Laser-based measurements of complex high-frequency signals
von Paul StruszewskiThe constantly growing demands in the telecommunications industry require electrical signals
with large bandwidths that extend into the THz range. This poses considerable challenges
for metrology since conventional purely electrical measurement methods can only cover this
extended frequency range with large technical effort. As a consequence, optical time-domain
sampling techniques based on femtosecond lasers are increasingly used. With these sampling
techniques it is possible to detect ultrashort voltage signals with temporal width of a few
ps, corresponding to a bandwidth of more than 500 GHz, by utilizing the linear electro-optic
effect. The main challenge of these techniques is to identify all systematic effects caused by
the electro-optic interaction during the detection process and by electrical propagation and
reflections. Established optical approaches rely on electrical high-frequency measurements to
identify these systematic influences which, however, lead to frequency limitations determined
by the electrical instrumentation. Therefore, in this thesis new purely optical measurement
techniques are developed to characterize the influence of the electro-optic interaction and electrical propagation and reflections on electro-optically measured signals. These findings can
be used to traceably retrieve the original undistorted waveform of a complex high-frequency
signal.
In the first part of the thesis, a novel purely optical approach, based on electro-optic measurements at different positions on a planar waveguide, is studied to determine the electrical
reflection and propagation properties of a transmission line. A systematic investigation enabled a deeper understanding of the physical principles of this novel approach and provided
accurate reflection characteristics of a transmission line in a frequency range between 5 GHz
and 500 GHz. A further improvement of the reflection measurement is achieved by implementing an alternative sampling method based on two asynchronous laser systems. This method
requires no moving components and enables a significantly improved frequency resolution
of the electro-optic detection from 500 MHz to 76 MHz. A key element of the alternative
sampling method is the synchronization of the two laser systems. By implementing a new
digital stabilization system, the temporal jitter of the measurement could be halved to below
46 fs while simultaneously enabling an unstabilized signal source. This significantly increases
the range of applications for the electro-optic detection.
In the second part, the physical properties of the electro-optic interaction are analyzed by
describing this interaction within a linear response theory using an electro-optic transfer function. This investigation includes both a numerical simulation for the theoretical prediction of
the transfer function and a new experimental measurement scheme relying on an analytical
model for the transfer function. The comparison between numerical and experimental results reveals a good agreement and thus validates the physical model and the experimentally
found transfer function. Using this function, the original waveform of voltage pulses on a
waveguide can be found from the electro-optically measured signal resulting in a reduction
of the pulse width from 2.21 ps to 1.94 ps. A precise knowledge of the electro-optic transfer
function is also essential to provide traceable voltage values of the original high-frequency
signals. These quantitative measurements are performed using a low-frequency signal with
an exactly known voltage amplitude as a reference standard. However, in this thesis it was
shown that the electro-optic transfer function in the frequency region of the reference signal
is not constant as expected but exhibits a pronounced frequency dependence. This causes a
scaling of the specified voltage values that is difficult to determine and thus makes traceability
more difficult. By means of a systematic investigation, the value of this scaling factor could
be narrowed down to an interval between 0.8 and 1.0.
Finally, the performance of the newly-developed optical methods is demonstrated by the
characterization of two different high-speed photodetectors. For a 100 GHz photodetector,
the impulse response is determined where all systematic effects caused by mismatches of the
transmission line and the electro-optic interaction are eliminated. This results in a response
function with frequency components up to 190 GHz. These high-frequency components are
essential to specify the original waveform in the time domain. A balanced high-speed photodetector is characterized by measuring the common-mode rejection. The results obtained
are compared in an international study with the measurements of two different conventional
methods. The comparison indicates a good agreement between the three measurement methods but also demonstrates that the characterization is very sensitive to tiny differences in the
experimental alignment.
with large bandwidths that extend into the THz range. This poses considerable challenges
for metrology since conventional purely electrical measurement methods can only cover this
extended frequency range with large technical effort. As a consequence, optical time-domain
sampling techniques based on femtosecond lasers are increasingly used. With these sampling
techniques it is possible to detect ultrashort voltage signals with temporal width of a few
ps, corresponding to a bandwidth of more than 500 GHz, by utilizing the linear electro-optic
effect. The main challenge of these techniques is to identify all systematic effects caused by
the electro-optic interaction during the detection process and by electrical propagation and
reflections. Established optical approaches rely on electrical high-frequency measurements to
identify these systematic influences which, however, lead to frequency limitations determined
by the electrical instrumentation. Therefore, in this thesis new purely optical measurement
techniques are developed to characterize the influence of the electro-optic interaction and electrical propagation and reflections on electro-optically measured signals. These findings can
be used to traceably retrieve the original undistorted waveform of a complex high-frequency
signal.
In the first part of the thesis, a novel purely optical approach, based on electro-optic measurements at different positions on a planar waveguide, is studied to determine the electrical
reflection and propagation properties of a transmission line. A systematic investigation enabled a deeper understanding of the physical principles of this novel approach and provided
accurate reflection characteristics of a transmission line in a frequency range between 5 GHz
and 500 GHz. A further improvement of the reflection measurement is achieved by implementing an alternative sampling method based on two asynchronous laser systems. This method
requires no moving components and enables a significantly improved frequency resolution
of the electro-optic detection from 500 MHz to 76 MHz. A key element of the alternative
sampling method is the synchronization of the two laser systems. By implementing a new
digital stabilization system, the temporal jitter of the measurement could be halved to below
46 fs while simultaneously enabling an unstabilized signal source. This significantly increases
the range of applications for the electro-optic detection.
In the second part, the physical properties of the electro-optic interaction are analyzed by
describing this interaction within a linear response theory using an electro-optic transfer function. This investigation includes both a numerical simulation for the theoretical prediction of
the transfer function and a new experimental measurement scheme relying on an analytical
model for the transfer function. The comparison between numerical and experimental results reveals a good agreement and thus validates the physical model and the experimentally
found transfer function. Using this function, the original waveform of voltage pulses on a
waveguide can be found from the electro-optically measured signal resulting in a reduction
of the pulse width from 2.21 ps to 1.94 ps. A precise knowledge of the electro-optic transfer
function is also essential to provide traceable voltage values of the original high-frequency
signals. These quantitative measurements are performed using a low-frequency signal with
an exactly known voltage amplitude as a reference standard. However, in this thesis it was
shown that the electro-optic transfer function in the frequency region of the reference signal
is not constant as expected but exhibits a pronounced frequency dependence. This causes a
scaling of the specified voltage values that is difficult to determine and thus makes traceability
more difficult. By means of a systematic investigation, the value of this scaling factor could
be narrowed down to an interval between 0.8 and 1.0.
Finally, the performance of the newly-developed optical methods is demonstrated by the
characterization of two different high-speed photodetectors. For a 100 GHz photodetector,
the impulse response is determined where all systematic effects caused by mismatches of the
transmission line and the electro-optic interaction are eliminated. This results in a response
function with frequency components up to 190 GHz. These high-frequency components are
essential to specify the original waveform in the time domain. A balanced high-speed photodetector is characterized by measuring the common-mode rejection. The results obtained
are compared in an international study with the measurements of two different conventional
methods. The comparison indicates a good agreement between the three measurement methods but also demonstrates that the characterization is very sensitive to tiny differences in the
experimental alignment.