Direct measurement of constellation diagrams of optical sources

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    Direct measurement of constellation diagrams of optical
                                           C. Dorrer, J. Leuthold and C. R. Doerr
                          Bell Laboratories-Lucent Technologies, 101 Crawfords Corner Road, Holmdel, NJ, 07733
                                   Phone: 732-332-6463, Fax: 732-949-2473, email:

         Abstract: We present the first temporal diagnostic that measures statistical information on both
         the intensity and phase of data-encoded channels. Experimental characterization of differential-
         phase shift keyed signals at 10 Gb/s and 40 Gb/s is presented.
         2004 Optical Society of America
         OCIS codes: (320.7160) Ultrafast technology, (060.5060) Phase modulation

1. Introduction
Eye diagram measurements are commonly used to assess statistical information on an optical communication
channel for example to track impairments such as amplified spontaneous emission or dispersion. Such eye diagrams
are composed of samples of the temporal intensity, and can be measured directly if a photodetector and electronic
sampling circuits with bandwidth comparable to the bandwidth of the pulses of the source under test are available.
Samples of the temporal intensity of an optical source can also be measured using nonlinear optical sampling
techniques, i.e. by implementing a temporal gate using the nonlinear interaction of a short optical pulse with the
source under test, or using high-speed modulators, and these approaches have extended the measurement of eye
diagrams to bandwidth that cannot be obtained using electronics [1]. Eye diagrams are particularly useful for sources
with on-off keying data modulation. However, they do not contain any phase information, and none of the
techniques mentioned previously allow the measurement of samples of the phase of the source under test. With the
increasing use of phase-encoding, such as differential phase shift keying (DPSK),[2] there is a need for a technique
that can gather samples of the temporal phase of an optical source that could, for example, be used to optimize a
data-encoder or to directly track noise on the data stream, without having to perform demodulation of the source.
         We demonstrate that the linear interference of the source under test with a train of sampling pulses can be
used to obtain not only intensity information, as was demonstrated previously in linear optical sampling [2], but also
phase information about the source under test. A simple setup and various processing operations can be used to
obtain a complete constellation diagram of the source. Experimental demonstrations are performed on various 10
Gb/s and 40 Gb/s DPSK signals.
2. Theoretical analysis
Let us consider a waveform under test E D (t ) and a copolarized train of sampling pulses with period T. As depicted
in Fig. 1a, the sampling pulses have identical electric fields excepted for a constant phase ϕN of pulse N that
describes the offset between the envelope of the electric field (its slowly varying component) and the carrier (its
quickly varying component, with a period around the optical cycle of the source). The variations in the phase ϕN
arise for example because of the difference between the group and phase velocities in the laser cavity of a mode-
locked laser [3]. In general, for a steady state system, the relative phase between successive pulses is an unknown
constant, but environmental changes lead to non-controlled variations in this relative phase. The field of the
sampling source is therefore the sum of the fields E S (t − NT ) exp(iϕ N ) , where E S is the electric field common to
all the sampling pulses.
          A phase-sensitive interference of the waveform under test with each of the sampling pulses can be
measured with balanced detection of the combined sources using detectors with bandwidth much smaller than the
bandwidth of the source under test, but larger than the repetition rate of the sampling source, leading to the
collection of samples:
                     [∫           *
         S R, N = Re E D (t ) ⋅ E S (t − NT )dt exp(−iϕ N )    ]                                                 (1)
A simultaneous measurement of the orthogonal quadrature can be performed using an identical setup with the
introduction of a relative π/2 phase shift between the two sources, leading to:
                     [∫            *
         S I , N = Im E D (t ) ⋅ E S (t − NT )dt exp(−iϕ N )   ]                                                 (2)
The two collections of samples can be combined to calculate

          S N = S R , N + iS I , N = E D (t ) ⋅ E S (t − NT )dt ⋅ exp(−iϕ N )                                                             (3)
The samples SN of Eq. 3 directly depend on the relative phase between the two sources, and it therefore appears that
the train of sampling pulses could act as a phase reference under the assumption of sufficient correlation of the
phases of the sampling pulses over the measurement time. Optimally, a sampling pulse with flat spectral density and
phase      over        the        spectral   support     of         the   source      under        test      leads to
         ~        ~*                                    ~
      ∫                                                          ∫
 S N = E D (ω ) ⋅ E S (ω ) ⋅ exp(iNωT )dω exp(−iϕ N ) = E D (ω ) ⋅ exp(iNωT )dω exp(−iϕ N ) , and therefore:
          S N = E D (nT ) exp(−iϕ N )                                                                         (4)
    Therefore, under optimal conditions, the samples directly represent the instantaneous value of the electric field of
the source under test up to the set of constants ϕN. Such sensitivity to the phase of the source under test remains
provided that the sampling pulses have a bandwidth similar to that of the source under test. However, the presence
of the phases ϕN randomizes the phase of the samples of Eq. 3 and 4, as can be seen in Fig. 1b that displays the
samples SN measured on a 10 Gb/s DPSK signal in the complex plane. As in the optimal case the phase difference
between successive sampling pulses is a constant, the phase difference between successive measured samples can be
calculated. Such phase difference is representative of the various phase shifts between data pulses in the source
under test. The phase samples corresponding to a single level can be fitted using a slowly varying function in order
to remove the drift of the phase difference between successive samples pulses (this operation is made possible by the
sufficient mutual coherence of the two sources over the measurement time). This leads to new samples ΣN, which
are representative of the phase difference between pulses in the waveform under test. Additional concatenation of
the phase of these new samples, after the removal of the drift of the phase of the sampling pulses can also be
performed as a final step. The samples obtained from Fig. 1b after processing are displayed on Fig. 1c, and the two
phase level separated by π are clearly visible.

          Fig. 1. (a) Representation of the electric field of the train of sampling pulses. The three successive pulses have a different
          envelope-carrier offset, as can be seen on the relative position of the envelope (dashed line) and phase (continuous line).
          (b): constellation diagram of the samples measured by the diagnostic on a DPSK signal before processing. (c) Constellation
          diagram of the samples of Fig.1b after processing.

3. Experimental implementation
Our experimental implementation (Fig. 2) uses a waveguide structure (labeled as hybrid) to combine the source
under test and the sampling source in order to obtain two pairs of combined fields that are used to measure the
quadratures of Eq. 1 and 2 using two balanced detectors (BDA and BDB). The angle between the two quadratures is
set to π/2 via the voltage controlled thermo-optic phase shifter. The quadratures are measured with an analog-to-
digital conversion board (A/D) synchronized to the sampling pulses with a slow photodiode and a pulser. The
requirement on the slow drift of the relative phase between successive sampling pulses is easily met, even with the
non-stabilized passively mode-locked 10-MHz fiber laser that we used. As can be seen in Fig. 2, which displays the
intensity of the samples given by Eq. 3 and the relative phase between successive samples for a 10 Gb/s DPSK
signal, no intensity encoding is performed; but the relative phase between successive samples can take two values
separated by π. Note the slow fluctuation of each level on Fig. 1c. Removal of the slow drift on the phase around the
maximum of the intensity yields constellation diagrams similar to Fig. 1c.

          Fig. 2. Setup for the direct characterization of the instantaneous value of the electric field of a source under test (left),
          intensity of the samples SN and relative phase between successive samples SN for a 10 Gb/s DPSK signal.
4. Experimental results
The direct characterization of phase-encoded signals was first tested on 10 Gb/s phase-encoded signals generated
using a pulse carver based on a LiNbO3 Mach-Zehnder modulator (MZM) followed by a data-encoder either based
on a LiNbO3 phase modulator or an x-cut LiNbO3 MZM. The phase modulator allows encoding of various phase
levels but the noise on the drive voltage induces noise on the encoded phase. On the other hand, a MZM biased at
extinction generates noiseless phase shifts exactly equal to π, but the noise on the drive voltage induces intensity
noise [4]. Without phase encoding (Fig. 3a) the samples ΣN have identical phase. As is clearly visible on Fig. 3b and
3c, the MZM has more intensity noise and less phase noise than the phase modulator for DPSK encoding. For the
MZM and the phase modulator, the standard deviation on the intensity normalized to the average value are
respectively 0.046 and 0.028, while the standard deviation on one of the relative phase levels is 0.17 rad and 0.37
rad. Note that the significant phase noise of the phase modulator would lead to a significant decrease in
performance, but would not be detected by conventional diagnostics. The phase modulator can also be set to
generate arbitrary phase shifts; for example Fig. 3d displays the samples concentrated around π/2, 0 and -π/2
obtained when the phase modulator is driven to obtain π/2 phase shifts.

           Fig. 3. Measured constellation diagrams of the samples ΣN for a train of pulses without data encoding (a), for a DPSK
           signal encoded with a MZM (b), for a DPSK signal with π phase shifts encoded with a phase modulator (c) and for a DPSK
           signal with π/2 phase shifts encoded with a phase modulator (d).
The direct characterization of phase-encoded signals was then tested at 40 Gb/s. A 40 Gb/s transmitter was
implemented using pulse carving of a monochromatic laser with an electroabsorption modulator driven by a 40 GHz
sine wave followed by a LiNbO3 x-cut MZM driven by a 40 Gb/s PRBS signal. The OSNR of such source was
varied by attenuating the input power to an EDFA. The constellation diagram for the corrected samples SN is plotted
on Fig. 4a for an OSNR of 27 dB and 13 dB. Incoherent ASE adds up to the two sets of samples representing the
deterministic values of the coherent electric field, and the instantaneous values of the electric field are dispersed in
two circles centered symmetrically in the complex plane. Additionally, the constellation diagram is plotted when no
signal is input to the EDFA, in which case only incoherent ASE is sampled. As expected, the samples have a random
intensity and evenly distributed phase in the complex plane.

          Fig. 4. Measured constellation diagram of the processed samples SN for a 40 Gb/s DPSK signal at an OSNR of 27 dB (a)
          and 13 dB (b), and constellation diagram of an incoherent source (c).

 4. Conclusion
The first experimental measurement of constellation diagrams of optical sources has been performed using a phase
sensitive measurement of the interference of the source under test with a train of sampling pulses. Application to the
characterization of 10-Gb/s and 40 Gb/s DPSK signals has been presented. This could lead to direct evaluation of
impairments that affect the phase of an optical channel, and could be implemented at higher bitrates
straightforwardly by increasing the optical bandwidth of the sampling source.
[1] Peter Andrekson, “Ultra high bandwidth optical sampling oscilloscopes,” OFC 2004, TuO1.
[2] C. Dorrer, D. C. Kilper, H. R. Stuart, G. Raybon and M. G. Raymer, “Linear optical sampling”, Photon. Technol. Lett.. 15, 1746-1748 (2003).
[3] S. T. Cundiff, J. Ye, and J. L. Hall, “Optical frequency synthesis based on mode-locked lasers,” Rev. Sci. Instr., 72, 3749-3771 (2001).
[4] A. H. Gnauck, “40-Gb/s RZ-differential phase shift keyed transmission,” ThE1, Optical Fiber Communications conference (2003).