558 Generation of Extreme Wavelengths
Sum frequency
Semiconductor
Solid state
Difference
frequency
Dye
Excimer
Color center
0.1 0.5 1.0
Wavelength (
m)
2
Figure 12.1 Femtosecond pulse generation in different wavelength regions.
12.1. GENERATION OF TERAHERTZ (THz)
RADIATION
Two mechanisms can lead to terahertz (THz) radiation through focalization
of an ultrashort light pulse onto a sample: (a) optical rectification and (b) a
radiative current transient. In the original experiment on optical rectification using
femtosecond light pulses Auston et al. [1] demonstrated the generation of THz
waves through Cherenkov radiation. A fs pulse with an energy of about 100 pJ
was focused into a LiTaO
3
crystal (Figure 12.2). The optical pulse propagating
through the crystal produces a polarization pulse via optical rectification. The
latter is a second-order nonlinear optical process that occurs simultaneously with
SHG. Indeed, an instantaneous polarization quadratic in the electric field is:
P
(2)
=
0
χ
(2)
E
2
(t) cos
2
[ω
t + ϕ(t)]
=
1
2
0
χ
(2)
E
2
(t)
{
cos 2[ω
t + ϕ(t)]+1
}
, (12.1)
which includes a SH term centered at 2ω
and a dc field of the same ampli-
tude centered at zero frequency. Optical rectification can also be understood as
difference frequency generation. A frequency domain form of Eq. (12.1) is
P
(2)
(ω
d
= ω
1
− ω
2
) =
0
χ
(2)
E(ω
1
)E(ω
2
) (12.2)
where ω
1
and ω
2
can be any two frequencies from the pulse spectrum. Thus, the
difference frequency ω
d
can cover a spectral range from zero to several THz,
which corresponds to far infrared (FIR) radiation. For a Gaussian pulse with a
Generation of Terahertz (THz) Radiation 559
Pump
LiTaO
3
Probe
c
ᐉ
ν
FIR
ν
g
Figure 12.2 Schematic diagram for the generation of terahertz radiation through optical rectifica-
tion. (Adapted from Auston et al. [1].) A time-delayed optical pulse sampled the FIR field by probing
the induced birefringence.
temporal intensity profile I(t) ∝ exp[−4ln2(t/τ
p
)
2
], the THz radiation can be
described as a single-cycle infrared radiation of frequency
√
ln 2(2τ
p
)
−1
[2].
The optical rectification pulse is basically an electric dipole field that moves
with the group velocity of the optical pulse. At a given position along its path
in the crystal, this dipole generates a field that travels with the group velocity
ν
FIR
associated with its low carrier frequency (of the order of the inverse pulse
duration τ
−1
p
). For LiTaO
3
, ν
FIR
≈ 0.153c, which is rather low because (quasi-
resonant) lattice vibrations contribute substantially to the dispersion behavior
in the FIR spectral range. Because the group velocity of the optical pulse is
ν
g
≈ 0.433c, we have an interesting situation where the source velocity is larger
than the velocity of the emitted wave. This condition leads to the formation of
an electromagnetic shock wave (Cherenkov) radiation propagating on a conical
surface in the crystal. The characteristic angle between the surface normal of the
cone and its symmetry axis (propagation direction of the optical pulse) is
cos θ
c
=
ν
FIR
ν
g
(12.3)
560 Generation of Extreme Wavelengths
12
12
8
4
0
4
8
3
Time delay (ps)
456 1
12
8
4
0
023
Frequency (THz)
45
Figure 12.3 Temporal behavior of the THz field and the corresponding Fourier spectrum obtained
from optical rectification (Adapted from Auston et al. [1]).
which is 69
◦
for LiTaO
3
[1]. The electric field of the far infrared pulse transient
was measured using a second fs optical pulse which probed the FIR-induced
birefringence. By varying the time delay between pump and probe pulse the
FIR field can be sampled. This detection gives a complete recording of the FIR
waveform—hence, the FIR radiation is completely determined in amplitude and
phase. Figure 12.3 displays the temporal behavior of the FIR field as well as
its Fourier spectrum. If the (external) angle of incidence of the optical pulse is
chosen to be α = 51
◦
, a portion of the Cherenkov cone propagates normally to
the crystal surface and thus can propagate into free space (air) [3]. In this manner
the crystal acts like an emitter for THz radiation.
Instead of a moving dipole in a dielectric medium, an ultrashort electrical
pulse on a coplanar transmission line can also serve as source for THz radiation,
as reported by Fattinger and Grischkowsky [4]. The physical situation is sketched
in Figure 12.4. The transmission line consisted of two 5-µm wide, 5-µm thick
aluminum lines separated by 10 µm. The substrate was heavily implanted silicon
on sapphire to ensure a short carrier lifetime of about 600 fs [5]. The latter is
crucial for generating the short electrical transients and for a short response time
of the detection switch.
More recently even simpler techniques turned out to be effective means
to generate THz radiation. These include biased metal–semiconductor inter-
faces [5] and semiconductor surfaces between biased metal electrodes [6], which
is similar to a technique already used by Mourou et al. [7] to produce ps
microwave pulses. Their common operational principle rests on the production
of a fast carrier transient in an external bias field, following the optical excitation.
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