4 Results and Discussion
4.2 Electrically Controlled Phase Shifter
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