DIFFERENTIAL PHASE-SHIFT-KEYED (DPSK) and

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1 718 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 27, NO. 6, MARCH 15, 2009 Measurement of Differential Phasor Diagram of Multilevel DPSK Signals by Using an Adjustment-Free Delay Interferometer Composed of a 3 3 Optical Coupler Y. Takushima, Member, IEEE, H. Y. Choi, and Y. C. Chung, Fellow, IEEE, Fellow, OSA Abstract We develop an adjustment-free differential-phase demodulator based on a delay-interferometer (DI) made of a optical coupler, which is used as a 120-degree optical hybrid, and demonstrate the possibility of using it as a phasor monitor for the multilevel differential phase-shift keyed (DxPSK) signal. The key features of the proposed demodulator are twofold: (a) in-phase and quadrature (I-Q) components and the phasor diagram can be obtained only by using a single DI, and (b) the phase delay of the DI can be derived from the output power of the DI without the knowledge of the signal under test. These features enable us to demodulate the I-Q components of DxPSK signals without any adjustments. We formulate a theoretical model for deriving the differential phasor from the output signals of the coupler regardless of unbalances in the phase retardations and the splitting ratios of the coupler. Thus, the discrepancy from the ideal 120-degree optical hybrid is not a problem, and hence the requirements of the couplers are greatly relaxed. For a demonstration, we implement the proposed demodulator by using a fiber Michelson interferometer with Faraday rotator mirrors and use it as a differential phasor monitor capable of the plug-and-play (wavelength- and polarization-independent) operation. We show that this phasor monitor can be used for diagnosis of differential phase-shift keyed (DPSK) and differential quadrature phase-shift keyed (DQPSK) transmitters by identifying the sources of impairments from the measured constellation diagram and phasor trajectories. The proposed phasor monitor can also be used for monitoring the optical signal-to-noise ratio (OSNR) of DPSK signal. Index Terms Differential phase shift keying, optical fiber communication, optical interferometry, optical modulation. I. INTRODUCTION DIFFERENTIAL PHASE-SHIFT-KEYED (DPSK) and multilevel DPSK (DxPSK) formats have many advantages such as high spectral efficiency and high tolerance to linear/nonlinear impairments [1] [12]. Recently, there have been numerous reports demonstrating the superior performances of DxPSK-based transmission systems [3] [12]. As the complexity of the modulation format increases, the fidelity of Manuscript received March 12, Current version published April 17, This work was supported by the IT R&D program of MKE/IITA, [2008- F017-01, 100Gbps Ethernet and Optical Transmission Technology Development] and the Brain Korea 21 Project, KAIST. The authors are with the Department of Electrical Engineering, Korea Advanced Institute of Science and Technology, Yuseong-gu, Daejeon , Korea ( ytaku@ee.kaist.ac.kr; enoch3000@kaist.ac.kr; ychung@ee.kaist.ac.kr). Color versions of one or more of the figures in this paper are available online at Digital Object Identifier /JLT Fig. 1. Conventional DxPSK demodulator by using two DIs. (a) Setup. (b) Effect of the error in the phase delays of two DIs. the phase modulation becomes more critical because even a small error in the phase deviation can cause a significant intersymbol interference and degrade the receiver sensitivity. Thus, the phasor monitor, which evaluates the constellation diagram of the phase-modulated signal on the complex plane (i.e., phasor diagram), is expected to play an important role for the precise adjustment of the DxPSK modulator, trouble shooting of the DxPSK transmitter, and monitoring of the DxPSK signal s quality [10], [13] [16]. For these applications, the phasor monitor should be able to measure the phasor diagram of the DxPSK signal regardless of its wavelength and polarization. In fact, it would be highly desirable if the phasor could be observed simply by plugging the signal under test into the phasor monitor without any adjustment (i.e., the plug-and-play operation). To implement a phasor monitor, it is necessary to utilize a differential phase demodulator for the detection of the in-phase (I) and quadrature (Q) components of the DxPSK signal separately. In principle, we should be able to implement a phasor monitor by using optical phase demodulators developed for DxPSK receivers. However, it is not straightforward to utilize conventional demodulation techniques for the phasor monitor capable /$ IEEE

2 TAKUSHIMA et al.: DIFFERENTIAL PHASOR DIAGRAM OF MULTILEVEL DPSK SIGNALS 719 of plug-and-play operation, because their operations usually require troublesome adjustments. As an example, we consider a DxPSK demodulation technique based on two delay interferometers (DIs) shown in Fig. 1(a). In order to obtain the I-Q components, the phase delays of two DIs must be adjusted to 0 and (or, ), respectively, [1], [10], [17], [18]. One method to achieve these phase delays is to adjust the peak (or dip) wavelengths of the transmittance of each DI precisely in accordance with the center frequency of the signal light. Therefore, this method requires the knowledge of the signal frequency in advance. In addition, the DIs should be readjusted whenever the signal frequency changes. The other method is to adjust the phase delay so as to maximize the eye opening measured at the output of the balanced receiver. However, the method requires a reference signal having a frequency identical to the signal under test. In this way, both of these methods need some extra preparations for the initial setting of the DIs. In addition, the phase delays of these DIs are sensitive to the external perturbation and the frequency drift of the signal light, whereas a minute change in these phase delays can cause a significant error in the measured phasor [18], [19]. In particular, when the phase delays of the two DIs independently change, the orthogonality of I-Q components is lost. As a result, the observed phasor diagram is distorted as if the signal under test is degraded by the intersymbol interference, as depicted in Fig. 1(b). In this case, it is not possible to distinguish the true signal distortion from the problem of the phasor monitor itself. Thus, the conventional DxPSK demodulator based on two DIs is not well suited for the phasor monitoring of unknown signals (although it is suitable for the use in a DxPSK receiver operating at a fixed wavelength with a known format). As discussed in Section IV, the other demodulation techniques also suffer from similar difficulties. In this paper, we propose a novel differential-phase demodulator composed of a 3 3 optical coupler. It is well known that a symmetric 3 3 coupler acts as a 120-degree optical hybrid, and has been used for the optical heterodyne/homodyne receiver with a local oscillator and optical fiber sensors [20] [23]. We utilize the 3 3 coupler for the DI demodulator of DxPSK signals [24]. The key features of the proposed demodulator are twofold; (a) the I-Q components and phasor diagram can be obtained by using only a single DI, and (b) the phase delay of the DI can be derived from the output power of the DI without the knowledge of the signal under test. These features enable us to demodulate the I-Q components of the differential phasor without any adjustments. In addition, the imperfect splitting ratio of the couplers used in the DI and the unequal receiver sensitivities can be completely compensated, and consequently, the requirements for the components are relaxed. For a demonstration, we implement the proposed demodulator by using a fiber Michelson interferometer with Faraday rotator mirrors (FRMs) and realize the plug-and-play (i.e., wavelength- and polarization-independent) operation of the phasor monitor. The implemented phasor monitor is used for diagnosis of the DPSK and differential quadrature phase-shifted-keyed (DQPSK) transmitters and monitoring of the optical signal-to-noise ratio (OSNR) of DPSK signals. The rest of this paper is organized as follows. In Section II, we describe the operating principle of the proposed differential phase demodulator and discuss the methods used for the estimation of the phase delay of the DI. In Section III, we show the im- Fig. 2. Proposed differential-phase demodulator composed of a optical coupler. (a) Schematic diagram of the proposed DI. (b) Reconstruction of the differential phasor diagram. plementation of the proposed phasor monitor and demonstrate its capability for diagnosis of DPSK and DQPSK signals. We then discuss the cons and pros of the proposed phasor monitor in comparison with other phasor monitors in Section IV. The information on the trajectory of the differential phasor is also discussed. Finally, we summarize this paper in Section V. A simple method used for determining the parameters of the phasor monitor is described in the Appendix. II. OPERATING PRINCIPLE OF THE DELAY INTERFEROMETER USING A 3 3OPTICAL COUPLER Fig. 2 shows the schematic diagram of the proposed differential-phase demodulator. We denote the electric field of the signal light and the bit period by and, respectively. In DxPSK format, the information is encoded in the differential phase. In a conventional DxPSK receiver, two independent DIs are used to demodulate the cosine and sine components of [10] [12]. On the contrary, we use only one DI for the I-Q demodulation in the proposed setup. The signal light is first divided evenly by the 2 2 coupler. The output signal from the lower port of the 2 2 coupler traverse through an optical delay of and then combined with the signal transmitted through the upper delay arm by the 3 3 coupler. The output signals of the 3 3 coupler are detected by using three photodetectors. Our objective is to obtain the differential phasor described as where and are the I-Q components of the differential phasor, respectively. Although there is no orthogonal relation among the output signals of the 3 3 coupler, these signals have full information on the differential phasor. In order to obtain the differential phasor from these output signals, we divide the (1)

3 720 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 27, NO. 6, MARCH 15, 2009 calculation into two steps as shown in Fig. 2(b): 1) calculation of the intermediate phasor, which is the differential phasor tilted by the phase delay of the DI, and 2) estimation of from the intermediate phasor obtained in the first step. If the splitting ratios of these couplers are uniform, the theoretical treatment would be simple and straightforward [22]. However, in realistic cases, the splitting ratio is not necessarily uniform. Thus, we take into account the unbalance of the splitting ratio for the calculation of the differential phasor. We express the electric fields of the output signal incident on the input ports 1 and 2 of the 3 3 coupler by and, respectively, where and are the power transmittances of the 2 2 coupler, is the differential delay time, and is the difference of the phase delays between the signals in two arms of the DI. (It should be noted that can be considered as a real positive number without loss of generality.) We denote the transmittance of the 3 3 coupler from input port to output port by. Then, the signal power at the output port is expressed as where and. The output light from the output port is detected by a photodetectors having a responsivity of. The detected signal current from output port, can be expressed as (1) Equation (4) shows the relation between the differential phasor and the detectors outputs. However, due to the second term on the right-hand side (RHS), cannot be determined only from the detectors outputs, even if all parameters (such as, and ) are given. Thus, to observe the phasor diagram without distortion, it would be necessary to measure the intensity waveform,, independently and compensate for the error term given by. However, we note that this error term becomes zero under the following conditions: (a) the splitting ratios of the couplers are uniform (i.e., for all ), or (b) the intensity of the signal under test is constant or periodical (i.e., ). We further note that, even if the splitting ratios are not perfectly uniform, the vector in (4) becomes small when the extinction ratio of the DI is high (since is roughly proportional to, which is the inverse of the extinction ratio of the DI.) In addition, for nonreturn-to zero (NRZ) DxPSK signals with constant intensity, we can omit this error term because condition (b) is satisfied. For return-to-zero (RZ) DxPSK signals, this error term also becomes zero because the intensity changes with a period of. However, if the NRZ-DxPSK signal is generated by using a dual-drive phase modulator, the intensity is neither constant nor periodical. Even in such a case, the intensity at the decision point is constant. Therefore, as far as the constellation diagram is concerned, this term does not affect the measurement. As a result, we can practically neglect this error term, and obtain the differential phase in the following simple form: (6) where In (2), the terms and represent the I-Q components of the differential phasor tilted by the angle of (i.e., the intermediate phasor). Equation (2) can be transformed as (2) (3) In principle, the parameters and are dependent on the splitting ratios of the two couplers and the conversion efficiency of the photo detectors. However, these constants can be obtained by a very simple method described in Appendix without measuring each parameter one by one. It should be noted that the phase delay of the DI,, does not distort the phasor diagram, but rotates the measured phasor diagram by. Therefore, by estimating and rotating by, we can obtain the accurate differential phasor diagram of the signal under test. For an arbitrary input signal, the argument of can be expressed as Since is the differential phase, its time average is always zero regardless of the signal format (because under the assumption of stationarity). Therefore, by averaging (7), we obtain (7) where (4) (5) In practice, it is not straightforward to evaluate the argument of, because the value obtained by the measurement is folded into a finite range of and has discontinuities when crosses. Thus, we need to unfold the measured argument by considering the continuity of the phase. (8)

4 TAKUSHIMA et al.: DIFFERENTIAL PHASOR DIAGRAM OF MULTILEVEL DPSK SIGNALS 721 Fig. 3. Phasor diagrams (center) and their differential phasor diagrams (right) calculated for various NRZ-DxPSK signals. The phasor diagram is the plot of the real and imaginary parts of the phasor E(t) itself, and the differential phasor diagram is the plot of those of the differential signal, E(t)E (t 0 T ). The configuration of the modulators is shown in the left column. The arrow in the differential phasor diagrams indicates the average vector of the trajectory of the differential phasor. For clarity, the length is magnified by a factor of 5. (a) DPSK (PM). (b) DPSK (Dual-drive PM). (c) DQPSK (Dual-drive PM (0, ) and PM(0, /2)). (d) DQPSK (DQPSK modulator). (e) D8SPK (DQPSK modulators (0, /2,, 3/2) and PM (0, /4).

5 722 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 27, NO. 6, MARCH 15, 2009 Fig. 4. Phasor diagrams (center) and their differential phasor diagrams (right) calculated for various RZ-DQPSK signals. The configuration of the modulators is shown in the left column. The arrow in the differential phasor diagrams indicates the average vector of the trajectory of the differential phasor. For clarity, the length is magnified by a factor of 20. (a) DQPSK modulator, duty ratio 50 %. (b) DQPSK modulator, duty ratio 67 %. (c) Dual-drive PM+PM, duty ratio 67 %. However, for conventional DxPSK formats, there exists a simple and practical method to estimate. When we average the differential phasor diagram of DxPSK signals on the complex plane, the average vector does not become zero, but always indicate the direction of the differential phase of zero (i.e., the direction of axis). For example, Fig. 3 shows the phasor diagrams and trajectories of the differential phasor of NRZ-DPSK, DQPSK, and differential 8-ary PSK (D8PSK) signals. Although the phasor diagram is symmetric, the differential phasor is asymmetric with respect to the imaginary axis. The arrow in the differential phasor represents the average vector of its trajectory (i.e., ). These figures show that the average vector of the differential phasor indicates the direction of the real axis. The situation is the same for the cases of RZ-DxPSK. For example, Fig. 4 shows the phasor and the differential phasor of the RZ-DQPSK signal. The results are similar to those of Fig. 3. The trajectory of the differential phasor is asymmetric, and the average vector indicates the direction of axis. (Noted that the average vector becomes shorter as the duty ratio decreases.) Thus, can be found by This calculation is quite simple compared with the evaluation of (8). It should be noted that (8) and (9) are not mathematically equivalent, and (9) is not always satisfied for the arbitrary signal. However, it can be proved that (9) is applicable for the signal which has a symmetric optical (power) spectrum with single peak (including not only the aforementioned DxPSK formats, but also the amplitude shift keyed (ASK)-DxPSK formats). Therefore, most of the conventional modulation formats can be covered by (9). It should also be noted that, if the modulation format of the signal under test is known in advance, we can apply the phase estimation algorithm developed in wireless communications for the estimation of [25], [26]. By using (9)

6 TAKUSHIMA et al.: DIFFERENTIAL PHASOR DIAGRAM OF MULTILEVEL DPSK SIGNALS 723 Fig. 5. Experimental setup. The transmittance of the DI is shown in the inset. Fig. 6. Measured differential phasor trajectory diagrams of DPSK signal (1 = 0:7) (a) without and (b) with the phase delay compensation, respectively. these phase estimation algorithms in conjunction with (9), the estimation accuracy could be further improved. Thus, the differential phasor can be obtained by the following equation: where (10) (11) Equation (10) shows that the required calculation is a simple matrix operation and the amount of calculation time is very small. III. DEMONSTRATION OF WAVELENGTH- AND POLARIZATION-INDEPENDENT MONITORING OF PHASOR DIAGRAM We implemented the proposed demodulator by using a 3 3 fiber coupler and used it as a differential phasor monitor. Fig. 5(a) shows the experimental setup. We used a Michelson interferometer instead of a Mach-Zehnder (MZ) interferometer. The delay time between two arms of the Michelson interferometer was adjusted to be 100 ps. The insertion losses of the 3 3 coupler were in the range of db. To improve the stability against the external perturbation, we placed the two fiber arms of the Michelson interferometer closely in parallel, so that the common-mode perturbation can be canceled out (as in fiber-optic gyros [28]). We then put the whole DI in a plastic box for thermal isolation. As a result, although fiber Fig. 7. Wavelength and polarization dependence of the proposed phasor monitor. (a)-(d) Differential phasor trajectories measured at various wavelengths; (a) 1532 nm, (b) 1540 nm, (c) 1550 nm, and (d) 1560 nm. (e) Differential phasor trajectory of the polarization- scrambled signal measured at 1550 nm. interferometers are known to be instable, we could suppress the phase drift down to rad/min. The change of the state of polarization (SOP) of the input light as well as the drifts of the birefringence and polarization-dependent loss of various optical components used in this setup were canceled out by using two FRMs [29]. We detected the output power of the demodulator by using a sampling oscilloscope with dc-coupled optical detectors (bandwidth: GHz). The time resolution of the sampling oscilloscope was set to 4.9 ps (20.6 points/bit). The detected signals were processed by using a personal computer after resampled at 32 points/bit. All the splitting ratios, receiver sensitivities, and signal skews were measured in advance by using the method described in the Appendix and calibrated by using the software based on (10). Thus, this setup was completely adjustment-free. For the signal under test, we first used a DPSK signal modulated at Gb/s with a LiNbO phase modulator. The pattern length of the pseudorandom bit sequence was. We used an external-cavity tunable semiconductor laser with a linewidth of less than 1 MHz as a light source. The signal wavelength was nm. Fig. 6(a) and (b) shows the phasor trajectories

7 724 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 27, NO. 6, MARCH 15, 2009 Fig. 8. Monitoring of DPSK signals with arbitrary phase deviation 1 : (top) differential phasor trajectories, (middle) phase eye diagrams, and (bottom) demodulated output, X(t). The phase deviations were set to (a) /4, (b) /2, and (a), respectively. measured before and after the compensation of the phase delay, respectively. We intentionally set the phase deviation to a value smaller than for clarity. The results in Fig. 6(a) clearly show the phase trajectory with three bright points corresponding to the differential phases of 0 (space) and (mark), respectively. Note that the measured phasor in Fig. 6(a) was rotating gradually in time due to the drift of. However, by applying the algorithm described in the previous section for the estimation of, we could compensate for this phase delay completely and obtain a stable phasor diagram as shown in Fig. 6(b). The proposed phasor monitor requires no phase adjustment of the delay line and its performance is not affected by the frequency drift of the signal under test. Thus, the wavelength-independent operation is possible. Fig. 7(a) (d) shows the trajectories of the differential phasors measured at various signal wavelengths. Due to the compensation of the phase drift, the differential phasor diagram was obtained without any phase offsets regardless of the signal wavelength. The measurement was also not affected by the changes of the input polarization. Fig. 7(e) shows the trajectory of the differential phasor measured after scrambling the SOP of the signal by using a polarization scrambler ( khz). The polarization-dependent phase error was measured to be negligible. Thus, we concluded that the performance of the proposed phasor monitor was not affected by the wavelength and polarization fluctuations of the input signal. The proposed phasor monitor can provide the complete vector information of the DxPSK signal in various formats such as the phasor trajectory, constellation map, phase eye diagram, and demodulated output. Thus, this phasor monitor can be used in many different ways for diagnosis of DxPSK signals. The followings are some examples. Fig. 9. Phase eye diagrams (upper) and the demodulated output (lower) of DPSK signals modulated with normal (left) and bad (right) driver amplifiers. A. Measurement of the Phase Deviation of DxPSK Signals The precise phase adjustment is indispensable to minimize the intersymbol interference of DxPSK signals [1], [10] [12]. In particular, when the DxPSK modulation is carried out with two or more phase modulators, the phase deviation of the phase modulator used for the least significant bit should be set to an integer fraction of (e.g., for DQPSK and for D8PSK) precisely. However, it is not easy to monitor such phase deviations precisely when the conventional DI is used. This is because the demodulated output is not necessarily correlated with the correct phase information in the vicinity of due to the cosine profile of the DI output. On the contrary, the proposed phasor monitor can cope with this problem by measuring I and Q

8 TAKUSHIMA et al.: DIFFERENTIAL PHASOR DIAGRAM OF MULTILEVEL DPSK SIGNALS 725 Fig. 10. Monitoring of DPSK signals modulated with the dual-drive MZ phase modulator for normal and bad modulator setting. (a) Normal. (b) The case when one of the modulation arm has the small phase deviation. (c) The case when the skew (difference of the time delays) exists. The lower figures show the demodulated output for each signal. components of the signal simultaneously. Fig. 8 shows the measured phasor trajectories, phase eye diagrams, and demodulated outputs of the DPSK signals with phase deviations of, and. Since the proposed phasor monitor can directly measure, the adjustment of the phase deviation becomes easy and intuitive. In addition, using the proposed phasor monitor, we can adjust the phase deviation to any value. This is a great advantage over the use of a conventional DI. B. Fidelity Test of DxPSK Modulation The proposed phasor monitor is also useful to evaluate the fidelity of the phase modulation (i.e., how accurately the optical phase is modulated). For example, Fig. 9 shows the phase eye diagrams and demodulated outputs measured for the DPSK signals obtained by using different driver amplifiers (having normal and strong pattern dependences). From these phase eye diagrams, we could easily identify the degraded fidelity of phase modulation in Fig. 9(b). It would not be easy to differentiate these two cases if we just observed the demodulated output by using a conventional DI. For example, Figs. 9(c) and (d) show the eye diagrams when the same input signals used in Fig. 9(a) and (b) was demodulated, respectively. Fig. 9(d) shows that the thick mark and space levels caused by the strong pattern dependence of the driver amplifier are compressed by the cosine profile of the DI. As a result, it is difficult to identify the root cause of the problem from the eye diagram shown in Fig. 9(d). Fig. 10 shows the trajectories of the differential phasors of DPSK signals obtained by using a dual-drive MZ phase modulator. In this measurement, we intentionally detuned the phase deviation (Fig. 10(b)) and the skew between the electric signals applied to two arms of the modulator (Fig. 10(c)). Fig. 10(b) and (c) shows that the phasor trajectories have unique shapes depending on the degradation factors. In order to understand the implications of these phasor trajectories, we numerically calculated the phasors and differential phasors of DPSK signals with imperfect phase modulations. Fig. 11 shows the results. When the phase deviation in one of the arms is smaller than, the differential phasor has Y-shaped trajectory, as shown in Fig. 11(a). On the other hand, when there is a skew (time delay) between two arms of the modulator, the trajectory of the differential phasor becomes to have a figure-of-eight shape (Fig. 11(b)). We note that the measured trajectories of the differential phasors in Fig. 10(b) and (c) are similar in shape with those in Fig. 11(a) and (b), respectively. Thus, we conclude that it should be possible to identify the sources of the degradations from the measured trajectories. As shown in the lower part of Fig. 10, these types of the imperfect modulation problems cannot be identified by using the conventional demodulation technique. The proposed phasor monitor is also applicable to multilevel DPSK signals. For a demonstration, we first generated an imperfect DQPSK signal by using the setup in Fig. 12(a). The DQPSK signal was obtained by using a dual-drive MZ modulator and a phase modulator. However, in this experiment, we intentionally used a bad driver amplifier having strong pattern dependence (the same amplifier used in Fig. 9(b)) for the phase modulator to impair the signal quality. Fig. 12(b) shows the demodulated eye diagrams of the I-Q components for reference. Although we could easily recognize the severely degraded eye openings from these demodulated outputs, it was not possible to identify which factor was primarily responsible for this degradation between the additive optical noise and the distortion caused by the pattern effect. In contrast, the measured constellation diagram in Fig. 12(c) shows that it is stretched to the azimuthal direction while the broadening in the radial direction is relatively small. Thus, we could recognize that the distortion was caused not by the additive noise, but the imperfect phase modulation. C. Monitoring of OSNR The proposed phasor monitor can also be used for monitoring the OSNR of DxPSK signal [13]. Fig. 13 shows the measured constellation diagrams of the DPSK signal at various OSNRs. In this experiment, we added the amplified spontaneous emission (ASE) noise from an Erbium-doped fiber amplifier (EDFA) to the DPSK signal generated by using a phase modulator, and adjusted the OSNR by changing the power of the ASE noise.

9 726 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 27, NO. 6, MARCH 15, 2009 Fig. 11. Trajectories of phasor and differential phasor of DPSK signals when the dual-drive DPSK modulator has improper settings. (a) Small phase deviation. (b) Skew. (c) Asymmetric coupling ratio of the dual-drive modulator (low extinction ratio, 13.5 db). The results show that the constellations became scattered more widely as we decreased the OSNR by increasing the ASE noise. Fig. 14 shows the signal-to-noise (S/N) ratio of the constellation diagram, which is defined to be the ratio of the amplitude noise to the signal, as a function of the OSNR with a resolution of 0.1 nm. The result shows that the proposed phasor monitor can accurately measure the OSNR up to 25 db. The large errors observed in the range above 25 db were caused by the limited S/N ratio of the phasor monitor itself. IV. DISCUSSION The proposed phasor monitor acquires two orthogonal components of the phasor diagram by using three output signals from the DI based on a 3 3 coupler. Since this technique utilizes three parameters to obtain two unknown values, one of the three parameters is redundant. However, this redundancy enables us to calibrate out the unbalanced splitting ratios of the couplers and the asymmetric phase retardations of the 3 3 coupler. In general, the splitting ratios and the phase retardations of the 3 3 coupler are stable and their wavelength dependence is small. Thus, the proposed phasor monitor does not require any adjustment after the initial calibration of those parameters. As a result, the subsequent measurements become plug-and-play and stable. In addition, an accurate phasor diagram can be obtained regardless of the phase delay of the DI. It should also be noted that the obtained I-Q components are equivalent to the output signals of two sets of balanced detectors, though the proposed phasor monitor utilizes only three detectors. These advantages of the proposed phasor monitor can be revealed clearly by comparing it with other phasor monitors based on the conventional demodulation techniques. As an example, we first discuss the phasor monitors based on a delay interferometer. As described in the introduction, the most common method for measuring the I-Q components of DxPSK signal is the use of two DIs. However, this method is not attractive for the phasor monitor due to the troublesome adjustments required. In addition, the orthogonarity of the I-Q components can not be ensured since the phase delays of two DIs can drift independently. One way to cope with this problem is the use of 90-degree optical hybrid. In [16], the phasor monitor was realized by using a 90-degree optical hybrid, which is based on the manipulation of the SOP of the input signals. However, this method is not only bulky

10 TAKUSHIMA et al.: DIFFERENTIAL PHASOR DIAGRAM OF MULTILEVEL DPSK SIGNALS 727 Fig. 12. Monitoring of DQPSK signal. (a) Configuration of the DQPSK modulator. The driver amplifier for the phase modulator (6=2) had a strong pattern dependence as shown in the eye diagram of the inset. (b) Demodulated output for both tributaries. (c) Constellation diagram measured by the proposed phasor monitor. and complex but also polarization dependent, and as a result, requires precise adjustments of the SOP of the optical signals incident on the two arms of the DI. These problems may be solved if the 90-degree optical hybrid is replaced with better options. For example, it has been proposed to realize the 90-degree optical hybrid by using four 2 2 couplers with a variable phase delay [14], [30]. However, this method also requires a precise adjustment of the variable phase delay to achieve the 90-degree phase retardation. As a result, a slight adjustment error in the phase retardation can destroy the orthogonality of the I-Q components, which, in turn, would result in the intersymbol interference in the measured phasor. Another method to solve this problem is to use a 2 4 (or 4 4) optical coupler. If the excess loss of the 2 4 coupler is negligible and the splitting ratio is symmetric, the 2 4 coupler can be used as an ideal 90-degree optical hybrid [23]. Therefore, the I-Q demodulation can be achieved by using a single DI made of a 2 4 coupler with two balanced detectors, as shown in Fig. 15(a). Recently, a DQPSK receiver has been demonstrated by using this configuration [31]. In fact, the setup shown in Fig. 15(a) could be the most apposite configuration for the phasor monitor if an ideal 90-degree optical hybrid were available. This is because the I-Q components can be obtained from the balanced receivers (after a simple signal processing of the compensation of the phase drift of ). In practice, however, the 2 4 coupler is usually far from the ideal 90-degree optical hybrid. In principle, the phase retardation is related to the splitting ratio through the unitary property of the transfer matrix of the coupler [22]. As a result, the unbalanced splitting ratios can induce significant errors in the retardation angle. Thus, considering the difficulties in controlling the splitting ratios of multiport devices, the accuracy of the phase retardation is likely to be inaccurate. In order to compensate for errors in the phase retardation of the 2 4 coupler, it is imperative to measure the output signals independently as shown in Fig. 15(b), and reconstruct the I-Q components in a similar way to our method described in Section II. However, in this case, there is no merit of using the 2 4 coupler since the use of 2 3 (or 3 3) coupler provides a simpler solution. The phasor monitor can also be implemented by using the coherent detection (i.e., heterodyne or homodyne detection) technique with a local oscillator. Unlike the techniques based on the DI, this technique would enable us to directly monitor the phasor (not the differential phasor). This is a great advantage. Although the coherent detection has some inherent difficulties such as the polarization dependence and the phase noise of the local oscillator, there are now many solutions to these problems.

11 728 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 27, NO. 6, MARCH 15, 2009 Fig. 13. Constellation diagrams of DPSK signal for various OSNRs. (a) OSNR = 40.3 db. (b) OSNR= 20.3 db. (c) OSNR=15.3 db. Fig. 14. OSNR monitoring from the standard deviation of the amplitude noise of the constellation diagram (SNR on the phasor). Fig. 16. Effect of the limitation of the receiver bandwidth on the measured phasor trajectory. (a), (b), and (c) show the constellations and the trajectories when the ratios of the receiver bandwidth to the bitrate, Bo/B, are set to 3, 2, and 1, respectively. of the measured constellation diagram [12] [14]. Thus, it appears that if we can avoid the meticulous adjustments required for the local oscillator, the use of the coherent detection provides an excellent solution for the phasor monitor. However, since the adjustment of the optical frequency of the local oscillator is required at the present time, the plug-and-play operation cannot be realized. So far, there have been only a few demonstrations of the measurement of the phasor trajectory [10]. However, as shown in this paper (particularly in Fig. 10), the phasor trajectory is quite useful for the diagnosis of the DxPSK modulator as well as the DxPSK signal. However, unlike the measurement of the constellation diagram, the measurement of the phasor trajectory requires the receiver bandwidth much wider than the symbol rate. For example, Fig. 16 shows the errors in the trajectories of the differential phasor of the DPSK signal when the receiver bandwidth is limited. In this calculation, we assumed that the DPSK signal in NRZ format was obtained by using a phase modulator at the bit-rate of and the bandwidth of the optical detectors was. The results show that the distortion in the observed phasor trajectory becomes significant, when is much narrower than. Fig. 15. Phasor monitors using a 2 2 4(424) optical hybrid in a DI. (a) Ideal 90-degree optical hybrid. (b) Non-ideal optical hybrid. In fact, the constellation diagrams have been shown in the recent coherent detection experiments [27], [32]. In addition, a phasor monitoring system based on the coherent optical sampling has been proposed and demonstrated with good accuracy V. SUMMARY We have proposed and demonstrated a phase-adjustment-free DI composed of a 3 3 optical coupler for the differential phasor monitoring of DxPSK signals. In the proposed DI, the delayed homodyne signals were obtained from the output ports of the 3 3 coupler. Since the 3 3 coupler served as a 120-degree optical hybrid, the three output signals had

12 TAKUSHIMA et al.: DIFFERENTIAL PHASOR DIAGRAM OF MULTILEVEL DPSK SIGNALS 729 delayed interference components with different phase retardations. Although these output signals were not orthogonal, they had sufficient information for obtaining the orthogonal I-Q components of the differential phasor diagram. To obtain the differential phasor diagram from the outputs of the DI, we first acquired an intermediate phasor diagram (which was tilted by the phase delay of the DI), and then used it to estimate the phase delay. We formulated a theoretical model for deriving the differential phasor by taking account of the unbalances in the phase retardations and the splitting ratios of the 3 3 coupler. It was shown that the I-Q components could be obtained by a very simple matrix operation using the three output signals of the 3 3 coupler as the input vector. It was also found that, when the splitting ratios were not uniform, the derived intermediate phasor could have an error originating from the intensity variation of the signal under test. We discussed the conditions for negating this problem and showed that this error could be ignored for almost all DxPSK modulation formats. Unlike in the case of the conventional I-Q demodulator based on two DIs, the change of the phase delay simply rotated the intermediate phasor diagram (and did not distort the diagram). Thus, by estimating the tilt in the intermediate phasor diagram (i.e., the phase delay), we should be able to compensate for the phase drift of the DI simply by re-rotating it. For this purpose, we developed a simple method to estimate of the phase delay by calculating the average vector of the intermediate phasor. As a result, the proposed method did not need any phase adjustment of the DI. In addition, since all the unbalances in the splitting ratios and the phase retardations of the 3 3 coupler could be compensated, the requirements to the 3 3 coupler were greatly relaxed. We have implemented the proposed differential-phase demodulator made of two FRMs in Michelson interferometer configuration, and used it as a differential phasor monitor capable of the plug-and-play (wavelength- and polarization-independent) operation. It was shown that the proposed phasor monitor did not require any phase adjustments owing to the proposed algorithm for estimation of the phase delay. Also, the wavelength- and polarization-independent operation was experimentally shown. The implemented phasor monitor could acquire the complete vector information of the signal under test on the complex plane, and display it in various formats such as the constellation diagram, phasor trajectory, phase eye diagram, and demodulated output with respect to any phase reference angles. Thus, these features facilitate the intuitive and efficient diagnosis of the DxPSK signal. For a demonstration, we have measured the phase deviation of the DPSK signal and showed that the phasor monitor enabled us to adjust the phase deviation to any values accurately. We have also demonstrated that the proposed phasor monitor could be used to evaluate the fidelity of the DxPSK signal and OSNR. Thus, the proposed phasor monitor can be used as a powerful diagnostic tool for systems using DxPSK signals. APPENDIX DETERMINATION OF AND The constants and can be obtained by using a broadband source such as the ASE light from an EDFA as a signal light. First, we measure the transmittance of the DI and obtain from the differences between the peaks of the transmittances of ports and (, and 3). Then, by assuming, we can determine and. (Note that the absolute value of is not important because the offset in is equivalent to the offset of ). 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Kikuchi, Optical homodyne receiver comprising phase and polarization diversities with digital signal processing, presented at the ECOC2006, Cannes, France, 2006, paper Mo Y. Takushima (M 96) received the B.S. degree in electrical engineering and the M.S. and Ph.D. degrees in electronic engineering from the University of Tokyo, Tokyo, Japan, in 1990, 1992, and 1995, respectively. He joined Research Center for Advanced Science and Technology at the University of Tokyo in 1995 as a Research Associate, and was promoted to Associate Professor in From 2002 to 2003, he was with Research Laboratory of Electronics at Massachusetts Institute of Technology as Visiting Scientist on leave from University of Tokyo. In 2006, he joined Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Korea, where he is currently a Research Professor. His current research interests include nonlinear fiber optics and photonic network systems. Dr. Takushima is a member of the IEEE Lasers and Electro-Optics Society and the Institute of Electronics, Information, and Communication Engineers of Japan (IEICE). H. Y. Choi received the B.S. degree in electrical engineering from the University of Seoul, Seoul, Korea, in 2003, and the M.S. degree in electrical engineering from Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Korea, in 2005, where she is currently pursuing the Ph.D. degree in optical communication systems. Her research interests include optical performance monitoring (OPM) and advanced modulation formats in WDM networks. Y. C. Chung (F 99) is Professor of electrical engineering at Korea Advanced Institute of Science and Technology (KAIST), Daejon, Korea, which he joined in From 1987 to 1994, he was with the Lightwave Systems Research Department at AT&T Bell Laboratories. From 1985 to 1987, he was with Los Alamos National Laboratory under AWU-DOE Graduate Fellowship Program. His current activities include high-capacity WDM transmission systems, all-optical WDM networks, optical performance monitoring techniques, WDM passive optical networks, and fiber-optic networks for wireless communications, etc. He has published over 400 journal and conference papers in these areas and holds over 60 patents. Prof. Chung is a Fellow of IEEE and a Fellow of OSA.