96
5 High-Field Terahertz Time-Domain Spectroscopy …
β 1 and β 2 were calculated as a function of θ d from Eqs. 5.9 and 5.12. In these calculations, various grating groove densities were used, m = 1, λ 0 = 800 nm, n g,opt = 2.23
and n = 2.16 [54], and the pulse front tilt and grating image angles were set to
match the cut angle of the LiNbO 3 crystal γ c = θ g = 63
◦ . Using an 1800 lines mm
−1
grating the optimal value of β 1 , β 2 = 0.6. The cylindrical lenses chosen had focal
lengths of f 1 = 130 mm and f 2 = 75.6 mm which give a demagnification factor
β = f 2 / f 1 = 0.582, close to the optimum value. This then allows us to calculate
the optimal angles of incidence and diffraction from Eqs. 5.10 and 5.11, which give
values of θ i = 38.0
◦ and θ d = 55.6
◦ for this system.
5.2.2 Experimental Setup
The experimental setup of the high-field THz-TDS system used in this chapter is
shown schematically in Fig. 5.2a. A quarter of the output of a regeneratively amplified
Ti:Sapphire laser system (Spectra-Physics Spitfire Ace-PA-40) was used to produce
pulses with a central wavelength of 800 nm (40 nm bandwidth at FWHM) with pulse
energies of 3 mJ and duration of 40 fs at a repetition rate of 1 kHz. The pulses from
the laser were then split by a 70/30 beamsplitter, with 70% of the laser output being
used for the high-field THz generation. This high-field THz pump portion of the
beam passes through a variable delay stage, in order to change the relative arrival
times of the THz and gate beams at the detection crystal. The pump beam is then
reduced in size from ∼12 to ∼4 mm in diameter by an f = 200 mm plano-convex
lens and f = −50 mm convex mirror beam telescope, in order to match the size
of the LiNbO 3 THz generation crystal. This smaller beam is then incident upon a
diffraction grating and 4- f cylindrical lens setup, in order to generate high-field THz
radiation via the tilted-pulse-front-pumping technique in LiNbO 3 (discussed in detail
in Sect. 5.2.1).
Using the 4- f cylindrical lens scheme to create the grating image inside the
LiNbO 3 causes the generated THz radiation to be produced in a roughly collimated
beam [38], hence the generated THz radiation was collected after a short distance of
∼25 mm by a 12.7 mm diameter, f OAP1 = 15 mm off-axis parabolic mirror (OAP1 in
Fig. 5.4). This first OAP focuses the THz radiation, and constitutes the first mirror in
a telescope system; the expanding beam of THz radiation after the focus is collected
by a second OAP mirror (OAP2 in Fig. 5.4) with 50.8 mm diameter and f OAP2 =
152.4 mm. This second OAP was positioned a distance f OAP1 + f OAP2 = 167.4 mm
away from OAP1 in order to expand the THz beam by a factor f OAP2 / f OAP1 = 10.16,
to better fill the focussing optics and create a smaller spot size at the sample focus.
This step is important to achieve the highest possible THz electric fields, since the
electric field strength is inversely proportional to the THz spot size, which will be
discussed further in Sect. 5.2.3. The expanded beam is focused onto the sample space
then collected and collimated by a pair of 50.8 mm diameter, f = 76.2 mm OAPs
(OAP3 and OAP4 in Fig. 5.4). The 76.2 mm focal length of these optics is not the
shortest possible, which would achieve the smallest possible THz spot size, but is
5 High-Field Terahertz Time-Domain Spectroscopy …
β 1 and β 2 were calculated as a function of θ d from Eqs. 5.9 and 5.12. In these calculations, various grating groove densities were used, m = 1, λ 0 = 800 nm, n g,opt = 2.23
and n = 2.16 [54], and the pulse front tilt and grating image angles were set to
match the cut angle of the LiNbO 3 crystal γ c = θ g = 63
◦ . Using an 1800 lines mm
−1
grating the optimal value of β 1 , β 2 = 0.6. The cylindrical lenses chosen had focal
lengths of f 1 = 130 mm and f 2 = 75.6 mm which give a demagnification factor
β = f 2 / f 1 = 0.582, close to the optimum value. This then allows us to calculate
the optimal angles of incidence and diffraction from Eqs. 5.10 and 5.11, which give
values of θ i = 38.0
◦ and θ d = 55.6
◦ for this system.
5.2.2 Experimental Setup
The experimental setup of the high-field THz-TDS system used in this chapter is
shown schematically in Fig. 5.2a. A quarter of the output of a regeneratively amplified
Ti:Sapphire laser system (Spectra-Physics Spitfire Ace-PA-40) was used to produce
pulses with a central wavelength of 800 nm (40 nm bandwidth at FWHM) with pulse
energies of 3 mJ and duration of 40 fs at a repetition rate of 1 kHz. The pulses from
the laser were then split by a 70/30 beamsplitter, with 70% of the laser output being
used for the high-field THz generation. This high-field THz pump portion of the
beam passes through a variable delay stage, in order to change the relative arrival
times of the THz and gate beams at the detection crystal. The pump beam is then
reduced in size from ∼12 to ∼4 mm in diameter by an f = 200 mm plano-convex
lens and f = −50 mm convex mirror beam telescope, in order to match the size
of the LiNbO 3 THz generation crystal. This smaller beam is then incident upon a
diffraction grating and 4- f cylindrical lens setup, in order to generate high-field THz
radiation via the tilted-pulse-front-pumping technique in LiNbO 3 (discussed in detail
in Sect. 5.2.1).
Using the 4- f cylindrical lens scheme to create the grating image inside the
LiNbO 3 causes the generated THz radiation to be produced in a roughly collimated
beam [38], hence the generated THz radiation was collected after a short distance of
∼25 mm by a 12.7 mm diameter, f OAP1 = 15 mm off-axis parabolic mirror (OAP1 in
Fig. 5.4). This first OAP focuses the THz radiation, and constitutes the first mirror in
a telescope system; the expanding beam of THz radiation after the focus is collected
by a second OAP mirror (OAP2 in Fig. 5.4) with 50.8 mm diameter and f OAP2 =
152.4 mm. This second OAP was positioned a distance f OAP1 + f OAP2 = 167.4 mm
away from OAP1 in order to expand the THz beam by a factor f OAP2 / f OAP1 = 10.16,
to better fill the focussing optics and create a smaller spot size at the sample focus.
This step is important to achieve the highest possible THz electric fields, since the
electric field strength is inversely proportional to the THz spot size, which will be
discussed further in Sect. 5.2.3. The expanded beam is focused onto the sample space
then collected and collimated by a pair of 50.8 mm diameter, f = 76.2 mm OAPs
(OAP3 and OAP4 in Fig. 5.4). The 76.2 mm focal length of these optics is not the
shortest possible, which would achieve the smallest possible THz spot size, but is