Top Curr Chem (Z) (2018) 376:6
1 3
optical crystal. The typical picosecond (ps) to sub-ps durations of THz pulses allow
detection of their electric field profiles in the time domain, gated by fs laser pulses.
2.1.1 Intense THz Pulse Generation Methods
OR is a second-order (χ
(2)
) nonlinear process. Typically, a broadband fs laser pulse
at 800 nm from a Ti:sapphire amplifier is used to pump a nonlinear optical crystal in collinear geometry. Field components at nearby frequencies, E(ω 1 ) and E(ω 2 ),
within the laser pulse bandwidth undergo difference-frequency mixing and generate electromagnetic radiation centered at |ω 1 − ω 2 |, which is in the THz frequency
range. In the perturbative regime, the THz-frequency fields are radiated by a χ
(2)
polarization P
(2)
[41] given by
Similar to other nonlinear processes [41], the χ
(2)
nonlinear coefficient of the
crystal and the phase matching of the optical pump and the generated THz pulses in
the crystal are crucial for efficient generation of the THz fields. The phase-matching
condition for THz generation by OR with collinear optical and THz wavevectors is
given by a scalar equation,
where k is the wavevector magnitude, ω the angular frequency, and ω THz = |ω 1 − ω 2 |
is satisfied. From the perspective of photons, ω THz = |ω 1 − ω 2 | dictates photon
energy conservation and Eq. (2) dictates photon quasi-momentum conservation. The
index matching condition can be obtained from Eq. (2) and is given by
where n THz = c · k(ω THz )/ω THz is the THz refractive index and n
g
op = c · dk(ω 2 )/dω
the optical group index in the nonlinear optical crystal (c is the speed of light in
vacuum).
Inorganic nonlinear crystals including ZnTe, GaP, and GaAs have optimal index
matching between 800 nm and THz pulses. Phase matching can be satisfied in a
simple collinear geometry, and the experimental implementation is hence straightforward. But these crystals have relatively small χ
(2)
nonlinear coefficients and largearea crystals are typically required for strong THz pulse generation [16]. LiNbO 3
has a large χ
(2)
nonlinear coefficient, but the large phase mismatch between 800 nm
and THz pulses in LiNbO 3 leads to inefficient THz generation in collinear geometry. To circumvent the phase-matching problem and utilize the large χ
(2)
coefficient
in LiNbO 3 , a non-collinear phase-matching scheme involving tilting of the 800-nm
pulse intensity front to match the THz wavefront has been developed [20, 21, 42,
43], which enabled the rapid proliferation of tabletop nonlinear THz spectroscopy
experiments [25].
The geometry for the tilted-pulse-front method is shown schematically in
Fig. 1a. The broadband fs pump pulses from the Ti:sapphire laser with a flat intensity front are incident onto a grating. The first-order diffraction, which has a tilted
intensity front, is collected and imaged into a specially cut LiNbO 3 crystal. The
(1)
P
(2) ( THz ) =
(2) ( THz ; 1 , − 2 )E( 1 )E
∗ ( 2 ).
(2)
k( THz ) = k( 1 ) − k( 2 ) ≈ k( 2 ) + dk( 2 )∕d ⋅ THz − k( 2 ),
(3)
n THz = n
g
op
,
278
Reprinted from the journal
1 3
optical crystal. The typical picosecond (ps) to sub-ps durations of THz pulses allow
detection of their electric field profiles in the time domain, gated by fs laser pulses.
2.1.1 Intense THz Pulse Generation Methods
OR is a second-order (χ
(2)
) nonlinear process. Typically, a broadband fs laser pulse
at 800 nm from a Ti:sapphire amplifier is used to pump a nonlinear optical crystal in collinear geometry. Field components at nearby frequencies, E(ω 1 ) and E(ω 2 ),
within the laser pulse bandwidth undergo difference-frequency mixing and generate electromagnetic radiation centered at |ω 1 − ω 2 |, which is in the THz frequency
range. In the perturbative regime, the THz-frequency fields are radiated by a χ
(2)
polarization P
(2)
[41] given by
Similar to other nonlinear processes [41], the χ
(2)
nonlinear coefficient of the
crystal and the phase matching of the optical pump and the generated THz pulses in
the crystal are crucial for efficient generation of the THz fields. The phase-matching
condition for THz generation by OR with collinear optical and THz wavevectors is
given by a scalar equation,
where k is the wavevector magnitude, ω the angular frequency, and ω THz = |ω 1 − ω 2 |
is satisfied. From the perspective of photons, ω THz = |ω 1 − ω 2 | dictates photon
energy conservation and Eq. (2) dictates photon quasi-momentum conservation. The
index matching condition can be obtained from Eq. (2) and is given by
where n THz = c · k(ω THz )/ω THz is the THz refractive index and n
g
op = c · dk(ω 2 )/dω
the optical group index in the nonlinear optical crystal (c is the speed of light in
vacuum).
Inorganic nonlinear crystals including ZnTe, GaP, and GaAs have optimal index
matching between 800 nm and THz pulses. Phase matching can be satisfied in a
simple collinear geometry, and the experimental implementation is hence straightforward. But these crystals have relatively small χ
(2)
nonlinear coefficients and largearea crystals are typically required for strong THz pulse generation [16]. LiNbO 3
has a large χ
(2)
nonlinear coefficient, but the large phase mismatch between 800 nm
and THz pulses in LiNbO 3 leads to inefficient THz generation in collinear geometry. To circumvent the phase-matching problem and utilize the large χ
(2)
coefficient
in LiNbO 3 , a non-collinear phase-matching scheme involving tilting of the 800-nm
pulse intensity front to match the THz wavefront has been developed [20, 21, 42,
43], which enabled the rapid proliferation of tabletop nonlinear THz spectroscopy
experiments [25].
The geometry for the tilted-pulse-front method is shown schematically in
Fig. 1a. The broadband fs pump pulses from the Ti:sapphire laser with a flat intensity front are incident onto a grating. The first-order diffraction, which has a tilted
intensity front, is collected and imaged into a specially cut LiNbO 3 crystal. The
(1)
P
(2) ( THz ) =
(2) ( THz ; 1 , − 2 )E( 1 )E
∗ ( 2 ).
(2)
k( THz ) = k( 1 ) − k( 2 ) ≈ k( 2 ) + dk( 2 )∕d ⋅ THz − k( 2 ),
(3)
n THz = n
g
op
,
278
Reprinted from the journal