PEM200 User Manual
49
Figure A.1 Typical Optical Setup
The modulator is placed between crossed polarizers, each of which is oriented with its
passing axis at 45 degrees with respect to the modulator axis. For some calibration
procedures, a retarder is required. If so, it should be placed between one polarizer and
the modulator, with the fast axis parallel or perpendicular to the modulator axis.
The space between the two polarizers should contain nothing but the modulator and the
waveplate (if needed). Mirror, prisms, filters, windows, lenses, monochromators or
other wavelength selecting devices should be located outside the polarizers, if possible.
Kemp
1
has derived the equations for the intensity of the light reaching the detector, as a
function of time.
0
A
is the amplitude of the sinusoidal retardation function; B is the
retardation magnitude of the waveplate and
Ω
is the angular frequency of the
modulator. The general expression for the intensity function is:
(
)
(
)
{
}
t
A
B
t
A
B
Ω
+
Ω
−
=
Ι
cos
sin
sin
cos
cos
cos
1
2
1
0
=
{
( )
(
) }
t
A
B
Ω
+
−
cos
cos
1
2
1
0
(1)
For the majority of applications, expansion of this expression using a Fourier Series is
very useful;
( ) ( )
{
}
0
0
cos
1
2
1
A
J
B
−
=
Ι
DC
(2)
( ) ( ) ( )
t
A
J
B
Ω
+
cos
sin
2
0
1
1f
( ) ( ) (
)
t
A
J
B
Ω
+
2
cos
cos
2
0
2
2f
higher
...
+
}
terms
The latter expression shows the DC component of the expression and the first and
second harmonics of the optical intensity signals. Using the reference signals from the
modulator controller, these harmonics can be easily detected with a lock-in amplifier.
If there is no birefringence present, the above equations reduce to the following. Note
that there is no fundamental (first harmonic) component in the intensity signal.
Monochromatic
Light Source
+45°
Polarizer
Modulator
0°
Polarizer
Controller
Oscilloscope
Reference
-45°
Detector
