Frequency-dependent electric dc power
consumption model including quantumconversion efficiencies in ultrafast all-opticalsemiconductor gates around 160 Gb/s
Jun Sakaguchi1, Ferran Salleras1, Kohsuke Nishimura2 and Yoshiyasu Ueno1
1
University of Electro-Communications, 1-5-1 Chohugaoka, Chohu, Tokyo, Japan
KDDI R&D Laboratories Inc., 2-1-15 Ohara, Kamifukuoka-shi, Saitama 356-8502, Japansakaguchi@ultrafast.ee.uec.ac.jp

2

Abstract: Based on nine up-to-date types of semiconductor-opticalamplifier (SOA) samples, we devised a power-consumption model of SOAbased all-optical gates as a tool to develop faster and more efficient OTDM
systems for bitrates from 10 to 160 Gb/s and those over 160 Gb/s. The
conventional effect of a continuous wave (cw) holding beam was includedin the model. Furthermore, in this work we defined three step-wise quantum
conversion efficiencies η1, η2, and η3 from current-injected carriers throughphotons. The dependence of each of the three efficiencies on the SOAstructure was studied. The total efficiency ηT observed for the nine SOAs
ranged widely from 0.07 to 0.46. The validity of the power-consumption
model was verified by systematically measuring the effective carrier
recovery rate. According to our model, the power consumption of the best
existing SOA-based gate for 160-Gb/s signals is 750 mW, and this increases
at a rate approximately proportional to (bitrate)2, and decreases
proportionally to (1/ηT)2.
©2007 Optical Society of America
OCIS codes: (060.0060) Fiber optics and optical communications; (060.1155) All-optical
networks; (120.5060) Phase modulation; (190.5970) Semiconductor nonlinear optics including
MQW; (190.7110) Ultrafast nonlinear optics; (250.5980) Semiconductor optical amplifiers;(320.7080) Ultrafast devices; (320.7160) Ultrafast technology.

References and links
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#87129 - $15.00 USD(C) 2007 OSA

Received 31 Aug 2007; revised 23 Oct 2007; accepted 24 Oct 2007; published 26 Oct 2007

29 October 2007 / Vol. 15, No. 22 / OPTICS EXPRESS 14887

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1. Introduction
All-optical signal-processing gates based on the nonlinearities of semiconductor opticalamplifiers (SOAs) are promising devices for future OTDM networks because they are capableof ultrafast signal processing and low power consumption [1,2]. All-optical demultiplexing,
3R regeneration, and wavelength conversion based on cross-phase modulation (XPM) in
SOAs have been achieved for operating frequencies exceeding 100 GHz [3-5], and 320- to
640-GHz operation of all-optical SOA gates using ultrafast chirp dynamics has recently been
demonstrated [6-8]. These devices typically consumed 0.4 to 1.0 W electrical power, while
the latest electrical demultiplexer consumes 5.5 W in 100-GHz operation [9]. As thecapabilities of SOAs for ultrafast gating have become clear, the lower limit of electric power
consumption and its origin have become important design issues. A practical engineeringmodel that describes dc power consumption has, however, not yet been reported to the best of
the authors' knowledge. Because such a model has not been available, it has been very
difficult for system researchers to design the total power consumption of the various largescale 160-Gb/s OTDM systems now under research.
The electrical power consumption of an SOA in an all-optical gate is dominated by two
factors: the amount of optical-pulse-induced modulation as the optical phase shift in the caseof XPM, and the recovery time of the depleted carrier density after optical modulation. It haslong been recognized that the so-called optical holding beam effectively accelerates thecarrier's recovery time [10,11], while the holding beam itself consumes a significant part ofthe injected carriers via the stimulated recombination process and consequently reduces theamount of optical phase shift in the co-propagating optical signal component. It has also been
qualitatively well known that to accelerate the recovery time while maintaining the amount of
optical phase shift in the 0.3-to-1.0 π range, the carrier injection rate (i.e., the injection current
density) must be increased, and this increases in the dc power consumption.
To discuss the power consumption, a detailed understanding of the quantum conversion
efficiency from the number of injected carriers to the number of optical-pulse-induced#87129 - $15.00 USD(C) 2007 OSA

Received 31 Aug 2007; revised 23 Oct 2007; accepted 24 Oct 2007; published 26 Oct 2007

29 October 2007 / Vol. 15, No. 22 / OPTICS EXPRESS 14888

stimulated recombinations in the SOA is needed. It is reasonably expected that an SOA withlow conversion efficiency requires a large current injection for the gating operation.
Furthermore, an increase in the injection current density might slightly degrade the quantum
conversion efficiency. This quantum efficiency was not taken into account in most previous
studies. Some researchers discussed SOA gain within continuous wave (cw) regime andcarrier recovery using one conversion efficiency parameter [12,13], but no one has studied
how conversion efficiency is influenced by the SOA properties. Furthermore, no study of theconversion efficiency in ultrafast optical gating has been reported, even though this has turned
out to be significantly lower than that for cw-light amplification.
In this paper, we explain our development of a practical engineering model thatscientifically describes the dc power consumption of an SOA-based all-optical gate as afunction of its working frequency up to 160 Gb/s. The validity of this model is verified with
one series of measured power consumption values. A model of the holding beam's
contribution, which is a part of our power-consumption model, is verified through a series ofmeasured results. In these verification processes, measured parameter values are put into mostof the independent model parameters, such as several types of quantum efficiencies. The
observed dependence of the measured quantum efficiencies on the SOA structural parameters
are also discussed.
2. Our model of carrier conversion efficiency
We define three different carrier conversion efficiencies, and use them to evaluate different
carrier losses in the SOA. Figure 1 shows the loss model for injected carriers.

η1(a) Injection current Iop(Current at transparency, I0 )η2(b) Current over transparent condition, Iop-I0

η3(c) carriers which contribute to cw light amplification

ASE emission, carrier overflow, Auger recombination(spectral hole burning, increase in ASE, etc. )(d) carriers which contribute to pulse light amplification
Fig. 1. Loss model of injected carriers. η1 to η3 stand for conversion efficiencies.

2.1 Definition of carrier conversion efficiency
We start from the total carrier number N and carrier density n in the active region. When n is
below the population inversion threshold n0, the SOA has a negative gain and shows no bandfilling nonlinearity. Thus, the injection current Iop should be larger than the transparent current
I0 (where n=n0) and the number of carriers available for the gating should be reduced to theexcess carrier number Nex, where Nex=N-N0. For this process, we define the first conversion
efficiency η1 as η1=Nex/N.
Next, we introduce the carrier number Ncw, which is the maximum number of stored
carriers available for amplification of saturating cw light. This can also be understood as thenumber of carriers available for optical gating at the low frequency limit. Ncw is supposed tobe smaller than Nex defined above, because of the effects of ASE, Auger recombination,
carrier overflow, intervalence band absorption, and free carrier absorption. The second
conversion efficiency η2 is defined as η2=Ncw/Nex. In this paper, we will not discuss theindividual loss contributions, because of the experimental difficulty of determining these.
Finally, we introduce the carrier number Npulse, which is the maximum number of stored
carriers available for amplification of ultrafast optical pulses. Npulse is supposed to be smaller#87129 - $15.00 USD(C) 2007 OSA

Received 31 Aug 2007; revised 23 Oct 2007; accepted 24 Oct 2007; published 26 Oct 2007

29 October 2007 / Vol. 15, No. 22 / OPTICS EXPRESS 14889

than Ncw, and the third efficiency η3 is defined as η3=Npulse/Ncw. Its potential causes arespectral hole burning and carrier heating, or increases in ASE recombination caused by thehigher average-carrier density compared with the cw-light amplification case, and so on. Notethat this difference in SOA reactions to cw light and ultrafast pulses only appears well above
the small signal regime, where practical gating operation is carried out. We consider Npulse tohave the largest influence on ultrafast gating performance. Therefore, we define the total
carrier-conversion efficiency ηT for ultrafast gating as ηT=Npulse/N=η1η2η3. If the dominantfactors of each efficiency can be revealed, we will be able to maximize the total efficiency by
improving each contribution separately.
2.2 Characterization of the conversion efficiency
We suppose that the carrier numbers and conversion efficiencies defined above can becharacterized from fundamental SOA parameters as follows. When the carrier loss rate is 1/τC
and the total carrier number is N, the carrier loss N/τC should balance the injection flow Iop/q(q: elemental charge). Thus, the total carrier number N can be estimated asI
N = OP τ C .
(2.1)
qη1 and the excess carrier number are supposed to be given by the transparency current I0 as

η1 =N ex I OP − I 0
=
.
N
I OP

(2.2)

Here, we should mention that N and Nex obtained from these relations contain certain
underestimations when the dependence of the carrier loss rate on the injection current is large.
We will discuss it in Section 3.
Ncw is supposed to be obtained from the gain-saturation measurement of the SOA for cw
light. As the intensity of the input light increases, the SOA chip gain G decreases from thesmall signal gain (SSG) G0. For an SOA with saturation power Psatcw, G is suppressed by 3 dB
when the output power reaches P3dB= Psatcw ·ln 2. Taking the conventional discussion [14,15]
regarding the gain saturation into account, we relate Ncw to Psatcw, G0 and the carrier lifetime
τC as
N
P cwτ
η2 = cw ,(2.3)
N cw = sat C ln G0cw .
N exhνSimilarly, Npulse is supposed to be obtained from the gain-saturation measurement of the
SOA for ultrafast pulses. If the injected pulse train has a much longer interval than τC, the net
gain of the pulse will be as follows:

G pulse (Eout ) =

Eout
1
.
pulse
pulse
E sat ln exp Eout / E sat + G0 − 1 − ln G0

{ (

)

}

(2.4)

The pulse saturation energy Esatpulse can be obtained from the 2.35-dB suppression point, andwe relate it to Npulse as follows:

η3 =#87129 - $15.00 USD(C) 2007 OSA

N pulseN cw,

N pulse =

pulse
E sat
ln G0pulse .
hν

(2.5)

Received 31 Aug 2007; revised 23 Oct 2007; accepted 24 Oct 2007; published 26 Oct 2007

29 October 2007 / Vol. 15, No. 22 / OPTICS EXPRESS 14890

Table 1. List of SOA samples and their structure

Type

Active region
length,Leff ( μm)

A#1
A#2
A#3
A#4

Bulk

1000
700
300
700

B#1
B#2
B#3

MQW

1100
700
500

C#1

Bulk

D#1

Bulk

SampleActive region
width,wA (μm)Active region
thickness,dA (μm)Confinement
factor,Γ

2

0.1

0.1~0.2

1.25

0.038 (*2)

~0.2

700

1.2

0.2

0.3~0.4

1500

0.6

0.35

0.5

(*1)
(*1)
(*1)

(*1) Effective length, considering 50 % contribution from taper regions

ASE power from chip (dBm/nm)(*2) Sum of well thickness

0
-20
-40
-60
-80

A#1
A#2
A#3
A#4

B#1
B#2
B#3

-100

C#1, 150 mA
D#1

1.2 1.3 1.4 1.5 1.6 1.2 1.3 1.4 1.5 1.6 1.2 1.3 1.4 1.5 1.6 1.7

Wavelength ( μm)
Fig. 2. Measured ASE spectra of SOA samples at IOP = 200 mA.

Fig. 3. Experimental setup for SOA chip characterization. VOA: variable optical attenuator,
Pol: polarizer, PC: polarization controller, PBS: polarizing beam splitter, BPF: band-pass filter,
MLFL: mode-locked fiber laser#87129 - $15.00 USD(C) 2007 OSA

Received 31 Aug 2007; revised 23 Oct 2007; accepted 24 Oct 2007; published 26 Oct 2007

29 October 2007 / Vol. 15, No. 22 / OPTICS EXPRESS 14891

The intrinsic difference between Ncw and Npulse seems to be overlooked in the conventional
gain-saturation theory. In the new rate equation model (see Section 4), both cw and pulse
saturation are modeled as independent characteristics.
3. Conversion efficiency measurement and results

To evaluate the carrier conversion efficiency of actual SOAs, we measured the fundamental
parameters of several custom-designed SOA chips and commercial modules from different
manufacturers (A to D). Attributes of the SOA samples and examples of ASE spectra areshown in Table 1 and Fig. 2, respectively. For series A and B, we prepared chips withdifferent (effective) active-region lengths Leff. For each custom-designed chip, except for the
shortest one (A#3), more than two wires per electrode were bonded to enable injection
currents over 500 mA.
The typical setup for SOA-chip characterization is shown in Fig. 3. We coupled lensed
fibers to the input and output facets of the chip using precision stages, and obtained 2- to 5-dB
coupling losses for each facet. Temperature was stabilized at close to 25°C. The ASE
intensities from both facets were continuously monitored by power meters, and throughcareful adjustment of the couplings fluctuations were kept below 0.2 dB. First, we measured
the cw-gain by using a DFB-LD (λ2= 1548 nm) and an optical spectrum analyzer. Figure 4
plots the measured SSG of each sample against IOP. The transparent currents I0 were obtained
from these results. Figure 5(a) shows typical gain-saturation profiles. We obtained Psatcw as afunction of IOP from the 3-dB suppression points. As can be seen in Fig. 6(a), Psatcw increased

Chip Gain (dB)+40
Leff (μm)
A#1, 1000
A#2. 700
A#3, 300
A#4, 700

+30
+20
+10

B#1, 1100
B#2, 700
B#3, 500

0
-10

20

100

500

20

100

500

C#1 700
D#1 1500

20

100

500

Nominal injection current, I op (mA)
Fig. 4. Measured small-signal gains of SOA samples versus current. Sample details are
given in Table 1. Gains were measured with cw light, λ2=1548 nm. Input cw power into
each chip was kept under –30 dBm.

(b)

+20

+10

0
-30

B#3, Leff = 500μm
Iop
200 mA
150 mA
100 mA
80 mA-20 -100+10 +20

Output cw power from chip (dBm)

(c)
+30

+40

+20

+10

0
1

B#3, Leff = 500μm
Iop
200 mA
150 mA
100 mA
80 mA

10Chip Gain (dB)+30

Chip Gain for pulse (dB)

Chip Gain for cw light (dB)(a)

100 1000 10000

Output pulse energy from chip (fJ)Iop
400 mA
300 mA
200 mA
150 mA+30+20

100 mAB#1 sample

+10
0
-200

0

+200

+400

+600

Time (ps)Fig. 5. Typical SOA chip characteristics (a) Gain-saturation profiles for cw light. (b) Gainsaturation profiles for ultrafast pulses (2-ps width, 0.65-GHz repetition). The dashed linesin (b) show the theoretical fit using Eq. (2.4). (c) Typical XGM profiles measured with across correlator. The cw-probe intensity and pulse energy into the chip were set to –25
dBm and 10 fJ, respectively.

#87129 - $15.00 USD(C) 2007 OSA

Received 31 Aug 2007; revised 23 Oct 2007; accepted 24 Oct 2007; published 26 Oct 2007

29 October 2007 / Vol. 15, No. 22 / OPTICS EXPRESS 14892

(c)

100.0
50.0

L eff (μm)
A#1, 1000
A#2. 700
A#3, 300
A#4, 700

Leff (μm)
B#1, 1100
B#2, 700
B#3, 500

C#1 700
D#1 1500

10.0
5.0
1.0

20

100

500

20

100

500

20

100

500

Nominal injection current, Iop (mA)

3000.01000.0300.0
Leff (μm)
A#1, 1000
A#2. 700
A#3, 300
A#4, 700

100.0
30.0

20

100

500

Leff (μm)
B#1, 1100
B#2, 700
B#3, 500

20

100

500

C#1 700
D#1 1500

20

100

500

Nominal injection current, Iop (mA)
Carrier recovery rate, 1/τC (GHz)

Saturation energy, Esat

pulse

(b)

(fJ) Saturation power, P(a)cw
sat (mW)

almost linearly with IOP without convergence. The SOA gains for ultrafast pulses were
measured for each sample. To obtain ultrafast optical pulses with lower frequency than 1/τC,
we used a mode-locked fiber laser (MLFL: Pritel Inc., UOC-3) with an external LiNbO3
modulator. Pulses with a 2-ps width, λ1=1555 nm, and 10.5-GHz frequency from the MLFL
were modulated down to a 0.65-GHz pulse train. We monitored the auto-correlation trace ofthe pulse train so that we could keep its extinction ratio above 20 dB. Typical gain-saturation
profiles are shown in Fig. 5(b). We see that for each IOP, the SSGs for the cw input are almost
the same as for ultrafast pulses. We fitted the measured profiles to Eq. (2.4), and they showed
good agreement up to Eout ~ 3000 fJ. The difference at Eout > 3000 fJ was probably caused by
the slight residual of the 10.5-GHz pulses. From the fit results, we obtained Esatpulse of each
SOA as a function of IOP (Fig. 6(b)). In contrast to the case of Psatcw, they converged as IOP
increased.

50
A#1, 1000
A#2. 700
A#3, 300
A#4, 700

Leff (μm)
B#1, 1100
B#2, 700
B#3, 500

10
5
C#1 700
D#1 1500

1

20

100
500
20
100
500
Nominal injection current, Iop (mA)

20

100

500

Fig. 6. Measured SOA parameters used for evaluation of the conversion efficiencies (a)Saturation power of SOA chips versus current for cw light. (b) Saturation energy for ultrafast
pulses (2-ps width, 0.65 GHz). (c) Carrier-recovery rate 1/τC.

#87129 - $15.00 USD(C) 2007 OSA

Received 31 Aug 2007; revised 23 Oct 2007; accepted 24 Oct 2007; published 26 Oct 2007

29 October 2007 / Vol. 15, No. 22 / OPTICS EXPRESS 14893

The carrier recovery rates 1/τC of each SOA at several injection currents were determinedfrom XGM measurements using a cross-correlator (Femtochrome Research Inc., FR-103XR)
and mode-locked pulses modulated down to 1.3 GHz. External variable delays and an
elaborate calibration process were used to expand the scan range to 600 ps. The intensity ofthe probe cw light was typically set to -25 dBm to suppress the holding beam effect. Pulse
energies into each SOA chip were adjusted within 10~500 fJ so that no gain modulation due
to residual 10.5-GHz pulses appeared. Figure 5(c) shows examples of measured XGM
waveforms. We can see two recovery processes after gain depletion. From the slower process,we obtained 1/τC (Fig. 6(c)). In one exception, we assumed τC~100 ps for sample A#3 without
fitting, since its small gain seriously degraded the S/N ratio of the output signal and prevented
a precise determination of τC. From Fig. 6(c), we see that the SOA samples can be categorized
into two types: the recovery rates of B#1 and D#1 increased rapidly to 30 GHz with IOP, while
those of the others increased slowly around 5 to10 GHz.
Using the measured fundamental parameters, we calculated the conversion efficiencies(Fig. 7). The efficiency values for each sample at IOP = 200 mA were η1 = 0.68 to 0.87, η2 =0.17 to 1.30, η3 = 0.29 to 0.53, and ηT = 0.07 to 0.40. These values indicate that total
efficiency ηT strongly depends on the SOA structure. This dependence resulted mostly from
η2. The B-series MQW samples had a much larger η2 than the other bulk samples. Among the
A-series, the longer chips had a larger η2, whereas the B-series showed the opposite η2dependence on Leff. The reason for this difference is unclear. η1 depends on I0, and decreases
with Leff since I0 is proportional to Leff. η3 was significantly smaller than unity. The results in
Fig. 7(c) indicate that η3 decreases as IOP goes above the optimum condition, and that longer
SOAs tend to have larger η3 values at large IOP. The total efficiency ηT of longer SOAs also
tends to be higher at large IOP. Sample B#1 will be the most economical device for IOP ~ 400mA (ηT ~0.34), while B#3 has the best efficiency for IOP ~ 150 mA (ηT ~0.46).
There appears to be a problem with the definition of Nex using Eqs. (2.1) and (2.2), since
the calculated η2 sometimes exceeds unity. This underestimation of Nex will be reduced if we
use another definition asI OP

τ C (I )I0q

N ex = ∫

dI ,

(3.1)

taking into acount that the carrier lifetime τC, which is related to the differential carrier
injection rate, decreases with the injection current. Determination of Nex using Eq. (3.1) isdifficult, however, because it requires precise measurement of τC at small IOP. Then we thinkusing Eqs. (2.1) and (2.2) is not a concern and appropriate since the idea is to get a roughunderstanding of the SOA-characteristics.
Thus, our interpretation of the dependence of the efficiencies on the SOA structure can besummarized as follows. First, the MQW structure is advantageous for increasing η2. A longer
active region decreases η1, increases or decreases η2, and increases both η3 and total
efficiency at large IOP. We could not obtain conclusive results for width, thickness orconfinement factor, though some of these factors seemed to significantly affect efficiencies.
Although these results are useful, we will need to perform more systematic characterizations
before we can completely understand the SOA-structure effects.
4. Estimation of SOA electrical power consumption of all-optical gating

Here we propose a model for determining the electrical power requirements of SOAs used inultrafast all-optical gates. First, we discuss the carrier dynamics of SOAs. Then, we estimate
the power consumption from the calculated carrier dynamics. Finally, we compare thecalculated power consumption with measured results.
4.1 Rate equation model including conversion efficiencies#87129 - $15.00 USD(C) 2007 OSA

Received 31 Aug 2007; revised 23 Oct 2007; accepted 24 Oct 2007; published 26 Oct 2007

29 October 2007 / Vol. 15, No. 22 / OPTICS EXPRESS 14894

(a)η1=(Iop-I0)/Iop

1
0.8
0.6
0.4

Leff (μm)
A#1, 1000
A#2. 700
A#3, 300
A#4, 700

0.2
0

(b)

20

η2=Ncw /Nex

20

100

500

20

100

500

Leff (μm)
A#1, 1000
A#2. 700
A#3, 300
A#4, 700

1
0.5
0Leff (μm)
B#1, 1100
B#2, 700
B#3, 500

20

100

500

20

100

500

C#1 700
D#1 1500

20

100

500

Nominal injection current, Iop (mA)(c)
η3=Npulse /Ncw

500

C#1 700
D#1 1500

Nominal injection current, Iop (mA)

1.5

1
Leff (μm)
B#1, 1100
B#2, 700
B#3, 500

Leff (μm)
A#1, 1000
A#2. 700
A#3, 300
A#4, 700

0.8
0.6

C#1 700
D#1 1500

0.4
0.2
0

20

(d)
Efficiency, ηT = η 1×η 2×η 3

100

Leff (μm)
B#1, 1100
B#2, 700
B#3, 500

100

500

20

100

500

20

100

500

Nominal injection current, Iop (mA)
0.6

B#1, 1100
B#2, 700
B#3, 500

Leff (μm)
A#1, 1000
A#2. 700
A#3, 300
A#4, 700

0.5
0.4

C#1 700
D#1 1500

0.3
0.2
0.1
0

20

100

500

20

100

500

20

100

500

Nominal injection current, Iop (mA)
Fig. 7. Measured dependence of SOA sample conversion efficiency on IOP(a): η1, (b): η2, (c): η3, according to Eqs. (2.2) to (2.5), and (d): total efficiency

ηT=η1×η2×η3.

#87129 - $15.00 USD(C) 2007 OSA

Received 31 Aug 2007; revised 23 Oct 2007; accepted 24 Oct 2007; published 26 Oct 2007

29 October 2007 / Vol. 15, No. 22 / OPTICS EXPRESS 14895

In our preceding analyses, we used a single rate equation to calculate the carrier-density
modulation in one SOA module [2,16]. This is a simple but powerful tool to explain thegating characteristics in the time domain [17]. To account for the effect of the three different
conversion efficiencies, we expanded the rate equation to the following form:
dn pulse
dt

=

I op
qV

η1η 2η 3 −n pulse

τC

⎧
⎛
⎞ ⎫ P
dg cw
n pulse ⎟⎟ − 1⎬ cw− η 3 ⎨exp ⎜⎜ Γ Leffdn⎝
⎠ ⎭ ωV⎩pulse⎧ ⎛⎞ ⎫ Ppulsedgn pulse ⎟⎟ − 1⎬− ⎨exp ⎜⎜ ΓLeffdn⎝⎠ ⎭ ωV
⎩(4.1)(npulse=Npulse/V: carrier density available for ultrafast gating, Ppulse and PCW: input lightintensities, Leff and V=Leff wA dA: active region effective length and volume, Γ: confinement
factor, dg/dn: differential gain). Note that η3 is multiplied by the cw-light term, in view of thedifference between npulse and ncw (the carrier density available for cw light). Both cw gain andpulse gain were supposed to be determined by npulse, since we did not observe much difference
between them unless gain saturation occurred (Fig. 5). We also supposed there are reserved
carriers (nreserve=ncw - npulse) which do not explicitly affect gain, and (1-η3) of the photons areconverted from reserved carriers through intraband interactions in the case of cw-light
amplification. This rate-equation model can explain the experimental results regarding thegain saturation for ultrafast pulses quite well, and those regarding the cw-gain saturation up to
3-dB suppression points (Fig. 8(a)). For stronger cw light, other theories may provide better
predictions of the gain suppression [18].
The rate equation can be used to calculate the optical carrier modulation and nonlinear
phase shift. Injection of Ppulse causes carrier recombination Δnpulse, and the nonlinear phaseshift is given byΔΦ = k 0 dn r dn Γ Leff Δn pulse(4.2)(k0: wave number in vacuum, nr: refractive index).
To verify the model, we simulated the SOA characteristics under holding-beam injection.
We used the measured values of η and τC at each IOP, and extracted dgcw/dn and dgpulse/dn
from the corresponding SSG values. Figure 8(b) shows measured and calculated results forthe effective carrier recovery rate of sample B#3 accelerated by the holding-beam. Figure 8(c)shows measured and calculated results for pulse-gain saturation with and without a holding
beam. We see that both results approximately agree with each other.
Table 2. Estimated refractive index change of each sample, and related parameters.

SampleRefractive index change, Carrier density for gating, Differential gain,
Confinement
dnr/dnpulse (10-20 cm3)
npulse (1018 cm-3)
dgcw/dn(10-17 cm2) factor,
pulse

(*2)

(*2)

A#1
A#2
A#3

3.8
3.8 (*1)
3.8 (*1)

0.17
0.11
0.15

142
196
136

B#1
B#2
B#3

1.4
1.2
0.7

0.43
1.0
2.0

76
42
30

Γ (*3)

0.2

0.2(*1) Estimated from the value for sample A#1.
(*2) Typical values measured at IOP = 200 mA are shown.
(*3) Assumed in view of the values in Table 1.

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Received 31 Aug 2007; revised 23 Oct 2007; accepted 24 Oct 2007; published 26 Oct 2007

29 October 2007 / Vol. 15, No. 22 / OPTICS EXPRESS 14896

We also compared measured and calculated nonlinear phase shifts for samples A#1 andB#1 to #3. These can be experimentally determined from XPM spectra out of the SOA [2,19].
The chosen pulse frequency was either 2.6 GHz or 10.5 GHz, depending on the carrier
recovery rate of the SOA. dnr/dn was estimated for each sample from the measured phaseshifts at IOP = 200 mA (Table 2). The difference between samples seemed to be negatively
correlated to the typical carrier densities. The SOA simulation could approximately reproduce
the measured nonlinear phase shifts at various IOP, PCW and Ppulse values (Fig. 8(d)), and ourmodel seems feasible for power-consumption simulations.

(b)

(a)

+20
+10

B#1, Iop = 100, 150,
200, 300, 400 mA
measured
calculated

0
-20

(c)
+40

Chip Gain (dB)

Recovery Rate 1/τeff (GHz)

+30

-10

0

+10

+20

Output power (dBm)
without holding beamwith -5 dBm holding beam

+20
+10

Iop
measured calculated
400 mA,
200 mA,

B#3, Iop = 200 mA

50

measured
calculated

10
5-50 -40 -30 -20 -10

2+10 +20 +30

B#1, IOP = 400 mA

1
0.5
0.2

holding beam intensity
measured calculated-25 dBm-15 dBm-5 dBm0.1

01
10
100 1000 10000
Output pulse energy from chip (fJ)0

Holding-Beam Intensity (dBm)

B#1 sample

+30

100

(d)
ΔΦ/π (rad)Chip Gain (dB)

+40

0.05
0.1

1

10

100

1000

Pulse energy (fJ)

Fig. 8. Comparison of measured and calculated SOA properties under holding-beam injection.
(a) Cw-gain saturation, (b) effective carrier recovery rate 1/τeff, (c) gain saturation for a 2-ps
pulse, and (d) nonlinear phase shift ΔΦ caused by ultrafast pulses.

4.2 Electrical power consumption
We calculated the correspondence between the electrical power consumption POP and theoperating frequency B for an SOA used in an XPM-based all-optical gate as follows. First, we∞
fixed the control pulse energy E pulse ≡ ∫−∞ Ppulse dt at a realistic value (340 fJ). Then, for each IOP
condition we calculated the induced ΔΦ as a function of the holding beam intensity. The
required amount of ΔΦ depends on the function of the gate: for 3R regeneration or
wavelength conversion it is ~0.3π [16]. Therefore, for each IOP, the equation ΔΦ =0.3π provides the maximum available holding-beam intensity PCW. The carrier recovery rate
1/τeff for this condition can be interpreted as the approximate frequency limit B of the gate.
POP was calculated from IOP using empirical V-I characteristics.
Before discussing the power consumption of actual SOAs, we will look at calculated
values using non-empirical parameter sets to find their dominant factors. Figure 9 shows our
results. Here, the dependences of dg/dn, η and τC on IOP were ignored, in contrast to the cases
shown in Figs. 8 or 10. Calculations were done down to nearly the low power limits, whereΔΦ = 0.3π can be satisfied only when PCW = 0. We found that the maximum frequency is#87129 - $15.00 USD(C) 2007 OSA

Received 31 Aug 2007; revised 23 Oct 2007; accepted 24 Oct 2007; published 26 Oct 2007

29 October 2007 / Vol. 15, No. 22 / OPTICS EXPRESS 14897

almost proportional to the total conversion efficiency ηT and dg/dn, but not sensitive to theintrinsic carrier recovery rate 1/τC. As for the conversion efficiencies of each process, η3affects the required holding-beam intensity as well as B. As long as we keep the SOA
parameters constant, IOP increases almost linearly with B, so POP increases with B2.

POP = VOP IOP (mW)at ΔΦ=0.3 π

30000

3000

Table 3. Parameters assumed for Fig. 9
ηT=1, τC=100 ps, dg/dn=20 × 10-17 cm2
τC= 50 ps
τC=200 ps,
ηT=0.5-17

SymbolLeff
wAdA

dg/dn= 40 × 10
-17dg/dn= 10 × 10

ΓDemux,( Electrical)ref [9]dgcw/dn
dgpulse /dn

300

τC

(1/τeff)2

dn r/dn pulse

ηT

30
1

10

100

1000

Description

Value

active region length
width
thicknessconfinement factor
differential gain for cw
differential gain for pulse
carrier recovery rate
without acceleration
refractive index change
total carrier-conversion
efficiency

1000 μm
1 μm0.05 μm0.2
20.0 × 10 -17 cm2
20.0 × 10 -17 cm2
100 ps
0.4 × 10-20 cm3
1.0

Bandwidth, 1/τeff (GHz)
Fig. 9. Calculated power consumption of
SOAs versus their maximum operating
frequencies when SOA parameters are
independent of IOP (Table 3)

POP = VOP IOP (mW)at ΔΦ=0.3 π

3000
1000

calculated

B#1 1100 μm
B#2 700 μm
B#3 500 μm

measuredB#3 500 μm

A#1 1000 μm
A#2 700 μm

300
100(1/τeff)2
30
1

10

100

1000

Bandwidth, 1/τeff (GHz)
Fig. 10. SOA electrical-power consumption versus carrier recovery rate under holding-beamacceleration. Calculated results using the measured parameters for each sample and measured
results for sample B#3 are shown. A control pulse with a 2-ps width and 340-fJ energy wasused.

Figure 10 shows the calculated power consumption for the SOA samples. We used the
SOA parameters from Section 4.1. The B-series shows better performance than the A-series.
When POP is small, B#3 has the best performance around 20 GHz. As the target frequency
increases to over 100 GHz, B#1 becomes preferable. The power consumption of B#1 at 160
GHz is about 750 mW. This is comparable to the power consumption, about 400 mW, of thelatest XPM-based 160-Gb/s wavelength conversion [5] or wavelength conversion using
ultrafast chirp dynamics [6]. For the A-series, the longer sample had a higher frequency, andthe shortest sample A#3 could not achieve ΔΦ = 0.3π under the injection-current limit. These
characteristics result from those of ηT as discussed in Section 3. Except for the difference in#87129 - $15.00 USD(C) 2007 OSA

Received 31 Aug 2007; revised 23 Oct 2007; accepted 24 Oct 2007; published 26 Oct 2007

29 October 2007 / Vol. 15, No. 22 / OPTICS EXPRESS 14898

scale, most of the POP-B profiles in Fig. 10 resemble the corresponding POP-1/τC profiles. Thisis due to the complicated correlations of SOA parameter changes. Consequently, POP of A#1
and B#1 increase with B2 within the range of about 300 to 1000 mW, and the corresponding
values of the others likely increase faster than that. Further discussion requires measurementof the efficiencies at larger POP.
To prove the validity of our power-consumption model, we measured POP and 1/τeff at
ΔΦ= 0.3π for sample B#3 (Fig. 10). We obtained good agreement between the measured andcalculated results. Hence, we believe that our model produces satisfactory results as an initial
power-consumption model, although it can be improved.

4.3 High-frequency limit
To discuss the future of photonic networks, it is useful to express the B-POP relation with asimple formula. In this section, we therefore derive an analytical expression for the highfrequency limit.
First, we assume that both the injection current IOP and holding-beam power PCW are large.
PCW is chosen according to IOP so that ΔΦ stays at a fixed value, as in Section 4.2. Without
control pulses the carrier density reaches an equilibrium at npulse= neq. The small difference in
dgcw/dn and dgpulse/dn is ignored for simplicity, and the saturated SOA gain is expressed as⎛

Geq = exp ⎜ ΓLeff⎝dg⎞
neq ⎟.
dn⎠(4.3)

Note that we can approximately suppose that Geq does not change with IOP, because of theconstraint on ΔΦ. The reason is as follows: The number of carrier-to-photon conversions
when a control pulse is injected into the SOA in the steady state is given from the net gain of
the pulse Gpe and Epulse:
Δn pulse ≈G pe − 1ωV

E pulse(4.4)

as long as the pulse width is short enough compared to the carrier relaxation time. Then, Gpe
can be roughly estimated from Geq. Since ΔΦ is given from Δnpulse by Eq. (4.2), we cantransform Eq. (4.4) into
Geq ≈ G pe ≈ 1 +ωVΔΦ
E pulse ΓLeff k 0

dnr
dn

.

(4.5)

Both ΔΦ and Epulse are regarded as constant when we obtain the B-Pop relation. We also
assume that dnr/dn does not depend on IOP. Therefore, we can approximately regard Geq as
constant. For example, ΔΦ=0.3π and Epulse=340 fJ result in Gpe= 2.5 for sample B#1.
By assuming a steady state and taking only terms including IOP or PCW in Eq. (4.1), we
obtain the following relation from Eqs. (4.1) and (4.3):
ηT I OPPCW≈
ωV η3 (Geq − 1)qV

(4.6)

The operating frequency limit can then be obtained as follows: After first-order expansionof Eq. (4.1) in terms of npulse around neq, the relaxation of the carrier density deviationΔn(t)=npulse(t)-neq after the control-pulse injection can be expressed asGeq ΓLeff dg
d (Δn(t ))
Δn
=−
− η3
PCW Δndt
τCωV dn= − B ⋅ Δn.

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Received 31 Aug 2007; revised 23 Oct 2007; accepted 24 Oct 2007; published 26 Oct 2007

29 October 2007 / Vol. 15, No. 22 / OPTICS EXPRESS 14899

After substituting Eq. (4.6) into the above, we obtain
B≈

1

τ C (I OP )+Geq ΓLeff dg(I OP ) ⋅ ηT (I OP ) ⋅ I OP .
Geq − 1 qV dn(4.8)

When 1/τC converges to a finite value as IOP increases, the second term will dominate. The
applied voltage Vop approaches RIOP (R: resistance). Then, when we assume both dg/dn and ηT
are independent of IOP, POP is expressed as⎛ Geq − 1POP ≈ R⎜
⎜
⎝

Geq

2

−2

qV ⎞⎟ ⎛ dg ⎞−2 2⎜
⎟ ηT B
ΓLeff ⎟⎠ ⎝ dn ⎠= constant × B 2 .

(4.9)

Therefore, the B-Pop relation will be quadratic under the above assumption. This explains
the Fig. 9 results. The total conversion efficiency has an inverse-square contribution to POP for
the actual SOA, so it should be elaborately optimized to reduce the dc power consumption.
5. Conclusion

We developed a new model of the electrical power consumption of SOAs used in ultrafast alloptical gates. The dominant factors of this model are three different carrier-conversion
efficiencies and the differential gain of the SOA.
To predict power consumption we measured the conversion efficiencies of current SOAs
with our original method. They were ηT = 0.07 to 0.46 in total. A systematic study of theefficiencies of SOAs with different structures revealed that a longer SOA with an MQW
structure will have high conversion efficiency at a high injection current. Further study isneeded with this method to understand the dependences on the SOA width, thickness, andconfinement factor, and through such studies we hope to design a more efficient SOA in thenear future.
We calculated the power consumption POP as a function of operating frequency limit B,
based on our power consumption model and measured SOA parameters. We obtained good
agreement between the calculated and measured results. A longer SOA with an MQW
structure should consume less electric power when the operation frequency is about 100 GHz.
The calculated power consumption at 160 Gb/s for our best SOA (B#1) was 750 mW, and it iscomparable to experimental values in the literature. At high bit-rate, POP will increase as B2 oreven faster, depending on the decrease in the conversion efficiencies and differential gain. We
believe that the dc power-consumption model that we have developed in this work can beextrapolated to higher frequencies, for example to the 400 to 640 Gb/s range. Such design
extrapolation will help material, device, and system researchers in these fields to develop theirvisions regarding ultrafast, all-optical signal-processing systems in the near future at andbeyond the 160-Gb/s level.
Acknowledgements

We thank Mr. Tomonori Yazaki in KDDI Research Laboratories for his valuable technicaldiscussions and supports regarding some of the SOA samples. This work was supported byresearch project grant #B15360027, “Optical logic gates in the sub-terahertz frequency
region,” of the Ministry of Education (MEXT) and the research project grant, “Ultra-lowpower and ultrafast optical memory/switching device,” of the New Energy and Industrial
Technology Development Organization (NEDO).

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Received 31 Aug 2007; revised 23 Oct 2007; accepted 24 Oct 2007; published 26 Oct 2007

29 October 2007 / Vol. 15, No. 22 / OPTICS EXPRESS 14900