56
3 Rotatable-Polarisation Terahertz Time-Domain Spectroscopy of Anisotropic Media
3.4.1 Sample Details
3.4.1.1 ZnO
The first test case material under study is ZnO, which is a wide-gap semiconductor
of interest in optoelectronics. With a hexagonal structure (space group C6mc), ZnO
consists of alternating hexagonal stacks of Zn
2+ and O
2− ions along the c-axis, with
each Zn
2+ ion coordinated tetrahedrally with the O
2− , and vice versa. Measurements
presented in this section were performed on a 0.6 mm thick single crystal of ZnO,
oriented with the a-axis as the surface normal and the c-axis in the plane. The
birefringence in the THz range can be linked to the differences in phonon mode
frequency and strength for directions parallel to and perpendicular to c [29], and also
to any additional anisotropy in the electronic contribution to the dielectric function.
The dielectric tensor for a uniaxial crystal can be expressed as
=
⎡
⎣
xx 0 0
0 xx 0
0 0 zz
⎤
⎦ ,
(3.4)
where xx and zz are the components of the dielectric tensor along the mutually
orthogonal principal axes of the material x, y and z, xx = yy , and z is the optical
axis.
3.4.1.2 LaAlO 3
The second test case material is LaAlO 3 , which is a useful substrate for epitaxial growth of complex oxides. At room temperature LaAlO 3 is a rhombohedrallydistorted perovskite with space group R ¯
3c [30]. The optical axis is in the [111]
pseudocubic direction [1]. While ZnO forms a homogeneous single crystal, LaAlO 3
is inhomogeneous with twin domains bounded along the [010] direction. The size
of these twin domains has been shown to sensitively influence the apparent birefringence in the THz region [1]. Here, measurements were performed on a 0.5 mm
thick [001]-oriented single crystal of LaAlO 3 , with twin domains that were small
in comparison to the THz spot size. The in-plane crystallographic directions were
oriented arbitrarily with respect to the incident THz polarization.
3.4.1.3 CuO
Having a monoclinic crystal structure with space group C2/c, CuO is a biaxial
crystal. Due to its monoclinic crystal structure, the dielectric tensor in CuO is
3 Rotatable-Polarisation Terahertz Time-Domain Spectroscopy of Anisotropic Media
3.4.1 Sample Details
3.4.1.1 ZnO
The first test case material under study is ZnO, which is a wide-gap semiconductor
of interest in optoelectronics. With a hexagonal structure (space group C6mc), ZnO
consists of alternating hexagonal stacks of Zn
2+ and O
2− ions along the c-axis, with
each Zn
2+ ion coordinated tetrahedrally with the O
2− , and vice versa. Measurements
presented in this section were performed on a 0.6 mm thick single crystal of ZnO,
oriented with the a-axis as the surface normal and the c-axis in the plane. The
birefringence in the THz range can be linked to the differences in phonon mode
frequency and strength for directions parallel to and perpendicular to c [29], and also
to any additional anisotropy in the electronic contribution to the dielectric function.
The dielectric tensor for a uniaxial crystal can be expressed as
=
⎡
⎣
xx 0 0
0 xx 0
0 0 zz
⎤
⎦ ,
(3.4)
where xx and zz are the components of the dielectric tensor along the mutually
orthogonal principal axes of the material x, y and z, xx = yy , and z is the optical
axis.
3.4.1.2 LaAlO 3
The second test case material is LaAlO 3 , which is a useful substrate for epitaxial growth of complex oxides. At room temperature LaAlO 3 is a rhombohedrallydistorted perovskite with space group R ¯
3c [30]. The optical axis is in the [111]
pseudocubic direction [1]. While ZnO forms a homogeneous single crystal, LaAlO 3
is inhomogeneous with twin domains bounded along the [010] direction. The size
of these twin domains has been shown to sensitively influence the apparent birefringence in the THz region [1]. Here, measurements were performed on a 0.5 mm
thick [001]-oriented single crystal of LaAlO 3 , with twin domains that were small
in comparison to the THz spot size. The in-plane crystallographic directions were
oriented arbitrarily with respect to the incident THz polarization.
3.4.1.3 CuO
Having a monoclinic crystal structure with space group C2/c, CuO is a biaxial
crystal. Due to its monoclinic crystal structure, the dielectric tensor in CuO is