5.5 Fourier-Space Spectroscopy
171
ton dispersions using a fundamentally different approach, but no measurement on a
monolayer has been obtained yet, according to [66].
An exciton–polariton branch or the literature-predicted big interaction-mediated
exciton splitting at finite k within the light cone (cf. [141–145]) can only be detected
when the spectral lines are very narrow (i.e. with a small dephasing rate) and the optical resolution in E and k is sufficiently high. In fact, optical measurements allowed
to evidence a pronounced dispersion feature in Fourier-space-resolved spectra on
the order of meV with sub-meV precision in the determination of angle-dependent
energy changes for WSe 2 and MoSe 2 (the latter with less curvature). Furthermore,
an underlying exchange-energy-affected dispersion feature of TMDC excitons with
predicted meV changes within the light cone could also facilitate observation of
the polariton-branch curvature (see considerations in [66]). By merely evaluating
the effective curvature of the measurable average dispersion feature, which due to
contributions of incoherent excitons and e–h plasma can be (partially) washed out,
through a parabola approximation, mean effective masses of as little as 10
−4 can be
extracted in both PL and reflection contrast [66]. Both, pump-power dependencies
[66] (the investigated excitation densities were set by a neutral density filter wheel in
discrete steps in the linear regime) and detuning dependencies [46] showed changes
in the measurable dispersion. Moreover, the latter (i.e. excitation detuning) modified
the overall (as well as the momentum-dependent) helicity degree of the excitonic
emissions obtained in experiments.
5.6 Additional Methods
At the end of this chapter, a few more optical methods are briefly described which
can be used for the characterisation of photonic devices, semiconductor structures
or even bare materials.
5.6.1 Beam Characterisation
For the characterisation of laser output beam profiles, typically the beam quality factor
M
2 is obtained. This is the parameter, which reflects the degree of variation of a beam
compared to an ideal Gaussian beam of the same wavelength. A definition of this
beam quality factors and how to derive it on the basis of measuring second moment
widths D4σ , which are the beam diameters along beam-propagation direction, is for
instance given in [146, 147]. The closer a beam (profile) is to an ideal Gaussian beam,
the closer the M
2 values in the two cross-sectional directions x and y become to one.
For most common wavelength ranges, there are commercial solutions available to
measure the beam quality. Nevertheless, the quality of measurements is not reduced
when employing homemade tools evaluated without commercial software solutions,
such as used to measure the beam quality factor of a type-II VECSEL [148].
171
ton dispersions using a fundamentally different approach, but no measurement on a
monolayer has been obtained yet, according to [66].
An exciton–polariton branch or the literature-predicted big interaction-mediated
exciton splitting at finite k within the light cone (cf. [141–145]) can only be detected
when the spectral lines are very narrow (i.e. with a small dephasing rate) and the optical resolution in E and k is sufficiently high. In fact, optical measurements allowed
to evidence a pronounced dispersion feature in Fourier-space-resolved spectra on
the order of meV with sub-meV precision in the determination of angle-dependent
energy changes for WSe 2 and MoSe 2 (the latter with less curvature). Furthermore,
an underlying exchange-energy-affected dispersion feature of TMDC excitons with
predicted meV changes within the light cone could also facilitate observation of
the polariton-branch curvature (see considerations in [66]). By merely evaluating
the effective curvature of the measurable average dispersion feature, which due to
contributions of incoherent excitons and e–h plasma can be (partially) washed out,
through a parabola approximation, mean effective masses of as little as 10
−4 can be
extracted in both PL and reflection contrast [66]. Both, pump-power dependencies
[66] (the investigated excitation densities were set by a neutral density filter wheel in
discrete steps in the linear regime) and detuning dependencies [46] showed changes
in the measurable dispersion. Moreover, the latter (i.e. excitation detuning) modified
the overall (as well as the momentum-dependent) helicity degree of the excitonic
emissions obtained in experiments.
5.6 Additional Methods
At the end of this chapter, a few more optical methods are briefly described which
can be used for the characterisation of photonic devices, semiconductor structures
or even bare materials.
5.6.1 Beam Characterisation
For the characterisation of laser output beam profiles, typically the beam quality factor
M
2 is obtained. This is the parameter, which reflects the degree of variation of a beam
compared to an ideal Gaussian beam of the same wavelength. A definition of this
beam quality factors and how to derive it on the basis of measuring second moment
widths D4σ , which are the beam diameters along beam-propagation direction, is for
instance given in [146, 147]. The closer a beam (profile) is to an ideal Gaussian beam,
the closer the M
2 values in the two cross-sectional directions x and y become to one.
For most common wavelength ranges, there are commercial solutions available to
measure the beam quality. Nevertheless, the quality of measurements is not reduced
when employing homemade tools evaluated without commercial software solutions,
such as used to measure the beam quality factor of a type-II VECSEL [148].