5.4 Nonlinearities
165
of the second-order susceptibility of a medium χ
(2) . In bulk, the microscopic dipole
fields contributing to the nonlinear polarisation signal cancel each other out, but the
symmetry-break at the surface of a highly symmetric crystal leads to considerable
nonlinear frequency conversion. Thus, as a surface- and interface-sensitive tool, it
can become useful for the study of 2D materials. Particularly, when the incident
polarisation is tuned, different crystalline domains of different orientation in polycrystalline monolayers and their grain boundaries can become visible, for example
demonstrated by imaging microscopy in [128].
On the other hand, frequency conversion can be used to generate new wavelengths
from incident light on a nonlinear crystal, such as SHG (frequency doubling), DFG
and sum-frequency generation (SFG). SHG is particularly desired as a means to
expand the available frequencies of a pulsed laser towards higher energies for offresonant excitation schemes or excitation of high-gap materials. For example, in
[129], a mode-locked ultrafast VECSEL’s output was frequency doubled externally
to achieve a high-repetition-rate pump for the excitation of a quantum-dot singlephoton source (see Fig. 4.2), thereby obtaining a world-record single-photon flux
rate (see Fig. 4.7).
Similarly, DFG can be attractive to access spectral regions, for which light sources
are rare, for instance in the previously labeled THz gap, and to produce emitters
useful for applications in spectroscopy or industry. One example employs intracavity
DFG in an open cavity of a VECSEL to provide a strong coherent THz output in
the sub-mW to mW range [111]—a well-studied concept of multi-mode TEM 00
THz generation [112, 130], which has been recently made power-scalable using a
two-chip design [113]. This approach was previously explored and demonstrated
with the help of intracavity SHG and SFG for tunable frequency conversion [131]
using angle-dependencies of the chip resonances [132]. Typically, periodically-poled
lithium niobate crystals are employed for efficient DFG designed for 1 THz output.
In fact, the use of such crystals with aperiodical poling enables even tunable THz
generation as demonstrated recently in the range of 0.79-1.11 THz [114] (Fig. 5.15).
SHG imaging, which has been described above as a means to obtain information about symmetries in crystalline systems, has not only become useful for the
characterisation of monolayers on substrates, but also of the bilayer configurations
and their twist angles [8, 133]. A comparison of PL and SHG images for instance
enables one to identify monolayer, bilayer or few-layer TMDCs and their stacking
symmetry, as the example of a homobilayer-system study in [8] shows (see Fig. 5.6).
For PL images, the laser radiation is filtered for instance by a holographic notch filter,
whereas for SHG, the fundamental light is blocked by a short-pass wavelength filter.
Both spatially-resolved signals can be well recorded using a scientific intensified
CCD. For the CW excitation of PL, a frequency-stabilised 532-nm Nd:YAG-based
laser of a μPL-Raman setup with emission above material band gap can be employed.
For spectrally-integrated SHG measurements, a pulsed Ti:sapphire laser (with 100 fs
pulse duration) of a time-resolved PL setup at wavelengths below the band gap serves
well. Both lasers can be conveniently used for common 2D semiconductors due to
the energetic position of their excitons.
165
of the second-order susceptibility of a medium χ
(2) . In bulk, the microscopic dipole
fields contributing to the nonlinear polarisation signal cancel each other out, but the
symmetry-break at the surface of a highly symmetric crystal leads to considerable
nonlinear frequency conversion. Thus, as a surface- and interface-sensitive tool, it
can become useful for the study of 2D materials. Particularly, when the incident
polarisation is tuned, different crystalline domains of different orientation in polycrystalline monolayers and their grain boundaries can become visible, for example
demonstrated by imaging microscopy in [128].
On the other hand, frequency conversion can be used to generate new wavelengths
from incident light on a nonlinear crystal, such as SHG (frequency doubling), DFG
and sum-frequency generation (SFG). SHG is particularly desired as a means to
expand the available frequencies of a pulsed laser towards higher energies for offresonant excitation schemes or excitation of high-gap materials. For example, in
[129], a mode-locked ultrafast VECSEL’s output was frequency doubled externally
to achieve a high-repetition-rate pump for the excitation of a quantum-dot singlephoton source (see Fig. 4.2), thereby obtaining a world-record single-photon flux
rate (see Fig. 4.7).
Similarly, DFG can be attractive to access spectral regions, for which light sources
are rare, for instance in the previously labeled THz gap, and to produce emitters
useful for applications in spectroscopy or industry. One example employs intracavity
DFG in an open cavity of a VECSEL to provide a strong coherent THz output in
the sub-mW to mW range [111]—a well-studied concept of multi-mode TEM 00
THz generation [112, 130], which has been recently made power-scalable using a
two-chip design [113]. This approach was previously explored and demonstrated
with the help of intracavity SHG and SFG for tunable frequency conversion [131]
using angle-dependencies of the chip resonances [132]. Typically, periodically-poled
lithium niobate crystals are employed for efficient DFG designed for 1 THz output.
In fact, the use of such crystals with aperiodical poling enables even tunable THz
generation as demonstrated recently in the range of 0.79-1.11 THz [114] (Fig. 5.15).
SHG imaging, which has been described above as a means to obtain information about symmetries in crystalline systems, has not only become useful for the
characterisation of monolayers on substrates, but also of the bilayer configurations
and their twist angles [8, 133]. A comparison of PL and SHG images for instance
enables one to identify monolayer, bilayer or few-layer TMDCs and their stacking
symmetry, as the example of a homobilayer-system study in [8] shows (see Fig. 5.6).
For PL images, the laser radiation is filtered for instance by a holographic notch filter,
whereas for SHG, the fundamental light is blocked by a short-pass wavelength filter.
Both spatially-resolved signals can be well recorded using a scientific intensified
CCD. For the CW excitation of PL, a frequency-stabilised 532-nm Nd:YAG-based
laser of a μPL-Raman setup with emission above material band gap can be employed.
For spectrally-integrated SHG measurements, a pulsed Ti:sapphire laser (with 100 fs
pulse duration) of a time-resolved PL setup at wavelengths below the band gap serves
well. Both lasers can be conveniently used for common 2D semiconductors due to
the energetic position of their excitons.