resulting in a 5.1 ms total response time at 50 °C and 4.6 ms one at 60 °C. That means that by using LCM-2018 we can achieve a ~200 Hz frame rate for 6G communication at λ = 1550 nm.

_{2}layer is used, its anchoring energy could be lower. As a result, the corresponding threshold voltage would decrease, and decay time would increase slightly due to the weaker restoring force [28].

## 3. Coating Design

_{2}and SiO

_{2}as the high and low refractive index materials, respectively, which are commonly used in DBR fabrication [31,32,33]. The wavelength-dependent refractive indices of TiO

_{2}and SiO

_{2}were taken from [31] and [32], respectively. Since we require a broad reflection band in the UV–blue region, in our design we adopted two groups of DBR stacks [33] corresponding to the two reflection peaks at 360 and 480 nm, respectively. Each group consists of eight pairs of TiO

_{2}/SiO

_{2}. Each pair in the first group (corresponding to the 360 nm reflection peak) has a thickness of TiO

_{2}(32 nm)/SiO

_{2}(61 nm), and the second group (corresponding to the 480 nm reflection peak) has the thickness of TiO

_{2}(47 nm)/SiO

_{2}(81 nm). The transmission spectrum of this DBR is shown in Figure 8. The transmittance is less than 0.5% from 300 to 510 nm but is as high as 97.2% at 1550 nm.

## 4. Conclusions

_{rms}. To enhance the photostability, we also designed a DBR coating, which has a transmittance lower than 0.5% from 300 to 510 nm, and higher than 97% at 1550 nm. These two materials are promising candidates for LCoS-based 6G communications.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Brackett, C.A. Dense wavelength division multiplexing networks: Principles and applications. IEEE J. Sel. Areas Commun.
**1990**, 8, 948–964. [Google Scholar] [CrossRef] - Zhu, L.; Zhu, G.; Wang, A.; Wang, L.; Ai, J.; Chen, S.; Du, C.; Liu, J.; Yu, S.; Wang, J. 18 km low-crosstalk OAM+ WDM transmission with 224 individual channels enabled by a ring-core fiber with large high-order mode group separation. Opt. Lett.
**2018**, 43, 1890–1893. [Google Scholar] [CrossRef] [PubMed] - Panwar, N.; Sharma, S.; Singh, A.K. A survey on 5G: The next generation of mobile communication. Phys. Commun.
**2016**, 18, 64–84. [Google Scholar] [CrossRef][Green Version] - Giordani, M.; Polese, M.; Mezzavilla, M.; Rangan, S.; Zorzi, M. Toward 6G networks: Use cases and technologies. IEEE Commun. Mag.
**2020**, 58, 55–61. [Google Scholar] [CrossRef] - Chowdhury, M.Z.; Shahjalal, M.; Ahmed, S.; Jang, Y.M. 6G wireless communication systems: Applications, requirements, technologies, challenges, and research directions. IEEE Open J. Commun. Soc.
**2020**, 1, 957–975. [Google Scholar] [CrossRef] - Tibuleac, S.; Filer, M. Transmission impairments in DWDM networks with reconfigurable optical add-drop multiplexers. J. Lightwave Technol.
**2010**, 28, 557–568. [Google Scholar] [CrossRef] - Wang, S.; Feng, X.; Gao, S.; Shi, Y.; Dai, T.; Yu, H.; Tsang, H.K.; Dai, D. On-chip reconfigurable optical add-drop multiplexer for hybrid wavelength/mode-division-multiplexing systems. Opt. Lett.
**2017**, 42, 2802–2805. [Google Scholar] [CrossRef] - Geng, M.; Jia, L.; Zhang, L.; Yang, L.; Chen, P.; Wang, T.; Liu, Y. Four-channel reconfigurable optical add-drop multiplexer based on photonic wire waveguide. Opt. Express
**2009**, 17, 5502–5516. [Google Scholar] [CrossRef] - Ma, Y.; Stewart, L.; Armstrong, J.; Clarke, I.; Baxter, G.W. Recent Progress of Wavelength Selective Switch. J. Lightwave Technol.
**2020**, 39, 896–903. [Google Scholar] [CrossRef] - Marom, D.M.; Neilson, D.T.; Greywall, D.S.; Pai, C.S.; Basavanhally, N.R.; Aksyuk, V.A.; López, D.O.; Pardo, F.; Simon, M.E.; Low, Y.; et al. Wavelength-selective 1 x K switches using free-space optics and MEMS micromirrors: Theory, design, and implementation. J. Lightwave Technol.
**2005**, 23, 1620–1630. [Google Scholar] [CrossRef] - Scherger, B.; Reuter, M.; Scheller, M.; Altmann, K.; Vieweg, N.; Dabrowski, R.; Deibel, J.A.; Koch, M. Discrete terahertz beam steering with an electrically controlled liquid crystal device. J. InfraredMillim. Terahertz Waves
**2012**, 33, 1117–1122. [Google Scholar] [CrossRef] - Baxter, G.; Frisken, S.; Abakoumov, D.; Zhou, H.; Clarke, I.; Bartos, A.; Poole, S. Highly programmable wavelength selective switch based on liquid crystal on silicon switching elements. In Proceedings of the 2006 Optical Fiber Communication Conference and the National Fiber Optic Engineers Conference, Anaheim, CA, USA, 5–10 March 2006. [Google Scholar]
- Wang, M.; Zong, L.; Mao, L.; Marquez, A.; Ye, Y.; Zhao, H.; Vaquero, C.F.J. LCoS SLM study and its application in wavelength selective switch. Photonics
**2017**, 4, 22. [Google Scholar] [CrossRef][Green Version] - Frisken, S.; Baxter, G.; Abakoumov, D.; Zhou, H.; Clarke, I.; Poole, S. Flexible and grid-less wavelength selective switch using LCOS technology. In Proceedings of the 2011 Optical Fiber Communication Conference and Exposition and the National Fiber Optic Engineers Conference, Los Angeles, CA, USA, 6–10 March 2011. [Google Scholar]
- Zou, J.; Yang, Q.; Hsiang, E.L.; Ooishi, H.; Yang, Z.; Yoshidaya, K.; Wu, S.T. Fast-response liquid crystal for spatial light modulator and LiDAR applications. Crystals
**2021**, 11, 93. [Google Scholar] [CrossRef] - Lazarev, G.; Chen, P.J.; Strauss, J.; Fontaine, N.; Forbes, A. Beyond the display: Phase-only liquid crystal on Silicon devices and their applications in photonics. Opt. Express
**2019**, 27, 16206–16249. [Google Scholar] [CrossRef] - Huang, Y.; He, Z.; Wu, S.T. Fast-response liquid crystal phase modulators for augmented reality displays. Opt. Express
**2017**, 25, 32757–32766. [Google Scholar] [CrossRef][Green Version] - Yang, Q.; Zou, J.; Li, Y.; Wu, S.T. Fast-response liquid crystal phase modulators with an excellent photostability. Crystals
**2020**, 10, 765. [Google Scholar] [CrossRef] - He, Z.; Yin, K.; Wu, S.T. Miniature planar telescopes for efficient, wide-angle, high-precision beam steering. Light Sci. Appl.
**2021**, 10, 134. [Google Scholar] [CrossRef] [PubMed] - Wu, S.T.; Wu, C.S. Rotational viscosity of nematic liquid crystals a critical examination of existing models. Liq. Cryst.
**1990**, 8, 171–182. [Google Scholar] [CrossRef] - Dąbrowski, R.; Kula, P.; Herman, J. High Birefringence Liquid Crystals. Crystals
**2013**, 3, 443–482. [Google Scholar] [CrossRef] - Wu, S.T.; Efron, U.; Hess, L.D. Birefringence measurements of liquid crystals. Appl. Opt.
**1984**, 23, 3911–3915. [Google Scholar] [CrossRef] [PubMed] - Wu, S.T. Birefringence dispersions of liquid crystals. Phys. Rev. A
**1986**, 33, 1270–1274. [Google Scholar] [CrossRef] - Wu, S.T.; Lackner, A.M.; Efron, U. Optimal operation temperature of liquid crystal modulators. Appl. Opt.
**1987**, 26, 3441–3445. [Google Scholar] [CrossRef] - Wu, S.T. Design of a liquid-crystal-based electro-optic filter. Appl. Opt.
**1989**, 28, 48–52. [Google Scholar] [CrossRef] - Chen, H.; Gou, F.; Wu, S.T. Submillisecond-response nematic liquid crystals for augmented reality displays. Opt. Mater. Express
**2017**, 7, 195–201. [Google Scholar] [CrossRef][Green Version] - Nie, X.; Xianyu, H.; Lu, R.; Wu, T.X.; Wu, S.-T. Anchoring energy and cell gap effects on liquid crystal response time. J. Appl. Phys.
**2007**, 101, 103110. [Google Scholar] [CrossRef][Green Version] - Jiao, M.; Ge, Z.; Song, Q.; Wu, S.T. Alignment layer effects on thin liquid crystal cells. Appl. Phys. Lett.
**2008**, 92, 061102. [Google Scholar] [CrossRef][Green Version] - Gauza, S.; Li, L.; Wu, S.T.; Spadlo, A.; Dabrowski, R.; Tzeng, Y.N.; Cheng, K.L. High birefringence and high resistivity isothiocyanate-based nematic liquid crystal mixtures. Liq. Cryst.
**2005**, 32, 1077–1085. [Google Scholar] [CrossRef] - Gauza, S.; Wang, H.; Wen, C.H.; Wu, S.T.; Seed, A.; Dabrowski, R. High birefringence isothiocyanato tolane liquid crystals. Jpn. J. Appl. Phys.
**2003**, 42, 3463–3466. [Google Scholar] [CrossRef][Green Version] - Lin, K.C.; Lee, W.K.; Wang, B.K.; Lin, Y.H.; Chen, H.H.; Song, Y.H.; Huang, Y.H.; Shih, L.W.; Wu, C.C. Modified distributed Bragg reflector for protecting organic light-emitting diode displays against ultraviolet light. Op. Express
**2021**, 29, 7654–7665. [Google Scholar] [CrossRef] [PubMed] - Gao, L.; Lemarchand, F.; Lequime, M. Refractive index determination of SiO
_{2}layer in the UV/Vis/NIR range: Spectrophotometric reverse engineering on single and bi-layer designs. J. Eur. Opt. Soc. Rapid Publ.**2013**, 8, 13010. [Google Scholar] [CrossRef][Green Version] - Ding, X.; Gui, C.; Hu, H.; Liu, M.; Liu, X.; Lv, J.; Zhou, S. Reflectance bandwidth and efficiency improvement of light-emitting diodes with double-distributed Bragg reflector. Appl. Opt.
**2017**, 56, 4375–4380. [Google Scholar] [CrossRef] [PubMed]

**Figure 1.**(

**a**) Schematic diagram of optical telecommunication network; (

**b**) Example of ROADM architecture.

**Figure 2.**(

**a**) The optical system of WSS; (

**b**) illustration of beam steering principle using an LCoS phase modulator.

**Figure 3.**Temperature-dependent birefringence of LCM-1107 and LCM-2018 at λ = 1550 nm and f = 1 kHz. Dots and triangles are measured data and solid lines are fitting curves with Equation (1).

**Figure 4.**Wavelength-dependent birefringence of LCM-1107 and LCM-2018 at 40 °C and 1 kHz. Dots and triangles are measured data and solid lines are fitting curves with Equation (2).

**Figure 5.**Temperature-dependent viscoelastic constant of LCM-1107 and LCM-2018. Dots and triangles are measured data and solid lines are fitting curves with Equation (3).

**Figure 6.**Temperature-dependent FoM of (

**a**) LCM-1107 and (

**b**) LCM-2018. Squares are measured data and solid lines are fitting curves.

**Figure 7.**Measured (red lines) voltage-dependent phase change in a transmissive LCM-1107 cell (

**a**–

**c**) and LCM-2018 cell (

**d**–

**f**) at λ = 1550 nm, and the extrapolated (blue lines) voltage-dependent phase change of the corresponding optimal cell gaps at V

_{2π}= 5 V

_{rms}.

LC Mixture | LCM-1107 | LCM-2018 | BL038 |
---|---|---|---|

T_{c} (°C) | 99.2 | 115.6 | 100.0 |

T_{m} (°C) | <−20 | <−20 | - |

Δn@1550 nm | 0.312 | 0.344 | 0.257(@633 nm) |

Δε@1 kHz | 16.3 | 17.3 | 14.4 |

ε_{ꓕ}@1 kHz | 4.84 | 5.07 | 5.0 |

K_{11} (pN) | 12.7 | 14.6 | 19.1 |

γ_{1}/K_{11} (ms/µm^{2}) | 17.6 | 14.5 | 30.2 |

LC Mixture | Δn_{0} | β | G@40 °C (µm ^{−2}) | λ*@40 °C (µm) | A (ms/µm ^{2}) | E_{a}(meV) |
---|---|---|---|---|---|---|

LCM-1107 | 0.451 | 0.236 | 3.67 | 0.276 | 1.69 × 10^{−5} | 342 |

LCM-2018 | 0.500 | 0.260 | 3.91 | 0.284 | 1.16× 10^{−4} | 288 |

**Table 3.**Measured response time of a transmissive LCM-1107 cell with d = 8.03 µm and the extrapolated response time to the corresponding reflective cells at 40, 50 and 60 °C with λ = 1550 nm.

T (°C) | d (µm) | V_{th} (V) | V_{2π} (V) | τ_{on} (ms) | τ_{off} (ms) | τ_{total} (ms)Transmissive | τ_{total} (ms)Reflective |
---|---|---|---|---|---|---|---|

40 | 8.03 | 0.8 | 1.88 | 40.4 | 56.6 | 97.1 | 24.3 |

40 | 5.88 | 0.8 | 5.0 | 2.4 | 30.4 | 32.8 | 8.2 |

50 | 8.03 | 0.8 | 1.94 | 27.1 | 39.2 | 66.3 | 16.6 |

50 | 6.05 | 0.8 | 5.0 | 1.9 | 22.3 | 24.2 | 6.0 |

60 | 8.03 | 0.8 | 2.04 | 17.9 | 30.9 | 48.8 | 12.2 |

60 | 6.52 | 0.8 | 5.0 | 1.6 | 20.4 | 22.0 | 5.5 |

**Table 4.**Measured response time of a transmissive LCM-2018 cell with d = 8.10 µm and the extrapolated response time to the corresponding reflective cells at 40, 50 and 60 °C with λ = 1550 nm.

T (°C) | d (µm) | V_{th} (V) | V_{2π} (V) | τ_{on} (ms) | τ_{off} (ms) | τ_{total} (ms)Transmissive | τ_{total} (ms)Reflective |
---|---|---|---|---|---|---|---|

40 | 8.10 | 0.9 | 1.80 | 54.4 | 52.1 | 106.4 | 26.6 |

40 | 5.20 | 0.9 | 5.0 | 2.3 | 21.5 | 23.7 | 5.9 |

50 | 8.10 | 0.9 | 1.84 | 38.3 | 41.5 | 79.8 | 19.9 |

50 | 5.42 | 0.9 | 5.0 | 1.8 | 18.6 | 20.4 | 5.1 |

60 | 8.10 | 0.85 | 1.85 | 29.8 | 33.7 | 63.4 | 15.9 |

60 | 5.73 | 0.85 | 5.0 | 1.7 | 16.8 | 18.5 | 4.6 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Zou, J.; Yang, Z.; Mao, C.; Wu, S.-T. Fast-Response Liquid Crystals for 6G Optical Communications. *Crystals* **2021**, *11*, 797.
https://doi.org/10.3390/cryst11070797

**AMA Style**

Zou J, Yang Z, Mao C, Wu S-T. Fast-Response Liquid Crystals for 6G Optical Communications. *Crystals*. 2021; 11(7):797.
https://doi.org/10.3390/cryst11070797

**Chicago/Turabian Style**

Zou, Junyu, Zhiyong Yang, Chongchang Mao, and Shin-Tson Wu. 2021. "Fast-Response Liquid Crystals for 6G Optical Communications" *Crystals* 11, no. 7: 797.
https://doi.org/10.3390/cryst11070797