Detection of THz Radiation Using PC Antennas

and the speed of radiation beam in the medium, respectively.

2.1.3 Detection of THz Radiation Using PC Antennas

The electric field of a Gaussian beam on the detector [12] as shown in Fig. 2.1 can be expressed as:

2 2 2

0 1

( , ) exp[ ( ) / ]

E x y =E − x + y w (2.8) where w1 is spot size. The total resistance over the detector is:

MLM MLS SLS resistivities, respectively, and d is the width of the electrode and the gap area.The average resistivity ρS is much larger than ρM owing to the low duty cycle of the driving laser (100 fs/10 ns =10^-5). The resistivity ρS

depends on the photogenerated carrier density, which for homogeneous illumination of power Plaser scales as

S where ξ is a conversion factor between laser power and number of photogenerated carriers. The average field strength E across the detector gives rise to a potential difference U =E L( _M +L_S), so the average current is

2

The average electric field across the detector area is

/ 2 / 2 electric field, E0, can be expressed in terms of the total power in the THz beam:

0

1 0

2 P_THz E w π εc

⇒ = (2.14)

By inserting Eq. (2.14) into the expression for the detector current, Eq.

(2.11), we get when focusing spot size ₁

0 0

Fig. 2.1 Structure of antenna detector 2.1.4 Detection of THz Radiation Using EO Materials

Detection of the polarization change of an optical probe beam produced by the THz field when both fields are applied on an electro-optic crystal; this method is called free-space-electro-optic sampling (FS-EOS).

The FS-EOS uses the linear electro-optic effect in an EO crystal excited by an optical probe field and the THz field. Both fields propagate in the same direction but have different polarizations. For instance, if z is the propagation direction, the optical probe is polarized at 45° in the (x, y)

plane perpendicular to z owing to birefringence of the EO crystal, while the THz field is perpendicular to the y axis. Since the electro-optic effect is practically instantaneous at the THz scale, the output of a FS-EOS detector is directly proportional to ETHz(t). Due to the presence of the THz field a phase retardation ∆ϕ of the optical field is produced over the distance dz, which is strongly dependent on the electro-optic crystal type and orientation. ZnTe is a material for which a high signal-to-noise ratio is obtained. For ZnTe the phase retardation is given by

3

( ) ( / ) c n r E

0 41 _THz

( ) dz const

_ZnTe

E

_THz

( ) dz

ϕ τ ω τ τ

∆ = = ×

(2.16)

where ω is the optical frequency of the probe and r41 is the electro-optic coefficient. From the above equation it follows that the THz field can be obtained after propagating over a length L in a ZnTe crystal, a material with small absorption and a refractive index difference of ∆n = nTHz-nopt = 0.22, is

( ) ( ) /( )

THz ZnTe

E τ = ∆ ϕ τ L const ×

. (2.17) Thus, measuring the phase change we can determine the time variation of the THz signal ETHz(t).

2.1.5 Applications

THz technologies have made great progress for aiming at applications such as radio astronomy, remote-sensing, spectroscopy [13-15], optical properties of semiconductors and dielectrics [16], imaging of general substances [17-19], and biomedical imaging [20-21].

It also can be applied to find specific spectroscopic fingerprints of biological matter in this region [22].

2.2 Metallic Photonic Crystals

Photonic crystals are periodically structured electromagnetic media, generally possessing photonic band gaps: ranges of frequency in which light cannot propagate through the structure.The crystal can thus form a kind of perfect optical “insulator,” which can confine light losslessly around sharp bands, in lower-index media, and within wavelength-scale cavities, and among other novel possibilities for control of electromagnetic phenomena.

2.2.1 Metallic Photonic Crystals

Photonic crystals made of metals are called “Metallic Photonic Crystals” (MPCs) which have been widely used to form bandpass filters, reflector surfaces, Fabry-Perot interferometers, and so forth.

2.2.1.1 Infinite-long Circular waveguides

Fig. 2.2 shows electromagnetic (em) waves can propagate inside round metal pipes with radius of a. Equations of time-harmonic electric and magnetic field can be written as following:

2 2

2 2

0 0 E k E H k H

∇ + =

∇ + = (2.18)

Fig. 2.2 A circular waveguides

For a straight and uniform circular waveguide, as shown in Fig. 2.2, it is convenient to decompose the 3-D Laplacian operator ▽² into two parts:

▽_rf² and ▽_z² for transverse and longitudinal components, respectively.

For TM waves, H_z = 0 and E_z ≠ 0, all fields can be expressed in terms of equation listed above.

For TM waves in circular waveguides, ( , , ) 0( , ) ^z eigenvalues of TM modes are determined from the boundary condition that E must vanish at r = a: _z⁰

( ) 0 which yields the lowest cutoff frequency:

01

For TE waves in circular waveguides, ( , , ) 0( , ) ^z

where Cn’ is a coefficient. The eigenvalues of TE modes are determined from the boundary condition that the normal derivative of H must _z⁰ vanish at r = a: which yields the lowest cutoff frequency:

01 11

( ) 0.293

( ) 2

TE c TE

f h

π µε a µε

= = (Hz) (2.29)

2.2.1.2 Chen’s theory

In this thesis a robust theory [23] based on microwave circuit problems to calculate transmission spectra of our MPCs was used. The theory in detail is shown below:

Fig. 2.3 Geometry of a perforated plate

The fields on both sides of the plate as shown in Fig. 2.3 are expanded into a complete set of Floquet modes Φpqr, with two spatial harmonic number p and q, and a third subscript r, used to denoted TE or TM mode. Each Floquet mode has a propagation constant γpq along the z axis and a characteristic modal wave admittance ξprq

f. The fields inside the holes between two apertures are expressed in terms of conventional waveguide modes Ψmn with a characteristic modal wave admittance ηmn

and a propagation constant βmn. The incident wave is of arbitrary polarization with modal voltage coefficient A₀₀₁ and A₀₀₂. By matching the transverse electric and magnetic fields at the aperture z = - l₁, an integral equation for the unknown transverse field at z = - l₁ is obtained:

∑∑∑

where F_mnr and Y_mnr are the modal coefficient of the conventional waveguide modes and the input admittance looking into the waveguide from the aperture at z = - l₁, respectively. In the cases of open and short circuits at z = 0, the input admittance is

tan(

1

)

mnr mnr mnr

Y = + j η β l

for open circuit

= - j η

_mnr

cot( β

_mnr

l

₁

)

for short circuit (2.31) By substituting (2.31) into (2.30), two integral equations, one for the open-circuit and the other for the short-circuit problem, are obtained. The open- and short-circuit aperture fields at z = - l1, Eo and Es are obtained by solving these two integral equations independently by the method of moments. Thus the transverse aperture fields at z = - l₁ of the original problem are

1

( ) 1[ ]

t 2 o s

E z =ml = E ±E (2.32) where the positive sign applies to the aperture field on the incident side of the plate, and the negative sign applies to the aperture field on the transmitted side. The reflection coefficient at z = - l₁ is

*

where δpq =1 for p = q = 0, otherwise δpq =0.

The transmission coefficient at z = l₁ is

*

( 1)

pqr t pqr

aperture

B =

∫∫

E z =l ⋅ Φ da (2.34) For the case of normal incidence, the reflection and the transmission coefficients are reduced to the forms

)] 1

where A and B are functions of element spacing and aperture size. For circular openings with equilateral triangular lattice:

2

where a is the radius of circular apertures and d is the spacing between any two apertures.

2.2.1.3 Theory of Surface Plasmons (SPs) [24]

The electron charges on a metal boundary can perform coherent fluctuations that are called surface plasma oscillations [25]. The field of surface plasma on smooth surface, Fig. 2.4, can be expressed as

0

exp[ (

_{x z}

)]

The dispersion relation (2.42) can be written as

1 2 1/ 2

Fig.2.4 The charges and the em field of SPs propagating on a surface in the x direction.

Fig. 2.5 The dispersion relation of SPs and light in vacuum

From the results of Fig. 2.5, it indicates that SPs cannot transform into light without any assistance. Grating components are used to couple the light to SPs as depicted in Fig. 2.6. Light wave vector is increased by a

∆kx = ^υ g (υ: integer) value to “transform” the photons into SPs.

sin 0 ^{m d}

x sp

m d

w w

k g k

c c

θ ν ε ε

ε ε

= ± = =

+ (2.45)

The reverse also takes place: SPs propagate along the grating to reduce Kx by ^∆Kx. Then SPs is transformed into Light.

Fig. 2.6 The grating coupler. SP: dispersion relation of SPs, l: light line For a 2-D rectangular grating [26], and tilted incident light with wave vector kr

,

2 2

sp x x y sin

k k i G j G k i x j y

a b

π π

→ → → → →

θ

∧ ∧

= + + = + + (2.46)

where Gr_x

and Gr_y

are reciprocal lattice vectors, i and j are integers, a and b are holes periodicities along the principal axes, and θ is incident angle. In the case of a square lattice with periodicity of a0 , together with Eq. (2.45), the dispersion relation of SPs is given by

2 2 1/ 2

For a triangular lattice of holes, however, Eq. (2.47) gives the position of the maxima if normal incidence:

2 2 1/ 2 1/ 2

2.2.2 Transmission Characteristics of MPCs

From this theory, transmission properties of MPCs are independent on the polarization of normal incident waves. Recently, Miyamaru et al.

[3] showed that no polarization change was observed because two orthogonal-polarized electric fields along the principal axes of the triangular lattice after passing through the MPC had equal transmittance and phase shifts.

3. Experimental Methods

3.1 THz-TDS System

The THz-TDS system was shown in the Fig. 3.1(a), and transient current was generated optoelectronically by femtosecond laser pulses (1) impinging on a photoconducting material, dipole antenna on a GaAs:As⁺ substrate (2). Emission of electromagnetic (em) pulses (3), THz radiation, of about ps duration were produced by the current. The THz pulse was collected and guided by gold-coated parabolic mirrors (4). Fs laser pulse as a probe beam with time delayed by motor stage (6) and the THz pulse collinearly impinged on a nonlinear crystal (ZnTe) (8). The transmitted laser pulse with polarization changed by electro-optical effect was separated into two beams with orthogonal polarizations by Wollaston beam splitter (9). The two beams coupled to a balanced detector (10) connecting to a lock-in amplifier (LIA) (11). Signal from LIA can be easily obtained using PC.

To reduce the water vapor absorption of THz signal, an acrylic box by continuously introducing pure nitrogen was used as a humidity controller in THz optics. The humidity can be rapidly lowered to few percents in tens of minutes. Furthermore, due to the stable atmosphere in THz optics, the THz system became more stable.

Assuming that the THz beam was spatial Gaussian distribution, the THz radiation can be considered as a plane wave, i.e. normal incident to the sample when the sample was located in the image plane, as shown in Fig. 3.1 (b).Consequently, the analysis was simplified to normal transmission.

(a)

(b)

Fig. 3.1 THz-TDS system s

l d

THz wave

(a)

(b)

Fig. 3.2 Real pictures of (a) THz-TDS system and (b) Ti-sapphire ultrafast laser

3.2 Fabrication methods

One of fabrication methods for MPCs is to use laser cutting by a high-power pulsed laser. Laser cutting provided high-speed, precise orientation to form vector, raster cutting and etching capabilities over a range of materials. Its mechanism was shown in Fig. 3.3. Another method is mechanical manufacture. It also provides sufficiently fine structures to meet our need.

Fig. 3.3 Laser cutting mechanism (from MIT Media Lab)

3.3 Structures of MPCs Samples

All samples were metal slabs perforated periodically with a triangular array of circular holes. Three parameters (s: spacing between holes, d: diameter of holes, l: slab thickness) can be controlled to change the transmission properties of MPCs. One of samples named JMPC is made of aluminum alloy and produced by mechanical manufacture in Japan. The others named #1 to #3 are made of stainless steels SUS-304 and produced by laser cutting by La Kang Co., LTD.

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)

υ_c~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

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

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