Optics Communications 459 (2020) 124871

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Optics Communications

journal homepage: www.elsevier.com/locate/optcom

Demonstration of wavelength tunable optical modulation format conversionfrom 20 and 30 Gbit/s QPSK to PAM4 using nonlinear wave mixingAhmad Fallahpour a,∗, Fatemeh Alishahi a, Ahmed Almaiman a,b, Yinwen Cao a,Amirhossein Mohajerin-Ariaei a, Peicheng Liao a, Cong Liu a, Kaiheng Zou a, Carsten Langrock c,Martin M. Fejer c, Moshe Tur d, Alan E. Willner a

a Department of Electrical Engineering, University of Southern California, Los Angeles, CA 90089, USAb King Saud University, Riyadh, Saudi Arabiac Edward L. Ginzton Laboratory, 348 Via Pueblo Mall, Stanford University, Stanford, CA 94305, USAd School of Electrical Engineering, Tel Aviv University, Ramat Aviv 69978, Israel

A R T I C L E I N F O

Keywords:Modulation format conversionNonlinear wave mixingQuadrature phase shift keying (QPSK)Four-level pulse amplitude modulation (PAM4)

A B S T R A C T

We experimentally demonstrate tunable modulation format conversion of quadrature phase shift keying (QPSK)to four-level pulse amplitude modulation (PAM4) using nonlinear wave mixing in periodically-poled Lithium-Niobate (PPLN) waveguides. The conversion operation is accomplished by: (a) rotating the data constellationby applying a phase offset, and (b) offsetting the data constellation in the radial direction by adding a constantbias optical power. In this manner, the constellation data points can be tailored to have different amplitudelevels, thus realizing the PAM4 format. In a tunable fashion, we convert 20- and 30-Gbit/s QPSK channels toPAM4, and open eye diagrams and low bit-error-rates (BER) are obtained at the receiver. We investigate theimpact of phase rotation on the eye diagram of the received signal, and we determine that a phase rotationof ∼71◦ provides substantially good performance. Wavelength tunability of the output PAM4 is demonstratedby tuning the wavelength of the pump. In addition, open eye is also obtained when a high phase noise laseris used for modulating QPSK signal.

1. Introduction

High-order modulation formats have been of great importance foroptical communications systems due to their higher system capacity, in-creased spectral efficiency, and lower speed requirement of electronics[1,2]. One of the most common data formats is quadrature-phase-shift-keying (QPSK), which encodes 2 bits per symbol and typicallyrequires coherent detection at the receiver. The coherent receivers cansubstantially compensate many transmission impairments [3–5].

More recently, simple direct-detection approaches have gainedmuch interest, especially for data centers and short-haul applications.For example, four-level pulse amplitude modulation (PAM4) can: (a)have higher capacity and spectral efficiency as compared to conven-tional on–off keying (OOK), and (b) be received using relatively simpleand cost-effective direct-detection schemes [6–8]. Note that PAM4 issimilar to QPSK in its spectral efficiency as each symbol represents twobits.

A potential challenge is that the preferred modulation format maybe different for data channels in different parts of an optical network.For example, QPSK may be preferred for a long-haul segment whereasPAM4 may be preferred for a short-distance link in a local area.

∗ Corresponding author.E-mail address: fallahpo@usc.edu (A. Fallahpour).

Therefore, it may be valuable to have an optical gateway that canconvert a data-channel’s format between QPSK and PAM4 and avoidoptical-to-electrical-to-optical conversion.

The following operations have previously been reported: (a) de-aggregation of a 16-ary quadrature amplitude modulation (16-QAM)channel into two PAM4 channels using coherent detection and notdirect detection [9,10]. (b) binary-phase-shift-keying (BPSK) to OOKbased on phase-sensitive amplification [11], (c) OOK to BPSK usingcross-phase modulation (XPM) in a highly nonlinear fiber [12]; and (d)PAM4 to QPSK format conversion [13].

In this paper, we demonstrate optical format and wavelength con-version of 20 and 30 Gb/s QPSK-to-PAM4 by using two nonlinearwave mixing stages [14]. We manipulate the input QPSK constellationto generate PAM4 in the output. The QPSK constellation is firstlyrotated and then offset (biased) by adding with a constant power. Theproposed method maps four symbols of QPSK signal to four differentamplitude levels which can be directly detected in a photo-diode (PD).Open eyes are obtained for the received PAM4 signal and bit errorrate (BER) measurements are also shown for 20 and 30 Gb/s signals.Wavelength tunability of the converted PAM4 is investigated as well.

https://doi.org/10.1016/j.optcom.2019.124871Received 14 August 2019; Received in revised form 30 October 2019; Accepted 1 November 2019Available online 14 November 20190030-4018/© 2019 Elsevier B.V. All rights reserved.

A. Fallahpour, F. Alishahi, A. Almaiman et al. Optics Communications 459 (2020) 124871

Furthermore, a distributed feedback (DFB) laser with high phase noiseis used as another laser source for QPSK signal. We demonstrate thatthe produced delayed signal conjugate and nonlinear wave mixing canreduce the phase noise of the laser and open eye can be observed.

2. Concept

The concept of the proposed QPSK to PAM4 modulation formatconverter is shown in Fig. 1. On a constellation diagram, QPSK hasfour equi-amplitude symbols with equidistant phases. Therefore, if aQPSK signal is sent into a PD, only one amplitude level is captured,and the phase information is erased. In order to detect four amplitudelevel at the PD, the QPSK constellation should be manipulated such thatevery constellation point should have a distinct amplitude. As shownin Fig. 1(a), if the QPSK constellation is rotated and then added witha constant-amplitude wave, the four constellation points would havedifferent amplitude levels. Thus, by sending the resultant signal to thePD, a PAM4 signal would be detected. Here the phase rotation angle𝛥𝜑 is explained in Fig. 1(a).

The conceptual block diagram for the demonstration of QPSK intoPAM4 conversion using nonlinear wave mixing is illustrated inFig. 1(b). The input QPSK signal 𝑆𝑖𝑛 (𝑡) is coupled with a continuouswave (CW) pump laser 𝑃1 (𝑡) and then injected into first nonlinear stageto generate the phase conjugate copy of the signal. The electric fieldsof the signal and the pump can be written as follow:

𝑆𝑖𝑛 (𝑡) = 𝐴𝑖𝑛𝑒𝑗(𝜔𝑖𝑛𝑡+𝜑𝑖𝑛(𝑡)) = 𝐴𝑖𝑛𝑒

𝑗(𝜔𝑖𝑛𝑡+𝜑𝐷𝑖𝑛(𝑡)+𝜑

𝑁𝑖𝑛 (𝑡)) (1)

𝑃1 (𝑡) = 𝐴𝑃1𝑒𝑗(𝜔𝑃1 𝑡+𝜑𝑃1 (𝑡)) = 𝐴𝑃1𝑒

𝑗(𝜔𝑃1 𝑡+𝜑𝑁𝑃1

(𝑡)) (2)

where 𝐴𝑖𝑛 and 𝐴𝑃1 are the amplitudes, 𝜔𝑖𝑛 and 𝜔𝑃1 are the angularfrequencies and 𝜑𝑖𝑛 (𝑡) and 𝜑𝑃1 (𝑡) are the phases of 𝑆1 (𝑡) and 𝑃1 (𝑡),respectively. The phase of the signal includes both data and noise,𝜑𝐷𝑆1

(𝑡) and 𝜑𝑁𝑆1

(𝑡); however, the pump only carries the phase noise. Inour experimental implementation, periodically-poled-lithium-niobate(PPLN) waveguides are used as nonlinear elements. The conjugate copyis generated in the first nonlinear stage, i.e., PPLN-1. The wavelength ofthe pump is set to the PPLN quasi-phase matching (QPM) wavelength.In this way, pump interacts with itself through second-harmonic gener-ation (SHG) and generate 𝑃 2

1 (𝑡) at 2𝜔𝑃1 . Then, 𝑃 21 (𝑡) interacts with the

input signal through difference frequency generation (DFG) to createthe conjugate copy where its electric field is proportional to:

𝑃 21 (𝑡) × 𝑆∗

𝑖𝑛 (𝑡) = 𝐴2𝑃1𝐴𝑖𝑛𝑒

𝑗((

2𝜔𝑃1−𝜔𝑖𝑛

)

𝑡+(

2𝜑𝑁𝑃1

(𝑡)−𝜑𝐷𝑖𝑛(𝑡)−𝜑

𝑁𝑖𝑛 (𝑡)

))

(3)

The output of PPLN-1 is sent to a programmable filter based on LiquidCrystal on Silicon (LCoS) technology in order to (i) select the signal,the conjugate copy, and the pump by filtering them and reducing theout of band amplified spontaneous emission (ASE) noise, (ii) adjustrelative amplitude of these selected waves, (iii) apply the phase rotationof 𝛥𝜑 to the signal which is basically the constellation rotation, and(iv) apply one symbol delay (T) between signal and its conjugate copyto compensate the relative phase between the pump and the signal.As a result, the electric fields of the signal, the conjugate copy, andthe pump after LCoS filter are 𝑆𝑖𝑛 (𝑡) × 𝑒𝑗𝛥𝜑, 𝑃 2

1 (𝑡 − 𝑇 ) × 𝑆∗𝑖𝑛 (𝑡 − 𝑇 ), and

𝑃1 (𝑡), respectively. The output of the LCoS filter is then sent into secondnonlinear stage, i.e., PPLN-2. The QPM wavelength of the second PPLNis the same as the first one. As a result, the pump 𝑃1 (𝑡) interacts withitself through SHG and generate the following:

𝐸 (𝑡) = 𝑃 21 (𝑡) ∝ 𝑒

𝑗(

2𝜔𝑃1 𝑡+2𝜑𝑁𝑃1

(𝑡))

(4)

Furthermore, since the signal and the delayed conjugate copy are lo-cated symmetrically with respect to the QPM wavelength, they interactthrough sum frequency generation (SFG) and generate the following:

𝑋 (𝑡) = 𝜷 × 𝑃 21 (𝑡 − 𝑇 ) × 𝑆∗

𝑖𝑛 (𝑡 − 𝑇 ) × 𝑆𝑖𝑛 (𝑡) × 𝑒𝑗𝛥𝜑

∝ 𝜷𝑒𝑗(

2𝜔𝑃1 𝑡+(

2𝜑𝑁𝑃1

(𝑡−𝑇 )−𝜑𝐷𝑖𝑛(𝑡−𝑇 )−𝜑

𝑁𝑖𝑛 (𝑡−𝑇 )+𝜑

𝐷𝑖𝑛(𝑡)+𝜑

𝑁𝑖𝑛 (𝑡)+𝛥𝜑

))

(5)

where 𝜷 is a weight that can be adjusted in the LCoS filter. Both𝑋 (𝑡) and 𝐸 (𝑡) are at 2𝜔𝑃1 and they are frequency locked. To performcoherent addition of 𝑋 (𝑡) and 𝐸 (𝑡) the relative phase between themshould be compensated. Assuming the source of phase noises for both𝑆𝑖𝑛 (𝑡) and 𝑃1 (𝑡) are from their lasers linewidth, the fluctuation of theirphase noise is much slower than the symbol rate [15]. Therefore, wecan assume:

𝜑𝑁𝑖𝑛 (𝑡) ≃ 𝜑𝑁

𝑖𝑛 (𝑡 − 𝑇 ) (6)

𝜑𝑁𝑃1

(𝑡) ≃ 𝜑𝑁𝑃1

(𝑡 − 𝑇 ) (7)

By making these assumptions eq. (5) is simplified as follows:

𝑋 (𝑡) ∝ 𝜷𝑒𝑗(

2𝜔𝑃1 𝑡+(

2𝜑𝑁𝑃1

(𝑡)+𝜑𝐷𝑖𝑛(𝑡)−𝜑

𝐷𝑖𝑛(𝑡−𝑇 )+𝛥𝜑

))

(8)

Therefore, although 𝑃1 (𝑡) is generated from an independent laser than𝑆𝑖𝑛 (𝑡), it can act as a bias that would offset the constellation aftermixing the signal with its delayed conjugate copy. In order to convertback the generated signal at 2𝜔𝑃1 into C-band, another pump 𝑃2 (𝑡)at 𝜔𝑃2 is also injected in PPLN-2. The pump 𝑃2 (𝑡) is interacted withthe resultant wave at 2𝜔𝑃1 through DFG and generate the output at2𝜔𝑃1 − 𝜔𝑃2 as follow:

𝑆𝑜𝑢𝑡 (𝑡) = 𝑃 ∗2 (𝑡) × (𝐸(𝑡) +𝑋 (𝑡)) (9)

where 𝑆𝑜𝑢𝑡 (𝑡) is the generated output signal at 2𝜔𝑃1 − 𝜔𝑃2 . PAM4 eyediagram is expected to be observed after PD by properly adjusting theweight and the phase rotation angle. Please note that the received datais the differential data and the original data should be recovered fromit.

3. Experimental setup

The experimental setup of the proposed QPSK to PAM4 modulationformat converter is shown in Fig. 2. At the transmitter, a laser atwavelength of 𝜆𝑆 = 1552.8 nm is modulated in a nested Mach–Zehndermodulator with 10/15 Gbaud QPSK data generated by a 215 −1 pseudorandom bit sequence (PRBS). The output of the modulator is amplifiedin a low-noise erbium-doped fiber amplifier (EDFA), sent into high-power EDFA (EDFA1) and injected into PPLN-1. Another CW lasersource, P1, at the wavelength of 𝜆P1 = 1550.7 nm is amplified in EDFA2and also sent into PPLN-1. The conjugate copy of the signal is generatedat the PPLN-1 output as shown at node A in Fig. 2. Subsequently, theoutput of PPLN-1 is passed through a spool of dispersion compensa-tion fiber (DCF) of length ∼100 m and dispersion of 160 ps/nm/km;this dispersion can induce ∼65 ps delay between the signal and itsconjugate. The residual delay for applying one symbol delay betweenthe signal and its conjugate is imposed by the LCoS filter which canalso adjust phase and amplitude at the expense of ∼6 dB loss. Theoutput is amplified in EDFA3 and coupled with the second pump at𝜆P2 = 1554.6 nm into PPLN-2. The QPM wavelengths of both PPLNsare temperature tuned to be the same at 1550.7 nm. The spectrum ofPPLN-2 is shown at node B in Fig. 2. The final output is filtered at aband pass filter (BPF) and sent into the PD for eye diagrams and BERprocessing.

4. Experiment results

Fig. 3 shows the output eye diagrams for different phase rotationangles when the input is 20 and 30 Gb/s QPSK. Phase rotation angle 𝛥𝜑is shown in Fig. 1(a). When the phase rotation angle is 90◦, the offsetand rotated symbols will only produce two amplitude levels. Similarly,if 𝛥𝜑 = 90◦, three amplitude levels are detected, which means two ofthe four symbols are distorted and cannot be recovered. Substantially,equal eye opening for PAM4 is observed when the phase rotation angleis 𝛥𝜑 = 71◦. Open eyes are captured for both 20 and 30 Gb/s cases.

Here, we define a ratio, which measures the dependence of the eyeopening between the middle two levels as x/A, where x is the amplitude

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A. Fallahpour, F. Alishahi, A. Almaiman et al. Optics Communications 459 (2020) 124871

Fig. 1. (a) Concept of QPSK to PAM4 format conversion using constellation rotation and bias addition; (b) the block diagram of the proposed QPSK to PAM4 converter usingnonlinear wave mixing. Phase rotation is applied in LCoS filter and the power bias is added in the second nonlinear element. PPLN: Periodically-Poled-Lithium-Niobate, QPM:Quasi-Phase Matching, LCoS: Liquid Crystal on Silicon, SHG: Second-Harmonic Generation, SFG: Sum Frequency Generation, DFG: Difference Frequency Generation.

Fig. 2. The experimental setup for the proposed QPSK to PAM4 converter along withthe corresponding spectra measured at each PPLN output. Output spectrum of the firstand second PPLN is shown in A and B, respectively. PC: Polarization Controller, EDFA:Erbium-Doped Fiber Amplifier, BPF: Band Pass Filter, PPLN: Periodically-Poled-Lithium-Niobate, DCF: Dispersion Compensation Fiber, LCoS: Liquid Crystal on Silicon, PD:Photo-Diode.

of the middle eye and A is the peak-to-peak amplitude (see Fig. 3(b)).Fig. 3(b) shows how this ratio changes according to changing the phasevalues from 𝛥𝜑 = 45◦ to 𝛥𝜑 = 90◦ in simulation. Equal eye opening can

Fig. 3. (a) Eye diagram of the output signal with different rotation angle (𝛥𝜑 =45◦ , 90◦ and 71◦) for 20 and 30 Gb/s QPSK input. (b) Simulation of continuous phaserotation from 45◦ to 90◦ and its impact on eye opening.

be achieved when x/A = 1/3. As it is pointed earlier in Fig. 3(a), thisis the case when 𝛥𝜑 = 71◦.

Wavelength tunability of the proposed system is shown in Fig. 4. Bytuning the wavelength of the second injected pump P2 at the secondnonlinear stage, the converted PAM4 wavelength can be tuned. InFig. 4, the input QPSK wavelength is set to 1552.8 nm while the outputPAM4 wavelength is tuned to either 1546.8 nm or 1543.2 nm in Fig. 4(a)and (b), respectively. Open eyes are observed in both cases and the

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A. Fallahpour, F. Alishahi, A. Almaiman et al. Optics Communications 459 (2020) 124871

Fig. 4. Wavelength tunability of the proposed QPSK to PAM4 format and wavelength converter. The input is 20 Gb/s QPSK at 1552.8 nm while the output PAM4 wavelength is(a) 1546.8 nm and (b) 1543.2 nm.

quality of the eyes are almost the same. Therefore, our proposed schemenot only converts the modulation format from QPSK to PAM4, butalso can perform wavelength conversion from the input wavelength toanother desired wavelength that might be useful in some applications.For example, the wavelength of interest of two networks, connected bythis gateway, may not be necessarily the same.

The BER measurement of the QPSK to PAM4 converter is shown inFig. 5. The BER of the input QPSK signal and the output PAM4 signalversus optical signal-to-noise ratio (OSNR) for both 20 and 30 Gb/sare illustrated. To measure the BER of QPSK at the transmitter side,we used an optical coherent receiver that can recover the amplitudeand phase of the QPSK signal with the aid of a local oscillator. Onthe other hand, a single PD is used to detect the PAM4 signal at thereceiver side. The generated electronic signal’s waveform at PD output,is recorded and then processed offline to calculate BER for PAM4. Wenote that the received PAM4 is a differentially encoded signal. In orderto validate the quality of the generated PAM4 signal, the BER for a backto back (B2B) differentially encoded PAM4 is also measured. The BERis calculated by comparing the recorded pattern at the receiver and thedifferential pattern that is loaded at the transmitter.

By comparing the input QPSK and output PAM4 curves at BER of1e–3, the OSNR difference of ∼22 dB can be seen. Although it seemslike a huge OSNR penalty from input to output, it mostly results fromthe addition of the bias constant power to generate PAM4. This factcan become clearer when the BER of the generated PAM4 from formatconversion is compared with the BER of the B2B scenario where thePAM4 is generated at the transmitter and directly received at the PDwithout going through the system.

In order to evaluate the system’s penalty, we remove the biasaddition in the second stage by blocking P1 in the LCoS filter. In otherwords, E = 0 in Eq. (9) at the output of the PPLN-2. Therefore, theoutput cannot be detected using the PD since the amplitude of all foursymbols are equal. However, the system output will become differen-tially encoded QPSK, which can be recovered by coherent detection. Bymeasuring the output BER for this case, we can see OSNR difference of∼3 dB at BER of 1e–3 between the final output and the input.

By comparing the BER of QPSK and PAM4 with the theoreticalvalues, approximately 7–8 dB penalty is observed in the experiment.We believe this is mainly due to the distortions caused by the imperfectfrequency response of the electrical devices in the transceiver as well assome polarization sensitivity of the modulator. We note that the BERof the input and the output of the experimental setup are measuredunder similar measurement condition (e.g. frequency response andpolarization state). Theoretically, the BER curves of 20 and 30 Gb/s

Fig. 5. BER measurement of the system input and output. Input is the 20 and 30Gb/s QPSK signal (TX-QPSK). Output is PAM4 when the pump for bias is included(RX-PAM4). The output BER curve without the bias is also illustrated (RX-w\o Bias).PAM4 B2B BER measurement is also reported to compare with the converted PAM4 atthe output (PAM4-B2B).

are expected to have ∼1.7 dB difference. However, this difference is∼0.5 dB in Fig. 5. We believe the reason for this discrepancy betweentheory and experiment is the resolution of the optical spectrum analyzerwhile measuring the OSNR. The resolution is 12.5 GHz that can filterout some of the signal power in 30 Gb/s case.

We also investigate the system performance by varying the phasenoise value of the input signal. In our experiment, we utilized a narrow-linewidth laser which has low phase noise. In order to show the impactof higher input phase noise, we replace the original narrow-linewidthsignal’s laser with a distributed feedback laser (DFB) laser, which haslarger linewidth. The constellation of the input signal is shown inFig. 6 for both lasers. We define the parameter 𝛥𝜃 to quantify thephase deviation from the expected value on constellation diagrams. Theconstellation of the output is also shown when the bias is not added.By comparing the constellation of the output and the input, it can beseen that the 𝛥𝜃 is reduced from 47◦ to 28◦ when DFB laser is used.This feature is the result of phase-noise differentiation in the secondstage, when multiplying the signal with its delayed conjugate [15,16].However, this feature cannot be observed when the phase noise of theinput is small. By comparing the output PAM4 eye diagram, it can beseen that both eyes provide four distinct amplitude levels.

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A. Fallahpour, F. Alishahi, A. Almaiman et al. Optics Communications 459 (2020) 124871

Fig. 6. Captured eye diagram at the receiver by imposing two different phase noiselevels. Two different lasers are utilized at the transmitter and they are modulated with20 Gb/s QPSK data.

5. Conclusion

In this paper, modulation format conversion of QPSK to PAM4 isexperimentally demonstrated. The QPSK data channel is rotated andadded with a bias to map each constellation point at different amplitudelevel. This function is implemented using two stage nonlinear wavemixing. The impact of phase rotation on the quality of the recoveredeye diagram is investigated. Four-level eyes can be obtained when thephase rotation angle is 71◦. The wavelength of the generated PAM4at the output is tunable and it can be set to the desired wavelengthby tuning the wavelength of the second stage pump. Open eyes areobserved when the generated PAM4 wavelength is either 1546.8 nm or1543.2 nm. Finally, we demonstrate that PAM4 can be detected even ifthe input QPSK suffers from laser phase noise.

Although the proposed technique is demonstrated for a single chan-nel, future work could include wavelength multiplexed channels usingnonlinear wave mixing and a frequency comb. For such a system, achallenge might be the processing of multiple channels while avoidingcrosstalk mixing between channels. It might be possible to increase thenumber of channels by making the channels close to each other suchas subcarriers [17].

Acknowledgment

National Science Foundation (NSF), USA Center for Integrated Ac-cess Networks under Grant Y501119, Huawei Technologies.

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