28
2 Terahertz Time-Domain Spectroscopy
second metallization layer is placed between every second electrode finger to ensure
optical excitation only occurs in substrate regions where the electric field points in the
same direction, resulting in constructive interference in the far field. If the gap size of
the device is 5 µm, high biasing electric fields of around 20 kV cm
−1 can be produced
in the gap by applying a voltage of only 10 V to the electrodes, removing the need
for high-power voltage supplies. The THz field strength produced by interdigitated
emitters can potentially be scaled by increasing the size of the emitting area and
exciting them using amplified laser pulses [8].
The PCEs used throughout this thesis were fabricated at the University of Warwick
by Michele Failla, with the exception of the work presented in Chap. 4, in which a
new PCE design was developed and fabricated by myself as part of this doctoral
work, details of which are presented in that chapter. The other PCEs used were
interdigitated PCEs consisting of 5 µm gold wires with a 5 µm gap between wires,
with an active area of 1.3 mm×2.0 mm, and were fabricated on 350 µm-thick semiinsulating gallium arsenide (SI-GaAs) substrates. The bandgap of GaAs (1.42 eV at
room temperature) makes it an effective pairing with the peak output wavelength of
Ti:Sapphire lasers (800 nm, or 1.55 eV).
2.1.2 Optical Rectification
In an optically linear medium the induced electric polarisation P has a linear relationship P = 0 χ E with the applied electric field E. However, in an optically nonlinear
medium the polarisation is described by a series of increasing order terms; in the
case of optical rectification (OR) the second order term is important [9],
P
(2)
i
= 0
j,k=x,y,z
χ
(2)
i jk E j E k ,
(2.2)
where i, j and k correspond to the cartesian axes x, y and z respectively. The electric
field components E j and E k here refer to the components of the incident electric
field vector along the corresponding crystal axes. In the case where the electric field
is a continuous wave, E(t) = E 0 e
iωt , the induced polarisation will be static, |P| ∝
|E 0 |
2 . However if the electric field is a time-dependent pulse, E(t) = E 0 e
−at
2 e
iωt ,
the induced polarisation also has a time dependence, |P| ∝ E
2
0 e
−2at
2 [9]. When using
an optical pulse to create a time-varying electric field in the nonlinear crystal, the
induced polarisation will be proportional to the envelope of the pulse, and this timevarying polarisation will generate electromagnetic radiation. This technique was first
demonstrated to generate terahertz radiation using picosecond optical pulses [10,
11] and then adapted to produce higher frequency THz radiation using femtosecond
pulses [2, 12].
2 Terahertz Time-Domain Spectroscopy
second metallization layer is placed between every second electrode finger to ensure
optical excitation only occurs in substrate regions where the electric field points in the
same direction, resulting in constructive interference in the far field. If the gap size of
the device is 5 µm, high biasing electric fields of around 20 kV cm
−1 can be produced
in the gap by applying a voltage of only 10 V to the electrodes, removing the need
for high-power voltage supplies. The THz field strength produced by interdigitated
emitters can potentially be scaled by increasing the size of the emitting area and
exciting them using amplified laser pulses [8].
The PCEs used throughout this thesis were fabricated at the University of Warwick
by Michele Failla, with the exception of the work presented in Chap. 4, in which a
new PCE design was developed and fabricated by myself as part of this doctoral
work, details of which are presented in that chapter. The other PCEs used were
interdigitated PCEs consisting of 5 µm gold wires with a 5 µm gap between wires,
with an active area of 1.3 mm×2.0 mm, and were fabricated on 350 µm-thick semiinsulating gallium arsenide (SI-GaAs) substrates. The bandgap of GaAs (1.42 eV at
room temperature) makes it an effective pairing with the peak output wavelength of
Ti:Sapphire lasers (800 nm, or 1.55 eV).
2.1.2 Optical Rectification
In an optically linear medium the induced electric polarisation P has a linear relationship P = 0 χ E with the applied electric field E. However, in an optically nonlinear
medium the polarisation is described by a series of increasing order terms; in the
case of optical rectification (OR) the second order term is important [9],
P
(2)
i
= 0
j,k=x,y,z
χ
(2)
i jk E j E k ,
(2.2)
where i, j and k correspond to the cartesian axes x, y and z respectively. The electric
field components E j and E k here refer to the components of the incident electric
field vector along the corresponding crystal axes. In the case where the electric field
is a continuous wave, E(t) = E 0 e
iωt , the induced polarisation will be static, |P| ∝
|E 0 |
2 . However if the electric field is a time-dependent pulse, E(t) = E 0 e
−at
2 e
iωt ,
the induced polarisation also has a time dependence, |P| ∝ E
2
0 e
−2at
2 [9]. When using
an optical pulse to create a time-varying electric field in the nonlinear crystal, the
induced polarisation will be proportional to the envelope of the pulse, and this timevarying polarisation will generate electromagnetic radiation. This technique was first
demonstrated to generate terahertz radiation using picosecond optical pulses [10,
11] and then adapted to produce higher frequency THz radiation using femtosecond
pulses [2, 12].