5.2 High-Field Terahertz Time-Domain Spectrometer
95
The pair of cylindrical lenses apply a horizontal demagnification β 1 to the pump
pulse, which changes the tilt angle according to
tan γ CL =
tan γ
β 1
,
(5.7)
where γ CL is the pulse front tilt angle after the pair of cylindrical lenses. As the pulse
propagates into the LiNbO 3 crystal, refraction at the interface causes an alteration in
the pulse length l c = l/n g,opt , causing a corresponding change in the pulse front tilt
angle of
tan γ c =
tan γ CL
n g,opt
(5.8)
where γ c is the pulse front tilt inside the LiNbO 3 crystal. Combining Eqs. 5.6–5.8,
we obtain the equation describing the pulse front tilt angle inside the LiNbO 3 crystal
as
tan γ c =
m N λ 0
n g,opt β 1 cos θ d
.
(5.9)
Finally, by rearranging Eqs. 5.9 and 5.4, we can obtain the expressions for the angles
of diffraction and incidence which produce the required pulse tilt as
θ d = cos
−1
m N λ 0
n g,opt β 1 tan γ c
,
(5.10)
and
θ i = sin
−1
m N λ 0 − sin
cos
−1
m N λ 0
n g,opt β 1 tan γ c
.
(5.11)
5.2.1.2 Optimising the Pulse Front Tilt for THz Generation Efficiency
For efficient generation of THz radiation by this scheme, an important factor is having
the pulse front tilt angle γ c match the angle of the grating image θ g created in the
LiNbO 3 [50]. The grating image created in the LiNbO 3 can be shown to be [50]
tan θ g = nβ 2 tan θ d ,
(5.12)
where β 2 is the demagnification factor of the cylindrical lens pair. As such, the
greatest THz generation efficiency occurs when β 1 = β 2 .
The THz generation crystal used in this thesis was a 0.6 mol % MgO-doped stoichiometric LiNbO 3 crystal, which has dimensions of 5 mm × 5 mm × 9.81 mm, with
the crystal cut at an angle of θ LN = 63
◦ between the pump beam entrance and THz
beam exit face. The pump beam entrance face was anti-reflection coated for 800 nm.
To find the optimal optics for the pulse front tilting setup, the demagnification factors
95
The pair of cylindrical lenses apply a horizontal demagnification β 1 to the pump
pulse, which changes the tilt angle according to
tan γ CL =
tan γ
β 1
,
(5.7)
where γ CL is the pulse front tilt angle after the pair of cylindrical lenses. As the pulse
propagates into the LiNbO 3 crystal, refraction at the interface causes an alteration in
the pulse length l c = l/n g,opt , causing a corresponding change in the pulse front tilt
angle of
tan γ c =
tan γ CL
n g,opt
(5.8)
where γ c is the pulse front tilt inside the LiNbO 3 crystal. Combining Eqs. 5.6–5.8,
we obtain the equation describing the pulse front tilt angle inside the LiNbO 3 crystal
as
tan γ c =
m N λ 0
n g,opt β 1 cos θ d
.
(5.9)
Finally, by rearranging Eqs. 5.9 and 5.4, we can obtain the expressions for the angles
of diffraction and incidence which produce the required pulse tilt as
θ d = cos
−1
m N λ 0
n g,opt β 1 tan γ c
,
(5.10)
and
θ i = sin
−1
m N λ 0 − sin
cos
−1
m N λ 0
n g,opt β 1 tan γ c
.
(5.11)
5.2.1.2 Optimising the Pulse Front Tilt for THz Generation Efficiency
For efficient generation of THz radiation by this scheme, an important factor is having
the pulse front tilt angle γ c match the angle of the grating image θ g created in the
LiNbO 3 [50]. The grating image created in the LiNbO 3 can be shown to be [50]
tan θ g = nβ 2 tan θ d ,
(5.12)
where β 2 is the demagnification factor of the cylindrical lens pair. As such, the
greatest THz generation efficiency occurs when β 1 = β 2 .
The THz generation crystal used in this thesis was a 0.6 mol % MgO-doped stoichiometric LiNbO 3 crystal, which has dimensions of 5 mm × 5 mm × 9.81 mm, with
the crystal cut at an angle of θ LN = 63
◦ between the pump beam entrance and THz
beam exit face. The pump beam entrance face was anti-reflection coated for 800 nm.
To find the optimal optics for the pulse front tilting setup, the demagnification factors