Top Curr Chem (Z) (2018) 376:6
1 3
such as absorption [51], frequency shifts [52], optical harmonic generation [53],
birefringence [54], and polarization rotation [55], are detected. Examples of THz
pump-optical birefringence probe spectroscopy include the THz Kerr effect in liquid
molecules [37, 54, 56] and ferroelectric crystals [57, 58] and THz-induced dipolar
alignment of polar gas molecules [59, 60]. Here, THz electric fields orient or align
the molecules and the orientational diffusion in the liquid or alignment revivals in
the gas phase are monitored by optical birefringence through the anisotropic polarizability. Raman-active vibrational modes have also been observed using the THz
pump-optical birefringence probe method, where anharmonic couplings between
THz-driven THz-active modes and optically detected Raman-active modes are
believed to play a role [37, 56, 58].
2.2 Nonlinear 2D THz Spectroscopy Methods
2.2.1 Pulse Sequences in 2D THz and 2D THz‑Raman Spectroscopies
In 2D IR and visible spectroscopies, three pulses with controlled time delay between
two neighboring pulses are usually used to conduct the experiments. In 2D THz
spectroscopy, there is only one example to date using three time-delayed THz pulses
[33, 34]. This is limited in part by experimental difficulties in the generation of multiple THz pulses and the recombination of the pulses at the sample. Most importantly, a very long data acquisition time is usually required, as all the inter-pulse
delays and the time-domain signal detection time need to be scanned by mechanical
delay stages. In this chapter, we mainly consider three types of pulse sequences and
relevant light-matter interactions represented by the Feynman diagrams (details on
the Feynman diagrams can be found in Refs. [1, 61, 62], etc.) shown in Fig. 4, which
are typically used in different types of 2D THz spectroscopies. In the Feynman diagrams, the notations of the states may indicate the number of quanta in a particular
degree of freedom in some cases, and in others they denote various levels of different modes. In the hybrid THz-Raman spectroscopies of liquid molecules, the transitions induced through THz or Raman excitations can in general include overtone
and combination band transitions that are usually allowed in liquids where the intraand intermolecular vibrations largely have strong anharmonicity [63].
In the THz-THz-THz sequence shown in Fig. 4a, all field-matter interactions
involve THz fields. An example of the χ
(3)
interaction pathways following the pulse
sequence is illustrated here with examples of typical nonrephasing (NR) and rephasing (R) pathways shown by the Feynman diagrams. As shown in Fig. 4a, THz field
E A generates a first-order coherence that evolves during time period τ. THz field E B
interacts with the sample twice, generating in succession a second-order population
and a third-order coherence. The third-order coherence evolves during time period t
and radiates the signal, which is detected by EOS as a function of t. If we index the
possible time delays by which field interaction they follow, then inter-pulse delay τ is
the coherence time t 1 and population time t 2 = 0 (field interactions 2 and 3 are timecoincident), and the detection time t corresponds to t 3 . E A can also interact twice to
generate in succession a first-order coherence and a second-order population, the
282
Reprinted from the journal
1 3
such as absorption [51], frequency shifts [52], optical harmonic generation [53],
birefringence [54], and polarization rotation [55], are detected. Examples of THz
pump-optical birefringence probe spectroscopy include the THz Kerr effect in liquid
molecules [37, 54, 56] and ferroelectric crystals [57, 58] and THz-induced dipolar
alignment of polar gas molecules [59, 60]. Here, THz electric fields orient or align
the molecules and the orientational diffusion in the liquid or alignment revivals in
the gas phase are monitored by optical birefringence through the anisotropic polarizability. Raman-active vibrational modes have also been observed using the THz
pump-optical birefringence probe method, where anharmonic couplings between
THz-driven THz-active modes and optically detected Raman-active modes are
believed to play a role [37, 56, 58].
2.2 Nonlinear 2D THz Spectroscopy Methods
2.2.1 Pulse Sequences in 2D THz and 2D THz‑Raman Spectroscopies
In 2D IR and visible spectroscopies, three pulses with controlled time delay between
two neighboring pulses are usually used to conduct the experiments. In 2D THz
spectroscopy, there is only one example to date using three time-delayed THz pulses
[33, 34]. This is limited in part by experimental difficulties in the generation of multiple THz pulses and the recombination of the pulses at the sample. Most importantly, a very long data acquisition time is usually required, as all the inter-pulse
delays and the time-domain signal detection time need to be scanned by mechanical
delay stages. In this chapter, we mainly consider three types of pulse sequences and
relevant light-matter interactions represented by the Feynman diagrams (details on
the Feynman diagrams can be found in Refs. [1, 61, 62], etc.) shown in Fig. 4, which
are typically used in different types of 2D THz spectroscopies. In the Feynman diagrams, the notations of the states may indicate the number of quanta in a particular
degree of freedom in some cases, and in others they denote various levels of different modes. In the hybrid THz-Raman spectroscopies of liquid molecules, the transitions induced through THz or Raman excitations can in general include overtone
and combination band transitions that are usually allowed in liquids where the intraand intermolecular vibrations largely have strong anharmonicity [63].
In the THz-THz-THz sequence shown in Fig. 4a, all field-matter interactions
involve THz fields. An example of the χ
(3)
interaction pathways following the pulse
sequence is illustrated here with examples of typical nonrephasing (NR) and rephasing (R) pathways shown by the Feynman diagrams. As shown in Fig. 4a, THz field
E A generates a first-order coherence that evolves during time period τ. THz field E B
interacts with the sample twice, generating in succession a second-order population
and a third-order coherence. The third-order coherence evolves during time period t
and radiates the signal, which is detected by EOS as a function of t. If we index the
possible time delays by which field interaction they follow, then inter-pulse delay τ is
the coherence time t 1 and population time t 2 = 0 (field interactions 2 and 3 are timecoincident), and the detection time t corresponds to t 3 . E A can also interact twice to
generate in succession a first-order coherence and a second-order population, the
282
Reprinted from the journal