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Liquid Crystals
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Experimental investigation of liquid crystals in the
millimetre frequency range
V.V. Meriakri a , I.P. Nikitin b , Ci-Ling Pan b , Ru-Pin Pan b , M.P. Parkhomenko a & E.E. Chigryai a
a
Kotel'nikov Institute of Radio Engineering and Electronics, Russian Academy of Sciences , Fryazino, Moscow, Russia
b
National Chiao Tung University , Hsinchu, Taiwan Published online: 15 Nov 2010.
To cite this article: V.V. Meriakri , I.P. Nikitin , Ci-Ling Pan , Ru-Pin Pan , M.P. Parkhomenko & E.E. Chigryai (2010)
Experimental investigation of liquid crystals in the millimetre frequency range, Liquid Crystals, 37:11, 1453-1457, DOI: 10.1080/02678292.2010.520749
To link to this article: http://dx.doi.org/10.1080/02678292.2010.520749
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Vol. 37, No. 11, November 2010, 1453–1457
Experimental investigation of liquid crystals in the millimetre frequency range
V.V. Meriakria∗, I.P. Nikitinb, Ci-Ling Panb, Ru-Pin Panb, M.P. Parkhomenkoaand E.E. Chigryaia
aKotel’nikov Institute of Radio Engineering and Electronics, Russian Academy of Sciences, Fryazino, Moscow, Russia;bNational Chiao Tung University, Hsinchu, Taiwan
(Received 2 July 2010; final version received 31 August 2010)
Dielectric properties of n·CB (n = 5, 6, 7, 8) liquid crystals (LCs) are investigated in the frequency intervals of 50–80, 120–160 GHz, and at 0.6 THz. The measurements are carried out in the millimetre wave range by the resonance method and with use of a reflectometer designed on the basis of a Michelson interferometer and quasi-optical metal-dielectric waveguides. Of most interest are the room temperature measurements of the birefringence of LCs. These measurements show that LCs can be used as polarisation transformers in the short wavelength region of the millimetre wave band and the long wavelength region of the sub-millimetre wave band.
Keywords: liquid crystals; dielectric properties; refractive index; birefringence
1. Introduction
Liquid crystals (LCs) are important objects of both physical and applied investigations. LCs represent complex heterogeneous media whose dielectric prop-erties in the millimetre wave range have been stud-ied insufficiently in spite of numerous publications devoted to their experimental investigation.
The basic factor that determines the interaction between electromagnetic waves and LCs in the mil-limetre wave range is the Debye relaxation [1]. There exist adequate methods for measuring the dielectric properties of LCs both at low and high frequencies in the microwave band (up to 5 GHz) [2] and at frequen-cies above 400 GHz, where the dielectric time-domain spectroscopy methods are effective [3]. However, there are few experimental data on the dielectric properties of LCs in the millimetre wave band (at frequencies from 30 to 300 GHz). These data are extremely impor-tant both for understanding the mechanisms of inter-action between millimetre waves and LCs, especially near the phase transition points, and for the practi-cal application of LCs, for example, in phase-shifters, lenses and polarisers [4, 5].
In the present study, we describe two sufficiently simple methods for measuring the dielectric properties of LCs which involve a measurement cell consisting of two plane-parallel plates of fused quartz and a plane (0.1–1) mm thick layer of LC sandwiched between these plates. These methods were used to measure the dielectric properties of LC samples of the homologous series n·CB (n = 5, 6, 7, 8) in the frequency interval 50–160 GHz.
∗Corresponding author. Email: meriakri@ms.ire.rssi.ru
2. Method using a resonance in an LC cell
The measurement cell has a symmetric shape and rep-resents two plane parallel fused quartz plates of known thickness and refractive index, and an LC layer of thickness h2with unknown n∗2= n2− ik2 (Figure 1). The LC layer was aligned by unidirectional rubbing of the inner surfaces of the quartz plates.
Here, 1 and 2 are fused quartz plates of thickness
h1,3and known complex refractive index n∗1,3= n1,3− ik1,3, k1,3<< n1,3; the LC layer of thickness h2and of sought refractive index n∗2 = n2 − ik2 is sandwiched between the quartz plates. For the structure shown in Figure 1, according to [6], the frequency spectrum of reflection is described by:
r(f )= 1−n∗ 1 1+n∗ 1 + r2(f )· exp(2i2πfn ∗ 1h3 c ) 1+1−n∗1 1+n∗ 1 + r2(f )· exp(2i2πfn ∗ 1h3 c ) , (1) where: r2(f )= n∗1−n∗2 n∗1+n∗ 2 + r1(f )· exp(2i2πfn ∗ 2h2 c ) 1+ n∗1−n∗ 2 n∗1+n∗2 · r1(f )· exp(2i 2πfn∗ 2h2 c ) , r1(f )= n∗2−n∗1 n∗2+n∗ 1 +n∗1−1 n∗1+1 · exp(2i2πfn∗1h1 c ) 1+ n∗2−n∗ 1 n∗2+n∗1 ·n∗1−1 n∗1+1 · exp(2i2πfn∗ 1h1 c ) ,
Here, f is frequency, i is the square root of−1, and c is the speed of light.
ISSN 0267-8292 print/ISSN 1366-5855 online © 2010 Taylor & Francis
DOI: 10.1080/02678292.2010.520749 http://www.informaworld.com
1454 V.V. Meriakri et al.
h1 h2 h3 fused quartz
LC
r
t
Figure 1. Cross-section of the measurement cell.
Using Equation (1), we calculated the frequency dependence of the power reflection coefficient (R = 20 log(|r|) of a typical three-layer structure shown in Figure 1), in which two layers (the first and the third) are fused quartz plates with refractive index n∗1,3 = 1.95− i·10−4and the middle layer is a layer of LC with refractive index n∗2= 1.610 − i·9.3·10−4.
This function is calculated for the parameters of the 5CB LC measured at frequency 59 GHz by the method described for the layer thicknesses of h1,3 = 1.152 and h2= 0.533 mm. The analysis of this function shows that the frequencies (fm) and the magnitudes (Rm) of the even-order minima are determined by the refractive index n∗2 of the middle layer, whereas the frequencies of odd-order minima very weakly depend on the refractive index of the middle layer. The physics behind this fact is that the value of the electric field
E in the LC layer is minimal for even-order minima
and maximal for odd-order minima. The phenomenon considered underlies the method for determining the parameters of liquid crystals. Additional means for increasing the accuracy of measurements are provided by measuring the transmission through the measure-ment cell at the frequency fm of the reflection mini-mum (Tmax). Since Tmax is sufficiently large (it varies from−0.2 to −0.5 dB), the effect of interference (spu-rious interference in the horn–sample region) is less than that when measuring the minimum of the reflec-tion coefficient Rmfor small values of the latter (from −30 to −40 dB).
3. Results of measurements
The method for measuring the reflection coefficient is implemented in the scheme involving a horn in front of which the measurement cell is placed (Figure 2).
To determine the refractive index of an LC, it is necessary to know the parameters of the quartz plates and the thickness h2 of the LC layer. The refrac-tive index of quartz can be measured by standard
5 3 2 6 4 1
Figure 2. Scheme of the measurement set-up: 1 is a
rectan-gular waveguide with mode H10, 2 is a waveguide bend, 3 is a
horn, 4 is a liquid crystal under test, 5 are fused quartz plates, and 6 is a directional coupler for measuring the reflection coefficient.
methods. The measurement error of the thickness is about±5 µm.
For a specific three-layer structure, we should first calculate the calibration functions in the coordinates
fm, n2 and Rm, k2 (or Tmax, k2) and, using the mea-sured values of fmand Rm, determine n2and k2. These functions for the first even-order minimum of reflec-tion for the LC sample 5SV are shown in Figures 3 and 4.
Similar calculations can be performed for the sec-ond even minimum of reflection, and n2and k2can be determined for that frequency.
Using the method proposed, we measured the complex refractive indices of LCs nSV (n = 5, 6, 7, 8). The temperature dependence of neand noof these samples measured at frequency of 0.6 THz is presented in Figure 5. This shows that, for all samples in the nematic phase,n ranges from 0.1 to 0.16.
Table 1 compares the results of measurements carried out in the frequency interval 50–60 GHz at
59.5 59.0 58.5 58.0 57.5 57.0 56.5 56.0 1.55 1.60 1.65 fm , GHz 1.70 1.75 n2
Figure 3. Calibration function in the coordinates fm, n2.
–26 –28 Rm –30 –32 –34 –36 –38 –40 –42 1 2 3 4 5 k2 102 cm–1
Figure 4. Calibration function in the coordinates Rm, k2.
1.80 n T–Tc 1.75 1.70 1.65 1.60 1.55 1.50 1.45 1.40 –12 –10 –8 –6 –4 –2 0 2 5CB 6CB 7CB 8CB
Figure 5. Temperature dependence of the refractive indices
of n CB LCs. Tcis the temperature of transition to the liquid
phase.
room temperature with those at 500 GHz [7]. One can see that the values of birefringencen measured at frequencies 50–60 GHz and 500 GHz are in good agreement.
The values of the imaginary part k2of the complex refractive index were the same (within the measure-ment accuracy of about 0.002) for both polarisations, virtually did not depend on temperature, and were equal to 0.010–0.015 for 5SV and 0.040–0.045 for 8SV at a frequency of 59 GHz.
The sample of 5SV has been investigated previ-ously [2, 3]. The comparison with our data shows that the values of the real part of the complex refractive index for 5SV are somewhat less than the asymptotic
Table 1. Birefringencen measured at frequencies 50–60
GHz and 500 GHz. LC ne† no† n† ne‡ no‡ n‡ 5CB 1.71 1.60 0.11 1.66 1.57 0.09 6CB 1.69 1.59 0.10 1.69 1.59 0.10 7CB 1.69 1.58 0.12 1.66 1.55 0.11 8CB – – – 1.62 1.57 0.05 E7 – – – 1.74 1.62 0.12
Notes:†Results of measurements at 500 GHz. ‡Results of measure-ments at 50–60 GHz.
value of 1.69, measured at a frequency of 5 GHz [2], and is close to the value 1.65 at frequency 250 GHz, measured in [3] on a sample of 5SV containing 0.6 vol.% of 10 µm quartz particles. As for the value of
k2, the data presented by Belyaev et al. [2] and Oh-e et al. [3] for frequencies of 0.065 and 250 GHz are 3–4
times greater than those obtained in our experiments. The measurement of 6CB in the frequency interval 150–160 GHz yielded the values ne= 1.69 and no = 1.60, i.e. nearly the same values as those at 50–60 GHz. This means that the dispersion region of neand noin this LC is rather broad: it ranges from 50 to 160 GHz.
4. Method involving an interferometer
We developed a new method for measuring the dielec-tric properties of LCs in the short millimetre wave range and designed an experimental set-up that imple-ments this method at wavelengths of about 2 mm (frequencies from 130 to 180 GHz). LC samples of the homologous series n CB (n = 5, 6, 7, 8) were investigated in the frequency interval 130–160 GHz.
The method employs a Michelson interferometer designed on a quasi-optical square metal–dielectric waveguide of cross-section 20 mm × 20 mm [8]. A characteristic feature of such a waveguide is that it is a single-mode waveguide and that the field at the output is quasiplane and has no appreciable side lobes. This allows high-precision measurements to be performed of the parameters of the plane-parallel dielectric plates placed behind the output aperture of the waveg-uide. The scheme of the interferometer is shown in Figure 6.
To determine the real part nLC of the complex refractive index in the interferometer, we measured the phase shiftϕ introduced by an LC sample. To this end, we placed the LC sample between the output aperture of arm 6 and the reflecting mirror 8 in arm
6 of the interferometer.
The measurements are carried out at the oscilla-tor frequency fecorresponding to an even minimum of the reflection coefficient of the LC sample when the
1456 V.V. Meriakri et al. 1 2 11 3 9 10 5 6 8 4 7
Figure 6. Scheme of the interferometer: 1 is a millimetre wave oscillator, 2 is the input directional coupler, 3 is the input arm of the interferometer, 4 is a side arm, 5 is the out-put arm connected to the indicator display, 6 is the working arm of the interferometer, 7 is a fixed mirror, 8 is a moving mirror, 9 is the output directional coupler, 10 is an absorber, and 11 is an interference pattern.
electric field vector of a wave in the waveguide is par-allel to the extraordinary axis of the LC. A minimum of the signal in arm 5 of the interferometer is found by shifting the moving mirror. Then, we remove the LC sample from the interferometer and, shifting the mov-ing mirror byl, again find a minimum of the signal in arm 5. The required parameter neis related tol by the formula:
[(ne− 1)lLC+ (ns− 1)ls]= l + mλ0
2 . (2) Here lLC is the known thickness of the LC layer, ns and ls are the known refractive index and the thick-ness of the quartz plates between which the LC layer is sandwiched, m is an integer, andλ0 is the wavelength corresponding to f0= c/λ0. The number m can easily be determined for known ns, ls, lLC≤ 0.5 mm, and nLC ≈ 1.5 −1.7.
To determine the refractive index neof the ordinary wave, we apply the same procedure after rotating the LC sample through 90◦around the axis perpendicular to the plane of the sample. Figure 7 presents the refrac-tive indices neand noof 6CB vs. temperature, measured with the use of the interferometer for two orthogonal polarisations at a frequency of 150 GHz.
This method allows the direct determination (with-out measuring ne and no separately) of the birefrin-gencen = ne– no. To this end, at a fixed frequency, one determines the shiftδl of the mirror in arm 2 when the LC sample in this arm is rotated from the position corresponding to the transmission of the extraordi-nary wave through the sample to the position when the
1.70 ne , n o 1.69 1.68 1.67 1.66 1.65 1.64 1.63 1.62 1.61 1.60 1.59 18 20 22 24 26 28 30 32 T, °C
Figure 7. Refractive indices ne and no of 6CB vs.
tem-perature for two orthogonal polarisations at frequency 150 GHz.
Table 2. Birefringence of LC samples in the frequency interval 140–160 GHz and at 5 GHz. LC n† n‡ 5CB 0.17 0.14 6CB 0.14 0.08 7CB 0.22 0.09 8CB 0.12 0.08 E7 – 0.10
Notes:†Results of measurements at 5 GHz.‡Results of measure-ments at 140–160 GHz.
ordinary wave passes through the LC sample. Sincen
<< λ / lLC, we have
n = ne− no= δl lLC
. (3)
Note that the accuracy of determiningn is higher than the accuracy of determining neand noseparately. In the frequency interval 140–160 GHz, we mea-sured the birefringence n of LC samples. Table 2 presents these results together with the same parame-ters measured at frequency of 5 GHz [2]. Table 2 shows thatn at 140–160 GHz is smaller than that at 5 GHz, but agrees well with the results presented in Table 1.
5. Discussion
The results of our measurements carried out in the millimetre wave range can be compared with the results available in the literature only for 5CB; for other LC samples, there are no relevant data in the literature. The results for 5CB reported by Lim and Margerum [9] are ne = 1.60 and no = 1.52 at
a frequency of 38 GHz and temperature T = 25◦C. These data significantly differ from the values ne = 1.71 and no= 1.62 obtained at frequency 50 GHz by Nose et al. [10]. This fact may be attributed either to measurement errors or to the difference in the fab-rication techniques of the LC samples. For example, we measured the parameters of two 5CB samples at frequencies 50 and 60 GHz. The data for one of these samples are shown in Table 1 (ne = 1.66 and no = 1.57), while the data for the other are ne = 1.65 and no = 1.62 (Figure 7); it can be seen that there is a significant difference in the values of neand no.
The birefringence n of LC samples calculated by Equation (3) in the frequency interval 140–160 GHz, as well as the results obtained by Vieweg et al. [7] at 500 GHz, can be used in the design of devices such as polarisation converters and phase shifters. Forn = 0.1 and for imaginary part of the complex refractive index k= 0.02 (these or smaller values of k were measured in the millimetre wave range for almost all the LC samples investigated by us), such devices can have small longitudinal size (about 2–3 mm) and suffi-ciently low insertion loss (roughly about 1 dB or less) at frequencies of about 500 GHz.
6. Conclusions
We have developed two new methods for measuring the dielectric properties of LC samples in the millime-tre wave range, designed set-ups operating at these frequencies, and investigated LC samples of the series
n CB (n= 5, 6, 7, 8) at frequencies of 50–70 GHz and
130–180 GHz. The results indicate the existence of dis-persion regions of ne, no, andn in these LCs in the millimetre wave range. This fact should be taken into account when designing devices on LCs (first of all, polarisation converters) in the short wavelength region of the millimetre wave band and in the sub-millimetre
band. Some of the results of our investigations have been described in two conference presentations [11, 12] and in two journal articles [13, 14].
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