4.2 Characteristics of MHAs
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 the causes of multi-peak appearance.
Details of peak frequencies and reasons of the peak drift are still not clear, but it is clear that SPPs play an important role in enhanced transmission characteristics.
5. Conclusions and Future Works
We experimentally and numerically investigate the role of material in the holes on transmission characteristics of the 2D-MHA. 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 SPP model also cannot predict the peak frequencies. When the holes filled with UV-gel, the transmission peak broadened and multi-peak features are observed. The transmittance of the peaks are reduced, but they are still larger than those according to the porosity. Further, with the thickness becomes thinner, all peaks shift to high frequencies and disappear when they approach the diffraction limit. Finally, multi-peaks return to one when the thickness reaches around 100 mµ . Peaks shift to the left and decrease as the SPP resonances approach the cutoff frequencies when we attach translucent ScotchTM tapes on the incident side of 100µm-thick 2D-MHA filled with UV-gel. Upon increasing the number of the tape, a side peak on the high frequency side grew gradually and red-shifted and for the number of tapes up to fifteen layers, the trend of shift still persists. For deeper holes, SPP can exhibit two distinct modes, coupled and uncoupled types as confirmed in the simulated results for the electric field.
In the future, we want to design a sensor using 2-D MHA for detecting the absorption line.
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