Theoretical and Experimental Analysis of Burst-Mode Wavelength Conversion via a Differentially-Biased SOA-MZI

Abstract

This paper presents a theoretical and experimental analysis of an all optical Burst Mode Wavelength Converter (BMWC), exploiting a deeply saturated differentially biased Semiconductor Optical Amplifier - Mach-Zehnder Interferometer (SOA-MZI) configuration to provide both power equalization and wavelength conversion (WC) for intensity modulated input signals. The device operation and performance have been mathematically analyzed through a novel theoretical framework that considers finite extinction ratio signals entering a deeply saturated differentially biased SOA-MZI. Based on the theoretical model, the BMWC is capable of both power equalization and WC of intensity modulated input pulses with > 9 dB loud/soft ratio. The theoretical results were verified experimentally for 10 Gb/s Non-Return to Zero (NRZ) intensity modulated data, revealing successful power equalization and WC for up to 8 dB loud/soft ratio, almost perfectly matching the theoretical analysis. Its burst-mode WC credentials were then experimentally validated in realistic non-dispersion compensated transmission links with 10Gb/s NRZ data packets propagating over differential distances of 14 km and 25 km SSMF (Standard Single Mode Fiber), providing error free operation with 2.3 dB and 2.2 dB BER improvement respectively. Finally, the BMWC performance was also experimentally evaluated with 20 Gb/s NRZ data packets with up to 5 dB loud/soft ratio for a wavelength span of up to 8.3 nm, revealing for the first-time simultaneous power equalization and WC at 20 Gb/s data rates with NRZ data.

Full text

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
Abstract— This paper presents a theoretical and experimental
analysis of an all optical Burst Mode Wavelength Converter
(BMWC), exploiting a deeply saturated differentially biased
Semiconductor Optical Amplifier - Mach-Zehnder Interferometer
(SOA-MZI) configuration to provide both power equalization and
wavelength conversion (WC) for intensity modulated input
signals. The device operation and performance have been
mathematically analyzed through a novel theoretical framework
that considers finite extinction ratio signals entering a deeply
saturated differentially biased SOA-MZI. Based on the theoretical
model, the BMWC is capable of both power equalization and WC
of inten sity modula ted i nput pulses with > 9 dB lo ud/s oft r atio. The
theoretical results were verified experimentally for 10 Gb/s Non-
Return to Zero (NRZ) intensity modulated data, revealing
successful power equalization and WC for up to 8 dB loud/soft
ratio, almost perfectly matching the theoretical analysis. Its burst-
mode WC credentials were then experimentally validated in
realistic non-dispersion compensated transmission links with
10Gb/s NRZ data packets propagating over differential distances
of 14 km and 25 km SSMF (Standard Single Mode Fiber),
providing error free operation with 2.3 dB and 2.2 dB BER
improvement respectively. Finally, the BMWC performance was
also experimentally evaluated with 20 Gb/s NRZ data packets with
up to 5 dB loud/soft ratio for a wavelength span of up to 8.3 nm,
revealing for the first-time simultaneous power equalization and
WC at 20 Gb/s data rates with NRZ data.
Index Terms—Burst mode switches, intensity modulation,
power equalization, semiconductor optical amplifier-mach-
zehnder interferometer, wavelength conversion.
Manuscript received Month XX, 2019; revised Month XX, 2019; accepted
Month XX, 2019. Date of publication Month XX, 2019; date of current version
Month XX, 2019. This work was supported by the EC through H2020 projects
5GPPP PhaseII 5GPHOS (Contract 761989) and MSCA ITN 5G STEP-FWD
(Contract 722429).
A. Tsakyridis, M. Moralis-Pegios, C. Vagionas, E. Ruggeri, G. Mourgias-
Alexandris, A. Miliou and N. Pleros are with the Department of Informatics,
Aristotle University of Thessaloniki, Thessaloniki 54621, Greece and Center
for Interdisciplinary Research and Innovation (CIRI-AUTH), Balkan Center,
Buildings A & B, Thessaloniki, 10th km Thessaloniki-Thermi Rd, P.O. Box
8318, GR 57001 (emails: atsakyrid@csd.auth.gr, mmoralis@csd.auth.gr,
chvagion@csd.auth.gr, eugenior@csd.auth.gr, mourgias@csd.auth.gr,
amiliou@csd.auth.gr, npleros@csd.auth.gr).
I. INTRODUCTION
ll-optical signal processing has received significant
research interest during the last two decades [1]-[4], with
WC and regeneration modules [5]-[8] standing out due to their
unique advantages in terms of enhanced network versatility and
inherent support of long transmission distances. Among
alternative WC implementations, SOA-based devices offer a
unique set of advantages i.e high data rate operation [9]-[12],
easy integration [13] and low footprint. However, previous
high-data rate SOA-based WC demonstrations, confined by
SOA-gain recovery time limitations, favored the Return-to-
Ze ro (RZ ) data forma t, ach ievin g data ra tes up to 320 Gb/s [14]-
[19], by leveraging either cross-gain Modulation (XGM) or
cross-phase modulation (XPM) phenomena. Nevertheless, with
NRZ data formats being the dominant and favored format in
commercial optical networks, research efforts shifted towards
SOA-based WC elements that could reach high data rates even
when employing NRZ data formats [20]-[23].Within this scope,
the differentially-biased SOA-MZI scheme [23] offered the best
available WC and regeneration performance, with previous
demonstration achieving record-high operational speeds of 40
Gb/s, while providing high cascadability potential [24].
Demarcating, however, from lab-based experimental
demonstrations towards realistic optical networks, the bursty
nature of the traffic circulated between the optical nodes forms
a significant challenge, as asynchronous variable-length data
packets with intense power variation are arriving at the node
ingress. In this case, wavelength based-routing should also be
accompanied with power equalization capabilities on a per
packet basis, in order to ensure balanced optical power levels of
the traffic to the next segment of the network. To this end,
several burst mode SOA-based schemes have been proposed
[25]-[31], with the majority of them employing the RZ data
format when targeting linerates beyond 10 Gb/s [25]-[27].
However, when NRZ burst-mode operation is required, such as
in reach extender applications for PON uplink transmission or
5G digital fronthaul architectures [32], SOA-based WC
schemes have been limited to 10 Gb/s operational data-rates
[28]-[31]. It should be noted , that previously proposed burst-
mode Erbium Doped Fiber Amplifier (EDFA)-based schemes
[33],[34] could be utilized in conjunction with a WC, to offer
Theoretical and experimental analysis of Burst-
mode Wavelength Conversion via a
Differentially-biased SOA-MZI
A. Tsakyridis, M. Moralis-Pegios, C. Vagionas, E. Ruggeri, G. Mourgias-Alexandris, A. Miliou and
N. Pleros
A

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the same power equalization and WC functionality, yet at a cost
of increased complexity and power consumption.
In this paper, we present, for the first time to the best of our
knowledge, a detailed theoretical and experimental analysis of
a BMWC that relies on a deeply saturated differentially-biased
SOA-MZI. This device can provide burst-mode WC operation
at up to 20 Gb/s linerates even for NRZ data packets, using a
single SOA-MZI device in a differentially-biased layout, where
both SOAs are forced to operate in their strongly saturated
regime [23],[35]. Combining the high-quality WC
characteristics of the differentially-biased SOA-MZI scheme
with the clipping properties of the SOA-MZI non-linear transfer
function emerging in the strongly saturated semiconductor
region, wavelength conversion can be accompanied with strong
power equalization capabilities in a single device, decreasing
the number of required active elements by 50% compared to
state of the art BMWCs [31]. A detailed mathematical analysis
has been carried out for the BMWC operation and its
performance by expanding the equations of a differentially
biased SOA-MZI in strongly saturated conditions, revealing
successful power equalization of intensity modulated pulses for
>9 dB loud/soft ratio. It should be noted that the loud/soft ratio
denotes the maximum ratio between the operable power levels
of the strongest (loud) and weakest (soft) signals from the input
packets and as such can be directly used for assessing the
device’s functionality across strenuous network environments.
The theoretical outcomes were validated with experimentally
acquired results for 10 Gb/s NRZ data packets with up to 8 dB
loud/soft ratio, revealing almost perfect matching between
theory and experiment. Moreover, the device was tested under
realistic non-dispersion compensated 14 & 25 km Standard
Single Mode Fiber (SSMF) transmission links achieving error
free operation with a 2.3 dB and 2.2 dB BER improvement
respectively, reinforcing its potential to perform successfully in
realistic burst-mode traffic conditions or PONs, where both
propagation losses and dispersion accumulation vary on a
packet level with typical operating fiber length up to 25 km
[36]. Finally, the BMWC’s broadband operation was
investigated for 20 Gb/s NRZ data packets with 5 dB loud/soft
ratio and an input wavelength range of 8.3 nm, achieving burst-
mode operation with the highest yet reported operational speed
for NRZ traffic, while offering at least 2.39 dB power BER
improvement.
II. THEORETICAL ANALYSIS
In this section a brief qualitive description of the operation of
the BMWC will be provided, followed by a detailed theoretical
analysis that relies on the first-order perturbation theory applied
onto the semiconductor gain and phase responses, which has
already been employed as a reliable mathematical framework
for analyzing SOA-based device non-linear dynamics in the
time-domain [37] and frequency domain [23],[38],[39]. The
layout of the BMWC is presented in Fig. 1 (a). A SOA-MZI
operating in its strongly saturated regime is configured in a
differentially biased scheme [35] in order to perform both
power equalization and wavelength conversion. The SOA-MZI
comprises two separate optical paths, with each one
incorporating a SOA as the nonlinear optically controlled active
element. A Continuous Wave (CW) with optical power 𝑃 is
injected to the input B of the SOA-MZI, while two other CWs,
i.e CW1 and CW2 are being fed into SOA1 and SOA2 as
auxiliary holding beams, through ports E and D respectively.
Moreover, all three CW signals have sufficiently high optical
power levels enforcing both SOA1 and SOA2 to operate in the
strongly saturated regime. The injection of the appropriate
amount of power of CW1 and CW2 beams at SOA1 and SOA2
respectively, leads to a differential gain between the two SOAs
that corresponds to a π differential phase-shift between the two
SOA-MZI branches. So, at the steady state conditions and in the
absence of any control pulse, the incoming input signal exits the
gate through port F, henceforward denoted as the switched port
(S-port). The control signal of power 𝑃 entering the device
gets split in an optical coupler with the two resulting
constituents being forwarded to both SOA-MZI branches, with
its Pctr1 control signal constituent being attenuated by a factor
equal to B prior being launched as a co-propagating signal into
SOA1 and the x-branch of the SOA-MZI. The Pctr2 signal gets
inserted as a counter-propagating signal into SOA2 and the y-
branch of the SOA-MZI.
To ease our device description, a schematic illustration of the
BMWC principle of operation comprising the input/output
signals as well as the SOAs’ gain and phase response is
illustrated in Fig. 1 (b)-(e). Fig. 1 (b) depicts the power level of
a pulsed control signal that comprises two successive optical
pulses with unequal power levels and gets inserted into the
SOA-MZI. Fig. 1 (c) depicts the time evolution of the gain
response of both the upper and lower SOA modules, clearly
illustrating that in the absence of any control pulse the two SOA
gains have different values, while both SOA gains are driven to
Fig. 1 (a) BMWC layout, (b) intensity modulated control pulses, (c) gain
response of the two SOAs over time, (d) phase response of the two SOAs ove
r
time, (e) output switched signal.

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their unitary end-point when a control pulse enters. This can
take place when having a peak power for the lower control pulse
that is still high enough for depleting the SOA gain and reaching
its unitary value, immediately implying that also the higher
control pulse will be strong enough to drive the SOA gain to its
unitary value. Fig. 1 (d) shows the time evolution of the
respective phase response experienced at both SOA-MZI
branches, revealing that the initial π differential phase bias
stemming from the different steady-state SOA gain values
becomes zero during control pulse injection, following the
principle described in [40]. Assuming that the low intensity
optical control pulse has enough power to drive the SOA gain
to transparency then obviously any optical control pulse will
also yield to unitary SOA gain values, suggesting that optical
control pulses with different intensity levels will yield the same
𝛥𝜑𝑡 = 0 phase difference between the two SOA-MZI arms.
This will result to a perfect "zero" level at the switched output
port F of the SOA-MZI, with the respective F port output
sequence being depicted in Fig. 1 (e). As it can be observed, this
sequence is an inverted but power equalized copy of the original
control pulse stream, which had strongly intensity modulated
pulses, revealing the simultaneous WC and power equalization
properties of the BMWC.
The following mathematical analysis aims to provide
theoretical insight into the switching mechanism of the device
and investigate the intensity modulation of the switched
waveform, when intensity modulated NRZ (Non-Return to
Zero) pulses are used as control signals. Moreover, the
theoretical analysis has the main target of extracting the
frequency domain transfer function of the device so as to
calculate the transmission coefficient for every possible
harmonic that contributes to the amplitude modulation. Also, as
it well known from systems and signal theory, transfer function
extraction has to be carried out over a sinusoidal input signal
and this has been the main reason that we have considered here
a sinusoidal dependence on modulation frequency for the
control signal which forms the input in our system [23],[41].
Defining as 𝑃 the incoming CW input signal power and, as
𝐺𝑡and 𝐺𝑡 the power gains experienced by the CW signal
in each SOA in the upper and lower branch of the SOA-MZI,
respectively, the switched optical power at the switched port is
expressed as:
𝑃𝑡

𝐺𝑡𝐺𝑡2𝐺𝑡∗𝐺𝑡∗cos𝛥𝜑𝑡
(1)
In (1), 𝛥𝜑𝑡 represents the phase difference between the two
CW components and is expressed as in [42] by:
𝛥𝜑𝑡
ln𝐺𝑡/𝐺𝑡 (2)
with 𝑎 denoting the linewidth enhancement factor of each SOA.
Considering operation at the steady state conditions, in which
𝐺𝑡𝐺𝑐𝑤1, 𝐺𝑡𝐺𝑐𝑤2 and 𝛥𝜑𝑡𝜋 , then using (2)
it can be derived that
𝐺exp
∗𝐺 . (3)
The two optical control pulses that are injected through ports
A and H of the SOA-MZI respectively, are considered to have
a finite extinction ratio and be intensity modulated at both
logical power levels ‘1’ and ‘0’, with the respective modulation
indexes being 𝑚 and 𝑚. The following mathematical
equations describe the input signal as well as its average,
minimum and maximum values, with 𝛺 denoting the
modulation frequency, 𝑇 the bit period, 𝑎𝑡 representing the
pulse waveform and 𝑖 referring to the power levels ‘1’ and ‘0’.
𝑃""𝑡𝑃∗1𝑚∗cos𝛺𝑇∗𝑎𝑡, with
𝑃""𝑃,
𝑃""𝑃∗1𝑚
𝑃""𝑃∗1𝑚, where i=0,1 (4)
It should be noted, that the bit period is assumed to be greater
than the SOA stimulated carrier recombination time, which has
been reported to be in the order of some picoseconds, with prior
demonstrations achieving even 40 Gb/s operation with current
semiconductor technology [23].
Considering the SOA-MZI control pulses, the two cases
where a logical 1 and a logical 0 are injected as control signal
are analyzed separately. In case 𝑃 is at logical power level
‘0’, and taking into account that the control signal injected into
SOA1 contains identical information but attenuated by a factor
B in comparison with the one injected into SOA2, the gains
𝐺𝑡 and 𝐺𝑡 of the two SOAs at ‘0’ power level can be
expressed as
𝐺𝑡 11 
exp𝐵∗


 
(5)
𝐺𝑡11 
exp


 
(6)
where 𝑈 is the saturation energy of SOA1 and SOA2,
considered equal for the rest of this analysis.
In order to avoid pulse-shape distortions in the switched
signal, the maximum value of 𝑃𝑡 must temporally coincide
wi th the min imum v alue o f 𝐺𝑡, 𝐺𝑡, for every respective
control pulse, which in turn corresponds to the moment 𝑡,
where the whole pulse energy has been inserted into the SOA.
This condition, in conjunction with the assumption that the
amplifier is a spatially concentrated device, allow for the
replacement of the time-dependent 𝑎𝑡𝑑𝑡′

 with a time-
independent, constant value 𝐴. So, now the equations (5) and
(6) can be expressed as:
𝐺𝑡11 
 exp∗∗∗∗
 
(7)
𝐺𝑡11 
exp∗∗∗
 
(8)
To this end, the signal that appears at the switched port of the
SOA-MZI, and its phase, after inserting equations (7) and (8)
into (1), are provided by:

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𝑃𝑡
𝐺𝑡𝐺𝑡2𝐺𝑡∗𝐺𝑡∗
cos 𝛥𝜑𝑡 (9)
𝛥𝜑𝑡
ln𝐺𝑡/𝐺𝑡 (10)
By properly biasing the SOA-MZI and assuming that 𝑃 is
significantly lower than 𝑃,, the maximum value of equation
(9) occurs when the power at the logical ‘0’ level is minimum,
i.e. 𝑃""𝑃∗1𝑚0, while the minimum value of (9)
when the power of the ‘0’ level is maximum, i.e. 𝑃""𝑃∗
1𝑚0, and the average value of (9) when 𝑃"" 𝑃. As
such, inserting these values in equations (7) and (8) the resulting
gain values, phase and the respective output switched waveform
for each case are given by:
𝐺
""𝑡11 
exp∗∗""
  (11)
𝐺
""𝑡11 
exp∗""
  (12)
𝛥𝜑""
ln𝐺
""𝑡/𝐺
""𝑡 (13)
, where (j,i)=(max,min),(min,max),(avg,avg)
Equivalently, in case 𝑃 is at logical power level ‘1’, and
taking into account the same assumptions that were used for the
case of 𝑃 at logical power level ‘0’, the gains of the two
SOAs at power level ‘1’ can be expressed as
𝐺𝑡11 
exp∗∗∗∗
 (15)
𝐺𝑡11 
exp∗∗∗
  (16)
While the corresponding expression for the switched output
power and the phase are:
𝑃𝑡
𝐺𝑡𝐺𝑡2𝐺𝑡∗𝐺𝑡∗
cos 𝛥𝜑𝑡 (17)
𝛥𝜑𝑡
ln𝐺𝑡/𝐺𝑡 (18)
Given that the SOA-MZI employs the differential biased
scheme in strongly saturated conditions, when 𝑃 is at
logical power level ‘1’, the phase shift between the two arms
becomes zero. As such, setting equation (18) equal to zero and
solving for 𝐺 results in:
𝐺𝑡𝐺𝑡. (19)
Based on the aforementioned expression, equations (15) and
(16) are equal, resulting after exploiting equation (3) to:
∗ 
ln

  /1𝐵, (20)
Considering the switched waveform output, as it can be
observed through equation (17), when the control signal is at
the logical power level ‘1’, or equivalently when 𝑃""𝑡
𝑃""𝑃, it leads to a zero phase difference 𝛥𝜑𝑡=0 and the
𝑃
""𝑡𝑃
4⎣
⎢
⎢
⎢
⎢
⎢
⎡
11 1
𝐺𝑐𝑤1exp𝐵∗𝐴∗𝑃""
𝑈𝑠𝑎𝑡 11 1
exp2𝜋
𝛼∗𝐺 exp𝐴∗𝑃""
𝑈𝑠𝑎𝑡 
 211 1
𝐺𝑐𝑤1exp𝐵∗𝐴∗𝑃""
𝑈𝑠𝑎𝑡 ∗11 1
exp2𝜋
𝛼∗𝐺 exp𝐴∗𝑃""
𝑈𝑠𝑎𝑡 
∗𝑎2𝑙𝑛 11 1
𝐺𝑐𝑤1exp𝐵∗𝐴∗𝑃""
𝑈𝑠𝑎𝑡 
11 1
exp2𝜋
𝛼∗𝐺exp𝐴∗𝑃""
𝑈𝑠𝑎𝑡 ⎦
⎥
⎥
⎥
⎥
⎥
⎤
24
𝑃
""𝑡𝑃
4⎣
⎢
⎢
⎢
⎢
⎢
⎡
11 1
𝐺𝑐𝑤1exp𝐵∗𝐴∗𝑃""
𝑈𝑠𝑎𝑡 11 1
exp2𝜋
𝛼∗𝐺 exp𝐴∗𝑃""
𝑈𝑠𝑎𝑡 
 211 1
𝐺𝑐𝑤1exp𝐵∗𝐴∗𝑃""
𝑈𝑠𝑎𝑡 ∗11 1
exp2𝜋
𝛼∗𝐺 exp𝐴∗𝑃""
𝑈𝑠𝑎𝑡 
∗𝑎2𝑙𝑛 11 1
𝐺𝑐𝑤1exp𝐵∗𝐴∗𝑃""
𝑈𝑠𝑎𝑡 
11 1
exp2𝜋
𝛼∗𝐺exp𝐴∗𝑃""
𝑈𝑠𝑎𝑡 ⎦
⎥
⎥
⎥
⎥
⎥
⎤
14

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5
output switched waveform is equal to 0. However, when the
powers of the control pulses are different than 𝑃"", i.e.
𝑃""𝑃∗1𝑚1, 𝑃""𝑃∗1𝑚1, the value of
the output switched waveform has to be calculated. To this end,
the gain and the phase of the two SOAs are given by
𝐺
""𝑡11 
exp∗∗""
  (21)
𝐺
""𝑡11 
exp∗""
  (22)
𝛥𝜑"" 
ln𝐺
""/𝐺
"" (23)
, while the output switched waveform is provided in the bottom
of this page, where 𝑗𝑚𝑎𝑥,min. So, the maximum,
minimum and average value of the output switched waveform
are finally given by:
𝑃
""𝑡max 𝑃
"",𝑃
"") (25)
𝑃
""𝑡 min 𝑃
"",𝑃
"") (26)
𝑃
""𝑡𝑃
""𝑡/2 (27)
Fig. 2 provides a visual representation of the device
functionality depicting how the input pulses translate into the
inverted output pulse sequence. More specifically, Fig. 2 (a)
illustrates the transfer function of the device switched port
versus the power of the control signals. The same graph
illustrates also the different power levels of the control signal
sequence over time, clearly highlighting the “𝑚𝑖𝑛” “𝑚𝑎𝑥” and
“𝑎𝑣𝑔” value for both the “0” and the “1” power levels as well
as the minimum and average extinction ratio values, defined as:
𝐸𝑅
""= ""
"" = ∗
∗ (28)
𝐸𝑅
""= ""
"" = 
 (29)
Applying this transfer function to the incoming control pulse
peak powers gives the switched output pulse sequence at the S-
port of the device, which is shown in Fig. 2 (b). It is worth
mentioning that in case of 𝑃""𝑡𝑃""𝑃, the output
switched power 𝑃0 as has already been noted, due to the
differential biased scheme. Moreover, 𝑃"" must be always
lower than 𝑃"", in order to have a reasonable value of
𝐸𝑅
"". Defining again the average and minimum ER values
in the output pulse sequence, as shown in the figure, one gets
the following expressions:
𝐸𝑅
""= 
""

"" (30)
𝐸𝑅
""= 
""

"" (31)
By introducing the expressions of 𝑃
""𝑡 and 𝑃
""𝑡
provided by equations (14) and (24) for 𝑗𝑚𝑖𝑛 and 𝑗𝑎𝑣𝑔
into the equations (30) and (31), respectively, the 𝐸𝑅
"" and
𝐸𝑅
"" expressions become functions of 𝑃, 𝑃, 𝑃, 𝑚, 𝑚,
𝐵, 𝑎, 𝐺𝑐𝑤1, 𝐴, and 𝑈𝑠𝑎𝑡.
In order to evaluate the intensity equalization properties of
the BMWC, we introduce a new figure of merit, called
Extinction Ratio Variation (𝐸𝑅𝑉) and given by the following
expressions for the input and output pulse sequences:
𝐸𝑅𝑉10∗log
""

"" (32)
𝐸𝑅𝑉 10∗log
""

"" (33)
The ERV provides an accurate description for the peak power
uniformity taking into account both the variations at the “1” and
“0” power levels, with a value of 𝐸𝑅𝑉0, designating the
ideal case where the ER value is identical along the entire pulse
sequence without experiencing any minimum value that is
different from its average. Based on the above definitions, if the
output 𝐸𝑅𝑉 is greater than the input 𝐸𝑅𝑉, the optical power
intensity variation of the signal traversing the BMWC is
minimized, corresponding to successful power equalization.
𝐸𝑅𝑉 can be expressed as 𝐸𝑅𝑉
 , after the
insertion of (28), (29) into the equation (32). It should be noted
that the modulation index at logical level ‘1’ represents the
intensity modulation of the incoming pulses, from which using
equations (4), the loud/soft ratio of the incoming packet can be
derived and expressed as 𝑙𝑜𝑢𝑑/𝑠𝑜𝑓𝑡 𝑟𝑎𝑡𝑖𝑜  10 ∗
log
 . At the same time, inserting the 𝐸𝑅
"" and
𝐸𝑅
"" expressions from equations (30) and (31) into equation
(33), the 𝐸𝑅𝑉 expression turns also into a function of the
𝑃, 𝑃, 𝑃, 𝑚, 𝑚, 𝐵, 𝑎, 𝐺𝑐𝑤1, 𝐴, and 𝑈𝑠𝑎𝑡 variables.
The results of the theoretical analysis are illustrated in Fig. 3.
Fig. 3 (a) depicts the 𝐸𝑅𝑉 for different intensity modulation
indexes m0, plotted against the loud/soft ratio of the incoming
signal, that can be derived by using equation (4) and the m1
intensity modulation index of the logical ‘1’ power levels. As
can be observed, as m0 and/or the loud/soft ratio increases, the
𝐸𝑅𝑉 decreases suggesting that the pulse peak power
variations at the BMWC output will become stronger. This
behavior is expected since the numerator and denominator of
𝐸𝑅
"" in its expression in eq. (28) decreases and increases
respectively. Moreover, this graph illustrates the close
correlation of the 𝐸𝑅𝑉 value with signal quality, which is
Fig. 2 (a) Output switched power vs control power, and control power vs time
(b) Output switched power vs time.

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6
heavily degraded due to the high intensity modulation of ‘0’ and
‘1’ power levels, respectively. Figure 3 (b) assesses the
performance of the BMWC in terms of 𝐸𝑅𝑉 for different
Gcw1 and different incoming control signal loud/soft ratio and
it is depicted with solid lines. The linewidth enhancement factor
α was chosen to have a value of 6, which is in the range of
typical values reported in the literature [44]. The ratio of P1/P0
and the attenuation factor 𝐵 value, were 10 and 0.1,
respectively. The constant value 𝐴 and 𝑃 and the saturation
energy 𝑈𝑠𝑎𝑡 of the SOAs were chosen to be 100, 10 and 1000,
respectively.
As 𝐺𝑐𝑤1 decreases, the SOAs are driven deeper in
saturation, and an improved power equalization performance is
obtained over an increased range of loud/soft ratio values. For
example, for 𝐺𝑐𝑤1=2, the value of 𝐸𝑅 is -2.5 dB and
remains almost constant for loud/soft ratios up to 9 dB. As
𝐺𝑐𝑤1 increases and the SOA operation moves into its small-
signal gain regime, the power equalization properties gradually
degrade, with 𝐸𝑅𝑉 values remaining, however, lower than -
4 dB for the entire range of input signal loud/soft ratios as long
as the SOA steady-state gain (𝐺𝑐𝑤1) remains below 10.
Figure 3 (c) evaluates the theoretical performance of the
BMWC in terms of 𝐸𝑅𝑉 for different attenuation factor 𝐵
and for different loud/soft ratio in the same way as in Fig. 3 (b).
The operational values of the BMWC were, 𝑎 =6, 
 =10 and
𝐺𝑐𝑤1=2. As it can be observed, as the attenuation factor 𝐵
increases, the equalization performance decreases, e.g.
𝐸𝑅𝑉 is -6 dB for 𝐵=0.9. The above behavior was
theoretically expected, since the gains of the two SOAs at the
steady state are different. Fig. 3 (d), (e) and (f) illustrate the
normalized output-versus-input power for different linear gains
𝐺𝑐𝑤1=2, 𝐺𝑐𝑤1=10 and 𝐺𝑐𝑤1=1000 respectively. As the SOAs
are driven in strongly saturated conditions, they provide low
gains in the range of 2 to 10, and the transfer function of the
SOA-MZI has a non-linear shape almost parallel to the x axis,
as shown in Fig. 3 (d) and (e). In this case, the output power
decreases with the control pulse energy until a zero phase shift
is obtained, but then greater control pulse energies cause zero
phase shift, since the semiconductor is forced to operate near
the material transparency and does not allow for gain values
lower than unity. On the other hand, as 𝐺𝑐𝑤1 increases and the
SOAs move into their small signal gain regime, as shown in
Fig. 3 (f) where the 𝐺𝑐𝑤1=1000, the transfer function has the
well-known near-sinusoidal form that is responsible for low
values of 𝐸𝑅𝑉. In this case, the output power decreases with
the control pulse energy to the minimum value that corresponds
to a zero phase shift and then increases since the phase becomes
greater than zero. Finally, it is worth mentioning that in strongly
saturated conditions the input pulse energies are obviously
greater than the small signal gain regime of the SOAs.
III. EXPERIMENTAL VERIFICATION
The experimental setup employed for the verification of the
BMWC’s theoretical model is illustrated in Fig. 4, following
the design principles we reported in [43]. To ensure operation
of the SOAs in the deeply saturated conditions, two CW
auxiliary assist light holding beams at λas1=λas2=1548 nm and
powers of 7.13 dBm and -11.93 dBm were fed to the ports D
and E of the SOA-MZI respectively. As such, the two SOAs are
led to their saturation regimes, while a constant π phase shift
between the two arms is achieved due to differential biasing at
the steady state conditions. A CW beam at λ1=1550.4 nm, was
injected into two cascaded LiNbO3 modulators driven by
Programmable Pattern Generators (PPGs) with the first
producing two sequential 10 Gb/s PRBS7 packets, while the
second modulator was used to apply different power level to the
PRBS7 packets by changing its driver gain. The resulting signal
after amplification in an EDFA and filtering at a 3 nm
bandwidth Optical Bandpass Filter (OBPF) was injected into a
50:50 coupler. The two resulting copies were bit level
synchronized by an optical delay line in order to simultaneously
feed the two control ports A and H of the BMWC with powers
Fig. 4 Experimental setup for evaluating the BMWC, utilizing 10 Gb/s data
packets with up to 8 dB loud/soft ratio.
Fig. 3 (a) 𝐸𝑅𝑉 for different intensity modulation indexes 𝑚 and 𝑚, (b)
Theoretical (solid lines) and Experimental (square dots) values of 𝐸𝑅𝑉. for
different loud/soft ratio and Gain 𝐺𝑐𝑤1, (c) Theoretical (solid lines) and
Experimental (square dots) values of 𝐸𝑅𝑉. for different loud/soft ratio and
attenuation factor 𝐵. (d), (e) and (f) Normalized output power vs normalized
input pulse energy 
 for 𝐺𝑐𝑤1=2, 10 and 1000, respectively.

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7
of -0.8 dBm and 9.2 dBm respectively, effectively driving the
SOA-MZI in a push-pull configuration [23]. Finally, a CW
beam λ
2
=1549.3 nm was injected into the BMWC through port
B, as the input signal. The introduction of push-pull operation
in a strongly saturated regime, drives both SOAs close to their
gain transparency region, with completely identical gains and
phase levels between the two arms, resulting in a zero
differential phase shift and yielding strongly power equalized
output pulses. SOA1 and SOA2 were electrically driven with a
current of 268 mA and 330 mA, respectively, while SOA1
operating in the deeply saturated regime, featured an
attenuation factor 𝐵 of 0.1 and a gain 𝐺𝑐𝑤1 of 2.
The experimental results of the BMWC at 10 Gb/s are
depicted in Fig. 5. More specifically, Fig. 5 (a), (b) and (c)
illustrate the input traces of the incoming packets at 4, 6 and
8 dB loud/soft ratios respectively, showing two loud and three
soft packets interleaved, while Fig. 5 (d), (e) and (f) depict the
respective output traces where flat and equalized peak power
levels for all bits can be observed.
A comparison of the experimental results with the theoretical
projections, is illustrated in Fig.3 (b) and (c) in Section II of the
manuscript. Figure 3 (b) provides a comparison between the
theoretical derived results and the experimental results that are
depicted with solid lines and square dots respectively, revealing
strong convergence between the two measurements. It should
be noted, that the parameters of the experimental measurements
match with the theoretical measurements. Figure 3 (c) presents
a comparison between the experimental and theoretical data
measurements in the same way as in Fig. 3 (b) for different
attenuation factor 𝐵 and for different loud/soft ratio. The
operational values of the BMWC employed for both the
theoretical and experimental study, were, 𝑎=6,




=10 and
𝐺𝑐𝑤1=2. As it can be observed, the experimental results show
strong convergence with the theoretical derived curves for all
cases, validating successful power equalization for the
operational conditions with 𝐵=0.1.
IV. 10
G
B
/
S
BMWC
IN
14
KM
-
AND
25
KM
-L
ONG
F
IBER
T
RANSMISSION
E
XPERIMENTS
Following the theoretical analysis and its experimental
verification, the performance of the BMWC was investigated in
10 Gb/s NRZ non-dispersion compensated SSMF transmission
links of up to 25 km, towards evaluating the device’s
performance for both different loud/soft ratio optical packets
and different levels of accumulated dispersion.
Figure 6 illustrates the employed experimental setup,
incorporating two different scenarios one with 14 km and one
with 25 km SSMF, while the BWMC follows the same
operating principles as described extensively in Section II and
III. The two SOAs of the BMWC are each powered by a CW
assist-light beam, at λ
as1
=λ
as2
=1548 nm, through SOA-MZI
ports D and E respectively. Two separate signals at
λ
1
=1550.4 nm and λ
5
=1551.1 nm are combined in a 3 dB
coupler and injected into a PPG-driven Electro Absorption
Modulator (EAM) to produce a 284-bit pattern including one
optical data packet of 10 Gb/s PRBS7. The two signals were
then demultiplexed in an Arrayed Waveguide Grating (AWG),
and transmitted through two different optical paths of 14 or
25 km difference, with one of the branches featuring an Optical
Delay Line (ODL) for controlling the time synchronization of
the data. The two optical streams were then combined through
a 3 dB coupler into a single stream comprising two sequential
loud/soft PRBS7 packets of 127 bits, with an intermediate
guardband of 15 bits, towards an overall 284-bit long multi-
wavelength pattern. The resulting signal was amplified by an
EDFA and filtered by a 3 nm OBPF, and then split into two
identical copies through a 3 dB coupler before reaching the
BMWC device. The two signals were bit-level synchronized
through an ODL, so as to be simultaneously injected at the two
available control ports A and H of the SOA-MZI and act as
control signals of an optical push-pull configuration. A CW
beam at λ
2
=1549.3 nm was injected as input into the BMWC
through port B, while the SOAs were driven at 297 mA and
329 mA respectively. At various stages of the setup, Isolators
(ISO), Variable Optical Attenuators (VOA), ODLs and 99:1
couplers were used to control and optimize the operational
settings of the experiment, while Polarization Controllers (PC)
were utilized in order to handle the polarization gain
dependence of the SOA-MZI employed in the BMWC.
The results obtained for the 14 km fiber transmission
experiment are illustrated in Fig. 7. More specifically, Fig. 7 (a)
Fig. 7 Experimental results for 10 Gb/s packets and 14 km fiber transmissio
n
(a) input trace (3.5 μs/div), (b) input eye diagram (50 ps/div), (c) BMWC outpu
t
trace, (d) BMWC output eye diagram and (e) BER measurements with and
without BMWC.
Fig. 6 Experimental setup for testing the chromatic dispersion tolerance of the
BMWC with 14&25 km fiber transmission.
Fig. 5 Experimental results for 𝐺𝑐𝑤1=2 and 𝐵 =0.1, for 4 dB loud/soft ratio (a)
input trace (5 μs/div), (d) output trace (2 μs/div). For 6 dB (b) input trace, (e)
output trace. For 8 dB (c) input trace, (f) output trace.

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8
and (b) show the time traces and eye diagrams of the incoming
packet streams, exhibiting 3.5 dB loud/soft ratio due to the
propagation losses of the 14 km SSMF, and broadened pulses
stemming from the chromatic dispersion effect. The BMWC’s
output signal is illustrated in Fig. 7 (c) and (d), exhibiting
equalized peak power levels and an eye diagram with an ER of
6.5 dB. Fig. 7 (e) depicts the BER measurements for the 14 km
fiber transmission with and without the BMWC, revealing error
free operation with 2.3 dB BER improvement for the case of the
BMWC. The power levels of the control signals that were
injected through ports A and H, were measured to be -14.5 dBm
and 5.8 dBm respectively, while the input signal had an optical
power of 6.57 dBm. The power levels of λ
as1
and λ
as2
were
measured to be 8.58 dBm and 1.7 dBm respectively. The
difference in the optical power levels of the assist light beams
is purposely defined in order to set the SOA-MZI in the correct
biasing point, so as to operate both as a WC and an optical
power equalizer. More specifically, in the steady state
conditions, i.e. when no other control data signal is present,
such difference in the power levels allows setting the steady-
state gain levels of two SOAs in an asymmetrically biased
condition that corresponds to a constant differential phase shift
close to π between its two branches. To achieve this, the first
SOA needs to be deeply saturated in the transparency region,
i.e. allowing all the signal to simply pass through its waveguide
structure without any amplification, while the second SOA
needs to operate in a slightly less saturated condition with small
gain In addition, the SOA-MZI device employed in this
demonstration, as with all Optical Interferometers and Photonic
Integrated Chip is prone to fabrication processes (i.e. not
exactly ideal 50:50 splitting ratio) and temperature variations,
resulting in a not fully symmetric operation that has to be
compensated externally.
Equivalently, Fig. 8 illustrates the experimental results for
the 25 km SSMF transmission scenario. Fig. 8 (a) and (b) depict
the input trace and eye diagrams, exhibiting 6.25 dB loud/soft
ratio due to the losses of the 25 km long fiber transmission. The
output optical stream of the BMWC is depicted in Fig. 8 (c) and
(d), revealing power equalization of all bits with an ER of 6.4
dB. Moreover, the device’s performance was also evaluated
with the aid of BER curves, revealing error free operation with
a 2.2 dB BER improvement for the BMWC case. The power
levels of the control signals inserted through ports A and H,
were measured to be -4.3 dBm and 7 dBm respectively, while
the input stream had a 6.3 dBm. Considering the two CW assist-
light beams, λ
as1
optical power was 7.7 dBm and λ
as2
-3.6 dBm.
Finally, it is worth mentioning, that the BMWC could
potentially support higher transmission lengths, as the achieved
error-free operation at 8 dB loud/soft ratio effectively translates
to 40 km of transmission in SSMF with 0.2 dB/km propagation
losses when the dispersion related impairments are neglected.
When dispersion and pulse broadening are also taken into
account, then the BMWC will be capable of retaining
successful operation as long as the broader pulses will still
allow the saturated SOA gain to recover within the duration of
a single “0” bit.
V.
20
G
B
/
S
B
ROADBAND EXPERIMENT AND RESULTS
Figure 9 illustrates the experimental setup employed, for
assessing the high-speed and broadband operational spectrum
capabilities of the proposed BMWC. The experimental setup
follows the same layout and principles, as in the case of the
10 Gb/s experimental verification, described in Section III, but
scales in terms of operating speed, to reach 20 Gb/s NRZ data,
and wavelength variability by using a tunable laser source
(TLS) at the input signal. A CW beam at λ
1
=1550.4 nm was
injected into two cascaded LiNbO
3
modulators driven by two
PPGs, with the first producing two sequential 20 Gb/s PRBS7
packets and the second imprinting different power level
variations to the two packets, by changing its driver gain. The
resulting signal was amplified by an EDFA and filtered by a 3
nm OBPF, before being split into two identical signals by a 3
dB coupler that were injected into the BMWC as control signals
through ports A and H after bit level synchronization by an
Fig. 10 Experimental results for 20 Gb/s broadband testing of the BMWC (a)
input eye diagram with 5 dB loud/soft ratio, (b)–(f) output eye diagrams a
t
(1541-1549.3 nm). All eye diagrams are obtained at 20 ps/div. (g) BER
measurements before the BMWC (input) and after the BMWC for differen
t
input wavelength (1541nm-1549.3nm).
Fig. 9 Experimental setup for testing the broadband capabilities of the BMWC
at 20 Gb/s.
Fig. 8 Experimental results for 10 Gb/s packets and 25 km fiber transmissio
n
(a) input trace (3.5 μs/div), (b) input eye diagram (50 ps/div), (c) BMWC outpu
t
trace, (d) BMWC output eye diagram and (e) BER measurements with and
without BMWC.

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9
ODL. Two CW assist light beams λas1=λas2=1548 nm were fed
to the ports D and E of the BMWC, to ensure SOA operation in
the strongly saturated conditions. Finally, in order to test the
operating WC range of the BMWC, light from a TLS with a
varying wavelength of λ2 =1541-1549.3 nm was injected as
the input signal in port B. It is worth mentioning that, the
experimental procedure was carried out by optimizing, at first,
the BER for the reference wavelength (1549.3 nm), and then
evaluating the rest wavelengths, without altering the BMWC
electrical-optical driving settings.
The results obtained for the broadband experiment at 20 Gb/s
are depicted in Fig. 10. More specifically, Fig. 10 (a) illustrates
the input eye diagram with 5 dB loud/soft ratio, while Fig. 10
(b)-(f) depict the output eye diagrams for 5 different input
wavelengths, with a maximum spectral distance of 8.3 nm,
revealing successful power equalization and wavelength
conversion for all cases. The system performance was also
evaluated through BER measurements, illustrated in Fig. 10 (g)
revealing error free operation for all cases, with at least 2.39 dB
BER improvement. It should be noted, that the BER
measurement setup employed for the 20 Gb/s demonstration
differentiates from the one used in the 10 Gb/s case described
in section IV, comprising in the first case a 10 GHz InGaAs
linear APD paired with a 10 Gb/s BERT and in the second case
a 38 GHz InGaAs PIN paired with a 25 Gb/s BERT. As such,
the difference in the received optical power between these two
demonstrations, originates from the difference in the BER
measurement systems’ sensitivities being -26 dBm and -12
dBm, respectively. The power levels of the control signals
injected through ports A and H, were measured to be 0 dBm
and 6.08 dBm, respectively, while the input signal had an
optical power of 6.54 dBm. For the two-assist light beams the
power levels were measured at 8.63 dBm and 0.53 dBm,
respectively, while the SOAs operated in strongly saturated
conditions featuring driving currents of 297 mA and 330 mA,
respectively.
VI. CONCLUSIONS
In conclusion, we demonstrated a detailed theoretical and
experimental investigation of a BMWC, comprising a
differentially biased SOA-MZI in strongly saturated conditions,
towards simultaneous power equalization and wavelength
conversion. A novel theoretical platform was developed,
employing the first-order perturbation theory, revealing the
power equalization properties of the device, for > 9 dB loud/soft
ratio incoming optical packets. The theoretical analysis was
verified experimentally for 10 Gb/s data packets, while
comparison of the theoretical versus experimental derived
behavior, revealed strong convergence of theory and
experiment. The device performance was also investigated in
10 Gb/s NRZ, 14 km and 25 km long SSMF transmission links,
with the results reinforcing its credentials for applicability in
dispersion and loud/soft ratio intense data links. Finally, the
BMWC’s high speed and broadband performance was
evaluated using 20 Gb/s NRZ data packets with up to 5 dB
loud/soft ratio and up to 8.3 nm wavelength variation, achieving
for the first-time simultaneous power equalization and WC for
20 Gb/s NRZ data.
ACKNOWLEDGEMENTS
This work is supported by the European Commission through
H2020 projects 5GPPP Phase II 5GPHOS (contract 761989),
and MSCA ITN 5G STEP-FWD (contract 722429).
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