All-optical digital-to-analog converter based oncross-phase modulation with temporal integrationDEMING KONG,1,2,* ZIHAN GENG,1,2 BENJAMIN FOO,1 VALERY ROZENTAL,1 BILL CORCORAN,1,2 AND

ARTHUR JAMES LOWERY1,2

1Electro-Photonics Laboratory, Department of Electrical and Computer Systems Engineering, Monash University, Clayton, VIC 3800, Australia2Centre for Ultrahigh-Bandwidth Devices for Optical Systems (CUDOS), Australia*Corresponding author: deming.kong@monash.edu

Received 3 August 2017; revised 3 October 2017; accepted 4 October 2017; posted 5 October 2017 (Doc. ID 303340); published 31 October 2017

We propose and experimentally demonstrate an all-opticaldigital-to-analog converter based on cross-phase modula-tion with temporal integration. The scheme is robust fordriving signal noise due to the low-pass filtering feature ofthe temporal integrator. The proof-of-concept experimentdemonstrates the generation of pulse-amplitude modula-tion (PAM) sequences up to eight levels. The performanceof random PAM 2 and PAM 4 signals with different opticalsignal-to-noise ratios of the binary driving signal is alsoinvestigated. The scheme is scalable for high-speed opera-tion with an appropriate dispersion profile of the nonlinearmedium. © 2017 Optical Society of America

OCIS codes: (060.2330) Fiber optics communications; (060.4080)

Modulation; (060.4370) Nonlinear optics, fibers.

https://doi.org/10.1364/OL.42.004549

The digital-to-analog converter (DAC) is a key component forthe generation of spectrally efficient multi-level modulation for-mats. Optical DACs have been proposed for their ability toachieve high baud rates and potentially low power consump-tion. Multi-modulator-based schemes [1–6] offer flexibilityin terms of number of bits, but are complex in terms of controlmechanisms. Cross-phase modulation (XPM)-based schemes,either using binary optical inputs with different amplitudes[7,8], cascaded XPM stages [9], or different fiber lengths[10], have a weak tolerance to pump noise. Other schemesbased on the summing of weighted multi-wavelength pulses[11], optical correlation [12], or micro-ring resonators [13,14]are also potentially vulnerable to the noise of the driving se-quences. Recently, we have proposed an electro-optical DAC,based on counter-propagating electrical binary pulses with op-tical pulses in a conventional optical Mach–Zehnder modulator[15]. The optical pulses accumulate phase shifts according tothe duration of the electrical pulses (i.e., temporal integration),suppressing noise and fluctuations from the electrical signal,resulting in improved signal quality.

In this Letter, an all-optical DAC (AO-DAC), based onXPM with temporal integration, is proposed. The generationof pulse-amplitude modulation (PAM 2, 3, 4, 5, 6, and 8)

sequences has been demonstrated at 1.25 GHz in a proof-of-concept experiment with 13 dBm of pump power. Theperformance of random PAM 2 and PAM 4 signals has alsobeen investigated with different pump optical signal-to-noiseratios (OSNRs), confirming noise suppression capability ofthe scheme. We also discuss paths to improving this schemetowards providing a high-fidelity and high-speed AO-DAC.

Figure 1(a) illustrates the principle of the proposed AO-DAC with two main components, including an XPM-basedtemporal integrator and an interferometer-based phase-to-amplitude converter. For the XPM-based temporal integrator,a probe pulse sequence and a coded pump signal are coupled ina nonlinear medium. The probe is then phase-modulated bythe pump due to XPM. The key idea of this scheme is tointroduce an appropriate walk-off between the probe andthe pump so that the probe experiences the pump-pulse-induced phase rotation from the leading edge to the falling edgeof the pump (or vice versa). In this way, the probe is modulatednot by the amplitude of the pump, but rather by the integrationof the optical power across the designed walk-off time.

(a)

(b) (c)Wavelength separation (nm)

0

200

400

600

800

1000

Pum

p du

rati

on (

ps)

Working point for 1.25 Gbaud

0 0.5 1 1.5 2 2.5 3

2.304 nm

walk-off:800 ps

Walk-off valueNon-overlapping pulsewidth requirement

Frequency offset (GHz)

3 dB bandwidth:0.558 GHz.

0 2 4 6 8 10-40

-30

-20

-10

0

XP

M e

ffic

ienc

y (d

B)

First dip:1.25 GHz.

OBPFNonlinear medium

XPM with walk-off as temporal integrator of

phase shift

Optical coupler

Optical coupler

Interferometer as phase-amplitude converter

Vg1

Vg2

probe

pump

variable width

Tn

60° 120° 180°0°

out

Fig. 1. (a) Principle of the proposed AO-DAC; (b) calculated walk-off and non-overlapping pulse-width requirement for 3.4 km DCF;(c) and XPM efficiency at a probe rate of 1.25 Gbaud.

Letter Vol. 42, No. 21 / November 1 2017 / Optics Letters 4549

0146-9592/17/214549-04 Journal © 2017 Optical Society of America

The integrated phase modulation from the pump pulse canthen be expressed as

ϕn � 2γffiffiffiffiffiffiffiffiffiffiηXPM

pLeff

R Tw0 P�t�dt

T w; (1)

where γ is the nonlinear coefficient of the medium; ηXPM is theXPM efficiency [16]; Leff is the effective length of the nonlinearmedium given by Leff � �1 − eαL�∕α; P�t� is the optical powerprofile of the pump pulse; and Tw is the walk-off time.Considering that T n is the actual pump pulse width withinTw and T n ≤ Tw, the integral will differ for various Tw du-rations if either the optical power profile, P�t�, or the pulsewidth, T n, is adjusted. For example, if the pump is a multi-levelsignal with a fixed duration T n � T p, the probe would bephase-modulated depending on the input level of the pumpPn�t�, �n � 1; 2;…N �. Alternatively, if the pump is a binarynon-return-to-zero (NRZ) signal and N symbols with a vari-able total duration T n ≤ Tw, �n � 1; 2;…N � are treated asone input digital word, the probe will walk off with each digitalword, and the accumulated phase will differ according to T n. Inother words, the pump pulse width could be adjusted in dis-crete steps by binary NRZ modulation to get different modu-lation depths. To get a maximum modulation efficiency, themaximum pulse width of the pump should equal Tw. Theprobe should be aligned with either the leading or falling edgeof the pump, if it travels slower or faster than the pump, re-spectively. Following the temporal integrator, an interferometeris used for phase-to-amplitude conversion, generating analogoutput levels according to the phase modulation depth [15].

Figure 1(b) gives an example of the calculated walk-offvalues from a 3.4 km dispersion compensating fiber (DCF)when the pump wavelength is fixed around 1550 nm(α � 0.765 dB∕km, D� −107.4 ps∕nm∕km, and S �−0.3567ps∕nm2∕km at 1566 nm). The dashed curve givesthe minimum NRZ pulse width for the pump and the probe

without overlapping in the frequency domain. To easilyfilter out the probe after phase modulation, a wavelength sepa-ration of 2.304 nm is chosen, resulting in a walk-off value ofTw � 800 ps. Then the repetition rate of the probe is1∕800 ps � 1.25 GHz.

Figure 1(c) illustrates the calculated efficiency of the XPMeffect [16] against frequency offset from the center of thepump. First, this figure indicates that the temporal integratorcan be represented by a rectangular window of width Tw,which will suppress most of the out-of-band noise from thepump. Second, as the temporal integrator acts as a low-passfilter, the operating baud rate of the DAC is limited, such thatthe phase modulation from the transitions of the pump will befiltered and distorted. However, as long as the probe experien-ces the same number of rising and falling transitions of thepump during the walk-off time Tw, the amount of nonlinearphase modulation will be the same and will not affect the phase-to-amplitude conversion for each generated level. This requiresspecial coding for the pump signal. Two complementarypumps can also be used to cancel out the effect of transitions.If four output levels are required, the combined duration of thefour symbols of the input binary waveform can be treated asone pump symbol. With the coding scheme shown in Table 1,the probe will experience only one rising edge and one fallingedge for each Tw. Note that an extra guard interval is insertedto accommodate the probe pulse.

Figure 2(a) shows the proof-of-concept experimental setup,consisting of five functional modules: pump generation, probegeneration, noise-loading, AO-DAC, and baseband receiver.For the implementation of the AO-DAC, a nonlinear opticalloop mirror (NOLM) is used. Since dispersion in optical fibersis isotropic, the clockwise propagated probe pulses, modulatedby the pump signal experience the same amount of dispersionas the counterclockwise propagated probe pulses, so that thepulse shape of the output can be preserved. However, thecounterclockwise propagated probe pulses are also modulatedby the pump signal but, since the walk-off for counter-propagation is so large, the counterclockwise propagated probepulses will experience the pump signal as a continuous waveand will have a constant phase rotation θ if the pump averagepower is constant. As illustrated in Fig. 2(b), the filtered outputof the NOLM is a vector sum of both clockwise and counter-clockwise modulated pulses, this counter-propagating phase

Table 1. Pump Coding Scheme for Four Levels of DAC

Digital Word Tw Phase Modulation Analog Output Level

0, 0, 0, 0 ϕ0 31, 0, 0, 0 ϕ1 21, 1, 0, 0 ϕ2 11, 1, 1, 0 ϕ3 0

(b)

Wavelength (nm)

Opt

ical

pow

er (

dBm

)

-60

-40

-20

0

20

1549 1550 1551 1552 1553

15 dB

pump

probe

NOLM closed statusNOLM with 13 dBm pump powerNOLM with 20 dBm pump power

(c)

counter-prop.

co-prop.

counter-prop.

out 0

out 1

co-prop.

pump pulse no pump pulse

θ θ

ϕ1 ϕ0 =0

(a)

Pump generation

WSS

100 GHz EDFA

EDFA Att.

pump code

ECL MOD

PC 1

EDFA Att.

HPF 1 nm

OBPF1550.235 nm 3 dBOC

OSNR monitoring

ECL

1552.539 nm

MOD

EDFA

WSS

20 GHz Gaussian - shaped

delay line

PC 2Isolator

Probe generation

All-optical DAC

Noise loading

OC

NOLM

OC

MON

DCF

Walk-off800 ps

WSS

3.4 km

3 dB

Rx. power monitor

20 GHz Gaussian - shaped

3 dB

Baseband receiver

OC10 dB

EDFA

OBPF100 GHz

PD70 GHz

OS

C 10 GHz Rx. btw, 40 GSa/s

Att.

Fig. 2. (a) Experimental setup (ECL, external cavity laser; MOD, modulator; OC, optical coupler; VOA, variable optical attenuator; WSS,wavelength-selective switch; PC, polarization controller; OBPF, optical bandpass filter; PD, photodetector; OSC, oscilloscope). (b) Illustrationon the effect of counter-propagation in NOLM. (c) Optical spectra of the pump and the probe.

4550 Vol. 42, No. 21 / November 1 2017 / Optics Letters Letter

rotation will result in unwanted level shifts or even level jumpsat the output of the NOLM, affecting the level distribution ofthe AO-DAC-generated signal. The counter-propagation-induced level shifts can be solved by carefully adjusting thepolarization controller (PC) in the NOLM (PC 3) and thepolarization controller for the probe (PC 2) to intentionally in-troduce some residual output. Counter-propagation-inducedlevel jumps can be eliminated by the precoding of the pump.These issues related to counter-propagating only exist in aNOLM-based setup. In the experiment, a 3.4 km DCF withthe same parameters described previously, is inserted as thenonlinear medium. The measured static extinction ratio ofthe NOLM without the pump was 32 dB.

For the generation of the probe, an external cavity laser(ECL) running at 1552.539 nm is externally modulated to pro-duce 100 ps pulses at a repetition rate of 1.25 GHz, before it isamplified, filtered, and aligned with the guard interval of thepump. PC 2 is used to adjust the initial polarization state of theprobe to the NOLM. For the generation of the pump signal,another ECL working at 1550.235 nm, with a wavelength sep-aration of 2.304 nm from the probe, is used to get a total walk-off of 800 ps in the DCF. The ECL is modulated by a codedpump sequence with a guard interval of 200 ps betweenadjacent symbols. The noise-loading module composed ofan erbium-doped fiber amplifier (EDFA), a 100 GHz rectan-gular-shaped filter implemented with a wavelength-selectiveswitch (WSS), a booster EDFA, and a variable optical attenu-ator (VOA), is used to load an appropriate amount of noisepower to the pump signal for performance investigation.The in-band OSNR of the pump is calculated using the “signalon/off” method [17]. The polarization of the noise-loadedpump signal is adjusted by PC 1 before it is amplified and fil-tered by cascaded high-pass and 1 nm bandpass optical filterswith a bandwidth of ∼100 GHz. A VOA is inserted before theNOLM to adjust the power of the pump signal. The basebandreceiver includes an EDFA, a 100 GHz optical bandpass filter(OBPF), a 70 GHz photodetector (PD), and a real-time oscillo-scope set to a 10 GHz electrical bandwidth with a 40 GSa/ssampling rate. The EDFA used for the receiver has a noisefigure of 5.5 dB and is set to give a controlled output powerof 3 dBm.

Figure 2(c) shows the optical spectra at the output of theNOLM. The power difference between the NOLM “on” (with13 dBm of pump power) and “off” states (no pump) from thespectra is 15 dB. Considering the optical spectra correspond toaverage power, the dynamic extinction ratio is expected to bearound 18 dB, indicating that the modulation depth is limited.If the pump power keeps increasing, severe stimulated Brillouinscattering (SBS) effects can be observed, degrading the signalquality. In this experimental setup, the SBS threshold wasfound to be around 15 dBm.

Figure 3 shows the eye diagrams of the PAM2, 3, 4, 5, 6, and8 sequences generated with repeated binary pump sequences,demonstrating the scalability of the scheme. The insets showcorresponding eye diagrams of the pump sequences. Owingto the phase rotation, introduced by counter-propagating andnonlinear transfer function of phase-to-amplitude conversion,the pump width has been adjusted to obtain a more evenlyspaced output levels.

Figure 4 illustrates the eye diagrams of the pump and theAO-DAC-generated PAM 2 (OOK) signals under different

pump OSNR values, with random binary pump data with5456 words. Note that the calculated OSNR using the “signalon/off” method measures the in-band noise only. Since the op-tical filters used for the pump signals are off-the-shelf thin-filmfilters, there is a significant amount of out-of-band noise addedto the pump. However, the temporal integrator-based AO-DAC strongly attenuates the out-of-band noise. As can beobserved from the eye diagrams, all the output signals showa significantly improved eye opening. Figures 5(a) and 5(b)demonstrate the bit-error rate (BER) performance of the pumpsignals and the AO-DAC-generated PAM 2 signals for differentpump OSNRs. The performance of the AO-DAC-generatedPAM 2 signal under a pump OSNR of 25 dB is 9 dB betterdue to the elimination of the out-of-band noise and NRZ-to-return-to-zero (RZ) conversion. Figure 5(c) shows the BERperformance of the directly modulated RZ-OOK signal withthe same shape with the AO-DAC-generated PAM 2 signalfor comparison. The PAM 2 signal from the AO-DAC

100 ps

100 ps

100 ps100 ps

100 ps 100 ps

600 ps

Fig. 3. Eye diagrams of the AO-DAC-generated PAM 2, 3, 4, 5, 6,and 8 sequences. The insets show the corresponding eye diagrams ofthe pumps.

Pum

pO

utpu

t

Pump OSNR = 20 dB

200 ps

200 psPump OSNR = 30 dB

200 ps

200 psPump OSNR = 8 dB

200 ps

200 psPump OSNR = 10 dB

200 ps

200 ps

Fig. 4. Eye diagrams of the pump and the AO-DAC-generatedPAM 2 (OOK) signal with different pump OSNR values.

6

5

4

3

2

1

-log

(BE

R)

Received optical power (dBm)-50 -45 -40 -35 -30

OOK OSNR = 25 dBOOK OSNR = 20 dBOOK OSNR = 15 dBOOK OSNR = 10 dBOOK OSNR = 8 dB

Received optical power (dBm)-50 -45 -40 -35 -30

6

5

4

3

2

1

-log

(BE

R)

-44 -40 -36 -32 -28 -24 -206

5

4

3

2

1

-log

(BE

R)

Received optical power (dBm)

(a) (b) (c)

OSNR = 25 dBOSNR = 20 dBOSNR = 15 dB

Pump OSNR = 25 dBPump OSNR = 20 dBPump OSNR = 15 dBPump OSNR = 10 dBPump OSNR = 8 dB

Fig. 5. BERS of (a) the pump signals, (b) the AO-DAC-generatedPAM 2 (OOK) signals, and (c) the directly modulated RZ-OOKsignals, with different OSNR values.

Letter Vol. 42, No. 21 / November 1 2017 / Optics Letters 4551

outperforms the directly modulated RZ-OOK signal by at least1.5 dB at a BER value of 10−4, under various OSNR values.This confirms the noise suppression capability by temporalintegration.

Figure 6 depicts the eye diagrams of the pump and the AO-DAC-generated PAM 4 signals with different pump OSNRvalues using random binary pump data with 5456 words.As with the PAM 2 signal, the out-of-band noise is heavilysuppressed. Figure 7(a) shows the BER performance of theAO-DAC-generated PAM 4 signals with different pumpOSNR values. Figure 7(b) shows the BER performance ofdirectly modulated RZ-PAM 4 signals (fully modulated withoptimized level shifting) for different OSNR values. TheAO-DAC-generated PAM 4 signal performs approximately2 dB worse with 30 dB OSNR at a BER value of 10−4. Weattribute the lower performance of the AO-DAC-generatedPAM 4 signal to the nonlinear transfer function intrinsic tothe NOLM, as well as the limited extinction ratio.

There are a number of improvements that can be made tothe proposed scheme to improve the AO-DAC performance.The extinction ratio of the NOLM is partly limited by theSBS, effectively providing an upper limit to the pump power.This is further complicated by the counter-propagation-inducedphase shift in the NOLM. Both the counter-propagating phaseshift and the limited bandwidth of the AWG used to modulatethe pump make it difficult to perform a perfect level shifting tocompensate for the intrinsic nonlinear transfer function of theNOLM, resulting in degraded performance when targetingmultilevel output signals. To improve the extinction ratio ofthe output, switching to a high-SBS-threshold nonlinearmaterial would help to induce full switching, and using an inter-ferometer-based setup shown in Fig. 1 instead of a NOLMwould remove the effect of the counter-propagation phase shift.

AO-DACs often target high-bandwidth applications. TheAO-DAC scheme we propose here is not intrinsically limitedin bandwidth, and can be easily adapted to higher baud ratesby simply changing the nonlinear material with reduceddispersion and applying high-speed NRZ-shaped signal [18]for the pump.Moreover, we note that the coding scheme shownin Table 1 results in a reduced spectral efficiency. As the outputsignal is a low duty-cycle RZ signal, this loss in spectral efficiencycan be regained by time-division multiplexing the output signal.

In conclusion, AO-DAC based on XPM with temporalintegration has been proposed and demonstrated through aproof-of-concept experiment. The generation of PAM 2, 3,4, 5, 6, and 8 sequences has been experimentally demonstratedat 1.25 GHz with a NOLM setup. The performance of PAM 2and PAM 4 signals has also been investigated using randompump data for different OSNR values, proving the noise sup-pression capability. While the AO-DAC proposed here showssignificant resilience to noise drive signals, we believe that thereare further applications for walk-off induced temporal integra-tor, such as OSNR monitoring and the generation of advancedmodulation formats.

Funding. Australian Research Council (ARC) CUDOS–ARC Centre of Excellence for Ultrahigh Bandwidth Devicesfor Optical Systems (CE110001018); ARC LaureateFellowship (FL130100041).

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Pump OSNR = 30 dB

200 ps

200 ps

200 ps

200 psPump OSNR = 20 dB Pump OSNR = 18 dB Pump OSNR = 15 dB

200 ps

200 ps

200 ps

200 ps

Pum

pO

utpu

t

Fig. 6. Eye diagrams of the pump and the AO-DAC-generatedPAM 4 signal with different pump OSNR values.

-log

(BE

R)

Received power (dBm)-45 -40 -35 -30 -25 -20

6

5

4

3

2

1PAM4 OSNR = 30 dBPAM4 OSNR = 25 dBPAM4 OSNR = 20 dBPAM4 OSNR = 18 dBPAM4 OSNR = 15 dB

-log

(BE

R)

Received power (dBm)

Pump OSNR = 30 dBPump OSNR = 25 dBPump OSNR = 20 dBPump OSNR = 18 dBPump OSNR = 15 dB

-45 -40 -35 -30 -25 -206

5

4

3

2

1

(a) (b)

Fig. 7. BERs of (a) the AO-DAC-generated PAM 4 signals and(b) the directly modulated RZ-PAM 4 signals, with differentOSNR values.

4552 Vol. 42, No. 21 / November 1 2017 / Optics Letters Letter