r is P4 2.4GHz with 2G RAM. For
sed to numerically simulate the THz The equipment of our compute
convenience, we use the commercial software “FULLWAVE” invented by the RSOFT company to proceed the FDTD simulation. The parameters of the simulation are listed below.
The FDTD method is u
propagation problem. In this approach, the 2D-MHA occupies the space from z = 0 to t. Terahertz wave is normally incident in the z-direction from z<0 and polarized in the x-direction. The grid spacing for FDTD calculation are 30µm in x and y dimensions and 8µm in the z-direction.
For the periodic triangular arrays with period of 990µm, the total computational grid is about 7.5mm × 8.3mm × 0.9mm. The beam size is 6mm which is large enough to avoid the finite size effect. The system is defined by specifying the relative dielectric constant, εR(x, y, z, ω). At first, the hole material and the adjacent medium are air, so we set εR = εAir = 1, and for Aluminum we set εR = εAl(ω) using the Drude model shown in Fig. 3-11 (a). For example, it gives εAl = -3.3820×104 +2.1882×106i at 0.3THz. Complex refractive index is also shown below in Fig. 3-11 (b). The grids are truncated with uniaxial perfect matching layers to simulate absorption of field components approaching grid edges where appropriate [20].
1 10 100 1000
0.03 0.3 3 30
103 104 105 106 107 108
frequency (THz)
dielectric function (ε 1+iε 2) in Al
frequency (cm-1)
- ε
1
ε
2
Fig. 3-11 (a) Dielectric function of Aluminum versus frequency.
10 100 1000
0.3 3 30
10 100 1000 10000
frequency (THz)
refractive index (n-iκ) in Al
frequency (cm-1)
n - κ
Fig. 3-11 (b) Refractive index of Aluminum versus frequency.
4 Results and Discussion
4.1 Free Space THz-TDS Waveform and Spectrum
THz time domain waveform is shown in Fig. 4-1. The amplitude of oscillations after main peaks are due to the humidity can be seen in the tail of the waveform. It can speculate that the oscillation is caused by water vapor absorption.
0 20 40 60 80 100 120 140
-0.00010 -0.00005 0.00000 0.00005 0.00010 0.00015 0.00020
electric field (a.u.)
time delay (psec)
Reference
Fig. 4-1 Free space THz time domain waveform
Because of the silicon lens contacted with the substrate of antenna, we can eliminate the reflective signal from the waveform. Then, using numerical fast Fourier transform can obtain the frequency spectrum shown in Fig. 4-2. Some deep dips at 0.556, 0.754, 0.988, 1.113, 1.164, 1.208, 1.230, 1.413 THz are cause by water absorption [25].
0.0 0.5 1.0 1.5 2.0 2.5 3.0 1E-23
1E-22 1E-21 1E-20 1E-19 1E-18 1E-17 1E-16 1E-15 1E-14
power (a.u.)
frequency (THz)
Reference
Fig. 4-2 THz frequency domain spectrum
From the frequency spectrum, we can estimate the signal-to-noise ratio in our system is larger than and the bandwidth approaches 2THz.
Because this spectrum was measured in free space without passing any sample, we call this signal is reference signal.
106
4.2 Characteristics of MHAs
MHA in THz region is like a band-pass filter, and the normalized transmittance at peak frequency is about 260% to the porosity of the sample. The porosity means the area of holes divided by the total area of illuminating, the value is about 0.29 in our sample. Theory of this extraordinary phenomenon is still unclear; the widespread explanation is
the coupling between the incident electromagnetic wave and surface plasmon polariton. Recall the equation (2.2.26) about the resonant peaks in triangular structure,
1
2 2 2
max 0
[ ( 4 )]
3
da i ij j
λ = + +
−ε
(2.2.26)the maximum transmittance only concern with the spacing and the adjacent material. This phenomenon has been verified by experiments, for instance, the peak can be tuned when the adjacent dielectric material is changed from air to tape. However, in this formula, the max.
transmittance peak seems to be independent of the thickness of the MHA and the material stuffed with the holes. We want to check this point ,and then some brand-new phenomena happened in our experiments that the formal experiences can’t to expound.
4.2.1 Basic Transmission properties of MHAs
First, we measure the THz waveform in free space as the reference, and then we measure THz propagating through MHA as the siganl. Two time-domain waveforms can be used to obtain frequency-domain spectra using numerical fast Fourier transform, and dividing MHA signal by the reference in frequency domain will be the transmittance of this sample.
The transmission properties of certain sample with a board band frequency spectrum can be observed. From the above steps, we can obtain the basic transmission properties of MHAs.
From the above steps, we can obtain the basic transmittance properties of MHAs shown in Fig. 4-3 (a) is the time domain signal
FFT from (a). (c) is the power transmittance, we can observe a obvious characteristic of band-pass filter, and the magnitude of the peak almost get up to 100%. The little peaks at 0.55 and 0.75THz are the inaccuracies owing to the water absorption.
The finite time extent of the terahertz pulse scans, 136 ps (in 1024 steps), limits the frequency resolution of the numerical Fourier transforms in THz-TDS. To perform a numerical interpolation between the measured frequency points, the measured pulses in the time domain were extended with zeros (zero padding) [11] to a total time duration of 1500 ps.
0 20 40 60 80 100 120 140
-0.0002 -0.0001 0.0000 0.0001 0.0002 0.0003
electric field (a.u.)
time delay (psec) Ref.
MHA signal amplified to 300%
Fig. 4-3 (a) The time domain signal compared with the reference
0.0 0.5 1.0 1.5 1E-25
1E-24 1E-23 1E-22 1E-21 1E-20 1E-19 1E-18 1E-17 1E-16
2.0
power (a.u.)
Frequency (THz)
Ref.
MHA
Fig 4-3. (b) The frequency domain signals via the FFT from (a)
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0.0 0.2 0.4 0.6 0.8 1.0
water absorption power transmittance of the MHA
power transmittance
frequency (THz)
Fig. 4-3 (c) The power transmittance of the MHA. A obvious characteristic of band-pass filter, and the magnitude of the peak almost
In order to grasp this phenomena more, we use the FDTD algorithm to simulate this structure. It is successful that we got almost the same result compared with the experiments. Owing to the lack of our RAM, the spectral linewidth of the peak is wider slightly than the experiment, but the peak frequency is also located at 0.3THz nearby. So we can affirm that this simulated tool is accurate enough to express the real situation.
The simulated results shown Fig. 4-4 (a) is the time domain signal compared with the reference. (b) is the frequency domain signals via the FFT from (a). (c) is the power transmittance.
0 20 40 60 80 100 120 140
-0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20 0.25
electric field (a.u.)
time delay (psec) Ref.
MPC signal magnified to 300%
Fig. 4-4 (a) Simulated result: The time domain signal compared with the reference
0.0 0.3 0.6 0.9 1.2 1.5 1E-20
1E-19 1E-18 1E-17 1E-16 1E-15 1E-14 1E-13 1E-12 1E-11 1E-10
power (a.u.)
frequency (THz)
Ref.
MHA
Fig. 4-4 (b) Simulated result: The frequency domain signals via the FFT from (a)
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0.0 0.2 0.4 0.6 0.8 1.0
power transmittance of the MHA
power transmittance
frequency (THz)
Fig. 4-4 (c) Simulated result: The power transmittance of the MHA. The spectral linewidth of the peak is wider slightly than the experiment, but the peak frequency is also located at 0.3THz nearby.
From both experimental and simulated results above, we can observe a almost monochromatic waveform in time domain that can response to the peak at 0.3 THz in the power transmittance.
4.2.2 Using SPP Model to explain the extraordinary transmission peak The MHA we used is an Aluminum plate perforated with an array of triangular holes (hole diameter d=0.56 mm, lattice constant s=0.99 mm, and thickness of the metal plate t=0.5 mm). For this sample, the cut-off frequency is νcutoff=0.311 THz. In Fig. 4-3 (c), we can observe a obvious peak at 0.301THz which is left to the cutoff frequency. The enhanced transmission is commonly believed to be due to the resonant coupling of incident light with SPPs.
Nevertheless, the peak frequency calculated from eq.(2.2.26) is 0.348THz which is not accurate enough to the observed peak at 0.301THz shown in Fig. 4-5 (a). Furthermore, we checked the MHA with cubic arrays with the same parameters (d=0.56 mm, s=0.99 mm, and t=0.5 mm) to the triangular one using FDTD algorithm, the theoretical peaks also laid on the right side to the simulated peaks, as shown in Fig 4-5 (b).
Although the peak positions are not the same with SPP model, they are still very close to each other. And the spacing between the two peaks in Fig. 4-5 (b) show almost identical range. For this reason, we can presume SPPs play an important role in the extraordinary transmissions.
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.0
0.2 0.4 0.6 0.8 1.0
0.301THz 0.348THz
Power transmittance
Frequency (THz)
.0
Fig. 4-5 (a) Using SPP model to estimate the transmission peak in the triangular MHA. The peak frequency calculated from eq.(2.2.26) is 0.348THz right to the observed peak at 0.301THz
0.0 0.2 0.4 0.6 0.8 1
0.0 0.1 0.2 0.3 0.4 0.5
0.426THz 0.301THz
0.381THz 0.271THz
power transmittance
frequency (THz)
Fig. 4-5 (b) Using SPP model to estimate the transmission peak in the cubic MHA. The peak frequencies calculated both are right to the the
4.2.3 Altering the thickness of MHAs
In order to make sure that the maximum transmittance peak frequency won’t change with the thickness of MPC. We use two different samples to do experiments. The structure of the first sample is s (spacing)
=1.13mm, d (diameter) =0.68mm and the second sample is s =0.99mm, d
=0.56mm. From the experimental results shown in Fig. 4-6, we find only the cutoff frequency shifts to left, but the peak frequency is almost invariable. This agrees with the prediction from the equation (2.2.26).
0.1 0.2 0.3 0.4 0.5
0.0 0.2 0.4 0.6 0.8 1.0
d=0.68mm,s=1.13mm 0.20 mm
0.25 mm 0.30 mm 0.50 mm 1.00 mm 2.00 mm
power transmittance
frequency (THz)
Fig. 4-6 (a) Altering the thickness of the first sample. The structure of the first sample is s =1.13mm, d =0.68mm.
0.2 0.3 0.4 0.5 0.0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
power transmittance
frequency (THz)
d=0.56mm,s=0.99mm 500µm
400µm 300µm
Fig. 4-6 (b) Altering the thickness of the second sample. The structure of the second sample is s =0.99mm, d =0.56mm.
4.3 Features of MHAs when their holes filled up with UV-gel
We recently demonstrated a THz tunable filter by controlling the index of refraction of nematic liquid crystal filling the holes and adjacent to the MHA on one side. New phenomena appeared when holes of the MHA are filled with dielectric material. The effect of filling dielectric material into the holes cannot simply be explained by increased effective hole diameter of the 2D-MHA and equation (2.2.26) also cannot predict the peak frequencies. Therefore, we want to fill some dielectric material into holes of the MHA for studying the effect on hole material.
The optical constants of the UV-gel are very suitable for us to fill it into the holes in MHA. The real part of refractive index is about 1.68, and the attenuation is negligible in our case. The dispersion curve is shown in Fig. 4-7, it seems to be almost non-dispersive in THz region.
0.2 0.4 0.6 0.8 1.0
1.2 1.4 1.6 1.8 2.0
real part of refractive index (n)
frequency (THz)
UV-gel 68 produced by Norland company
Fig. 4-7 (a) The dispersion relation of the UV-gel in THz region. The real part of refractive index is about 1.68 with almost non-dispersion.
0.2 0.4 0.6 0.8 1.0 0.00
0.01 0.02 0.03 0.04
imaginary part of refractive index (κ)
frequency (THz)
UV-gel 68 produced by Norland company
Fig. 4-7 (b) The imaginary part of refractive index of the UV-gel in THz region. The attenuation seems to be negligible in our case.
The imaginary part of refractive index is related to attenuation, and it can be expressed below [26]. Fig. 4-8 shows the attenuation coefficient versus frequency.
2 c α = ωκ
(4.3.1) where α is attenuation coefficient. And the inverse of attenuation coefficient means the depth of penetration.
0.2 0.4 0.6 0.8 1.0 0
50 100 150 200
UV-gel 68 produced by Norland company
attenuation coefficient (m-1 )
frequency (THz)
Fig. 4-8 The attenuation coefficient of the UV-gel in THz region.
4.3.1 Transmission Properties When Holes of the MHA Filled with UV-gel
When the holes filled with UV-gel, the effective hole diameter becomes larger, so the cutoff frequency shifts to left. Except for this predictable result, frequency range between the cutoff frequency and the diffraction limit occurs some unusual phenomena. The transmission peak broadened and multi-peak features are observed. The original single transmittance peak changes into three peaks shown in Fig. 4-9. The transmittance of the peaks are reduced, but they are still larger than those according to the porosity (0.29).
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.0
0.2 0.4 0.6 0.8 1.0
power transmittance
frequency (THz)
pure MHA signal
holes of the MHA filled with UV-gel
Fig. 4-9 Power transmittance of the MHA which holes filled with UV-gel.
The transmission peak broadened and multi-peak features are observed.
For the pure sample, the cut-off frequency is νcutoff=0.311 THz, but when holes of the MHA filled with UV-gel, the effective hole diameter becomes larger so the cutoff frequency is reduced to 0.311/1.68
=0.185THz. Diffraction limit frequency remains the same due to the changeless lattice constant.
4.3.2 Dependence on Thickness When Holes of the MHA Filled with UV-gel
Further, altering the thickness of MHA will let the peaks shift strongly. With the thickness becomes thinner, all peaks shift to high frequencies and disappear when they approach the diffraction limit. The range of shift seems to be random. Finally, multi-peaks return to one when the thickness reaches around 100 mµ , as shown in Fig. 4-10.
0.15 0.20 0.25 0.30 0.35
0.0 0.2 0.4 0.6 0.8 1.0
original 2D-MHA Holes filled with
UV-gel (n=1.68) 500µm 400µm 300µm 200µm 100µm
power t ransmi ttance
frequency (THz)
Fig. 4-10 Altering the thickness of MHA when the holes filled with UV-gel. All peaks shift to high frequencies and disappear when they approach the diffraction limit.
0.15 0.20 0.25 0.30 0.35 0.0
0.2 0.4 0.6 0.8 1.0
FDTD simulated results original 2D-MHA Holes filled with
UV-gel (n=1.68) 500µm 400µm 300µm 200µm 100µm
frequency (THz)
power transmittance
Fig. 4-11 FDTD simulated results: Altering the thickness of MHA when the holes filled with UV-gel. It shows the same trend with experimental results in Fig. 4-9
The simulated results using FDTD algorithm as shown in Fig. 4-11 qualitatively agree with the experimental results. They have the same trend that all peaks shift to high frequencies and disappear when they approach the diffraction limit. However, owing to the rough grids (30µm) in x and y dimensions, the inaccuracy of cutoff frequency will be more obvious in the simulated results. The peak values are lower in experimental results owing to the inaccuracy of sample fabrication.
In order to look for the trend of these phenomena, we aim at the first and the second peaks from left, the first valley, and the spacing between
the first and the second peaks, as shown in Fig. 4-12 below.
0 100 200 300 400 500
0.18 0.19 0.20 0.21 0.22 0.23 0.24 0.25 0.26
frequency (THz)
thickness (µm) The first peak
FDTD simulation Experiment
Fig. 4-12 (a) The first peak frequency as the function of the thickness
0 100 200 300 400 500
0.25 0.26 0.27 0.28 0.29 0.30 0.31 0.32 0.33
frequency (THz)
thickness (µm)
The second peak FDTD simulation Experiment
Fig. 4-12 (b) The second peak frequency as the function of the thickness
0 100 200 300 400 500 0.20
0.22 0.24 0.26 0.28 0.30 0.32
frequency (THz)
thickness (µm)
The first valley
FDTD simulation Experiment
Fig. 4-12 (c) The first valley frequency as the function of the thickness
0 100 200 300 400 500
0.06 0.07 0.08 0.09 0.10
0.11 The spacing
FDTD simulation Experiment
frequency (THz)
thickness (µm)
Fig. 4-12 (d) The spacing between the first and the second peaks as the function of the thickness
From the above figures, we can see that there exists a gap, around 200µm, between two distinct regimes. There appears to be a line of demarcation:
only one transmission peak is observed when the thickness of the MHA is below 200µm. The first peak from left seems to be depressed by the cutoff frequency. So when the thickness becomes thicker, the shift of the first peak will tend to saturation. And if the thickness is thicker than 200µm, the second peak wavelength seems to be linear with the thickness of MHA.
4.3.3 Changing the adjacent medium When Holes of the MHA Filled with UV-gel
The transmission spectra when we attach translucent ScotchTM tapes on the incident side of 100µm-thick 2D-MHA filled with UV-gel is studied. Peaks shift to the left and decrease as the SPP resonances approach the cutoff frequencies, as shown in Fig. 4-13 (a). Refractive index of the tape is about 1.7 in THz region. These phenomena are analogous with previous reports elucidated in terms of the SPP. However, upon increasing the number of the tape, a side peak on the high frequency side grew gradually and red-shifted shown in Fig. 4-13 (b). For the number of tapes up to fifteen layers, the trend of shift still persists, as shown in Fig. 4-13 (c).
0.10 0.15 0.20 0.25 0.30 0.35 0.40 holes filled with UV-gel attach ScotchTM tapes on the incident side
no tape
Fig. 4-13 (a) 100µm-thick MHA which holes filled with UV-gel attach different layers of ScotchTM tapes on the incident side. The number of tapes is from zero to five.
0.10 0.15 0.20 0.25 0.30 0.35 0.40
0.00 holes filled with UV-gel attach ScotchTM tapes on the incident side
4 tapes
Fig. 4-13 (b) 100µm-thick MHA which holes filled with UV-gel attach different layers of ScotchTM tapes on the incident side. The number of
0.15 0.20 0.25 0.30 0.35 0.00
0.05 0.10 0.15
0.20 100µm-thick and holes filled with UV-gel attach ScotchTM tapes on the incident side
13 tapes 14 tape 15 tapes
frequency (THz)
power transmittance
Fig. 4-13 (b) 100µm-thick MHA which holes filled with UV-gel attach different layers of ScotchTM tapes on the incident side. The number of tapes is from thirteen to fifteen.
The same trend is also found in the case of 400µm-thick 2D-MHA filled with UV-gel, as shown in Fig. 4-14. Owing to the original double peaks in 400µm-thick sample, the situation of attaching tapes exhibited more complication.
0.10 0.15 0.20 0.25 0.30 0.35 0.40 holes filled with UV-gel attach ScotchTM tapes on the incident side
no tape
Fig. 4-14 (a) 400µm-thick MHA which holes filled with UV-gel attach different layers of ScotchTM tapes on the incident side. The number of tapes is from zero to five.
0.10 0.15 0.20 0.25 0.30 0.35 0.40
0.00 holes filled with UV-gel attach ScotchTM tapes on the incident side
6 tapes
Fig. 4-14 (b) 400µm-thick MHA which holes filled with UV-gel attach different layers of ScotchTM tapes on the incident side. The number of
4.2.4 Verify the Existence of Surface Plasmons Resonance by Observing the Electric Field in Near-Field Range
It is well-known that an in-plane momentum is needed to modify the incident wave to achieve the enhanced transmission. Either the SPP model, or the model of evanescent wave diffracted by the hole edges [27, 28] can provide such a mechanism. In order to identify these contentions, we have calculated distributions of Ez of the electric field amplitude for 400µm-thick 2D-MHA filled with UV-gel, as shown in Fig.
4-15. The frequencies of the incident THz wave are 0.191THz in Fig.
4-15 (a) and 0.276 THz in Fig. 4-15 (b), respectively. At 0.191 THz, the charge distribution on the side wall of each individual hole shows an anti-symmetric pattern between the top and bottom portion of the hole. At 0.276 THz, the charge distribution is symmetric, and surface waves on the top and bottom are coupled together. We also observe that the CW wave at 0.191THz impinges on the MHA, it will induce the maximum SPPs when a wave crest or trough passes through the medium of the MHA shown in Fig. 4-16 (a). Contrary to the first peak at 0.191THz, the CW wave at 0.276THz impinges on the MHA, it will induce the maximum SPPs when a wave crest arrives at the front surface of the MHA and a wave trough arrives at the back surface shown in Fig. 4-16 (b), and vice versa.
+
- + +
-- +
-Fig. 4-15 (a) Simulated z component Ez of the electric field amplitude for 100µm-thick MHA filling with UV-gel. The incident CW wave at 0.191THz.
- + +
-Fig. 4-15 (b) Simulated z component Ez of the electric field amplitude for 100µm-thick MHA filling with UV-gel. The incident CW wave at
(1)
(2)
Fig. 4-16 (a) Simulated Ex and Ez for the 400µm-thick 2D-MHA at 0.191THz. (1)-(6) shows a cycle of propagation.
(3)
(4)
Fig. 4-16 (a) Simulated Ex and Ez for the 400µm-thick 2D-MHA at
(5)
(6)
Fig. 4-16 (a) Simulated Ex and Ez for the 400µm-thick 2D-MHA at 0.191THz. (1)-(6) shows a cycle of propagation.
(1)
(2)
Fig. 4-16 (b) Simulated Ex and Ez for the 400µm-thick 2D-MHA at
(3)
(4)
Fig. 4-16 (b) Simulated Ex and Ez for the 400µm-thick 2D-MHA at 0.276THz. (1)-(6) shows a cycle of propagation.
(5)
(6)
Fig. 4-16 (b) Simulated Ex and Ez for the 400µm-thick 2D-MHA at
The intensity of electric field is normalized to the incident CW wave amplitude. The SPP-like surface wave showing in the simulations of the electric field amplitude agrees with the results studied by Miyamaru et al.
[29]. Different SPP modes were also reported by Ebbesen et al. in visible light [30]. However, in our samples, the effective hole depth become deeper and the band-pass frequency region become broader owing to filling UV-gel into the holes of MHAs. Therefore, we consider this is the reason why we can observe both modes at one sample. These might be
[29]. Different SPP modes were also reported by Ebbesen et al. in visible light [30]. However, in our samples, the effective hole depth become deeper and the band-pass frequency region become broader owing to filling UV-gel into the holes of MHAs. Therefore, we consider this is the reason why we can observe both modes at one sample. These might be