Comparative study on modulation dynamic characteristics of laser diodes using RZ and NRZ bit formats

INTERNATIONAL JOURNAL OF NUMERICAL MODELLING: ELECTRONIC NETWORKS, DEVICES AND FIELDSInt. J. Numer. Model. 2014; 27:138–152Published online 24 May 2013 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/jnm.1905

Comparative study on modulation dynamic characteristics of laserdiodes using RZ and NRZ bit formats

Moustafa Ahmed1,2,*,†, Safwat W. Z. Mahmoud2 and Alaa A. Mahmoud2

1Department of Physics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia2Department of Physics, Faculty of Science, Minia University, El-Minia, Egypt

SUMMARY

A comprehensive study on semiconductor laser characteristics under gigabit-per-second digital modulation ispresented. Comparison of the modulation characteristics under both formats of the return to zero (RZ) and non-return to zero (NRZ) bit formats is introduced. The modulation characteristics include the eye diagram, turn-onjitter (TOJ) and frequency chirp. The study elucidates how the laser modulation performance changes with variationof the modulation bit rate relative to the maximum bit rate and the setting bit rate of the relaxation oscillations. Therelative contributions of the intrinsic noise of the laser and the pseudorandom bit-pattern effect to the modulationcharacteristics are differentiated. The results showed that when the bit rate is higher than the setting bit rate, the eyediagram is partially closed and becomes completely closed when the bit rate increases beyond the maximum bit rate.When the bit rate is higher than 2.25Gbps, the TOJ values under NRZ modulation are smaller than those under RZmodulation near the threshold level. Under both RZ and NRZ formats, chirp increases with the bit rate with the chirpunder the RZ format being higher than that under the NRZ format. Copyright © 2013 John Wiley & Sons, Ltd.

Received 30 January 2012; Revised 23 December 2012; Accepted 3 April 2013

KEY WORDS: chirp; digital modulation; jitter; noise; semiconductor laser; simulation

1. INTRODUCTION

The behavior of semiconductor lasers under high-speed modulation is an important subject for manysemiconductor laser-based applications, especially digital fiber-optic communications. The first stepin the design of a digital optical communication system is to decide how the electrical signal excitingcan be converted into an optical bit stream. In the binary form, the presence of the light pulse wouldcorrespond to a binary ‘1’ and its absence corresponds to a binary ‘0’. There are two commontechniques to represent information in a binary electrical pulse train, namely, return to zero (RZ) andnon-return to zero (NRZ) formats. The NRZ modulation format has been used extensively in manydata communications systems mainly because of its relative ease of generation. Another reason is thatthe signal bandwidth of the NRZ pulse train is about 50% smaller than that of the RZ pulse train [1].The RZ format uses only half the bit duration for data transmission; therefore, it requires twice thebandwidth of NRZ coding [2].

Typical limitations of the performance of semiconductor lasers under digital modulation root to theintrinsic noise and transients. The origins of the intrinsic noise are inclusion of the spontaneousemission into the lasing mode and processes of electron–hole recombination [3, 4]. When the laseris subjected to high-speed pseudorandom digital modulation, the history of the ‘0’ bits preceding each‘1’ bit in the pseudorandom modulation bit pattern, or in other words the pseudorandom bit-patterneffect, adds further fluctuations to the intensity levels in both ‘1’ and ‘0’ levels [5]. Both the intrinsic noiseand the pseudorandom bit-pattern effect cause fluctuations in the turn-on delay time. These fluctuations

*Correspondence to: Moustafa F. Ahmed, Department of Physics, King Abdulaziz University, Jeddah, Saudi Arabia.†E-mail: [email protected]

Copyright © 2013 John Wiley & Sons, Ltd.

DIGITAL MODULATION OF LASER DIODES USING RZ AND NRZ BIT FORMATS 139

are measured in terms of the turn-on jitter (TOJ), which is an important aspect of communication systemsthat measures degradation of the communication system performance [6]. This TOJ is defined as thestandard deviation of the random turn-on delay. Gustavsson et al. [7] and Ahmed et al. [8] showed thatthe bit-pattern induced TOJ is enhanced when the bit slot is shorter than the setting time of the relaxationoscillations. It was shown also in [8] that when the laser is biased near threshold, the TOJ is mainly a bit-pattern effect, whereas the intrinsic noise dominates at high bias levels. Those results were obtained forlaser modulation with an NRZ pseudorandom bit code. Comparison of such results with those predictedunder RZ-code modulation is still required to explore the better code for achieving higher digitalmodulation performance especially under gigabit-per-second bit rates.

On the other hand, the modulating current source of the laser modulates the injected carriers in theactive layer, which causes variation in the refractive index giving rise to phase modulation, which inturn causes variation in the lasing frequency. This frequency variation is referred to as frequencychirping. Under large-signal modulation, chirping represents a form of intrinsic phase modulation,broadens the laser lineshape [9] and limits the transmission distance of high rates systems [10, 11].Semiconductor lasers are characterized by two types of chirp. The first type is the transient or peak-to-peak chirp, which originates from the relaxation oscillations that cause transient fluctuations inthe effective refractive index of the active layer and the carrier frequency [12]. The other type is theadiabatic chirp, which is induced when the laser reaches its steady state and the frequency chirpfluctuates around mean values in both ‘1’ and ‘0’ states [12].

In this paper, comprehensive numerical simulations are introduced for the modulation characteristics ofsemiconductor lasers subjected to RZ and NRZ pseudorandom bit formats with gigabit-per-second rates.The study is based on large-signal model of the laser rate equations in [12]. The modulation performanceis determined in terms of the signal power, frequency chirp, TOJ and the quality of the eye diagram. Theeye diagram is constructed by dividing the modulated laser waveform into segments of two-bit length andoverlaying each other. The degree of eye opening is evaluated in terms of a laser signal Q-factor, whichdefines the difference between the average intensities in the ‘1’ and ‘0’ states relative to summation ofthe corresponding standard deviations [5]. We elucidate the relations between the transient properties,and both the maximum modulation bit rate and the bit-pattern effect-free bit rate (setting bit rate) as wellas their dependence on the modulation conditions. Comparison of the simulated results under RZ andNRZmodulation formats is given over wide ranges of the bias current, modulation current andmodulationbit rate.

The paper is constructed as follows. In the following section, the simulation model of laser dynamicsunder digital modulation is introduced. Section 3 presents procedures of numerical calculations. In Section4, the results of numerical simulations of laser characteristics under RZ and NRZ pseudorandom bitformats with gigabit-per-second rates are given. The modulation characteristics include the signalpower, frequency chirp, TOJ and the quality of the eye diagram. Conclusions of the present work appearin Section 5.

2. SIMULATION MODEL OF SEMICONDUCTOR LASER DYNAMICS UNDER DIGITALMODULATION

The dynamics of semiconductor lasers subjected to pseudorandom digital modulation are described bythe following stochastic rate equations of the electron number injected into the active layer N(t), emittedphoton number S(t) and optical phase θ(t) [4]

dNdt

¼ 1eI tð Þ � AS� N

tsþ FN tð Þ; (1)

dSdt

¼ G� Gthð ÞSþ axV

N þ FS tð Þ; (2)

dθdt

¼ 2pdn ¼ aax2V

N � �Nð Þ þ Fθ tð Þ; (3)

where G is the optical gain (per second), which is described by the nonlinear form:

Copyright © 2013 John Wiley & Sons, Ltd. Int. J. Numer. Model. 2014; 27: 138–152DOI: 10.1002/jnm

140 M. AHMED, S. W. Z. MAHMOUD AND A. A. MAHMOUD

G ¼ A� BS (4)

where A and B are the linear and nonlinear (suppressed) gain coefficients. They are given by

A ¼ axV

N � Ng

� �(5)

B ¼ 92

pce0n2rℏl0

xtinV

� �2

a Rcvj j2 N � Nsð Þ (6)

In the previous equations, a is a tangential gain coefficient, x is the confinement factor of the electricfield to the active region whose volume is V and refractive index is nr, l0 is the emission wavelength,ℏ is the reduced Planck’s constant, c and e0 are the speed of light and permittivity in vacuum, Ng is theelectron number at transparency, tin is the electron intraband relaxation time, Ns is an electron numbercharacterizing the nonlinear gain, Rcv is the dipole moment, e is the electron charge and ts is the electronlifetime due to spontaneous emission. Gth represents the threshold gain level.

The current term of equation (1) varies with time as

I tð Þ ¼ Ib þ ImΨm tð Þ (7)

whereΨm(t) is a time-varying function describing pseudorandom square pulses of either ‘0’ or ‘1’ leveland with NRZ and RZ formats. The speed of this time variation is determined by the bit rate B= 1/Tb,with Tb representing the bit duration. The bit slot of the NRZ bit pattern is equal to the bit duration Tb,whereas in the case of the RZ bit format, the bit slot is multiplied by the duty cycle of the bit. It isconventional to use RZ bits with duty cycle of 0.5.

In equations (1)–(3), the terms FN(t), FS(t) and Fθ(t) are Langevin noise sources describing theintrinsic fluctuations in N(t), S(t) and θ(t), respectively, which are associated with quantum transitionsof electrons between the valence and conduction bands in the processes of absorption, spontaneousemission and stimulated emission [3, 4]. These noise sources represent white noise with Gaussianstatistics and are d-correlated [4]. They satisfy the following auto correlations:

FS tð ÞFS t0

� �D E¼ VSSd t � t

0� �

; (8)

FN tð ÞFN t0

� �D E¼ VNNd t � t

0� �

; (9)

Fθ tð ÞFθ t0

� �D E¼ Vθθd t � t

0� �

; (10)

and cross-correlations:

FS tð ÞFN t0

� �D E¼ VSNd t � t

0� �

; (11)

FN tð ÞFθ t0

� �D E¼ VNθd t � t

0� �

; (12)

where Vab, with a and b standing for S, θ and N, are the corresponding variances.The time-varying power value P(t) of the laser signal emitted from the front facet is calculated from

the corresponding emitted photon number S(t) via the relationship

P tð Þ ¼ hvc

2naL

1� Rf

� �ln 1=Rf Rb

� �S tð Þ

1� ffiffiffiffiffiffiffiffiffiffiRf Rb

p Þ 1þ ffiffiffiffiffiffiffiffiffiffiffiffiRf =Rb

p Þ�� (13)

where na and L are the refractive index and length of the active region, respectively, hn is the photonenergy of the emitted light, and Rf and Rb are the power reflectivities of the front and back facets,respectively.



3. NUMERICAL CALCULATIONS

Equations (1)–(3) are coupled first-order differential equation. Under large-signal modulation, thecomplexity of these equations increases, which necessitates resorting to numerical techniques to solvethem. In these calculations, the rate equations are solved numerically by means of the fourth-orderRunge–Kutta method [13], assuming rectangular-pulses of the modulating current in equation (7).The time step of integration Δt is set as short as 2 ps. The laser is modulated with RZ and NRZpseudorandom bit streams of word length 215-1 to collect significant statistics of modulation character-istics. The pseudorandom bit stream Ψm(t) is generated by the uniformly distributed random numbergenerations of the computer; random values less than 0.5 are converted to zero and other values areconverted to unity. The modulation characteristics are simulated as functions of the bias current Ib,modulation current Im and bit rate B, which is varied between 1Gbps and the maximum bit rate Bmax.We determine both the maximum bit rate Bmax and the setting bit rate Bsetting from the laser transients.The former is evaluated as the reciprocal of the turn-on delay time ton, whereas the latter is thereciprocal of the time at which the transients die away. The present numerical calculations are appliedto InGaAsP lasers emitting at wavelength l= 1.55 mm as the most popular light source in optical fibercommunication systems. The nonradiative recombination processes are taken into account in the rateequation through the lifetime ts as

1ts

¼ BeffN=V (14)

where Beff is the effective rate of electron recombination including both the radiative and nonradiativerecombination processes. Typical values of the parameters of these lasers are listed in Table I.

The Langevin noise sources in equations (1)–(3) are generated at instant ti of integration by usingthe values of photon number S(ti� 1) and electron number N(ti� 1) at the previous instant ti� 1 as [4]

FS tið Þ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiVSS tið ÞΔt

rgS; (15)

Fθ tið Þ ¼ 1S ti�1ð Þ þ 1

ffiffiffiffiffiffiffiffiffiffiffiffiffiVSS tið ÞΔt

rgθ; (16)

FN tið Þ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiVNN tið Þ þ 2kS tið ÞVNS tið Þ

Δt

rgN � kS tið Þ FS tið Þ þ 2 S ti�1ð Þ þ 1½ �Fθ tið Þf g (17)

The auto-correlation and cross-correlation coefficients of FS(t), Fθ(t) and FN(t) are given by thephoton and electron numbers at the preceding instance (ti� 1) as [4]

VSS tið Þ ¼ 2axV

S ti�1ð Þ þ 1½ � N ti�1ð Þ; (18)

Table I. Typical values of the parameters of a 1.55-mm InGaAsP laser.

Symbol Definition Value Unit

l Emission wavelength 1.55 mma Tangential gain coefficient 7.85� 10�12 m3 s�1

x Field confinement factor in the active layer 0.2 –V Volume of the active region 60 mm3

na Refractive index of the active layer 3.59 –L Length of the active region 250 mmNg Electron number at transparency 5.31� 107 –C Spontaneous emission factor 2.5� 10�5 –tr Radiative recombination lifetime 7.772 nstnr Nonradiative recombination lifetime 4.45 nsB Coefficient of nonlinear gain 332.5 s�1

Gth Threshold gain 7.82� 1010 s�1



VNN tið Þ ¼ 21tsþ ax

VS ti�1ð Þ

N ti�1ð Þ; (19)

Vθθ tið Þ ¼ VSS tið Þ4 S ti�1ð Þ þ 1ð Þ2 (20)

with

VNS tið Þ ¼ � axV

N ti�1ð Þ S ti�1ð Þ þ 1½ � þ NgS ti�1ð Þ; (21)

VNθ tið Þ ¼ VSN tið Þ2 S ti�1ð Þ þ 1ð Þ (22)

kS tið Þ ¼ �VNS tið ÞVSS tið Þ ; (23)

The Gaussian distributions of these Langevin noise sources are determined by the independentGaussian random numbers gS, gθ and gN of zero means and variances of unity.

The digital modulation performance of the laser is evaluated in terms of the time trajectory ofthe modulated laser signal, the corresponding eye diagram and the associated values of TOJ andQ-factor of the laser signal, Qsignal. The eye diagram is constructed by dividing the stream of P(t) into2-bits-long sequences and overlying each onto others. In this case of pseudorandom bit modulation,ton in each ‘1’ bit is defined as the time at which the power in the ‘1’ bit preceded by ‘0’ bit(s) firstsurpasses 50% of the summation of the steady-state powers corresponding to the bias and modula-tion currents [8]. TOJ is the standard deviation of the fluctuations in ton. Qsignal is a characteristicquantity analogous to the Q-factor that characterizes the eye diagram in optical fiber communicationsystems [5]. It is defined as [8]

Qsignal ¼ P�1 � P�0s0 þ s1

(24)

where P�j and sj, with j = 0 or 1, are the time average of the power and the standard deviation of thecorresponding fluctuations in either signal level, respectively.

Qsignal is used to determine the most open portion of the eye diagram over which the signal hasoptimum characteristics. This goal is achieved by following a technique similar to that proposed byAhmed et al. [8]. The eye diagram is divided into 10 sampling periods, each of length equal to Ts = 0.1Tb under the NRZ modulation and Ts = 0.05Tb under the RZ modulation, and determining thecorresponding value of Qsignal over each sampling period. Each sampling period corresponds to adifferent decision time in the range 0<Td≤ Tb� Ts. The section of most opening of the eye is thenof duration Ts and corresponds to the decision time Td at which Qsignal is maximum.

4. RESULTS AND DISCUSSION

4.1. Modulated laser waveform under different modulation conditions

Examples of the modulated laser waveforms under NRZ and RZ modulation formats when the bit rateis B= 5Gbps are plotted in Figure 1(a and b). The figure displays the bit sequence of the modulatingfunction Ψm(t) in equation (7). In the figure, waveform (i) corresponds to biasing the semiconductorlaser near-above threshold, Ib = 1.1Ith, with Im= 2Ith. Waveforms (ii) and (iii) correspond to above-threshold biasing, Ib = 2Ith; the former is simulated at the same modulation current Im= 2Ith as wave-form (i), whereas the latter corresponds to higher modulation current Im= 4Ith. As shown in Figure 1(a), the waveforms exhibit the relaxation oscillations that characterize the transient regime of the laser.These oscillations are most enhanced with lowest damping rate in waveform (i). Both the damping rateand relaxation frequency fr of the laser are higher for waveform (iii) than for waveform (ii), whichindicates an increase of the damping rate and fr with the increase of Im. The relaxation oscillationsare associated with inferior properties such as turn-on and turn-off delays in the ‘1’ and ‘0’ bits that


Figure 1. Plot of laser waveforms generated by modulation with (a) non-return to zero (NRZ) and (b) return tozero (RZ) formats. Waveform (i) corresponds to Ib = 1.1Ith and Im= 2Ith, waveform (ii) corresponds to Ib = 2Ithand Im = 2Ith and waveform (iii) corresponds to Ib = 2Ith and Im = 4Ith. The figure displays the corresponding

modulation bit sequence.


follow opposite bits. The turn-on delay time ton is the longest for waveform (i) and decreases inwaveforms (ii) and (iii) when Ib increases to 2Ith. Fixing Ib at 2Ith and increasing Im to 4Ith result onlyin increasing the output power P1 of the entire signal in the ‘1’ state as seen in waveform (iii). Thefigures show that ton and the steady-state value of the fluctuating power are different in the displayedthree windows of ‘1’ bit(s), which count to random fluctuations of these characteristics over the entirewaveform. The dispersion associated with fluctuations in ton determines the TOJ, which thenoriginates from both the intrinsic noise and the pseudorandom sequence of bits preceding each ‘1’bit in the modulation bit pattern. Figure 1(b) of the RZ format shows similar behaviors of the wave-forms except that the waveform does not continue over every ‘1’ bit, but drops to zero at the middleof the bit duration Tb. The short bit slot of Tb/2 = 1/ (2.5Gbps) = 0.1 ns allows only for setting the firstovershoot of the relaxation oscillations in the ‘1’ bits. The different heights of these overshoots aremanifestation of the pseudorandom nature of the RZ bit format.

4.2. Modulation characteristics near-above threshold

In the following, we present digital modulation characteristics when the laser is biased near-above thethreshold level, Ib = 1.5Ith.

A. Frequency chirp

Under large-signal modulation, frequency chirp represents a form of intrinsic phase modulation thatbroadens the laser lineshape [9] and limits the transmission distance of high rates systems [10]. Exam-ples of the modulated signal and frequency chirp are shown in Figure 2(a and b), which correspond toIm= 2Ith and B= 2.5Gbps under (a) NRZ and (b) RZ formats, respectively. As the laser current changesfrom the OFF state to the ON states, the laser attains gain switching in which both gain G(t) and carriernumber N(t) abruptly change. This carrier switching results in transient variations of the optical phase

Figure 2. Laser signal power and chirp when Ib = 1.5Ith with Im= 2Ith for B= 2.5Gbps under (a) non-return to zero(NRZ) and (b) return to zero (RZ) modulation.



θ(t), that is, in the frequency shift dn(t) (chirp) [12]. As can be seen in the lower part of the figures,the leading and trailing edges of the pulse have different carrier frequencies, which form the transientor peak-to-peak chirp [12]. This transient chirp originates from the relaxation oscillations, whichcause transient fluctuations in the effective refractive index of the active layer. When the laser reachesits steady-state case, the frequency chirp fluctuates around mean values in both ‘1’ and ‘0’ states. Thefrequency difference between the ‘1’ and ‘0’ states gives rise to the adiabatic chirp [12]. Figure 2(a)shows that the frequency of the output pulse undergoes a blue shift (positive peak chirp of dn= 10.37GHz) during the rising edge and a red shift (negative peak chirp of dn =�6.55GHz) during thetrailing edge under NRZ modulation, whereas under RZ shown in Figure 2(b), the frequencyundergoes a blue shift of dn = 21.68GHz during the rising edge and a red shift of dn =�9.07GHzduring the trailing edge.

Figure 3 shows variations of the peak-to-peak chirp with Im under both RZ and NRZ modulationwhen B = 2.5Gbps. The figure shows that under both the NRZ and RZ formats (but up to Im= 2.5Ith),the peak-to-peak chirp increases with the increase in Im, which can be interpreted as follows. Theincrease of Im results in an increase of the intensity of ‘1’ level, which then enlarges the blue shift.The increase in Im results in an increase in the intensity of both overshoots of the relaxation oscillationsand the level of the ‘1’ bits, which then enlarges the blue shift. The increase in chirp is rather small inthe low range of Im< Ith within which tsetting<Tb [14] and the population inversion in each bit reachesits steady-state value. Therefore, the small increase in Im results in a rather small increase in thepopulation inversion on the transition between ‘0’ and ‘1’ states, which induces a rather small increasein the frequency chirp. In the higher levels of Im, the bit slot Tb becomes shorter than tsetting and is notlong enough in a single ‘0’ bit sandwiched between ‘1’ bits to allow for the population inversion torelax to the steady state at I= Ib. That is, the population inversion in such ‘0’ bits becomes higher thanthe steady-state level, and the transition from such ‘0’ bits to the next ‘1’ bits is associated with strongerovershoots of the relaxation oscillations and larger values of the blue frequency chirp. The figureshows also that under the RZ modulation format when Im> 2.5 Ith, the chirp becomes almost constantat 34.5 GHz. The overall range of the peak-to-peak frequency chirp under the RZ modulation format(13.44–34.88GHz) is wider than that (12.56–29.41GHz) under the NRZ modulation format, whichindicates that the NRZ scheme has a better defined central frequency compared with the RZ scheme.Balle et al. [15] attributed this result to the fact that under the NRZ modulation, half of the ‘1’ bits,on the average, are preceded by similar ‘1’ bits and then have no chirp.

Dependence of the peak-to-peak chirp on the bit rate B for both NRZ and RZ modulation formats isillustrated in Figure 4. The modulation current is set as Im= 2Ith. The bit rate is varied from B= 1Gbpsto the maximum bit rate Bmax, which is equal to 8.69Gbps under the NRZ modulation, but is reducedto its half value (=4.345Gbps) under the RZ format, because the duration of each ‘1’ bit is set as Tb/2.The figure shows that under both modulation formats, the peak-to-peak frequency chirp increases withthe increase of B, which agrees with the results reported in [11] and [12]. The figure confirms again that

Figure 3. Variation of laser chirp with Im at Ib = 1.5Ith, when B= 2.5Gbps under both return to zero (RZ) and non-return to zero (NRZ) modulation.


Figure 4. Variation of peak-to-peak frequency chirp with B when Ib = 1.5Ith and Im = 2Ith for return to zero (RZ)and non-return to zero (NRZ) modulation formats.


the peak-to-peak frequency chirp under the RZ modulation is higher than that under the NRZ modula-tion over the relevant range of B.

B. Eye diagram analysis

The eye diagram is used to examine qualitatively the quality of the modulated laser signal includingthe random phenomenon of the turn-on delay. Figure 5 illustrates evolution of the eye diagram underthe NRZ modulation with the increase of the bit rate B while Im is fixed at 2Ith. The values of Bsetting

and Bmax determined from the laser transients without noise sources as 0.7 and 8.7Gbps, respectively.Four values of B are chosen, namely, B=Bsetting, Bsetting<B<Bmax, B=Bmax and B>Bmax to

Figure 5. Eye diagrams for non-return to zero (NRZ) modulation when Ib = 1.5 Ith and Im = 2Ith for (a) B=Bsetting,(b) Bmax>B>Bsetting, (c) B=Bmax and (d) B>Bmax.



elucidatehow the relation of B with both Bsetting and Bmax influence digital modulation performance ofsemiconductor laser. When B=Bsetting, Figure 5(a) shows that the eye diagram is well open and freefrom the bit-pattern effects; the rise and fall edges as well as the steady-state ‘1’ and ‘0’ levels aresharp. That is, the modulated laser signal in each ‘1’ bit following ‘0’ bit(s) is the same regardlessthe history of these ‘0’ bits. In this case, the TOJ records small value (4.5 ps), which may be due tothe quantum noise. The fluctuations seen at the steady-state power of both logic levels are also mani-festation of the quantum noise. The bit-pattern effect is seen in Figure 5(b) in which B= 2.5GbpsBsetting, and the bit slot Tb becomes shorter than the setting time tsetting of the relaxation oscillations.As seen in the figure, there are different turn-on edges (paths to the 1 level) and bulges-on-top of theeye, which result in partial closure of the eye diagram. These effects enhance as B increasesbeyond Bsetting. In this case, TOJ increases to 8.58 ps. In Figure 5(c), B reaches the upper limit ofthe modulation bit rate Bmax, which corresponds to as strong TOJ as 18.1 ps. The eye diagram isalmost closed with many turn-on edges and bulges-on-top. When B increases further, as shown inFigure 5(d), the eye diagram becomes completely closed and the digital modulation performance ofthe laser deteriorates.

The corresponding eye diagrams under the RZ modulation are shown in Figure 6. The width of theeye diagram is one half that of the NRZ eye diagrams as the bit slot of each ‘1’ bit is set as Tb/2.Therefore, as seen in the figures, the steady-state ‘1’ level nearly disappears because the ‘1’ bit doesnot continue longer than Tb/2. In this case, Bmax is reduced to its half value under the NRZ modulation.This is reflected in the shown eye diagrams as they exhibit similar behavior to those under the NRZmodulation with the increase of B. However, the eye diagram is almost closed with many turn-on edgesand bulges-on-top at bit rate Bmax = 4.345Gbps, which is one half that under the NRZ modulation.When B increases further as shown in Figure 6(d), the eye diagram becomes completely closed and

Figure 6. Eye diagrams under the return to zero (RZ) modulation when Ib = 1.5 Ith and Im= 2Ith for (a) B =Bsetting,(b) Bmax>B>Bsetting, (c) B=Bmax and (d) B>Bmax.



the digital modulation performance of the laser deteriorates. The investigation of the eye diagram char-acteristics with the increase of B relative to Bsetting was also reported by Gustavsson et al. [7] andAhmed et al. under NRZ modulation [8].

C. Turn-on jitter

As inferred from the previous discussion, TOJ is a critical property of the laser modulationperformance and is a limiting factor to the bit rate. Figure 7 plots variations of TOJ with Im underboth the NRZ and RZ modulation formats when B = 2.5 Gbps. This bit rate B is chosen such thatBsetting<B<Bmax over the relevant range of plotted modulation current Im. Bsetting = 0.349 Gbpswith Bmax = 5.88 and 2.94 Gbps under NRZ and RZ formats, respectively, when Im = 0.5Ith, andBsetting = 1.35 Gbps with Bmax = 11.11 and 5.55Gbps under NRZ and RZ formats, respectively, whenIm = 4.0Ith. The figure shows that TOJ decreases with the increase in Im, which is due to suppressionof the intrinsic intensity noise and improvement of laser coherency with the increase of the modulationcurrent [16]. The overall range of TOJ is (4.88–14.65 ps) under the NRZ modulation format, whereas itrecords (4.75–22.07 ps) under the RZ modulation format. The figure shows also that up to Im=1.1Ith,the RZ–TOJ values are greater than those of the NRZ–TOJ. Above this modulation current, theRZ–TOJ becomes little smaller than the NRZ–TOJ. According to the analysis by Ahmed et al. [8], boththe intrinsic laser noise and the pseudorandom bit pattern are the main contributors to TOJ. The formercontributes significantly at low currents and its effect decreases with the increase in current because of im-provement of laser coherency, whereas the latter effect adds to TOJ when Bsetting<B<Bmax. Therefore,the results shown in Figure 7 indicate that the turn-on delay of the RZ-modulated signal is more sensitiveto the intrinsic noise in the low range of modulation current than that of the NRZ-modulated signal. On theother hand, the RZ bit-pattern effect contributes more to the fluctuation of the turn-on delay than underNRZ modulation in which there are different histories of ‘0’ bits preceding the ‘1’ bit(s).

Dependence of TOJ on the bit rate B for both NRZ and RZ modulation formats is illustrated inFigure 8. The modulation current is set as Im= 2.0Ith, which corresponds to Bsetting = 0.7Gbps, whereasBmax = 8.69 and 4.345Gbps under the NRZ and RZ formats, respectively. The bit rate is varied fromB= 1Gbps to the maximum bit rate Bmax. The figure shows that under both modulation formats,TOJ increases with the increase of B. At the set point of Ib and Im, the intrinsic noise has little effecton the laser output. These TOJ values originate from the bit-pattern effect, which enhances with theincrease of the B. Similar results were reported in [8]. The figure shows that the TOJ values underthe NRZ modulation is little larger than those under the RZ modulation at low bit rates B< 2.25Gbps.Speeding the modulation above this bit rate is seen to significantly increase the RZ–TOJ values abovethose of the NRZ–TOJ, which indicates that the use of NRZ format is better than that of RZ at high bitrates and vice versa.

D. Q-parameter (Qsignal) of the Modulated laser signal

In this subsection, influence of the modulation parameters on the eye diagram opening is discussedquantitatively in terms of the Q-factor of the laser signal Qsignal. We apply the technique illustrated in

Figure 7. Variation of turn-on jitter (TOJ) with Im at Ib = 1.5Ith, when B= 2.5Gbps for return to zero (RZ) and non-return to zero (NRZ) modulation formats.


Figure 8. Variation of turn-on jitter (TOJ) with B when Ib = 1.5Ith and Im = 2Ith for return to zero (RZ) and non-return to zero (NRZ) modulation formats.


Section 3 to determine the most open section of the eye diagram. At each instant Td, the average powersP1�

and P0� and the corresponding standard deviations s1 and s0 in the ‘1’ and ‘0’ levels, respectively, are

evaluated. These values are then used to calculateQsignal via equation (23). The results showed thatQsignal

improves with shifting the decision time Td toward the end of the bit attaining maximum values whenTd = 0.9Tb for the NRZ modulation and Td = 0.45Tb for the RZ modulation. This far decision point(near the end of the bit) corresponds to the middle of the eye, which is the most open part of theeye diagrams as can be seen in Figures 5(b) and 6(b). These results agree with these predicted by Balleet al. [15] and Ahmed et al. [8].

Figure 9 plots variation of Qsignal with Im under both the NRZ and RZ modulation formats withB= 2.5Gbps. The obtained values of Qsignal under NRZ format match those obtained by Ahmedet al. [8]. The figure shows that Qsignal increases in general with the increase of Im, which can beinterpreted as follows. The increase of Im results in increase of the average power P1

� in the ‘1’ leveland slightly decrease of the average power P0

� in the ‘0’ level, as shown in Figure 9, which thenenlarges the numerator (P1

�� P0�) of equation (23). The power fluctuations in both ‘1’ and ‘0’ levels

are simultaneously suppressed because of improvement of laser coherency [4], which then contributesto decrease in the denominator (s1 + s0). The net result is the shown increase of Qsignal with theincrease of Im. The figure shows also that when Im> 0.6Ith, the Qsignal values under the NRZ formatare larger than those under the RZ format. That is, the eye diagram is more open and the modulationcharacteristics are better under the NRZ format over the entire range of Im.

Variation of Qsignal with the modulation bit rate B is illustrated in Figure 10 under both the NRZ andRZ modulation formats. The modulation parameters are similar to those in Figure 8. The figure showsthat Qsignal decreases with the increase of B. The decrease of Qsignal is expected to be due to

Figure 9. Variation of Qsignal with Im for Ib = 1.5Ith under non-return to zero (NRZ) and return to zero (RZ)modulation formats.


Figure 10. Variation of Qsignal with B when Ib = 1.5Ith and Im= 2Ith for the return to zero (RZ) and non-return tozero (NRZ) modulation.

Figure 11. Variation of laser chirp with Ib at Im= 2Ith, when B = 2.5Gbps for non-return to zero (NRZ) and returnto zero (RZ) modulation formats.


development of the power fluctuations induced by the bit-pattern effect. This effect corresponds toclosure of the eye diagram and deterioration of the laser modulation performance. The results show thatthe RZ–Qsignal values are smaller than those of the NRZ–Qsignal, which indicates that the quality of themodulated signal (i.e., modulation performance of the laser) is better under the NRZ modulation thanunder the RZ modulation.

E. Influence of biasing current on modulation characteristics

In the previous subsection, influences of the modulation current Im and bit rate B on the modulationcharacteristics of semiconductor lasers were analyzed when the laser is biased near the threshold level.In this subsection, influence of the bias current Ib on the modulation characteristics is illustrated. Themodulation current and bit rate are set to be Im= 2Ith and B= 2.5Gbps.

Figure 11 plots dependence of the laser peak-to-peak chirp on Ib for both the RZ and NRZ modu-lation formats. The figure shows that under both formats and with the increase of Ib, the chirp decreasesremarkably up to Ib = 1.5Ith and then decreases slightly up to Ib = 2.5Ith at which it saturates at~8.6GHz. The figure shows also that under and near-above threshold, the RZ chirp is higher thanthe NRZ chirp, whereas they attain similar values when Ib> 2.5Ith. A similar behavior of the chirp withthe variation of Ib around the threshold current Ith was predicted by Balle et al. [15].

Figure 12 plots dependence of TOJ on Ib under both the NRZ and RZ modulation formats. The resultsshow that under both formats, when the laser is biased under threshold, Ib< Ith, TOJ maintains largervalues and decreases remarkably with the increase of Ib because of the associated improvement of lasercoherency and suppression of quantum noise. Above the threshold current, Ib> Ith, TOJ decreases slightly


Figure 12. Variation of turn-on jitter (TOJ) with Ib at Im= 2Ith, when B= 2.5Gbps for return to zero (RZ) and non-return to zero (NRZ) modulation formats.

Figure 13. Variation of Qsignal with Ib for Im= 2Ith, when B= 2.5Gbps under return to zero (RZ) and non-return tozero (NRZ) modulation formats.


with the increase of Ib and saturates at ~2.5 ps when Ib increases beyond 2.5Ith. The large TOJ values arisefrom the pseudorandom bit pattern, which diminishes as Ib increases and the associated setting time of therelaxation oscillations decreases compared with the bit duration Tb. The displayed range of TOJ aroundI= Ith agrees with that predicted by Balle et al. [15]. The results show also that under and near-abovethreshold, RZ–TOJ is weaker than NRZ–TOJ, whereas they attain similar values in the regime of far-above threshold. Therefore, under this bit rate, the turn-on delay of the RZ-modulated laser signal is lessaffected by the quantum noise than that of the NRZ-modulated signal, whereas they are subject to similareffects from the pseudorandom bit pattern.

Variation ofQsignal with the bias current Ib under both the NRZ and RZmodulation formats is plotted inFigure 13. The results show that Qsignal increases in general with the increase of Ib. The results show alsothat the values of RZ–Qsignal are smaller than those of the NRZ–Qsignal, which indicates that the quality ofthe modulated signal is better under the NRZ modulation than under the RZ modulation. This improve-ment of modulation performance with the increase of Ib originates from suppression of both quantumnoise and pseudorandom bit-pattern induced noise in the modulated laser signal.

5. CONCLUSIONS

A comparative theoretical study of semiconductor laser dynamics under NRZ and RZ pseudorandombit formats with gigabit rates is presented. The eye diagram, TOJ and frequency chirp are calculated,and their dependence on the bias and modulation currents as well as the modulation bit rate were



examined. The degree of eye opening is measured in terms of a Q-parameter of the laser signal. On thebasis of the obtained results, the following conclusions can be traced.

When the modulation bit rate is higher than the setting bit rate of the relaxation oscillation, the laserexhibits enhanced TOJ and the eye diagram is partially closed. When the bit rate increases more, theeye diagram becomes completely closed and the digital modulation performance of the semiconductorlaser deteriorates. Under RZ modulation, the eye diagram is completely closed at bit rates equal to onehalf those under the NRZ modulation, which then requires more increase of Ib and/or Im to improve themodulation performance. TOJ decreases with the increase of Ib and/or Im for both formats ofmodulation. The decrease in TOJ with the increase of the Ib enhances with the increase of B. At highmodulation bit rates (B> 2.25Gbps), the NRZ format yields better digital modulation performancenear the threshold level, whereas the RZ format is more preferable far-above threshold.

The Q-factor of the laser signal Qsignal increases with the increase of Ib and/or Im, which confirmsthe improvement of modulation performance with the increase of Ib and/or Im. Qsignal attains largervalues under the NRZ modulation format than those under the RZ modulation format. On the otherhand, Qsignal decreases with the increase of B. This decrease is stronger at lower bit rates and moderateat higher rates.

The peak-to-peak chirp increases with the increase of the Im under both RZ and NRZ formats. Itdecreases remarkably with the increase of Ib and saturates at 8.6GHz when Ib increases beyond2.5Ith. The chirp is higher under the RZ modulation format than under the NRZ modulation format,which indicates that the NRZ scheme has a better defined central frequency compared with the RZscheme. Under both the RZ and NRZ modulation formats, the peak-to-peak chirp increases with theincrease of B. The chirp under the RZ modulation is higher than that under the NRZ modulationformat. The difference of chirp between the two formats decreases with the increase of Ib. That is, whenthe semiconductor laser is biased near the threshold level, the use of the NRZ format is advantageous tosuppress the peak-to-peak chirp under high-speed modulation. At higher bias currents, both formatyield almost similar chirp.

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t. J. Numer. Model. 2014; 27: 138–152DOI: 10.1002/jnm


AUTHOR’S BIOGRAPHIES

Copyright © 2013 John W

Moustafa Ahmed was born in Minia, Egypt, in 1966. He received the BSc and MScdegrees in Physics from Minia University, Minia, Egypt, in 1988 and 1993, respectively,and the PhD Eng. degree from Kanazawa University, Kanazawa, Japan, in 1999. He isworking as a Professor at the Department of Physics, King Abdulaziz University, SaudiArabia, and on-leave from the Department of Physics, Minia University, Egypt.

From 2000 to 2002, Dr. Ahmed was a JSPS postdoctoral fellow at the Department ofElectrical and Electronic Engineering, Kanazawa University, Japan. In 2004, he wasawarded the Egyptian national award in physics. His research interests are in the areasof semiconductor laser dynamics and optical fiber communications.

iley & Sons, Ltd. Int. J. Numer. Model. 2014; 27: 138–152DOI: 10.1002/jnm

Safwat W. Z. Mahmoud was born in 1966, in El-Minia, Egypt. He received the BSc andMSc degrees in Physics from Minia University in 1989 and 1994, respectively. In 2002, hereceived the Doctor’s degree of Engineering from Ulm University, Germany. Currently, heis an associate professor at the Department of Physics Minia University, Egypt. Hisresearch activity is in the field of semiconductor lasers and their applications in optical fibercommunication systems.

Alaa Mahmoud was born in 1984, in Beni Suif, Egypt. He received the BSc degree inPhysics from Cairo University, Beni Suif branch in 2005 and MSc degree in Physics fromMinia University in 2010. He is an assistant lecturer at high engineering and technologicalInstitute, Basic Science Department, El-Minia, Egypt. His research activity is in the field ofsemiconductor lasers for use in fiber links.

Comparative study on modulation dynamic characteristics of laser diodes using RZ and NRZ bit formats

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