Modeling of the polarization-discriminatingsymmetric-Mach-Zehnder-type optical-3R gatescheme and its available degree of randomamplitude-noise suppression
Yoshiyasu Ueno, Masashi Toyoda,*) Rei Suzuki, and Youhei Nagasue**)
Department of Electronic Engineering, University of Electro-Communications,
1-5-1 Chofugaoka, Chofu, Tokyo 182-8585, Japan.
y.ueno@ieee.org*)
present affiliation: The Mie Bank, Ltd..
**)
present affiliation: OAS Corporation.

Abstract: We have modeled the semiconductor-optical-amplifier (SOA) based polarization-discriminating-symmetric-Mach-Zehnder (PDSMZ) type (i.e., a UNI-type) 3R gating scheme, and have searched for an optimum
set of 3R-gating conditions. Primary parts of the optimum parameters we
obtained – such as the interferometer delay time Δt and the widths of input
data and clock pulses in the gate model – matched those from previously
reported 3R-loop transmission experiments fairly well. We also found thatthe 3R-gating mechanism which forms the regenerated output signal differs
greatly from what it has been thought to be. Based on this model, we havecharacterized the available degree of random-amplitude-noise suppression.

©2006 Optical Society of America
OCIS codes: (060.2330) Fiber optics communications; (120.5060) Phase modulation;(190.5970) Semiconductor nonlinear optics; (190.7110) Ultrafast nonlinear optics; (250.5980)
Semiconductor optical amplifiers; (320.7080) Ultrafast devices; (320.7160) Ultrafast technology.

References and links
1.
2.
3.
4.
5.
6.
7.

8.

A. E. Kelly, I. D. Phillips, R. J. Manning, A. D. Ellis, D. Nesset, D. G. Moodie, and R. Kashyap, “80 Gb/s
all-optical regenerative wavelength conversion using semiconductor optical amplifier based interferometer,”Electron. Lett. 35, 1477-1478 (1999).
Y. Ueno, S. Nakamura, and K. Tajima, “Penalty-free error-free all-optical data pulse regeneration at 84 Gb/s
by using a Symmetric-Mach-Zehnder-type semiconductor regenerator,” IEEE Photonics Technol. Lett. 13,
469-471 (2001).
Y. Ueno, S. Nakamura, and K. Tajima, “Ultrahigh-speed data regeneration and wavelength conversion for
OTDM systems (invited),” 27th European Conference on Optical Communication (ECOC 2001), Sept. 30 –Oct. 4, 2001, Amsterdam, Netherlands, paper Th.F.2.1.
K. Tajima, S. Nakamura, and Y. Sugimoto, “Ultrafast polarization-discriminating Mach–Zehnder all-opticalswitch,” Appl. Phys. Lett. 67, 3709-3711 (1995).
N. S. Patel, K. L. Hall, and K. A. Rauschenbach, “40-Gbit/s cascadable all-optical logic with an ultrafast
nonlinear interferometer,” Opt. Lett. 21, 1466-1468 (1996).
Y. Hashimoto, R. Kuribayashi, S. Nakamura, K. Tajima, and I. Ogura, “Transmission at 40 Gb/s with asemiconductor-based optical 3R regenerator,” 29th European Conference on Optical Communication(ECOC 2003), Sept. 2003, paper Mo 4.3.3.
R. Inohara, M. Tsurusawa, K. Nishimura, and M. Usami, “Experimental verification for cascadability of alloptical 3R regenerator using two-stage SOA-based polarization discriminated switches with estimated Qfactor over 20 dB at 40 Gbit/s transmission,” 29th European Conference on Optical Communication (ECOC
2003), Sept. 2003, paper Mo 4.3.2.
L. Billes, J. C. Simon, B. Kowalski, M. Henry, G. Michaud, P. Lamouler, and F. Alard, “20 Gbit/s optical
3R regenerator using SOA based Mach–Zehnder interferometer gate,” in Dig. 23rd Eur. Conf. OpticalCommunications (ECOC '97), Edinburgh, U.K., Vol. 2, Sept. 22–25, 1997, pp. 269-272.

#9131 - $15.00 USD(C) 2006 OSA

Received 14 October 2005; revised 1 December 2005; accepted 19 December 2005

9 January 2006 / Vol. 14, No. 1 / OPTICS EXPRESS 348

9.

S. Nakamura, T. Tamanuki, M. Takahashi, Y. Ueno, and K. Tajima, “Ultrafast optical signal processing withsymmetric-Mach-Zehnder-type all-optical switches,” Photonics West, San Jose, USA, 2003, SPIE number
4998-03.
10. Y. Ueno, “Theoretically predicted performance and frequency-scaling rule of a Symmetric-Mach-Zehnder
optical 3R gating,” Opt. Commun. 229, 253-261 (2004).
11. K. Tajima, S. Nakamura, Y. Ueno, J. Sasaki, T. Sugimoto, T. Kato, T. Shimoda, M. Itoh, H. Hatakeyama, T.
Tamanuki, and T. Sasaki, “Hybrid integrated symmetric Mach-Zehnder all-optical switch and its ultrafast,high extinction switching,” Electron. Lett. 35, 2030-2031 (1999).
12. V. Lal, M. L. Masanovic, J. A. Summers, L. A. Coldren, and D. Blumenthal, “40 Gbps operation of an offset
quantum well active region based widely-tunable all-optical wavelength converter,” Optical Fiber
Communication Conference (OFC 2005), Anaheim, USA, March 6-11, 2005, OThE3.
13. J. Sarathy, “Design and applications of all-optical regenerators,” Optical Fiber Communication Conference(OFC 2005), Anaheim, USA, March 6-11, 2005, OThE1.
14. R. J. Manning, and D.A.O. Davies, “Three-wavelength device for all-optical signal processing,” Opt. Lett.
19, 889-891 (1994).
15. J. Sakaguchi, M. L. Nielsen, T. Ohira, R. Suzuki, and Y. Ueno, “Observation of small sub-pulses out of thedelayed-interference signal-wavelength converter,” Jpn. J. Appl. Phys. 44, L1358-L1360 (2005).
16. Y. Ueno, S. Nakamura, and K. Tajima, “Nonlinear phase shifts induced by semiconductor optical amplifierswith control pulses at repetition frequencies in the 40-160 GHz range for use in ultrahigh-speed all-opticalsignal processing,” J. Opt. Soc. Am. B19, 2573-2589 (2002).
17. Y. Ueno, M. Takahashi, S. Nakamura, K. Suzuki, T. Shimizu, A. Furukawa, T. Tamanuki, K. Mori, S. Ae,
T. Sasaki, and K. Tajima, “Control scheme for optimizing the interferometer phase bias in Symmetric-MachZehnder-type all-optical switch,” IEEE Photonics Technol. Lett. 14, 1692-1694 (2002).

1. Introduction
Low-noise, error-free, input-polarization-insensitive optical-3R gating of 80-Gb/s-classpseudorandom data signals has been achieved experimentally [1-3] through use of thepolarization-discriminating symmetric-Mach-Zehnder (PDSMZ) semiconductor gate [4]shown in Fig. 1(a). (This PDSMZ gate structure is sometimes called an ultrafast nonlinear
interferometer (UNI) [5].) More recently, error-free optical-3R-loop transmission of 40-Gb/ssignals with two-cascaded PDSMZ- 3R gates (Fig. 2) was demonstrated by two independent
research teams, where the ASE noise that accumulated over each recirculation was clearlysuppressed by the PDSMZ-3R gating [6, 7].

Fig. 1. The two alternative optical-3R gates.
(a) PDSMZ-3R gate [1-3], (b) SMZ-3R gate [8, 9]

Error-free optical 3R gating of 40-Gb/s signals has also been achieved with the SMZ
semiconductor gate shown in Fig. 1(b) [8, 9]. In addition, a preliminary theoretical model ofthis SMZ-3R gating has been reported [10]. However, although this gate structure will be#9131 - $15.00 USD(C) 2006 OSA

Received 14 October 2005; revised 1 December 2005; accepted 19 December 2005

9 January 2006 / Vol. 14, No. 1 / OPTICS EXPRESS 349

more suitable than the PDSMZ gate structure for compact integration in the near future [9, 1113], there have been few reported studies regarding its optical-3R-loop transmission.

Fig. 2. The optical-3R gate scheme with two-cascaded PDSMZ-3R gates [6, 7].
SOA: semiconductor optical amplifier, BPF1, BPF2: optical band-pass filters, pol: polarizer.

To the best of our knowledge, no theoretical model of the PDSMZ-3R gating mechanism
has been reported. In particular, this mechanism’s ability to suppress random amplitude noisein the input data signal has never been examined with a reliable model. In addition, the detailsof the gating mechanism that regenerates the data pulses have never been experimentally
characterized, because of the limited time resolution in previous experiments. The gatewindow shape, for example, has been thought to be rectangular-like even if the gate is driven
by pseudorandom data pulses (Fig. 3), in a manner similar to the mechanism in all-optical
SMZ demultiplexing and PDSMZ demultiplexing [4]. The effective width of the gate window
has been thought to be close to the delay time Δt in Fig. 3. The gate-window shape in the
PDSMZ-3R gating, however, has not been experimentally measured nor theoreticallymodeled.

Fig. 3. Conventional PDSMZ-3R gate model.

In this work, we have built the first theoretical model of the PDSMZ-3R gate forcharacterizing and designing its amplitude-noise-suppression capability. In the modelingprocesses, we have paid particular attention to two issues:(1) Because the recovery of the carrier density is accelerated by the input clock pulses,
which obviously work as a holding beam [14], the recovery components in the two-split clock
pulses seem not to be smoothly cancelled after the optical interference inside the gate in amanner similar to that recently reported for the delayed-interferometer signal-wavelength
converter (DISC) [15]. How then will an effective gating window be formed and shaped?
(2) The random noise in the logic-zero signal is not suppressed so strongly as that in the
logic-one signal?

#9131 - $15.00 USD(C) 2006 OSA

Received 14 October 2005; revised 1 December 2005; accepted 19 December 2005

9 January 2006 / Vol. 14, No. 1 / OPTICS EXPRESS 350

2. Operating principle of the PDSMZ-3R gate scheme
The PDSMZ-3R gate in Fig. 1(a) has been supposed to regenerate the RZ-format data pulses
according to the following principle [2, 4]. When each of the input data pulses (which containrandom amplitude noise) is amplified by a polarization-insensitive SOA, the carrier density
inside the SOA is instantaneously depleted, and then recovered by the dc injection current to
the SOA.
On the other hand, the local clock pulses are split into two orthogonally polarizedcomponents. After one of the two components is given a delay time Δt, the two components
are combined and injected to the SOA. In the SOA, both of the two polarized components are
all-optically modulated (i.e., cross-phase modulated and cross-gain modulated), as aconsequence of the ultrafast carrier-density oscillation driven by the input data pulses. Afterthe SOA, the two orthogonally polarized components are split into the two respectively
polarized components by a polarization splitter, and then the delay time Δt between these twocomponents is compensated for. After the delay-time compensation, the two orthogonallypolarized components are combined and filtered by a 45° polarizer. The combined component
after the the 45° polarizer is an ‘optical-interference component’ between the two-split clockpulse components. Both of the two-split inteference components are cross-phase-modulated
and cross-gain modulated in the SOA between the first splitter and the second combiner (i.e.
interference combiner), in a manner similar to those in the SMZ-3R gate scheme in Fig. 1(b).
The optical interference can be constructive or destructive, depending upon the interference
phase bias ΔΦb which is optimized by a static optical phase shifter in front of the second
combiner in Fig. 1(a).
Each of the clock pulses after the optical interference in the 45° polarizer survives or not,depending upon the binary logic (either 1 or 0) of the co-propagating input data pulses. As aresult, the input clock pulses are digitally encoded by the input data pulses, and then reach theoutput port of the 3R gate as ‘regenerated’ data pulses. The co-propagating input data pulses
are removed by a bandpass filter due to a small difference between the wavelengths of input
data and clock pulses, in a manner similar to those in the SMZ-3R gate.
The magnitude of the amplitude noise in the ‘regenerated’ data pulses has been supposed
to be smaller than that in the input data pulses because of the sinusoidal transfer function of
the optical interferometer.
3. Our model equations and its validity
The all-optical driving forces in the two-cascaded PDSMZ gates in Fig. 2 consist of the crossphase modulation (XPM) and cross-gain modulation (XGM) in the two respective SOAs, andthe optical interference. In this work, in a manner similar to Ref. 10, the XPM and XGM ineach SOA are modeled by the following carrier-density rate equation:

1
1
2
2
2
Eclock (t ) + Eclock (t − Δt ) + Edata (t )I op nc (t ) 1
d2
2.
nc (t ) =−− ⋅ G nc (t ) − 1 ⋅
τc
ω
dt
qV
V

({ } )(1)
Here, n c (t ) is the excess carrier density averaged over the propagation distance throughout
the SOA chip, I op is the injection current, V is the volume of the active layer, and τ c is thecarrier lifetime. The XGM is expressed as

G (t ) ≡ exp[dg / dnc ⋅ nc (t ) ⋅ ΓL] ,#9131 - $15.00 USD(C) 2006 OSA(2)Received 14 October 2005; revised 1 December 2005; accepted 19 December 2005

9 January 2006 / Vol. 14, No. 1 / OPTICS EXPRESS 351

where Γ is the optical confinement factor and L is the length of the SOA active layer. For
simplicity, the differential gain dg / dnc is assumed to be independent of the carrier density.
The XPM in the optical phases of all propagating light components is expressed as

Φ (t ) = − k 0 ⋅ dn r / dn c ⋅ nc (t ) ⋅ ΓL ,(3)

where k0 is the wavevector in vacuum. The nonlinear index of refraction dn r / dn c , likedg / dnc , is assumed to be independent of the carrier density.
The validity of this nonlinear SOA model has been experimentally verified to some extent
with output spectra and waveforms from other types of all-optical gates, such as saturated
XPM and SPM spectra [16], all-optically demultiplexed waveforms [17], and DISC-typewavelength-converted waveforms [15, 16], mostly in a frequency range from 40 to 160 GHz.
On the other hand, the possible contributions from amplified spontaneous emission and thesecond-order terms in the gain and the refractive-index as a function of the carrier density
were neglected in our model equations. We sacrificed some of the preciseness of our modelby neglecting those contributions and keeping our core subroutines compact, so that we could
flexibly study these slightly complicated gate schemes. We have also been trying to modeland design the performance of these 3R gate schemes to enable scalable optical-circuitdesigns in the near future. We believe this modeling policy of ours will be justified by theabove-mentioned, previous series of experimental verifications [15-17].
The pseudorandom input data are modeled as

Edata (t ) =∑[C ⋅ E + (1 − C ) ⋅ E ]⋅ sech( t − mT× T − t ), m = 1, 2, ..., ∞ ,
m

1
m

m

0
m

tim

data
w

m

(4)

where Cm is the pseudorandom binary code (0 or 1, word length = 231-1). Independently fromthe random coding, pseudorandom analog numbers in a normal distribution are also
numerically generated and superimposed to the amplitude factor Em1 and Em0 . The pulse
shape is assumed to be secant-hyperbolic throughout this work. T is the frame time, ttim is the
input timing, and Twdata is a parameter that determines the pulse width.
The amplitude of the uniform input clock pulses is expressed as

Eclock (t ) =∑ E ⋅ sech( t −Tm ×T ), m = 1, 2, ..., ∞ .
clock

m

clock
w

(5)

The two-split clock pulses after experiencing the XGM and XPM in the SOA are respectively
expressed as{ } [ { }](t ) = G{n (t )}× exp[iΦ{n (t )}]× E

SOA,
Eclock1 (t ) = G nc (t ) × exp iΦ nc (t ) × Eclock (t )SOAEclock
2

c

c

clock

(t − Δt ) .

(6)

SOA
After passing through the SOA, the non-delayed component Eclockis delayed by Δt, is
1 (t )
SOA
interfered with the previously delayed component Eclock, and forms the output data pulses
2 (t )
as#9131 - $15.00 USD(C) 2006 OSA

Received 14 October 2005; revised 1 December 2005; accepted 19 December 2005

9 January 2006 / Vol. 14, No. 1 / OPTICS EXPRESS 352

output
SOA
SOA
Edata
(t ) = Eclock
1 ( t − Δt ) + exp(iΔΦ b ) ⋅ Eclock 2 ( t )

{
} [ {
}]
+ G{n (t )}× exp[iΦ{n (t )}+ iΔΦ ]× E

= G nc (t − Δt ) × exp iΦ nc (t − Δt ) × Eclock (t − Δt )
c

c

b

clock

(7)

(t − Δt )= Tw (t ) × Eclock (t − Δt )where ΔΦ b is the optical interference phase bias. The amplitude transmittance of theeffective gate window Tw (t ) in Eq. (7) is defined as

{

[ { }

}

]

{

}

[ {

}]

Tw (t ) ≡ G nc (t ) × exp iΦ nc (t ) + iΔΦ b + G nc ( t − Δt ) × exp iΦ nc (t − Δt ) .

(8)

In the conventional manner, the contribution from XPM to the intensity transmittance2

Tw (t ) is approximated by ignoring the XGM contribution:

[ { }

]

[ {

}]

Tw (t ) ≈ exp iΦ nc (t ) + iΔΦ b + exp iΦ nc (t − Δt )2

(ΔΦ(t ) + ΔΦ b )
= cos

2

.

(9)

2

2

The optical phase difference between the two-slit interference components ΔΦ(t ) isdefined as

{

} {

}

ΔΦ ( t ) ≡ Φ nc (t ) − Φ n c (t − Δt ) .

(10)

The formulae in Eqs. (8) to (10) are similar to those that have been repeatedly used todescribe all-optical SMZ demultiplexing, PDSMZ demultiplexing, and DISC wavelength
conversion [16].
4. Calculated results
4.1 Available degree of noise suppression after PDSMZ-type 3R gatingFirst, we numerically searched for the optimum set of 3R gating conditions; that is, the mostsuitable parameter values for the PDSMZ-type gates and for the optical inputs. For design
simplicity, the conditions for the second gate were expected to be identical to those for the
first gate. By testing most of the possible combinations of parameter values, we found that the
optimum parameter values, leading to the best output eye diagram, were as summarized inTables 1 and 2. Primary parts of the optimum parameters, such as the interferometer delay
time Δt (Table 1) and the widths of the input data and clock pulses (Table 2), matched thosereported from previous 3R-loop transmission experiments fairly well [6, 7]. (Note, though,that the previously reported relative delay time Δ t T has ranged from 40% to 61%, as shownin Table 3.)
Table 1. Parameter values for the PDSMZ-gates.

Description
Unsaturated gain, G0
Gain saturation energy, Psat
Carrier lifetime, τcNominal injection current, Inom
Enhanced injection current, Iop
Injection enhancement factor#9131 - $15.00 USD(C) 2006 OSA

42 Gb/s
28 dB
180 fJ
50 ps
150 mA
435 mA
2.9

168 Gb/s
28 dB
180 fJ
12.5 ps
600 mA
1740 mA
2.9

Received 14 October 2005; revised 1 December 2005; accepted 19 December 2005

9 January 2006 / Vol. 14, No. 1 / OPTICS EXPRESS 353

Interferometer delay time, ΔtInterferometer phase bias, ΔΦb
Width of the bandpass filter, ΔλBPF
Spectral shape of the bandpass filter

14.7 ps (61.7%)
1.00π0.80 nmGaussian

3.68 ps (61.7%)
1.00π
3.20 nmGaussian

The parameter values for 168-Gb/s data were used later for the results in Fig. 11(b).

The optimum injection current to the SOA in this work was the value of the enhanced
injection current in Table 1, in a manner similar to those in Ref. 10. In contrast, the values of
the unsaturated gain, the gain saturation energy, and the carrier lifetime in Table 1 wereintentionally assumed as those with the nominal injection current in Table 1. [As aconsequence, if we assume gating conditions with very weak optical inputs to the SOA, ourmodel calculation outputs unrealistically large carrier density and gain because the gain
coefficient in Eq. (2) was assumed to be independent of the carrier density.] When we
assumed gating conditions with relatively strong optical inputs such as those in Table 2, bothof the carrier density and the gain were saturated and modulated below their ‘nominal’unsaturated levels which correspond to the nominal injection current. This strong saturation in
the 3R scheme was the reason why we defined the injection current in the above-mentioned
two ways and why we assumed the gain coefficient and some other parameters nearly
constant [10].
Table 2. Parameter values for the optical inputs.

Description
Input signal's pulse width (FWHM)
Input signal's pulse energy
Input signal's pulse shape
Input signal's pulse distance, T
Input timing, ΔTin
Q2 value
Input clock's pulse width (FWHM)
Input clock's pulse energy
Input clock's pulse shape

42 Gb/s
6.0 ps100 fJsech
23.82 ps
+2.15 ps (+9.0%)
19.9 dB
3.0 ps
400 fJ
sech

168 Gb/s
1.5 ps100 fJ
sech
5.96 ps+0.54 ps (+9.0%)
19.9 dB
0.75 ps
400 fJ
sech

Table 3. Comparisons between the relative delay times, Δt/T.

Gate Scheme
3R gateLogic gate
Logic gate
3R gate3R gateTwo-cascaded 3R-loop
3R-loop
3R gateTwo-cascaded 3R-loop

Bit rate(Gb/s)
80
40
100
40
84
40
40
40
40

Delay timeΔt (ps)
5
12.5
5
12.5
6.2
13
15
15.3
15.3

Time frame
T (ps)
12.5
25
10
25
11.9
25
25
25
25

Ratio
Δt/T
40%
50%
50%
50%
52%
52%
60%
61%
61%

Two-cascaded 3R gate

42

14.7

23.8

62%

Ref.
[1]
[5]
a
b
[2]
[6]
c
b
[7]
This
work

(a) K.L. Hall and K.A. Rauschenbach, "100-Gbit/s bitwise logic," Opt. Lett. vol. 23, no. 16, pp.
1271-1273, 1998, (b) M. Tsurusawa, R. Inohara, K. Nishimura and M. Usami, "Operation
margin of all-optical regenerator at 40 Gbit/s by SOA-based polarization discriminated switch,"
Prco. Optical Fiber Communication Conference and Exposition (OFC 2003), Atlanta, USA,
Paper ThX3, Mar. 2003, (c) H.J. Thiele, A.D. Ellis, and I.D. Phillips, "Recirculating loop

#9131 - $15.00 USD(C) 2006 OSA

Received 14 October 2005; revised 1 December 2005; accepted 19 December 2005

9 January 2006 / Vol. 14, No. 1 / OPTICS EXPRESS 354

demonstration of 40 Gbit/s all-optical 3R data regeneration using a semiconductor nonlinear
interferometer," Electron. Lett., Vol. 35, no. 3, pp. 230-231, Feb. 1999.

Fig. 4. Calculated 42-Gb/s pseudorandom signals before and after the 3R gating.
(a), (b): Input signal, (c), (d): Intermediate signal after the first PDSMZ gate, (e), (f): Output
signal, (a), (c), (e): Eye diagrams, (b), (d), (f): Bit-error rates (BER), Dashed curves in (d) and(f): BER of the input signal in (b), for comparison.

Figure 4 shows calculated eye diagrams and bit-error rates (BERs) before and after thetwo-cascaded PDSMZ-type gates shown in Fig. 2 when the parameter values from Tables 1
and 2 were used. A 1-kbit-long data pattern was generated to draw the eye diagrams, while a
3-Mbit-long data pattern was generated to calculate the BER curves. The typical calculation
time for this set of BER curves with a standard 2.4-GHz personal computer and a standard
fast-Fourier-transformation (FFT) library was 34 hours. As shown in Figs. 4(e) and (f), thelogic-one-bit noise and the logic-zero-bit noise were both suppressed after the 3R gating. In
addition, as shown in Fig. 4(f), the one-bit noise was suppressed more strongly than the zerobit noise. There are three notable points here:(1) The range of the one-bit-noise distribution that caused a BER of 10-6 in Fig. 4(f) was
smaller than it appeared to be in the eye diagram in Fig. 4(e). In other words, the statistical
BER curve for the regenerated one-bit signals (the solid curve in Fig. 4(f)) was much steeper
than for standard one-bit signals with normally distributed noise (e.g., the dashed curve in Fig.
4(f)).
(2) In the intermediate state between the two-cascaded gates, the range of the one-bit noise
was expanded rather than suppressed. After the second 3R gate, the expanded one-bit noise
was strongly suppressed and was logic-inverted.
(3) The range of the one-bit-noise distribution that caused a BER of 10-6 in the output signal
was compressed to approximately 62% that in the input. The range of the zero-bit-noise
distribution that caused a BER of 10-6 in the output signal was compressed to 75% that in the
input signal.

#9131 - $15.00 USD(C) 2006 OSA

Received 14 October 2005; revised 1 December 2005; accepted 19 December 2005

9 January 2006 / Vol. 14, No. 1 / OPTICS EXPRESS 355

Fig. 5 Transition of 42-Gb/s eye diagrams from the first input to the final output of the twocascaded PDSMZ-3R gates.

Figure 5 shows the calculated eye diagrams from the first input through the final output inmore detail. The width of data pulses in front of BPF1 in the first PDSMZ-3R gate [Fig. 5(b)]was 2.5 ps, which is much narrower than the width of the input data pulses (6.0 ps). When
BPF1 was used with a spectral width of 0.80 nm, the width of the data pulses was nearly
equalized (6.4 ps) to that of the input data (Fig. 5(c)). The data pulses in front of BPF2 in thesecond PDSMZ-3R gate [Fig. 5(d)] were narrowed once again. When BPF2 was applied,
though, the data pulse’s width was again nearly equalized [Fig. 5(e)]. The calculatedparameter values of the regenerated data pulses from the two-cascaded 3R gates are
summarized in Table 4.
Table 4. Calculated parameter values of the 3R-regenerated data signal.

Description
Output logic
Output signal pulse width (FWHM)
Output signal pulse energy
Q2 value
Minimum bit-error rate
Nonlinear phase shift, ΔΦNL

#9131 - $15.00 USD(C) 2006 OSA

42 Gb/sinverted
6.4 ps
3.0 fJ
29.4 dB< 10-60.36π

168 Gb/s
inverted
1.6 ps
3.0 fJ
29.4 dB< 10-60.36π

Received 14 October 2005; revised 1 December 2005; accepted 19 December 2005

9 January 2006 / Vol. 14, No. 1 / OPTICS EXPRESS 356

Fig. 6. Physical mechanism that regenerates the 42-Gb/s patterned data pulses.(a) Carrierdensity oscillation (solid), induced by both ‘011’ input data (6.0 ps) and clock pulses, (b)Effective gate-window’s transmittance Tw(t) (dashed), with respect to the delayed clock pulses(3.0 ps, solid), (c) Logic-inverted ‘100’ output data pulses (before being bandpass-filtered), (d)Trace of the difference between the optical phases of the two-split clock-pulse components

Figure 6 shows the physical mechanism inside the first PDSMZ gate according to our
calculation. According to the rate equation (Eq. (1)), the carrier density in the SOA [Fig. 6(a)]was instantaneously depleted by three types of input pulse: the ‘011’ data pulses [dashedcurve in Fig. 6(a)], the clock pulses, and the Δt-delayed orthogonally polarized clock pulses.
The dotted vertical lines in Figs. 6(a) to (d) indicate the positions of non-delayed clock pulses.
Figure 6(b) shows the transmittance of the effective gate window Tw (t )2(Eq. (8)), withrespect to the Δt-delayed clock pulses Eclock (t − Δt ) .
22

outputFigure 6(c) shows the output data waveform E data(t ) in front of the BPF1, which was

generated from the overlaps Tw (t ) × Eclock (t − Δt ) between the effective gate-window
waveform and the delayed-clock-pulse waveform in Fig. 6(b), according to Eq. (7). In theexample shown in Fig. 6, the input data code was ‘011’ and the logic-inverted output datacode was ‘100’. As in Figs. 5(b) and (d), the output pulse in Fig. 6(c) was greatly narrowed.
Figure 6(b) indicates that this pulse narrowing was caused by the width of the corresponding
overlap between Tw (t ) and Eclock (t − Δt ) .
2

Note that the effective gate-window waveform Tw (t ) in Fig. 6(b) significantly differsfrom what it had previously been thought to be; that is, rectangular-like waveforms (Fig. 3).
Furthermore, Fig. 6(d) shows the time evolution of the temporal optical phase differenceΔΦ(t ) in Eq. (10), indicating that the contribution from XPM to the 3R-gate-window
waveform differed significantly from that of the SMZ demultiplexing in Eq. (9).
The magnitude of the so-called nonlinear phase shift ΔΦNL that is visible in Fig. 6(d) has
been recognized as one of the most important gating conditions in all interferometric types of
all-optical semiconductor gates (e.g., [16]). In the case of our PDSMZ-3R gating, we definedΔΦNL as the temporal phase shift from 1.0π at the time of the output pulse’s peak position.
According to this definition, ΔΦNL in Fig. 6(d) was 0.36π (Table 4).

#9131 - $15.00 USD(C) 2006 OSA

Received 14 October 2005; revised 1 December 2005; accepted 19 December 2005

9 January 2006 / Vol. 14, No. 1 / OPTICS EXPRESS 357

Fig. 7. Dependence on the magnitude of the nonlinear phase shift, ΔΦ NL solid curve: Q2 of theoutput signal after the two-cascaded PDSMZ gates, dashed curve: Q2 of the intermediate signal
between the two-cascaded 3R gates, dashed line: Q2 of the input signal.

Although the phase shift required for full switching from destructive to constructive
interference (or vice versa) in a Mach-Zehnder interferometer is 1.0π, the ΔΦNL value in Fig.
6(d) was much smaller than 1.0 π. In a calculation whose results are shown in Fig. 7, we
temporarily assumed larger and smaller dn r / dn c values and investigated how the resultant
larger and smaller ΔΦNL values would consequently affect the noise suppression capabilities.
According to our calculation, the noise was suppressed slightly more as ΔΦNL approached
0.7π (Fig. 7). When ΔΦNL was increased to more than 0.7π, the output data waveform wasdistorted and consequently the Q2 value of the output signal started dropping. Thus,
unexpectedly, we found that ΔΦNL of 1.0 π is too large for the PDSMZ-3R gating.
4.2 Possible output distortions and their respective origins
When one of the gating parameters is adjusted too far beyond its tolerance range, the output
waveform will obviously be distorted. Figures 8(a) and (b) show two types of such outputwaveform distortion, while Fig. 8(c) shows the waveform with very little distortion under the
optimum conditions.

Fig. 8. Possible output-waveform distortions. Upper: output waveforms, lower: gating
windows (dashed) with respect to the input clocks (solid), (a) Asynchronous clock leakage,
when the clock pulse’s width is too broad, (b) Synchronous clock leakage, when the clock
power is too weak, (c) Little distortion, when the conditions of the input clock are acceptable.

The waveform distortion in Fig. 8(a) occurred when the width of the secant-hyperbolic
clock pulses was broadened to 5.0 ps from the optimum value of 3.0 ps (Table 2). Three
separate leakage components can be clearly seen, which were generated by three unexpected#9131 - $15.00 USD(C) 2006 OSA

Received 14 October 2005; revised 1 December 2005; accepted 19 December 2005

9 January 2006 / Vol. 14, No. 1 / OPTICS EXPRESS 358

overlaps between the gating window and the input clock components. One of the threeleakage components was asynchronous and the other two were nearly synchronous to the datapulse positions.
The waveform distortion in Fig. 8(b) occurred when the energy of the input clock pulse
was decreased to 100 fJ from its optimum value of 400 fJ. Two separate leakage components
can be seen, which were generated by two unexpected overlaps between the gating window
and the input clock. Both of these leakage components were nearly synchronous to the datapulse positions.
We expect the clear difference between the leakage positions in Figs. 8(a) and 8(b) to be
useful for diagnosing such forms of output waveform distortion in experimental 3R research.
Our calculated results in Fig. 8 suggest that when leakage components are synchronous to thedata positions, they can be removed by increasing the input clock power; when one of theleakage components is asynchronous to the data positions, it can be removed by narrowing thewidth of the input clock pulses.
4.3 Tolerance to the input data pulse width and the input timing
We chose to use input secant-hyperbolic data pulses whose full width at half maximum(FWHM) was 6.0 ps (Table 2), narrower than the more common FWHM (10-12 ps) of datapulses used in recent RZ-formatted transmission experiments. We therefore investigated thedependence of the noise suppression capability on the width of input data pulses at about 6.0
ps (Fig. 9). The decision threshold limits in the figure were defined as the upper and lower
limits of the decision-threshold range where the calculated BER reached 10-6. The PDSMZ3R gating tolerated a width of approximately 8 ps (Fig. 9). As the width of the data pulses
increased from 6 ps, the noise in the logic-one signals was slightly less suppressed. In
contrast, the noise in the logic-zero signals was not very dependent on the data pulse width.
We speculate that the tolerance in Fig. 9 may be broadened when we study this using
Gaussian data pulses.

Fig. 9. Dependence of the decision-threshold limits on the width of the input signal. The
decision-threshold limit in this work is defined as a limit of the decision-threshold level where
the bit-error rate reaches 10-6.

We also studied the BER tolerance with regard to the input timing of 42-Gb/s data pulses
with 6.0-ps data pulses and the other optimum conditions from Tables 1 and 2. The width of
the tolerance range for the input timing in this work was approximately 4 ps (Fig. 10).

#9131 - $15.00 USD(C) 2006 OSA

Received 14 October 2005; revised 1 December 2005; accepted 19 December 2005

9 January 2006 / Vol. 14, No. 1 / OPTICS EXPRESS 359

Fig. 10. Dependence on the signal’s input timing.

4.4 Frequency-scaling rule
Our final step in this work was to numerically test whether the PDSMZ-3R gate would follow
the frequency-scaling rule that one of us analytically proposed and numerically verified withrespect to the SMZ-3R gate model [Fig. 1(b)] [10]. As was mentioned earlier in the text, ourgoal is to enable scalable optical-circuit design. According to the frequency-scaling rule givenin [10], we can quadruple, for example, the frequency of any type of 3R gating result if we
can scale the gate and input parameter values given in Tables 1 and 2 as follows: (1) narrow
the widths of the signal and clock pulses by a factor of 4, (2) maintain the energies of thesignal and clock pulses, (3) shorten the carrier lifetime of the SOA(s) by a factor of 4, (4)increase the carrier injection by a factor of 4, (5) maintain the injection enhancement factor,and (6) shorten the interferometer delay time by a factor of 4.
In this work, we calculated eye diagrams before the frequency-scaling (42 Gb/s) and after
the frequency-scaling (168 Gb/s), using the respective parameter values in Tables 1 and 2. As
a result, the frequency-scaled eye diagram which contained the compressed amplitude noise
completely matched the eye diagram before scaling. Thus, we have numerically verified thefrequency-scaling rule for the PDSMZ-3R gate.
5. Conclusion
We have modeled the semiconductor-optical-amplifier (SOA) -based polarizationdiscriminating-symmetric-Mach-Zehnder (PDSMZ) -type (i.e., a UNI-type) 3R gating
scheme, and have searched for an optimum set of 42-Gb/s 3R-gating conditions. Primary partsof the optimum parameters, such as the interferometer delay time Δt (62% of the frame time,T) and the widths of input data (6 ps) and clock pulses (3 ps) in the gate model, matched thosefrom previous 3R-loop transmission experiments fairly well. We also found that the 3R-gating
mechanism which forms the regenerated output signal differs dramatically from what it wasthought to be.
Based on this new model, we characterized the available degree of random-amplitudenoise suppression. The compression ratio of the noise distribution range (calculated at a BERlevel of 10-6) in the logic-one signal was approximately 62%, and that in the logic-zero signal
was 75%. We also investigated the dependence of the noise-suppression capability on several
3R-gating conditions, such as the required nonlinear-optical phase shift ΔΦNL inside the gate
and the widths of the signal and clock pulses.
These modeling results will provide basic guidelines for optical-3R transmission research
and for more fundamental 3R gating experiments.

#9131 - $15.00 USD(C) 2006 OSA

Received 14 October 2005; revised 1 December 2005; accepted 19 December 2005

9 January 2006 / Vol. 14, No. 1 / OPTICS EXPRESS 360