THz time-domain spectroscopy

A THz time-domain spectrometer (THz-TDS) in transmission and reflection geometry was used in collaboration with Dr. Markus Walther and Dr. Andreas Thoman at the University of Freiburg.^§ A Ti:sapphire laser (Femtosource, Femtolasers Inc.; ∼790nm center wavelength) pumped by a 532 nm Nd:YVO₄ solid state laser (Verdi, Coherent Inc.) provided pulses of 12fs duration with a repetition rate of 80MHz and an average output power of 400mW. For the generation and detection of THz radiation, the pulses were guided by a beam splitter and mirrors to photoconductive switches (Figure 2.4) made from semiconducting GaAs with DC biased metal striplines on the semiconductor. By focusing an ultrashort laser pulse in between the meltal striplines with a typical separation of (30−80)μm, charge carriers are created in the antenna. These are accelerated in the applied field, inducing a current I(t) between the conducting lines, which gives rise to emission of electromagnetic radiation within the approximate range of 100 GHz to 5THz.

For the receiver, a low-temperature-grown GaAs substrate with an H-shaped metal stripline of5μm spacing was used. When the laser pulse coincides spatially and temporally with the THz field, a photocurrent is induced that is proportional to the incident electric field. The photocurrent was measured by means of a lock-in amplifier and a chopper wheel operating at∼330Hz. By variation of the time delay between the laser pulse and the THz transient, the entire THz waveform was mapped. The transmission and reflection setups were kept in air-tight boxes purged with dry nitrogen to minimize absorption of the THz beam by water. A short introduction into the various setups will be given here; further details are given in refs. ^114–116114–116.

§We gratefully acknowledge the help of Dr. Andreas Thoman regarding the THz-TDS measurement of various samples.

Figure 2.4: Schematic representation of the THz-TDS transmission setup consisting of fs-L fs-laser, Ch the chopper wheel, M parabolic mirrors, S liquid sample placed between two windows, E emitter antenna, R receiver antenna. D is a delay line in the gate beam.

Transmission setup. The samples were placed in transmission cells with two parallel PTFE windows and an effective pathlength of ∼1.5mm as described by Schrödle.⁷¹ This setup has several advantages, including ease of filling and temperature control, but covers only a limited frequency band ( 2THz for the systems investigated) due to the declin-ing signal-to-noise ratio at higher frequencies. Usdeclin-ing thinner spacers would increase the bandwidth but at the cost of stronger multiple reflections. A cell with ∼0.5mm effective pathlength was designed and is currently being tested. The transmission setup is shown in Figure 2.4.

Temperature was controlled by a Julabo FP 50 thermostat and monitored using calibrated Pt-100 sensors (overall accuracy ±0.05^◦C).

The first step in a THz transmission measurement was the determination of the reference spectrum, E_r(t), of the empty cell. This was followed by subsequent measurement of the sample spectrum, Es(t). The time-domain data so obtained were transformed into the frequency domain by the Fourier integral,

Eˆ_r,s(ν) = 1 2π

+∞

−∞

e^{−i 2πνt}E_r,s(t)dt. (2.18)

The refractive index,n_s, and absorption coefficient,α_s, of the sample were determined from the phase, Δφ, and amplitude, A, of the ratio R(ν)ˆ of the Fourier transforms of sample

and reference pulses,

R(ν) = ˆˆ Es(ν)/Eˆr(ν) = A(ν)·e^{i Δφ(ν)}, (2.19) via the relations:

n_s =n_air+cΔφ/2πνd and (2.20)

α_s =−2 ln(f_r·A)/d, (2.21)

where d is the thickness of the sample, n_air = 1.00027 is the refractive index of air and f_r is a correction coefficient accounting for reflection losses at the sample/PTFE interface.⁷¹ The complex permittivity was calculated via¹¹⁷

ε_s=n²_s −k²_s and (2.22)

ε_s = 2n_sk_s², (2.23)

with k_s =c₀α_s/4πν.

Reflection setup. As mentioned above, transmission measurements were limited in the accessible frequency range. To circumvent these limitations, a reflection setup was used to measure highly absorbing liquids up to ∼3THz. The setup is shown in Figure 2.5.

Technical principles are the same in transmission and reflection measurements, but now only the reflected part of the signal is of interest. The THz pulse generated at the emitter was partly transmitted through a silicon wafer (beam splitter). This remaining pulse was focused on the sample (or reference), which was placed on a silicon window. The THz pulse was reflected at the sample/silicon (reference/silicon) surface back to the silicon wafer and subsequently detected by the receiver. The reflection at the front side of the silicon window was used to check the absolute positions of the silicon window in the reference and sample measurements. In that way, potential positioning errors could be corrected.

At the beginning of this thesis work, measurements were performed at room tempera-ture. Later, the setup was equipped with a cell, that allowed connection to a thermostat.

Temperature was determined with calibrated Pt-100 sensors (overall accuracy ±0.05^◦C).

The field strength of the reflected fraction, E^refl, of an incoming THz pulse, E^inc, is given by Fresnel’s equation,

E_s^refl_,r =E^incnˆ_Si−nˆ_s,r ˆ

n_Si+ ˆn_s,r, (2.24)

where nˆ_Si is the complex index of refraction of the silicon window and nˆ_s,r of the sample or reference, respectively. Air was used as reference material.

Assuming nˆ_Si=n_Si(= 3.42) and nˆ_r =n_r(= 1.00027),^71,114 the relation E_s^refl

E_r^refl = n_Si−ˆn_s

n_Si+ ˆn_s · n_r+n_Si

n_Si−n_r (2.25)

yields the complex index of refraction of the sample, nˆ_s = n_s−ik_s, which is transformed toε(ν)and ε(ν)via Eqs. 2.22 and 2.23.

S Ch M

Si

E R

Figure 2.5: Schematic representation of the THz-TDS reflection setup consisting of Sliquid sample, Ch the chopper wheel, M parabolic mirror, Si silicon wafer, E emitter antenna, R receiver antenna.