5.2 High-Field Terahertz Time-Domain Spectrometer
93
Fig. 5.2 a Velocity-mismatched generation of THz radiation in a nonlinear material, exhibiting a
Cherenkov-like emission geometry. The THz phase velocity is lower than the IR group velocity,
hence the phase front of the generated THz radiation is at an angle θ C to that of the pump pulse.
b Tilted pump pulse pumping geometry in LiNbO 3 . The pump pulse front is tilted to match the
angle of the THz phase front, resulting in constructive interference of the generated THz radiation
throughout the LiNbO 3 crystal
which this velocity matching condition is satisfied, the generated THz radiation is
emitted collinearly with the direction of propagation of the pump pulse, so constructive interference of the generated THz radiation occurs as the pump pulse propagates
through the material. Some materials such as LiNbO 3 have a very high nonlinear
coefficient, but velocity matching is not satisfied because v p,THz < v g,opt . In this case
the THz radiation is emitted in a Cherenkov-like cone [48, 49], as shown in Fig. 5.2a,
at an angle θ C to the direction of propagation of the pump pulse, defined by the ratio
of the optical group index and the THz phase index as
cos θ C =
n g,opt
n p,THz
=
v p,THz
v g,opt
.
(5.2)
This conical emission profile makes the THz radiation difficult to collect and collimate, and therefore the usefulness of the Cherenkov geometry as a source of THz
radiation is limited.
However, by using the technique of tilted pulse-front pumping (TPFP), intense
THz pulses can be generated in materials that have good nonlinear properties but
cannot meet the collinear velocity matching condition [37]. TPFP makes use of a tilt
in the the pulse front of the pump laser beam with respect to the phase front, causing
the geometry seen in Fig. 5.2b. The velocity matching condition now becomes
v g,opt cos γ c = v p,T Hz ,
(5.3)
where γ c is the tilt angle of the pump pulse front; now the most efficient THz generation is achieved when γ c = θ C , the angle at which the THz radiation would be
generated at in the Cherenkov geometry. In this way, the generated THz radiation
93
Fig. 5.2 a Velocity-mismatched generation of THz radiation in a nonlinear material, exhibiting a
Cherenkov-like emission geometry. The THz phase velocity is lower than the IR group velocity,
hence the phase front of the generated THz radiation is at an angle θ C to that of the pump pulse.
b Tilted pump pulse pumping geometry in LiNbO 3 . The pump pulse front is tilted to match the
angle of the THz phase front, resulting in constructive interference of the generated THz radiation
throughout the LiNbO 3 crystal
which this velocity matching condition is satisfied, the generated THz radiation is
emitted collinearly with the direction of propagation of the pump pulse, so constructive interference of the generated THz radiation occurs as the pump pulse propagates
through the material. Some materials such as LiNbO 3 have a very high nonlinear
coefficient, but velocity matching is not satisfied because v p,THz < v g,opt . In this case
the THz radiation is emitted in a Cherenkov-like cone [48, 49], as shown in Fig. 5.2a,
at an angle θ C to the direction of propagation of the pump pulse, defined by the ratio
of the optical group index and the THz phase index as
cos θ C =
n g,opt
n p,THz
=
v p,THz
v g,opt
.
(5.2)
This conical emission profile makes the THz radiation difficult to collect and collimate, and therefore the usefulness of the Cherenkov geometry as a source of THz
radiation is limited.
However, by using the technique of tilted pulse-front pumping (TPFP), intense
THz pulses can be generated in materials that have good nonlinear properties but
cannot meet the collinear velocity matching condition [37]. TPFP makes use of a tilt
in the the pulse front of the pump laser beam with respect to the phase front, causing
the geometry seen in Fig. 5.2b. The velocity matching condition now becomes
v g,opt cos γ c = v p,T Hz ,
(5.3)
where γ c is the tilt angle of the pump pulse front; now the most efficient THz generation is achieved when γ c = θ C , the angle at which the THz radiation would be
generated at in the Cherenkov geometry. In this way, the generated THz radiation