MB3

Theoretical models of theSOA-based SMZ-type optical-3R gates
Yoshiyasu Ueno, Masashi Toyoda, and Rei Suzuki
University of Electro-Communications, Chofugaoka, Chofu, Tokyo 182-8585, Japan, y.ueno@ieee.org

Abstract: We modeled the PDSMZ-type (UNI-type) 3R scheme and studied its available degree of amplitude-noise
suppression in both ‘1’ and ‘0’ signals and possible waveform distortion. For evaluating the noise distribution, bit-error
rates were calculated to below 1×10-6.
1. Introduction
After optical-3R gating with 80-Gb/s-class pseudorandom signals has experimentally been achieved [1, 2] with an SOA-basedpolarization-discriminating symmetric-Mach-Zehnder (PDSMZ) gate (the PDSMZ gate structure [3] is sometimes called ‘UNI’), its
3R capabilities has more practically been demonstrated in recirculating-loop, ultralong-haul transmission experiments with 40-Gb/s
RZ and CS-RZ signals [4-7]. Potential applications of such SOA-based interferometric 3R gates include burst- and packet-mode
network systems and optical buffer memories because of their low-power consumption and compactness after integration [8].
From theoretical modeling’s viewpoints, however, the SOA-based SMZ-type gates in the 3R-gating scheme have not beenmodeled as clearly as those in the optical demultiplexing scheme [9, 10]. This is because those in the 3R-gating scheme are driven bypseudorandom RZ signals in contrast to those in the optical demultiplexing scheme are driven by divided clock pulses.
In this work, we report the latest results from our theoretical design models that we have been building since 2002 [11, 12].
2. The PDSMZ-type optical-3R gate scheme, and its theoretical model
The PDSMZ-type optical-3R gate scheme (Fig. 1) that has been used in the previous 3R-transmission experiments [4-7] wasassumed in this work. The two cascaded PDSMZ gate structures in this 3R gate scheme were assumed to be identical to each otherand be identical to the structure in Refs. [1] and [2]. The first PDSMZ gate that is receiving the input data pulses all-optically encodes
the input clock pulses. At the output of the first PDSMZ gate, encoded data pulses are newly generated. The digital logic of the newlyencoded data pulses can be either inverted or non-inverted, in general. The second PDSMZ gate that is receiving the newly encoded
data pulses all-optically encodes the input clock pulses, once again. At the output of the second PDSMZ gate, the twice-encoded datapulses are generated whose digital logic is generally non-inverted.
The input data pulses in the theoretical model calculation were generated as,
E data (t ) = ∑ (C m ⋅ E m1 + E m0 ) ⋅ sech(mt − m × T0), m = 1, 2, ..., N b ,Tw(1)where T0 is the bit distance in time. The random binary sequence Cm (= 0 or 1) was generated with a pseudorandom binary numbergenerator whose pattern length was set to 231-1. The random amplitude noise in the input data pulses was modeled, as follows.
Analogue pseudorandom numbers in the normal distribution (pattern length= 232 = 4×109) were generated independently from thedigital random numbers and were superimposed separately on 1-bit amplitude Em1 and 0-bit amplitude Em0. The standard deviation ofEm0 was set to a half that of Em1. For calculating the bit error rate (BER) at the output of the 3R regenerator, three million bits of input
data pulses [i.e. Nb= 3,000,000] were repeatedly generated.
The carrier density nc in the respective SOA was assumed to be instantaneously depleted by both data pulses and clock pulses, andthen be recovered by the injection current with only one time constant τc. The rate equation that governs this ultrafast carrier-densityoscillation was simply described as,22

12E data ( t ) + E clock( t ) + E clock(t ) ,I op n c ( t ) 1
d−− ⋅ (G {n c ( t )} − 1) ⋅n c (t ) =τchωqVVdt2(2)in a manner similar to that in Refs [10]-[13]. The Eclock1 and Eclock2 are the non-delayed and ∆t-delayed clock pulses at the input of eachMB3SOA, respectively. The gain G and the optical nonlinearity coefficient of the SOAs were assumed to be insensitive to the input
polarization and wavelengths.
Regarding the gating conditions (i.e. the input pulses’ widths, the input pulses’ energies, the delay time ∆t, and the input datatiming with respect to the clock), we systematically optimized each condition to the respective value in Table 1 so that the best
regenerated eye diagrams were observed. (We have also paid attention to the previously reported conditions in Refs. [5] and [6].)It should be noted that the optimum delay time ∆t in this work was 61.7% of the bit distance. The bit logic after the first PDSMZ
gate was inverted. The width of the input clock pulses was adjusted to be narrower than the input data pulses, and consequently thewidth of the encoded clock pulses was narrower that the input data pulses. We adjusted the width of the encoded clock pulses to that of
the input data pulses by narrowing the spectral width of the two BPFs to 0.80 nm.
3. Available degree of amplitude-noise reduction after the two-cascaded 3R gate scheme
First, Fig. 2 shows calculated eye diagrams and BERs with using 42-Gb/s pseudorandom data pulses. At the output of thetwo-cascaded PDSMZ gates [Figs. 2(c) and 2(d)], the amplitude noise in the 1-bit pulses was remarkably suppressed in comparison
with that at the input of the first PDSMZ gate. The amplitude noise in the 0-bit pulses was also suppressed. As a result, the range of thedecision threshold that suppressed the bit error rate to below 10-6 was significantly expanded after this 3R regeneration [Fig. 2(f)]. The
slope shape of the ‘noise’ distribution after the 3R gate clearly differed from that of the standard amplifiers. (As a consequence of thisshape of noise distribution, the standard Q-factor may not be a good measure for evaluating this type of regeneration systems.)
For reference, Figs. 3(a) and 3(b) show calculated waveforms of the ‘100’-encoded clock pulses and the carrier-density oscillation
under these optimum gating conditions. The so-called time-differential interference in Fig. 2 occurred as a consequence of a nonlinear
optical phase shift of 0.36π induced by the carrier-density oscillation in Fig. 3(b), according to our calculation.
Second, we studied how this regenerator would tolerate to each of the gating conditions and what kinds of distortion and/orpattern-induced noise would outside the tolerance range, as follows. (1) When we broadened the width of the clock pulses from 3.0 ps
to 5.0 ps, for example, several transient leakage components were observed in the ‘100’-encoded waveform [Fig. 3(c)]. (2) When weweakened the input clock power, another type of leakage components was observed [Fig. 3(d)]. (3) When we changed the width of theinput data pulses in the range of 6-9 ps in contrast, the distortion in the waveform and eye diagram was relatively small. (4) We also
investigated how the regenerator tolerates to the input timing of the data pulses.
4. Conclusion
We studied available degree of amplitude-noise suppression capability and possible waveform distortion outside the tolerance
ranges, after building a theoretical design model of the cascaded-PDSMZ optical-3R scheme. The degree of noise suppression wasevaluated by calculating the bit error rates to below 1×10-6, for the first time to our knowledge. These modeling techniques will be
useful for designing all kinds of ultrafast SOA-based interferometric gates and for supporting experimental research activities withlimited monitoring equipments.
References: [1] A. E. Kelly, et al.., Electron. Lett. 35 (1999) 1477, [2] Y. Ueno, et al., IEEE PTL 13 (2001) 469, [3] K. Tajima, et al., Appl. Phys. Lett. 67 (1995) 3709, [4]H.J. Thiele, et al., Electron. Lett. 35 (1999) 230, [5] M. Tsurusawa, et al., OFC 2003, ThX3, [6] Y. Hashimoto, et al., ECOC 2003, Mo 4.3.3, [7] R. Inohara, et al., ECOC
2004, We 2.5.3, [8] J. Sarathy, OFC 2005, OThE1, [9] S. Nakamura, et al., IEEE PTL 12 (2000) 425, [10] Y. Ueno, et al., IEICE Trans. Electron. E86-C (2003) 731, [11] Y.
Ueno, Opt. Comm. 229 (2004) 253, [12] R. Suzuki, et al., OECC 2004, 13E2-1, [13] Y. Ueno, et al., J. Opt. Soc. Am. B19 (2002) 2573.

Fig. 1: The two-cascaded PDSMZ-type 3R gate scheme [5-7]MB3

Table 1: The parameters used in this work.
width: full width at half maximum.
Description

Value

Input data's pulse width
Input data's pulse energy
Input clock's pulse width
Input clock's pulse energy
Unsaturated gain of SOAs, G0
Gain saturation energy of SOAs, PsatCarrier lifetime of SOAs, τcNominal injection current, Iop
Enhanced current injection to the SOAs
Injection enhancement factor
Interferometer delay time, ∆tInterferometer phase bias, ∆ΦbNonlinear phase shift, ∆ΦNL
Width of the bandpass filter
Regenerated data's pulse width

6.0 ps @42 Gb/s
100 fJ
3.0 ps
400 fJ
28 dB
180 fJ
50 ps
150 mA
440 mA
2.9
14.7 ps (61.7%)
1.0π0.36π
0.80 nm (Gaussian)
6.4 ps0.8“1”“0” (a)

0.6
0.4
0.2
0.0-40-20

0.8+0+20+40Time (ps)1.0

Intensity (a. u. )

“0”

“1”

“0”

“0” (c)

0.6
0.4
0.2
0.0-40-20+0Time (ps)

1.0
0.8

“0”

+20+40“1”“1” (b)

0.6
0.4
0.2
0.0-40-20

1.0

Intensity (a. u. )Intensity (a. u. )1.0

Carrier density (a. u. )Fig. 2: Calculated eye diagrams and BERs with 42-Gb/s random data pulses(a), (b): Input data pulses.
(c), (d): Logic-inverted data at the output of the first PDSMZ gate.
(e), (f): Regenerated, non-inverted data at the output of the two-cascaded PDSMZ gates.
Dashed curves in (d) and (f) indicate the BERs in (b), for comparison.

0.8

“1”

0Time (ps)

“0”

2040

“0” (d)

0.6
0.4
0.2
0.0
-40

-20+0+20+40

Time (ps)Fig. 3: Calculated 42-Gb/s waveforms(a): Clock pulses after being encoded by 6.0-ps “001” data pulses (before broadened by the BPF).
(b): Carrier-density oscillation with the optimum conditions. Dashed curve: input data pulses “011”.
(c): Encoded clock pulses where the input clock pulse’s width was too broad (5.0 ps).
(d): Regenerated data waveform where the input clock pulse’s power was too small.