THz Time Domain Spectroscopy

Terahertz waves, with a frequency range of 0.1-10 THz, are termed

‘T-rays’. They occupy a large portion of the electromagnetic spectrum between the infrared and microwave bands, as shown in Fig. 2.1 [16].

The large terahertz portion of the spectrum has not been well developed because there were neither convenient high-power convenient high-power emitters to send out controlled terahertz signals nor efficient sensors to collect them and record information until the development of THz time domain spectroscopy (THz-TDS).

Fig. 2.1 A schematic representation of the electromagnetic spectrum showing the THz region

THz-TDS was initially developed in the early 1980s. Auston and Cheung used electro-optic materials to rectify fs optical pulses, thereby producing THz radiation of approximately one cycle. The coherence detection of the electric field of these THz pulses by electro-optic sampling enabled measurement of the changes in the shape of the waveform following reflection or transmission from materials. In this way the dielectric response of semiconductor materials was measured. A

A G Davis et al, Phys. Med. Biol. 47, 3679-3689

THz-TDS comprises a femtosecond laser source, the output from which is split such that a part is used to produce THz radiation which passes through the sample using an electro-optic sampling system (or PC antenna detection system). Fig. 2.2 and Fig. 2.3 show the conventional THz-TDS EO sampling system and antenna detection system [17].

Fig. 2.2 Conventional THz-TDS EO sampling system

Fig. 2.3 Conventional THz-TDS PC antenna detection system

The THz TDS system provides a direct measurement of the THz electric field pulse E_out as a function of time t using a coherent time- gating pulse form the same laser as the pump pulse. If the sample has a transmission coefficient T, which is a function of frequency f, and produces a phase shift φ(f) then the time-domain waveform in

Y. Cai et al, Appl. Phys. Lett. 73, 1998

Y. Cai et al, Appl. Phys. Lett. 73, 1998

transmission geometry can be derived from the incident THz spectrum Ein(f) by

∫

^∞

=

0

2 )

)

(

( ) ( )

( t E f T f e e df

E

_{out in} ^{iφ f πft} (2.1)

2.2 Generation and Measurement Principle of THz Radiation

At frequencies up to approximately 0.5 THz, EM radiation may be generated by electronic devices, including resonant tunneling diodes, Gunn devices, field effect or bipolar transistors [18]. Another popular approach is to use lasers to generates short pulses (of duration less than 100 fs) of near infrared radiation (output wavelength of approximately 800nm) which are directed onto a non-linear optical crystal (such as ZnTe) or photo-conductive structure (such as photo conductive(PC) antenna).

Conventional detectors for THz radiation rely on bolometers cooled by liquid helium . These devices measure only the intensity of the radiation and do not provide any phase information. The sensitivity of

these devices is also limited by background radiation. Thus a more common approach called free-space electro-optical sampling is developed

by Wu and Zhang [19].

2.2.1 Generation of THz Radiation with PC antenna

When a femtosecond laser excites a biased semiconductor with photon energies greater than its bandgap (Fig. 2.4), electrons and holes are produced at the illumination point in the conduction and valence

with the help of an antenna is produced by the fast changes of the density of photocarriers and their acceleration due to the applied dc bias (Vb). The production of ultrashort currents with a full-width half-maximum (FWHM) of 1ps or less strongly depends on the carrier lifetime in the semiconductor [20].

Fig. 2.4 Schematic of PC antenna

The carrier density behavior in time is given by

/ /

_t

( )

dn dt = − n τ + G t

(2.2) where n is the carrier density and

G t ( ) = n

₀

exp( / ) t ∆ t

² is the generation rate of carriers due to laser pulse excitation, with ∆t the laser pulse width and n₀ the generated carrier density at t = 0. The generated carriers are accelerated by the electric field bias with a velocity rate given by

,

/

,

/ (

,

)/

, ,

e h e h rel e h eff e h

dv dt = − v τ + q E m

(2.3) where ve,h are the average velocity of the carrier, qe,h are the charge of the

electron and hole, τrel is the momentum relaxation time, and E is the local electric field, which is less than the applied bias Eb due to the screen effect of space charges. More precisely,

b

/ 3

r

E = E − P ε

(2.4) where εr is the dielectric constant and P is the polarization induced by the separation of electrons and holes. The polarization depends on time according to the expression

/ /

_rec

dP dt = − P τ + J

(2.5) where τrec is the recombination time between electrons and holes (τrec = 10 ps for LT-GaAs) and J= envh + (–e)nve is the current density. The far-field radiation is given by

/ / /

E

THz

∝ ∂ ∂ ∝ ∂ ∂ + ∂ ∂ J t ev n t en v t

, (2.6) where v = ve – vh. The transient electromagnetic field ETHz consists of two terms: the first term describes the carrier density charge effect while the second term describes the effect of charge acceleration due to the electric field bias.

2.2.2 Measurement Principle of THz Radiation with EO Sampling Fig. 2.5 is the schematic of EO sampling setup, which basically consists of an EO crystal, a quarter-wave plate, a Wollaston prism, and a balanced detector.

Electro-optic detection is a second-order nonlinear optical process in which an applied electric field induces a refractive index change in the EO crystal at visible-near IR frequencies that is

ellipticity of a circularly polarized, synchronized, ultra short laser pulse that is co propagating through the same material. This change in ellipticity is measured with the Wollaston prism that separates the two orthogonal polarization components of the probe beam. The balanced detector measures the intensity difference between the two components and gives a signal that is directly proportional to the electric field. By varying the delay between the THz pulse and the probe-laser pulse, one obtains the complete time-dependent electric field.

EO crystal

Quarter-wave plate

Wollaston Prism

Balanced Detectors EO crystal

Quarter-wave plate

Wollaston Prism

Balanced Detectors

Fig. 2.5 EO sampling setup

The calculation of THz radiation is dependent on the refractive index ellipsoid that arises when an electric field is applied to the EO crystal. This index ellipsoid defines the refractive index in the crystal that is experienced by, for example, visible-near IR light propagating through the crystal with a given propagation direction and polarization. For a cubic crystal such as ZnTe, the only nonzero coefficient of the electro-optic tensor is r41. If x, y, and z define the coordinate axes in the crystal [21], with the z axis corresponding to the (001) crystal axis, the refractive-index ellipsoid is given by

1 ETHz along the x, y, and z direction, respectively. We assume the THz wave propagate along the (110) axis (shown in Fig. 2.4), thus ETHz,2=-ETHz,1.

After rotating the (x, y, z) coordinate system around the z axis by 45°, the equation (2.7) becomes:

Fig. 2.6 Angles of the THz wave and probe beam polarization directions

1

by θ :

The components of the electric field are expressed in terms of the angle α ( the angle of the THz beam polarization with respect to the (001) axis shown in Fig. 2.6) :

The refractive indices for visible-near IR light propagating along the x” direction are :

The intensity detected by balance detector can be expressed as :

(2.11)

where φ is the angle of the probe beam polarization with respect to the (001) axis shown in Fig. 2.6.

2.3 Calculated Method of Optical Constant from THz-TDS

As shown in Fig. 2.7, the sample is taken as a multi-reflection structure for THz pulse [22]. The THz pulse before and after the sample insertion are denoted as E_ref (t) and E_sam (t), and their Fourier transforms are Eref* (ω) and Esam* (ω). If Eref* (ω) can be expressed as follows:

ikd

ref

E e

E

^*

=

₀ ⁻ (2.12) then the first, second and mth transmitted THz pulse E₁^*(ω), E₂^*(ω), and Em*(ω) are:

E

₁^*

= E

₀

e

^−in*kd

E

₂^*

= E

₀

e

^−i3n*kd

( r

_sa^*

)

²

t

_as^*

t

_sa^* (2.13)

E

_m^*

= E

₀

e

^{−i(2m−1)n*kd}

( r

_sa^*

)

^2m

t

_as^*

t

_sa^*

where n^* is the complex refractive index of the sample, t_as^*,t_sa^*, and rsa* are the real Fresnel coefficients for amplitude transmission and reflection at sample surfaces. n^*, t_as^*, t_sa^*, and r_sa^* can be expressed as follows:

κ i n

n

^*

= −

(2.14)

1 2

*

*

= +

t

_as

n

(2.15)

1 2

*

* *

= + n

t

_sa

n

(2.16)

1

Fig. 2.7 Schematic of multi-reflection structure of sample

Thus Esam* (ω) is the superposition all the transmitted electric fields.

The ratio of E_sam^* (ω) and E_ref^*(ω) can be given by n^* as: experimentally obtained power transmittance and relative phase.

Since it is difficult to obtain the complex refractive index n^* from

(2.18), the expressions for the real and imaginary parts of the complex refractive index of the sample are denoted as:

(2.19)

The value of the complex refractive index roughly estimated from the THz pulse in the time domain before and after the sample insertion is taken as a starting point for an iterative loop wherein n and κ are calculated in a self-consistent manner. By performing this cyclic procedure for only a few times, the value would lead to a convergence.

( ) ( )

1

Experimental Setup and Sample Preparation

3.1 Experimental Setup

The THz-TDS system is shown in Fig. 3.1(schematic) and Fig. 3.2 (real picture). Femtosecond pulses generated from a mode-locked Ti:

sapphire laser are divided into pump and probe beams by a beam splitter (2). The pump beam is impinging on the THz emitter (6), dipole antenna on a GaAs: As⁺ substrate to generate the transient current. Emission of electromagnetic pulses, THz radiation, with about picosecond duration is produced by the current. The THz radiation is collected and focused on a high reflection mirror (12) by the gold-coated parabolic mirrors (7) before passing through the sample (13) in reflected signal measurement.(In reflected signal measurement, the high reflection mirror is substituted with the sample). The probe beam with time delayed by motor stage (5) and the THz pulse collinearly impinged on a nonlinear crystal (ZnTe) (8).

The transmitted laser pulse with polarization changed by electro-optical effect is separated into two beams with orthogonal polarizations by Wollaston beam splitter (10). The two beams are coupled to a balanced detector (11) connecting to a lock-in amplifier. Signal from lock-in amplifier can be easily analyzed by a computer.

To reduce the water vapor absorption of THz signal, an acrylic box by continuously infusing pure nitrogen is set 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 becomes more stable.

1. λ/2 plate 2. beam splitter 3. chopper

4. translation stage 5. optical delay stage 6. THz emitter

7. parabolic mirrors 8. ZnTe

Fig. 3.1 Schematic of THz-TDS system Acrylic box

9. λ/4 plate

10. Wollaston prism 11. balance detector

12. high reflection mirror or sample position of reflected signal measurement

13. sample position of transmitted signal measurement or nothing

(a)

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

3.2 Sample Preparation

3.2.1 Preparation of Porcine Skin

The samples of porcine skins in the experiments are taken from streaky pork.

The thermal damage of burned porcine skins are formed by contacting normal skin using brass rod attached on welding machine or illuminating normal skin using cw laser.

The brass rod heating setup is shown in Fig. 3.3. Before contacting the porcine skin, the brass rod is preheated for 10 minutes with the

welding machine to make sure the heat is uniformly transmitted in the brass rod. This method is a direct way to form the burned area, and it gives the temperature information of the thermal source.

Another method to form the thermal damage is to let porcine skin be illuminated by the laser beam. The beam size of the laser is not large enough to generate large area burns, which is needed in the measurement, thus the beam need to be broadened before illuminating on the skin. Fig.

3.4 is the schematic of the simple setup to broaden the laser beam and heat samples. The total measured power of laser beam illuminated on the sample is about 3.3 watt, and the illuminated process is not terminated until the back of the porcine been burned. The burned area is about 15mm in diameter.

Laser beam

Parabolic mirror Sample

Laser beam

Parabolic mirror Sample

Fig. 3.4 Schematic of setup to broaden laser beam and heat samples

As a result of water has quite large absorption coefficient in the THz range (about 200cm^-1 at 1THz) [23], all the samples need to be dehydrated to before measurement. All the porcine skins are dehydrated with Acetone solution. The porcine skins are clipped by glass to maintain the flatness of sample surface as immersing in Acetone solution for about 2 days.

3.2.2 Preparation of Hemoglobin

The porcine hemoglobin samples are bought from UNI-WARD Corp. Two kinds of appearances of hemoglobin samples are made, as shown in Table 3.1.

I II III

Type Powder Powder Thin film

Thickness 320±10µm 960±10µm 350 µm±50µm

Table 3.1 Two kinds of hemoglobin samples

Sample Type I and sample Type II are powders of hemoglobin of different thickness: 320µm and 960µm (thickness uncertainty ~ 10µm).

This kind of appearance is applied to get the pure spectra of hemoglobin.

Sample Type III is thin-film hemoglobin of thickness about 350µm (thickness uncertainty ~ 50µm). The thin-film of hemoglobin, which is used to model the under skin blood, is the product made by evaporating hemoglobin solution.

4. Experimental Results

4.1 THz waveform and spectrum

The measured THz waveform as the reference signal is shown in Fig. 4.1. The nitrogen is continuously infusing to THz-TDS system to reduce water vapor absorption of THz radiation. Fig. 4.2 is the spectrum of the measured THz radiation. The signal to noise ratio(S/N ratio) is about 10⁶, and the absorption lines of water vapor at 0.557, 0.752, 0.988, 1.097, 1.113, 1.163, 1.208, 1.229 and 1.411 THz are not existed.

Fig. 4.1 Waveform of THz radiation

0 2 4 6 8 10 12 14 16 18

-2.0 -1.0 0.0 1.0 2.0 3.0 4.0

Time (ps) Amplitude(10-4 V)

Fig. 4.2 Spectrum of THz radiation

4.2 Characterization Difference between Normal and Burned Porcine Skin

The preparation process and thickness of samples are shown in Table 4.1.

Type Normal Porcine Skin Burned Porcine Skin

Preparation process Dehydrated with Acetone

1.Heated with brass rod attached on welding machine (130° C for 30secs)

2.Dehydrated with Acetone

Thickness 1.03±0.02mm 1.13±0.03mm

Table 4.1 Preparation process and thickness of samples

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 1E-18

1E-17 1E-16 1E-15 1E-14 1E-13 1E-12 1E-11

Power(a.u.)

Frequency(THz)

Fig. 4.3 shows the THz waveform of the reference signal and measured signals after passing through the samples (normal and burned porcine skin). From the time of flight of THz waveform, the refractive indices can be roughly calculated. The refractive index of normal porcine skin is about 1.65±0.01, while the burned porcine skin is about 1.74±0.02.

Burned porcine skin has larger refractive index than normal porcine skin.

Fig. 4.4 represents the Fast Fourier transform (FFT) spectrum of the measured waveform in Fig. 4.3. In comparison with the reference spectrum, there are broadband absorptions for both normal porcine skin and burned porcine skin.

The transmittance (spectrum of sample divided by spectrum of reference) of THz radiation through porcine skins is shown in Fig. 4.5.

From 0.2THz to 1.0THz, the transmittance decreases as the frequency increases for normal and burned porcine skins.

The refractive indices and absorption coefficients of porcine skins are shown in Fig. 4.6 and Fig. 4.7. In Fig. 4.6, the refractive index of normal porcine skin is from 1.77±0.01 to 1.66±0.01, which is smaller than the refractive index of burned porcine skin form 1.81±0.02 to 1.70±0.02 from 0.2THz to 1.0THz. In Fig. 4.7, the absorption coefficients of normal porcine skin and burned porcine skin is 1.5cm^-1 to 24.2cm^-1 and 0.1cm^-1 to 30.2cm^-1 from 0.2THz to 1.0THz individually. The uncertainties of refractive indices are calculated from the uncertainty of thickness. The change of absorption coefficients does not as obvious as refractive indices as the porcine skin is burned. The variation of refractive index can be a feature to differentiate burned porcine skin from unburned

porcine.

Fig. 4.3 Waveform of transmitted THz signal

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

1E-8 1E-7 1E-6 1E-5 1E-4 1E-3 0.01 0.1 1

Frequency (THz)

Power(a.u.)

Reference Normal Burned

6 8 10 12 14 16 18 20

-2.0 -1.0 0.0 1.0 2.0 3.0 4.0

Amplitude(10-4 V)

Time(ps)

Reference Normal Burned 2.80ps

2.24ps

Fig. 4.5 Transmittance of THz signal through porcine skins

Fig. 4.6 Refractive index of porcine skin from 0.2 THz to 1.0 THz

0.2 0.4 0.6 0.8 1.0

0.0 0.2 0.4 0.6 0.8 1.0

Transmittance

Frequency(THz)

Normal Burned

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

1.65 1.70 1.75 1.80 1.85

Refractive index

Frequency(THz)

Normal Burned

Fig. 4.7 Absorption coefficient of porcine skin from 0.2 THz to 1.0 THz

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0 5 10 15 20 25 30

Absorption coefficient(cm-1 )

Frequency(THz)

Normal Burned

Rotating axis

Sample

THz radiation propagating direction THz radiation

θ

Rotating axis

Sample

THz radiation propagating direction THz radiation

Rotating axis

Sample

THz radiation propagating direction THz radiation

θ

4.3 Denature of Birefringence of Burned Porcine Skin

The burned sample is made using cw lasers in the lab.

Diameter of the burned area on the sample is about 15mm, with a measured power about 3.3 watts. The illuminated time is about 6 minutes.

Fig. 4.8 is the schematic of measurement mechanism. The sample rotates around the rotating axis shown in Fig. 4.6 to a certain angle θ for each measurement from 0^° to 360^°. THz radiation is measured after passing through the sample.

Fig. 4.8 Schematic of birefringence measurement

The transmitted THz radiation of normal porcine skin (thickness~1mm) is measured. Fig. 4.9 shows the measured waveform of

THz radiation.

Fig. 4.9 Measured waveform of THz radiation of normal porcine skin

In Fig. 4.9 only one THz pulse is observed in the full waveform.

Inasmuch as the birefringence of collagen molecules in the dermis is weak ( ∆n ~ 2.8×10^-3 of bovine lamellae) refer to former works [24], time of flight caused by the birefringence (∆n times sample thickness and divided by light velocity) is only about several one thousandth picoseconds, which is rather small in comparison with the FWHM (several picoseconds) of THz pulse. As a result, the measured waveform is the superposition of e-wave and p-wave.

As shown in Fig. 4.10, the data of time of flight have a periodic distribution for various angles. The angle difference from peak to peak of

5 10 15 20 25 30 35 40

12.0 12.2 12.4 12.6 12.8 13.0 13.2 13.4 -0.4

Relative time of flight

exists in the normal porcine skin, since the included angle between fast and slow axis of a birefringence material is 90^°.

Fig. 4.11 is the measuring results of relative time of flight versus angles of burned porcine skin. The data here are not as regularly as those of normal porcine skin, but there is still a little periodic distribution.

Fig. 4.12 and Fig. 4.13 demonstrate the refractive indices of normal porcine skin and burned porcine skin from 0.2 THz to 0.8 THz. In Fig. 4.12, the larger and smaller refractive indices correspond with the maximum and minimum time of flight shown in Fig. 4.10. Again it verifies the existence of birefringence of normal porcine skin. In Fig. 4.13, the distribution of refractive indices is more disorderly than those in Fig.

4.12. The birefringence of porcine skin denatures after suffering heating process, but there is still a little discrepancy of refractive index between two orthogonal angles.

Fig. 4.10 Relative time of flight of various angles of normal porcine skin

0 60 120 180 240 300 360

0.00 0.02 0.04 0.06 0.08 0.10

Relative time of flight(ps)

Angle(degree)

First measurement Second measurement

Fig. 4.11 Relative time of flight of various angles of burned porcine skin

Fig 4.12 Refractive index of normal porcine skin

0.2 0.3 0.4 0.5 0.6 0.7 0.8

1.68 1.69 1.70 1.71 1.72 1.73

Refractive index

Frequency(THz)

30 120 210 300

0 60 120 180 240 300 360

-0.01 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

First measurement Second measurement

Relative time of flight(ps)

Angle(degree)

Fig 4.13 Refractive index of burned porcine skin

There is a little difference of relative time of flight at 0^° and 360^° (represents the same included angle between sample and polarization of incident light) in Fig. 4.10. This phenomenon may cause form disturbance of the experimental setup. Fig 4.14 shows the maximum disturbances of reference signals by measuring the reference signals repeatedly. The maximum disturbance of time of flight is about 0.027ps.

As a result, several normal porcine skins are stacked to get a thicker sample (thickness~11.53±0.2mm) to check the existence of birefringence.

The measured result is shown in Fig. 4.15. The angle difference from peak to peak of time of flight is still 90^°, and effect of disturbance (0.02ps) is quite small in comparison with the maximum time of flight (0.6404ps).

0.2 0.3 0.4 0.5 0.6 0.7 0.8

1.71 1.72 1.73 1.74 1.75 1.76 1.77

60 150 240 330

Refractive index

Frequency(THz)

Fig. 4.14 Maximum disturbance of reference signal

Fig. 4.15 Relative time of flight of various angles of thicker sample

0 50 100 150 200 250 300 350

-0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Relative time of flight(ps)

Angle(degree)

0.60 0.65 0.70 0.75

2.3x10⁰ 2.3x10⁰ 2.3x10⁰ 2.4x10⁰ 2.4x10⁰ 2.5x10⁰ 2.5x10⁰ 2.6x10⁰ 2.6x10⁰

Amplitude(10-4 V)

Time(ps)

0.027ps

4.4 Transmission Spectroscopic Information of Hemoglobin

Fig. 4.16 is the transmission waveform of Hemoglobin (Hb) samples. THz radiation amplitude is decreased to about half of the reference THz waveform in case of the thin sample (320µm and 350µm).

It is decreased to about 1/3 in case of the thick sample (960µm). Fig. 4.17 shows the FFT spectrum. Transmission spectrum amplitude is also larger in thin sample compared with the thick sample. Broadband absorption from 0.4THz to 2.0 THz has been observed in these deoxy-Hb samples.

No special absorption line is found for powder or thin film hemoglobin, while broadband absorption from 0.4 to 2.0 THz is observed. THz transmittance spectrum of these Hb samples is calculated from spectrum

No special absorption line is found for powder or thin film hemoglobin, while broadband absorption from 0.4 to 2.0 THz is observed. THz transmittance spectrum of these Hb samples is calculated from spectrum

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