Abstract

Polarization-insensitive (PI) all-optical dual pump-phase transmultiplexing from 2 × 10-GBd OOKs to 10-GBd RZ-QPSK was successfully demonstrated in a birefringent nonlinear photonic crystal fiber (PCF), by utilizing cross-phase modulation (XPM) and the inherent birefringence of the device, for the first time. PI operation was achieved by launching the probe and one pump off-axis while the state of polarization (SOP) of the other pump was randomized. Optimum pump-probe detuning, all within the C-Band, was also utilized to reduce the polarization-induced power fluctuation. Receiver sensitivity penalty at 10−9 bit-error-rate was < 5.5 dB in PI operation, relative to the FPGA-precoded RZ-DQPSK baseline.

© 2014 Optical Society of America

1. Introduction

Traditional metropolitan area networks (MAN) use the non-return-to-zero on-off keying (NRZ-OOK) modulation format due to its technical simplicity and therefore low cost. However, in long-haul optical networks, OOK modulation formats exhibit less robustness to different transmission impairments including inter-channel cross-phase modulation (XPM) [1], and residual dispersion [2] compared to phase-shift keying (PSK) modulation formats. PSK formats are especially more advantageous in spectrally efficient long-haul transmission systems (when the spectral efficiency > 0.4 b/s/Hz) because of its constant power envelope, which mitigates the pattern-dependent XPM-dispersion fiber impairment [3,4]. Further performance enhancement can be achieved using higher M-ary PSK formats (M > 2), e.g. quadrature-PSK (QPSK) which has twice the spectral efficiency of binary-PSK (BPSK) for the same data rate [5]. QPSK can operate at a lower Baud rate for the same aggregate bit rate than BPSK and therefore, is more suitable for high-capacity data transmissions. Hence OOK data from MANs may require a modulation format change at the X-connects for ensuring efficient long-haul backbone transmissions. Consequently, it may become imperative to implement all-optical modulation format conversion at the X-connect to transfer data from OOK to more effectual PSK format, e.g. QPSK to ensure seamless high-capacity spectrally efficient data transmission for long-haul networks.

With the advancements in nonlinear optical signal processing (NOSP) and the state-of-the-art device design, several all-optical modulation format conversion techniques have been presented to transfer data from multiple OOKs to QPSK. Such NOSP has been realized using XPM in semiconductor optical amplifiers (SOAs) [6–8] and highly nonlinear fibers (HNLFs) [9–12]. Although SOAs offer the potential of signal amplification, integrated SOA operation conditions are prone to complexity and optimization difficulty due to their multistage fabrication procedure as well as their additional requirements for control electronics and heat sinking. In addition, for higher bit rates, the application of these schemes is limited by the slow recovery time of the SOAs.

Although a comparably longer interaction length is required to achieve a sufficient nonlinear interaction between co-propagating signals, highly nonlinear fibers (HNLFs) can be an attractive alternative platform due to their ultrafast nonlinear response. All-optical OOKs to QPSK conversion in a HNLF was first demonstrated by Mishina et al. [9] by launching an optical clock (probe) and 2 × OOK signals synchronously into the fiber and through controlling the dual pump-phase transmultiplexing on the probe via XPM. A similar NOSP technique was demonstrated by Kitagawa et al. using a single HNLF [10], by Maruta et al. using a complex configuration consisting of four HNLFs of different lengths and nonlinear properties [11], and by Terauchi et al. through critically adjusting the peak power of the OOK signals launched into the HNLF [12]. One of the limitations of these demonstrations was that no data and data¯de-correlation was considered between the OOK pumps (max PRBS order = 7), inducing XPM phase on the co-propagating probe, which could limit the resultant QPSK signal to be dependent on the bit pattern symmetry. In addition, both the OOK control signals were considered to be locally generated which allowed complete control over their states of polarization (SOPs). In this approach, the use of a QPSK modulator could be simpler than carrying out the modulation in a HNLF. Consequently, such an implementation may not be viable for realistic optical networks which may require phase transmultiplexing of a remotely generated signal at network X-connects. The nature of the remotely generated signals’ SOP in realistic systems is unpredictable, and hence more feasible NOSP opted for seamless pump-phase transmultiplexing at the X-connect, should include at least one of the OOK signals with an unknown SOP. In practice, it has been found that the SOP of signals propagating through the long-distance fiber fluctuates in the range of 0.016 - 3.14 rad/ms [13–17]. Hence it is desirable that pump-phase transmultiplexing techniques intended for data transfer from multiple OOKs to QPSK in realistic systems, should consider the unpredictable SOP characteristics of at least one remotely generated signal and therefore, should be polarization-insensitive (PI) by nature.

Here, we are reporting the first demonstration of PI all-optical dual pump-phase transmultiplexing from 2 × 10-GBd OOKs to 10-GBd RZ-QPSK in a birefringent nonlinear PCF, and in a multi-pump-probe configuration within the C-band, by utilizing XPM, and the inherent birefringence of the device. The transmission SOP fluctuations of the remotely generated signal were emulated by scrambling the polarization of one of the OOK pumps, and PI operation was achieved by launching the locally generated OOK pump and the probe off-axis. Optimum pump-probe detuning conditions were also utilized to further mitigate polarization-induced power fluctuations and impairing effects due to neighboring, partially degenerate and non-degenerate four wave mixing terms [18–23]. The rest of this report has been organized as follows: section 2 explains the concept of dual pump-phase transmultiplexing via XPM, section 3 describes the experimental setup which is followed by section 4 discussing the techniques implemented to achieve PI-XPM converted RZ-QPSK via dual-pump phase transmultiplexing, and experimental results. Finally, section 5 summarizes the experimental demonstration.

2. Concept of dual pump-phase transmultiplexing via XPM

Assuming the RZ-probe and both the OOK pumps are perfectly aligned to the same principle axis of the birefringent nonlinear medium whose physical length (L) << the smallest dispersion length (LD), and differences in linear loss (α), inter-channel walk-off length (LW) and nonlinear coefficient (γ) are negligible for the pump and probe wavelengths, the transmultiplexed phase on the probe, induced by dual OOK pumps, can be expressed in a simplest form as

ϕpr-out(t)=ϕpr-in(t)+ϕpr-SPM(t)+ϕXPM-1(t)+ϕXPM-2(t)=ϕpr-in(t)+γLeffPpr(t)+2γLeffPOOK1(t)+2γLeffPOOK2(t),
where Leff denotes the effective length of the nonlinear medium. Here Φpr-in/out represents the input/output phase of the RZ-probe at the input/output of the nonlinear medium, Φpr-SPM denotes the self-phase modulation (SPM) phase accumulation on the probe due to the probe peak power (Ppr) and ΦXPM-1/2 symbolizes the XPM phase shifts due to the pump peak powers (POOK1, P OOK2). Elimination of the effects of Φpr-in and Φpr-SPM can be realized by using a one-bit-delay asymmetric Mach-Zehnder interferometer (AMZI) at the receiver, which limits the dependence of Φpr-out variation in Eq. (1) to XPM effects. For all-optical transmultiplexing data from OOKs to RZ-QPSK, the XPM phase shifts induced by the pumps on the probe can be controlled in such a manner that the domain of the resultant phase of the probe turns out to be {0, π/2, π, 3π/2} as shown in Fig. 1.

 

Fig. 1 Scheme for dual pump-phase transmultiplexing via XPM to achieve RZ-QPSK at the output of the NOSP system.

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The physical implementation of this concept requires an adjustment of the peak power of one of the pumps to a certain level, so that the transmultiplexed XPM phase shift on the probe becomes ‘π’ when the OOK data is ‘1’ for that pump. Simultaneously, it also requires an adjustment of the peak power for the other pump to a level so that it induces ‘π/2’ XPM phase shift on the probe for the OOK data being ‘1’. This is achievable in the nonlinear system by converting the pulse format of a pump from NRZ to RZ. Consequently, a RZ-QPSK signal is generated at the output of the NOSP device, depending on the combination of the data on the OOK pumps as shown in Table 1.

Tables Icon

Table 1. Data on OOK Pumps and Corresponding XPM Phase Shift on RZ-probe

3. Experimental set-up

A schematic of the experimental setup is shown in Fig. 2. The polarization scrambler (PS) emulated the unpredictable SOP condition expected of a remotely generated signal. The combination of variable optical attenuator (VOA1) and EDFA1 emulated the ASE-limited transmission of the remotely generated OOK pump. Conversely locally generated OOK pump allowed comprehensive control over its SOP condition. Both pumps were 211-1 PRBS, 33-ps-FWHM RZ-OOK signals generated by conventional Lithium Niobate (LiNbO3) Mach-Zehnder electro-optic modulator. The probe was a 10 GHz, 18 ps pulsed source produced by filtering (−3 dB BW ≈0.35nm) a passively mode-locked Er3+-doped-glass waveguide laser at λpr ≈1547.7 nm. The probe FWHM pulse-width was measured using a Femtochrome autocorrelator (with its integration time set to 0.1 ps), and assuming a Gaussian pulse profile. A narrower probe pulse was used to minimize the XPM-induced chirp over its duration. The remotely generated OOK pump was at λR ≈1537.0 nm whereas the locally generated OOK pump was tuned at λL ≈1564.5 nm. The pump-probe detunings (PPDs) were optimized by placing the pumps near the 2nd and the 3rd minimal points of the PPD characteristic curve of the PCF, to achieve polarization-insensitive dual pump-phase transmultiplexing [21].

 

Fig. 2 Experimental setup for PI all-optical dual pump-phase transmultiplexing from 2 × 10-GBd OOKs to 10-GBd RZ-QPSK utilizing XPM in a birefringent nonlinear PCF. PS: polarization scrambler, ODL: optical delay line, VOA: variable optical attenuator, EDFA: Er3+-doped fiber amplifier, HPA: high power Er3+-doped fiber amplifier, OBPF: optical bandpass filter, PA: polarization analyzer, AWG: arrayed waveguide grating, LNF: low-noise figure, AMZI: asymmetric Mach–Zehnder interferometer, BPD: balanced photodetector, TIA: trans-impedance amplifier, LA: limiting amplifier, CDR: clock/data recovery, ED: error detector.

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The 30-m PCF (the NL∙1550∙NEG∙1), used in the experimental setup, was commercially available from NKT Photonics and its inherent group-index birefringence was found to be deterministic (10−4 ̶ 10−5) using the fixed-analyzer transmission technique [24,25]. Within the C-band (1530-1565 nm), the DGD of the device was ≈1 ps (equivalent to a PMD of ≈0.03 ps/m) and the nonlinear coefficient (γ) was ≈11 W−1km−1, approximately ten-times higher than that of SMF-28, which made the desired dual pump-phase transmultiplexing feasible over a short (sub-100-m) device length. The dispersion coefficient of the PCF was ≈-0.7 ps∙nm−1∙km−1, much smaller than that (≈17 ps∙nm−1∙km−1) of SMF-28, whereas linear propagation loss (α) was ≈0.008 dB∙m−1, relatively higher than that (≈0.00025 dB∙m−1) of SMF-28. Its high Kerr nonlinearity compensates for the high linear propagation loss, which determines the effective length of the device, and results in the desired XPM phase shift at its output.

The rest of experimental set-up for the dual pump-phase trans-multiplexing experiment was designed in such a way that it could explore two sets of polarization conditions. One was the stationary polarization condition where the SOP of the remotely generated OOK pump could be controlled locally and the other was the PI condition which considered random SOP characteristics of the remotely generated OOK pump. Hence, for the stationary polarization condition, the SOP of the remotely generated OOK pump was controlled by a mechanical polarization controller (PC) to align its SOP to the low-loss axis of the PCF, whereas it was randomized at a rate > 1 MHz using a polarization scrambler (PS) for the PI condition. Conversely the SOP of the locally generated OOK pump and probe were always controlled by their respective PCs, as shown in Fig. 2. After their corresponding HPAs and PCs, both pumps were combined using a 50/50 fused-fiber coupler, and the output of the aforementioned coupler was then combined with the probe through a 90/10 fused-fiber coupler and launched synchronously into the PCF. At the input of the PCF mode adapter, the random de-correlation between the pumps was estimated to be 1679 bits. For both conditions and at the input of the PCF mode adapter, the average pump powers of the locally and remotely generated OOK pumps were ≈30.6 dBm and 27.2 dBm respectively, whereas the average probe power was ≈18.1 dBm. According to the concept discussed in the Sec. 2, pumps were chosen to be at two different powers levels so that locally generated pump transmultiplexed ‘π’ XPM phase shift on the probe and the remotely generated pump induced ‘π/2’ XPM phase shift. Since the PCF dispersion profile was nearly flat (dispersion slope ≈10−3 ps∙nm−2∙km−1) across the entire C-band, the average power of the remotely generated OOK pump was chosen to be lower than the other pump to minimize the parametric amplification effect [26].

At the output of the PCF, a commercially available 100-GHz DWDM AWG was used to isolate the dual pump-phase transmultiplexed RZ-QPSK probe at λpr. The passband profile of the DWDM AWG was Gaussian with −3-dB bandwidth of 0.44 nm. However, the phase-transmultiplexed RZ-QPSK resultant probe was detected as RZ-DQPSK in the receiver, which employed phase-amplitude conversion, combined with differential direct-detection. The DQPSK pre-amplified receiver consisted of a dual-stage, linear high-gain, low-noise-figure (LNF) EDFA followed by a tunable OBPF (≈1.0 nm) to eliminate the out-of-band ASE resulting from the amplification in the EDFAs. An AMZI followed the signal amplification and filtering to realize the phase-amplitude conversion. The two VOAs just before and after the LNF-EDFA were used to emulate ASE-limited transmission. The 1st VOA was used to change the received OSNR, and the 2nd VOA before the AMZI was deployed to maintain constant average detected power (≈1 dBm) throughout the receiver sensitivity measurements. The receiver electronics subsequent to the AMZI included a balanced photodetector, a transimpedance amplifier (TIA), a limiting amplifier (LA) and a standard 10-Gb/s clock/data recovery (CDR) module, before the error-detector (ED). The AMZI bias was adjusted to ≈ ± π/4 to distinguish the in-phase (I) and quadrature (Q) components of the dual pump-phase transmultiplexed resultant RZ-QPSK probe and BER measurements were conducted with the help of uploaded non-PRBS data to the ED. The receiver sensitivity performance of the resultant RZ-QPSK probe was then compared with the back-to-back (BtB) ASE-limited transmission of the RZ-QPSK baseline signal generated using the Virtex-6 HX380T FPGA (as shown in Fig. 3). The I* and Q* at the FPGA egress in Fig. 3 were the precoded drive signals for the parallel QPSK modulator and can be expressed as

In*=A¯nB¯nI¯n1*+A¯nBnQ¯n1*+AnBnIn1*+AnB¯nQn1*Qn*=A¯nB¯nQ¯n1*+A¯nBnIn1*+AnBnQn1*+AnB¯nI¯n1*
where A and B represent decorrelated (by 512 bits) data and data¯ respectively [27]. The precoded FPGA I* and Q* outputs [Eq. (2)] were then modulated onto the probe using a conventional LiNbO3 nested IQ-modulator for BtB ASE-limited transmission so that PRBS can be achieved at the direct differential detection receiver for the RZ-QPSK baseline signal.

 

Fig. 3 Experimental setup for direct detection of precoded RZ-QPSK baseline. FS: frequency synthesizer, LVPECL: low-voltage positive emitter-coupled logic, LA: limiting amplifier.

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4. Experimental results and discussion

To minimize the polarization-induced fluctuation in phase transmultiplexing via XPM by dual pumps, both the locally generated pump and the probe were launched off-axis. To determine the optimal launch conditions, initially all the pumps and the probe were aligned to the low loss axis of the PCF. The single-axis launch condition was then verified by maximizing the four wave mixing (FWM) at the output of the device. That condition is also equivalent to 100% DOP, which could be verified using the polarization analyzers (PAs) (Fig. 2). A polarization controller (PC) was used at the input of the PA-1 (Fig. 2) to conveniently align the SOP of the probe with the horizontal polarization state, for which the normalized Stokes parameters were [s1A s2A s3A]T = [1 0 0]. After attaining the single-axis launch condition, the probe was turned off and the locally generated pump was aligned to other birefringence axis of the PCF, so that the resultant FWM terms were extinguished, and this condition was also verified using PA-2 (Fig. 2). Another PC was used at the input of the PA-2 (Fig. 2) using similar method to conveniently record the polarization state of the locally generated pump, for which the normalized Stokes parameters were [s1C s2C s3C]T = [1 0 0]. Then the probe was turned on as well as the scrambler so that the SOP of the remotely generated pump could be randomized at a rate > 1 MHz to realize PI condition. The SOP of the probe was then adjusted to maximize the eye-opening as far as possible, however with no adjustment to the PC at the input of the PA-1. This moved the SOP to marker B (elliptical polarization) in Fig. 4(a), for which the parameters became [s1B s2B s3B]T = [-0.05 −0.23 −0.97]. Finally the launch angle of the locally generated pump was adjusted to optimize the resultant QPSK-I/Q probe so that it resulted in an optimal receiver sensitivity or BER at the lowest achievable OSNR. The off-axis launch parameters of the locally generated pump, as shown by marker D in Fig. 4 (b), was found to be [s1D s2D s3D]T = [-0.61 0.66 −0.42].

 

Fig. 4 Measurement of the relative launch angle change of (a) the probe and (b) the locally generated pump using Polarization Analyzer Poincare sphere: Marker A represents the probe SOP when the remotely generated pump and the probe were aligned to the same birefringent axis, whereas Marker C represents the locally generated pump SOP when the pumps are orthogonal. Marker (B) and (D) denotes (a) the probe and the locally generated pump SOP respectively when the remotely generated pump was polarization-scrambled and for the best BER performance of the dual pump-phase transmultiplexed PI-QPSK probe.

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Using these four sets of Stokes parameters, the relative change in the launch angle of the probe, θ1 and the locally generated pump, θ2 were computed to be [22]

Δθ1=tan1(1s1B1+s1B)tan1(1s1A1+s1A)46o0o=46oΔθ2=90otan1(1s1D1+s1D)tan1(1s1C1+s1C)90o63o0o=27o
which were the same for the stationary polarization condition when the scrambler was off.

The PCF input and output spectra (OSNR > 25 dB/0.1 nm) at a resolution bandwidth of 0.06 nm are shown in Fig. 5. The lower trace in green represents the input PCF spectrum where the remotely and locally generated OOK pumps were centered at 1537 nm and 1564.5 nm respectively, whereas the probe was at 1547.7 nm. The upper output spectrum in blue and red represent the stationary polarization and PI conditions, respectively. For each of these polarization conditions, both the pumps at the output of the PCF show significant spectral broadening due to SPM and XPM. The primary non-degenerate and partially degenerate FWM terms, resulted from pump-probe mixings, are labeled numerically in Fig. 5. It should be mentioned that since equal PPDs result in complete overlapping among primary FWM components and interacting pumps and probe [23], unequal optimum PPDs were chosen from the power fluctuation vs. PPD characteristics of the PCF, established in [21].The other output signals were caused by higher order FWM, due to the flat dispersion profile of the PCF.

 

Fig. 5 Input and output spectra of the PCF, captured at a resolution bandwidth (RB) = 0.06nm for stationary polarization and PI conditions. The offset in the traces is for clarity.

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Figure 6 shows the SPM and XPM broadening effects on the pumps and the probe in a 1 nm span at the output of the PCF. The remotely generated pump, which was inducing π/2-XPM phase shift on the probe, demonstrated more XPM broadening than the locally generated pump inducing π-XPM phase shift on the probe. Since the locally generated pump was at higher power level, time-dependent XPM induced phase on the remotely generated pump results in more spectral broadening. The spectral asymmetry, present in the output spectrum of both pumps, was due to XPM [28]. Conversely, the probe demonstrated no such spectral asymmetry due to optimum XPM phase transmultiplexing and least temporal walk-off. The depth of the spectral ripples of the un-modulated probe also diminished which demonstrates the efficacy of desired XPM phase induction [22].

 

Fig. 6 SPM and XPM broadening of each of the pumps and the probe output spectra in a 1 nm span captured at a RB=0.06nm. Traces were aligned for comparison.

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The qualitative comparison of the degree of XPM-induced phase shift on the probe relative to the precoded RZ-QPSK baseline is shown in Fig. 7. Though the probe at the output of the PCF experienced significant XPM-induced broadening and had a broader spectrum than the conventional IQ-modulator-generated RZ-QPSK baseline, the −3dB bandwidth of the AWG (0.44 nm) at the receiver introduced no excessive filtering penalty [Fig. 7(a)]. Significant interactions with the roll-off of the AWG filter profile occurred approximately −12dB relative to spectral peak, which was not present in case of the baseline signal spectrum. Furthermore, since the baseline signal spectrum demonstrates less ripple in comparison to its phase transmultiplexed equivalent [Fig. 7(b)], qualitatively the RZ-QPSK probe should be expected to incur some receiver sensitivity penalty.

 

Fig. 7 Comparison of the dual pump-phase transmultiplexed RZ-QPSK probe and FPGA precoded RZ-QPSK baseline spectra captured at a RB = 0.06nm. Plots were aligned in (a) and were offset in (b) for comparison

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Since a direct detection receiver requires phase-to-intensity conversion for retrieving information encoded in the signal’s phase by square-law detection, RZ-QPSK signals were detected as RZ-DQPSK [29]. For the stationary polarization condition, the dual pump-phase transmultiplexed RZ-DQPSK received signal demonstrated qualitatively similar eye-diagrams to those of the FPGA-precoded baseline RZ-DQPSK (Fig. 8). The eye-opening decreased slightly due to an increase in peak-peak variation (mV) of the alternate-mark-inversion (AMI) 1-rail and duobinary 1-rail. For the PI condition, due to polarization scrambling and pump depletion, the duobinary 1-rail of the detected RZ-DQPSK probe demonstrated larger peak-peak variation (17%) compared to that of both the baseline and the XPM converted RZ-QPSK for the stationary polarization condition. But in both polarization conditions, essentially error free detection (BER < 10−9) of the dual pump-probe transmultiplexed RZ-DQPSK probe could be achievable due to a sufficient eye-opening at OSNR > 23.8 dB/0.1 nm. For the PI condition, when the remotely generated pump was scrambled and the locally generated pump and the probe were launched at 27° and 46° respectively [Eq. (3)], the receiver sensitivity penalty at 10−9 BER was < 5.5 dB compared to the baseline RZ-DQPSK signal. The dual pump-phase transmultiplexed RZ-DQPSK-I and -Q required 23.6dB/0.1 nm and 23.8dB/0.1 nm OSNR respectively, to reach 10−9 BER, whereas baseline-I and -Q required 18.5 dB/0.1 dB OSNR in the same receiver setup (Fig. 9). The baseline-I and -Q demonstrated similar receiver sensitivity performances, within the experimental error, due to the detected sequence being PRBS, whereas phase-transmultiplexed RZ-QPSK-I/Q were non-PRBS. For the stationary polarization condition, the receiver sensitivity penalty due to phase transmultiplexing alone was found to be < 2.5 dB, compared to the baseline RZ-DQPSK signal. This demonstrates that the penalty incurred due to polarization-insensitive operation was < 3 dB. Table 2 below summarizes all the receiver sensitivity performance results.

 

Fig. 8 Eye-diagrams of the RZ-DQPSK signals captured in color-grade infinite persistence mode using a sampling module with a 50 GHz bandwidth and a 40 GHz detector at OSNR > 25 dB/0.1nm. The three rows show a qualitative comparison among the baseline, the stationary polarization condition and the PI condition. The OSNR of the remotely generated OOK signal was ≈45.8 dB/0.1 nm for both polarization conditions.

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Fig. 9 Receiver sensitivity measurements for FPGA-precoded RZ-DQPSK baseline and the dual pump-phase transmultiplexed RZ-DQPSK probe in stationary polarization and PI conditions.

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Tables Icon

Table 2. Receiver Sensitivity Measurements

5. Conclusion

For the first time to the authors’ knowledge, polarization-insensitive (PI) all-optical dual pump-phase transmultiplexing from 2 × 10-GBd OOKs to 10-GBd RZ-QPSK was demonstrated in a passive, birefringent, nonlinear PCF. The targeted PI-NOSP was achieved by controlling the XPM-phase induction on the RZ-probe using optimum PPD combinations, all within the C-band, along with launching the locally generated OOK pump and the probe respectively at 27° and 46° at the input of the PCF. The optimal launch angle condition remained unchanged when the SOP of the remotely generated OOK pump was not randomized unlike in a realistic transmission network, and was aligned to the low loss axis of the PCF. Relative to the FPGA-precoded RZ-DQPSK baseline, the receiver sensitivity penalty due to XPM and SOP scrambling of the remotely generated pump all together was < 5.5 dB, and the receiver sensitivity penalty due to SOP scrambling of the remotely generated OOK signal alone was < 3 dB, both at 10−9 BER.

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16. D. L. Peterson, P. J. Leo, and K. B. Rochford, “Field Measurements of state of polarization and PMD from a tier-1 carrier,” in Proc. OFC 2004, Anaheim, CA, paper FI1.

17. H. Bulow, “System outage probability due to first- and second-order PMD,” IEEE Photon. Technol. Lett. 10(5), 696–698 (1998). [CrossRef]  

18. A. S. Lenihan and G. M. Carter, “Polarization-Insensitive Wavelength Conversion at 40 Gb/s Using Birefringent Nonlinear Fiber,” in Proc. CLEO 2007, Baltimore, MD, paper CThAA2. [CrossRef]  

19. A. S. Lenihan, R. Salem, T. E. Murphy, and G. M. Carter, “All-optical 80-gb/s time-division demultiplexing using polarization-insensitive cross-phase modulation in photonic crystal fiber,” IEEE Photon. Technol. Lett. 18(12), 1329–1331 (2006). [CrossRef]  

20. W. Astar, A. S. Lenihan, and G. M. Carter, “Polarization-Insensitive Wavelength Conversion by FWM in a Highly Nonlinear PCF of Polarization-Scrambled 10-Gb/s RZ-OOK and RZ-DPSK Signals,” IEEE Photon. Technol. Lett. 19(20), 1676–1678 (2007). [CrossRef]  

21. W. Astar, C. C. Wei, Y. J. Chen, J. Chen, and G. M. Carter, “Polarization-insensitive, 40 Gb/s wavelength and RZ-OOK-to-RZ-BPSK modulation format conversion by XPM in a highly nonlinear PCF,” Opt. Express 16(16), 12039–12049 (2008). [CrossRef]   [PubMed]  

22. B. M. Cannon, W. Astar, T. Mahmood, P. Apiratikul, G. A. Porkolab, C. J. K. Richardson, and G. M. Carter, “Data Transfer From RZ-OOK to RZ-BPSK by Polarization-Insensitive XPM in a Passive Birefringent Nonlinear AlGaAs Waveguide,” J. Lightwave Technol. 31(6), 952–966 (2013). [CrossRef]  

23. N. Shibata, R. Braun, and R. Waarts, “Phase-mismatch dependence of efficiency of wave generation through four-wave mixing in a single-mode optical fiber,” IEEE J. Quantum Electron. 23(7), 1205–1210 (1987). [CrossRef]  

24. R. Salem, A. S. Lenihan, T. E. Murphy, and G. M. Carter, “All-optical 80-Gb/s time-division demultiplexing using polarization-insensitive cross-phase modulation in photonic crystal fiber,” IEEE J. Sel. Top. Quantum Electron. 18, 1329–1331 (2008). [CrossRef]  

25. C. D. Poole and D. L. Favin, “Polarization-mode dispersion measurements based on transmission spectra through a polarizer,” J. Lightwave Technol. 12(6), 917–929 (1994). [CrossRef]  

26. B. M. Cannon, T. Mahmood, W. Astar, P. Boudra, T. Mohsenin, and G. M. Carter, “Polarization-Insensitive Phase-Transmultiplexing and Multicasting of CSRZ-OOK and 4 × RZ-BPSK to 4 × RZ-QPSK via XPM in a Birefringent PCF,” IEEE Photon. J. 6(2), 1–11 (2014). [CrossRef]  

27. J. M. Gene, M. Soler, R. I. Killey, and J. Prat, “Investigation of 10-Gb/s optical DQPSK systems in presence of chromatic dispersion, fiber nonlinearities, and phase noise,” IEEE Photon. Technol. Lett. 16(3), 924–926 (2004). [CrossRef]  

28. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2001).

29. P. J. Winzer and R. Essiambre, “Advanced Optical Modulation Formats,” Proc. IEEE 94(5), 952–985 (2006). [CrossRef]  

References

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  1. M. Rohde, C. Caspar, N. Heimes, M. Konitzer, E. J. Bachus, and N. Hanik, “Robustness of DPSK direct detection transmission format in standard fibre WDM systems,” Electron. Lett. 36(17), 1483–1484 (2000).
    [Crossref]
  2. O. Vassilieva, T. Hoshida, S. Choudhary, G. Castanon, H. Kuwahara, T. Terahara, and H. Onaka, “Numerical comparison of NRZ, CS-RZ and IM-DPSK formats in 43 Gbit/s WDM transmission,” in Proc. LEOS 2001, San Diego, CA, paper ThC2.
    [Crossref]
  3. T. Mizuochi, K. Ishida, T. Kobayashi, J. Abe, K. Kinjo, K. Motoshima, and K. Kasahara, “A Comparative Study of DPSK and OOK WDM Transmission Over Transoceanic Distances and Their Performance Degradations Due to Nonlinear Phase Noise,” J. Lightwave Technol. 21(9), 1933–1943 (2003).
    [Crossref]
  4. C. Xu, L. Xiang, L. F. Mollenauer, and Xing Wei, “Comparison of return-to-zero differential phase-shift keying and ON-OFF keying in long-haul dispersion managed transmission,” IEEE Photon. Technol. Lett. 15(4), 617–619 (2003).
    [Crossref]
  5. P. J. Winzer, G. Raybon, H. Song, A. Adamiecki, S. Corteselli, A. H. Gnauck, D. A. Fishman, C. R. Doerr, S. Chandrasekhar, L. L. Buhl, T. J. Xia, G. Wellbrock, W. Lee, B. Basch, T. Kawanishi, K. Higuma, and Y. Painchaud, “100-Gb/s DQPSK Transmission: From Laboratory Experiments to Field Trials,” J. Lightwave Technol. 26(20), 3388–3402 (2008).
    [Crossref]
  6. K. Mishina, S. M. Nissanka, A. Maruta, S. Mitani, K. Ishida, K. Shimizu, T. Hatta, and K. Kitayama, “All-optical modulation format conversion from NRZ-OOK to RZ-QPSK using parallel SOA-MZI OOK/BPSK converters,” Opt. Express 15(12), 7774–7785 (2007).
    [Crossref] [PubMed]
  7. I. Kang, M. S. Rasras, L. L. Buhl, M. Dinu, G. Raybon, S. Cabot, M. A. Cappuzzo, L. T. Gomez, Y. F. Chen, S. S. Patel, A. A. Piccirilli, J. Jaques, and C. R. Giles, “High-Speed All-Optical Generation of Advanced Modulation Formats Using Photonic-Integrated All-Optical Format Converter,” IEEE J. Sel. Top. Quantum Electron. 18(2), 765–771 (2012).
    [Crossref]
  8. S. M. Nissanka, A. Maruta, S. Mitani, K. Shimizu, T. Miyahara, T. Aoyagi, T. Hatta, A. Sugitatsu, and K. Kitayama, “All-Optical Format Conversion from NRZ-OOK to RZ-QPSK Using Integrated SOA Three-Arm-MZI Wavelength Converter,” in Proc. OFC 2009, San Diego, CA, paper OThM5.
    [Crossref]
  9. K. Mishina, S. Kitagawa, and A. Maruta, “All-optical modulation format conversion from on-off-keying to multiple-level phase-shift-keying based on nonlinearity in optical fiber,” Opt. Express 15(13), 8444–8453 (2007).
    [Crossref] [PubMed]
  10. S. Kitagawa, S. M. Nissanka, and A. Maruta, “All-Optical Modulation Format Conversion from NRZ-OOK to RZ-M-ary PSK Based on Fiber Nonlinearity,” in Proc. OFC/NFOEC 2008, San Diego, CA, paper OTuD6.
    [Crossref]
  11. A. Maruta and S. Kitagawa, “All-optical modulation format conversion from NRZ-OOK to RZ-multilevel APSK based on fiber nonlinearity,” in Proc. IEEE/LEOS 2009, Innsbruck, paper MC4.
    [Crossref]
  12. H. Terauchi, A. Tokunaga, N. Horaguchi, and A. Maruta, “Design of all-optical NRZ-OOK/RZ-QPSK modulation format converter by use of cross phase modulation in optical fiber,” in Proc. OECC 2012, Busan, papar 6F1.
    [Crossref]
  13. J. Cameron, L. Chen, X. Bao, and J. Stears, “Time evolution of polarization mode dispersion in optical fibers,” IEEE Photon. Technol. Lett. 10(9), 1265–1267 (1998).
    [Crossref]
  14. D. Waddy, P. Lu, L. Chen, and X. Bao, “The Measurement of Fast State of Polarization Changes in Aerial Fiber,” in Proc. OFC 2001, Anaheim,CA, paper ThA3.
    [Crossref]
  15. P. M. Krummrich, E.-D. Schmidt, W. Weiershausen, and A. Mattheus, “Field trial results on statistics of fast polarization changes in long haul WDM transmission systems,” in Proc. OFC 2005, Anaheim, CA, paper OThT6.
    [Crossref]
  16. D. L. Peterson, P. J. Leo, and K. B. Rochford, “Field Measurements of state of polarization and PMD from a tier-1 carrier,” in Proc. OFC 2004, Anaheim, CA, paper FI1.
  17. H. Bulow, “System outage probability due to first- and second-order PMD,” IEEE Photon. Technol. Lett. 10(5), 696–698 (1998).
    [Crossref]
  18. A. S. Lenihan and G. M. Carter, “Polarization-Insensitive Wavelength Conversion at 40 Gb/s Using Birefringent Nonlinear Fiber,” in Proc. CLEO 2007, Baltimore, MD, paper CThAA2.
    [Crossref]
  19. A. S. Lenihan, R. Salem, T. E. Murphy, and G. M. Carter, “All-optical 80-gb/s time-division demultiplexing using polarization-insensitive cross-phase modulation in photonic crystal fiber,” IEEE Photon. Technol. Lett. 18(12), 1329–1331 (2006).
    [Crossref]
  20. W. Astar, A. S. Lenihan, and G. M. Carter, “Polarization-Insensitive Wavelength Conversion by FWM in a Highly Nonlinear PCF of Polarization-Scrambled 10-Gb/s RZ-OOK and RZ-DPSK Signals,” IEEE Photon. Technol. Lett. 19(20), 1676–1678 (2007).
    [Crossref]
  21. W. Astar, C. C. Wei, Y. J. Chen, J. Chen, and G. M. Carter, “Polarization-insensitive, 40 Gb/s wavelength and RZ-OOK-to-RZ-BPSK modulation format conversion by XPM in a highly nonlinear PCF,” Opt. Express 16(16), 12039–12049 (2008).
    [Crossref] [PubMed]
  22. B. M. Cannon, W. Astar, T. Mahmood, P. Apiratikul, G. A. Porkolab, C. J. K. Richardson, and G. M. Carter, “Data Transfer From RZ-OOK to RZ-BPSK by Polarization-Insensitive XPM in a Passive Birefringent Nonlinear AlGaAs Waveguide,” J. Lightwave Technol. 31(6), 952–966 (2013).
    [Crossref]
  23. N. Shibata, R. Braun, and R. Waarts, “Phase-mismatch dependence of efficiency of wave generation through four-wave mixing in a single-mode optical fiber,” IEEE J. Quantum Electron. 23(7), 1205–1210 (1987).
    [Crossref]
  24. R. Salem, A. S. Lenihan, T. E. Murphy, and G. M. Carter, “All-optical 80-Gb/s time-division demultiplexing using polarization-insensitive cross-phase modulation in photonic crystal fiber,” IEEE J. Sel. Top. Quantum Electron. 18, 1329–1331 (2008).
    [Crossref]
  25. C. D. Poole and D. L. Favin, “Polarization-mode dispersion measurements based on transmission spectra through a polarizer,” J. Lightwave Technol. 12(6), 917–929 (1994).
    [Crossref]
  26. B. M. Cannon, T. Mahmood, W. Astar, P. Boudra, T. Mohsenin, and G. M. Carter, “Polarization-Insensitive Phase-Transmultiplexing and Multicasting of CSRZ-OOK and 4 × RZ-BPSK to 4 × RZ-QPSK via XPM in a Birefringent PCF,” IEEE Photon. J. 6(2), 1–11 (2014).
    [Crossref]
  27. J. M. Gene, M. Soler, R. I. Killey, and J. Prat, “Investigation of 10-Gb/s optical DQPSK systems in presence of chromatic dispersion, fiber nonlinearities, and phase noise,” IEEE Photon. Technol. Lett. 16(3), 924–926 (2004).
    [Crossref]
  28. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2001).
  29. P. J. Winzer and R. Essiambre, “Advanced Optical Modulation Formats,” Proc. IEEE 94(5), 952–985 (2006).
    [Crossref]

2014 (1)

B. M. Cannon, T. Mahmood, W. Astar, P. Boudra, T. Mohsenin, and G. M. Carter, “Polarization-Insensitive Phase-Transmultiplexing and Multicasting of CSRZ-OOK and 4 × RZ-BPSK to 4 × RZ-QPSK via XPM in a Birefringent PCF,” IEEE Photon. J. 6(2), 1–11 (2014).
[Crossref]

2013 (1)

2012 (1)

I. Kang, M. S. Rasras, L. L. Buhl, M. Dinu, G. Raybon, S. Cabot, M. A. Cappuzzo, L. T. Gomez, Y. F. Chen, S. S. Patel, A. A. Piccirilli, J. Jaques, and C. R. Giles, “High-Speed All-Optical Generation of Advanced Modulation Formats Using Photonic-Integrated All-Optical Format Converter,” IEEE J. Sel. Top. Quantum Electron. 18(2), 765–771 (2012).
[Crossref]

2008 (3)

2007 (3)

2006 (2)

A. S. Lenihan, R. Salem, T. E. Murphy, and G. M. Carter, “All-optical 80-gb/s time-division demultiplexing using polarization-insensitive cross-phase modulation in photonic crystal fiber,” IEEE Photon. Technol. Lett. 18(12), 1329–1331 (2006).
[Crossref]

P. J. Winzer and R. Essiambre, “Advanced Optical Modulation Formats,” Proc. IEEE 94(5), 952–985 (2006).
[Crossref]

2004 (1)

J. M. Gene, M. Soler, R. I. Killey, and J. Prat, “Investigation of 10-Gb/s optical DQPSK systems in presence of chromatic dispersion, fiber nonlinearities, and phase noise,” IEEE Photon. Technol. Lett. 16(3), 924–926 (2004).
[Crossref]

2003 (2)

T. Mizuochi, K. Ishida, T. Kobayashi, J. Abe, K. Kinjo, K. Motoshima, and K. Kasahara, “A Comparative Study of DPSK and OOK WDM Transmission Over Transoceanic Distances and Their Performance Degradations Due to Nonlinear Phase Noise,” J. Lightwave Technol. 21(9), 1933–1943 (2003).
[Crossref]

C. Xu, L. Xiang, L. F. Mollenauer, and Xing Wei, “Comparison of return-to-zero differential phase-shift keying and ON-OFF keying in long-haul dispersion managed transmission,” IEEE Photon. Technol. Lett. 15(4), 617–619 (2003).
[Crossref]

2000 (1)

M. Rohde, C. Caspar, N. Heimes, M. Konitzer, E. J. Bachus, and N. Hanik, “Robustness of DPSK direct detection transmission format in standard fibre WDM systems,” Electron. Lett. 36(17), 1483–1484 (2000).
[Crossref]

1998 (2)

J. Cameron, L. Chen, X. Bao, and J. Stears, “Time evolution of polarization mode dispersion in optical fibers,” IEEE Photon. Technol. Lett. 10(9), 1265–1267 (1998).
[Crossref]

H. Bulow, “System outage probability due to first- and second-order PMD,” IEEE Photon. Technol. Lett. 10(5), 696–698 (1998).
[Crossref]

1994 (1)

C. D. Poole and D. L. Favin, “Polarization-mode dispersion measurements based on transmission spectra through a polarizer,” J. Lightwave Technol. 12(6), 917–929 (1994).
[Crossref]

1987 (1)

N. Shibata, R. Braun, and R. Waarts, “Phase-mismatch dependence of efficiency of wave generation through four-wave mixing in a single-mode optical fiber,” IEEE J. Quantum Electron. 23(7), 1205–1210 (1987).
[Crossref]

Abe, J.

Adamiecki, A.

Apiratikul, P.

Astar, W.

B. M. Cannon, T. Mahmood, W. Astar, P. Boudra, T. Mohsenin, and G. M. Carter, “Polarization-Insensitive Phase-Transmultiplexing and Multicasting of CSRZ-OOK and 4 × RZ-BPSK to 4 × RZ-QPSK via XPM in a Birefringent PCF,” IEEE Photon. J. 6(2), 1–11 (2014).
[Crossref]

B. M. Cannon, W. Astar, T. Mahmood, P. Apiratikul, G. A. Porkolab, C. J. K. Richardson, and G. M. Carter, “Data Transfer From RZ-OOK to RZ-BPSK by Polarization-Insensitive XPM in a Passive Birefringent Nonlinear AlGaAs Waveguide,” J. Lightwave Technol. 31(6), 952–966 (2013).
[Crossref]

W. Astar, C. C. Wei, Y. J. Chen, J. Chen, and G. M. Carter, “Polarization-insensitive, 40 Gb/s wavelength and RZ-OOK-to-RZ-BPSK modulation format conversion by XPM in a highly nonlinear PCF,” Opt. Express 16(16), 12039–12049 (2008).
[Crossref] [PubMed]

W. Astar, A. S. Lenihan, and G. M. Carter, “Polarization-Insensitive Wavelength Conversion by FWM in a Highly Nonlinear PCF of Polarization-Scrambled 10-Gb/s RZ-OOK and RZ-DPSK Signals,” IEEE Photon. Technol. Lett. 19(20), 1676–1678 (2007).
[Crossref]

Bachus, E. J.

M. Rohde, C. Caspar, N. Heimes, M. Konitzer, E. J. Bachus, and N. Hanik, “Robustness of DPSK direct detection transmission format in standard fibre WDM systems,” Electron. Lett. 36(17), 1483–1484 (2000).
[Crossref]

Bao, X.

J. Cameron, L. Chen, X. Bao, and J. Stears, “Time evolution of polarization mode dispersion in optical fibers,” IEEE Photon. Technol. Lett. 10(9), 1265–1267 (1998).
[Crossref]

Basch, B.

Boudra, P.

B. M. Cannon, T. Mahmood, W. Astar, P. Boudra, T. Mohsenin, and G. M. Carter, “Polarization-Insensitive Phase-Transmultiplexing and Multicasting of CSRZ-OOK and 4 × RZ-BPSK to 4 × RZ-QPSK via XPM in a Birefringent PCF,” IEEE Photon. J. 6(2), 1–11 (2014).
[Crossref]

Braun, R.

N. Shibata, R. Braun, and R. Waarts, “Phase-mismatch dependence of efficiency of wave generation through four-wave mixing in a single-mode optical fiber,” IEEE J. Quantum Electron. 23(7), 1205–1210 (1987).
[Crossref]

Buhl, L. L.

I. Kang, M. S. Rasras, L. L. Buhl, M. Dinu, G. Raybon, S. Cabot, M. A. Cappuzzo, L. T. Gomez, Y. F. Chen, S. S. Patel, A. A. Piccirilli, J. Jaques, and C. R. Giles, “High-Speed All-Optical Generation of Advanced Modulation Formats Using Photonic-Integrated All-Optical Format Converter,” IEEE J. Sel. Top. Quantum Electron. 18(2), 765–771 (2012).
[Crossref]

P. J. Winzer, G. Raybon, H. Song, A. Adamiecki, S. Corteselli, A. H. Gnauck, D. A. Fishman, C. R. Doerr, S. Chandrasekhar, L. L. Buhl, T. J. Xia, G. Wellbrock, W. Lee, B. Basch, T. Kawanishi, K. Higuma, and Y. Painchaud, “100-Gb/s DQPSK Transmission: From Laboratory Experiments to Field Trials,” J. Lightwave Technol. 26(20), 3388–3402 (2008).
[Crossref]

Bulow, H.

H. Bulow, “System outage probability due to first- and second-order PMD,” IEEE Photon. Technol. Lett. 10(5), 696–698 (1998).
[Crossref]

Cabot, S.

I. Kang, M. S. Rasras, L. L. Buhl, M. Dinu, G. Raybon, S. Cabot, M. A. Cappuzzo, L. T. Gomez, Y. F. Chen, S. S. Patel, A. A. Piccirilli, J. Jaques, and C. R. Giles, “High-Speed All-Optical Generation of Advanced Modulation Formats Using Photonic-Integrated All-Optical Format Converter,” IEEE J. Sel. Top. Quantum Electron. 18(2), 765–771 (2012).
[Crossref]

Cameron, J.

J. Cameron, L. Chen, X. Bao, and J. Stears, “Time evolution of polarization mode dispersion in optical fibers,” IEEE Photon. Technol. Lett. 10(9), 1265–1267 (1998).
[Crossref]

Cannon, B. M.

B. M. Cannon, T. Mahmood, W. Astar, P. Boudra, T. Mohsenin, and G. M. Carter, “Polarization-Insensitive Phase-Transmultiplexing and Multicasting of CSRZ-OOK and 4 × RZ-BPSK to 4 × RZ-QPSK via XPM in a Birefringent PCF,” IEEE Photon. J. 6(2), 1–11 (2014).
[Crossref]

B. M. Cannon, W. Astar, T. Mahmood, P. Apiratikul, G. A. Porkolab, C. J. K. Richardson, and G. M. Carter, “Data Transfer From RZ-OOK to RZ-BPSK by Polarization-Insensitive XPM in a Passive Birefringent Nonlinear AlGaAs Waveguide,” J. Lightwave Technol. 31(6), 952–966 (2013).
[Crossref]

Cappuzzo, M. A.

I. Kang, M. S. Rasras, L. L. Buhl, M. Dinu, G. Raybon, S. Cabot, M. A. Cappuzzo, L. T. Gomez, Y. F. Chen, S. S. Patel, A. A. Piccirilli, J. Jaques, and C. R. Giles, “High-Speed All-Optical Generation of Advanced Modulation Formats Using Photonic-Integrated All-Optical Format Converter,” IEEE J. Sel. Top. Quantum Electron. 18(2), 765–771 (2012).
[Crossref]

Carter, G. M.

B. M. Cannon, T. Mahmood, W. Astar, P. Boudra, T. Mohsenin, and G. M. Carter, “Polarization-Insensitive Phase-Transmultiplexing and Multicasting of CSRZ-OOK and 4 × RZ-BPSK to 4 × RZ-QPSK via XPM in a Birefringent PCF,” IEEE Photon. J. 6(2), 1–11 (2014).
[Crossref]

B. M. Cannon, W. Astar, T. Mahmood, P. Apiratikul, G. A. Porkolab, C. J. K. Richardson, and G. M. Carter, “Data Transfer From RZ-OOK to RZ-BPSK by Polarization-Insensitive XPM in a Passive Birefringent Nonlinear AlGaAs Waveguide,” J. Lightwave Technol. 31(6), 952–966 (2013).
[Crossref]

R. Salem, A. S. Lenihan, T. E. Murphy, and G. M. Carter, “All-optical 80-Gb/s time-division demultiplexing using polarization-insensitive cross-phase modulation in photonic crystal fiber,” IEEE J. Sel. Top. Quantum Electron. 18, 1329–1331 (2008).
[Crossref]

W. Astar, C. C. Wei, Y. J. Chen, J. Chen, and G. M. Carter, “Polarization-insensitive, 40 Gb/s wavelength and RZ-OOK-to-RZ-BPSK modulation format conversion by XPM in a highly nonlinear PCF,” Opt. Express 16(16), 12039–12049 (2008).
[Crossref] [PubMed]

W. Astar, A. S. Lenihan, and G. M. Carter, “Polarization-Insensitive Wavelength Conversion by FWM in a Highly Nonlinear PCF of Polarization-Scrambled 10-Gb/s RZ-OOK and RZ-DPSK Signals,” IEEE Photon. Technol. Lett. 19(20), 1676–1678 (2007).
[Crossref]

A. S. Lenihan, R. Salem, T. E. Murphy, and G. M. Carter, “All-optical 80-gb/s time-division demultiplexing using polarization-insensitive cross-phase modulation in photonic crystal fiber,” IEEE Photon. Technol. Lett. 18(12), 1329–1331 (2006).
[Crossref]

Caspar, C.

M. Rohde, C. Caspar, N. Heimes, M. Konitzer, E. J. Bachus, and N. Hanik, “Robustness of DPSK direct detection transmission format in standard fibre WDM systems,” Electron. Lett. 36(17), 1483–1484 (2000).
[Crossref]

Chandrasekhar, S.

Chen, J.

Chen, L.

J. Cameron, L. Chen, X. Bao, and J. Stears, “Time evolution of polarization mode dispersion in optical fibers,” IEEE Photon. Technol. Lett. 10(9), 1265–1267 (1998).
[Crossref]

Chen, Y. F.

I. Kang, M. S. Rasras, L. L. Buhl, M. Dinu, G. Raybon, S. Cabot, M. A. Cappuzzo, L. T. Gomez, Y. F. Chen, S. S. Patel, A. A. Piccirilli, J. Jaques, and C. R. Giles, “High-Speed All-Optical Generation of Advanced Modulation Formats Using Photonic-Integrated All-Optical Format Converter,” IEEE J. Sel. Top. Quantum Electron. 18(2), 765–771 (2012).
[Crossref]

Chen, Y. J.

Corteselli, S.

Dinu, M.

I. Kang, M. S. Rasras, L. L. Buhl, M. Dinu, G. Raybon, S. Cabot, M. A. Cappuzzo, L. T. Gomez, Y. F. Chen, S. S. Patel, A. A. Piccirilli, J. Jaques, and C. R. Giles, “High-Speed All-Optical Generation of Advanced Modulation Formats Using Photonic-Integrated All-Optical Format Converter,” IEEE J. Sel. Top. Quantum Electron. 18(2), 765–771 (2012).
[Crossref]

Doerr, C. R.

Essiambre, R.

P. J. Winzer and R. Essiambre, “Advanced Optical Modulation Formats,” Proc. IEEE 94(5), 952–985 (2006).
[Crossref]

Favin, D. L.

C. D. Poole and D. L. Favin, “Polarization-mode dispersion measurements based on transmission spectra through a polarizer,” J. Lightwave Technol. 12(6), 917–929 (1994).
[Crossref]

Fishman, D. A.

Gene, J. M.

J. M. Gene, M. Soler, R. I. Killey, and J. Prat, “Investigation of 10-Gb/s optical DQPSK systems in presence of chromatic dispersion, fiber nonlinearities, and phase noise,” IEEE Photon. Technol. Lett. 16(3), 924–926 (2004).
[Crossref]

Giles, C. R.

I. Kang, M. S. Rasras, L. L. Buhl, M. Dinu, G. Raybon, S. Cabot, M. A. Cappuzzo, L. T. Gomez, Y. F. Chen, S. S. Patel, A. A. Piccirilli, J. Jaques, and C. R. Giles, “High-Speed All-Optical Generation of Advanced Modulation Formats Using Photonic-Integrated All-Optical Format Converter,” IEEE J. Sel. Top. Quantum Electron. 18(2), 765–771 (2012).
[Crossref]

Gnauck, A. H.

Gomez, L. T.

I. Kang, M. S. Rasras, L. L. Buhl, M. Dinu, G. Raybon, S. Cabot, M. A. Cappuzzo, L. T. Gomez, Y. F. Chen, S. S. Patel, A. A. Piccirilli, J. Jaques, and C. R. Giles, “High-Speed All-Optical Generation of Advanced Modulation Formats Using Photonic-Integrated All-Optical Format Converter,” IEEE J. Sel. Top. Quantum Electron. 18(2), 765–771 (2012).
[Crossref]

Hanik, N.

M. Rohde, C. Caspar, N. Heimes, M. Konitzer, E. J. Bachus, and N. Hanik, “Robustness of DPSK direct detection transmission format in standard fibre WDM systems,” Electron. Lett. 36(17), 1483–1484 (2000).
[Crossref]

Hatta, T.

Heimes, N.

M. Rohde, C. Caspar, N. Heimes, M. Konitzer, E. J. Bachus, and N. Hanik, “Robustness of DPSK direct detection transmission format in standard fibre WDM systems,” Electron. Lett. 36(17), 1483–1484 (2000).
[Crossref]

Higuma, K.

Ishida, K.

Jaques, J.

I. Kang, M. S. Rasras, L. L. Buhl, M. Dinu, G. Raybon, S. Cabot, M. A. Cappuzzo, L. T. Gomez, Y. F. Chen, S. S. Patel, A. A. Piccirilli, J. Jaques, and C. R. Giles, “High-Speed All-Optical Generation of Advanced Modulation Formats Using Photonic-Integrated All-Optical Format Converter,” IEEE J. Sel. Top. Quantum Electron. 18(2), 765–771 (2012).
[Crossref]

Kang, I.

I. Kang, M. S. Rasras, L. L. Buhl, M. Dinu, G. Raybon, S. Cabot, M. A. Cappuzzo, L. T. Gomez, Y. F. Chen, S. S. Patel, A. A. Piccirilli, J. Jaques, and C. R. Giles, “High-Speed All-Optical Generation of Advanced Modulation Formats Using Photonic-Integrated All-Optical Format Converter,” IEEE J. Sel. Top. Quantum Electron. 18(2), 765–771 (2012).
[Crossref]

Kasahara, K.

Kawanishi, T.

Killey, R. I.

J. M. Gene, M. Soler, R. I. Killey, and J. Prat, “Investigation of 10-Gb/s optical DQPSK systems in presence of chromatic dispersion, fiber nonlinearities, and phase noise,” IEEE Photon. Technol. Lett. 16(3), 924–926 (2004).
[Crossref]

Kinjo, K.

Kitagawa, S.

Kitayama, K.

Kobayashi, T.

Konitzer, M.

M. Rohde, C. Caspar, N. Heimes, M. Konitzer, E. J. Bachus, and N. Hanik, “Robustness of DPSK direct detection transmission format in standard fibre WDM systems,” Electron. Lett. 36(17), 1483–1484 (2000).
[Crossref]

Lee, W.

Lenihan, A. S.

R. Salem, A. S. Lenihan, T. E. Murphy, and G. M. Carter, “All-optical 80-Gb/s time-division demultiplexing using polarization-insensitive cross-phase modulation in photonic crystal fiber,” IEEE J. Sel. Top. Quantum Electron. 18, 1329–1331 (2008).
[Crossref]

W. Astar, A. S. Lenihan, and G. M. Carter, “Polarization-Insensitive Wavelength Conversion by FWM in a Highly Nonlinear PCF of Polarization-Scrambled 10-Gb/s RZ-OOK and RZ-DPSK Signals,” IEEE Photon. Technol. Lett. 19(20), 1676–1678 (2007).
[Crossref]

A. S. Lenihan, R. Salem, T. E. Murphy, and G. M. Carter, “All-optical 80-gb/s time-division demultiplexing using polarization-insensitive cross-phase modulation in photonic crystal fiber,” IEEE Photon. Technol. Lett. 18(12), 1329–1331 (2006).
[Crossref]

Mahmood, T.

B. M. Cannon, T. Mahmood, W. Astar, P. Boudra, T. Mohsenin, and G. M. Carter, “Polarization-Insensitive Phase-Transmultiplexing and Multicasting of CSRZ-OOK and 4 × RZ-BPSK to 4 × RZ-QPSK via XPM in a Birefringent PCF,” IEEE Photon. J. 6(2), 1–11 (2014).
[Crossref]

B. M. Cannon, W. Astar, T. Mahmood, P. Apiratikul, G. A. Porkolab, C. J. K. Richardson, and G. M. Carter, “Data Transfer From RZ-OOK to RZ-BPSK by Polarization-Insensitive XPM in a Passive Birefringent Nonlinear AlGaAs Waveguide,” J. Lightwave Technol. 31(6), 952–966 (2013).
[Crossref]

Maruta, A.

Mishina, K.

Mitani, S.

Mizuochi, T.

Mohsenin, T.

B. M. Cannon, T. Mahmood, W. Astar, P. Boudra, T. Mohsenin, and G. M. Carter, “Polarization-Insensitive Phase-Transmultiplexing and Multicasting of CSRZ-OOK and 4 × RZ-BPSK to 4 × RZ-QPSK via XPM in a Birefringent PCF,” IEEE Photon. J. 6(2), 1–11 (2014).
[Crossref]

Mollenauer, L. F.

C. Xu, L. Xiang, L. F. Mollenauer, and Xing Wei, “Comparison of return-to-zero differential phase-shift keying and ON-OFF keying in long-haul dispersion managed transmission,” IEEE Photon. Technol. Lett. 15(4), 617–619 (2003).
[Crossref]

Motoshima, K.

Murphy, T. E.

R. Salem, A. S. Lenihan, T. E. Murphy, and G. M. Carter, “All-optical 80-Gb/s time-division demultiplexing using polarization-insensitive cross-phase modulation in photonic crystal fiber,” IEEE J. Sel. Top. Quantum Electron. 18, 1329–1331 (2008).
[Crossref]

A. S. Lenihan, R. Salem, T. E. Murphy, and G. M. Carter, “All-optical 80-gb/s time-division demultiplexing using polarization-insensitive cross-phase modulation in photonic crystal fiber,” IEEE Photon. Technol. Lett. 18(12), 1329–1331 (2006).
[Crossref]

Nissanka, S. M.

Painchaud, Y.

Patel, S. S.

I. Kang, M. S. Rasras, L. L. Buhl, M. Dinu, G. Raybon, S. Cabot, M. A. Cappuzzo, L. T. Gomez, Y. F. Chen, S. S. Patel, A. A. Piccirilli, J. Jaques, and C. R. Giles, “High-Speed All-Optical Generation of Advanced Modulation Formats Using Photonic-Integrated All-Optical Format Converter,” IEEE J. Sel. Top. Quantum Electron. 18(2), 765–771 (2012).
[Crossref]

Piccirilli, A. A.

I. Kang, M. S. Rasras, L. L. Buhl, M. Dinu, G. Raybon, S. Cabot, M. A. Cappuzzo, L. T. Gomez, Y. F. Chen, S. S. Patel, A. A. Piccirilli, J. Jaques, and C. R. Giles, “High-Speed All-Optical Generation of Advanced Modulation Formats Using Photonic-Integrated All-Optical Format Converter,” IEEE J. Sel. Top. Quantum Electron. 18(2), 765–771 (2012).
[Crossref]

Poole, C. D.

C. D. Poole and D. L. Favin, “Polarization-mode dispersion measurements based on transmission spectra through a polarizer,” J. Lightwave Technol. 12(6), 917–929 (1994).
[Crossref]

Porkolab, G. A.

Prat, J.

J. M. Gene, M. Soler, R. I. Killey, and J. Prat, “Investigation of 10-Gb/s optical DQPSK systems in presence of chromatic dispersion, fiber nonlinearities, and phase noise,” IEEE Photon. Technol. Lett. 16(3), 924–926 (2004).
[Crossref]

Rasras, M. S.

I. Kang, M. S. Rasras, L. L. Buhl, M. Dinu, G. Raybon, S. Cabot, M. A. Cappuzzo, L. T. Gomez, Y. F. Chen, S. S. Patel, A. A. Piccirilli, J. Jaques, and C. R. Giles, “High-Speed All-Optical Generation of Advanced Modulation Formats Using Photonic-Integrated All-Optical Format Converter,” IEEE J. Sel. Top. Quantum Electron. 18(2), 765–771 (2012).
[Crossref]

Raybon, G.

I. Kang, M. S. Rasras, L. L. Buhl, M. Dinu, G. Raybon, S. Cabot, M. A. Cappuzzo, L. T. Gomez, Y. F. Chen, S. S. Patel, A. A. Piccirilli, J. Jaques, and C. R. Giles, “High-Speed All-Optical Generation of Advanced Modulation Formats Using Photonic-Integrated All-Optical Format Converter,” IEEE J. Sel. Top. Quantum Electron. 18(2), 765–771 (2012).
[Crossref]

P. J. Winzer, G. Raybon, H. Song, A. Adamiecki, S. Corteselli, A. H. Gnauck, D. A. Fishman, C. R. Doerr, S. Chandrasekhar, L. L. Buhl, T. J. Xia, G. Wellbrock, W. Lee, B. Basch, T. Kawanishi, K. Higuma, and Y. Painchaud, “100-Gb/s DQPSK Transmission: From Laboratory Experiments to Field Trials,” J. Lightwave Technol. 26(20), 3388–3402 (2008).
[Crossref]

Richardson, C. J. K.

Rohde, M.

M. Rohde, C. Caspar, N. Heimes, M. Konitzer, E. J. Bachus, and N. Hanik, “Robustness of DPSK direct detection transmission format in standard fibre WDM systems,” Electron. Lett. 36(17), 1483–1484 (2000).
[Crossref]

Salem, R.

R. Salem, A. S. Lenihan, T. E. Murphy, and G. M. Carter, “All-optical 80-Gb/s time-division demultiplexing using polarization-insensitive cross-phase modulation in photonic crystal fiber,” IEEE J. Sel. Top. Quantum Electron. 18, 1329–1331 (2008).
[Crossref]

A. S. Lenihan, R. Salem, T. E. Murphy, and G. M. Carter, “All-optical 80-gb/s time-division demultiplexing using polarization-insensitive cross-phase modulation in photonic crystal fiber,” IEEE Photon. Technol. Lett. 18(12), 1329–1331 (2006).
[Crossref]

Shibata, N.

N. Shibata, R. Braun, and R. Waarts, “Phase-mismatch dependence of efficiency of wave generation through four-wave mixing in a single-mode optical fiber,” IEEE J. Quantum Electron. 23(7), 1205–1210 (1987).
[Crossref]

Shimizu, K.

Soler, M.

J. M. Gene, M. Soler, R. I. Killey, and J. Prat, “Investigation of 10-Gb/s optical DQPSK systems in presence of chromatic dispersion, fiber nonlinearities, and phase noise,” IEEE Photon. Technol. Lett. 16(3), 924–926 (2004).
[Crossref]

Song, H.

Stears, J.

J. Cameron, L. Chen, X. Bao, and J. Stears, “Time evolution of polarization mode dispersion in optical fibers,” IEEE Photon. Technol. Lett. 10(9), 1265–1267 (1998).
[Crossref]

Waarts, R.

N. Shibata, R. Braun, and R. Waarts, “Phase-mismatch dependence of efficiency of wave generation through four-wave mixing in a single-mode optical fiber,” IEEE J. Quantum Electron. 23(7), 1205–1210 (1987).
[Crossref]

Wei, C. C.

Wellbrock, G.

Winzer, P. J.

Xia, T. J.

Xiang, L.

C. Xu, L. Xiang, L. F. Mollenauer, and Xing Wei, “Comparison of return-to-zero differential phase-shift keying and ON-OFF keying in long-haul dispersion managed transmission,” IEEE Photon. Technol. Lett. 15(4), 617–619 (2003).
[Crossref]

Xing Wei,

C. Xu, L. Xiang, L. F. Mollenauer, and Xing Wei, “Comparison of return-to-zero differential phase-shift keying and ON-OFF keying in long-haul dispersion managed transmission,” IEEE Photon. Technol. Lett. 15(4), 617–619 (2003).
[Crossref]

Xu, C.

C. Xu, L. Xiang, L. F. Mollenauer, and Xing Wei, “Comparison of return-to-zero differential phase-shift keying and ON-OFF keying in long-haul dispersion managed transmission,” IEEE Photon. Technol. Lett. 15(4), 617–619 (2003).
[Crossref]

Electron. Lett. (1)

M. Rohde, C. Caspar, N. Heimes, M. Konitzer, E. J. Bachus, and N. Hanik, “Robustness of DPSK direct detection transmission format in standard fibre WDM systems,” Electron. Lett. 36(17), 1483–1484 (2000).
[Crossref]

IEEE J. Quantum Electron. (1)

N. Shibata, R. Braun, and R. Waarts, “Phase-mismatch dependence of efficiency of wave generation through four-wave mixing in a single-mode optical fiber,” IEEE J. Quantum Electron. 23(7), 1205–1210 (1987).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (2)

R. Salem, A. S. Lenihan, T. E. Murphy, and G. M. Carter, “All-optical 80-Gb/s time-division demultiplexing using polarization-insensitive cross-phase modulation in photonic crystal fiber,” IEEE J. Sel. Top. Quantum Electron. 18, 1329–1331 (2008).
[Crossref]

I. Kang, M. S. Rasras, L. L. Buhl, M. Dinu, G. Raybon, S. Cabot, M. A. Cappuzzo, L. T. Gomez, Y. F. Chen, S. S. Patel, A. A. Piccirilli, J. Jaques, and C. R. Giles, “High-Speed All-Optical Generation of Advanced Modulation Formats Using Photonic-Integrated All-Optical Format Converter,” IEEE J. Sel. Top. Quantum Electron. 18(2), 765–771 (2012).
[Crossref]

IEEE Photon. J. (1)

B. M. Cannon, T. Mahmood, W. Astar, P. Boudra, T. Mohsenin, and G. M. Carter, “Polarization-Insensitive Phase-Transmultiplexing and Multicasting of CSRZ-OOK and 4 × RZ-BPSK to 4 × RZ-QPSK via XPM in a Birefringent PCF,” IEEE Photon. J. 6(2), 1–11 (2014).
[Crossref]

IEEE Photon. Technol. Lett. (6)

J. M. Gene, M. Soler, R. I. Killey, and J. Prat, “Investigation of 10-Gb/s optical DQPSK systems in presence of chromatic dispersion, fiber nonlinearities, and phase noise,” IEEE Photon. Technol. Lett. 16(3), 924–926 (2004).
[Crossref]

A. S. Lenihan, R. Salem, T. E. Murphy, and G. M. Carter, “All-optical 80-gb/s time-division demultiplexing using polarization-insensitive cross-phase modulation in photonic crystal fiber,” IEEE Photon. Technol. Lett. 18(12), 1329–1331 (2006).
[Crossref]

W. Astar, A. S. Lenihan, and G. M. Carter, “Polarization-Insensitive Wavelength Conversion by FWM in a Highly Nonlinear PCF of Polarization-Scrambled 10-Gb/s RZ-OOK and RZ-DPSK Signals,” IEEE Photon. Technol. Lett. 19(20), 1676–1678 (2007).
[Crossref]

H. Bulow, “System outage probability due to first- and second-order PMD,” IEEE Photon. Technol. Lett. 10(5), 696–698 (1998).
[Crossref]

J. Cameron, L. Chen, X. Bao, and J. Stears, “Time evolution of polarization mode dispersion in optical fibers,” IEEE Photon. Technol. Lett. 10(9), 1265–1267 (1998).
[Crossref]

C. Xu, L. Xiang, L. F. Mollenauer, and Xing Wei, “Comparison of return-to-zero differential phase-shift keying and ON-OFF keying in long-haul dispersion managed transmission,” IEEE Photon. Technol. Lett. 15(4), 617–619 (2003).
[Crossref]

J. Lightwave Technol. (4)

Opt. Express (3)

Proc. IEEE (1)

P. J. Winzer and R. Essiambre, “Advanced Optical Modulation Formats,” Proc. IEEE 94(5), 952–985 (2006).
[Crossref]

Other (10)

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2001).

S. Kitagawa, S. M. Nissanka, and A. Maruta, “All-Optical Modulation Format Conversion from NRZ-OOK to RZ-M-ary PSK Based on Fiber Nonlinearity,” in Proc. OFC/NFOEC 2008, San Diego, CA, paper OTuD6.
[Crossref]

A. Maruta and S. Kitagawa, “All-optical modulation format conversion from NRZ-OOK to RZ-multilevel APSK based on fiber nonlinearity,” in Proc. IEEE/LEOS 2009, Innsbruck, paper MC4.
[Crossref]

H. Terauchi, A. Tokunaga, N. Horaguchi, and A. Maruta, “Design of all-optical NRZ-OOK/RZ-QPSK modulation format converter by use of cross phase modulation in optical fiber,” in Proc. OECC 2012, Busan, papar 6F1.
[Crossref]

O. Vassilieva, T. Hoshida, S. Choudhary, G. Castanon, H. Kuwahara, T. Terahara, and H. Onaka, “Numerical comparison of NRZ, CS-RZ and IM-DPSK formats in 43 Gbit/s WDM transmission,” in Proc. LEOS 2001, San Diego, CA, paper ThC2.
[Crossref]

D. Waddy, P. Lu, L. Chen, and X. Bao, “The Measurement of Fast State of Polarization Changes in Aerial Fiber,” in Proc. OFC 2001, Anaheim,CA, paper ThA3.
[Crossref]

P. M. Krummrich, E.-D. Schmidt, W. Weiershausen, and A. Mattheus, “Field trial results on statistics of fast polarization changes in long haul WDM transmission systems,” in Proc. OFC 2005, Anaheim, CA, paper OThT6.
[Crossref]

D. L. Peterson, P. J. Leo, and K. B. Rochford, “Field Measurements of state of polarization and PMD from a tier-1 carrier,” in Proc. OFC 2004, Anaheim, CA, paper FI1.

A. S. Lenihan and G. M. Carter, “Polarization-Insensitive Wavelength Conversion at 40 Gb/s Using Birefringent Nonlinear Fiber,” in Proc. CLEO 2007, Baltimore, MD, paper CThAA2.
[Crossref]

S. M. Nissanka, A. Maruta, S. Mitani, K. Shimizu, T. Miyahara, T. Aoyagi, T. Hatta, A. Sugitatsu, and K. Kitayama, “All-Optical Format Conversion from NRZ-OOK to RZ-QPSK Using Integrated SOA Three-Arm-MZI Wavelength Converter,” in Proc. OFC 2009, San Diego, CA, paper OThM5.
[Crossref]

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Figures (9)

Fig. 1
Fig. 1 Scheme for dual pump-phase transmultiplexing via XPM to achieve RZ-QPSK at the output of the NOSP system.
Fig. 2
Fig. 2 Experimental setup for PI all-optical dual pump-phase transmultiplexing from 2 × 10-GBd OOKs to 10-GBd RZ-QPSK utilizing XPM in a birefringent nonlinear PCF. PS: polarization scrambler, ODL: optical delay line, VOA: variable optical attenuator, EDFA: Er3+-doped fiber amplifier, HPA: high power Er3+-doped fiber amplifier, OBPF: optical bandpass filter, PA: polarization analyzer, AWG: arrayed waveguide grating, LNF: low-noise figure, AMZI: asymmetric Mach–Zehnder interferometer, BPD: balanced photodetector, TIA: trans-impedance amplifier, LA: limiting amplifier, CDR: clock/data recovery, ED: error detector.
Fig. 3
Fig. 3 Experimental setup for direct detection of precoded RZ-QPSK baseline. FS: frequency synthesizer, LVPECL: low-voltage positive emitter-coupled logic, LA: limiting amplifier.
Fig. 4
Fig. 4 Measurement of the relative launch angle change of (a) the probe and (b) the locally generated pump using Polarization Analyzer Poincare sphere: Marker A represents the probe SOP when the remotely generated pump and the probe were aligned to the same birefringent axis, whereas Marker C represents the locally generated pump SOP when the pumps are orthogonal. Marker (B) and (D) denotes (a) the probe and the locally generated pump SOP respectively when the remotely generated pump was polarization-scrambled and for the best BER performance of the dual pump-phase transmultiplexed PI-QPSK probe.
Fig. 5
Fig. 5 Input and output spectra of the PCF, captured at a resolution bandwidth (RB) = 0.06nm for stationary polarization and PI conditions. The offset in the traces is for clarity.
Fig. 6
Fig. 6 SPM and XPM broadening of each of the pumps and the probe output spectra in a 1 nm span captured at a RB=0.06nm. Traces were aligned for comparison.
Fig. 7
Fig. 7 Comparison of the dual pump-phase transmultiplexed RZ-QPSK probe and FPGA precoded RZ-QPSK baseline spectra captured at a RB = 0.06nm. Plots were aligned in (a) and were offset in (b) for comparison
Fig. 8
Fig. 8 Eye-diagrams of the RZ-DQPSK signals captured in color-grade infinite persistence mode using a sampling module with a 50 GHz bandwidth and a 40 GHz detector at OSNR > 25 dB/0.1nm. The three rows show a qualitative comparison among the baseline, the stationary polarization condition and the PI condition. The OSNR of the remotely generated OOK signal was ≈45.8 dB/0.1 nm for both polarization conditions.
Fig. 9
Fig. 9 Receiver sensitivity measurements for FPGA-precoded RZ-DQPSK baseline and the dual pump-phase transmultiplexed RZ-DQPSK probe in stationary polarization and PI conditions.

Tables (2)

Tables Icon

Table 1 Data on OOK Pumps and Corresponding XPM Phase Shift on RZ-probe

Tables Icon

Table 2 Receiver Sensitivity Measurements

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

ϕ pr-out (t)= ϕ pr-in (t)+ ϕ pr-SPM (t)+ ϕ XPM-1 (t)+ ϕ XPM-2 (t) = ϕ pr-in (t)+γ L eff P pr (t)+2γ L eff P OOK 1 (t)+2γ L eff P OOK 2 (t),
I n * = A ¯ n B ¯ n I ¯ n1 * + A ¯ n B n Q ¯ n1 * + A n B n I n1 * + A n B ¯ n Q n1 * Q n * = A ¯ n B ¯ n Q ¯ n1 * + A ¯ n B n I n1 * + A n B n Q n1 * + A n B ¯ n I ¯ n1 *
Δ θ 1 = tan 1 ( 1 s 1B 1+ s 1B ) tan 1 ( 1 s 1A 1+ s 1A ) 46 o 0 o = 46 o Δ θ 2 = 90 o tan 1 ( 1 s 1D 1+ s 1D ) tan 1 ( 1 s 1C 1+ s 1C ) 90 o 63 o 0 o = 27 o

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