Optics Optik Optik Optik 116 (2005) 527–541 Investigation of SOA-assisted Sagnac recirculating shift register switching characteristics K.E. Zoiros , J. Vardakas, T. Houbavlis, M. Moyssidis Lightwave Communications Research Group, Department of Electrical and Computer Engineering, Democritus University of Thrace, 12 Vas. Sofias Street, GR 671 00, Xanthi, Greece Received 28 December 2004; accepted 30 March 2005 Abstract The switching characteristics of a Semiconductor Optical Amplifier (SOA)-assisted Sagnac recirculating shift register with an inverter are investigated by undertaking a numerical analysis that describes the dynamic gain response of the SOA to high speed and strong feedback optical pulses. The key performance parameters are identified and their role in the formation of the switching window is analyzed. The optimum values of these parameters are not unique and must be adapted to the specific all-optical shift register network application. For this reason, they must be properly selected and combined so as to ensure the satisfaction of the desired operating conditions. The technical restrictions that the derived values may impose on the state-of-the-art photonics technology are also discussed and efficient ways of overcoming them are proposed. r 2005 Elsevier GmbH. All rights reserved. Keywords: All-optical recirculating shift register; All-optical signal processing; Semiconductor optical amplifier (SOA); SOA- assisted Sagnac switch; Switching window 1. Introduction The unceasing bandwidth demand that is fuelled by the massive use of Internet and multimedia applications has spurred the development of ultrafast all-optical networks capable of offering large traffic capacities and supporting high-quality integrated services [1]. The main characteristic of these networks is that information remains exclusively in the optical domain along the communications path without opto-electrical (O/E) and electro-optical (E/O) conversions but only inevitably at the receiver nodes, thus eliminating the problem of electronic bottleneck [2] and opening the road for the performance of all-optical packet switching functions with the inherent advantages of bandwidth use on demand, flexibility and granularity [3]. A fundamental and indispensable building module for the implementa- tion of such networks is an all-optical memory [3,4], which is essentially a shift register that can perform several critical network processing tasks. More specifi- cally, it can be employed at the interface between users nodes and the optical backbone to store either low-rate multiplexed data packets until bandwidth on the network becomes available or high bit rate received data packets while they are rate converted so that they can be further processed by the available lower-speed ARTICLE IN PRESS www.elsevier.de/ijleo 0030-4026/$ - see front matter r 2005 Elsevier GmbH. All rights reserved. doi:10.1016/j.ijleo.2005.03.005 Corresponding author. Tel.: +30 25410 79 975; fax: +30 25410 79 595. E-mail address: [email protected] (K.E. Zoiros).
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ARTICLE IN PRESS
OpticsOptikOptikOptik 116 (2005) 527–541
0030-4026/$ - se
doi:10.1016/j.ijl
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Investigation of SOA-assisted Sagnac recirculating shift register
switching characteristics
K.E. Zoiros�, J. Vardakas, T. Houbavlis, M. Moyssidis
Lightwave Communications Research Group, Department of Electrical and Computer Engineering,
Democritus University of Thrace, 12 Vas. Sofias Street, GR 671 00, Xanthi, Greece
Received 28 December 2004; accepted 30 March 2005
Abstract
The switching characteristics of a Semiconductor Optical Amplifier (SOA)-assisted Sagnac recirculating shift registerwith an inverter are investigated by undertaking a numerical analysis that describes the dynamic gain response of theSOA to high speed and strong feedback optical pulses. The key performance parameters are identified and their role inthe formation of the switching window is analyzed. The optimum values of these parameters are not unique and mustbe adapted to the specific all-optical shift register network application. For this reason, they must be properly selectedand combined so as to ensure the satisfaction of the desired operating conditions. The technical restrictions that thederived values may impose on the state-of-the-art photonics technology are also discussed and efficient ways ofovercoming them are proposed.r 2005 Elsevier GmbH. All rights reserved.
The unceasing bandwidth demand that is fuelled bythe massive use of Internet and multimedia applicationshas spurred the development of ultrafast all-opticalnetworks capable of offering large traffic capacities andsupporting high-quality integrated services [1]. The maincharacteristic of these networks is that informationremains exclusively in the optical domain along thecommunications path without opto-electrical (O/E) andelectro-optical (E/O) conversions but only inevitably at
e front matter r 2005 Elsevier GmbH. All rights reserved.
the receiver nodes, thus eliminating the problem ofelectronic bottleneck [2] and opening the road for theperformance of all-optical packet switching functionswith the inherent advantages of bandwidth use ondemand, flexibility and granularity [3]. A fundamentaland indispensable building module for the implementa-tion of such networks is an all-optical memory [3,4],which is essentially a shift register that can performseveral critical network processing tasks. More specifi-cally, it can be employed at the interface between usersnodes and the optical backbone to store either low-ratemultiplexed data packets until bandwidth on thenetwork becomes available or high bit rate receiveddata packets while they are rate converted so that theycan be further processed by the available lower-speed
electronic circuits. Furthermore, it can facilitate packetheader recognition by buffering an incoming packetwhile its header is processed to investigate if it matches alocal address and to determine how it must be routed.Moreover, it can be placed in routers to queue incomingpackets before their turn for switching arrives so as toavoid packet contentions and destination conflicts at therouting ports. It can play also a role equivalent toelectronic shift registers as buffer for further processingof the data streams derived from the performance of all-optical Boolean logic functions. Finally, it can findapplication in the development of non-trivial complexall-optical circuits of enhanced functionality [5], such asan all-optical pseudo-random binary sequence generatorand an all-optical error counter, which in turn can beexploited for the demonstration of a high-speed, all-optical Bit Error Rate Tester.
Due to their multitasking capability and key role asnetwork elements, all-optical shift registers have at-tracted considerable research interest. Among thevarious all-optical shift register implementations, thosethat use a Semiconductor Optical Amplifier (SOA) andin particular in an interferometric configuration are verypromising for several reasons. Firstly, they are char-acterized by the attractive features of fast switchingtime, high repetition rate, low power consumption, noiseand jitter tolerance, compactness, thermal stability andhigh non-linear properties, which enable their efficientexploitation in a real ultra-high speed optical commu-nications environment [6]. Secondly, they have thepotential of being integrated, which in turn means thatthey can be repeatably and reliably manufactured andmassively produced so that they can be of commercialvalue and favorably compete with other bufferingsolutions [7]. Thirdly, they are operationally versatile,which means that they can be exploited in more complexall-optical signal-processing applications without signif-icantly changing their fundamental architecture [8].Finally, the storage/buffering time can be altered at willby simply adding or removing fiber without significantcost in power dissipation or energy loss [9].
In this paper, we investigate the switching character-istics of a regenerative, recirculating optical shift registerwith an inverter architecture that employs a SOA-assisted Sagnac switch [10]/Terahertz Optical Asym-metric Demultiplexer [11]. Although a model simulatingthis circuit has been presented [12,13], it focused mainlyon explaining and getting a deeper insight on itsbehavior by defining two modes of operation ratherthan exploring the dependence on its critical operationalparameters. It would be useful thus to investigate in anextensive and systematic manner how the performanceof this circuit, that is governed by factors such as theSOA small signal gain and carrier lifetime, the switchingpulses energy and width and the Sagnac loop asymme-try, can be improved and optimized. In order to achieve
this goal, a model is developed that describes propaga-tion and amplification of optical pulses through a SOAin an interferometric switch as well as the interaction ofthe SOA carriers with an intense optical field and isappropriately applied to the case of the specific shiftregister operating at 10GHz. The model is thennumerically solved to derive the switching window,which is the ultimate performance evaluation metric ofan all-optical interferometric configuration [14], andstudy the influence of the critical parameters on its widthand contrast so as to extract the conditions under whichthese two characteristics become optimum. The validityof the model is proved through comparison of thesimulated switching window against the availableexperimental one that reveals good agreement. Thisessentially implies that it can also be exploited tothoroughly analyze other more complex all-opticalsignal-processing circuits that employ semiconductor-based all-optical shift registers as the basic buildingblock, particularly in applications where more than onefeedback path may exist [15].
2. Principle of operation
The operation of the recirculating shift register can bebetter described with the help of the simplified blockdiagram of Fig. 1, which consists of a SOA-assistedSagnac switch arranged in such a way that its outputdrives its input. The switch consists of an optical loopmirror formed by the joined output ports of a 2� 2 3 dBcoupler and a SOA that is offset from the midpoint ofthe loop as the non-linear element. A clock pulse thatcan be provided by a pulsed laser (either a gain-switchedDFB or a mode-locked ring laser) enters the loopthrough the input port of the 3 dB coupler and is splitinto two counter-propagating pulses, the clockwise(CW) and counter-clockwise (CCW), of equal ampli-tudes and identical phases. The power of the clock signalis small enough so that it does not affect the opticalproperties of the SOA. In the absence thus of control/
ARTICLE IN PRESSK.E. Zoiros et al. / Optik 116 (2005) 527–541 529
switching pulses, the dynamics of the SOA remainunchanged and consequently its action is the same onthe two conjugate pulses when they pass through. Inthat case no phase difference is created between bothpulses and the whole configuration operates as asymmetric loop mirror resulting in the reflection of therecombined clock signal at the corresponding couplerport. The reflected signal is then appropriately amplifiedby an optical amplifier to obtain an energy of at least tentimes higher than that of the inserted clock signal [16]and is fed back to the switch as control signal. Thisamplifier can be either an EDFA [11], which results inlarge physical size of the shift register and consequentlyinhibits integration and impedes ‘‘on-the-fly’’ signalprocessing, or preferably a SOA [10], which due to itscompact size can minimize the time-of-the flight of theswitch and ensure reasonable access times to recirculat-ing information. The control and clock signals can bediscriminated by appropriately adjusting their polariza-tion states so that they are orthogonal to each other.This enables also the insertion and extraction of thecontrol signal in and from the loop using two polariza-tion selective couplers, PSC1 and PSC2, respectively,and at the same time eliminates the need for complexwavelength conversion that would be otherwise required[17]. Provided that the injected strong control pulses areappropriately timed with respect to the clock pulses,they can alter the SOA carrier density and greatlychange its refractive index. Since the SOA is asymme-trically placed in the loop, the counter-propagatingclock pulses reach it with relative delay and soexperience different dynamic states. As a result, thetwo components suffer a different gain, which in turninduces a different phase shift between them so thatwhen they recombine at the coupler switching can occurat the transmission port.
The use of the reflection port for feedback inevitablycauses the inversion of the logical value of the insertedpulses so that the temporal output at the transmissionport of the shift register consists of alternating blocks of‘‘1’’ and ‘‘0’’. The period of each block is
TD ¼ L � ðn=cÞ (1)
time units, where L is the total length of the Sagnac loopand the feedback path, c the speed of light in vacuumand n the refractive index in fiber. In other words, TD isthe memory storage time and is equivalent to thenumber of bits, m, that are contained inside the totallength, L, multiplied by the period of each bit, Tbit,
TD ¼ m � Tbit. (2)
The number of bits, m, that are contained in thememory, essentially corresponds to the delay elements(flip-flops) created by the physical length of the fiber aspulses travel it and is also a measure of the total capacityof the memory. In this sense and in order also to ensure
pulse synchronization within the shift register, m mustbe an integer number, which can be achieved byappropriately adjusting the total round-trip delay ofthe switch and the feedback path. In the experimentaldemonstration in [10], for example, the transit timethrough the switch and feedback path was 606 ns, whichcorresponds from (2) to a memory capacity, m, of 6061electronic equivalent flip-flops.
3. Model formulation
In this section, we develop a comprehensive theore-tical model based on the SOA gain dynamics to simulatethe shift register’s operation according to the descriptionof the previous section.
The analysis starts from the following basic interfero-metric equations that describe the output signal at thetransmission and reflection port [18],
respectively, where GCWðCCWÞðtÞ is the SOA gain seen bythe CW (CCW) pulse and fCWðCCWÞðtÞ the correspond-ing phase shift. These two parameters are related to eachother by
fCWðtÞ � fCCWðtÞ ¼ �a2ln
GCWðtÞ
GCCWðtÞ
� �, (5)
where a is the SOA linewidth enhancement factor.From (3)–(5) it can be seen that the calculation of T(t)
and R(t) requires the knowledge of the gain GCWðCCWÞðtÞ.For this purpose, the equations that describe pulsepropagation in a SOA as well as the SOA carrierresponse to an injected optical field are appropriatelycombined and applied for each pulse (CW and CCW)according to the operation principle of the shift register.This approach results in a system of partial differentialequations over the temporal and longitudinal variablesthat characterize the pulse shape and SOA length [19],respectively, which inevitably increases the computa-tional complexity of the theoretical model. This problemcan be overcome by using a time-dependent power gaincoefficient integrated over the SOA space variable z,h(t), that takes implicitly into account the variation ofthe gain coefficient, g, along its length, L, [20].
hðtÞ ¼
Z L
0
gðz; tÞdz. (6)
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In this way, the dependence on the spatial variable canbe dropped and the two-dimensional system of differ-ential equations reduces to the following ordinarydifferential equation that under certain approximationscan be solved analytically:
dhðtÞ
dt¼
gssL � hðtÞ
tcar�
cng�0A
2
PinðtÞ
U satexp½hðtÞ � 1
� . (7)
In this equation, the only variable is the local time t inthe retarded reference frame moving with the pulse thatis obtained through the transformation t ! t � z=ug,where ug is the group velocity [20]. Furthermore, gss ¼
GaNN trðI=I tr � 1Þ is the small signal gain coefficient perunit length when the SOA internal loss is neglected,where G is the confinement factor, aN is the differentialgain, N tr and I tr ¼ qVN tr=tcar are the carrier densityand injection current required for transparency, respec-tively, with q being the electron charge, tcar the carrierlifetime and V ¼ wdL the volume of the active region,with w and d being the corresponding width and depth.Also ng is the group index of refraction, �0 is thedielectric constant in vacuum, A is the cross-sectionalarea of the active region that equals wd/G, Pin the inputpower and U sat the saturation energy of the amplifier
U sat ¼ _o0A=aN , (8)
where _o0 is the photon energy and for typical valuesd ¼ 250 nm, w ¼ 2mm, G ¼ 0:48, aN ¼ 3:3� 10�20 m2,ng ¼ 3:62 at an operating wavelength l ¼ 1550 nmequals approximately 1000 fJ.
In deriving Eq. (7), the contribution of SOA intra-band processes, such as carrier heating and spectral holeburning [21] that can be included in the description of itsgain dynamics under pulsed operation by using thecorresponding non-linear gain compression factors[22,23], is neglected, since these effects become impor-tant for pulses shorter than 2 ps [22,24], which is not thecase, however, in this model where pulses longer thanthis critical value are only considered. It must be alsonoted that the performance of the configuration in Fig. 1can be limited by the presence of noise (amplifiedspontaneous emission – ASE) that is inserted in the shiftregister circuit from the SOA in the loop and thefeedback path and accumulates in each pulse recircula-tion. However, this problem is resolved by using atechnique that exploits the SOA in the feedback pathnot only for amplification, but also to provide a reflectedsignal as noise-free as possible [10]. This is necessary inorder to avoid the strong saturation of the SOA in theloop and the degradation of the switching performance.For this purpose, a clean signal that is provided by aclock source is inserted to this SOA whose gain ismodulated by the ‘‘1’’ and ‘‘0’’ in the reflected signal.This second SOA of the shift register circuit acts thus asan encoder that maps the noisy reflected signal to thenoise-free clock signal, essentially isolating the control
signal that is inserted in the switch through the feedbackpath from the directly reflected signal. In this manner,most of ASE can be removed, while any remaining parthas relatively less power compared to the control signalthat enters the loop, so that it cannot alter in anundesired way the gain dynamics of the intraloop SOA.Since the developed model aims at simulating theexperimental setup in [10], which in turn relies on thisapproach that essentially enables to eliminate ASE sothat its influence on the shift register performance isnegligible, it is reasonable and acceptable to neglect alsoASE in the simulation equations, without affecting theaccuracy of the obtained results and the main conclu-sions drawn for the proper selection of the criticalparameters.
Eq. (7) forms the basis for calculating the SOAimpulse response, h(t), that is subsequently used todescribe the SOA gain response features. This isseparately done for the gain rapid saturation and slowrecovery regions, as it is described in the followingsubsections, respectively.
3.1. Gain saturation by a short optical pulse
The gain saturation of the SOA can be analyticallydescribed if it is assumed that the width of the incomingpulses is much lower than the carrier lifetime of theamplifier [20] so that the gain has no time to recoverduring pulse duration. This in turn means that the firstterm in the right-hand side of (7), which is proportionalto 1=tcar; can be neglected with a good approximation,because the spontaneous recombination and carrierinjection are too slow to respond within the pulseinterval to the change of carrier density caused by thestimulated emission. This assumption is justified in thecase of the developed model since pulses have a full-width at half-maximum (FWHM) of a few picoseconds(ps), while the typical values of the carrier lifetime are ofthe order of several hundreds of ps. The solution of (7) isthus
hðtÞ ¼ � ln 1� 1�1
Gss
� �exp �
U inðtÞ
U sat
� � �, (9)
where
U inðtÞ ¼cng�0A
2
Z 1
0
Pinðt0Þdt0 (10)
is the energy fraction contained in the leading edge ofthe control pulse until the moment t0pt. By definitionU inðt ! 1Þ ¼ Up, where Up is the total energy of thepulse inserted in the SOA. The instantaneous SOA gain,
GðtÞ ¼PoutðtÞ
PinðtÞ,
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The parameter Gss is the SOA small signal gain seen bythe leading edge of the pulse as it is inserted in theunsaturated SOA and whose value, which equalsexpðgssLÞ when the SOA internal losses are neglectedfor simplicity, can be varied by changing the injectioncurrent. The gain seen by the trailing edge of the pulse isobtained from (11) letting t ! 1 and is essentially thefinal gain reached at the saturation level to which theSOA is brought
Gf ¼ Gðt ! 1Þ ¼Gss
Gss � ðGss � 1Þ expð�Up=U satÞ.
(12)
This equation has the physical meaning that as theintense control pulse travels through the SOA, itprovokes a rapid depletion of the available carriers inthe active region that are provided by the injectioncurrent, which is directly followed by a decrease of thegain from the initial and high small signal value to thefinal and smaller saturated value.
3.2. Gain recovery
After the SOA is saturated to a final value accordingto (12), the action of the control stops and so the gainbegins to recover slowly, due to the injection of carriersby the corresponding current, with a time constant tcar.The absence of the control can be thus mathematicallyexpressed by setting in (7) Pin ¼ 0, so that the stimulatedrecombination term (second term) in the right-hand sideof (7) diminishes resulting in
dhðtÞ
dt¼
gssL � hðtÞ
tcar(13)
with solution
hðtÞ ¼ B expð�t=tcarÞ þ gssL. (14)
The constant B can be found if the appropriate initialtemporal conditions are satisfied. This can be achievedby realizing that the response of the SOA to the controlpulse sequence is different from that to a single pulseand is related to the pulse repetition period, which inultrafast all-optical signal applications like the shiftregister is less than the SOA carrier lifetime. This resultsin an incomplete recovery between the continuouslyinserted pulses, so that the SOA gain has not enoughtime to return to the small signal value, Gss, but insteadto a smaller gain value, G0, which approaches asympto-tically Gss as t ! 1, while at time ts it has reachedthe saturated, final gain Gf . With these conditions,the expression for the SOA gain recovery is obtained
finally from (14)
GðtÞ ¼ exp½hðtÞ ¼ GssGf
Gss
�exp½�ðt�tsÞ=tcar
; tXts. (15)
3.3. Application to SOA-assisted Sagnac
recirculating shift register with an inverter
The results obtained for the SOA gain saturation andrecovery regions are applied now to the case of a SOA-assisted Sagnac recirculating shift register with aninverter that receives a train of clock pulses.
According to the description in Section 2, the firstclock pulse is inserted in the loop but since there isno control pulse present, its counter-propagatingcomponents exhibit an equal, unsaturated SOA gainso that GCW ¼ GCCW ¼ Gss and hence, from (5), nophase difference occurs, i.e. fCW � fCCW ¼ 0. Thispulse is thus totally reflected by the switch and itspower is from (4)
PoutðtÞ ¼ RðtÞPinðtÞ ¼ GssPinðtÞ (16)
where the shape of the input optical clock pulses isassumed to be Gaussian with power
PinðtÞ ¼Up
t0ffiffiffip
p exp �t2
t20
� �. (17)
In this equation t0 is related to the FWHM by tp ffi
1:665t0 [20].The first reflected pulse is then appropriately ampli-
fied and fed back in the circuit to act as control/switching pulse but since the propagation delay that isinserted by the loop and the feedback path must be suchthat, according to (2), m pulses are contained inside thememory, this means that it takes m pulses before thecontrol pulse that corresponds to the first reflected pulsearrives at PSC1. This control pulse transits thus the looptogether with the m+1 input clock pulse to which itinduces a phase shift equal to p so that it can beswitched at the transmission port. In a similar way, thepulses between m þ 1 and 2m are transmitted by theswitch and no reflected pulses are generated. The 2m þ 1pulse transits again the loop without a control pulsepresent and so it is reflected forming once again the newcontrol pulse. In this manner and depending on thepulse number, switching and unswitching regions areformed between which the shift register reverts periodi-cally, as shown in Fig. 2. Since, we are primarilyinterested in simulating the operation of the shift registerwhile being in the switching region, the involvedfunctions that describe in the following the controlpulses total energy and the SOA gain variation shouldhave a subscript to underline the fact that only pulsesthat lie within this region, namely pulses between m þ 1
ARTICLE IN PRESS
6m+1…4m+1…2m+1… 3m…m…1… 5m…0
2
4
6
8
10
12
14
16
18
Co
ntr
ast
Rat
io
Pulse Number
Fig. 2. Sequence of shift register transmission output, where
individual pulses are shown as filled circles representing the
peak pulse amplitude. The maximum unit is 15.8, according to
Eq. (23). The solid lines are not realistic and are plotted for
illustration purposes only.
K.E. Zoiros et al. / Optik 116 (2005) 527–541532
and 2m, 3m þ 1 and 4m, and so on, are considered. Thissubscript is, however, implied and omitted for conve-nience and simplicity of presentation.
According to the previous description, the input CWclock pulse enters the SOA together with the control,reflected pulse but as it has much less energy (at least 10times as mentioned in Section 2), it cannot saturate theSOA and its leading edge sees an initial, unsaturatedgain. Since a periodic train of pulses is inserted in theSOA and not just one pulse, this means that a quasi-saturating state is quickly established so that it isimpossible for the SOA gain to reach the small signalgain value, Gss, but instead a smaller one, G0, so thatGCW ¼ G0. As the control pulse transits thus the SOA,the gain reduces from G0 to a final saturated gain Gf ,seen by the trailing edge of the pulse, according to (11),which is modified by replacing Gss with G0 and, from(10), (16) and (17), U inðtÞ with
UoutðtÞ ¼12U tot½1þ erfðt=t0Þ, (18)
where erfð�Þ is the error function and U tot ¼ GssUp,so that
GðtÞ ¼ 1� ð1� 1=G0Þ exp �UoutðtÞ
U sat
�� �1
. (19)
The SOA saturation time, ts, is practically equal to thecontrol pulse width, tp, because if the time t in (18) isreplaced with tp, then UoutðtÞ � 99%U tot, or in otherwords, 99% of the control pulse has transit the SOA.Using thus ts ¼ tp in (19), the final gain can be obtained
Gf ¼ GðtsÞ ¼G0
G0 � ðG0 � 1Þ expð�U tot=U satÞ. (20)
After the CW pulse transit and the SOA saturationby the control pulse, the CCW pulses that arriveswith a delay equal to the asymmetry, tasym, sees
from (15) a gain
GCCW ¼ GssGf
Gss
�exp½�ðtasym�tsÞ=tcar
; tXts. (21)
After one time period,T c, the SOA gain has not reachedGss but G0, because the clock and control pulses arrivefaster than the SOA carrier lifetime and thus
G0 ¼ GssGf
Gss
�exp½�ðT c�tsÞ=tcar
; tXts. (22)
With the arrival of the next CW pulse, the gain startsreducing again and the same process is repeated for therest of the incoming clock pulses that lie within theswitching region.
In order to calculate GCW and GCCW it is necessary toknow G0 and Gf . This can be achieved by replacing Gf
from (20) in (22) and solving the transcendentalequation that occurs recursively for G0 in terms of Gss,T c, tp, tasym, tcar and U tot=U sat (or equivalentlyUp=U sat). The solution is substituted then in (20) tocalculate Gf , which together with G0 allows to find thegains of the CW and CCW pulses from GCW ¼ G0 and(21), respectively, as well as the phase shift from (5) forgiven values of a. Finally, the obtained gains and phaseshifts are replaced in (3) and (4) to calculate T(t) andR(t), respectively.
4. Results and discussion
4.1. SOA dynamic gain response
Given the central role of the SOA in the operation ofthe SOA-assisted Sagnac shift register and beforeapplying the results obtained in Section 3 to thesimulation of the shift register, it is important toinvestigate and understand first the SOA dynamicalbehavior with respect to several critical operationalparameters, such as the control pulse energy and widthand the SOA small signal gain and carrier lifetime. Thiscan be achieved if Eqs. (11), (12) and (15) are used,assuming a Gaussian pulse profile so that UoutðtÞ ¼12U tot½1þ erfðt=t0Þ; to plot the variation of the instanta-neous gain in the saturation and recovery regionsagainst the mentioned parameters. This task is per-formed for simplicity for a single pulse only but thequalitative results apply also for the case of a pulse train.
Figs. 3 and 4 show the SOA dynamic gain response tocontrol pulses of different energy and width, respec-tively. From Fig. 3 it can be seen that when there is nocontrol pulse injection or its energy is small enough (lessthan 10% of the SOA saturation energy [16]), the gain isequal to the small signal value. However an intensecontrol pulse is inserted in the SOA, the gain decreasesrapidly and becomes minimum at the final saturation
ARTICLE IN PRESS
9
11
13
15
17
19
21
-5 10 25 40 55 70 85 100
Inst
anta
neo
us
Gai
n (
dB
)
Up=10fJ
Up=100fJ
Time (ps)
Fig. 3. Dynamic gain response of SOA to control pulses of
different energy.
16
17
18
19
20
21
-5 10 25 40 55 70 85 100
Time (ps)
Inst
anta
neo
us
Gai
n (
dB
)
Tp=12ps
Tp=6ps
Fig. 4. Dynamic gain response of SOA to control pulses of
different width.
16
18
20
22
24
26
28
30
32
-5 10 25 40 55 70 85 100
Inst
anta
neo
us
Gai
n (
dB
) Gss=20dB
Gss=30dB
Time (ps)
Fig. 5. Dynamic gain response of SOA to different small signal
gain.
16
17
18
19
20
21
-5 10 25 40 55 70 85 100
Time (ps)
Inst
anta
neo
us
Gai
n (
dB
)
Tcar=100ps
Tcar=200ps
Fig. 6. Dynamic gain response of SOA to different carrier
lifetime.
K.E. Zoiros et al. / Optik 116 (2005) 527–541 533
point, which is reached when the whole pulse energy haspassed by. The gain recovers then slowly in time. Thelarger is the control pulse energy, the deeper is the SOAsaturation and the steeper is the gain curve, which ishighly desirable in order to impart a differential phase asclose as p between the counter-propagating clock pulsesand achieve full switching. Fig. 4 shows that thedynamic gain response is also significantly affected forcontrol pulses having the same energy but differentwidths. More specifically, the decrease of the pulse widthresults in a steeper gain transition from the initial smallsignal to the final saturation value. This happensbecause a shorter pulse enhances the rapid depletionof carriers and passes quickly through the SOA, incontrast to a longer pulse that needs more time totraverse the SOA and cause a change in its opticalproperties.
The influence of the small signal gain on the SOAdynamic response is depicted in Fig. 5 and as it can beclearly seen, for specific pulse energy and width thechange of the gain is more significant as the value of thisparameter becomes higher. This suggests that a largegain would be preferable in order to create the desireddifferential gain and hence phase difference between the
counter-propagating clock components. At the sametime this would enable the reduction of the requiredpulse energy, which is an attractive feature from apractical point of view since it can be provided fromcommercially available optical amplifiers. As it will bedescribed in the following subsection, however, a veryhigh small signal gain can lead to phase changes greaterthan p that result in the distortion of the output pulsesand the degradation of the switching performance. Onthe contrary, a decreased small signal gain results in again variation far away from heavy saturation that canbe compensated for by increasing the pulse energy, asdescribed in Fig. 3, but with negative impact on the costand complexity of the feedback optical amplifier. Thereis thus a trade-off between the small signal gain and thepulse energy in order to ensure optimum operatingconditions.
Finally, the dependence on the spontaneous carrierlifetime is illustrated in Fig. 6. This parameter deter-mines critically the duration of gain recovery, which inturn affects the gain suffered by the counter-propagating
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clock pulses as well as the induced phase differencebetween them and hence the quality of switching. As thecarrier lifetime increases, it takes more time for the gainto recover and the gain curve tilts towards the horizontalaxis. For ultra-high speed all-optical shift registerapplications, the carrier lifetime must be significantlyreduced so that the SOA can handle properly the pulsesthat arrive more often. However, this cannot beachieved by simply varying the driving current or usinga longer SOA [25], as it will explained in more detail inthe following subsection.
4.2. Switching characteristics of SOA-assisted
Sagnac recirculating shift register with an inverter
The results obtained in the previous subsection for theSOA dynamic gain response are exploited now tocharacterize the switching window of the SOA-assistedSagnac recirculating shift register with and inverter. Thisis a performance metric that provides valuable informa-tion regarding the shape, amplitude and temporal widthof the optical transfer function of the all-optical circuit.This window is opened by the fast change of the SOAoptical properties provoked from the strong controlpulse and their subsequent recovery. In order to achievethus switching, the clock pulses must be containedwithin this window, which ideally must be characterizedby a sharp edge on its rising and falling sides. The widthof this window is approximately equal to the timedifference in the arrival of the counter-propagatingclock pulses at the SOA, which is twice the temporaloffset of the SOA from the fiber loop center [16], andcan be practically altered by using an optical delay lineinside the loop. Furthermore, this width essentiallydetermines the maximum aggregate data rate that theshift register can support [8], which implies that if theshift register must be capable of storing ultra-high speedall-optical information, a narrow switching window isrequired. At the same time, a short switching window isnecessary in order to store each single bit of a datastream, which may be, for example, the outcome of theXOR comparison with a local address [26], for furtherprocessing in an error counter circuit [5]. This, however,does not guarantee the best operational conditions,because if the switching window is too narrow, apossible timing jitter in the incoming information willbe transformed into intensity noise at the outputresulting in an increase of the bit error rate and inperformance degradation [23]. On the other hand, awide switching window is required to store an entirepacket [27] and also to increase the timing jittertolerance so as to enable regeneration of the recirculat-ing pulses [17]. This widening can, however, increase thegain difference outside the switching window and hencethe signal leakage from the transmission port, which is
therefore undesirable for feedback applications like theshift register. The selection of the switching windowwidth depends thus decisively on the specific applicationof the shift register, while its optimization in order toensure the best performance is not a trivial task. This isdue to the fact that the switching window is heavilydependent on the actual operational conditions, whichin turn are influenced by several critical parameters,such as the control pulse energy and width, the SOAsmall signal gain and carrier lifetime and the loopasymmetry.
Concerning also the amplitude of the switchingwindow, this can be actually described by the contrastratio, which is the signal ratio between the on-off statesof the switch at its two output ports, i.e. T/R. This mustideally be as high as possible so that the largest fractionof the incoming clock signal exits at the transmissionand not at the reflection port. By dividing (3) and (4) fora p phase change ðfCW � fCCW ¼ pÞ it is obtained
and substituting GCCW=GCW ¼ 0:35; which is derivedfrom (5) for a typical value a ¼ 6; the contrast ratio canbe calculated to be approximately 12 dB (15.8), which isthe upper limit of the amplitude of the switchingwindow in the obtained curves. Here it must be notedthat in the case of a counter-propagating pulse inter-ferometric geometry, like the SOA-assisted Sagnacswitch, the SOA finite length can become a limitingfactor concerning the switching window characteristics,especially as the control pulse width or asymmetryvalues approach the SOA transit time. However, thiseffect has been investigated in detail elsewhere [28] and isnot taken into account in the developed model. This isalso justified by the fact that the equations it consists ofare solved using the amplification function of (6), whicheliminates the spatial dependence. The results presentedin the following focus thus on examining the influence ofthe rest of the critical involved parameters on theswitching window.
In order to numerically simulate and calculate theswitching window, the time that elapses between thecontrol and the CW clock pulses entering the loop isintentionally varied. This can be mathematically de-scribed by
PoutðtÞ ¼U tot
t0ffiffiffip
p exp �t � tdð Þ
2
t20
�. (24)
In this equation, which essentially expresses the controlinput power, the parameter td can be varied betweenpositive and negative values of the operating period.Physically, a positive value means thus that the control
ARTICLE IN PRESS
Fig. 7. Switching window variation versus SOA small signal
gain.
Fig. 8. Switching window variation versus switching energy.
Fig. 9. Switching window variation versus control pulse width.
K.E. Zoiros et al. / Optik 116 (2005) 527–541 535
pulses are td time units behind the clock pulses, while anegative value corresponds to an advance by the sameamount of time.
According to the definition for the energy in (10), Eq.(24) implies that
UoutðtÞ ¼1
2U tot 1þ erf
t � tdð Þ
t0
�� . (25)
Using the same rational for the SOA saturation time, ts;as in (18), it can be deduced that in the case of (25)ts � td ¼ tp ) ts ¼ td þ tp; so that in a similar way 99%of the control pulse has transit the SOA.
Before proceeding with the analysis, it is necessary tospecify the range of permissible values that theasymmetry can take. This is due to the fact that thisparameter essentially determines the width of theswitching window and hence the performance of theshift register. In order to achieve thus optimumoperation, the asymmetry must be less than half theclock bit period, Tc, otherwise the two counter-propagating halves of the pulse being processed by theswitch will not follow each other inside the SOAresulting in incomplete switching. An additional re-quirement for a pulse to be fully transmitted is that itswidth, tp, must be as short as possible and ideally lessthan the asymmetry so that when the CCW pulse isinserted in the SOA, the CW pulse has already passedthrough and the SOA gain has started recovering aftersaturation by the control pulse. This in turn implies thatthe width of the switching window cannot be shorterthan the control pulse width [29]. Moreover, theasymmetry must be less than the gain carrier lifetime,tcar, so that the CCW pulse enters the SOA beforecarrier recombination is completed in order to experi-ence a decreased gain and acquire the required phaseshift. The simultaneous satisfaction of all these condi-tions is expressed as
tpotasymoTc=2otcar, (26)
which essentially defines the range of permissible valuesthat the asymmetry can take.
The switching characteristics of the shift register areplotted in Figs. 7–11, in which the output at thetransmission port is calculated as a function of the timedelay between the CW clock pulse and the control pulsefor different operational conditions. The variation ofthis temporal separation effectively changes both outputports of the interferometer, since when the clock pulsegoes far beyond or behind the control pulse, these is nooutput at the transmission port and only when the timedelay varies in a certain range there is output at the sameport. A switching window is thus created between theinput and output of the shift register circuit. The curveswere obtained by scanning through each involvedparameter, while keeping constant the others to a fixedvalue, and this process was repeated until all parameters
were covered. These fixed values were selected inaccordance to the experimental ones [10] and namelyare: (a) for the small signal gain, 20 dB, (b) for theswitching pulse energy, 100 fJ, (c) for the control pulsewidth, 12 ps, (d) for the carrier lifetime, 100 ps and (e)for the asymmetry, 30 ps.
ARTICLE IN PRESS
0
2
4
6
8
10
12
14
16
18
Co
ntr
ast
Rat
io
Tas=30 ps
Tas=40 ps
Tas=50 ps
-100 -80 -60 -40 -20 0 20 40 60 80 100
Delay Time (ps)
Fig. 10. Switching window variation versus Sagnac loop
asymmetry.
0
2
4
6
8
10
12
14
16
18
Co
ntr
ast
Rat
io
Tcar=100 ps
Tcar=150 ps
Tcar=200 ps
-100 -80 -60 -40 -20 0 20 40 60 80 100
Delay Time (ps)
Fig. 11. Switching window variation versus SOA carrier
lifetime.
K.E. Zoiros et al. / Optik 116 (2005) 527–541536
Fig. 7 illustrates the effect on the switching windowfor different small signal gain values, which are all over10 dB. This lower limit can be obtained by recallingthat the control energy must be at least 10 times higherthan that of the clock, which means that U tot ¼
GssUpX10Up or GssX10: The curve obtained at10GHz enables to assess first the validity of the modelby comparing it against the experimental one [26]. Sincethe experimental pulses had a width of 12 ps, the createdwindow must be flat and high for a duration that is atleast equal to this value so as to guarantee an adequateswitching performance. The numerical results show thatthis condition is satisfied for a time interval of 16 ps.Although in that case the control pulses are containedwithin the switching window, as it is required accordingto the principle of operation of the Sagnac switch, at thesame time its size is small compared to the 12 pulses,which justifies the obtained moderate contrast ratio [26]and extinction ratio [10]. It must be noted, however, thatunlike the theoretical prediction, the shape of theexperimental switching window in [26] was asymmetric.
This discrepancy is attributed to the SOA finite lengththat determines the propagation time of the pulses and,as it was mentioned, limits the minimum achievablewidth of the switching window. More specifically, theleading part of the switching window had a rise time ofseveral ps, partially because the experimental measure-ment convolved the transmission function with the 12 pspulses. There was, however, an additional time regionattached to the trailing part that equalled 22 ps, i.e. twicethe transit time for a 1000 mm long SOA, in accordancewith other reported results [30]. In other words, the riseand fall time of the switching window were determinedby the width of the control pulses and were limited bythe length of the SOA, respectively [31]. Moreover, therewas a floor outside the main switching window, whichoriginated from the experimental conditions and couldbe attributed, for example, to an imperfect input 3 dBcoupler or to the pedestal that was inevitably present atthe gain-switched output pulses of the frequency doublerused in the experiment. Furthermore, the shift of thetheoretical window towards the left-hand side of thetime axis compared to the experimental one is exactlydue to the fact that the SOA is considered as a point.From the observation of Fig. 7 it can be also seen thatthere is an optimum small signal gain value, orequivalently a SOA injection current, to realize a highand symmetric switching window. More specifically, aninsufficient injection current reduces the small signalgain below values that result in a phase difference muchless than the required of p. This in turn severelydegrades the amplitude of the switching window, whichmay even not be opened, as it happens for example for17 dB. Inversely, an over-biased SOA generates a smallsignal gain greater than the optimum value, whichaccording to Fig. 5 affects drastically the SOA dynamicsand can induce a large differential gain between thecounter-propagating clock components. This in turninduces a strong phase modulation and makes the phasedifference between the counter-propagating clock pulsesexceed by far p. In this manner fluctuations occur in theswitching window, which becomes dented and distorted,as for example for 29 dB. These simulation results areconfirmed from the characterization of the phasedynamics of bulk SOAs [32] as well as from theirexploitation in interferometric configurations for thedemonstration of all-optical logic applications [33].Therefore, the SOA small signal gain and hence theinjection current must be carefully selected to lie withina range of values that ensure an acceptable switchingwindow. Provided that this condition is satisfied, theexact value that optimizes the switching window can bechosen depending on the specific shift register applica-tion. More specifically, Fig. 7 reveals that as the smallsignal gain increases, the width of the window issignificantly reduced because this results, according toFig. 5, to the creation of a higher differential gain. This
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in turn is highly desirable for ultrafast applications. Thefact that the small signal gain must increase to accountfor higher operating frequencies is also in accordancewith experimental results obtained from SOA-basedinterferometric configurations. In particular, the in-crease of the frequency decreases the differential phaseshift to values less than p, which in turn can becompensated for by increasing the SOA injectioncurrent and hence the small signal gain [34]. The pricepaid for this increase is that more costly, complex andpower consuming current sources with the associateddriving electronics are required.
Fig. 8 depicts the influence that the switching energy,E ¼ U tot, has on the switching window. This is theenergy required to achieve a differential phase shift of pbetween the counter-propagating clock pulses and hencefull constructive interference at the transmission output.From a practical point of view, it must be low enough sothat it can be provided from commercially availableoptical amplifiers. Its maximum allowable value, on theother hand, is constrained by the saturation character-istics of the SOA and the corresponding energy, whichtypically is 1 pJ. The observation of this figure revealsthat as the energy increases, the switching window isshifted towards the right of the horizontal axis in orderto achieve the highest degree of contrast ratio. Thismeans that the temporal deviation, td, takes positivevalues, or equivalently the control pulse lags behind theCW pulse. This behavior is attributed to the fact thatsince an intense control pulse causes a deep saturation ofthe SOA, according to Fig. 3, it must arrive later thanthe CW pulse so that the latter exhibits an unsaturatedSOA while the CCW pulse a recovering SOA and therequired gain difference between these two clockcounterparts can be created. On the contrary, if thestrong control pulse arrives earlier in the SOA then bothCW and CCW pulses will experience a partiallyrecovered gain and the quality of switching will bedegraded. Inversely, a control pulse of reduced energy,which cannot alter significantly the SOA properties,must arrive earlier at the SOA than the CW pulse, sothat the latter experiences a higher gain than itscounterpart, which is sufficient to create the necessarydifferential shift. In that case the values of td arenegative and the curves are shifted to the left as theenergy decreases. If the control and CW pulses areappropriately synchronized so that the former arrive atthe SOA before the latter, then the energy required forswitching is 100 fJ, which can be also seen in Fig. 8 andis close to the experimental value [10]. At the same time,it can be observed that the switching window widthincreases and decreases with an increase and decrease ofthe control energy, respectively, which is also inaccordance with other similar simulation results [35].This can be explained by recalling that the switchingwindow is created by the CW and CCW clock pulses
that exhibit the SOA fast saturation and slow recoverycharacteristics, respectively. If the energy is increasedthus, then the SOA becomes strongly saturated so thatthe CCW pulse has enough time to see a partlyrecovered gain. In contrast, if the energy is decreased,then the SOA initial gain is also decreased but to a valuethat is significantly higher than the final, saturated one,so that the time interval of the recovery region that theCCW pulse must lie within is much shorter. Thisbehavior is similar to the one described in Fig. 6. Forhigh line rate memory applications, an energy valuebelow 100 fJ is thus sufficient, while for packet bufferingapplications it must increase over this value. This hasalso a physical meaning, since the information bits of apacket have less average power compared to the bits of afull duty cycle stream. Therefore, the power and hencethe energy per packet bit must be increased tocompensate for this difference and reach the same levelrequired for switching. In the latter case, however, theprice paid is the increase in the cost and complexity ofthe EDFAs, which they must be capable of providingmuch more optical power. Note also that if the resultsfor the switching window size are considered incombination with the ones of Fig. 7, then the interplaybetween the energy and the small signal gain that wasmentioned in Fig. 5 can be explained once again.
Fig. 9 shows the dependence of the switching windowon the control pulse width. As this parameter is reduced,the window is shifted to the left and its size is alsoreduced. This behavior can be understood in combina-tion with Fig. 4, in which, as it was mentioned, differentcontrol pulse widths result in a different gain transitionregion of the SOA. This in turn affects differently theCW and CCW signals and consequently the output ofthe shift register. More specifically, since a short controlpulse of appropriate energy can quickly saturate theSOA, this essentially means that it must advance withrespect to the CW pulse, otherwise the fast saturationwill be accompanied by a quick gain recovery and theCCW pulse will see a highly recovered gain that is veryclose to that of its counterpart. As a result of the SOAfast saturation, the CCW pulse has inevitably lesseffective time to arrive at the SOA [18], which enablesthe creation of a narrow switching window. Theopposite occurs if the control pulse width is increased,because in that case the SOA needs more time to bebrought to saturation and the control pulse must by allmeans arrive after the clock pulse. If this synchroniza-tion condition is not satisfied and the control arrivesearlier, then due to its long pulse width it will need moretime to alter the gain dynamics of the SOA so thatfinally the difference between the gains (phases) of theCW and CCW pulses will be very small. Therefore, thisparameter must be properly adjusted according to thespecific application that the shift register must serve, andcan be provided from a wide range of available laser
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sources [36]. Here it must be also noted that, as it wasmentioned, the control pulse width in the proposedmodel is over 2 ps, which justifies not taking intoaccount the intraband non-linear gain compressioneffects. This in turn results in a uniform shape of theswitching window in all curves, except of course wheninvestigating the influence of the small signal gain, whichis not the case, however, in other models of the SOA-assisted Sagnac switch where control pulses less than2 ps were used. In that case, the intraband effects aremore pronounced causing amplitude fluctuations of theswitching window, which may even take the form of anoscillating multi-peak structure [22].
The switching window variation versus the asymme-try of the loop is shown in Fig. 10. This figure indicatesthat as the asymmetry increases, the curves are shifted tothe right so that td is positive and the control pulse isdelayed with respect to the CW pulse. The physicalmeaning of this behavior is that since under thiscondition the CCW pulse needs more time to arrive atthe SOA, the control pulse has enough time to reach theSOA and induce the required phase difference. On thecontrary, if the asymmetry decreases, the curves areshifted to the left or equivalently to negative values of td,which in turn implies that the control must be theleading pulse so as to saturate properly the SOA beforethe CCW pulse arrives. At the same time, it can beobserved that the size of the switching window followsthe asymmetry variation. As the SOA offset is reducedthus, the switching window size decreases too, which ishighly desirable for ultra-high speed applications. Theopposite occurs as the asymmetry increases, whichwould be ideal for storing an entire packet, such as inall-optical packet switching networks [3]. Furthermore,a change of the fixed offset time, which in turncorresponds to an effective movement of the SOAposition in the loop, results in a different time delay forwhich the maximum contrast ratio is achieved. Morespecifically, when the time delay is equal to tasym or�tasym, both CW and CCW clock components experi-ence an unsaturated or partially recovered SOA gain,respectively. In that case, the situation td ¼ �tasym isequivalent to a zero SOA displacement from the centerof the loop so that the desired phase difference andhence optimum switching cannot be achieved. As thetime delay is varied either side of �tasym, a phasedifference begins to develop between the clock counter-parts so that gradually the majority of the input powerexits at the transmission port. In order to ensure thus anenhanced performance, the time delay must be less than�tasym=2, which can be considered as a general rule ofthumb. The plus and minus sign depends on whether awide or a narrow switching window is desired, accordingto the above interpretation of Fig. 10.
The final parameter that is examined is the SOAcarrier lifetime, which is depicted in Fig. 11. Clearly, the
curves are shifted to left and the switching windowwidth becomes shorter as this parameter decreases. Thishappens because in that case the SOA gain is quicklyrecovered and so the control pulse must arrive first tosaturate the SOA in time and induce the necessary phaseshift. This in turn results in a narrower window, in a waysimilar to the one described in Fig. 9 concerning themoment that the CCW pulse enters the SOA. Forultrafast applications, it is imperative thus to signifi-cantly decrease the carrier lifetime, which can beachieved by increasing the SOA bias current or using alonger SOA [25]. The first method has, however, alimited efficiency, so that other gain recovery techniquesmust be applied, such as the injection of a continuouswave strong holding beam [37] or the use of an assistlight near the SOA transparency point [38]. Although,these techniques can speed-up the gain recovery rate, atthe same time they can greatly distort the shape of theswitching window so that care must be taken to preventperformance deterioration [39]. This can be achieved byensuring that the width of the control and clock pulsesas well as the loop asymmetry are small enough so as toavoid the creation of an undesirable secondary switchingwindow. The requirement for a decreased pulse width,however, can be satisfied only by using optical sourcesof increased complexity. Moreover, a pulse width wellbelow 2 ps may degenerate the performance of the shiftregister due to intense non-linear intraband effects thatoccur in that case inside the SOA. On the other hand,the second method has, as it was mentioned, a negativeimpact on the shape and width of the switching window.At the same time, an increase of the physical dimensionsof the SOA imposes significant limit on the maximumpermissible operating frequency [40]. More specifically,if the SOA transit time, which in turn is determined byits length, is greater than half the bit period, then acontrol pulse interacts with more than one counter-propagating clock pulses causing undesirable differen-tial phase shift. This control pulse interaction withmultiple clock pulse components leads to partial switch-ing of unwanted bits, which in turn degrades the qualityof the output pulse stream. These problems can beovercome if the completely different technologicalapproach of quantum-dot SOAs is used [41]. Thesedevices are characterized by the very wide gainbandwidth, the inhomogeneous broadened gain spectra,the high saturation power, the fast recovery time of theorder of hundreds of fs that can enable the achievementof ultra-high switching speeds and the low patterndependence that arises from the decoupling of gain andrefractive index modulation [42]. Intense research effortscontinue in this new field of optical technology so as totranslate its attractive features to a comparativeadvantage over bulk and quantum-well amplifiers andexploit it in various all-optical signal processing tasks.Obviously, these severe technological restrictions are
ARTICLE IN PRESSK.E. Zoiros et al. / Optik 116 (2005) 527–541 539
relaxed if an entire packet must be stored, since fromFig. 11 the necessary wider window can be achieved witha larger carrier lifetime.
Finally, it must be noted that another way forassessing the validity of the developed model is bycomparing Figs. 7–9 and 11 with Fig. 10. Morespecifically, if for example a narrow switching windowis desired then, according to Figs. 7–9 and 11, a highsmall signal gain, a low energy, a short pulse width and asmall carrier lifetime are required, respectively. Fromthe observation of the same figures it can be alsodeduced that these requirements are satisfied when theparameter td is negative or equivalently when thecontrol pulse arrives earlier at the SOA than the co-propagating clock pulse. If a negative value of td issubsequently replaced in Fig. 10, it can be seen that themaximum contrast ratio is obtained for a decreasedasymmetry, which in turn is necessary in order to obtaina narrow switching window. The opposite occursobviously when a wide switching window is required.The comparison of these figures according to thisrational reveals thus that there is an excellent qualitativeagreement between them, which proves the robustnessof the simulation analysis.
5. Conclusion
In conclusion, we have comprehensively analyzed theswitching characteristics of an all-optical shift registerimplemented with a SOA-assisted switch in a feedbackconfiguration. For this purpose, numerical simulationshave been carried-out using a set of equations thatdescribe the interaction between the control and clockpulses in the switch as well as the output power variationcaused by changing their relative delay. The switchingwindow created through this procedure is evaluated interms of its contrast ratio and width, which are governedby several critical operational parameters. The requireddegree of performance depends on the specific shiftregister application, which in turn determines theselection and combination of these parameters. Sincethe aggregate capacity is the inverse of the temporal sizeof the switching window, a narrow switching window isnecessary in order to meet the increasing bandwidthdemand that is driven by the broadband services andthe associated applications. The initial technical require-ments in order to achieve this goal are a switchingenergy less than 100 fJ, a small signal gain over 20 dBand a carrier lifetime less than 100 ps. Although thetwo first requirements can be satisfied by simplyusing commercially available EDFAs and appropriatelyadjusting the SOA injection current, respectively, thethird requirement essentially constitutes the majorlimiting factor that impedes direct extension to higher
rates. A way to overcome this problem is by deployingeither complex gain recovery enhancement techniquesor alternatively the novel technology of quantumdot SOAs. Furthermore, since the duration of theswitching window is lower-limited by the width of thecontrol pulse, a value of less than 10 ps is sufficientat 10GHz. For higher line rates, however, where thepulse width must be significantly reduced to less thana few ps, the non-linear intraband carrier dynamicsthat are present in active devices like the SOA in theSagnac switch must be seriously taken into accountsince they can ultimately limit the size and shape of theswitching window. This in turn affects the asymmetryvalue, which for a short switching window must behigher than but also close to the pulse width as well asless than half the operating period. This parameter,however, can be easily adjusted using commerciallyavailable optical delay lines and does not impose atechnical restriction. On the other hand, these require-ments can be relaxed when the shift register is requiredto function as a packet buffer, since in that case theswitching window must be wider, but at the cost ofinevitable energy increase. For both shift registerapplications, the absolute value of the time delaybetween the control and clock pulses must be less thanhalf the asymmetry of the loop. Although, the mainresults of this work have been obtained for an operatingfrequency of 10GHz, they can be also extended forhigher frequencies in a similar manner. In this sense, thedeveloped model is suitable for investigating andoptimizing the operation of a variety of more complexall-optical signal-processing circuits, in which the shiftregister is the basic building block.
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The book provides a fundamental overview of thefield of photonic crystal fibres, their properties andunique features. After an introduction, Chapter 2describes fundamentals of photonic crystal waveguides,especially the development from one- to three-dimen-sional photonic crystal optical waveguides. The bookalso addresses the issue of the design of efficientstructures for the creation of photonic bandgaps andsilica-air photonic crystals are introduced as a first steptowards the silica-based photonic crystal fibre technol-ogy. Chapter 3 contains a description of 11 differenttheoretical and numerical methods applied in theanalysis of photonic crystal fibres. Chapter 4, thefundamental issues of the fabrication of photonic crystalfibres are described. This include elements such as
[41] M. Sugawara, T. Akiyama, N. Hatori, Y. Nakata, H.
Ebe, H. Ishikawa, Quantum-dot semiconductor optical
amplifiers for high-bit-rate signal processing up to
160Gbs-1 and a new scheme of 3R regenerators, Meas.
Sci. Technol. 13 (2002) 1683–1691.
[42] A.V. Uskov, E.P. O’Reilly, R.J. Manning, R.P. Webb, D.
Cotter, M. Laemmlin, N.N. Ledentsov, D. Bimberg, On
ultrafast optical switching based on quantum-dot semi-
conductor optical amplifiers in nonlinear interferometers,
IEEE Photonics Technol. Lett. 16 (2004) 1265–1267.
perform realisation, fibre drawing, as well as a descrip-tion of microstructured fibres in new materials. Chapter5 describes the basic issues of the presently most widelyused class of photonic crystal fibres, namely the high-index-core fibres. The chapter includes a description offundamental waveguiding properties. Chapter 6 focuson the photonic bandgap class of PCFs. The concept ofair-guiding fibres will be discussed and reviewed.Finally, Chapter 7 contains descriptions of some of themost significant applications of photonic crystal fibresknown at present time. Especially, the area of applica-tions is developing at a very high speed because thephotonic Crystal Fibres very often provide completelynew and alternative functionalities compared to stan-dard optical fibres. This book is not only a very godreview but also a comprehensive handbook of the fieldof PCFs.
