170
5 Optical Measurement Techniques
from coherent free excitons (macroscopic polarisation) in monolayer WSe 2 , a quasiresonant excitation around 695 nm with a CW-operated Ti:sapphire laser is feasible,
with the laser light blocked in the detection path by the aforementioned high-aspectratio long-pass filter. In contrast, off-resonant pumping was achieved with a CW
diode laser emitting at 445 nm well above the electronic gap of WSe 2 . Naturally,
Fourier-space signal acquisition requires using a 2D chip read-out, giving access to
dispersion curves, which are intensity (counts per integration time) over wavelength
(long axis) over momentum (short axis), via the exposed CCD area.
In the pioneering work on optically-measurable exciton(–polariton) dispersions
within the light cone of [66] (Fig. 5.17), care had to be taken with the choice of
the measurement parameters. For a maximised optical collection of emitted angles
θ = arcsin
sin (θ0)
n
(θ 0 is the angle in vacuum, n the material’s refractive index),
which correspond to the in-plane momentum by
k =
2π n
λ 0
tan
arcsin
sin (θ 0 )
n
,
(5.13)
a cryostat-compatible numerical aperture (NA = 0.6) had to be chosen for the
employed microscope objective, as the samples were placed behind a cryostat window. μPL signal detection from the sample took place behind a spatially-filtering
aperture in the real-space projection plane of the confocal microscope, which selected
a spot of ≈ 1 µm diameter. The laser-spot diameter amounted to approximately 2 µm.
By Fourier-space projection (Fig. 5.17), the imaging optics of the setup project angles
up to θ 0 = ±37
◦ onto the imaging spectrometer, whereas the monochromator disperses the signal behind the entrance slit horizontally and preserves the angle information in the vertical direction. The light cone in the medium (vacuum) amounts
to
k
≈ 34 (8.7) µm
−1 , the maximum detectable angle of ±37
◦ corresponds to
k
≈ 5.2 µm
−1 in WSe 2 .
It is explained in [66] that in contrast to angle-resolved photo-electron spectroscopy (ARPES), which resolves mainly the electronic band structure but can
provide indirect evidence of the exciton dispersion [140] (not easily understood),
Fourier-space-resolved μPL spectroscopy provides an effective access to the optical
dispersion within the measurable light cone (Fig. 5.17), i.e. the polaritonic exciton’s
dispersion.
15 In addition, electron energy-loss spectroscopy could also measure exci15 Note that as far as exciton emission is concerned which arises from the coupling of the induced
macroscopic polarisation in matter with the light field, the oscillator strength results in hybridisation
and radiation out of the upper polariton branch within the light cone, or from the lower branch
outside the light cone through phonon scattering processes [69]. In a crystal, polarisation waves
propagate, whereas outside the crystal beyond the matter–vacuum interface photons represent the
propagating electromagnetic wave carrying the information of the hybrid states according to energy
and momentum conservation. Incoherent excitons (microscopic polarisation, with effective masses
on the order of electron masses) and electron–hole plasma (due to statistics in the emission processes,
no centre-of-mass information is contained in the emission’s momentum distribution) do not feature
a measurable angle-dependent energy as discussed in [66].
5 Optical Measurement Techniques
from coherent free excitons (macroscopic polarisation) in monolayer WSe 2 , a quasiresonant excitation around 695 nm with a CW-operated Ti:sapphire laser is feasible,
with the laser light blocked in the detection path by the aforementioned high-aspectratio long-pass filter. In contrast, off-resonant pumping was achieved with a CW
diode laser emitting at 445 nm well above the electronic gap of WSe 2 . Naturally,
Fourier-space signal acquisition requires using a 2D chip read-out, giving access to
dispersion curves, which are intensity (counts per integration time) over wavelength
(long axis) over momentum (short axis), via the exposed CCD area.
In the pioneering work on optically-measurable exciton(–polariton) dispersions
within the light cone of [66] (Fig. 5.17), care had to be taken with the choice of
the measurement parameters. For a maximised optical collection of emitted angles
θ = arcsin
sin (θ0)
n
(θ 0 is the angle in vacuum, n the material’s refractive index),
which correspond to the in-plane momentum by
k =
2π n
λ 0
tan
arcsin
sin (θ 0 )
n
,
(5.13)
a cryostat-compatible numerical aperture (NA = 0.6) had to be chosen for the
employed microscope objective, as the samples were placed behind a cryostat window. μPL signal detection from the sample took place behind a spatially-filtering
aperture in the real-space projection plane of the confocal microscope, which selected
a spot of ≈ 1 µm diameter. The laser-spot diameter amounted to approximately 2 µm.
By Fourier-space projection (Fig. 5.17), the imaging optics of the setup project angles
up to θ 0 = ±37
◦ onto the imaging spectrometer, whereas the monochromator disperses the signal behind the entrance slit horizontally and preserves the angle information in the vertical direction. The light cone in the medium (vacuum) amounts
to
k
≈ 34 (8.7) µm
−1 , the maximum detectable angle of ±37
◦ corresponds to
k
≈ 5.2 µm
−1 in WSe 2 .
It is explained in [66] that in contrast to angle-resolved photo-electron spectroscopy (ARPES), which resolves mainly the electronic band structure but can
provide indirect evidence of the exciton dispersion [140] (not easily understood),
Fourier-space-resolved μPL spectroscopy provides an effective access to the optical
dispersion within the measurable light cone (Fig. 5.17), i.e. the polaritonic exciton’s
dispersion.
15 In addition, electron energy-loss spectroscopy could also measure exci15 Note that as far as exciton emission is concerned which arises from the coupling of the induced
macroscopic polarisation in matter with the light field, the oscillator strength results in hybridisation
and radiation out of the upper polariton branch within the light cone, or from the lower branch
outside the light cone through phonon scattering processes [69]. In a crystal, polarisation waves
propagate, whereas outside the crystal beyond the matter–vacuum interface photons represent the
propagating electromagnetic wave carrying the information of the hybrid states according to energy
and momentum conservation. Incoherent excitons (microscopic polarisation, with effective masses
on the order of electron masses) and electron–hole plasma (due to statistics in the emission processes,
no centre-of-mass information is contained in the emission’s momentum distribution) do not feature
a measurable angle-dependent energy as discussed in [66].