Note: Descriptions are shown in the official language in which they were submitted.
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SYSTEM AND METHOD FOR DETERMINING THE ENVELOPE OF A
MODULATED SIGNAL
Technical Field
[0001] The present disclosure relates generally to systems and methods for
determining
the modulating envelope of modulated signals. In particular, the present
disclosure relates
to systems and methods for determining the envelope of modulated signals where
phase
noise is present. The systems and methods of the present disclosure may be
suitable for
equivalent-time or real-time oscilloscopes.
Background
[0002] Phase modulated signals such as binary phase shift keying (BPSK) and
quadrature
phase shift keying (QPSK) may be commonly used in optical communications.
Techniques to measure the complex optical field of high bit rate signals have
been
considered. Examples of conventional techniques for obtaining the signal
trajectory and
constellation diagram include linear optical sampling [1]-[3], coherent
detection and post-
processing of real-time sampled waveforms [4]-[7], and complex spectral
analysis [8].
[0003] Previously, an interferometric approach with real-time sampling has
been
demonstrated for low bandwidth signals under the assumption that the relative
phase
between two interfering signals is stable during the measurement time (100 ns)
[9].
However, techniques that rely on real-time sampling may be limited by the
bandwidth
and sampling rate of the oscilloscope. For example, a conventional real-time
sampling
oscilloscope such as a Tektronix Digital Serial Analyzer 72004B may have
bandwidth
and sampling rate limits of 20 GHz and 50 GSample/s, respectively.
[0004] It would be useful to allow for determination of modulated signals
without such
restrictions.
Summary
[0005] In some example aspects, the present disclosure provides systems and
methods for
measuring or determining a modulating envelope of a modulated signal, for
example a
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modulated optical signal. For examples, disclosed methods and systems may use
electrical and optical components and a high-bandwidth equivalent-time
sampling
oscilloscope, which may be the same as or similar to conventional components.
In some
examples, the system may include a signal modulator, a mixer (e.g., an optical
mixer),
and samplers for obtaining high bandwidth samples and low bandwidth samples.
In some
examples, an equivalent-time sampling oscilloscope with two low-speed (or low
bandwidth) sampling modules (e.g., at 50 kHz) and two high-speed (or high
bandwidth)
optical sampling modules (e.g., at 65 GHz) may be used. Using the example
system, the
simultaneous measurement of four de-skewed (i.e., without relative time
differences)
signals may allow for the separate determination of the phase noise, amplitude
and phase
of the modulated signal. From these determined values, any amplitude and/or
phase
modulation of the modulated signal may be determined and the complete
trajectory in
time of the complex modulated signal may be constructed.
[0006] In some example aspects, there is provided a method for determining an
envelope
of a modulated signal, the method comprising: receiving at least two hybrid
signals, the
hybrid signals being obtained from mixing the modulated signal with a carrier
signal,
each of the hybrid signals having a phase noise difference that is a
difference between
phase noise of the modulated signal and phase noise of the carrier signal;
obtaining a set
of low bandwidth samples for each of the hybrid signals; obtaining a set of
high
bandwidth samples for each of the hybrid signals; determining the phase noise
difference
from the sets of low bandwidth samples; and determining the envelope of the
modulated
signal based on the determined phase noise difference, phase measurements of
the sets of
high bandwidth samples and amplitude measurements of the sets of high
bandwidth
samples, wherein the determination includes calculating for effects of the
determined
phase noise difference.
[0007] In some examples, the method may further comprise: receiving the
modulated
signal; and mixing the modulated signal with the carrier signal to obtain the
at least two
hybrid signals. For example, the method may further comprising receiving the
carrier
signal, or the mixing may further comprise determining the carrier signal from
the
modulated signal.
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[0008] In some examples, determining the envelope may comprise determining
phase
and amplitude of the envelope of the modulated signal.
[0009] In some examples, the sets of low bandwidth samples and high bandwidth
samples may be all substantially synchronized in time.
[0010] In some examples, measurements of the sets of high bandwidth samples
may be
taken over a time interval greater than a repetition cycle of the modulating
signal.
[0011] In some examples, the phase noise difference may be due to a time delay
between
the modulated signal and the carrier signal. For example, the time delay may
arise due to
a propagation delay between the modulated signal and the carrier signal.
[0012] In some examples, the low bandwidth samples may be samples of the
hybrid
signal at a rate lower than a repetition rate of the modulated signal and the
high
bandwidth samples are samples of the hybrid signal at a rate higher than a
repetition rate
of the modulated signal. For example, the low bandwidth samples may be
obtained at a
rate in the range of about 1 Hz to about 100 kHz. For example, the high
bandwidth
samples may be obtained at a range in the range of about 1 GHz to about 100
THz.
[0013] In some examples, the repetition rate of the modulated signal may be in
the range
of about 100 Hz to about 100 THz. For example, the repetition rate of the
modulated
signal may be in the range of about 100 Hz to about 100 kHz. For example, the
repetition
rate of the modulated signal may be in the range of about 1 GHz to about 40
GHz.
[0014] In some examples, the method may further comprise applying a time shift
between the sets of high bandwidth samples to correct for any time difference
between
the sets of high bandwidth samples.
[0015] In some examples, the modulated signal may be an optical signal or an
electromagnetic signal.
[0016] In some examples, the method may further comprise calculating
adjustments for
the determined envelope of the modulated signal to compensate for any known
deviations
in at least one of the modulated signal, the carrier signal and the hybrid
signal.
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[0017] In some examples, obtaining the sets of low bandwidth samples may
comprise
applying a bandpass filter to the hybrid signal, the bandpass filter having
pass frequencies
centered about an integer multiple of a repetition rate of the modulated
signal.
[0018] In some examples, the method may further comprise: receiving timing
information about the high bandwidth samples and the low bandwidth samples;
and
storing the timing information corresponding to the determined envelope of the
modulated signal.
[0019] In some example aspects, there is provided a method for determining a
phase
noise difference between a modulated signal and a carrier signal, the method
comprising:
receiving at least two hybrid signals, the hybrid signals being obtained from
mixing the
modulated signal with a carrier signal, each of the hybrid signals having a
phase noise
difference that is a difference between phase noise of the modulated signal
and phase
noise of the carrier signal; obtaining a set of low bandwidth samples for each
of the
hybrid signals; and determining the phase noise difference from the sets of
low
bandwidth samples.
[0020] In some example aspects, there is provided a method for characterizing
a
modulator, the method comprising: receiving at least two hybrid signals, the
hybrid
signals being obtained from mixing a modulated signal from the modulator with
a carrier
signal, each of the hybrid signals having a phase noise difference that is a
difference
between phase noise of the modulated signal and phase noise of the carrier
signal;
obtaining a set of low bandwidth samples for each of the hybrid signals; and
determining
the phase noise difference from the sets of low bandwidth samples; and
characterizing the
modulator based on at least the determined phase noise difference.
[0021] In some examples, the method for characterizing may comprise: obtaining
a set of
high bandwidth samples for each of the hybrid signals; determining an envelope
of the
modulated signal from the sets of high bandwidth samples; and comparing phase
and
amplitude of the determined envelope with phase and amplitude of a desired
envelope.
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[0022] In some example aspects, there is provided a system for determining an
envelope
of a modulated signal, the system comprising: a first set of at least two
samplers for
obtaining a set of low bandwidth samples for each of two hybrid signals, the
hybrid
signals being obtained from mixing the modulated signal with a carrier signal,
each of the
hybrid signals having a phase noise difference that is a difference between
phase noise of
the modulated signal and phase noise of the carrier signal; a second set of at
least two
samplers for obtaining a set of high bandwidth samples for each of the hybrid
signals;
and a processor adapted to: determine the phase noise difference from the sets
of low
bandwidth samples; and determine the envelope of the modulated signal based on
the
determined phase noise difference, phase measurements of the sets of high
bandwidth
samples and amplitude measurements of the sets of high bandwidth samples,
wherein the
determination includes calculating for effects of the determined phase noise
difference.
[0023] In some examples, the system may further comprise: a modulator for
modulating
the carrier signal to provide the modulated signal; and a mixer for mixing the
modulated
signal with the carrier signal to obtain the at least two hybrid signals. For
example, the
mixer may be an optical hybrid. In some examples, the system may further
comprise a
carrier source of providing the carrier signal to the mixer. In some examples,
the carrier
signal input to the mixer may be determined from the modulated signal.
[0024] In some examples, the system may further comprise at least two signal
splitters
for splitting each of the hybrid signals in two, for sampling by a respective
one of the first
set of samplers and a respective one of the second set of samplers.
[0025] In some examples, the processor may be further adapted to determine
phase and
amplitude of the envelope of the modulated signal.
[0026] In some examples, the first set of samplers may be low bandwidth
samplers.
[0027] In some examples, the first set of samplers may be also capable of high
bandwidth
sampling.
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[0028] In some examples, the system may further comprise an oscilloscope
having the
first set of samplers, the second set of samplers and the processor. For
example, the
oscilloscope may be an equivalent-time oscilloscope or a real-time
oscilloscope.
[0029] In some examples, the system may further comprise a carrier source for
providing
the carrier signal.
[0030] In some examples, measurements of the sets of high bandwidth samples
may be
taken over a time interval greater than a repetition cycle of the modulating
signal.
[0031] In some examples, the first set of samplers may have two samplers and
the second
set of samplers may have two samplers.
[0032] In some examples, the low bandwidth samples may be obtained at a rate
or at an
equivalent rate lower than a repetition rate of the modulated signal and the
high
bandwidth samples may be obtained at a rate or at an equivalent rate higher
than a
repetition rate of the modulated signal. For example, the sets of low
frequency samples
may be obtained at a rate in the range of about 1 Hz to about 100 kHz. For
example, the
sets of high frequency samples may be obtained at a rate in the range of about
1GHz to
about 100 THz.
[0033] In some examples, the repetition rate of the modulated signal may be
known
beforehand or may be determined from the modulated signal. For example, the
modulated
signal may be periodic at the repetition rate, or the modulated signal may be
aperiodic
and its repetition rate may be known beforehand or determined from the
modulated
signal.
[0034] In some examples, the first and second sets of samplers may obtain the
high and
low bandwidth samples at a same real-time rate that is lower or higher than a
repetition
rate of the modulated signal.
[0035] In some examples, timing information about the low and high bandwidth
samples
may be recorded.
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[0036] In some examples, the system may further comprise a time shift
component to
correct for any time difference between the sets of high bandwidth samples.
For example,
the time difference may arise from at least one of: a difference in signal
path length
between the sets of high bandwidth samples, an inherent time skew of the high
bandwidth
samplers, or an overall time skew of the system.
[0037] In some examples, the processor may be further adapted to calculate
adjustments
for the determined envelope of the modulated signal to compensate for any
known
deviations within the system.
[0038] In some examples, the system may further comprise a bandpass filter
having pass
frequencies centered about an integer multiple of a repetition rate of the
modulated
signal, and the sets of low bandwidth samples are obtained after applying the
bandpass
filter to the hybrid signals.
[0039] In some example aspects, there is provided a system for determining a
phase noise
difference between a modulated signal and a carrier signal of the modulated
signal, the
system comprising: a first set of at least two samplers for obtaining a set of
low
bandwidth samples for each of two hybrid signals, the hybrid signals being
obtained from
mixing the modulated signal with the carrier signal, each of the hybrid
signals having a
phase noise difference that is a difference between phase noise of the
modulated signal
and phase noise of the carrier signal; and a processor adapted to: receive the
sets of low
bandwidth samples; and determine the phase noise difference from the sets of
low
bandwidth samples.
[0040] In some example aspects, there is provided a system for characterizing
a
modulator, the system comprising: a first set of at least two samplers for
obtaining a set
of low bandwidth samples for each of two hybrid signals, the hybrid signals
being
obtained from mixing the modulated signal with the carrier signal, each of the
hybrid
signals having a phase noise difference that is a difference between phase
noise of the
modulated signal and phase noise of the carrier signal; and a processor
adapted to:
receive the sets of low bandwidth samples; determine the phase noise
difference from the
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sets of low bandwidth samples; and characterize the modulator based on at
least the
determined phase noise difference.
[0041] In some examples, the system for characterizing may further comprise: a
second
set of at least two samplers for obtaining a set of high bandwidth samples for
each of the
hybrid signals; wherein the processor is further adapted to: determine an
envelope of the
modulated signal from the sets of high bandwidth samples; and compare
amplitude and
phase of the determined envelope with amplitude and phase of a desired
envelope.
[0042] In some example aspects, there is provided a computer program product
for
determining an envelope of a modulated signal, the computer program product
comprising a computer readable storage medium having computer executable
instructions
embedded thereon, the instructions, when executed, causing a processor to:
receive at
least two hybrid signals, the hybrid signals being obtained from mixing the
modulated
signal with a carrier signal, each of the hybrid signals having a phase noise
difference that
is a difference between phase noise of the modulated signal and phase noise of
the carrier
signal; obtain a set of low bandwidth samples for each of the hybrid signals;
obtain a set
of high bandwidth samples for each of the hybrid signals; determine the phase
noise
difference from the sets of low bandwidth samples; and determine the envelope
of the
modulated signal based on the determined phase noise difference, phase
measurements of
the sets of high bandwidth samples and amplitude measurements of the sets of
high
bandwidth samples, wherein the determination includes calculating for effects
of the
determined phase noise difference.
[0043] In some examples, the instructions further cause the processor to:
receive timing
information about the high bandwidth samples and the low bandwidth samples;
and store
the timing information corresponding to the determined envelope of the
modulated
signal.
[0044] In some example aspects, there is provided a use of the methods,
systems and
computer program products described above for characterizing a modulator, a
modulated
signal, or an envelope of the modulated signal.
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[0045] In some examples, the modulator may be a Mach Zenhder modulator or an
electro-absorptive modulator. For example, the modulator may be made of at
least one of:
gallium arsenide, indium phosphide and lithium niobate.
[0046] In some examples, the modulated signal may be a phase-shift keying
(PSK)
signal. For example, the PSK signal may be one of. a quadrature PSK signal, a
binary
PSK signal, a differential PSK signal, or a higher-order PSK signal.
[0047] In some examples, the modulated signal may be an amplitude modulated
signal, a
frequency modulated signal, or a quadrature amplitude modulated signal.
Brief Description of the Drawings
[0048] Reference will now be made to the drawings, which show by way of
example
embodiments of the present disclosure, and in which:
[0049] FIG. 1 shows a block diagram of an example system for determining an
envelope
of a modulated signal;
[0050] FIG. 2 shows an example spectrum of the phase noise difference about
the Fourier
coefficients for an example modulated signal within an example system;
[0051 ] FIG. 3 shows an example calculated trajectory of an example normalized
signal in
the complex plane;
[0052] FIG. 4 shows an example measured trajectory of an example normalized
signal in
the complex plane;
[0053] FIG. 5 shows an example plot illustrating the in-phase portion of an
example
signal with and without averaging;
[0054] FIG. 6 shows an example measured signal trajectory in the complex plane
of an
example phase modulated signal;
[0055] FIG. 7 shows an example calculated optical spectrum from example
measured in-
phase and quadrature data for an example modulated optical signal; and
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[0056] FIG. 8 shows an example measured optical spectrum for the example
modulated
optical signal of FIG. 7.
Detailed Description
[0057] The present disclosure describes examples of systems and methods for
determining an envelope of a modulated signal, for example a modulated optical
or
electromagnetic signal. The modulated signal may have in-phase and quadrature
components, in some examples. In general, a carrier signal may be modulated by
a
modulating envelope, to produce the modulated signal. The envelope of the
modulated
signal may contain signal information in its phase and/or amplitude.
[0058] Such systems and methods may be implemented using electrical and/or
optical
components, which may be conventional components, which may include a high-
bandwidth equivalent-time sampling oscilloscope, such as a conventional
equivalent-time
sampling oscilloscope. For a repeating signal (e.g., as in the case of a
modulated signal),
equivalent-time oscilloscopes typically obtain samples of a signal over
multiple cycles of
the same signal. Rather than attempting to take multiple samples of a single
cycle of the
signal in real-time (as may be the case with real-time sampling
oscilloscopes),
equivalent-time oscilloscopes may obtain samples from different points of the
cycle, but
over multiple cycles. For any one sample, the samplers may be have very high
bandwidths and may capture the signal relatively accurately. However, the
actual time
(which may be also known as the re-arm time for the sampler) between
consecutive
samples may be long compared to the repetition rate. This may be useful where
the signal
is a high bandwidth signal. For example, conventional real-time oscilloscopes
may not be
fast enough to sample a 10 GHz signal; however, an equivalent-time
oscilloscope may
sample multiple cycles of the 10 GHz signal and take those samples together,
along with
the timing information, to obtain samples that are equivalent to a very high
rate of
sampling. Thus, an equivalent-time oscilloscope may have an equivalent rate of
sampling
that is much higher than the actual rate of sampling.
[0059] Thus, equivalent-time sampling oscilloscopes may have relatively higher
bandwidths than conventional real-time oscilloscopes. Using an equivalent-time
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oscilloscope to measure the modulated signal may allow for visualization,
characterization and/or measurement of current and/or yet to be developed high-
speed
modulators. Although the present description describes the use of equivalent-
time
oscilloscopes, in some examples, such as where the modulated signal is
relatively slow, a
real-time oscilloscope may also be used.
[0060] Phase noise and/or thermal drift in a transmission system (e.g., from
the carrier
source itself) may cause rotation (i.e., phase noise) in the modulated signal
trajectory in
the complex plane. Using examples of the disclosed systems and methods,
measurements
of this rotation may be obtained from the signal samples detected with low
bandwidth
samplers, which may allow the effects of such rotation to be mitigated or
removed from
the signal samples detected with high bandwidth samplers.
[0061] In some examples, the present disclosure may be used for a single
polarization
signal (e.g., based on the available optical hybrid), but may be extended to a
signal from a
polarization diversity configuration. Although the present disclosure provides
examples
using optical signals, the methods and systems disclosed may also be used for
other
modulated signals, such as electromagnetic signals, for example where it may
be more
convenient or technologically necessary to detect the signal by means of
mixing the
modulated signal with a carrier signal.
[0062] A block diagram depicting an example system is shown in FIG. 1. This
example
system includes a carrier source (in this case a laser), a modulator and a
mixer (in this
case an optical hybrid), although in other examples the system may not include
such
components.
[0063] In some examples, the system may receive at least two hybrid signals.
The hybrid
signals may be obtained from mixing of the modulated signal and the carrier
signal (e.g.,
using a mixer). Each of the modulated signal and the carrier signal may
include phase
noise, and the hybrid signals may include a phase noise difference that is the
difference
between the phase noise of the modulated signal and the phase noise of the
carrier signal.
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[0064] In the example of FIG. 1, the modulated signal may be provided by a
modulator
within an arbitrary optical waveform generator (AOWG) that modulates a carrier
signal.
In this example, the AOWG may include an arbitrary pattern generator (APG) and
a
modulator that modulates the signal according to the APG. In this example, the
modulated signal is a modulation of a carrier signal, in this case a
continuous wave (CW)
signal provided by a carrier source, for example, a laser. The carrier signal,
which may
also be referred to as a local oscillator (LO), may be provided by any other
suitable
source. The modulated signal may thus include a modulating envelope (from the
modulator) that modulates the carrier signal (from the carrier source). In the
example of
in FIG. 1, the carrier signal from the laser may be split into two branches,
with the lower
branch being modulated by the modulator to provide the modulated signal. In
other
examples, the system may not include the modulator and/or the carrier source.
[0065] In some examples, the carrier signal may be directly obtained from the
carrier
source (e.g., where the carrier source is accessible to or is part of the
system). In some
examples, where the system does not include the carrier source or where there
is no
independent carrier signal provided, the carrier signal used to produce the
hybrid signal
may be a suitable reproduction or simulation, which may be substantially the
same as the
true carrier signal. For example, a reproduction may be estimated from known
characteristics of the modulated signal and/or the hybrid signals.
[0066] In the example of FIG. 1, the modulated signal and the carrier signal
may be
mixed in a signal mixer, in this example an optical hybrid. The mixer may
produce at
least two hybrid signals. Other types of mixers may be used, which may produce
more
than two hybrid signals, for example. Any type of suitable mixer may be used,
according
to the signals being mixed. For example, the mixer may be any suitable
component that
outputs product terms or non-linear terms from two or more input signals. In
other
examples, the system may not include the mixer but may instead receive the
hybrid
signals from an external source.
[0067] Each of the hybrid signals may be sampled by a respective one high
bandwidth
(or high-speed) sampler and a respective one low bandwidth (or low-speed)
sampler. For
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example, there may be at least two high bandwidth samplers each sampling one
of the at
least two hybrid signals; and two low bandwidth samplers, each sampling one of
the at
least two hybrid signals.
[0068] In some examples, the system may additionally include signal splitters.
Each
signal splitter may each split one of the hybrid signals in two, to be sampled
by a
respective low bandwidth sampler and a respective high bandwidth sampler. In
some
examples, the signal splitters may be integrated with the mixer.
Alternatively, the system
may receive hybrid signals that are already split by an external component.
[0069] In the example of FIG. 1, there are two high bandwidth samplers and two
low
bandwidth samplers, for example using a four-channel equivalent-time sampling
oscilloscope having at least two low-speed sampling modules and at least two
high-speed
sampling modules. In this example, the example oscilloscope may be a
conventional
equivalent-time sampling oscilloscope that includes two low-speed sampling
modules
(which may receive electrical inputs at about 50 kHz) and two high-speed
sampling
modules (which may receive optical inputs at about 65 GHz). As explained
above, in the
case of an equivalent-time oscilloscope, the high bandwidth samplers may be
sampling at
a high equivalent rate, rather than a high actual rate, in order to obtain the
high bandwidth
samples.
[0070] In some examples, rather than using low bandwidth samplers, low
bandwidth
samples may be obtained by passing high bandwidth samples through an
appropriate low-
pass filter. Alternatively, low bandwidth samples may be obtained using high
bandwidth
samplers, by selecting for sampling of only low frequencies. Thus, although
low
bandwidth samplers have been described, all samplers may in fact be capable of
high
bandwidth sampling. This may be useful where low-speed sampling modules are
not
available. In some examples, low-speed sampling modules may be more suitable,
for
example in order to reduce costs and/or to improve the signal-to-noise ratio.
[0071] Generally, a set of high bandwidth samples and a set of low bandwidth
samples
may be produced from each hybrid signal. For example, where there are two
hybrid
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signals, this may result in a total of four samples - two sets of high
bandwidth samples
and two sets of low bandwidth samples.
[0072] In some examples, more than two high bandwidth samplers and more than
two
low bandwidth samplers may be used, for example where there are more than two
hybrid
signals (such as where the mixer is a balanced hybrid with four outputs) or
where
redundant samples are desired, such as for error-checking.
[0073] In some examples, the high bandwidth samplers may be configured to
obtain
samples at a bandwidth that is equal to or higher than the repetition rate of
the modulated
signal. Similarly, low bandwidth samplers may be configured to obtain samples
at a
bandwidth that is lower than the repetition rate of the modulated signal. In
general, the
low bandwidth samplers may be suitably fast to measure the phase noise of the
carrier
signal (which may be known beforehand, from characterization of the carrier
source, for
example). In general, the high bandwidth samplers may be suitably fast to
measure the
spectral content of the modulated signal (e.g., ten times the repetition rate
of the signal or
higher), for example at least higher than the Nyquist frequency of the signal.
For
example, the high bandwidth samples may be obtained at a suitably high
frequency
sampling rate suitable for capturing the desired information from the
modulated signal
(e.g., based on conventional calculations of the expected signal). In some
examples, only
certain frequencies of the modulated signal may be of interest, and the high
frequency
sampling rate may be chosen accordingly to determine characteristics of the
modulated
signal at only the frequencies of interest. For example, to determine
information about the
modulated signal only in a lower bandwidth region, a lower sampling rate may
be used
for the high bandwidth samples; conversely, to determine information about the
modulated signal in a high bandwidth region, a higher sampling rate may be
used for the
high bandwidth samples. Typically, the repetition rate of a modulated signal
may be
known beforehand, and may be at least twice the linewidth of the carrier
source.
[0074] For example, a modulated signal may have a repetition rate in the range
of about
100 Hz to about 100 THz, for example between 100 kHz and 100 GHz, between
about
100 Hz to about 100 kHz, or between about 1 GHz to about 40 GHz, or any other
sub-
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range. The modulated signal may have any repetition rate higher or lower than
the rates
described. For example, a higher quality or faster modulator may produce a
modulated
signal with a repetition rate higher than 40 GHz. Current or future
developments in
modulators may give rise to modulated signals with much higher repetition
rates.
[0075] The sampling rates (or equivalent rates in the case of equivalent-time
oscilloscopes) of the low bandwidth and high bandwidth samplers may be
configured
according to the repetition rate of the modulated signal. For example, for a
100 Hz
modulated signal, low bandwidth samplers may sample in the range of about 1 Hz
to
about less than 100 Hz and high bandwidth samplers may sample in the range of
about 1
MHz to about 1 GHz. For example, for a 1 GHz modulated signal, low bandwidth
samplers may sample in the range of about 1 kHz to about 100 kHz and high
bandwidth
samplers may sample in the range of about 10 GHz to about 100 THz. For an
example
modulated signal having a repetition rate of about 10 MHz, sampling with an
equivalent-
time sampling oscilloscope having low-speed sampling modules at about 50 kHz
bandwidth and high-speed sampling optical modules at about 65 GHz bandwidth
may be
suitable. Generally, the low bandwidth samples may be obtained at a bandwidth
much
lower than the repetition rate of the modulated signal, such as half the
repetition rate; and
the high bandwidth samples may be obtained at a bandwidth much higher than the
repetition rate of the modulated signal, such as ten times the repetition
rate. These
bandwidth ranges are provided for the purpose of illustration only, and other
suitable
bandwidth ranges may be used.
[0076] In the example of FIG. 1, a low-speed photodiode (LS-PD), for example a
50 kHz
bandwidth photodiode, may be used to convert the hybrid optical signals to
electrical
signals for sampling by the low-speed sampling modules. In other examples, low
bandwidth samples may be obtained directly from the hybrid optical signals,
without
conversion to electrical signals, and the LS-PD may be omitted. Alternatively,
the hybrid
signals may already be electrical or electromagnetic, and no conversion to
electrical
signals may be required.
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[0077] In some examples, a signal time shift component, such as an optical
delay, may be
introduced for each of the high bandwidth samples, in order to remove any time
delay
(i.e., de-skew) between the high bandwidth samples. In the example of FIG. 1,
a variable
optical delay (VOD) component may be provided to the signals sampled by the
high-
speed sampling modules. The signal delay component may be used to correct for
any
time difference, which may be due to propagation delays arising from: signal
path length
differences between the two high bandwidth sample paths, internal delays of
the samplers
and/or the oscilloscope, signal path through system components, and/or overall
time skew
of the system. In some examples, the signal delay may be implemented
electrically, such
as with a tunable delay element, for example a phase shifter may be used after
the photo
detector but before the high bandwidth sampler. In some examples, such as
where signal
path length difference is negligible, the time delay correction may not be
necessary and
the delay component may be omitted.
[0078] Generally, the sampled signals may be substantially synchronized in
time and
may be measured substantially simultaneously. The phase noise difference may
be
determined and taken into account (e.g., corrected for using appropriate
calculations)
when determining the envelope of the modulated signal. The amplitude and phase
of the
envelope may be determined, and accordingly the amplitude and/or phase
modulation of
the signal. Thus, the trajectory in time of the modulated signal may be
constructed (e.g.,
using suitable calculations).
[0079] In the example of FIG. 1, the sampling by the oscilloscope may be
triggered using
a trigger signal from the AOWG. In other examples, for example where the
trigger signal
is unavailable (e.g., in long-range transmission), the trigger signal may be
derived from
the hybrid signal (e.g., using suitable calculations). The trigger signal may
be useful for
substantially synchronizing the samples in time and may allow for
determination of the
relative time point of each sample. In other examples, such as where an
oscilloscope is
not used, a trigger signal may not be required. Other methods of signal
synchronization
and/or determining the time dependence of the signals may be used.
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[0080] In some examples, the modulated signal may be periodic or aperiodic.
Where the
modulated signal is aperiodic, a suitable trigger signal related to the
modulated signal
may be used or derived from the modulated signal. For example, if the
modulated signal
is a modulated bit stream, the trigger signal may be at the symbol rate, or
the symbol rate
divided by 16, or any other suitable trigger rate.
[0081] Example equations and calculations are now discussed. These equations
and
calculations are provided to assist in understanding the disclosure, and are
not intended to
be limiting.
[0082] In the example of FIG. 1, the envelope of the optical signal from the
carrier, in
this case the laser, may be described as
[0083] E(t) = Aexp(jq$ (t)) (1)
[0084] where A is the amplitude and qõ (t) is the random process that
describes the
phase noise in the carrier. The modulated signal that is output from the
modulator and
received at the input to the mixer (in this example the optical hybrid) may be
described as
[0085] Emod (t) = M(t) exp(j(0(t) + cn (t))) (2)
[0086] where M(t) is the amplitude modulation and 0(t) is the phase modulation
from
the modulating envelope. Both M(t) and 0(t) may be periodic (e.g., bit
patterns with
repetition rates of 10 MHz in this example). In some examples, the modulated
signal may
have only phase modulation (i.e., M(t) is a constant) or only amplitude
modulation (i.e.,
0(t) is a constant). The output signal from the carrier source (LO branch)
received at the
input to the mixer may be described as
[0087] ELO (t) = B exp(j On (t - r)) (3)
[0088] where B is the amplitude and r is the time delay relative to Emod (t)
due to the
different path lengths traveled by the carrier signal and the modulated signal
(in this
example, the LO branch may be a reproduction or simulation of the carrier
signal that
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was applied to the input of the modulator). The time delay r may give rise to
a phase
noise difference, as will be described further below. In theory, it may be
possible to
reduce or eliminate the time delay between the carrier signal and the
modulated signal
arriving at the mixer, with the result that the phase noise difference may be
negligible or
zero.
[0089] In practice, it may be difficult or impossible to reduce or eliminate
this time delay.
For example, with fiber pigtailed devices (e.g., with each component path
length on the
order of meters), it may be difficult or undesirable (e.g., in a high-volume
testing
environment) to completely remove the difference in path lengths between the
signal path
of the carrier signal (i.e., the LO branch in the example of FIG. 1) and the
signal path of
the modulated signal (i.e., the modulator branch in the example of FIG. 1),
and so this
difference may be carried forward in the example analysis. For example, for a
laser
carrier source having a linewidth on the order of a few megahertz, the path
length
difference may be up to about 10 meters, giving rise to a corresponding time
delay on the
order of several nanoseconds. Other path length differences may be found in
other
systems, resulting in corresponding time delays.
[0090] The electric fields at the output ports of the hybrid may be provided
in two
components, which may be described as
[0091] Ep, (t) = Y,,modEmod (t) + YI,LOELO (t) (4)
[0092] and Ep2(t) =-jY2,modEmod(t)+Y2,LOELO(t). (5)
[0093] The different attenuations through the mixer are given by Y,,LO/mod '
where i=1
indicates the first hybrid signal and i=2 indicates the second hybrid signal,
mod indicates
the modulated signal component and LO indicates the carrier signal component.
In
general, the attenuations Y;,LO/mod may be characteristic of the mixer used
for generating
the hybrid signals, and may or may not be interrelated. In some examples, the
attenuations may be all equal.
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[0094] When the electric fields are detected, the corresponding photocurrents
to be
sampled (e.g., by the equivalent-time sampling oscilloscope) may be described
as
[0095] ipl(t) = 721, LO I B I2 +Yi modM2(t)+...
2yl,modY1,LOM(t)B x , , ,
cos(O(t) + 0, (t) - 0n (t - Z)) (6)
[0096] ' , 2W = Y2 LO I B I2 +Y2,modM 2 (t) + .. .
272,modY2,LOM(t)B X...
sin(O(t) +'b (t) - 0(t - Z)). (7)
[0097] The equations for the photocurrents may be considered to be a
superposition of
three terms. The first term may be related to the average power of the carrier
signal. The
second term may be related to the amplitude modulation (i.e., M 2 (t)) of the
modulated
signal, and the third term may be related to the electric field of the
modulated signal.
Ignoring the first two terms of equations (6) and (7), one can see that the
measurement is
of the envelope, and that the two measurements are orthogonal (or
substantially
orthogonal with a laboratory hybrid).
[0098] In some examples, the mixer may be a balanced optical hybrid, in which
case the
first two terms of equations (6) and (7) may be zero, or near zero (depending
on the
quality of the balance).
[0099] Each photocurrent may be detected using a high bandwidth sampler and a
low
bandwidth sampler. For example, detection may be carried out using a four-
channel
equivalent-time sample oscilloscope. As described above, the number of high
and low
bandwidth samplers may be more or less than two each, depending on the
application.
For example, as in conventional equivalent-time oscilloscopes, the samplers
may have
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relatively high bandwidths (e.g., 65 GHz), but relatively low real-time sample
rates (e.g.,
1000 samples per second).
[00100] In the example of FIG. 1, the output hybrid signals from the mixer may
be
split provide the separate high- and low-speed sampling modules of the
oscilloscope.
Splitting of the hybrid signals may be done using any suitable signal splitter
including,
for example, digital or analog splitters, electrical or optical splitters, and
passive or active
splitters. This signal split may be unequal, for example to provide the
sampling modules
with suitable signal-to-noise ratios and/or signal strengths, and/or split
based on the
availability of standard industry components. In this example, the first
hybrid signal,
obtained from the first port of the mixer, may be split using a 99:1 optical
splitter. The
99% portion may be detected with a high-speed sampling module (e.g., having a
bandwidth of about 65 GHz), in order to improve the signal-to-noise ratio of
the high
bandwidth samples. The 1% portion may be detected with a low-speed module
(e.g.,
having a bandwidth of about 50 kHz), for example where the signal-to-noise
ratio is not
as critical. The setup for sampling the second the hybrid signal may be
similar.
[00101] In some examples, the hybrid signals may be evenly split and provided
to
the samplers. In some examples, there may be other signal processing performed
on the
hybrid signals before being sampled by the samplers. For example, the hybrid
signals
may be amplified to improve the signal-to-noise ratio. In some examples,
suitable
calculations may be performed on the hybrid signals to correct for any known
deviations
or error characteristics of the mixer (e.g., where the outputs from the mixer
are not purely
orthogonal signals).
Determination of phase noise
[00102] The low bandwidth samples obtained by the low-speed modules may be
used to measure the phase noise difference (i.e., 0õ (t) - q$n (t - r) ). When
sampled at a low
bandwidth (i.e., a bandwidth lower than the repetition rate of the modulated
signal), the
first term in (6) and (7) may be a DC signal (i.e., the average power of the
carrier signal).
The second term in (6) and (7) may be considered as a low-pass filtered
version of the
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amplitude modulation M2 (t) . When the low-speed sampling (and hence the low-
pass
filter) bandwidth is below the repetition rate (or frequency) of the modulated
signal, the
second term may be proportional to the average power of the modulated signal.
The third
term of (6) may be proportional to a low-pass filtered version of
[00103] M(t) cos(O(t) + ¾n (t) - On (t - r)) (8)
[00104] which may be the same as,
[00105] t{M(t) exp(j (9(t) + cn (t) - 0" (t - r)))} (9)
[00106] where R is the real part of the modulated signal (i.e., the in-phase
portion). Expanding the modulation using a Fourier series yields,
[00107] 91{exp(j(Y (t)-cn(t-r)))=
Mn exp(j (2nnf t + 9n )) (10)
n=-oo
[00108] where Mn and Bn are the coefficients of the complex Fourier series,
and
f, is the repetition rate of the signal modulation. While exp(j cn (t)) may
have a
bandwidth of several megahertz depending on the carrier linewidth, for example
path
length differences (e.g., on the order of 10 m), the bandwidth of exp(j(cn (t)
- 0" (t -'r)))
may be relatively small.
[00109] FIG. 2 provides an example frequency spectrum for an example hybrid
signal. This example frequency spectrum shows the total phase modulation,
including the
phase noise difference. In the example of FIG. 2, the coefficients Mn are
depicted at
frequencies nf, , n = 0,1,2,3, and the spectrum of exp(j(0, (t) - 0" (t - r))
about each of
them. The frequency content about each of the Fourier components may be
determined
by the phase noise and the path length difference r ; a decrease in the phase
noise or path
length difference may reduce the spectral bandwidth. Typically, the larger the
r, the
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wider the spectra about nf,. Therefore, after low-pass filtering the third
term of the
photocurrent is approximately,
[00110] R{exp(j(cn(t)-O (t-z)))M0 exp(j0o)}. (11)
[00111] Since MO exp(j0o) may be a fixed constant, the frequency of the low
bandwidth samples of the real part of the hybrid signal may provide a direct
measurement
of the real part (i.e., in-phase component) of the phase noise difference of
the modulated
signal, from the frequency spectrum. Similarly, from (7), the imaginary part
(i.e., the
quadrature component) of the phase noise difference of the modulated signal
may be
measured from the frequency of the low bandwidth samples imaginary part of the
hybrid
signal. With these two measurements, the phase noise difference may be
determined and
may thus be accounted for in determining amplitude and phase of the envelope
of the
modulated signal. In some examples, where the modulated signal is aperiodic,
the
modulated signal may still have a fixed value at low frequency (such as where
the
modulated signal is an AC coupled bit stream with a DC offset added), in which
case the
phase noise difference may still be measured using the example techniques
described
here.
[00112] In some examples, such as in carrier-suppressed modulation formats, a
small imbalance in the number of ones in the bit patterns for the in-phase and
quadrature
components of the modulated signal may increase the value of MO , which may
aid the
measurement of the phase noise difference by facilitating the measurement of
the
frequency spectrum at low frequencies. In some examples, instead of a low-pass
filter, a
band-pass filter may be used to determine the phase noise difference from an
n# 0 term
in (10). In some examples, a band-pass filter may be used in addition to a low-
pass filter,
for example where redundancy is desired for error-checking purposes.
[00113] The lower limit on the repetition rate of the modulated signal, f,,
may be
determined by being able to separate the n = 0 term in (10), for example as
illustrated in
FIG. 2. For example, the repetition rate may not be so low as to allow overlap
of the
frequency spectra. For the low bandwidth samples, a high-order, low-pass
response with
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appropriate bandwidth may allow for the smallest possible values of f,. In
some
examples, such as in a fibered measurement system, thermal drift between the
signal
paths of the carrier signal and the modulated signal may contribute to the
phase noise.
[00114] Since example equivalent-time oscilloscopes may require measurement
times on the order of seconds (and possibly longer if averaging of
measurements is used),
phase noise in the system may have a detectable effect on the signal measured
by the
oscilloscope, and hence measurement of the phase noise difference, for example
as
described above, may be useful for determining the phase modulation of the
modulated
signal.
Determination of amplitude modulation
[00115] The amplitude modulation, as represented by M2(t), may be determined
by taking a plurality of amplitude measurements of the high bandwidth samples
over a
predetermined time interval. The predetermined time interval may be a time
interval
longer than a repetition period of the modulated signal, at least sufficient
for the phase
terms of equations (6) and (7) to average out to zero. The mean value, over a
period
greater than the repetition time of the modulated signal, of the third term in
the
photocurrent equations (6) and (7) is zero because the cos(O(t) + 0,, (t) - On
(t -r)) and
sin(O(t) + Yb (t) - 0, (t - a)) functions and fluctuations in cn (t) - On (t -
r) (e.g., phase noise
due to the thermal drift between the carrier signal and the modulated signal
and/or due to
inadvertent vibration of the components) has an average value of zero over a
relatively
long time interval (e.g., longer than a repetition period of the modulated
signal). By
averaging the high-speed samples obtained over the predetermined time
interval, the third
term in (6) and (7) may be zeroed out and M2(t) may be determined from the
remaining
terms (e.g., using suitable calculations).
[00116] For example, amplitude measurements of the high bandwidth samples may
be taken for 128 samples sampled from a time interval equal to two or more
repetitions of
the modulated signal. Generally, the repetition time of the modulated signal
may be
known and the appropriate time interval for averaging amplitude measurements
may be
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determined accordingly. In some examples, the respective levels of the carrier
signal and
the modulated signal contributing to the hybrid signal may be adjusted to
reduce the
contribution of the amplitude modulation terms in equations (6) and (7). In
such
examples, the amplitude modulation in these measurements may be ignored,
possibly at
the expense of an increase in measurement error.
Determination of phase modulation
[00117] Since the measured phase of the hybrid signals may include the effects
of
the phase noise difference, after the phase noise difference has been
determined (e.g., as
described above), calculations may be made to account for its effects when
determining
the phase modulation.
[00118] In some examples, such as where an equivalent-time oscilloscope is
used
to obtain high and low bandwidth samples of the hybrid signal at substantially
the same
time, time shift or skew (e.g., on the order of hundreds of picoseconds)
between the low
bandwidth samples and the high bandwidth samples may not be significant, as
the low
bandwidth samples may have relatively low bandwidths in comparison to the time
shift
(e.g., on the order of a few kilohertz). However, where there are two or more
high
bandwidth samplers, any time shift between the high bandwidth samplers may
affect the
measurements of the phase.
[00119] In the example system of FIG. 1, the skew between the high-speed
modules may be removed using two variable optical delay (VOD) lines. Removing
the
skew using post-processing software after detection may not be suitable
because the high-
bandwidth oscilloscope uses equivalent-time sampling. In an equivalent-time
oscilloscope, while the samples are plotted on the oscilloscope sequentially,
adjacent
samples are captured at different times. That is, a new sample may be captured
after each
pattern trigger (in some cases, several trigger events could be ignored while
the
oscilloscope trigger re-arms). In this example, the traces for the four
measured signals at
the oscilloscope may be obtained by using the AOWG to trigger the
oscilloscope.
Consequently, samples may be separated in time by several milliseconds even
though
they are displayed on the oscilloscope with a spacing of a few picoseconds.
After several
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milliseconds, the random phase noise difference would have changed and so the
sample
information on one channel may be no longer correlated to that on the other.
[00120] In this example, the measurement technique described above (e.g.,
using
VODs) may accommodate the sampling rate limitation caused by the re-arming
time of a
high bandwidth, sampling oscilloscope and may not be dependent on the specific
sampling rate. In some examples, other methods of matching the sampling to a
time point
may be used instead of a trigger signal.
Determination of in phase and quadrature components
[00121] With the determination of the phase noise difference terms
(cos(On (t) - On (t - r)) and sin(On (t) - cn (t - r)) ), the determination of
the intensity
modulation M 2 (t) , the skew removed from the high-speed modules, and
suitable
calibrations to determine the attenuation through the optical hybrid, the
amplitude and
phase of the in-phase and quadrature of the modulating envelope may be
determined at
any sampling instance displayed on the oscilloscope. Any suitable calculations
may be
used. For example, equations (6) and (7) can be considered as a system of two
equations
in the two unknowns M(t) cos(O(t)) and M(t) sin(9(t)), and may be solved
accordingly.
[00122] In some examples, the levels of the carrier signal and modulated
signal
contributing to the hybrid signal may be adjusted so that measurement of the
intensity
modulation may not be necessary. In such examples, not measuring the intensity
modulation may contribute a relatively small measurement error which may be
acceptable, depending on the application.
Further processing
[00123] In some examples, there may be further processing or calculations of
the
determined envelope. For example, the system or parts of the system may be
known to
introduce errors. This may be determined by calibration of the system and/or
its parts
prior to receiving the modulated signal. For example, through calibration, the
mixer may
be known to generate unbalanced hybrid signals, such that rather than each
output hybrid
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signal being described purely by a respective one of equations (4) and (5),
each hybrid
signal is described by an algebraic combination of equations (4) and (5). In
another
example, through calibration, the samplers may be known to have attenuation at
certain
frequencies. When such error characteristics are known, they may be corrected
for using
suitable post-processing calculations on the determined envelope.
Alternatively, such
corrects may be carried out on the high and low bandwidth samples prior to
determination of the envelope.
Characterization
[00124] In some examples, the disclosed systems and methods may be used to
characterize system components, such as the carrier source and/or the
modulator.
Characterization may include comparing the obtained results to desired or
intended
results. Calculations may also be made to determine the noise or variance of
components,
such as the carrier source, for example as described below.
[00125] The low bandwidth samples may be summed to form the complex process,
[00126] MO exp(j 00) exp(j(woro))exp(jAcõ (t, r)) (12)
[00127] where Mo and 00 are the coefficients of the complex Fourier series for
the periodic modulation, coo is the optical center frequency of the laser, z
is the delay (in
time) between the carrier and modulated signal branches, and Acb (t, z) = 0,
(t) - 0" (t - z)
is the random process for the laser phase noise difference. In this example,
the first
exponential does not vary with time. The second exponential in this example
varies
slowly (e.g., due to temperature variation which may cause differential
expansion and
contraction of the fibers, and/or drift of the center frequency). Both of
these may be
assumed to be changing very slowly and may be tracked by the detectors.
[00128] An example statistical description of the last term involving the
laser
phase noise difference may be found in [10]. For small bandwidth detectors the
random
process may be low-pass filtered and replaced by its expectation, which is a
real number
with an angle of zero. This means that the high-speed measurements may have an
error
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associated with the angle which is approximately given by Aq5 (t, z) . The
error may be a
zero-mean random process, which may allow for averaging of the measured
points. The
variance of the error may be a function of the laser linewidth and path length
difference,
which may be described as
[00129] < 0O,2jz) >= T2 ,,, = OLP1 2nftiõ (13)
vg
[00130] where fl,, is the full-width half-maximum linewidth (in Hz), ALP, is
the
path length difference, and vg is the group velocity of light in the fiber.
[00131] For an example carrier source, such as a tunable, external cavity
laser with
a linewidth of 100 kHz, a path length difference of 10 m may yield a variance
of error of
about 0.01 7r.
Example studies
[00132] An example study implementing an example of the systems and methods
described above is now disclosed. This example is for the purpose of
illustration only and
is not intended to be limiting.
[00133] In this example, an arbitrary optical waveform generator (AOWG) (for
example as described in [11]) may be used to generate a 20 Gb/s quadrature
phase-shift
keying (QPSK) signal using a single dual-drive Mach-Zehnder modulator (for
example as
described in [12]). This example setup may require multi-level signals to
drive the
modulator. In this example, the AOWG may include an optical modulator driven
by high-
speed electrical signals from a two-channel arbitrary pattern generator. The
arbitrary
pattern generator may have a sampling rate of 20 GSample/s and 6-bit digital-
to-analog
converters. This may allow for the independent control of the magnitude and
phase of the
output signal from the modulator, and thus for the generation of arbitrary
optical
waveforms. In this example, the linewidth of the external cavity laser was 100
kHz. The
delay r was about 0.5 ns; the optical components in the interferometer were
measured
and a suitable patch cord was used to obtain a path length difference of less
than 10 cm.
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In this example, variable optical delays with delays of 50 ps may be used to
remove the
skew between the high-speed modules.
[00134] For an example dual-drive Mach-Zehnder modulator biased at extinction
and peak-to-peak RF drive voltages of V,t, the accessible region of the
complex plane is
shown by the gray shaded region in FIG. 3 for an example 20 Gb/s QPSK signal
obtained
with the example dual-drive Mach-Zehnder modulator.
[00135] V is the voltage required to change the phase of the signal in an arm
of
the modulator by 7r radians. During one symbol (e.g., of duration 100 ps), the
first
sample generated may correspond to the electric field associated with the
symbol. In this
example, the second sample was used to shape the signal trajectory in
accordance with
the constraint indicated in FIG. 3. To select the value for the second sample,
the next
symbol was examined to determine the necessary transition. For a repeated
symbol, the
second sample was a repeat of the first. For horizontal and diagonal
transitions (in this
example, (0,1) to (1,1) or (0,0) to (1,1)), the second sample was set to the
origin. For
vertical transitions (in this example, (1,0) to (1,1)), the second sample was
set to
0.5 + j0. Simulation results for the signal trajectory are also shown in FIG.
3. In this
example, the digital-to-analog conversion causes the RF drive voltages to
occasionally
exceed V,r , in which case the optical field extends outside the gray shaded
region.
[00136] An example of the measured trajectory for the 20 Gb/s QPSK signal
obtained with the dual-drive Mach-Zehnder modulator of this example, with a 29
symbol
sequence, is shown in FIG. 4 in the complex plane.
[00137] Since ideal QPSK is carrier suppressed (i.e., MO = 0), in this example
the
number of ones for the I channel was 266 and the number of ones for the Q
channel was
245. The non-ideal responses of the digital-to-analog converters and drive
amplifiers may
lead to a pattern dependence in the multi-level drive signals. This may cause
the broad
rails in the eye diagram, which maybe consistent with the signal trajectory
shown in FIG.
4. In this example, the setup may be stable, and so averaging of signals over
a plurality of
signal repetitions may be applied to the trajectories to reduce the impact of
oscilloscope
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noise. An example of the measured in-phase signal is shown in FIG. 5 for seven
symbol
periods with and without averaging (in this example, of 128 traces).
[00138] In another example study, an example AOWG was used to generate a
phase modulated signal with a normalized envelope of
[00139] E(t) = exp(j/3cos(2nfmodt)) (14)
[00140] where /3 is the phase modulation index (in this example set to 1.9 to
demonstrate the measurement), and fmod is the frequency or repetition rate of
the signal
modulation (in this example 10.7 GHz, which is half of the sampling rate). In
this
example, the phase modulated signal has spectral content above 10 GHz, and so
the high-
speed sampling modules with bandwidths of 65 GHz were useful for the
measurement.
An example measured trace for the example signal is shown in the complex plane
in FIG.
6. From the time domain data, the corresponding optical spectrum may be
calculated and
an example is shown in FIG. 7. The frequency resolution of this example
technique may
be dependent on the pattern length captured. For the example result in FIG. 7,
the
resolution is approximately 20 MHz. The example calculated optical spectrum
was found
to be in relatively good agreement with the example measured optical spectrum
illustrated in FIG. 8 (in this example, with a resolution bandwidth of 0.01
nm).
Applications
[00141] The disclosed methods and systems may be useful for decoding or
characterizing suitable modulated signals or modulating envelopes. Such
signals may be
a phase-shift keying (PSK) signal, for example a quadrature PSK signal, a
binary PSK
signal, a differential PSK signal or a higher-order PSK signal. Although in
some
examples the modulated signal may have in-phase and quadrature components, in
other
examples, other types of modulated signals may be used. For example, other
types of
modulated signals that may also be determined using the disclosed methods and
systems
may include amplitude modulated (AM) signals, frequency modulated (FM)
signals, and
quadrature amplitude modulation (QAM) signals, among others.
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[00142] The disclosed methods and system may be useful where the signal has a
relatively fast repetition rate, such as in optical signals or electromagnetic
signals. For
example, the signal may be obtained from optical clock pulse sources, for
example
having repetition rates in the range of about 10 GHz to about 40 GHz.
[00143] The disclosed methods and systems may also be useful for
characterization of modulators and/or carrier sources. For example, a
modulator may be
used to encode a known or desired pattern in the modulated signal, and the
resultant
envelope of the modulated signal, as determined using the disclosed methods
and
systems, may be compared to the desired pattern. Any suitable modulator may be
characterized in this manner, including, for example, a Mach Zenhder modulator
or an
electro-absorptive modulator. The modulator may be made of any suitable
material
including, for example, gallium arsenide (GaAs), indium phosphide (InP), or
lithium
niobate (LiNBO3). The modulator may be any suitable modulator, including
modulators
for optical signals or electromagnetic signals, digital or analog modulations,
or any other
modulators of interest. Characterization of modulators and/or carrier sources
may be at
least partly based on determination of the phase noise difference.
[00144] As explained above, calculations may also be made to characterize
system
components based on determinations of noise or variance.
[00145] Example methods and systems have been described and demonstrated for
measuring the envelope a modulated optical signal, based on high- and low-
bandwidth
sampling. In some examples, the disclosed methods and systems may make use of
the
high-bandwidth available with an equivalent-time sampling oscilloscope. The
use of
equivalent-time oscilloscopes may be useful over conventional real-time
oscilloscopes
because equivalent-time oscilloscopes may be able to take samples at a higher
equivalent
rate and thus able to directly detect higher bandwidth signals without being
limited by the
real-time speed of the oscilloscope. However, the disclosed methods and
systems may be
used with both equivalent-time oscilloscopes (e.g., for faster signals) as
well as real-time
oscilloscopes (e.g., for slower signals).
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[00146] Although certain example oscilloscopes have been described, the
disclosed methods and systems may be performed by any one or more suitable
components capable of obtaining the low bandwidth and high bandwidth samples,
which
may include other types of oscilloscopes and non-oscilloscope components.
Other types
of suitable oscilloscopes may include, for example, any oscilloscope having at
least four
input ports having at least two ports capable of high bandwidth sampling and
at least two
ports capable of low bandwidth sampling. In some examples, the samplers used
to obtain
low bandwidth samples may also be capable of high bandwidth sampling. In some
examples, low-speed sampling modules may be used for the low bandwidth
samplers
since they may be less costly than high-speed sampling modules.
[00147] In some examples, from the measured results, the complete electric
field
modulation (e.g., including the in-phase and quadrature components) may be
determined
as the signal trajectory in time. Although the disclosure describes certain
signal
bandwidths, the methods and systems of the present disclosure may be extended
to higher
bandwidths (e.g., by using higher quality or faster components).
[00148] The disclosed systems and methods may be useful for measurement of
high-speed optical signals, for example in research, development and/or
manufacturing
environments. The disclosed systems and methods may be used to augment
commercially
available oscilloscopes.
[00149] The present disclosure also discloses computer program products and
computer readable storage media (e.g., CDs, hard disks, RAM or ROM memories,
etc.)
that embody computer executable instructions that may be executed by a
processor to
carry out the disclosed methods. The present disclosure also discloses
computer signals
that may cause a processor to carry out the disclosed methods.
[00150] The embodiments of the present disclosure described above are intended
to be examples only. Alterations, modifications and variations to the
disclosure may be
made without departing from the intended scope of the present disclosure. For
example,
one or more of the example components described above may be replaced with one
or
more other suitable components. Functions of one or more of the example
components
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described above may be combined into one suitable component or divided into
multiple
suitable components.
[00151] In particular, selected features from one or more of the above-
described
embodiments may be combined to create alternative embodiments not explicitly
described. All values and sub-ranges within disclosed ranges are also
disclosed. The
subject matter described herein intends to cover and embrace all suitable
changes in
technology. All references mentioned are hereby incorporated by reference in
their
entirety.
References
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Winzer,
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[00153] [2] P.A. Williams, T. Dennis, I. Coddington, W.C. Swann, N.R.
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