3 Experimental Methods
3.3 Data Processing
In this experiment, we use the “high voltage source” to generate high voltage, and use the “pulse generator” to transfer the high voltage to voltage pulse. Therefore, if we need a 100V peak to peak square wave to be our bias, we should setup these machines and generate 200V by the high voltage source, and connect it to the pulse generator, then the 100Vp-p signal would be obtained from the output of the pulse generator.
Of course, the frequency of the output signal can be tuned by changing the synchronized input signal.
Using THz-TDS system, amplitude and phase information can be easily obtained. But not only information of liquid crystal, additional influences of glass substrates, and air are also included in the original data, we can resolve this problem by the following way: at first, we measure the waveform of zero bias applying for referential data, which include above-mentioned information, and then we apply bias voltage to change the refractive index of NLC cell and measure the result (of course it also includes above-mentioned information), subtract the reference and get the data which only includes the influence of liquid crystal. The transmitted THz spectra were deduced from the time domain of the THz pulse with fast Fourier transform (FFT) algorithm.
Two time-domain waveforms can be used to obtain frequency-domain spectra using numerical fast Fourier transform, and then the experimental data divided by the reference should be the amplitude transmittance of this sample. The difference of phase was the phase retardation. Compare the phase retardation data of different
voltages applied to NLC samples; the voltage versus phase shift curve can easily be drawn. Also, v-Φ curve in various frequencies are obtained.
Fig. 3.15 The oscilloscope
Fig. 3.16 The high voltage source and the pulse generator
Fig. 3.17 The experimental sample with holder and conductive equipment
Fig. 3.17 Program for THz-TDS system
4. Experimental results and discussion
In this chapter, we show the experimental data, the theoretical curve and discussion, and then compare with the former work to find the characteristics and advantages.
4.1 THz-TDS Waveforms and Spectra
Using lock-in amplifier, we can obtain the waveform in time domain, after fast Fourier transform (FFT), spectrum in frequency domain can also be obtained. The reference signal in fig 4.1 means the THz signal which was received by receiving antenna in our experimental system without passing though the NLC sample. The amplitude of signal was expressed in the form of electrical field. In this experiment, we scanned the THz radiation for ~70 Pico seconds, which equals to scan 21 millimeters in the space. By observing fig 4.1, we can get the main signal amplitude is 2.92×10-4 units, and locates between 0 to 10 ps, the swing signal behind the main signal mainly comes from the moisture in the air, the SN ratio (signal-noise ratio) can be observed in fig. 4.2 is about 106, the bandwidth is about 1 THz.
0 10 20 30 40 50 60
-2.0x10-4 -1.0x10-4 0.0 1.0x10-4 2.0x10-4 3.0x10-4
Electrical Field (a.u.)
Time Delay (ps)
Reference Sample
Fig. 4.1 Waveform of reference and NLC sample in this experiment
0 1 2 3 4 5 6 7
1E-9 1E-8 1E-7 1E-6 1E-5 1E-4 1E-3 0.01 0.1 1
reference
Frequency (THz)
Power (a.u.)
Fig. 4.2 Spectrum of the reference signal
By observing fig 4.1 again, we know the amplitude of sample signal (THz radiate though the NLC sample with 0V applied voltage) is smaller than the reference signal; the peak value is probably 3.35×10-5 units, therefore, transmittance of the sample can be derived by dividing the reference data, it is 11.47%. Additionally, there is a period of time delay between main signal and sample signal, we can get 6.603ps time delay by the peak value of the sample signal (15.007ps) subtracting the peak value of the main signal (8.404ps), it also means 1.981 mm optical difference in space.
If we carefully observe the part after the main signal in fig 4.3, we can know that beside the oscillation which was produced by the moisture, there are also some multi-refract signals mixed in it.
0 10 20 30 40 50 60 70
-2.0x10-5 -1.0x10-5 0.0 1.0x10-5 2.0x10-5 3.0x10-5 4.0x10-5
Electrical Field (a.u.)
Time Delay (ps)
Sample
Fig. 4.3 The sample signal without any applied voltage.
Fig 4.4 is the power spectrum of the reference data and the sample data; we can see the phenomenon in 0.55THz, 0.7THz, 1.0THz, etc. the moisture absorption occurred. The maximum value of the power spectrum locates at ~0.3THz.
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
1E-9 1E-8 1E-7 1E-6 1E-5 1E-4 1E-3 0.01 0.1 1
sample reference
Frequency (THz)
Power (a.u.)
Fig. 4.4 The reference and sample spectrum
Refract index is frequency dependent; therefore the refraction coefficients measured in the visible range are not suitable use in the THz range. Fortunately, refract index of E7 in THz range was measured. In THz range, ne~1.75 and no~1.6; the birefringence in THz range was also determined (~0.17). These experimental results are shown in Fig.4.5.
Fig. 4.5 Refract index of E7 in THz range
4.2 Electrically Controlled Phase Shifter
4.2.1 In-Plane Switch Shifter
The temporal waveforms of the THz beam passing through the 500µm-thick LC phase shifter at various applied field are illustrated in Fig. 4.6. The total scanning range for the time delay was more than 70 ps, and we only show the 10~20 ps for clearly observing the main waveform, and emphasize it in fig. 4.7, the transmitted THz waves for 0V voltage applying show obvious time delay to the wave for 125V voltage applying.
The spectral amplitude and phase of the transmitted THz wave were deduced by fast Fourier transform (FFT) algorithms.
Fig. 4.6 The temporal waveforms of the THz pulse transmitted through the E7 sample at various applied voltages
15.6 15.8 16.0 16.2 16.4 16.6 16.8 17.0
-2.0x10-5 0.0 2.0x10-5 4.0x10-5 6.0x10-5
5V 25V 45V 65V 95V 115V
THz Field amplitude (a.u.)
Delay time (ps)
Fig.4.7 The close-up of the temporal waveforms
According to eq. 2.47, the phase shift is proportional to the product of the effective index change ∆neff and frequency of the electromagnetic wave. The THz wave is thus expected to experience a larger phase shift at the higher frequencies in the measured THz range. This is also confirmed in Fig. 4.8. The data for the 500µm-thick cell at 1 THz are also show in Fig. 4.8. Maximum phase shift of 84.4° have been obtained at 1 THz by using NLC cells. But 84.4° phase shift is not enough for a quarter wave plate, additionally, compare the in-plain switch phase shifter to the copper electrode phase shifter which will be described in section 4.2.2, the theoretical prediction curve is harder to draw, and the fabricated process is more complex and expensive, Alternatively, newly developed liquid crystal material with high birefringence can be explored for this application. In the experiments, this can be explained simply by considering the Fresnel equations. The ordinary and extraordinary refractive indices of E7 are 1.62 and 1.79, respectively. With the increasing applied voltage, the effective refractive index of LC will increase from 1.62 to 1.79 and become closer to the refractive index of quartz substrate ~1.9. The transmitted field will then increase according
to Fresnel equations.
0.2 0.4 0.6 0.8 1.0 0
20 40 60 80
5V 25V 45V 65V 95V 115V
Phase shift(Degree)
Frequency (THz)
Fig. 4.8 The phase shift from 0.20 to 1.00 THz with varying the driving voltages
0 20 40 60 80 100 120
0 20 40 60 80 100
Phase shift (degree)
Frequency (THz) 0.3THz
0.5THz 0.8THz 1.0THz
Fig. 4.9 The phase shift as a function of driving voltage for several frequencies.
4.2.2 Copper Electrode Phase Shifter
The temporal waveforms of the THz wave, which transmitted through the device at various applied voltages, are shown in Fig. 4.10. In Fig. 4.11, we show the experimental data from 14 to 16 ps so as to emphasize the time shifting of the THz waveforms. The transmitted THz signals exhibit clear large delay and transmittance for the increasing applied voltages in time domain. The reason is mentioned below. The no
and ne of E7 are 1.62 and 1.79, respectively, at 0.3 THz. With increasing applied voltages, the effective index of E7 will rise from 1.62 to 1.79 and become closer to 1.95 which is the index of quartz substrate. Along the Fresnel equation, the transmitted THz field increases at the two interfaces between LC layer and quartz substrate.
10 20 30 40 -15
0 15 30 45
0V 15V 30V 35V 40V 125V
THz Field amplitude (a.u.)
Delay time (ps)
Fig. 4.10 The temporal waveforms of the THz pulse transmitted through the E7 sample at various applied voltages
14.0 14.5 15.0 15.5 16.0
-15 0 15 30 45
THz Field amplitude (a.u.)
Delay Time (ps)
0V 15V 30V 35V 40V 125V
Fig 4.11 The close-up of the temporal waveforms from 14 to 16 ps
The transmitted THz spectra were deduced from the temporal profiles of the THz pulse with fast Fourier transform (FFT) algorithms.
Fig. 4.12 is the phase shifts with 0.20 to 1.00 THz by varying the driving voltages. According to equation (2.34),
( )
c v n df∆ eff
= π δ 2
(2.34) The larger phase shift is expected with increasing frequency.
0.2 0.4 0.6 0.8 1.0
0 20 40 60 80 100
P h ase S h if t ( D egree)
Frequency (THz) 15V
30V 35V 40V 125V
Fig. 4.12 The phase shift from 0.20 to 1.00 THz with varying the driving voltages
According to equation (2.35), the threshold voltage of the NLC sample can be derived by mathematical computation software. In this experiment, we substitute each parameter to obtain the answer by using the convenient software, “MathCad”.
v π 17.1 10⋅ −12 13.8 8.85⋅ ⋅10−12
⋅ 12 10⋅ −3
524 10⋅ −6
⋅ :=
v =26.921
We obtain 26.9 volts for threshold voltage of our sample; the mention is theoretically we should apply more than 16.9 volts, the liquid crystal molecules can be rotated by electrical field.
Then, we can calculate our theoretical v-Φ curve, form (2.45) and (2.46), we know the theoretical curve divides into two parts, therefore we use MathCAD once more, calculate the two parts of curves with each other.
(a)For 0<v-vth<<vth
(b)For v-vth>>vth
We combine the 0<v-vth<<vth part of (a) and the v-vth>>vth part of (b), a theoretically curve in one frequency can be obtained. If we want to obtain the theoretical curve in another frequency, so long as change the frequency value for the new one. Fig 4.13 shows the theoretically curve in ~0.3, ~0.6, ~0.8 and ~1.0 THz, respectively.
0 10 20 30 40 50 60 70 80 90 100110120 0
20 40 60 80 100
P h ase shi ft ( d egree)
Applied voltage (V
rms
) 0.3075THz
0.6003THz 0.8053THz 0.9956THz
Fig. 4.13 The theoretical curves in different frequency
Fig. 4.14 shows the phase shifts as a function of driving voltage for 0.31, 0.60, 0.81 and 1.00 THz. A maximum phase shift of 93.7° was obtained at 1.00 THz when the LC cell was driven at 125 V (rms). For a 524-µm-thick E7 layer, the theoretical phase shift is 91.8° at 1.00 THz according to equations (2.45) and (2.46). In Fig. 4.14, the theoretically predicted phase shifts were also drawn as the solid curve in order to be compared with experimental data. We can observe that the tendency of the experimental data pretty matches the theoretical curve; the slope of the data curve is very sharp from 25V to 35V. fig. 4.15 emphasizes the applied voltage axis from 25V to 35V, the experimental results have a good agreement with theoretic values.
0 25 50 75 100 125 0
15 30 45 60 75 90
Phase shift (degree)
Applied voltage (V
rms) 0.31THz
0.60THz 0.81THz 1.00THz
Fig. 4.14 The phase shift as a function of driving voltage for several frequencies.
26 28 30 32 34
0 15 30 45 60
Phase shift (degree)
Applied voltage (V
rms) 0.31THz
0.60THz 0.81THz 1.00THz
Fig. 4.15 The emphasis of fig.3.15 from 25V to 35V
We measured the response time and demonstrate the results in fig.
4.16 and fig. 4.17. By utilizing multi-meter to measure the current of the receiving antenna, we can obtain the transmitted electrical field of the NLC sample, therefore, we record the transmittance of the NLC cell with zero bias or with saturated voltage applying, respectively, and then, Bias from 0Vrms was instantaneously increased to saturation voltage (125Vrms), i.e. switch ON, the transmitted electrical field can gradually increase to the saturated state in a few seconds. According to definition, after normalizing we can obtain the demanded time as the normalized transmittance achieving 10% and 90%, the value of 90% normalized transmittance subtracts the value of 10%; we can get the rise time. The calculating result is shown in fig. 4.16. In the similar way, bias from 125Vrms was decreased to 0Vrms, i.e. switch OFF, the transmitted electrical field can gradually decrease from saturated state to original state, let the 10% normalized transmittance subtracts the value of 90%, fall time can be achieved as shown in fig. 4.17. The rise time of the electrically controlled quarter wave plate is 7.5 seconds, and the fall time is 373.5 seconds.
Fig. 4.16 The rise time of the NLC cell
Fig. 4.17 The fall time of the NLC cell
Fig. 4.18 and fig. 4.19 illustrate the results of stabilization in this experiment, we measured the phase shift angle at 45V (rms) (linear changed area) and 125V (rms) (saturated area) for several times, and find the difference of each result. Fig.4.18 shows the original phase shift angle, by observing fig. 4.19, we could know the inaccuracy is smaller than 2°.
0.2 0.4 0.6 0.8 1.0
0 20 40 60 80 100 120
Phase shift (degree)
Freqency (THz)
45V-a 45V-b 125V-a 125V-b
Fig. 4.18 Stabilization of shift angle at fixed applied voltage
0.2 0.4 0.6 0.8 1.0 -9
-6 -3 0 3 6 9
Phase shift (degree)
Frequency (THz)
45V 125V
Fig. 4.19 Stabilization of shift angle at fixed applied voltage
Fig. 4.20 and fig.4.21 show the stabilization of phase shift angle with tuning applied voltage from one to another, we tuned the applied voltage from 85V (rms) to 120V (rms), after period of time (more than the rise time ) we measured the shift angle; then return to 85V (rms) and after another period of time (more than the fall time) we measured the shift angle again, repeated for several times and recorded the result in fig.
4.20, fig.4.21 shows the deviation of shift angle of fig. 4.20, it is smaller than 4°.
0.2 0.4 0.6 0.8 1.0 0
20 40 60 80 100 120
Phase shift (degree)
Frequency (THz)
85V-a 85V-b 125V-a 125V-b
Fig. 4.20 Stabilization of shift angle after tuning the applied voltage
0.2 0.4 0.6 0.8 1.0
-5 -4 -3 -2 -1 0 1 2 3 4 5
Phase shift (degree)
Frequency (THz)
85V 125V
Fig. 4.21 Stabilization of shift angle after tuning the applied voltage
Fig. 4.22 shows the normalized power (at 1THz) received by the receiving antenna when we rotated our sample at different angle; we rotated our sample from 0° to 180° and measured the power every 15°.
By eq. 2.xx we can draw a theoretical curve, compare with the experimental data, we can discover some deviation, we infer the deviation was produced by the instability of laser source and the scattering of our sample.
0 15 30 45 60 75 90 105 120 135 150 165 180 0.4
0.5 0.6 0.7 0.8 0.9 1.0
Normalized Power
Rotating angle (degree)
Theoretical curve Experimental curve
Fig. 4.22 The receiving power with rotating the sample at different angle
4.2.3 Compare with the Former Work
We compare the experimental data with our sample and of the former sample, and we can discover their respective characteristics and find a suitable way to use.
4.2.3.1 Compare with the Electrically Controlled Sample with Gold Strip Line
Now we compare our copper electrode sample with the gold strip one. The electrical fields applied to the liquid crystal of the gold strip sample are 0V/cm, 235.7V/cm, 353.7V/cm, and 589.3V/cm, respectively.
We know that with the electric field increasing, the delay in time domain moved in order backward. We can observe the space between the leftmost curve (initial voltage) and the rightmost curve (saturated voltage) is clearly distinguished. Therefore, we can predict the phase shift angle. By comparing with temporal waveforms of the gold strip sample, we can qualitatively know the phase shift angle of cooper electrode is bigger.
The transmitted THz wave spectra of the gold strip sample were obtained from the time-domain THz waveform by fast Fourier transform (FFT) algorithm. The threshold voltage required to rotate the LC occurs at 35.4 V (rms), it is slightly higher than the copper electrode sample’s.
The influence affected by bias voltage is similar to the effect in the cooper electrode sample. When the driving field is smaller than the threshold value, the nematic LC director will maintain their original uniform alignment. and no phase shift was observed. When the bias field is larger than the threshold value, the effective refractive index of the LC will be changed. The phase shift rises above threshold and slowly
approaches a steady state value. According to eq. 2.33, the phase shift is proportional to the product of the effective index ∆neff change and frequency of the electromagnetic wave. With the same driving voltage applying, the terahertz wave experiences a larger phase shift at the higher frequencies. The phase shift will reach a saturated value when the liquid crystal is completely aligned by the applied electric field. A maximum phase shift of 4.07° was obtained at 1.07 THz when the LC cell was driven at 589.3 V/cm. Compare with the cooper electrode cell, we can find that because of the arrangement of the gold strips, even the gold strip cell fully aligned the liquid crystal molecules, the rotated angle of LC molecules does still not achieve 90°, therefore, higher applied voltage and amendment the structure are both important for achieving higher shift angle.
4.2.3.2 Compare with the Magnetically Controlled Sample
For magnetically controlled sample, THz passing through the LC phase shifter at various magnetic inclination angles (θ = 0°, 30° and 50°).
The transmitted THz waves show obviously longer time delay for larger angle, θ. It is because the magnitude of magnetic field is strong enough to almost fully align the LC molecules. The THz field amplitudes increase with θ for θ < 43º. This can be explained by the increasing transmittance at the quartz-LC interface according to the Fresno equations. With increasing θ, the effective refractive index of LC will rise and become closer to the refractive index of quartz substrate, which is 1.95. The transmitted field amplitudes will then increase according to Fresno equations. The THz field amplitudes decrease for θ > 43º due to partial
blocking of the THz wave by the magnet. The threshold field required to reorient LC molecules in the LC cell when the magnetic field is perpendicular to the alignment direction is less then 0.01 T, which is much lower than the magnetic field employed in this work (~ 0.43 T).
Compare with the cooper electrode cell, magnetic aligned cell does not have threshold voltage because the magnetic field is always the same and strong enough to align whole the LC molecules in the cell. The spectral amplitude and phase of the transmitted THz wave are also deduced from the temporal waveforms by fast Fourier transform (FFT) algorithms. The same as the situation in electrically controlled cell, the THz waves experience larger phase shift at higher frequencies as expected from eq.
2.31. The maximum phase shift achieved was 368º at 1.025 THz and θ = 54º. Compare with the electrically controlled cell again, the characteristic of magnetically controlled cell is aligning LC molecules by rotating the magnet to control the magnetic field; we only need to prepare a magnet and rotating it, and then we can exactly know the direction of the LC molecules and continuously control the phase shift angle.
By observing Fig. 4.23 and Fig. 4.24, we can clearly compare the magnetically controlled phase shift and electrically controlled phase shift.
The magnetically controlled sample can tune the phase shift angle by rotating the magnet; the magnet can be precisely rotated by the rotating plate, and the magnetic field is high enough, so the shift angle can be continuously and accurately tuned.
For electrically controlled sample, it is more compact and practical, but restricted by accuracy of the voltage source, the applied voltage is not
difficulty to obtain the accurate tuning from 26.9 to 35 V. It is hard to control the electric field as so stable, especially under the sharp slope of the δ-V relation. That is why we need magnetic controlled one in the previous work.
0.2 0.4 0.6 0.8 1.0
0 50 100 150 200 250 300
Phase Shift (Degree)
Frequency (THz) 10o
20o 27.5o 30o 35o 40o
Fig. 4.23 The phase shift of the magnetically controlled sample
0.2 0.4 0.6 0.8 1.0 0
20 40 60 80 100
Phase Shift (Degree)
Frequency (THz) 15v
30v 35v 40v 45v 125v
Fig. 4.24 The phase shift of the electrically controlled sample
5. Conclusions and Future Works
In chapter 5, we make a conclusion to our experiment and show the future work for further research and more applications.
In summary, we demonstrate the tunable room temperature π/2 NLC THz phase shifters. The phase shift with electrical controlling the effective refractive index of LC E7 layer is achieved. In addition, our measured results in this experiment are in good agreements with theoretical predictions. With the 524µm NLC cell, a maximum phase shift of 92.2° was observed at 1.00 THz when the applied voltage was driven at 125 V (rms). This device is also regarded as the tunable quarter wave plate in the THz region.
In principle, the phase shift can be increased by employing a LC cell with larger optical thickness and/or larger refract index. To achieve a 2π phase shift at 1 THz, we can increase the cell thickness to 2 mm with the
In principle, the phase shift can be increased by employing a LC cell with larger optical thickness and/or larger refract index. To achieve a 2π phase shift at 1 THz, we can increase the cell thickness to 2 mm with the