Japanese Journal of Applied Physics
Vol. 47, No. 9, 2008, pp. 7182–7189#2008 The Japan Society of Applied Physics

Analysis of Subpulse Generation from Delayed-Interference Signal-Wavelength Converter
for Wide Carrier Recovery Rate Range
Jun S AKAGUCHI, Mads L. NIELSEN1 y, Takashi O HIRAz, Rei S UZUKIx, and Yoshiyasu U ENO
Department of Electronics Engineering, University of Electro-Communications, 1-5-1 Chofugaoka, Chofu, Tokyo 182-8585, Japan
1
Research Center COM, Technical University of Denmark, Bldg. 345v, DK-2800 Kgs. Lyngby, Denmark(Received January 11, 2008; accepted April 24, 2008; published online September 12, 2008)

The generation of subpulses in delayed-interference signal-wavelength converters (DISCs) had been suspected as a cause of
waveform degradation in their application in ultrafast (160 GHz) optical time division multiplexing (OTDM)
communication systems. We reported its ﬁrst observation in our previous letter. In this paper, after a detailed explanationof our model, experimental method and improved results with respect to those in the previous letter, we discussed theapplicability of our model in a wide range of carrier recovery rates in the semiconductor optical ampliﬁer (SOA). Subpulse
waveforms were systematically measured for several carrier recovery rates (carrier lifetimes eff ¼ 11{ 280 ps), and anincrease in subpulse intensity with recovery rate was observed. The calculated intensities showed good agreement withmeasured data for most recovery rates, which supports our model. Using this model, we numerically showed the trade-oﬀ
between subpulses and pattern-induced intensity noise, in the same recovery rate range. This trade-oﬀ suggests that part of the
DISC structure needs improvement. [DOI: 10.1143/JJAP.47.7182]
KEYWORDS: all-optical signal processing, wavelength conversion, delayed-interference signal-wavelength converter (DISC),
semiconductor optical amplifier (SOA), nonlinear phase shift, subpulse, pattern-dependent noise

1.

Introduction

Several types of all-optical gates based on semiconductor
optical ampliﬁers (SOAs) have been intensively studied,1,2)
with the goal of realizing ultrafast, compact, low-powerconsumption signal processors for use in future optical time
division multiplexing-wavelength division multiplexing(OTDM-WDM) networks and systems. Notably, the delayed-interference signal-wavelength converter (DISC) andits variants have led to some of the most successfulachievements in the last decade. 168 Gbps error-free wavelength conversion3) and 40 Gbps error-free ultralong-distance 2R transmission4) have been demonstrated using
DISCs in their original conﬁguration, and a 320 Gbps
wavelength conversion has also been demonstrated usingtransient cross-phase modulation in the SOA.5)
It has been noticed, however, that the eye diagram of the
DISC output signal often suﬀers from serious degradation,
which could not be ascribed to the well-known patterndependent intensity noise. Some modeling research studies6,7) have been focused on explaining this phenomenon,
and one fundamental issue has been recognized as thepotential source: the generation of small subpulses between
return-to-zero-formatted output pulses. We actually observed the generation of subpulses through a gate experiment, and reported it in our former letter.8) In addition, we
explained the measured characteristics of subpulse waveforms quantitatively using our subpulse generation model.
However, we described these issues only partially because of
the limited paper length. Furthermore, we reported only aweak generation of subpulses, since the carrier recovery
in the SOA had been kept slow throughout the former
experiment. It has not been proved, therefore, whether

Present address: Nara Institute of Science and Technology, Ikoma, Nara
630-0192, Japan.
yPresent address: u2t Photonics AG., Berlin 10553, Germany.
z
Present address: Fujitsu Access Ltd., Kawasaki 213-8586, Japan.
xPresent address: Hitachi Communication Technology Ltd., Yokohama
244-8567, Japan.

subpulse generation can be an actual, serious cause of signal
degradation.
In this paper, we ﬁrst report further details of ourmeasurement and theoretical analysis of subpulse generation
with improved accuracy using the latest results of SOAcharacterization. Then we demonstrate a theoretically
predicted increase in the subpulse intensity with the carrier
recovery rate of the SOA through systematic subpulse
measurement. From the measured and calculated results,
we conclude that our model is applicable for use in wide
recovery rate range. Finally, we discuss the trade-oﬀ
between the subpulses and pattern-induced intensity noise
associated with the recovery rate change, which we referred
to only brieﬂy using one quick particular example in ourprevious letter, in a wider recovery rate range. This result
illustrates that subpulse generation can be a signiﬁcantlimiting factor for practical DISC operations. The present
modeling work will be of great help in the future development of solutions for this issue, and will also assist otherresearchers in modeling all-optical gate operations based on
SOAs and delayed interferometers.
2.

Theoretical Model of DISC-Gate Operation Based on
SOA Carrier Dynamics

A DISC gate in its original concept consists of a single
SOA as an optical nonlinear element, and a Mach–Zehnderinterferometer (MZI), which determines the output timing
window [Fig. 1(a)]. Input pulse train with a wavelength of
1 is combined with continuous-wave (cw) light (2 ) andinjected into the SOA. The all-optical modulation process
can be modeled based on the rate equation of the excess
carrier density in the SOA asd
T IOP nc ðtÞ
nc ðtÞ ¼

dt
c
qV

 ð2:1Þ
1
jEpulse ðtÞj2 jECW j2
 ½Gðnc ðtÞÞ  1þ:Vhpulsehcw
Here, nc ðtÞ is the average nc ðz; tÞ over the active region
length. nc ðz; tÞ, the carrier density which contributes to the7182

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J. S AKAGUCHI et al.

(a)data input
λ1

SOA

cw

∆t

λ2

(b)

(c)

λ2

∆Φ(t)

+0.0

4
3
2
1
0
-100

BPF

[π]

[x1016]δ∆Φ(t)

Excess carrier density
nc(t) (1/cm3 )5

λ2
data output

∆ΦB

IOP

0

+100

+200

-1.0

∆Φ(t-∆t)

-2.0
+1.5
+1.0
+0.5
-25

+300

∆Φ(t)+∆ΦB

∆t

0

+25

+50

+75

Time (ps)Time (ps)Fig. 1. Schematic and operation principles of the DISC gate: (a) Schematic of the gate. (b) Calculated example of the time proﬁle of
SOA carrier density during optical modulation. (c) Time proﬁles of the nonlinear phase shifts for the split optical components in the
MZI, and the phase diﬀerence between them.

SOA gain, is diminished from the total carrier density, as
represented by the quantum conversion eﬃciency T . IOP is
the injection current, c is the carrier lifetime, V is the active
region volume, and Epulse ðtÞ and ECW are the amplitudes of
the input optical signals. The ﬁrst, second, and third termson the right-hand side of eq. (2.1) represent the carrier
injection, carrier relaxation, and stimulated recombinations,
respectively. Epulse ðtÞ for a clock operation is expressed assﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
X Epulset  mT
sech
Epulse ðtÞ ¼
ð2:2Þ
TW
2TW
m
ðm ¼ 1; 2; . . . ; 1Þ;each pulse injection, but recovers slowly according to theeﬀective carrier relaxation time eff . The delayed interference scheme has been adopted to inhibit this slow response
as follows: The gain-modulated and phase-modulated cw
light is split into two components at the MZI, which are
combined after suﬀering a time diﬀerence t and a phase
diﬀerence (phase bias) B at the end of the MZI. Then theamplitude of the combined signal is expressed as
1 pﬃﬃﬃﬃﬃﬃﬃﬃﬃ
Eout ðtÞ ¼ f GðtÞ exp½iððtÞ þ B Þ
2
ð2:6Þ
pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
þ Gðt  tÞ exp½iðt  tÞgEcw ;and the output signal intensity Pout ðtÞ is expressed aswhere Epulse is the pulse energy and TW is a parameter related
to the full-width at half-maximum pulse width TFWHM as
TW ¼

TFWHM
pﬃﬃﬃ :
2 lnð1 þ 2Þ

ð2:3ÞSince the material gain of the SOA is considered to be givenby dg=dn  nc ðz; tÞ,9) the chip gain of the SOA is expressed asdgGðnc ðtÞÞ ¼ exp Leffnc ðtÞ :ð2:4Þ
dnHere,  is the conﬁnement factor, Leff is the eﬀective lengthof the active region, and dg=dn is the diﬀerential gain of theactive region. nc ðtÞ decreases through stimulated recombinations as each control pulse incidents on the SOA[Fig. 1(b)], and this decrease causes an ultrafast change inthe refractive index nr of the active region through the bandﬁlling eﬀect. Then the co-propagating cw signal suﬀers
nonlinear phase modulation9) expressed asðtÞ ¼ 

Pout ðtÞ ¼ jEout ðtÞj2
pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
 1¼
GðtÞGðt  tÞ cos2 ðtÞ=2 þ GðtÞ2
4
2
ð2:7Þ
 jEcw j ;


dg
dnr
Leff
nc ðtÞ ¼ k0 Leffnc ðtÞ: ð2:5Þ
2dndn

Here,  is the linewidth enhancement factor and k0 ¼
2cw =c is the wave number of the light in vacuum. The
conﬁnement factor  relates nr to the eﬀective index of the
SOA. ðtÞ increases within less than one picosecond afterðtÞ  ðtÞ  ðt  tÞ þ B ;pﬃﬃﬃﬃﬃﬃﬃﬃﬃ pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃGðtÞ  GðtÞ  Gðt  tÞ:

ð2:8Þ
ð2:9Þ

Thus, the output signal intensity is dominated by the phase
diﬀerence ðtÞ. It is largely shifted from B only withint0 < t < t0 þ t, where t0 is the pulse incident time, and theoutput gate window is shortened to t [Fig. 1(c)]. Since theinput data pulses at 1 do not pass the band-pass ﬁlter (BPF),
we obtain wavelength-converted signals from the DISC gate.
There remains a problem with this scheme, however,since the recovery of ðtÞ is not linear-function-like but
exponential with t, expressed as expðt=eff Þ. dðtÞ=dt
and dðt  tÞ=dt do not balance as it is, implying thatcomplete cancellation of the phase shift after t > t0 þ t is
not possible. Instead there occurs a subpulse outside the gatewindow, potentially causing a bit error. Note that if we can
induce asymmetric phase shifts for the two components
as 1  expðt=eff Þ and 2  fphase  exp½ðt  tÞ=eff ,
we can suppress subpulse generation by selecting fphase ¼expðt=eff Þ.6)7183

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J. S AKAGUCHI et al.

(a)
CW light (λ2)

DISC gate

VOA P H Q
EDFA

MZI

DFB LDQEDFAVOA P H

output pulses (λ2)∆t=5.0 ps
calcite

100m SMF

SOA #1

BPF
3nm

MLFL

isolator Q0

MUX

Q1 P1

P0 C1

12.5GHz

input pulses (λ1)
EDFA

probe

Q H

input
cross
correlator

digital storage
oscilloscope

(b)

BPF
5nm

EDFA

HQ
spectrometer

DISC gate
Power
Meter

Power
Meter

PM
lensedfiber

circulator
Power
Meter

lensedfiber
SOA #2(chip)PBS

MZI∆t=5.0 ps
calciteQ0 P0 C1

BPF
3nm

Q1 P1

FP-LD (λassist)
Fig. 2. Setup of the DISC-gate experiment. (a) Setup for §4.1. VOA: variable optical attenuator, MZI: Mach–Zehnder interferometer,
SOA: semiconductor optical ampliﬁer, Q: quarter-wave plate, H: half-wave plate, P: polarizer, MLFL: mode-locked ﬁber laser, andMUX: optical time-division multiplexer. (b) Modiﬁed DISC-gate setup for §4.2.

3.

Experimental Setup for Subpulse Measurement

3.1 Overview
The generation of subpulses had not been revealed clearly
before our measurement owing to the lack of monitoring
resolution in previous experiments. Precise, quantitative
investigation of subpulses requires waveform monitoring ina high dynamic range with a high time resolution over a longtime span. Thus, we employed a cross-correlator (Femtochrome Research FR-103XR), that had a dynamic range
exceeding 27 dB. Its time resolution was determined by thewidth of optical sampling pulses, and 2.2 ps could beachieved using pulse trains from a frequency-tunable modelocked ﬁber laser (MLFL; Pritel UOC-3).
The setup for waveform monitoring in §4.1 is shown in
Fig. 2(a). In this case, we used a commercially available
SOA module #1 (InPhenix IPSAD1503, drive current =250 mA) in the DISC. Some of the measured characteristicsof this SOA are shown in Table I and Figs. 3(a), and 3(b).
Particularly, precise characterization of the gain saturation
for temporally isolated optical pulses was indispensable forthe accurate subpulse calculation in §4.1. In addition, thedegree of nonlinear phase shift for particular optical inputs
Table I. Measured characteristics of SOA #1 used in §4.1, at IOP ¼
250 mA.
Small signal gain G0 (dB)
Coupling loss against pigtail ﬁbers (dB)

23
2

sat
(fJ)
Saturation energy for 2-ps pulse Epulse

600

Carrier lifetime c (ps)200

was estimated from the cross-phase-modulated (XPM)
spectrum, as shown in Fig. 3(c),2) to determine dnr =dn later.
We used a set of high-precision, high-extinction-ratio
polarization-control devices Q0 –P1 (Optoquest) in order toconstruct the MZI. The rotating quarter-wave plate Q0 andthe rotating polarizer P0 were used to adjust the polarizationof the cw light to exactly 45 oﬀ the principal axis of thecalcite crystal C1 (DGD, t ¼ 5 ps). The next quarter-wave
plate Q1 and rotating polarizer P1 were used to control B
precisely. Details of this polarization-based MZI will be
discussed in §3.2. 25 and 12.5 GHz clock pulses weregenerated from the MLFL and an optical multiplexer todrive the DISC gate. The width of the pulses sent to the
DISC was broadened from 2.2 to 3.8 ps with a 100-m-longsingle-mode ﬁber, to suppress carrier-heating-related phenomena inside the SOA.10) The polarization of cw light fromthe distributed-feedback laser diode (DFB-LD) as well as theclock signal was aligned to either the transverse electric (TE)or transverse magnetic (TM) axis of the SOA at the SOA input
facet, to suppress the nonlinear polarization rotation.11,12)
For the measurement discussed in §4.2, where a much
faster SOA was required, we used a custom-designed multiple
quantum well SOA chip #2 (Leff ¼ 1100 mm), instead of theprevious SOA module. The small-signal gain, the gain
saturation proﬁle, and example of the XPM spectrum areshown in Figs. 3(a), 3(b), and 3(d), respectively. The detailed
properties of this SOA are also explained in ref. 13. Part of theexperimental setup was modiﬁed as shown in Fig. 2(b).
Signal injection to the SOA chip was achieved using apolarization-maintaining dispersion-shifted lensed ﬁber, with
its PM axis aligned to the TE axis of the SOA. Counter-7184

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J. S AKAGUCHI et al.

(c)
+40

+20

+20

∆ΦNL~ 0.54 π

00

SOA #1
SOA #2

-20
30

100

300

1000

Nominal injection current (mA)(b)
+40

Chip Gain (dB)

25 GHzcw
5 mW
pulse 475 fJ(chip)

SOA #1,

Intensity (dBm/nm)

Chip Gain (dB)

(a)
+40

+30

-20

-60
+40

0
-20

SOA #1, 250 mA
SOA #2, 400 mA

1

10

100

∆ΦNL~ 0.69 π-40

SOA #2, 10.5 GHz

-60
1547

2 ps, 0.65 GHz, 1555 nm
0cw 0.3 mW
pulse 30 fJ(chip)

(d)

+20

+20
+10

1000 10000

1548

1549

propagating assist light14) of assist ¼ 1480 nm was used insome measurements to obtain an eﬀective recovery time as
short as eff ¼ 11 ps. The polarization-based MZI was
improved so that all the components were directly connectedto each other without ﬁber connections. This reduced the driftof the polarization-transfer property inside the MZI.
3.2 Phase bias of polarization-based MZI
As we discussed in §2, the MZI in the DISC plays acritical role in wavelength conversion and subpulse generation. Since the subpulse waveform is quite sensitive to the
MZI phase bias as we will show in §4.1, precise determination of the bias value B is essential for comparison of
the measured and calculated results. In this subsection,
0lexp 2i
@
MC ¼

0


1550

Wavelength (nm)Output energy from chip (fJ)

MP ¼

Fig. 3. Measured characteristics of SOAs. (a) Smallsignal gains for cw light,  ¼ 1548:5 nm. (b) Gainsaturation proﬁles for temporally isolated pulses.
Dashed lines show ﬁtting results with a theoretsat
ical function,9) GðEout Þ ¼ Eout =Epulse
fln½expðEout =1sat
Epulse Þ þ G0  1  ln G0 g . (c, d) Spectra of thecross-phase-modulated cw outputs from the SOAs.
Dashed lines indicate the cw light wavelength.

-40

1

0

0

0




;

Rð Þ ¼
B exp i 4
B
MQ ¼ B
@
0

;

1



The Jones matrices of a calcite with an optical path length
diﬀerence of l, a quarter-wave plate, a polarizer, and arotation operation are expressed as0

10A

therefore, we discuss how the set of wave plates, calcite andpolarizers acts as an MZI, how we can determine B fromthe wave-plate settings, and the precision of B .
In the ﬁrst step, cw light is evenly split into two
orthogonally polarized components aligned to the C1 axes,
by adjusting the Q0 , P0 , and C1 angles. Seen from one of theC1 axes, the Jones vectors of these components are expressed as
 
 
1
0
Ein1 ¼; Ein2 ¼
:
ð3:1Þ
0
1

cos

 sin

sin

cos

respectively.
In the MZI used in §4.1, a dispersion-shifted single-mode
ﬁber was used to connect C1 and Q1 . The Jones matrix ofa single-mode ﬁber is generally expressed by a unitarymatrix15) ascosð M Þ expðiM Þsinð M Þ expði M Þ
MF ¼; ð3:3Þ sinð M Þ expði M Þ cosð M Þ expðiM Þwhere M , M , and M are parameters to be measured
separately.
Thus, the two components Ein1 and Ein2 are converted toEout1 ¼ MP R½ð P1  Q1 ÞMQ Rð Q1 ÞMF Rð C1 ÞMC Ein1 ;Eout2 ¼ MP R½ð P1  Q1 ÞMQ Rð Q1 ÞMF Rð C1 ÞMC Ein2 ;
ð3:4Þ





1
0
C
C

 C;
 A
exp i4

ð3:2Þ

;where C1 , Q1 , and P1 are the angles of the corresponding
devices’ axes. Then the complex ratio of these parallel
vectors determines B ð Q1 ; P1 Þ and the mixing ratiorð Q1 ; P1 Þ as
Eout2 ¼ Eout1  r expðiB Þ:

ð3:5Þ

The output signal of the MZI is given by Eout ¼ Eout1 þEout2 . Eout becomes zero when r ¼ 1 and B ¼ . Thiscan be achieved by adjusting Q1 and P1 properly, so that Q1
eliminates the ellipticity of the combined signal and P1
extinguishes its outcome. Slight detunings of Q1 and P1
from these conditions lead to a shift in B . Figure 4 shows
the calculated dependence of B for the MZI used in§4.1 on  Q1 , while keeping  P1   Q1 constant (l= ¼973:392,
M  1:98 rad,C1 ¼ 68 ,M  0:85 rad,7185

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J. S AKAGUCHI et al.

2.0

+1.10

+1.05
1.0
+1.00

+0.95
+5

0

mixing ratio r∆ΦB/π (rad)∆θP1 -∆θQ1 = +2.0 (deg)

0.0
-10

-5

∆θQ1 (deg)Fig. 4. Calculated dependences of MZI-bias (solid) and mixing ratio(dashed) on quarter-wave plate angle.

þ  Q1 , P1  64:5 þ  P1 ).
 P1   Q1 was kept constant as an approximate meansof reducing r shift, and it was shifted from 0 to +2 in order
to slightly compensate for the r shift at around  Q1 ¼ 3
to 6 . Then B shifts linearly with  Q1 , anddB =d Q1 ¼ 7:3  103  (rad/deg). Thus, we could
accurately control B ( 0:004 rad) through precise( 0:5 ) adjustments of wave-plate angles. Here we notethat the actual ﬁber transfer matrix MF slightly driftedwith time. To compensate for this issue, we periodicallyadjusted Q1 and P1 to angles where B became  inthe case in §4.1, and carefully compensated for the angle
drifts.
M  2:76 rad,4.

Q1  131

Results

4.1

Subpulse measurement and calculation with systematic
MZI-bias shifts
In this subsection, we review our ﬁrst observation of
subpulses reported in ref. 8. First, we operated the DISC
at 25-GHz operation frequency, with clock pulse input(+12.3 dBm, 1 ¼ 1560 nm) and cw input (+9 dBm, 2 ¼
1548:5 nm) into the SOA module #1, and observed its output

1000
300
100
30
10
3
1
0.3
0.1 0

(b)

50

100

150

Signal intensity (arb.unit)

Signal intensity (arb.unit)

(a)

1000
300
100
30
10
3
1
0.3
0.1 0

∆ΦB =1.036π

t0

50

150

(d)
∆ΦB =1.058π

50

100

Time (ps)150

Signal intensity (arb.unit)

Signal intensity (arb.unit)

(c)

100

Time (ps)Time (ps)
1000
300
100
30
10
3
1
0.3
0.10

waveform. Figure 5(a) shows a typical cross-correlation
trace of the DISC output that we measured after maximizing
the extinction ratio by adjusting Q1 and P1 . As shown in
Fig. 5(a), the extinction ratio was limited to 25 dB by small
subpulse-like components between the output pulses. Then,
to observe the waveform of the remaining components inmore detail, we dropped the pulse frequency from 25 to12.5 GHz and carefully optimized the wave-plate angles
once again. The average power of the 12.5 GHz pulse train
was +13.5 dBm. At this frequency, the extinction ratio waslimited to about 18 dB by several types of relatively large
subpulse-like components depending on the Q1 and P1
settings [Figs. 5(b)–5(d)].
After that, we calculated the DISC output waveform todemonstrate that the above subpulse-like components actually result from the operating principle modeled in §2.
First, we chose the parameter values for use in thesimulation, taking measured chip gain, saturation energy,
and the recovery time of the SOA into account (Table I).
The saturation energy was changed to 600 fJ from that usedin our previous report8) (1080 fJ). The new value wasobtained from the precise measurement of gain saturationenergy for temporally isolated ultrafast pulses [Fig. 3(b)],while the former value was estimated indirectly from ameasured result of gain saturation for a 25 GHz pulse train
and using numerical simulation. dnr =dn was chosen so thatthe degree of the nonlinear phase shift in the 25 GHz
operation becomes 0:5 [Fig. 3(c)]. The chosen parametervalues are summarized in Tables II and III. Then we
calculated output waveforms using eqs. (2.1)–(2.9). We
could obtain subpulse waveforms quite similar to themeasured data, as shown in Figs. 6(a)–6(d), after choosingB values properly. The calculated relative peak intensities of the subpulses were 24 dB in Fig. 6(a) and 18 dB
in Fig. 6(b). Note that the calculated subpulse intensities
increased by approximately 2 dB than before, and approached the measured values. This was due to the more suitablechoice of SOA parameters as discussed previously. Also,

1000
300
100
30
10
3
1
0.3
0.10

∆ΦB =1.072π

50

100

Time (ps)
7186

150

Fig. 5. Measured cross-correlation traces of the
DISC output with diﬀerent Q1 and P1 settings: (a)with +12.3-dBm, 25-GHz input pulses, (b)–(d) with
+13.5-dBm, 12.5-GHz input pulses [(b)  Q1 ¼
3 ,  P1 ¼ 1 , (c)  Q1 ¼ 6 ,  P1 ¼ 4 ,(d)  Q1 ¼ 8 ,  P1 ¼ 6 ]. Calculated phasebiases are shown in each graph.

Jpn. J. Appl. Phys., Vol. 47, No. 9 (2008)

J. S AKAGUCHI et al.

Table II. Parameters used in the DISC-gate simulation.
Fig. 6(a) Figs. 6(b)–6(d)§4.2

Pulse repetition frequency f (GHz)

25

12.5

Input pulse width (FWHM) TFWHM (ps)

3.8

3.8

2.0

1129
5

30
0.3

Input pulse energy (into chip) Epulse (fJ) 429
5Input cw power (into chip) Pcw (mW)

10.5 (50)

Delay time in the MZI t (ps)

5.0

5.0

5.0

Correlator probe width Tprobe (ps)

2.2

2.2

2.0

Frequency of cw light cw (THz)

193.7

193.7

193.7

Frequency of pulsed light pulse (THz)

192.1

192.1

192.8

Table III. SOA fundamental parameters used in the calculation, andderived quantities.
§4.1

§4.2

Injection current IOP (mA)

250

400  aActive region length(eﬀective) Leff (mm)

700

1100

Active region volume V (cm3 )1:4  1010

5:2  1011Conﬁnement factor 

0.2

0.2

SOA carrier lifetime c (ps)

200

35=a

SOA diﬀerential gain dg=dn (cm2 )Carrier-conversion eﬃciency T

2:17  1015
0.079

6:36  1016
0.34

refractive index change dnr =dn (cm3 )1:87  1019

1:4  1020

Maximum-available carrier(cm3 )
density nmaxc

1:76  1017

5:72  1017

SOA small-signal gain G0 (dB)

23.4

34.8

sat
(fJ)
Saturation energy for pulse Epulse

600

473

þ6:0

þ2:3

Phase shift at complete carrier
depletion max

4.2

B values in Figs. 5(b), 5(c), 6(b), and 6(c) showed
improved matchings.
The behavior of relative intensities of subpulse-likecomponents as functions of the phase bias B is shown50

Signal intensity (arb.unit)

150

Time (ps)

(c)
1000
300
100
30
10
3
1
0.3
0.1

100

0

50

100

Time (ps)

1000
300
100
30
10
3
1
0.3
0.10

∆ΦB =1.030π

50

150

1000
300
100
30
10
3
1
0.3
0.1

100

150

Time (ps)(d)∆ΦB =1.060π

Trade-oﬀ regarding subpulse generation andpattern-induced intensity noise
The subpulse intensity of the DISC output discussed in§4.1 could be suppressed by tuning the MZI bias down to20 dB, which is negligible for practical applications.
Nevertheless, we have regarded subpulse generation as amajor issue in the case of random-data operation, because of
the trade-oﬀ relationship between subpulse generation andpattern-induced intensity noise. If the input signal is not acontinuous clock but has a random pattern, the instantaneous
carrier density in the SOA varies upon each signal injection
depending on the preceding input-signal pattern. Then theintensities of the output signals become pattern-dependent.
This eﬀect can be reduced by accelerating the carrier recovery
with current injection or assist light injection. Our subpulse
model indicates, however, that a subpulse becomes large as
we increase carrier recovery rate. In this subsection, we will
discuss the measured and calculated results for this eﬀect.

(b)
Signal intensity (arb.unit)∆ΦB =1.075π

Signal intensity (arb.unit)

Signal intensity (arb.unit)

(a)
1000
300
100
30
10
3
1
0.3
0.1 0

in Fig. 7. The relative intensity was taken at three time
positions (t ¼ t0 þ 15 ps, t0 þ 40 ps, and t0 þ 65 ps, wheret0 is the primary pulse’s position). The calculated behavior
was quite similar to the measured data, taking the 27-dB
dynamic range of the cross-correlator into account. The
mismatch in the intensity was small, 1 to 2 dB for t ¼
t0 þ 15 ps series, at B ¼ 1:00 to 1:08. We are awarethat the phase-bias dependence and extinction ratios are
dominated by many parameters, and future improvement in
the gate model may solve the remaining small mismatch.
Regarding subpulse intensity, we consider that the gatemodel in this paper provides the most reliable predictions
currently available.
Thus, as shown in Figs. 5–7, we observed a good match
between the measured and calculated waveforms and thephase-bias dependence. Therefore, we presume that our
subpulse generation model has been experimentally veriﬁed
for a particular recovery rate, and that we can predict
subpulse intensity with 1 to 2 dB accuracy using this model.

∆ΦB =1.100π

0

50

100

Time (ps)
7187

150

Fig. 6. Calculated cross-correlation traces of the
DISC output: (a) with 25-GHz input pulses,(b)–(d) with 12.5-GHz pulses [(b) B ¼ 1:030,(c) B ¼ 1:060, (d) B ¼ 1:100]. Other
parameter values are summarized in Tables II andIII.

J. S AKAGUCHI et al.

(a)Relative intensity (dB)

Relative intensity (dB)

Jpn. J. Appl. Phys., Vol. 47, No. 9 (2008)

0
-10
-20
-30
-40
1.00

1.04

1.08

1.12

∆ΦB /π0Fig. 7. Relative intensities of the subpulse-like components in 12.5-GHz DISC output: (a) from experimental results; (b) from calculations. These wereobtained at three time positions: t ¼ t0 þ 15 ps(solid), t0 þ 40 ps (dashed), and t0 þ 65 ps (dotted).

-10
-20
-30
-40
1.00

1.04

1.08

1.12

∆ΦB /π(b)
400 mA + assist light (τeff= 11 ps)
I OP = 400 mA (τc= 36 ps)
300 mA (τc= 40 ps)-5200 mA (τc= 75 ps)
150 mA (τc= 117 ps)
100 mA (τc= 281 ps)

-10
-200

0

+200

+400

10
400 mA with assist

1
400 mA
200 mA

0.1

150 mA

0.01

100 mA

0.001

0Time (ps)

+50

+100

Time (ps)

(a)

(b)

40

τC = 14 ps

30

Subpulse intensity (dB)

Signal intensity (arb. unit)

Fig. 8. DISC output waveforms for several carrier
recovery rates. (a) XGM proﬁles of SOA #2 forseveral operation currents, indicating the recovery
acceleration. The cw-probe intensity and pulse
energy injected into the chip were set at 25 dBm
and 10 fJ, respectively. Note that each plot istranslated intentionally in vertical direction. (b)10.5-GHz DISC output waveforms. B was set tobe 1:0.

20
10
0
8
6
4
2
0

τC = 70 ps

0+20Time (ps)

+12

-10

+9
-15
+6
-20
-25

-20

+15

-5

+40

+3

1

5 10
50 100Carrier recovery rate (GHz)0

Pattern-induced noise (dB)0Signal intensity (arb.unit)ln (XGM output) (arb.unit)

(a)

(b)

Fig. 9. Trade-oﬀ between pattern-dependent intensity noise and subpulse noise. (a) Calculated eye diagrams of the DISC output for
50 Gbps pseudo-random signal, for two carrier recovery rates. The cross-correlation process was omitted for simplicity. Parametervalues are summarized in Tables II and III. (b) Measured (solid) and calculated (dashed) subpulse intensities against the carrier
recovery rate 1=c at 10.5 GHz, and calculated pattern-induced noise for the 50 Gbps signal (dotted).

We systematically measured subpulse waveforms forseveral carrier lifetimes, using the customized SOA chip #2,
as explained in §3.1. Figure 8(a) shows the gain-recovery
proﬁles of the SOA for several injection currents, measured
with the cross-correlator.13) The recovery time c was
reduced from 280 to 36 ps as we increased the injection
current IOP from 100 to 400 mA, and it was approximately
inversely proportional to IOP above 150 mA. The eﬀective
recovery time eff was further shortened to 11 ps after we
injected 80 mW assist light with a nearly transparent
wavelength (1480 nm) into the chip. Using this SOA, wemeasured the DISC output waveforms on each IOP . The
operation frequency was 10.5 GHz. The input pulse width,
wavelength, and energy into the chip were 2 ps, 1555 nm and
30 fJ, respectively. The cw light wavelength and power into
the chip were 1548.5 nm and 5 dBm, respectively. The
delay time of the MZI was set to 5 ps. The MZI phase bias
was ﬁxed at 1:0 throughout the measurement, since theoptimum phase bias depends largely on c (eff ). The
measured waveforms are shown in Fig. 8(b). We found thatthe relative intensity of the subpulse increased up to 10 dB,

as we increased the carrier recovery rate 1=c [Fig. 9(b)].
The measured subpulse intensity for c ¼ 280 ps seems lessaccurate owing to the low output power and S/N ratio.
Meanwhile, we could predict this result qualitatively
using our gate model. For simplicity, we assumed that c wasinversely proportional to IOP , and that other fundamental
parameters did not change with IOP . The adopted values are
summarized in Tables II and III. The values in Table III
were determined in view of measured characteristics of SOA#2 at IOP ¼ 400 mA [Figs. 3(a), 3(b), 3(d), and 8(a)]. Thenthe measured and calculated subpulse intensities agreed
quite well for most 1=c values [(Fig. 9(b)]. We regarded
this matching as convincing evidence that our model isapplicable in a wide 1=c range. Some discrepancy atc ¼ 11 ps probably originates from the diﬀerence between
the acceleration mechanism with current injection and thatwith assist-light injection. This result clearly indicates that
we can suppress subpulse generation as long as we keep thecarrier recovery rate small.
As we mentioned above, this method of subpulse
suppression leads to an increase in pattern-induced intensity

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Jpn. J. Appl. Phys., Vol. 47, No. 9 (2008)

J. S AKAGUCHI et al.

noise. We calculated the DISC output waveforms for a
50 Gbps input pulse train with a pseudorandom bit sequence(pattern length = 215  1), and calculated the pattern-induced noise from the intensity ratio of the largest andsmallest signals in the output pulse train [Fig. 9(a)]. The
values of the other parameters remained unchanged from theformer calculations. The dotted line in Fig. 9(b) shows thedependence of the pattern-induced noise on recovery rate.
Evidently, this pattern-induced noise can be suppressed byincreasing recovery rate, which leads to the unwanted
increase in subpulse intensity.
In this way, our model shows the trade-oﬀ between
subpulse generation and the pattern-induced noise. Although
what we have shown is only a particular example, we
consider that this trade-oﬀ relation arises fairly universally.
We will encounter subpulses as large as 7 dB, in thepresent case for example, as we suppress the pattern-induced
noise down to 1 dB. The situation may become even worse
depending on other operating conditions such as signal bit
rate, signal duty ratio, and control pulse energy. Therefore,
we consider that a new gating scheme for resolving this issue
is necessary. Regarding the past wavelength conversions at1603) and 320 GHz,5) we speculate that additional phenomena such as nonlinear polarization rotation and carrier
heating in the SOA contributed to unexpected suppression of
subpulse generation.6) Also, employing a blue-shifted opticalﬁlter in the latter case is considered advantageous in
reducing pattern-induced noise16) at the cost of output signal
power and system simplicity. We consider that subpulse
generation should be one of the major design features for
DISC-type wavelength converters and should be evaluatedusing the current model or an expanded model in the near
future.
5.

Conclusions

We have studied subpulse generation in the wavelengthconverted signal from a DISC gate operated at 10 to 25 GHz,
both theoretically and experimentally. We described our
subpulse generation model and experimental method in
detail, and reviewed our ﬁrst observations of subpulse
generation described in our previous letter. As good
matching as 1 to 2 dB was obtained between the measured
and calculated subpulse intensities. The dependence of
subpulse waveforms on the MZI phase bias was well
explained at around B ¼ 1:00 to 1:08.
In addition to these results, we demonstrated that ourmodel is applicable in a wide range of SOA carrier recovery
rates. The impact of carrier-recovery acceleration (fromc ¼ 280 ps to eff ¼ 11 ps) on subpulse waveforms was
systematically studied using a DISC with a customized SOA
chip. We obtained good agreement between the measured
and calculated subpulse intensities for the majority of therecovery rate range.

Using our subpulse model, we discussed the trade-oﬀ
between subpulse generation and pattern-induced intensity
noise. Our calculations indicated that signiﬁcant subpulses
may emerge when we suppress pattern-induced intensity
noise, which may lead to diﬃculty in the practical highspeed operation of the DISC. This result suggests that part of
the DISC structure should be improved to overcome thistrade-oﬀ. We are in the process of solving this problem
using new gating schemes, for example, using an expanded
DISC including an optical spectral synthesizer.17) We
believe that success in such modeling will be valuable not
only for the practical applications of the DISC but also forthe detailed understanding of other kinds of all-optical gatesusing SOAs, delayed interferometers, and so on.
Acknowledgements
This research work was supported by research project
grant #B15360027, ‘‘Optical logic gates in the sub-terahertz
frequency region’’, of the Ministry of Education, Culture,
Sports, Science, and Technology (MEXT) and the research
project grant, ‘‘Ultra-low-power and ultrafast optical memory/switching device’’, of the New Energy and Industrial
Technology Development Organization (NEDO), and the
21st-Century University’s Center of Excellence (COE)program, ‘‘Innovation in coherent optical science’’, of the
University of Electro-Communications, Japan.
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