3 Experimental Methods
3.4 Sampling and Data processing
Transmission properties were noteworthy issue in MPCs. Using THz-TDS method, amplitude information can be easily obtained. First, resolution in frequency-domain corresponding to the empirical data sheet, shown in Appendix 1, was chosen.
Second, THz radiation propagating through W/O a MPC as a MPC signal or a reference, respectively, was measured. Two time-domain waveforms can be used to obtain frequency-domain spectra using numerical fast Fourier transform, and then the MPC data divided by the reference should be the amplitude transmittance of this sample. Power transmittance was the square of the amplitude transmittance. The transmission properties of a certain sample at different frequencies can be observed.
4. Experimental results and discussion
4.1 Free Space THz-TDS Waveforms and Spectra
When THz radiation propagates through optical component in the same distance but with different humidity, THz time-domain waveforms are shown in Fig. 4.1. The amplitude of oscillations after main peaks decreasing as the humidity decreases can be found. It can speculate that the oscillation is caused by water vapor absorption. From the Fig. 4.1 (d), the noise is lowered after N2 purged. Moreover, the signal to noise ratio (S/N ratio) is better after vapor exhausted. Fig. 4.2 depicted the spectra with 0.0073 THz resolution of fast Fourier Transform of these waveforms.
Some deep dips at 0.556, 0.754, 0.988, 1.113, 1.164, 1.208, 1.230, 1.413 THz disappear as the humidity goes down. This is obviously due to absorption of water vapor, which are consistent with the results of van Exter et al. [27].
Besides, in the insect of Fig. 4.2, regular oscillations, high frequency fringes, are found in spectrum. When other antennas of different kinds, i.e.
different refractive index, or thickness of substrate are used, the oscillation frequency is changed. It is obvious that the major factor comes from the etalon effect between radiation and the substrate of the emitter.
Appendix 2 shows the results in detail.
Fig. 4.1 Free space waveforms with humidity control Water (humidity ~45%) N2-purged (humidity ~3-4%)
0 20 40 60 80 100 120 140
N2-Purged (humidity ~4%)
0 20 40 60 80 100 120
N2-Purged (humidity ~8%)
0 20 40 60 80 100 120
0 1 2 3 1E-5
1E-4 1E-3
4% acceptable
8% OK
Am p li tu d e
Frequency (THz)
Water (humidity ~45%) Purged (humidity ~8%) Purged (humidity ~4%)
Fig. 4.2 FFT spectra of waveforms in Fig. 4.1
0.0 0.5 1.0 1.5
1E-5 1E-4 1E-3
∆υ = 0.095 THz
Amplitude
Frequency (THz)
In June 26, 2004, a fire accident occurred in the basement of Engineering Building V which our laboratory is located in. This accident causes the change of free-space spectra as shown in Fig. 4.3. A significant change is found at 0.131 THz, where a deep dip caused by characteristic absorption line of sulfur dioxide [28]. It is obvious that sulfur dioxide is produced after fire accident and it can be found using THz-TDS technique.
0 1 2 3 4
1E-7 1E-6 1E-5 1E-4 1E-3
0.131THz
Before accident After accident
Amplitude
Frequency (THz)
Fig. 4.3 Spectra comparison before and after fire accident
4.2 Metallic Photonic Crystals (MPCs)
4.2.1 Basic transmission properties of MPCs
Fig. 4.4 displayed pictures of four samples from a camera and an optical microscope. S, D, and L represent hole spacing, hole diameter, and plate thickness in unit of micron, respectively.
Individual THz waveforms and spectra of MPC samples were shown in Fig. 4.5 ~ 4.8. Each spectrum had clear forbidden band and almost unity transmittance at predicted frequency. Amplitude transmittance spectra ware depicted in Fig. 4.9. Obviously, it was hard to eliminate water vapor absorbed highly at 1.164, 1.669, 1.720 THz even though the low humidity ~5%. Some narrow and steep peaks were found due to too small signal at the specific frequencies by water vapor absorption.
In Fig. 4.10, it’s clear that the experimental spectra of power transmittance were excellently coincidental with calculated spectra by Chen’s theory. Among them, transmission spectrum of JMPC had better signal to noise ratio because the peak of the THz signal was around the cutoff frequency of JMPC.
The parameters used to characterize their transmission properties were listed in Table 4.1. In Table 4.1, experimental cutoff frequencies agreed well with those calculated according to Chen’s theory, but had a little difference from those corresponding to the infinite-long circular waveguide theory. However, cutoff frequencies were well inversely proportional to diameters of holes as shown in Fig. 4.11
(a) S= 995 D= 565 L= 480 (b) S= 425 D= 284 L= 200
(c) S= 295 D= 248 L= 150 (d) S= 225 D= 155 L= 100
Fig. 4.4 Real pictures of (a) JMPC, (b) sample #1, (c) sample #2, and (d) sample #3. In unit of µm
S D
(a)
0 20 40 60 80 100 120 140 160 180
-1.0x10-4 -5.0x10-5 0.0 5.0x10-5 1.0x10-4 1.5x10-4
Electric field (a.u.)
Time (ps) Reference JMPC
(b)
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 1E-6
1E-5 1E-4 1E-3
Reference JMPC
Frequency (THz)
Amplitude
Fig. 4.5 (a) THz waveforms and (b) spectra of reference and JMPC
0 5 10 15
-9.0x10-5 0.0 9.0x10-5
Electric field (a.u.)
Time (ps)
(a)
0 20 40 60 80 100 120
-0.00004 0.00000 0.00004 0.00008 0.00012 0.00016 0.00020
Electric field (a.u.)
Time delay (ps)
Reference (5% humidity) Sample #1
(b)
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
1E-6 1E-5 1E-4
1E-3
Referecne (5% humidity)
Sample #1
Frequency (THz)
Amplitude
Fig. 4.6 (a) THz waveforms and (b) spectra of reference and sample #1
0 5 10 15
-0.00004 0.00000 0.00004 0.00008 0.00012 0.00016 0.00020
Electric field (a.u.)
Time delay (ps)
(a)
0 20 40 60 80 100 120
-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020
Electric field (a.u.)
Time delay (ps)
Referecne (5% humidity) Sample #2
(b)
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
1E-9 1E-8 1E-7
1E-6 Referecne ~5% humidity
Sample #2
Frequency (THz)
Amplitude
Fig. 4.7 (a) THz waveforms and (b) spectra of reference and sample #2
0 5 10 15
-0.00004 0.00000 0.00004 0.00008 0.00012 0.00016 0.00020
Amplitude (a.u.)
Time (ps)
(a)
Referecne (5% humidity) Sample #3
Referecne ~5% humidity Sample #3
Frequency (THz)
Amplitude
Fig. 4.8 (a) THz waveforms and (b) spectra of reference and sample #3
0 5 10 15
(a)
0.2 0.4 0.6 0.8 1.0
0.0 0.2 0.4 0.6 0.8 1.0
Amplitude Transmittance
Frequency (THz) JMPC
(b)
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
0.0 0.2 0.4 0.6 0.8 1.0
1.720THz 1.669THz
Sample #1
Amplitude Transmittance
Frequency (THz) 1.164THz
(c)
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 0.0
0.2 0.4 0.6 0.8 1.0
Amplitude Transmittance
Frequency (THz) Sample #2
(d)
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 0.0
0.2 0.4 0.6 0.8 1.0
Water vapor absorption
Amplitude transmittance
Frequency (THz) Sample #3
Fig. 4.9 Amplitude transmittance of (a) JMPC, (b) sample #1, (c) sample
#2, and (d) sample #3
(a)
0.2 0.4 0.6 0.8 1.0
0.0 0.2 0.4 0.6 0.8 1.0
Power Transmittance
Frequency (THz) JMPC Calculated
(b)
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
0.0 0.2 0.4 0.6 0.8 1.0
1.720 THz 1.669 THz
1.164 THz
Power Transmittance
Frequency (THz) Sample #1 Calculated
(c)
0.2 0.4 0.6 0.8 1.0 1.2 1.4
0.0 0.2 0.4 0.6 0.8 1.0 1.2
Power Transmittance
Frequency (THz) Sample #2
Calculated
(d)
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 0.0
0.2 0.4 0.6 0.8 1.0 1.2
1.720 THz
1.669 THz
1.164 THz
Power Transmittance
Frequency (THz) Sample #3
Calculated
Fig. 4.10 Power transmittance of (a) JMPC, (b) sample #1, (c) sample #2, and (d) sample #3
Table 4.1 Parameters and characteristics of MPCs Sample S D L υcut* υcut
c υcut
exp υdiff
$ Tporosity
JMPC 995 565 480 0.311
0.289 0.289
0.348 0.292#1 425 284 200 0.619
0.642 0.660
0.815 0.405#2 295 248 150 0.709
0.746 0.754
1.174 0.641#3 225 155 100 1.134
1.129 1.142
1.539 0.430 S, D, L: in unit of µm.υcut*,υcut c, υcut
exp , υdiff
#: in unit of THz c: according to Chen’s theory
*: infinite circular waveguide theory
Tporosity: the proportion of the hole area to the aperture area
100 200 300 400 500 600
0.2 0.4 0.6 0.8 1.0
1.2 y= P1 / x
Weighting:
y No weighting Chi^2/DoF = 0.00087 R^2 = 0.99291
P1 180.44477 ±3.43565
Cutoff frequency (THz)
Hole diameter (µm)
Fig. 4.11 Cutoff frequency vs. holes diameter of MPCs
4.2.2 Polarization rotated around the optical axis of sample #1
From the results of Fig. 4.12, it can be known that normal transmission of THz radiation with different polarizations is the same.
The same results are also shown in Miyamaru et al. When the incident angle is zero, transmission is independent of the polarization due to equal phase difference and transmittance of two orthogonal polarizations.
(a) (b)
Fig. 4.12 (a) Waveforms, (b) spectra, and (c) transmittances of Sample #1 with rotation
4.2.3 Transmission properties of MPCs with 3M tapes
Fig. 4.13 shows that the spectra and the transmittance of 1 to 4 layers of 3M tapes of 60 mm thickness. In Fig. 4.13 (b), the tapes are almost transparent to THz radiation of 0.1 ~ 1 THz. If the tapes attached to the incident side of MPCs, Fig. 4.14 displays that transmission peaks shifted to low frequency and the peak amplitude dropped more than the attenuation effect of tapes in Fig. 4.13.
It is showed transmittance spectra of JMPC without tapes, with one tape on incident side, and with one tape on each side in Fig. 4.15. The magnitude of transmission peak dropped to ~60% and the peak frequency shifts from 0.309 THz to 0.282 THz as one tape is attached to the incident side of JMPC. If another tape is attached to the other side of JMPC, the magnitude of transmission peak rises to almost equal transmittance of JMPC without tapes, and the peak frequency shifts again to lower frequency ~ 0.266 THz. The change of peak frequency may be caused by the surface plasma effect. The transmittance of JMPC with one tape on each side is larger than that of JMPC with one tape on incident side, which is attributed to impedance matching on both interfaces of input and output sides.
Fig. 4.16 shows that shifts of peak frequencies are obviously observed. Transmittance at peak frequency monotonically decayed until the saturation when number of tapes is four. Moreover, peak frequencies shift to lower frequencies below cutoff. Shifting to lower frequency is related to surface plasma effect.
From Fig. 4.15 and 4.17, it could be deduced that tapes attached to each side of JMPC should produce larger transmittance
(a)
0.2 0.4 0.6 0.8 1.0 1.2
0.0000000 0.0000005 0.0000010 0.0000015 0.0000020 0.0000025
Reference 1-layer 2-layer 3-layer 4-layer
Frequency (THz)
Amplitude
(b)
0.2 0.4 0.6 0.8 1.0
0.0 0.2 0.4 0.6 0.8 1.0 1.2
Transmittance
Frequency (THz)
1-layer 2-layer 3-layer 4-layer
Fig. 4.13 Spectra and transmittances of 1-4 layers of tapes
(a)
Fig. 4.14 (a) Spectra and (b) transmittance of Sample #1 with tapes on incident side
0.2 0.4 0.6 0.8 1.0 0.0
0.2 0.4 0.6 0.8 1.0
Amplitude transmittance
Frequency (THz) JMPC only
JMPC with 1 tape on incident side JMPC with 1 tape on each side
Fig. 4.15 Amplitude transmittance of JMPC with one tape on incident/each side
Table 4.2 Peak frequency and amplitude transmittance of JMPC with tapes on each side
Film thickness (µm)
υpeak (THz) ∆υ/∆td TA Tn
0 0.309 NA 0.884 2.68
60 0.267 7E-4 0.711 1.73
120 0.240 5.75E-4 0.621 1.32
180 0.230 4.39E-4 0.444 0.67
240 0.230 3.29E-4 0.318 0.35
TA: amplitude transmittance at peak frequency Tn: normalized transmittance at peak frequency
0.22 0.24 0.26 0.28 0.30 0.32 0.3
0.4 0.5 0.6 0.7 0.8 0.9
Transmittance
Peak frequency (THz)
υc~0.293THz
Fig. 4.16 Transmittance vs. peak frequency of JMPC with layers of tapes on each side
0.2 0.4 0.6 0.8 1.0
0.0 0.2 0.4 0.6 0.8 1.0
Water vapor
Amplitude Transmittance
Frequency (THz)
JMPC only
JMPC with 1 tape JMPC with 2 tapes JMPC with 3 tapes JMPC with 4 tapes
Fig. 4.17 Amplitude transmittance of JMPC with different layers of tapes on each side
due to the impedance matching and more obvious peak shifts owing to refractive index change, respectively.
From the results of Fig. 4.18, peak frequency shifts exponentially to lower frequency and peak frequency change is linearly decayed as the thickness of attached tapes was changed,. It could be due to increasing of the attenuation length with the thickness increasing.
Fig. 4.19 displays that normalized transmittance equals ~2.68 times of porosity at peak frequency of JMPC. Normalized transmittance of JMPC with 0 to 2 tapes (0-120 µm) shows larger than unity of porosity.
Hence, extraordinary transmission occurs at some transmission frequencies of JMPC.
4.2.4 Fabry-Perot etalon made by two JMPCs with a cavity of ~ 0.5 mm spacing
A Fabry-Perot etalon as shown in Fig. 4.20 was fabricated by two JMPCs with a cavity of around 0.5 mm spacing. According to etalon effect, the 0.5 mm spacing corresponds to 0.3 THz and its higher-order harmonic frequencies. Fig. 4.21 shows the etalon effect makes the transmission peak sharper as the dash-dot circles indicated. Effect of a Fabry-Perot etalon with two mirrors replaced by MPCs is successfully accomplished.
0 50 100 150 200 250
Fig. 4.18 Thickness change of tapes vs. peak frequency and its magnitude of shifts
Fig. 4.19 Power transmittance normalized to porosity of JMPC with tapes attached to each side
0.5mm
Fig. 4.20 Pictures of a Fabry-Perot etalon
0.2 0.4
0.0 0.2 0.4 0.6 0.8 1.0
Amplitude Transmittance
Frequency (THz) 2 slabs cavity
JMPC only
Fig. 4.21 Transmittance of a Fabry-Perot cell with a cavity of ~ 0.5mm spacing
5. Conclusions and Future Works
The transmission properties of metallic photonic crystals perforated with a triangular array of circular holes in THz region are known.
Transmission band of MPCs can be well controlled by changing the three parameters of MPCs. Besides, 3M tapes shows no obvious absorption in 0.1~1THz. When they are attached to incident side of the MPCs, transmission bands of MPCs displays anomalous drop in a certain region.
Furthermore, if they are attached on each side with equal layers of tapes, peak frequency of transmission band shifts to lower frequency below the cutoff. This phenomenon may be caused by refractive index change derived from surface plasmon theory. Finally, a Fabry-Perot cell of two MPCs is constructed. The results of this cell show shaper transmission band. It could be attributed to the Fabry-Perot effect.
In the future, effect of defect structures will be an interesting topic because it may have some large transmission peaks in the forbidden band.
In addition, THz components of MPCs with tunable transmission band will be fabricated. To achieve this goal, liquid crystals (LCs) will be essential elements. Therefore, a MPC cell infiltrated with LCs can be made to change the transmission band by tuning the effective refractive index of LCs applied by magnetic field because metals of the MPCs in this study show no magnetic response.
Appendices
Appendix 1 Resolution in Sampling
Table A1 Time resolution vs. Frequency resolution for 1024 sampling points
1Time Resolution (ps) = [Sampling Delay step size (µm) * 2] / Light Speed in vacuum 300 (µm /ps)
2Frequency Range (THz): Full positive frequency range after fast Fourier transform (FFT).
3Frequency Resolution (THz) = Frequency Range (THz)/ [1024 /2+1]
0 5 10 15 20 25 30 35 40 45 0.000
0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040
0.00 0.05 0.10 0.15 0.20 0.25 0.30
Time resolution (ps)
Data: Data6_points1024 Model: Allometric1
Chi^2/DoF = 1.1032E-11 R^2 = 1
a 0.14613 ? .00003
b -1.00004 ? .00009
Frequency resolution (THz)
Step size (
µm) For 1024 sampling points
Fig. A1.1 Sampling step size vs. frequency and time resolution
Appendix 2 Etalon effect
Etalon effect is caused by multiple internal reflections when
radiation passes through a parallel-sided material. The exiting light with numbers of internal reflections interferes so that fringes occur.
Assuming normal incidence and the material located in air (n=1), the electric field Et (ω) of exiting light can be written as a function of electric field Ei (ω) of incident light:
r1, r2 are reflection coefficients in 1st and 2nd interfaces, respectively:
1
n(ω) is the frequency-dependent refractive index of the material, and δ is the phase difference induced by internal reflections:
)d 2n( ω δ =
where d is thickness of the material. Summed to infinity, the transmitted electric field can be reduced to:
δ Multiplying Et(ω) by its complex conjugate yields the irradiance of the exiting light:
δ
If introducing the coefficient of finesse F such that2
Fig. A2.1 Illustration of Fabry-Perot etalon effect
5 10 15 20 25 30 0.2
0.4 0.6 0.8 1
δ It/Ii
F=0.2
F=1
F=200
Fig. A2.2 Airy function
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