## Abstract

Optical communication using high-speed on-off-keying signal by directly modulated semiconductor lasers (DML) was one of the most significant breakthroughs for telecommunication in 1960s. The wide deployment of 2.5-Gb/s per-channel transoceanic optical fiber links in 1990s drove the internet as a global phenomenon. However, the detrimental frequency chirp of DML prevents its application to the subsequent internet capacity evolution. Today, the state-of-the-art long-haul optical transponder uses external modulators to support high-order complex modulation. In contrast, this paper shows that the “detrimental” chirp effect can be exploited to generate complex modulation with a single DML, which achieves dramatic sensitivity gain of signal-to-noise-ratio compared to the conventional intensity modulation of DML. By using large chirp parameters, complex-modulated DML paves an attractive pathway towards high-order pulse-amplitude modulation with an ultra-low transmitter cost, which has great potential in future medium reach optical communications.

© 2016 Optical Society of America

## 1. Introduction

Directly modulated semiconductor laser (DML) with direct detection (DD) was employed for long-haul submarine optical transmission in early 1990s [1–3]. However, the detrimental frequency chirp impeded its implementation to the subsequent Internet capacity evolution [2–6]. During past 3 decades, researchers have endeavored to minimize the chirp effect of DML. The most straightforward way is to avoid direct modulation (DM) by external modulator (EM). Combined with coherent detection (COHD), EM-COHD nowadays has become the most powerful solution to enable multi-Terabit/s long-haul communications [7,8].

Meanwhile, DML still holds its position in cost-sensitive short reach applications, because its cost is 2 or even 3 orders less than EM [9–14]. The conventional thinking is to minimize the chirp in order to optimize system performance. Nevertheless, the chirp induced laser frequency shift can be recovered using COHD. By time integral, the frequency shift can be converted to a regular phase variance. In essence, DML can be regarded as a 2-dimensional (2-D) complex transmitter, while coherent receiver characterizes both the optical intensity and phase. Using this scheme, we experimentally demonstrated the first complex modulation (CM) of DML [14], which significantly increases the system OSNR sensitivity by 9 dB in a single polarization 4-level pulse-amplitude-modulation (PAM-4) coherent system compared to the conventional DML-COHD using intensity-only modulation (IM) [13].

In this paper, we will investigate the capability of CM-DML supporting higher-order modulation. In contrast to the conventional IM-DML, larger frequency chirp is required to enhance the system performance. We will present by simulation the potential of CM-DML to support PAM-8 or even PAM-16 modulation. Combined with polarization multiplexing, we experimentally demonstrate the first dual polarization (DP) PAM-8 signal over 320-km standard single mode fiber (SSMF), which offers a record electrical spectral efficiency (E-SE) of 6-bit/s/Hz for optical PAM transmission. CM-DML paves an attractive pathway towards high order modulation with an ultra-low-cost transmitter.

## 2. Complex modulation of semiconductor lasers

Conventionally, DML works as the 1-D transmitter using IM. The drive current changes the electron density inside the laser active region, leading to the variation of effective refractive index. The laser frequency, as a result, shifts during modulation. This phenomenon, normally named frequency chirp, is long regarded as a vital impairment of optical transmission systems. The chirp can be regarded as frequency modulation (FM). By using COHD which provides a frequency reference, FM can be converted to phase modulation (PM) by time integral. Normally, FM only results in the pure PM. However, in DML, FM exists simultaneously with IM. Namely, DML performs complex modulation (CM) involving both IM and PM. Derived from the laser diode rate equations, the frequency shift *∆f* of DML is approximately expressed by the laser output power *P(t)* with high accuracy [2,3],

*α*is the laser linewidth enhancement factor [6], and

*κ*is the adiabatic chirp coefficient. As a result, the phase can be expressed as:

The phase at time *t* is determined by the power output covering the past period [*0, t*], due to the integral operation. Namely, CM-DML gives rise to a convolutional channel model, which can be handled by the maximum likelihood sequence estimation (MLSE) [15].

To simplify the channel model, we calculate the differential phase of the discrete time model at sampling point *t _{1}* and

*t*, using the mean-value theorem of integral within [

_{2}*t*,

_{1}*t*]:

_{2}*T = t*is the sampling period. The differential operation provides two advantages: (i) the memory of the convolutional channel decreases to 1 tap, which simplifies the MLSE computational complexity; (ii) laser phase noise is naturally cancelled if assuming a quasi-constant phase noise variation during [

_{2}-t_{1}*t*,

_{1}*t*], which simplifies the carrier recovery process.

_{2}We have fully revealed the principle of CM-DML. The coherent receiver reconstructs the intensity *P(t)* and differential phase *∆φ(t)*, then applies MLSE to determine the maximum likelihood sequences [14,15]. We define two data sets for MLSE: (i) the state {*x _{t}*} (each state corresponds to a constellation point); (ii) the transition {

*χ*|

_{t}*χ*(

_{t}≜*x*)}. Each transition is a state pair containing the states at the adjacent sampling points. In order to characterize the transition probability, we define the transition distance as:

_{t}, x_{t-1}*∆φ*is the estimated differential phase calculated by Eq. (3). The transition distance contains two parts: (i) the IM difference at previous sampling point, which represents the intensity-only decision; and (ii) the CM difference at current sampling point, which represents the phase assisted decision. We will show below the significant benefit from part (ii).

_{E}(t)## 3. Towards high order PAM utilizing large frequency chirp

The differential phase in Eq. (3) contains two parts: (i) the logarithmic part *ln P(t _{2})/P(t_{1})* has a coefficient

*c*; and (ii) the linear part

_{1}= α/2*P(t*has a coefficient

_{1}) + P(t_{2})*c*. We conduct numerical simulation in Fig. 1 to investigate the impact of frequency chirp parameters

_{2}= ακT/4*c*and

_{1}*c*on the system performance. The DML emulator first maps the baseband PAM signal to optical intensity levels; then adds phase modelled by Eq. (3) with the initial phase of 0. We ignore phase noise and other detrimental DML effects to reveal the optimal performance of CM-DML. The channel is modelled as additive white Gaussian noise (AWGN) channel. The optical signal is launched into a standard coherent receiver.

_{2}A PAM-*m* signal is modelled as [*1 2 … m*], with a normalized power of 1. Chirp parameters are set as common values for commercial DMLs, *c _{1} = 2* and

*c*. Figure 2(a) shows the PAM-4 system SNR sensitivity. We adopt

_{2}= 1.5*3.8 × 10*as 7% hard-decision forward error correction (FEC) threshold; while

^{−3}*2.4 × 10*as soft-decision FEC threshold. CM-DML achieves more than 10-dB sensitivity gain over the conventional IM-DML. Furthermore, the sensitivity gap between CM-DML PAM-4 and QAM-4 shrinks to only 5-dB, converting PAM-4 to a suitable format for optical transmissions with large amplified spontaneous emission (ASE) noise, namely, a longer distance with more optical amplifiers.

^{−2}Maintaining the same chirp coefficients, we move to PAM-8 in Fig. 2(b) and PAM-16 in Fig. 2(c). For higher order modulation, the sensitivity difference gradually reduces between CM-DML and IM-DML. More vitally, from PAM-4 to PAM-16, CM-DML requires 16-dB more SNR at 7% FEC threshold; in contrast, from QAM-4 to PSK-16, the SNR increment at 7% FEC threshold is 10 dB; while from QAM-4 to QAM-16, the increment is only 6 dB.

QAM has the best SNR sensitivity, because of its better conditioned constellation distribution on the 2-D plane. In contrast, CM-DML suffers large sensitivity degradation when modulation order increases. Considering the CM-DML performance has a close relationship to the differential phase *∆φ(t)*, we inspect the *∆φ(t)* distribution in Fig. 3 by Eq. (3). Each circle in Fig. 3 represents a power level *P(t)* of the current sampling point, and each point represents a value of $\sqrt{P(t)}\cdot \mathrm{exp}(i\cdot \Delta \phi (t))$. Figure 4 provides the system SNR sensitivity corresponding to the *∆φ(t)* distribution in Fig. 3. For PAM-4 in Fig. 3(a), when *c _{1} = 2* and

*c*, the 4

_{2}= 1.5*∆φ*values on each circle approximately distribute uniformly at [

*0,2π*). The system sensitivity decreases when chirp parameters decrease, because

*∆φ*distribution does not fully utilize the 2-D space. For example, when

*c*reduces by half in Fig. 3(b), the range of

_{1}*∆φ*shrinks to [

*0,0.5071∙2π*), which corresponds to a SNR sensitivity penalty of 2 dB in Fig. 4(a). Further increase of chirp parameters in Fig. 4(a) does not benefit the sensitivity of PAM-4, because the

*∆φ*distribution is already close to optimum.

Maintaining *c _{1} = 2* and

*c*, 8

_{2}= 1.5*∆φ*values falls within [

*0,1.0333∙2π*) in Fig. 3(c); while 16

*∆φ*values within [

*0,1.3039∙2π*) in Fig. 3(e). MLSE decoder faces more difficult tasks to distinguish the discrete

*∆φ*values, resulting in a bad decoding performance. For high-order modulation formats beyond PAM-4, CM-DML requires larger chirp parameters to achieve more SNR sensitivity gain over IM-DML. In Fig. 3(d), we double

*c*as 4 to expand the

_{1}*∆φ*range to [

*0,1.6952∙2π*). As a result, the SNR sensitivity of PAM-8 system increases about 2.5 dB at 7% FEC threshold in Fig. 4(b). The sensitivity increment is more dramatic for PAM-16. When

*c*,

_{1}= 4*∆φ*is expanded to [

*0,2.1864∙2π*) in Fig. 3(f). Correspondingly, the SNR sensitivity of PAM-16 system increases 6 dB at 7% FEC threshold in Fig. 4(c). Similar trends exist when

*c*increases. In Fig. 4(b), doubling

_{2}*c*results in 3 dB SNR sensitivity increment for PAM-8; while in Fig. 4(c), doubling

_{2}*c*results in 6 dB increment for PAM-16. In practice,

_{2}*c*is related to the symbol period

_{2}= ακT/4*T*. Thus, for high baud-rate,

*c*decreases, which may degrade the SNR sensitivity. However,

_{2}*c*is independent to the modulation parameters, and previous literatures [6] have reported some types of DML with high

_{1}*c*, which can be applied to the CM-DML system in the future.

_{1}It is intriguing to find that after doubling the chirp parameters, the gap between CM-DML enabled PAM-16 and QAM-16 has the potential to shrink to only 6 dB. This sensitivity gap is similar to what we have achieved in PAM-4 system (compared to QAM-4) [14]. After doubling the chirp, the CM-DML enabled high-order PAM is promising to compete with the commercialized EM based QAM transmitter in cost-sensitive medium reach transmissions.

## 4. Experiment

We demonstrate the first CM-DML enabled high-order modulation beyond PAM-4, using dual polarization (DP) PAM-8. Experiment setup is illustrated in Fig. 5. The baseband PAM signal is generated by an arbitrary waveform generator (AWG) sampling at 10 GSa/s, which drives a distributed feedback (DFB) laser working at wavelength of 1550 nm, with linewidth of 10 MHz, *c _{1}* of 1.8 and

*c*of 0.5. The laser output is fed into a DP emulator, which splits the signal into two paths, with one path delayed by 600-m to achieve phase de-correlation. The optical spectrum after the polarization beam combiner (PBC) is captured in Fig. 5(i). The 10-dB optical bandwidth of 10-Gbaud signal is about 0.2 nm, broadened by the frequency chirp. The signal is launched into a fiber recirculating loop. At receiver, an external cavity laser (ECL) with linewidth of 10 kHz is used as local oscillator (LO). Signal and LO are fed into a DP coherent receiver, whose output is sampled by a real-time oscilloscope at 50-GSa/s with 16-GHz bandwidth. The offline DSP is shown in Fig. 5(iii). A 40-tap 2 × 2 adaptive equalizer is applied to the polarization demultiplexing, and the intensity-only decision is made immediately after this step for performance comparison.

_{2}Figure 6(a) illustrates the optical SNR (OSNR) sensitivity for DP PAM-4 system. CM-DML achieves about 9-dB OSNR sensitivity improvement over IM for back-to-back measurement. To achieve bit-error-rate (BER) below 20% FEC threshold, CM only requires an OSNR of 12 dB for 40 Gb/s signal, which coincides well with the simulation results above. Compared to the previous DP PAM-4 DML-COHD experiment [13], this has about 8-dB OSNR sensitivity advantage normalized to the same data rate. Figure 6(b) illustrates the performance of DP PAM-8 system. The gap between CM and IM at 20% FEC is 8 dB, which is shrunk compared to PAM-4, predicted by the simulation. The required OSNR sensitivity at 20% FEC increases to 24 dB, which is because: (1) the PAM-8 intensity-only decision exhibits a BER floor, caused by the DML modulation performance limitation, and the imperfect square operation in digital domain after coherent detection; (2) the DML chirp is not sufficiently large for PAM-8; (3) the phase model is not as accurate as PAM-4 when the modulation order increases. It is noted that even when the PAM-8 constellation cannot distinguish any boundaries among the 8 rings at 36-dB OSNR in Fig. 5(ii), CM can still achieves a BER of 0.006. In Fig. 6(c), after 320-km SSMF transmission, DP PAM-8 system can achieve a BER under 20% FEC threshold.

## 5. Conclusions

We report the first dual polarization PAM-8 coherent system over 320-km SSMF with record electrical spectral efficiency of 6-bit/s/Hz for optical PAM transmission. By using large frequency chirp, the SNR sensitivity gap between QAM-16 and CM-DML enabled PAM-16 may be shrunk to <6 dB. CM-DML offers an attractive ultra-low-cost transmitter towards higher order modulation, which has great potential to support a wide range of medium reach optical applications from data-center interconnects to metropolitan area networks.

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