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3 Rotatable-Polarisation Terahertz Time-Domain Spectroscopy of Anisotropic Media
after transmission through the sample, as described in Sect. 1.1.4, for which methods
of resolving the full resulting polarisation state are required. The second challenge
is having the ability to change the relative orientations of the electric field of the
probing light and the polarisation eigenvectors in the plane of the material under
investigation. Along with the use of complimentary techniques such as Laue X-ray
diffraction, this allows both the nature of the anisotropy and the particular direction
in which it occurs in the material to be investigated.
This section will explore the solutions to these two challenges currently available
in the literature, to serve as background for the rotatable-polarisation THz-TDS
system described later in this chapter.
3.1.1 Disambiguating Spectral Features Using
Polarisation-Resolved Detection Methods
Commonly THz-TDS detection methods are sensitive to only one polarisation state,
for example along the lab-coordinate x-axis. The optical properties of a material
under study will then be calculated from the transmission along the x-axis only, as
T xx = E x,sample /E x,reference . Whilst this may be suitable for spectroscopy of isotropic
materials, it is not sufficient in the study of materials with anisotropic properties;
what appear to be absorption peaks, as reduced transmission T xx , can in fact be
frequencies at which the medium is acting as a quarter- or half-wave plate, altering the
incident polarisation state and producing some transmitted amplitude in a direction
orthogonal to x. Polarisation-resolved detection methods (as discussed in Sect. 2.2.1)
are therefore required, which ideally will measure two orthogonal components of the
THz electric field, allowing the full determination of the THz polarisation state.
An example of the requirement for polarisation-resolved detection methods can be
found in the study of the birefringent properties of lanthanum aluminate (LaAlO 3 )
in the THz region by Lloyd-Hughes et al. [1]. As part of this study the authors
investigated THz transmission through a [001]-surface normal, 500 μm-thick single
crystal of LaAlO 3 , with the incident THz polarisation not parallel to one of the
polarisation eigenvectors in the material, and as such there were components of the
incident THz electric field along both eigenvectors. Whilst the polarisation of the
incident pulse was linear, mainly polarised in the y direction with a very small xcomponent, after transmission through the sample the x-component of the THz pulse
was much larger, forming a complex polarisation state. If a typical one-dimensional
detection method were to have been employed, sensitive to only E y , then the change in
the time-domain waveform of E y , which was accompanied by a dip in the spectrum
of the y-component around 2.1 THz, would make it appear as though there were
a resonant absorption feature in LaAlO 3 around this frequency. However because
polarisation-resolved detection was used, it is evident that the change in E y occurs
due to the alteration of the polarisation state as a result of birefringence, rather than
3 Rotatable-Polarisation Terahertz Time-Domain Spectroscopy of Anisotropic Media
after transmission through the sample, as described in Sect. 1.1.4, for which methods
of resolving the full resulting polarisation state are required. The second challenge
is having the ability to change the relative orientations of the electric field of the
probing light and the polarisation eigenvectors in the plane of the material under
investigation. Along with the use of complimentary techniques such as Laue X-ray
diffraction, this allows both the nature of the anisotropy and the particular direction
in which it occurs in the material to be investigated.
This section will explore the solutions to these two challenges currently available
in the literature, to serve as background for the rotatable-polarisation THz-TDS
system described later in this chapter.
3.1.1 Disambiguating Spectral Features Using
Polarisation-Resolved Detection Methods
Commonly THz-TDS detection methods are sensitive to only one polarisation state,
for example along the lab-coordinate x-axis. The optical properties of a material
under study will then be calculated from the transmission along the x-axis only, as
T xx = E x,sample /E x,reference . Whilst this may be suitable for spectroscopy of isotropic
materials, it is not sufficient in the study of materials with anisotropic properties;
what appear to be absorption peaks, as reduced transmission T xx , can in fact be
frequencies at which the medium is acting as a quarter- or half-wave plate, altering the
incident polarisation state and producing some transmitted amplitude in a direction
orthogonal to x. Polarisation-resolved detection methods (as discussed in Sect. 2.2.1)
are therefore required, which ideally will measure two orthogonal components of the
THz electric field, allowing the full determination of the THz polarisation state.
An example of the requirement for polarisation-resolved detection methods can be
found in the study of the birefringent properties of lanthanum aluminate (LaAlO 3 )
in the THz region by Lloyd-Hughes et al. [1]. As part of this study the authors
investigated THz transmission through a [001]-surface normal, 500 μm-thick single
crystal of LaAlO 3 , with the incident THz polarisation not parallel to one of the
polarisation eigenvectors in the material, and as such there were components of the
incident THz electric field along both eigenvectors. Whilst the polarisation of the
incident pulse was linear, mainly polarised in the y direction with a very small xcomponent, after transmission through the sample the x-component of the THz pulse
was much larger, forming a complex polarisation state. If a typical one-dimensional
detection method were to have been employed, sensitive to only E y , then the change in
the time-domain waveform of E y , which was accompanied by a dip in the spectrum
of the y-component around 2.1 THz, would make it appear as though there were
a resonant absorption feature in LaAlO 3 around this frequency. However because
polarisation-resolved detection was used, it is evident that the change in E y occurs
due to the alteration of the polarisation state as a result of birefringence, rather than