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Abstract
This article is to summarize the development of technology of the liquid crystal based antenna. Two major trends of such antennas are discussed. One is the electronically steered phased array, and the other is the antenna based on the metamaterials concept. The major function of liquid crystal in a phased-array antenna is obviously to adjust the phase of electromagnetic waves. Hence different kinds of phase shifters made of liquid crystal are talked over in this article. As for the metamaterial or metasurface based antenna, the liquid crystal is used to adjust the refractive index of the surroundings of the highly dense antenna elements to further determine if they resonate or not. Other than the liquid crystal based microwave devices, the development of liquid crystal itself is of great importance. The very heart of all the devices mentioned above shall be the characteristics of liquid crystal at microwave range. The material development is summarized as well.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Corrections
19 June 2019: A typographical correction was made to the article title.
1. Introduction
Liquid crystal is well known for its dielectric anisotropy and widely used in flat panel display industry. It is fair to say that the success of such material completely changes the human behavior and reshape the modern life. The dielectric anisotropy at the frequency range of the quasi-electrostatic allows one to control the orientation of LC molecules by electric field while that at the optical range gives control of the phase and further the polarization of light. These two characteristics of liquid crystal together gave rise of the LCD industry. Now that the phase of light can be adjusted by liquid crystal, one is able to conclude easily that the phase of electromagnetic waves at frequencies other than optical range can be controlled by liquid crystal as well. The thought of applying liquid crystal to such frequencies is absolutely reasonable.
With the rapid development of wireless communication such as 802.11ac (Wi-Fi), 4G-LTE, 5G-mmW, and Ku- to Ka-band satellite communication, microwave (300MHz to 300GHz) now has been the most important frequency range for fast and massive data transmission. It is a clear trend that the carrier frequency is getting higher to provide sufficient bandwidths of which the demand is remarkable. With the development of communication system, adaptive array antennas are now of great interest. The adaptive array antennas provide reconfigurability to ensure stable connection with changing environment or system requirement. For example, in a mobile terminal like cars, the adaptive array antenna allows this moving terminal to connect to the desired point such as satellites in a reliable way. Phased-array antennas with individual phase shifters applied to each antenna element are able to provide such function. There are several ways to implement a phase shifter including RF MEMS, semiconductor solution, ferroelectrics (e.g. barium-strontium-titanate, BST), and of course liquid crystal.
Comparing the solutions of phase shifters above, liquid crystal is occupying a favorable position because of the mature fabrication of LCD. One must know that the price of LCD has been descending for more than a decade. This means the manufacture of LCD has already been extremely effective. If this superiority could be exploited to produce microwave phase shifters, the liquid crystal based phased-array antenna will possess the cost-effective advantage over other solutions. Beside the cost-effective issue, the weight and profile are also its strengths. Traditional ones are mostly controlled by hybrid tracking method, where the antenna is steered electronically in elevation angle but mechanically in azimuthal plane. This guarantees wide-angle scanning with small gain loss, but causes the problem of heavy weight and high profile of the antennas. By LCD manufacturing process, it is possible to have light weight and low profile of a 2-D steering phased-array antenna.
In the first part of this paper, different kinds of liquid crystal based phase shifters are reviewed. The second part: A model calculating the linearity of such phase shifters is demonstrated for the first time. The linearity is very important in the communication system adopting carrier aggregation, and the issue is known as passive intermodulation, PIM. By examining the performance of LC phase shifter and its linearity, the possibility to apply such devices to terrestrial communication could be justified. The third part is to discuss the liquid crystal based phased-array antenna which provides beam steering or polarization agility. The fourth part is to brief the liquid crystal based metamaterial or metasurface antenna. This kind of antenna provides the possibility of controlling not only the phase but also the amplitude at the same time, which could be very useful when considering low side lobes. The reason why the author chooses to discuss these two types of LC based antennas is the possibility of commercialization. Certain progress has been made by separate start-up companies in recent years with the help of LCD makers. This means in the near future one may see the commercial product of these two kinds of LC based antennas. The last part is the material development of liquid crystal for microwave applications. How to evaluate the liquid crystal at microwave range is discussed.
2. Liquid crystal based phase shifters
Generally speaking, a passive phase shifter is evaluated by the figure of merit (FoM), the ratio of the maximum phase shift (ΔΦmax) and the maximum insertion loss (ILmax), given as follows in (1). Obviously one would like the phase shifter to have larger FoM.
There are three major topologies of passive phase shifters. The first one is the switched-line phase shifter with predefined paths of different electrical lengths and the switch realized by P-I-N diodes, MOSFETs, or MEMS [1]. Since the paths have already been defined, there’s no need for adjustable dielectric constant and thus liquid crystal is not suitable for this topology. Besides, for a large antenna array the compactness and high phase-shift resolution are required. The switched-line phase shifter is not appropriate for such application.
The second one is the reflection-type phase shifter (RTPS). This topology includes a 3dB/90° coupler and two tunable reflective loads which can be implemented by a varactor diode [2]. There are, however, very limited studies about the liquid crystal based RTPS [3]. The schematic of the RTPS is shown in Fig. 1, where the variable capacitor can be realized by liquid crystal. The reported FoM is only 12°/dB, which may not be the best performance of the phase shifter of this type.
The third type is the transmission lines loaded with shunt varators. There are basically two structures of this type. The first one is the microstrip line (MSL) with bulk-like liquid crystal as shown in Fig. 2. An MSL with bulk-like liquid crystal layer is formed [4–8]. Liquid crystal is filled into the space between the signal and ground plane. By applying DC (or quasi-electrostatic) voltage across the signal and ground electrode, the liquid crystal orientation is altered. Since the mode of microwave propagating in an MSL is quasi-TEM, the electric field is mostly perpendicular to the ground plane within the signal-electrode region, and thus the shunt capacitance perceived by microwave will be determined by the liquid crystal orientation. Owing to the nature of the microstrip line, the thickness of the liquid crystal layer has to be larger than 100um when considering propagation loss [4]. This causes a problem of extremely slow response of liquid crystal, which could take several seconds to switch from one state to another. If the phased array requires fast response, the structure will not be suitable. Among these researches, the highest FoM that has been reported is 110°/dB [6] because of properly designed liquid crystal for microwave range.
Figure 3 demonstrates the other structure of the loaded transmission line. It is the coplanar waveguide (CPW) periodically loaded by shunt liquid-crystal varactors [9,10]. Because the periodic capacitance has relatively short electric length comparing to the wavelength, it can be regarded as the lumped-circuit element. The amount of shift of phase of one period will be determined by the ratio of each periodically loaded capacitance to the shunt capacitance of the original transmission line in one period. Due to the nature of a periodic structure, this kind of phase shifters always has a Bloch frequency at which strong reflection occurs. To avoid poor S11, it is necessary to make Bloch frequency much higher than the operation frequency. The voltage controlling liquid crystal should be applied across the signal and ground electrode in Fig. 3. Au balls are implemented to connect the GND on the bottom substrate to those on the top substrate. This is a very common process in standard LCD fabrication. The gold balls have diameters slightly larger than the designed cell gap to guarantee the connection between GND electrodes. The cell gap (less than 10um) is much smaller than the spacing between signal and ground electrodes (could be several hundred microns, depending on the impedance of CPW) on bottom substrate. Only the liquid crystal sandwitched by signal and top GND electrodes will be reoriented by the DC (or quasi-electrostatic) voltage. The major benefit of this structure is that the thickness of the liquid crystal layer can be lowered to several micrometers, which is almost the same as the cell gap of an LCD. This brings two advantages over the previous LC-bulk MSL. One is the response time restored to milliseconds, and the other is the compatibility of LCD manufacturing process. The former one is certainly important and easy to understand, and yet the latter one matters as well. Since the modern liquid crystal filling process (ODF) of an LCD mass-production line is specifically designed to produce LC cells with several microns, it is difficult for current equipment to manufacture devices with cell gap larger than 100um. From the viewpoint of mass production, designing a liquid crystal based phase shifter with cell gap less than 10um is very helpful. According to author’s experience, this structure could give similar FOM performance as that in Fig. 2.
Besides the above topologies, there are several other types of phase shifters made with liquid crystal [11–15] including CPW with liquid crystal filled into space between coplanar ground and signal electrodes [12,15], a CMOS slow-wave CPW incorporated with liquid crystal [11], a ring-resonator [13] and a bandpass filter [14] whose passband and phase can be tuned by liquid crystal at the same time. These types of LC phase shifters are however not as compatible to current LCD manufacturing process as the three types mentioned above. Hence, the author chooses not to discuss them in details.
3. Liquid crystal based phase shifters
Whatever the topology is, one usually aims to increase the FoM and shrink the size of the phase shifter so as to apply this technology to the phased-array antennas. However, these two factors are not only requirements. For example, the base stations of a cellular network may use phase shifters to adjust the elevation of the phased array to have different coverage when it’s necessary. With the popularity of 4G-LTE, mulitcarrier is introduced to exploit ultra-wide bandwidth, which is called carrier aggregation. The base-station antenna radiates multiple carriers with different frequencies simultaneously. This makes the linearity of the whole communication system a very important issue. For a passive microwave component like a liquid crystal based phase shifter, to evaluate its linearity is to measure its PIM. To study this phenomenon in a liquid crystal based phase shifter means to figure out the third-order term of susceptibility, χ(3), of liquid crystal at the frequency range of microwave. Lots of researches about the nonlinearities of liquid crystal at the optical range have been made [16,17] but few at the microwave range [18]. The IP3 in [18] of a LC phase shifter looks quite promising, and the reason is that the LC molecules are much slower in their reaction to the RF beat. In this paper a simulation model to describe such phenomenon is developed. A transmission line with periodically loaded LC capacitance can be equivalent as the circuit shown in Fig. 4(a). The CLC is the shunt varactor to adjust phase, and one can combine it to the original capacitance of transmission line to form a total capacitance. Because of the nonlinearity of liquid crystal, CLC may change with the voltage across itself. Therefore, the total capacitance will be considered as a function of time and position to reflect the fact of wave travelling as shown in Fig. 4(b).
Fig. 4 Equivalent circuit of transmission line (a) with shunt LC varicap and (b) with time and position dependent capacitance
To describe the wave travelling with equivalent circuit of Fig. 4(b), the telegrapher’s equations can be re-written as (2) and (3). They lead to Eq. (4) which gives the behavior of voltage of transmission line. Comparing to the original equation, the extra two terms on the right hand side of (4) account for the nonlinear effect caused by the voltage dependent capacitances. This is very similar to the equation of electric field of wave propagation in nonlinear medium as given by (5), where E is the electric field; n is the refractive index of the medium and accounts for the linear part of the medium; c is speed of light in vacuum, and PNL is the nonlinear terms of the medium including all the orders of electric susceptibility. Comparing (4) to (5), one could interpret the right hand side of (4) as the nonlinear terms as that of (5).
To use (4) to predict the PIM performance of an LC based phase shifter, one must know how capacitance changes with time and position. The Ericksen-Leslie Eq. (6) can be used to describe the dynamics of LC directors reacting to applied electric field. The cell is assumed to be homogeneously aligned. In (6), x-direction is along cell gap, and θ represents the LC director tilt angle with respect to the homogenous alignment. K1 and K3 are splay and bend elastic constants, respectively. Δε is the dielectric anisotropy of liquid crystal at microwave frequencies. E is of course the electric field of microwave. By assigning LC initial state derived from (7), the LC states evolving with microwave electric field and further the capacitance variation can be calculated. This method gives nonlinearity of the collective molecular reorientation, and the results show that only longer microwave pulses lead to capacitance variation as demonstrated in Fig. 5. The pulses in Fig. 5(a) and 5(b) are signals of the same central frequency but different bandwidths. The narrower the full width half magnitude (FWHM) is, the longer the pulse will be. The central frequency here is 3.5GHz, and the FWHMs of the signals are 100Hz and 10MHz, respectively. The initial state is set by Ddc to have the LC director at the mid-point of cell gap to be 45° tilt angle. The transmission line has its peak voltage of 8V which is large enough to alter the orientation of liquid crystal. The cell gap is 5um, and thus the microwave electric field peak strength can be calculated by peak voltage divided by cell gap. Simulation results show that the shunt capacitance doesn’t change with time when the shorter pulse propagates through transmission line. This indicates that the collective motion of LC directors happens only when the microwave pulse is long enough. The conclusion that the LC molecules are much slower in their reaction to the RF beat as stated in [18] is proved not only by experiment but also by theory.
Fig. 5 Shunt capacitances varied by microwave electric field with different FWHMs: (a) 100Hz and (b) 10MHz
Collective molecular reorientation is not the only nonlinear effect that occurs in the liquid crystal cell. According to I. C. Khoo’s study [16], the nematic liquid crystal has a very large χ(3) of 10−4 in esu unit from collective molecular reorientation, and this mechanism can only respond when excitation lasts for millisecond to second. Since it has been proven that such motion cannot have influence when RF pulse is short enough, one may turn to other motions of liquid crystal which causes nonlinear effect. The smallest χ(3) is from individual molecular reorientation, which is less than 10−12. The electronic hyper polarizability has larger χ(3), which is believed to be as large as 10−9. The response of these two mechanisms is as fast as picosecond, which is much shorter than usual pulses in communication system. This means that the nonlinear effects caused by individual molecular reorientation and hyper electronic polarizability will be able to follow the pulse applied to an LC phase shifter. By assuming χ(3) to be 10−9 in esu unit, which corresponds to 1.4 × 10−17 in SI unit, the PIM of the LC phase shifter has been calculated as demonstrated in Fig. 6. The central frequencies f1 and f2 of the input signals are 3.4 and 3.6GHz, respectively. Both signals have peak power of 43dBm and FWHM of 10MHz. The results indicate first that no peaks occur at frequencies of 2f1-f2 and 2f2-f1, which may be good news to PIM requirement, and yet at frequencies of 3f1, 3f1 + f2, 3f2 + f1 and 3f2, peaks representing triple frequencies are observed. The author has to emphasize that the nonlinear coefficients listed in [16] are actually at optical range. Because of the lack of data at microwave range, the author can only use the optical nonlinear coefficients to estimate whether the PIM will be a severe problem for the LC phase shifters applied to the terrestrial cellular base stations. The calculation gives us a hint that the nonlinear effects do exist when high-power (43dBm) signals are sent to the LC phase shifters even though no peaks are found at 2f1-f2 and 2f2-f1. This is still an open question that remains to be solved if one wants to use the LC phase shifter in the cellular network in the future.
Fig. 6 The nonlinear effect of the LC phase shifters (a) power spectrum around carrier frequencies and (b) power spectrum around 3-fold carrier frequencies
4. Phased-array antennas based on liquid crystal
The phased-array antennas based upon liquid crystal belongs to the category of the passive electronically scanned array (PESA), in which all the antenna elements are connected to a single transmitter and/or a receiver as shown in Fig. 7. In Fig. 7, two kinds of beam steering technique are shown. One is the digital beam steering as Fig. 7(a) where the complex weight is made by finite-impulse-response (FIR) digital filter [19], which has been replaced by digital precoders nowadays. The other is the analog beam steering as Fig. 7(b) in which the RF-end phase shifters are the key components. The digital method has the advantage that the digital signals can be copied perfectly while the analog ones cannot. Thus many possible manipulations can be applied to the digital signals. The analog method, however, has the benefit of low cost. The digital beam steering requires RF feed for each antenna element, and yet the analog needs only one. This significantly reduces the cost of the phased array. To incorporate the benefits of both methods, a hybrid structure has been used [20,21]. Besides, the LC phased array is believed to have cost advantage over other kinds of passive phased array at the microwave range, especially the frequencies higher than Ku band. One can consider the speed of the price drop of an LCD, which now may cost the consumers less than $500 per square meter, as an example. If applying the same price level to the phased array, the price of the phase shifters in a 4096-element (64 × 64) phased array antenna operating at 30GHz could be only at the level of $100 by assuming the distance of adjacent elements to be half the wavelength in air. This means that each LC phase shifter will cost less than $0.1. Undoubtedly the cost-effective LC phased-array antennas are of great interest in the future.
Even though the cost effectiveness is very attractive, it is still a question whether the LC phased array can be realized. The most intuitive way to use liquid crystal to fulfill the function of a phased array is to adopt the LC phase shifter as an individual component [22]. Such structures may be simple and intuitive, but not efficient enough because the degree of integration is relatively low. To realize a phased-array antenna by LCD fabrication technology, one must combine several parts including the SMA connector as I/O of microwave, the power dividers composing parallel [23,24] or series [25] feed network, the bias pins and lines controlling liquid crystal, the LC phase shifters, the DC block that allows each phase shifter to be biased independently, and lastly the patch antenna array into one panel. Such an LC-based 2 × 2 phased-array antenna operating at 17.5GHz with parallel feed network was exhibited by [23]. The LC phase shifter here is the inverse micorstrip line (IMSL) with 100um cell gap as mentioned in the previous section. Therefore this structure is mostly, not totally, compatible to current LCD process. Other than the cell gap issue, there exists one more problem for LCD process to be applied to manufacture phased-array antennas: the metal film thickness. On a standard PCB the copper film thickness is generally several microns, while on a standard LCD glass substrate it is even less than 0.5um. At 10GHz the skin depth of Cu is 0.652um, which has already been larger than normal thickness in LCD process. Because the glass substrate is quite large (The generation-6 glass substrate size: 1500 × 1850mm), it is very difficult to deposit more than 1um-thick copper film on a glass substrate of such sizes by sputter, not to mention 3 times or 5 times of skin depth for reducing ohmic loss. When the deposition thickness of Cu is over 0.5um, the glass substrate starts to bend. Once the bending is too severe, either the glass substrate will be broken due to large stress, or it cannot be sent into the photolithography equipment for further process due to the failure of vacuum sucker. This indicates the necessity of development of the electro-plating equipment for large-size glass substrates if one wants to surmount the issue of the copper-film stress.
Beside the process issue, the slow response time caused by high cell gap is an important issue as well. As mentioned in the previous section, the response time could be as slow as several seconds when switching liquid crystal from one state to another. Such slow response time puts constraints on the phased-array antenna based on this technology. For example, to apply the LC phased array to satellite communication, one must consider the relative motion between the terminal on Earth and the satellite at the orbit. As long as the satellite isn’t orbiting Earth geostationarily or the terminal is in motion, the relative position keeps changing. If the response time of the phased array steering the beam is too slow, satellite communication is not an option. The low-Earth-orbit (LEO) satellite, however, is the trend of the future satellite communication. The satellites will never be stationary with respect to Earth surface. The beam will be continuously steered no matter the terminal is moving or not. Once the connected satellite is out of sight, the terminal phased-array antenna must be able to locate the other satellite in sight fast enough to prevent communication from interruption. The LC phased array with high cell gap may not suit for this kind of application. It is very natural to consider using the low-cell-gap LC phase shifter to replace the IMSL variable delay line to realize a phased-array antenna.
Other than the high-gain phased-array antennas, the LC based polarization agile antennas are of great interest as well [26,27]. In [26], the IMSL variable delay line is applied to produce a continuously polarization agile antenna. In [27], however, liquid crystal varactors are used to realize tunable coupled line (TCL) followed by a dual-fed radiating structure as demonstrated in Fig. 8. As shown in Fig. 8(b) such combination utilizes the nature of LCD fabrication to form an LC varactor easily by overlapping copper lines on top and bottom substrates. Multistage structure is used to form a 3dB coupler. For example, it is much easier to achieve an 8.34dB coupler with smaller overlapping area, and by cascading two 8.34dB couplers a 3dB coupler can be realized. Comparing to the typical branch-line 3dB coupler whose transmitted port is 90° ahead of the coupled port, the TCL here has its transmitted port 90° ahead or behind the coupled port to be flexible. Thus by adjusting the capacitances of varactors the antenna could operate with two linear polarizations (uncoupled mode and fully coupled mode), two circular polarizations (3dB/90° and 3dB/-90°), or any other state in between. The polarization agility can be realized.
Fig. 8 Schematic of a polarization agile antenna realized by LC-varactor TCL (a) top view, (b) cross-section view of TCL, and (c) cross-section view of patch
5. Liquid crystal based metamaterial antenna
Other than the phased array, the antennas based on the metasurface or metamaterials concept is of great interests now. The simultaneous negative values of permittivity and permeability were first introduced by Veselago in 1968 [28]. The microwave-range surface plasmons causing negative permittivity was demonstrated by Pendry et al. in 1996 [29]. Then the split ring resonator (SRR) was then presented in [30], which enables the possibility of the negative permeability. Afterwards, many different structures inspired by SRR, e.g. the electric-field-coupled resonator, were introduced [31–33]. Based on the concept, plenty of efforts were put to realize the antennas with such metasurface or metamaterial concept [34–37]. These studies, however, have not provided the reconfigurability, the very heart of the phased array nowadays. Several methods have been proposed to implement reconfigurability such as micro-motor [38], PIN-diode switch [39,40], and varactor [41]. A sketch of a transmission line composite right/left-handed (CRLH) metamaterial antenna is shown as Fig. 9 [36]. In this structure the radiation direction depends on the frequency. When the frequency equals the transition frequency of the CRLH strucutre, f0, the antenna has broadside radiation along z-axis. If the frequency is larger or smaller than the transition frequency, the radiation will be forward or backward on x-z plane. Of course the frequency must be in the range between backfire and endfire radiation, which corresponds to θ of −90° and 90°, respectively. In this way backfire-to-endfire frequency scanning capability is provided by this transmission line CRLH metamaterial antenna.
Fig. 9 Sketch of a CRLH transmission line leaky wave antenna illustrating three radiation regions: broadside, backward (left-hand) and forward (right-hand)
As mentioned before, liquid crystal has the tunable dielectric characteristic. It is entirely reasonable to use such nature to adjust the electric characteristics of a metasurface or metamaterial [42–44]. According to these studies, the resonant frequency of the metasurface, which could be formed by collective split-ring or electric-field-coupled resonators, varies with the state of liquid crystal. For example, the CRLH metamaterial antenna above has the capability of frequency scanning. If the transition frequency of the CRLH, however, can be adjusted, the radiation direction of the same frequency will be altered. This indicates the feasibility of beam steering by tuning the resonant frequency of a metamaterial antenna. The equivalent circuit of the CRLH transmission is presented in Fig. 10(a), and its ω−β dispersion diagram is represented by (8) and Fig. 10(b). Between the backfire frequency ωBF and the endfire frequency ωEF, the CRLH transmission line functions as a leaky-wave antenna as stated in the previous paragraph. Obviously, the CL or CR here could be varicaps made by liquid crystal for beam steering. Such structure, however, has one major problem when fabricated by standard LCD process, i.e. how to form the shunt inductance LL. For PCB it is very easy to have such shunt inductance by using via holes to connect the branches to GND as shown in Fig. 9. For glass, however, it is very difficult to form such via holes. The vendors of LCD glass substrates, e.g. Corning Inc. and AGC Inc., are now investing lots of R&D resources to realize such technology and yet it may take 1 to 2 years before making mass production ready.
Fig. 10 (a) Equivalent circuit for the unit cell and (b) Band diagram of CRLH of a CRLH transmission line
Due to the lack of via holes on glass substrates, to implement the liquid crystal based antennas with metamaterial or metasurface concept, one has to choose the metasurface composed of resonant elements without via holes such as SRR [32], complementary SRR (CSRR) [45], electric-field inductive-capacitive resonator (ELC) [33], or complementary ELC (CELC) [46]. No matter which type of element is chosen, the liquid crystal based metamaterial or metasurface antennas usually have thousands of elements which are controlled independently so as to realize beamforming and beam steering [47]. Kymeta Co. has demonstrated and commercialized an electronically scanned metasurface antenna [48,49]. Since the numerous elements have to be controlled independently, it is very important to decide which elements to be tuned or detuned. The tuned/detuned pattern of the metasurface elements, or say the holographic pattern, will determine the quality of the far-field radiation pattern, such as beam steering accuracy and side lobe level. How to calculate the corresponding holographic pattern fast and accurately given the desired far-field radiation is critical to this type of antenna [50]. Comparing to the liquid crystal based phased-array antenna which assigns phases to each element independently, the densely distributed elements of liquid crystal based metasurface antenna are controlled to radiate when the phase of feeding wave is correct and not to radiate when it’s wrong. In a further way, the metasurface element can be operated in grayscale instead of binary mode, which means each element can be tuned to partially radiate electromagnetic energy. This is very similar to an active electronically scanned array (AESA). As mentioned earlier, the liquid crystal based phased-array antenna is regarded as a PESA. Thus one may consider the metasurface antenna to have better beamforming ability than the phased array. For example, the passive phased array has the lowest side lobe level −13.5dBc in theory if no amplitude control is applied [51], while that of a metasurface antenna can be as low as −18dBc [50]. However, it is a pity that the aperture efficiency has not been discussed for the liquid crystal based metasurface antenna yet.
6. Liquid crystal for microwave application
The optical properties of liquid crystal have been investigated thoroughly, and plenty of R&D efforts have been laid upon the material development. However, the microwave application of liquid crystal didn’t draw as much attention as the display application in the past few decades. It is natural that the LC manufacturers have not put comparable resources for microwave LC material development. For example, different LCD modes such as twisted nematic (TN), vertically aligned (VA), in-plane switching (IPS) and fringe-field switching (FFS) require different types of liquid crystals so as to fulfill the mode operation and achieve optimized optical performance. As mentioned before, the liquid crystal for microwave application is to form varactors. As long as the relation between the slow axis of LC and microwave electric field is known, one can design the varactor correctly. Thus there’s no need to develop different types of LC for microwave. Currently there’s only one type of microwave liquid crystal, which has positive dielectric anisotropy at both quasi-electrostatic and microwave frequencies.
Usually one will measure the polarization evolution caused by optical path difference between ordinary and extraordinary wave to characterize the optical properties of liquid crystal, namely ne and no. To characterize the microwave properties of liquid crystal, the same method does not work anymore. This is because the wavelength of microwave is much longer than the optical wave. If using the same method, to accumulate the phase difference between extraordinary and ordinary wave the cell gap will be too large to be fabricated. Besides, it is easy to manufacture the optical lens to form an optical beam so that the incident light can be precisely controlled to enter the cell as one’s expectation. To achieve the same goal with microwave, all the devices will be magnified 1000 times because of the wavelength. Therefore different methods have to be developed to characterize the microwave properties of liquid crystal [52–56]. These studies can be categorized into two groups. One is to perturb the known cavity by magnetostatic-field-aligned liquid crystal [52]; the other is to inversely derive the LC characteristics by measuring the devices composed of liquid crystal [53–55]. Comparing these two categories, the upside of the perturbation method is that the liquid crystal is fully aligned by the parallel magnetostatic field and the liquid crystal stored in a tube occupies very limited space in the cavity, which is why it’s named as perturbation method, and thus the fringe field effect is negligible. The downside is that the cavity only resonates at specific frequencies, and hence it’s difficult to use one cavity to retrieve wide-band characteristics. One will choose a proper method based on the needs.
To evaluate the liquid crystal for microwave applications, two aspects are important. One is the tunability, and the other is the tangent loss. Tunability is defined as (9), the ratio of delta epsilon and epsilon parallel. Just like permittivity, tangent loss of liquid crystal possesses anisotropy as well. Usually tanδ⊥ is larger than tanδ∥. This is because the liquid crystal molecules perceive torque when microwave electric field is not parallel to its long axis. The torque here may cause the molecules to slightly vibrate about the LC short axis perpendicular to electric field. When the microwave electric field is parallel to the long axis, torque only exists for dipole moment of LC molecules if any. The dipole moment usually follows the long axis of LC molecules, and it’s very difficult for these dipoles to turn around given the electric field oscillates at microwave frequencies. Therefore, the motion of LC molecules is much smaller. One may estimate the liquid crystal by material FOM as (10) [57]. The development of microwave liquid crystal has been summarized clearly in [58–60]. The author would like to point out one thing worth notes. To increase the tunability, one may use highly polar LC singles into the mixture. Permanent dipole moment of such molecules could be very strong. This will induce the flexoelectric effect in the cell. On an LCD, the flexoelectric effect can be clearly observed by lowering the frame rate [61]. Its influence on response time has been investigated [62]. One has to be careful when pursuing high tunability by adding highly polar molecules.
7. Conclusion
Liquid crystal has been widely used in LCD industry for more than four decades. It is such a great success and brings huge impact to human life. People born nowadays may never be able to imagine the display used to be large and heavy (CRT). Can liquid crystal succeed again in the realm of microwave applications? It is possible. Human communication will not be restricted to the surface of Earth. The LEO satellites will be the next breakthrough. When the LEO-satellite constellation is in its place, the demand of terminal antennas with beamforming and beam steering capability will be huge. The traditional parabolic antenna is not a good choice for its high profile. The conventional panel antenna with mechanical parts to realize beam steering is not a good choice either for its heavy weight. As for the electronically scanned array realized by semiconductor technology, the price will be an issue. The liquid crystal based phased-array or metasurface antennas happen to fulfill all three requirements above. Perhaps in the near future, with the help of this technology the satellite communication will be just like terrestrial mobile communication to us.
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