We present a novel method to measure the chromatic dispersion of fibers with lengths of several kilometers. The technique is based on a rapidly swept Fourier domain mode locked laser driven at 50kHz repetition rate. Amplitude modulation with 400MHz and phase analysis yield the dispersion values over a 130nm continuous wavelength tuning range covering C and L band. The high acquisition speed of 10µs for individual wavelength-resolved traces Δt(λ) can reduce effects caused by thermal drift and acoustic vibrations. It enables real-time monitoring with update rates >100Hz even when averaging several hundred acquisitions for improved accuracy.
© 2009 Optical Society of America
Optical fibers represent the backbone of today’s long haul telecommunication network. Besides the specific attenuation over length, the fiber’s chromatic dispersion is one of the most important properties. Typically, the chromatic dispersion is quantified by group velocity dispersion (GVD) and GVD slope. In order to avoid temporal washout of the transmitted bit-pattern, the chromatic dispersion has to be minimized such that all wavelength components of the transmitted optical signal channel arrive at the detector simultaneously. Often, a balanced sequence of standard single mode fiber and special dispersion compensation fiber (DCF) is used to realize optical links of many km with minimum dispersion. A central issue is to measure dispersion values for these long lengths of fiber. Apart from telecom applications, there is high interest in measuring and minimizing fiber dispersion on a km scale for the recently developed Fourier domain mode locked (FDML) lasers . In these rapidly wavelength swept laser sources, a several km long fiber delay is used to synchronize the optical roundtrip time with the tuning period of a narrowband intra-cavity tunable bandpass filter. It has been shown that minimized dispersion improves performance , in particular the instantaneous coherence length. As these lasers have already proven superior performance in many biomedical imaging [3–6] and sensing applications [7, 8], a further improvement of their characteristics may even extend their field of applications. An accurate measurement of the net dispersion of the km long fiber cavity in the FDML laser is crucial to optimize these sources .
While for short fiber lengths up to several meters, dispersion is usually measured using interferometric methods [9, 10], a number of different dispersion measurement techniques have been developed for long fibers in the km range. These include a variety of time-of-flight as well as phase shift methods [11–16] which measure the timing deviation at several distinct wavelengths step-by-step or provide continuous tuning merely over a GHz range . In contrast, the time-of-flight method  acquires a whole dispersion trace Δt(λ) at a time using comb-shaped supercontinuum pulses but it is limited to monotonic spectral behavior and hence cannot measure near the zero dispersion wavelength. However, most telecom and FDML laser applications require the use of small dispersion values around a dispersion zero. Ref . presents an approach for km long fibers using a phase modulator in a Sagnac interferometer. This “rapid, cost-effective measurement” takes less than 30s to measure the dispersion over a wavelength range of 185nm centered around 1530nm and is especially interesting because of its overall cost efficiency. In this Letter, we present a novel dispersion measurement technique which is more than 3 orders of magnitude faster than the approach described in : We measure over a continuous tuning range of more than 130nm (including C and L band) in typically 10µs, resulting in an update rate of ~200Hz when several hundred wavelength sweeps are averaged for improved accuracy. This ultra-rapid dispersion measurement technique can measure across zero dispersion without difficulty and is, depending on the desired accuracy, ideally suited for fiber spans >~1km which may include optical amplifiers like semiconductor optical amplifiers (SOAs). The high acquisition speed makes the method robust against changes in fiber length, similar to the method shown in , so that the impact of thermal drift and acoustic vibrations is suppressed.
2. Ultra-Rapid dispersion measurement method
2.1. Experimental setup
We present a new chromatic dispersion measurement technique based on an FDML rapidly wavelength-swept laser which measures 50,000 complete wavelength-resolved dispersion traces Δt(λ) per second over a range of more than 130nm. Individual measurements are averaged for improved accuracy.
Figure 1 shows the setup for ultra-rapid dispersion measurement, including the FDML laser. The laser is operated at a center wavelength of ~1550nm and a total sweep range of ~150nm. The cavity of the laser consists of ~3.6km standard single mode fiber (SMF, OFS AllWave ZWP) resulting in a sweep repetition rate of f FDML~56kHz. A Fabry-Perot tunable filter (FFP-TF, LambdaQuest LLC) is driven by one channel of an arbitrary waveform generator (AWG, TTi TGA12104) synchronously to the optical roundtrip time. A semiconductor optical amplifier (SOA, Covega) is used as gain medium, the current from the laser diode controller (LDC; WL-LDC10D, wieserlabs.com) can be arbitrarily modulated by the phase locked second channel of the AWG. This way, the SOA is switched off during the backward sweep (long to short wavelength), so that only the forward sweep (short to long wavelength) remains . Two isolators (ISO) in the ring ensure uni-directional lasing. Polarization controllers (PC) are used to optimize the gain in the SOA. 70% of the light is extracted from the cavity by a fused fiber coupler (70/30), providing an average FDML laser output power of 13mW. 5% of that light is fed into an optical spectrum analyzer (OSA, Yokogawa AQ6370), the other 95% pass a λ/2 waveplate to adjust polarization, followed by a LiNbO3 electro-optic modulator (EOM; Lucent 2623na). After the EOM, the light is coupled into a 1GHz photo diode (PD, WL-PD1GA, wieserlabs.com). The fiber under test is inserted with fiber connectors between the EOM and the PD. The EOM is used to modulate the transmitted light intensity at a frequency of 440MHz which is detected by the PD and sampled with a real time oscilloscope (Osci, Tektronix DPO7104) set to 16x averaging, 500MHz bandwidth and a sampling rate of 5GS/s. The oscilloscope is triggered from the sync output of the AWG each time an FDML sweep starts so that a fixed relationship between time and wavelength is obtained. In order to benefit from averaging in the oscilloscope, the modulated intensity waveform at ~440MHz has to be phase-locked to the wavelength sweeps as well. This is accomplished via a home-built phase-locked loop (PLL) which multiplies the incoming 56kHz roundtrip frequency by a factor of n PLL=7900. The PLL output is fed into a power amplifier (PA; Mini-Circuits ZHL-6A) followed by a 3dB attenuator to drive the EOM.
2.2 Spectrally resolved propagation time measurement
The ultra-rapid dispersion measurement method directly measures the difference in propagation time for different wavelength components by observing the FDML sweep compression or stretching within the fiber. This is done by modulating the intensity of the FDML wavelength sweep with a sinusoidal 440MHz radio frequency (RF) signal as described above. After acquisition in the oscilloscope, the accumulated RF phase is computed both, for the reference signal, i.e. the signal without the test fiber, and the measurement signal, i.e. the signal with the test fiber inserted. To extract the phase ϕ over time, a fast Hilbert transform H and successive phase unwrapping is used:
For light at a wavelength λ, the propagation time difference with and without the fiber under test can be calculated in the following way: First, λ is mapped to a sample time t(λ) of the reference signal via a wavelength calibration described below. At this time t(λ), the reference phase value of the Hilbert transform is directly evaluated via interpolation between nearest samples. Now, the time t’(λ) at the same phase value of the Hilbert transform in the measurement signal is found via interpolation: The time difference Δt(λ)=t’(λ)-t(λ) is the propagation time difference of the spectral component λ through the fiber under test plus a constant offset which is irrelevant for dispersion measurements.
2.3. Wavelength calibration
A wavelength calibration step is required to map time to wavelength. To achieve high accuracy, we chose to obtain the wavelength calibration data by modulating the intensity of the laser with the AWG by modulating the diode current of the laser. We drive the SOA with a comb of 20 spikes per sweep instead of the rectangular waveform. Due to the laser driver’s high analog bandwidth in the MHz range, we can achieve 70ns full width at half maximum (FWHM) peak width of the SOA current resulting in an even smaller optical pulse FWHM. These spikes are visible in the OSA and in the oscilloscope with excellent signal-to-noise ratio and show a precise correlation between time and wavelength (see Fig. 2 ). After setting suitable noise threshold levels and the sweep direction, the calibration works fully automatic by acquiring one OSA trace and an averaged oscilloscope trace. The acquisition software detects all peaks with a center-of-gravity measurement and performs a third order spline interpolation to obtain λ(t). For future low cost systems, a series of several FBGs or the application of a gas vapour absorption cell for calibration could be envisioned. This wavelength calibration is acquired once before the actual dispersion measurement without test fiber inserted and takes a few seconds, limited by the sweep duration of the OSA.
An alternative approach using the EOM to modulate features onto the spectrum and measure those with the oscilloscope and the OSA was dismissed due to poor signal-to-noise ratio in the OSA, making automatic peak detection over the whole sweep range difficult.
Although this method could theoretically provide better wavelength resolution, we found that the LDC modulation method is sufficient for the presented system since in our case, the wavelength accuracy is mainly limited by a slow center wavelength drift of the FDML laser.
3.1. Chromatic dispersion measurements: Error estimation by comparison to literature values
For the actual dispersion measurement, the oscilloscope is operated at 5GS/s sampling rate, yielding about 5×104 samples per FDML sweep. The sampled data is decimated (with averaging of neighboring points) by a factor of 16 to 64 so that a wavelength resolution of ~0.1nm/sample is obtained. To reduce temporal jitter, 16 wavelength sweeps were averaged inside the oscilloscope, yielding a theoretical update rate of ~3kHz. Due to limitations, mainly in the data transmission between oscilloscope and computer, as well as inefficient numerical data analysis, our setup was only able to update the wavelength-resolved dispersion measurement with ~1Hz. For the measurements shown here, 16 oscilloscope acquisitions were averaged in the computer resulting in a theoretical update rate of ~200Hz.
Figue 3 (left) shows propagation time difference graphs Δt(λ) obtained with the presented ultra-rapid dispersion measurement method for different fibers. Each trace consists of >2000 samples (decimation factor 16). One of the analyzed fibers, Corning SMF 28, is specified with a zero dispersion wavelength (ZDW) λ 0 of 1302nm to 1322nm and a zero dispersion slope S0≤0.092ps/nm2/km with a typical value of 0.087ps/nm2/km. Using the equation
The values also agree with those presented in earlier publications : reported 16.58ps/nm/km for 1km and 16.25ps/nm/km for 3km fiber measured with the Sagnac interferometer method and 16.65ps/nm/km obtained via the phase shift method from .
3.2. Chromatic dispersion measurements: Error estimation by comparison to values using an independent method with the same fiber samples
The comparison of our measurements to literature values, described in the previous section, can be used as fully independent method to give an upper limit for systematic error. However, since the dispersion values of a specific fiber type vary within their specifications, we measured the same pieces of fiber with different methods for comparsion.
For this verification, the results obtained with the presented ultra-rapid dispersion measurement technique have been compared to direct measurements of the signal propagation time for different wavelengths. This technique is much slower, but it serves as a reference to identify potential systematic errors. A self-developed pulse generator triggered from the AWG and directly attached to the EOM (replacing PLL and PA in Fig. 1) generates an optical pulse of <1ns length. The wavelength of this pulse is chosen by adjusting the pulse generator trigger time relative to the FDML sweep start. After the EOM, the signal is split in a 50/50 fused coupler and fed into the OSA for wavelength measurement and the photodiode for time measurement. The PD signal is acquired at 10GS/s (interpolated time) and averaged 64 times in the oscilloscope. The time of flight is measured by fitting a Gaussian curve into the intensity peak and averaging the peak position over a couple of acquisitions. The direct measurement of propagation time for different wavelengths is much slower and suffers from poor signal to noise ratio in the OSA due to the short duty cycle of <10−4. However, it provides direct access to optical signal propagation time for comparison and to identify potential systematic errors in the ultra-rapid dispersion measurement setup.
Several comparative measurements using this “pulse method” were obtained for 6km DSF and for 4km SMF. Each time, roughly a dozen different wavelengths were selected and directly measured in the OSA using center-of-gravity peak detection above a manually chosen threshold. At the same time, the signal propagation time was measured in the oscilloscope. These measurements are shown as data points in Fig. 3 (left) and are in very good agreement with the results of the presented “ultra-rapid dispersion method”. After taking several successive pulse measurements, we found that the discrepancy between these pulse measurements is as high as the discrepancy between the “pulse method” and the “ultra-rapid method”: In case of 4km SMF, the RMS deviation is about 15ps, in case of 6km DSF only 3ps. The smaller error in the DSF case shows that the uncertainty originates from the residual errors in the wavelength measurement and not from the time measurement. Due to more than 10 times higher dispersion D of the SMF compared to the DSF, errors during the wavelength measurement contribute much more to the overall discrepancy in the SMF case. This finding should be underlined insofar, as many dispersion measurement techniques are limited by the timing (or phase) measurement error and therefore they have a smaller relative error for very long fibers with high dispersion. The ultra-rapid dispersion measurement setup presented here exhibits an error characteristic which is not as strongly dependent on the total dispersion. It can be applied for a wider range of dispersion values with similar (relative) accuracy.
3.3. Chromatic dispersion measurements: Error values for different fiber lengths and different amounts of fiber dispersion
In order to investigate the robustness and the repeatability of the ultra-rapid dispersion method, several measurements with different fiber lengths, different FDML sweep ranges and speeds were compared. Figure 4 (left) shows the difference in ps/km between two measurements of DSF. The first measurement setup (called S1) used an FDML sweep range of 153nm and a central wavelength of 1551nm and was applied to 2km fiber. The system was then switched off over night. The second measurement setup (S2) was performed the next day with a sweep range of 170nm (resulting in 11% higher wavelength tuning speed) and a central wavelength of 1547nm and was applied to 6km of the same fiber. The RMS deviation of the two measurements is <0.6ps/km (it would be completely invisible in Fig. 3).
In a similar fashion, the setup S1 was used to measure 50km SMF on one day, and on the next day, the setup S2 was used to measure 1km, 4km and two times 50km SMF. The difference between the result from S1 and those from S2 can be seen in Fig. 4 (right). The RMS deviation is 0.3 to 0.4ps/km except for the 1km case with 0.8ps/km. The baseline noise when measuring no fiber at all is 0.75ps RMS (Fig. 3, right). As stated above, all these measurements were made by averaging 256 FDML sweeps (16 times in the oscilloscope, 16 times in the computer). The 16 oscilloscope traces averaged in the computer exhibited a trace-to-trace standard deviation of 1.5ps for the baseline measurement as well as for fiber lengths 1km and 4km, and 3ps in case of 50km SMF.
Above ~4km, the difference between the measurements in ps/km does not scale inversely with the fiber length but merely smoothes out. This, and the different shape of curves (C) and (D) in Fig. 4 indicate that above ~4km, the deviation is dominated by errors in the wavelength measurement (smooth 3rd order interpolation between 20 distinct measurement points) rather than in the measurement of the propagation time (RF phase). The problem with the wavelength recalibration in our case was caused by a slight drift of the FDML laser sweep range. Even after warm-up, this wavelength drift of the FDML laser introduces a measurement error of ~0.3ps/km for SMF within 15 minutes, and therefore most measurements were made within 15 minutes after the previous calibration. We expect an even better error performance of the presented ultra-rapid dispersion measurement using an active stabilization of the FDML laser.
We estimated the maximum achievable accuracy, i.e. the minimum baseline noise (Fig. 3), of the demonstrated setup by successively increasing the number of averaged traces. Even for substantially more than 256 traces, the error converged to roughly ~0.5ps, depending on various parameters like applied power, relative intensity noise of the FDML laser etc. This value of time accuracy translates to a minimum length of ~50m of SMF, if the GVD should be measured with 1% accuracy. This theoretical accuracy can be achieved at ~100Hz. The fiber under test should be long enough to generate an amount of dispersion such that the propagation time difference is sufficiently higher than the baseline noise.
Hence, in most practical cases, the presented technique will be ideally suited for medium to very long lengths of fiber, where classical interferometric detection becomes difficult to implement and where sufficient propagation time difference accumulates. Typically this would be from ~1km to >50km.
Comparing these results to literature values, it can be seen that the ratio of accuracy per measurement time is orders of magnitude better than comparable techniques. On the one hand, this potentially results in improved accuracy, if many of these measurements are averaged. On the other hand, the fast acquisition speed of the ultra-rapid dispersion measurement technique minimizes errors due to thermal fluctuations and other slowly varying error sources allowing true real-time monitoring of fiber dispersion. The method could potentially be improved by use of a higher modulation frequency for increased phase accuracy and by use of a polarizing beam splitter and a Faraday rotation mirror as in  to effectively double the fiber length. The application of an FDML laser with stabilized center wavelength may further increase the accuracy.
In conclusion we presented a novel setup to measure chromatic dispersion of long fibers over a wide and continuous wavelength range. A thorough analysis and estimation of the error is provided by comparison of the measurement results to literature values and by comparing the method to measurements with an independent and different technique using the same fiber samples. We show that, compared to other techniques described in literature, the measurement time of the ultra-rapid dispersion measurement setup is orders of magnitude faster at comparable or even improved accuracy. The high measurement speed makes the method robust against thermal fiber length drift. The technique can potentially be applied anywhere, where high speed dispersion measurement is desired, like in process control of fiber production, real-time monitoring of optical networks, trimming and fine tuning of dispersion compensation modules and dispersion critical optical setups etc. The method can measure through fiber amplifiers (SOAs) and operates both on highly dispersive fibers like DCF as well as near zero dispersion. Since individual traces are acquired at a rate of 50kHz, the measurement update rate can easily be increased beyond the presented 200Hz by sacrificing the resulting accuracy.
We would like to acknowledge support from Prof. W. Zinth at the Ludwig-Maximilians-University Munich. This research was sponsored by the Emmy Noether program of the German Research Foundation (DFG - HU 1006/2-1) and the European Union project FUN OCT (FP7 HEALTH, contract no. 201880).
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