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Dynamic Behavior of Wavelength Converters Based on FWM in SOAs Christina (Tanya) Politi, Dimitrios Klonidis, and Mike J. O’Mahony, Senior Member, IEEE
Abstract—As wavelength converters based on four-wave mixing (FWM) in semiconductor optical amplifiers (SOAs) attract more attention, dynamic effects and wavelength dependent performance become key aspects to be investigated. Such issues are particularly important, as complex configurations are likely to be used to overcome challenges like tunability and polarization dependence. In this paper a numerical model is used to predict the dynamic performance of three FWM configurations and an analytical model is used to derive design rules. First, the wavelength dependent behavior of a wavelength converter is investigated and the requirement for a widely tunable converter is identified. Secondly, a configuration for extinction ratio (ER) improvement is studied and novel design rules are obtained analytically, tested experimentally and explained by the numerical model; experimental results with ER improvement at 10 Gb/s were achieved for the first time. The third configuration studied is a dual-pump arrangement enabling wide tunability. Fixed input/tunable output and tunable input/fixed output configurations are discussed in terms of optical signal-tonoise ratio and tunability. Design rules are extracted and verified for all three configurations that are likely to be deployed: simple wavelength converters, regenerating converters and tunable wavelength converters. Index Terms—Optical amplifiers, optical frequency conversion.
I. INTRODUCTION
A
S BROAD-BAND Internet access is rapidly penetrating world markets and homes, Internet traffic is increasing rapidly in the core network. Associated with the expansion of Broad-band is the paradigm shift in telecommunications from voice-optimized to IP centric networks. Optical networks have been considered as the only means to ensure delivery of large capacity links in a flexible, dynamic and reliable way. Wavelength conversion is one of the first processing functions that are envisaged to be deployed in the optical layer. In particular, all optical wavelength conversion is expected to be very beneficial not necessarily only because it supports high bit rates, but because it relaxes the requirements for costly optoelectrooptic conversion that limits the upgradability of optical nodes. Recently wavelength conversion based on four-wave mixing (FWM) in semiconductor optical amplifier (SOAs) has gained Manuscript received June 1, 2005; revised October 10, 2005. The work of D. Klonidis and M. J. O’Mahony was supported in part by the U.K. EPSRC Project Ultrafast Photonics Collaboration. C. Politi is with the School of Electrical and Computer Engineering, National Technical University of Athens, Athens 15773, Greece (e-mail:
[email protected]). D. Klonidis is with the Athens Information Group, Athens 15773, Greece (e-mail:
[email protected]). M. J. O’Mahony is with the Department of Electronics Systems Engineering, University of Essex, Colchester CO43SQ, U.K. (e-mail:
[email protected]). Digital Object Identifier 10.1109/JQE.2005.861822
a lot of attention and has been used in optical network demonstrators [1], [2]. Optical wave-mixing results from nonlinear interactions among the optical waves present in a nonlinear optical material, here a semiconductor. The beating of two waves of different frequency modulates both the gain and refractive index of the medium and a grating is generated. A number of mechanisms have been suggested to account for the electronic excitation in semiconductors that leads to FWM [3]–[6] and are all related to the gain and refractive index dynamics in SOAs. These include carrier population pulsations (CPP), carrier heating (CH) and spectral hole burning (SHB), the relative strength of which is significant for the features of the products. The interaction of the input waves with the gratings leads to new frequency components. The origin of FWM in SOAs [3], [4], is related to intraband and interband carrier dynamics. This mechanism is sensitive to both amplitude and phase information, and in that sense is one of the wavelength conversion methods that offer strict transparency. FWM in SOAs is attractive as a wavelength conversion technique, despite the added amplified spontaneous emission (ASE), which degrades the optical signal-to-noise ratio (OSNR). The latter drawback is counterbalanced by the compactness of SOA based devices, which enables integration. The major disadvantage of FWM is its low efficiency, which results in low power FWM products and low OSNR value. The main parameter that affects both the efficiency and OSNR is the unsaturated gain [5]. This is defined as the gain experienced by low signal power and can be enhanced by utilising either longer SOAs, with a smaller active layer [6] or different structures such as multiquantum-well devices [5]. More recently the use of an assisted beam has been suggested for the enhancement of the FWM efficiency [7]. Another disadvantage is that FWM is normally polarization sensitive. The problem has been tackled with dual-pump configurations, or polarization diversity techniques [8], [9]. Furthermore, conversion efficiency drops rapidly for wide pump-signal separations and is asymmetric for up and down conversion. However dual-pump configurations have been proposed as an alternative. In [10], a 80-nm conversion bandwidth was achieved by dual-pump configuration at 2.5 Gb/s. The main advantage of FWM is that it is very fast, due to the nature of the nonlinearities. In [11] a 100 Gb/s multiplexed channel was converted by a 2-mm-long SOA, over a range of 3.2 nm. Other than converting high bit-rate pulses [12] the technique has been used for converting other transmission efficient formats [13]. It is quite important at it is one of the few techniques that offers strict transparency and, hence,
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POLITI et al.: DYNAMIC BEHAVIOUR OF WAVELENGTH CONVERTERS BASED ON FWM IN SOAs
supports formats that are significant for applications in ultra long haul networks. The performance of a wavelength converter (WC) based on FWM, is judged on the grounds of the quality of the output signal [14]. There are a number of impairments that may deteriorate the performance of a signal when converted by FWM in an SOA, usually due to counter-acting factors, namely the following: • limited efficiency and low product OSNR [1]; • extinction ratio (ER) degradation due to the saturation of SOA gain [14];. • gain modulation (GM) of the SOA due to the signal. In a WC this effect manifests itself as modulation of the pump, which in turn reduces the ER of the product [intersymbol interference (ISI)]. All the above depend on the relevant signal to pump power ratio; • pattern effects caused by the relatively long carrier lifetime of the amplifier [15]; • imperfect filtering of the pump that manifests itself as crosstalk; • phase noise accumulation which does not affect the performance of the device for large pump-signal frequency detuning ( 10 GHz) [4]; • pulse shape or waveform distortion due to nonlinear gain dynamics in the SOA. These are neglected here since high pump powers saturate the SOA [3], [4]. Several numerical models have been developed to describe the performance of a FWM wavelength converter; most of them, however, only treat the first effect of the above list. The model of [16] predicts the ER performance of a FWM WC. It makes, however, the assumption that the input signal has much lower power than the pump, and this assumption does not allow for the description of configurations like the one in [17]. There the conventional “pump” is modulated for ER enhancement. The model developed in [18] describes the regeneration effects that occur in the converted signals with this configuration. In this paper a multiwavelength model that accounts for arbitrary input powers is developed to describe the performance of the WC. This is particularly important for devices operating in multiwavelength mode like dual-pump configurations. An analytical model assists in deriving a set of simple rules that describe the performance. Both models are tested against experiment and the application of FWM in SOAs as WC is investigated. A. Theoretical Investigation of FWM in SOAs The theoretical model for wavelength conversion based on FWM in SOAs is described in this section. The model builds on the approach of [4], [16], [18], and [19]. Assume a SOA cavity with a number of electric fields propagating and interacting along . If only the fundamental transverse electric (TE) mode propagates in the cavity, the propagation characteristics can be obtained by solving the wave equation (1) where tivity,
is the modal refractive index, the vacuum permitis the velocity of light in vacuum, and is the time.
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The SOA is considered isotropic and the total induced polarand nonlinear ization is a function of the susceptibility . is the carrier density of the semiconductor polarization, and is the angular frequency of the wave. The index counts their angular frequency, the fields that co-exist in the cavity, their propagation constant, the complex varying has amplitude of each field, normalized in such a way that units of power. is the group velocity and its dispersion can be neglected for the bit rates of interest [4]. The linear susceptibility and nonlinear polarization are associated with the material gain and the refractive index of the SOA as follows [16], [19], [20]: (2) where is the modal gain for the th mode, is the linewidth enhancement factor, is the confinement factor, and is the material gain [19]. The nonlinear polarization is induced by all possible beatings between the electric fields in the cavity [19]
(3) where is the frequency separation between any two interacting electric fields. CPP, CH, and SHB have been introduced phenomenologically through response functions of gain, carrier temperature, and distribution of intraband population as , and corin [19]. These functions are denoted with , , and are the strengths of respondingly. , are the equivalents to the the nonlinear processes [4]. linewidth enhancement factors representing the contributions of the gain and index modulations due to CH and SHB. The response functions of the nonlinear processes are given by [16], [19]
(4) where , with CPP, CH, and SHB, is the characteristic timescale associated to each process. Specifically for the CPP and process [19]: , where the energy that corresponds to ,
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the total input power, the gain parameter, cross-secis the nonlinear tional area, and the carrier lifetime. strength of the CPP associated with the saturation power of the . The model parameters are amplifier shown in Table I. No rigorous analysis has been used to extract the parameters, but the methodology can be found in [4]. Parameters for the SOA are found in the literature for the device [21], or similar devices [16]. The values that are used for the parameters related to the nonlinear effects belong to the range of values found in literature [4]. The equations in (3) are now simplified and explicitly contain the beating between the different electric is the summafields, shown in (5) at the bottom of the page. tion of the propagation constants and the phase matching condition is fulfilled [4]. The material gain of the SOA is described by a parabolic model
The first term is the current term, which provides the section with carriers. The other terms represent different mechanisms that consume the reservoir of carriers which include recombination, stimulated emission and ASE correspondingly. The coefficients are given in Table I. is the average intensity in section given by
(6) the carriers at transparency, where is the carrier density, the wavelength that corresponds to the frequency . The and modal gain then is calculated by [16] (7) is the loss in the active layer, loss in the claddings and are the scattering losses. For the solution of (5), the SOA is divided into many sections hence longitudinal variation of gain, refractive index, and amplified spontaneous emission (ASE) are all accounted for. In each section , the rate equation is solved
(8) where current,
is the carrier density of the section , is the injection the electron charge, and the active region volume.
The model takes into account ASE by the means of effective is the spontaneous emission [21]. In the last term of (8) is the effective spontaneous emission factor, and peak gain, is the average spontaneous photon density generated in a given section. To implement the model, (5) in conjunction with (8) should be solved. The amplifier is segmented into sections of length dl at as in [15]. In each section , forward propagating fields different frequencies are entering the section. At the same time is entering the section spontaneous emission with power from both sides with and . To solve the equations (5) we use the finite forward difference approximations for the differential equations as implemented in [22] and used in [15]. The facet reflectance is assumed zero. Only collinear copropagating electric fields are considered and interference due to back propagation is neglected [15]. The method for this is described explicitly in [23]. Input Signal: The input signal is modulated at 10 Gb/s nonreturn to zero (NRZ) pattern using raised cosine pulse shape to imitate the modulated pulses. The power of mark “one” is noted with an index 1 and the power of space “zero” with the note 0. The model can be applied up to data rates of 160 Gb/s, as long as the envelope approximation holds and the widths of the pulses are longer than the timescales of the nonlinear processes. Another constraint occurs by not including the nonlinear gain suppression due to CH and SHB; this sets a limit on the pulse duration of 2.45 ps [24].
(5)
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TABLE I SOA MODELING PARAMETERS
NRZ modulated signal are used and the output product is shown. PP1, PS1, PF1, and PF2 are defined as the powers of the pump P1, signal S1, products F1 and F2, respectively, as shown in Fig. 1. Fig. 2(a) shows the shape of the output PS1 together with PF1 and PF2; the power levels are arbitrarily scaled for the sake of presentation. In Fig. 2(b) PS1 and PF1 are shown together with the output pump power PP1. B. Analytical Model Fig. 1. Output spectrum of a conventional FWM configuration with pump P1 and signal S1.
Fig. 1 shows a conventional configuration of a FWM converter. Fig. 2 shows the model results for the SOA with parameters shown in Table I. A continuous-wave (CW) pump and a
Although numerical models are required to accurately describe the time evolution of pulses in an amplifier, analytical models are useful in that they give good insight into behavior, especially for simple setups like a WC. Here the lumped model as described and implemented in [25] has been used; the model is presented in Appendix A.
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Fig. 2. Pulse streams of the conventional FWM wavelength converter with arbitrary units for the sake of presentation a) the shape of the output PS1 together with ! GHz . The input pump power used was PF1 and PF2 b) again output PS1 and PF1 are shown but now the output modulated pump power PP1 3 dBm and the signal power 7 dBm.
+
(1 = 2 1 200
0
)
Fig. 3. Experimental setup for the investigation of the dynamic performance of the FWM in SOAs.
II. EXPERIMENTAL SETUP Fig. 3 shows the experimental setup used for the investigation of FWM in SOAs. In this setup the pump source is a distributed nm . feedback (DFB) laser, here called Laser1 A second laser is used as a signal. The laser is tunable and unless nm. Depending otherwise stated it used at Laser2/ on the experiment Laser2 operates in a CW mode or is moduPseudorandom Binary Sequence data lated by a 10 Gb/s sequence. Both signals are amplified, filtered separately and then coupled together in a SOA. Unless otherwise stated the SOA was operated with 220 mA and the pump was at the wavelength of maximum unsaturated gain at this specific current. The device was a polarization insensitive (0.2 dB) multiquantum-well device 1 mm in length with 30-dB unsaturated gain at 200 mA at 1556 nm. The FWM product [at the SOA output] is filtered, amplified and filtered again before detection. This pre-amplified receiver comprises a low noise EDFA, and an 0.8-nm-wide tunable filter, a 10-GHz photodiode and electrical amplifiers. Input and output powers were measured using an OSA (at 0.1 nm), giving average powers. For one specific experiment the clock of the pattern generator is used to modulate Laser1 via an electro-absorption modulator (EAM). This configuration creates 20 ps FWHM pulses, with
nm. In that specific a 10 GHz repetition rate, at experiment, the tunable delay line shown in the Fig. 3 is incorporated in the configuration. In some experiments, a second pump is incorporated in the configuration. A. Static Results Transfer Function With Respect to the Signal Power: To determine the transfer function, an attenuator is used to change the signal power PS1 and the resulting transfer function (PF1 versus PS1) is plotted in Fig. 4(a). The curve has a linear evolution up to a point where the amplifier goes into saturation. This conventional FWM configuration has been widely investigated in the literature [4], [5]. In Fig. 4(b), analytical and numerical results, have been plotted where the models have been deployed to calculate the dBm. The transfer “static” transfer function for function here is used for calibration purposes and does not seek to find optimum performance, in terms of efficiency. Also note that we chose powers within the limits of operation of the analytical model, which are explained in Appendix. In the analytic model the R has been calculated and equals 30 dB (see Appendix A). From (A.1) the PF1 is expected to be almost linear with respect to the signal power PS1. As PS1 increases,
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Fig. 4. (a) Experimental transfer function versus signal power. The curve PF1 = PS1 is plotted for comparison. (b) Static transfer function PF1 = f (PS1) for PP1 = 11 dBm as derived from models and experiment.
0
its effect on amplifier gain increases, affecting the linearity of the transfer function. The interplay between PP1 and PS1 is essential for defining the optimal operation conditions for a WC. The numerical model shows better agreement with the experimental results, but is not accurate when the total input power is low. This is mainly due to the constant nonlinear factors used here for CH and SHB. The inclusion of the carrier density dependence and different transparency points would give better results in the low power region [4]. From the system viewpoint, and if it is assumed that the WC is configured like in Fig. 1, the interplay between PP1 and PS1 is essential for defining the optimal operation conditions for a is defined as the power of the mark “1” of the WC. Assume as the power of space “0.” The peak output input S1 and is reached when the derivative of (A.1) is set to power zero. is reached when the input signal powers equal to
the peak input signal should be approximately 1.45 dB less than the pump power for maximum PF1. Although maximization of the efficiency is a major parameter for the optimal operation of a wavelength converter, in a communication system signal power is less important than factors like the ER and OSNR for example. In Fig. 4(b) one can observe that the transfer functions are almost parabolic. Assume that two input signals with two different ERs (ER’ and ER) with the same , but two different “one” levels ( , and “zero” level ) input the SOA. According to the transfer function each of these signals would generate a similar FWM product. The two FWM products would have the same output extinction ), peak output power , and average output ratio ( power. Regarding the OSNR performance of the converter the is achieved when the maximum of the maximum ratio of (A.1) and (A.2) is achieved, which is different than the is achieved when maximum output power. Indeed (if ) (9)
For the amplifier above this translates to an average signal-topump ratio of 1.5 dB. Finally it is noted that OSNR alone cannot describe this converter and the ISI may be discussed in terms of the analytical model. GM is copied on both the pump and the signal and manifests itself as a reduction to the ER. Here, to investigate the efis introduced as the gain modulation—experimentally fect, defined as the modulation of the output pump power [26]. is the ratio of the gain when the signal power is “one” over the gain when the signal power is zero
In [26], the ISI has been investigated experimentally. The paper claims that in order to have an overall power penalty 0.5 dB, should be less than a value, say , for moderate input powers. This means that the above condition gives a good trade off between OSNR and ISI related impairments. This translates to signal power
Assuming that and
and
(10)
In conclusion, an analytical model has been used in order to study operating conditions for the signal-to-pump ratio, which may influence the performance of the WC as far as ER, OSNR, and ISI are concerned. It was argued that although a signal-topump ratio of 1.5 dB would be sufficient for a good performance in terms of output power, requirements for optimized OSNR would set this value to 1.5 dB, see (9). Nevertheless the ISI plays a significant role and this ratio must be compensated
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Fig. 5.
(a) Experimental transfer functions. (b) Transfer functions with respect to the pump power as calculated by the models for
for 9 dB ratio that gives both good ISI performance and OSNR and dB is used as stems from (10) when [26]. Transfer Function With Respect to the Pump Power: A system transfer function is usually defined by the output versus input power characteristic. In an FWM configuration, there are two input signals, and it is preferable that transfer functions are plotted for both signal and pump, namely S1 and P1. In Fig. 5(a) transfer functions with respect to the power of P1, for different PS1 powers, are plotted. This is because although in the conventional configurations S1 is modulated, there are cases where modulating P1 can lead to ER enhancement [17], [18] and format conversion [27]. In order to experimentally investigate this transfer function the lasers are set as before but the attenuator is now used to change the pump power PP1. ExperidBm mental, analytical and numerical results for are plotted in Fig. 5(b). The curves have a linear evolution up to the point where the amplifier goes into saturation. The linear part of the curve presents a steeper slope than the curve, indicating that if PP1 is modulated instead of PS1, the ER of the F1 will be higher than that of S1. As far as the analytical results are concerned the results in Fig. 5 show very good agreement with experiment in the region [ 10 dBm, 3 dBm] total optical power. In this region of total powers, the empirical model for the amplifier gain (see Appendix) is calibrated and performs well. For higher powers however the deviation between analytical and numerical models is evident. As far as the numerical model is concerned there is a better compatibility with the experimental results since the overall input power is higher than in the previous case.
III. WAVELENGTH DEPENDENT PERFORMANCE OF A WC The SOA gain peak wavelength is determined by the composition of the material and the structure of the active layer. At this wavelength, the signal experiences maximum amplification and the output ASE is at a maximum. In order to have high OSNR for the output product of a conventional FWM configuration (see Fig. 1), one needs to consider the following two factors. Firstly P1 should be placed close to the gain peak so
PS1 = 010 dBm.
Fig. 6. Numerically calculated (solid lines) and measured (dotted) OSNR for different pump positions and pump-signal separations. Three curves are shown where the pump which spectral position for each case is shown with the dashed line, is placed (a) at the gain peak wavelength, (b) 10 nm from the peak wavelength, and (c) 10 nm from the peak wavelength. : dBm and : dBm.
PP1 = 04 5
0
+
PS1 = 07 6
that the nonlinear effect is maximized, leading to maximum efficiency. Secondly the product should be ideally on the gain peak to achieve the highest possible amplification. Meanwhile the modulated signal, S1 should ideally be as far (spectrally) from the peak wavelength as possible to minimize GM effects. First, the wavelength dependent behavior of a FWM WC is investigated. The OSNR is measured in the configuration of Fig. 3, and calculated using the numerical model. The OSNR is plotted in Fig. 6, against the F1 wavelength position. The dotted lines are the experimental results and the solid ones the numerical model predictions. The three sets of OSNR results correspond to three different positions of the pump on the SOA gain spectrum. The pump, has been placed at: 1) the gain peak wavelength; 2) 10 nm from the peak wavelength; and 3) 10 nm from the peak wavelength. Note that the modulated signal causes instability in the OSNR measurements. This is further enhanced as modulation of the gain changes the gain peak wavelength, affecting in such a way the results and, hence, they are not conclusive. Furthermore the wavelength separation between pump
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Fig. 7. Calculated (a) ER and(b) OSNR of a FWM product versus the product wavelength position with respect to the gain peak. The separation between P1 and S1 is 2 nm, which means that F1 is placed at 2 nm when P1 is on the gain peak, and at 4 nm when S1 is on the gain peak.
0
and signal dictates the nonlinear process that is responsible for the FWM procedure, and this explains the behavior of OSNR with respect to the wavelength position. To understand overall performance it is necessary to investigate the ER and the OSNR of the output product; this is done by a numerical investigation for different positions of F1 on the spectrum with respect to the gain peak. Two sets of results were taken for the input powers of the pump and the average signal [2.44, 6.6 dBm] and [ 2.6, 6.6 dBm], respectively, and the results are plotted in Fig. 7. OSNR and ER are simultaneously optimized when the pump is located at the peak wavelength, which corresponds to maximum of the nonlinear effect. OSNR is slightly increased when the pump is placed at longer wavelengths and this is attributed to a combination of the efficiency shape, the ASE increase and the wavelength separation between signal and pump. ER is increased at the bandgap where dynamic effects are more relaxed. IV. ER ENHANCEMENT USING FWM IN SOAS The static transfer function with respect to the signal power PS1 (Fig. 4) indicates that no ER regeneration is possible with this configuration. When plotted against the pump power however, (in Fig. 5) it shows a steep slope that guarantees regeneration. In this case the system must be configured in a different way than in a conventional FWM configuration. In conventional FWM, a low power modulated signal S1 and a high power pump P1 create two FWM products, the conjugate (F1) and the satellite one (F2). To achieve enhancement, the modulated signal assumes the role of P1 and S1 alternatively [17], [18], [27]. The method has been used in [18], [27] and ER enhancement has been achieved. Static Behavior: The principle of operation is illustrated in Fig. 8. The modulated signal (here P1) acquires two discrete and their power levels. PS1 is the levels 1 and 0 with power level of the CW S1. These power levels are chosen in such is higher than PS1 and is lower than PS1. a way that P1 and S1 are mixed to produce F1. In the course of the modis less than PS1, i.e., S1 is beulation the power level of having like the pump. The product F1 is behaving like the satellite product, thus low power second FWM product [Fig. 8(a)].
0
Fig. 8. Principle of operation for the deployment of FWM with regenerative effects.
As the power of P1 increases and while , F1 reclaims its position as the main FWM product [Fig. 8(b)]. It is this alternating pump role that leads to enhancement of the ER, under specific conditions. To investigate the static behavior we utilize (A.1) that accurately reproduces the static transfer function in Fig. 5. The ER is given by the ratio of and of the FWM product [Fig. 8(c)]. Based on (A.2), if R is independent of power is given by and the pump is modulated,
The equation shows that the maximum that can be achieved is [dB], and is limited by a factor associated with , the ratio of the the gain saturation. Defining CW power of S1 to the peak power of PP1, the ER enhancement (DER), is given by
and
(11)
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Fig. 9. (a) Calculated ERout and DER from the experimental static transfer function (exp) and the analytical model (analysis) for a = 0:8 and different ER input values. (b) DER for different a parameters and ERin = 8 dB.
If , the conventional FWM process is represented and (11) is not valid. For this case, ER behavior has been extensively studied in [15]. In [15] it is noted that for a fixed signal power, ER decreases when the pump-to-signal ratio decreases. because The model in [15] describes only the regime of it assumes that CW power is much higher than the modulated , (11) is not valid as this is the convensignal power. For tional FWM case. However (11) is derived directly from (A.1) and can be used for the static analysis in this section. versus the Fig. 9 shows a plot of the “static” output input ER. Using the data from the static transfer function of Fig. 5, one obtains the plot in Fig. 9 as follows. Assume and dBm. This means that dBm corresponds to dBm. From Fig. 5 and for a specific ER is obtained. Keeping and thus the value, the values and the same, for increasing ER values different values are found. The static as a “corresponding” function of ER for a specific value of is then plotted together as predicted by (11). and DER are plotted with the in Fig. 9(a) and are both monotonically increasing. In Fig. 9(b) DER is plotted for a specific ER but for different parameters. The method of deriving the experimental “static” results is the and are calculated for different same as for a) but parameters while dB and for dBm. The for values ER is enhanced (12) For the specific example dB , (12) yields . This means that for any value of higher than 0.67, the ER will continuously increase, as shown in Fig. 9(b). In [18], a static analysis of the effect yields a similar trend. This trend is not demonstrated in the dynamic experimental results. Dynamic Behavior: The dynamic behavior of such a system is very different than the one described by the static analysis. This is attributed to the strong saturation conditions that the SOA is operated under. When the input power is high, the ER of the system is influenced by pattern effects. This means that the slow dynamics of the SOA act as a mechanism of ER degradation.
To investigate this, an experiment was performed using the configuration in Fig. 3. PP1 is modulated with PRBS data and dB are kept constant. The coefficient its power and is changed through the power of S1, PS1. DER is measured and meathe results, as a function, of are shown in Fig. 10. surements are performed by measuring the average and . The experimental results exhibit regenerthe average for . For values of ative features the ER regeneration effect decreases. Enhancement is based on the role of the pump that alternates between P1 and S1. Howand enhancement ever this effect ceases to exist when is relaxed; the effect is dependent upon input power. Optimum input power is a balance between the amplifier gain reduction and the influence of dynamic effects. When PS1 grows by more than 1 dBm the enhancement effects are saturated. dBm are Results for the numerical model, with illustrated in Fig. 11; where ER enhancement and the OSNR are shown as a function of . Both evolve in the same way when is increased. In [17], a theoretical investigation showed that for specific input powers, the scheme could act as a 2R regenerator. can Because of the shape of the transfer function, noise on be reduced. In [17], the regeneration occurs for mW, mW. This translates to . Obviously, for when the SOA in [17], this reflects a good balance between sufficient output power, OSNR, and noise regeneration. A. Extinction Ratio Improvement and Simultaneous Format Conversion By operating S1 in a pulsed mode, synchronising the pulses with the NRZ P1 and arranging for the power of S1 to range and the “one” level of between the “zero” level of P1 P1 , a very good quality F1 can be produced and format conversion is acheived. In Fig. 12 the ER output of F1 is plotted with respect to the parameter for three different S1 powers. The enhancement procedure saturates for , as expected. Direct comparison cannot be made with the results above as the parameter has been calculated using the average PS1 (from the pulsed clock). Note that the powers in the key of Fig. 12 refer to average powers
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Fig. 10. (a) ER enhancement of a FWM product at 10 Gb/s with modulated pump and ER = 8 dB, for three different PP1. (b) Eye diagrams of the input (above) and the regenerated signal (below) are shown (not to scale).
Fig. 11.
(a) Numerical calculations of DER for a signal at 10 Gb/s when PS1 =
of S1. The ER of P1 is 8 dB. A significant ER improvement is achieved and the results are closer to the ones predicted from the static analysis. This is because the pulses do not continually saturate the amplifier so pattern effects do not deteriorate the performance so much. The eye diagrams show the NRZ input and the RZ regenerated output (F1). The technique can potentially be used for retiming, if a clocked signal S1 is used. This is because if the input signal suffers from jitter and the S1 is correctly clocked, the product will not suffer from jitter.
V. DUAL-PUMP CONFIGURATIONS FWM in SOAs has been acknowledged as a useful technique for wavelength conversion. However, it suffers from conversion bandwidth limitations. To overcome the sensitivity of the technique to the spacing between pump and signal, many configurations have been suggested [28], [29]. The one used here is where the two pumps are widely spaced in wavelength, and the output signal is expected to be insensitive to the detuning
00 66 dBm. (b) Also the OSNR is plotted for different values of :
a
.
between pump and signal [30], [31]. The two pumps are either copolarized or orthogonally polarized. The principle of operation and the modeling of the method are explained in Appendix B. Fig. 18 illustrates an example of dual-pump FWM with copolarized or orthogonally polarized pumps. The second case will have a worse performance in terms of output power than the first case. Its immediate effect is the reduction of the product OSNR. The OSNR of F1 at 0.1 nm is calculated analytically and plotted as a function of wavelength separation that corresponds to in Fig. 13(a) according to (B.1). We dBm and dBm. It is consider only the OSNR of F1A that is considered here and it is plotted : a) 1.6 nm (200 GHz) and b) 8 for two cases of nm (1000 GHz). For the parallel case (key as ), the shape of and the curve is asymmetric with maximum at , as indian evident destructive interference at cated by the arrow. Preferably the converter should operate for . For the orthogonal case ( in the key) the OSNR is the same for the whole range of wavelengths. Smaller yields better results as expected from (B.1). For wider
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(a) ER enhancement and format conversion using FWM, for different input powers of S1. (b) Eeye diagrams of the P1 and F1 are shown (not to scale).
k
:
Fig. 13. (a) OSNR as calculated by the B.1 ( case) and B.2 ( case) together with the ASE. (b) OSNR versus input signal power as calculated by the analytical mode when one pump with 4.5 dBm is used (squares) and when two pumps are used with equal powers of 4.5 dBm (- - thick) and when two pumps with unequal powers 3.45 dBm and 4.5 dBm (- - light) are used. (R = 30 dB).
0
0
0
0
tuning range ( 10 nm), the shape will be very much affected by the gain. The OSNR versus PS1 is plotted in Fig. 13(b), for one-pump and dual-pump configurations. The function is assumed the same. Gain saturation does not permit the OSNR to be the same for the dual-pump and one-pump case unless higher powers are used. Maximization of OSNR takes place at (13) Evidently, the difference of a dual-pump configuration with respect to a single WC, is related to the overall input power, which in the case of the dual-pump system is double the one of the WC. All the design rules developed in previous section for the WC can be modified accordingly to describe the tunable ones. For example, the rule for the ISI is now relaxed by 3 dB. A. Tunable Wavelength Converters (TWC) The orthogonal pump configuration has many advantages and is a candidate for a TWC [32]. To achieve polarization
0
insensitive and tunable conversion simultaneously a combination of a dual-pump and a polarization diversity technique should be used. In this case, two SOAs are used and in each of the SOAs the pumps are parallel polarized with the signal. For this reason the performance of a TWC with parallel pumps is now investigated. For system applications, like optical cross connects, the TWC can operate in two modes: fixed input/tunable output (FITO) and tunable input/fixed output (TIFO). For the FITO case, the input signal has a specific wavelength and, hence, the first pump P1 also has a specific wavelength. To achieve translation in any wavelength the second pump P2, is tunable. In the opposite way the TIFO has to translate any input signal to a specific output wavelength. For that S1 is now tunable and, hence, P1. P2 has a is constant. specific wavelength. In both cases, For the investigation of these configurations, the study of the OSNR of the product is sufficient. The numerical model and experiment are used to explore the OSNR of F1A. The numerical model can predict the experimental results and the trend can be sufficiently explained in terms of Mecozzi’s model [33] since
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Fig. 14. Four cases for which the FITO is investigated, with respect to the wavelength placement of the FI. The TO (P2 and F1A) is in the circles in two different positions. There are two examples of TO indicated for each case to illustrate the tunability of the output.
the analytic model used here does not include wavelength dependent effects. B. Fixed Input/Tunable Output Wavelength Converter (FITO) In order to implement a dual-pump FWM WC that operates in a FITO mode, the positioning of the signal with respect to the gain peak wavelength is significant. There are four main possibilities of interest that are shown in Fig. 14. The FI signal S1 can be placed close to the gain peak or at the gain peak wavelength, close to bandgap, close to the transparency wavelength, while the TO product is placed at any wavelength. In Fig. 14, the dashed line shows the gain peak wavelength. In Case 1, the F1 is at the region of peak wavelength with the pump being exactly at peak wavelength. In Case 2, the signal is placed exactly at peak wavelength. In both cases the TO is at another wavelength. In Case 3, the FI is at an arbitrary low wavelength and the TO is at any other higher wavelength. In Case 4, the FI enters at a wavelength close to the bandgap and TO can be at any lower wavelength. Note that for better efficiency P1 and S1 are arranged in a way that F1 is produced by down wavelength conversion. The experimental results are all indicative of the complexity of the effects that are introduced. The input powers are dBm and dBm. The first column of Fig. 15 shows the OSNR measured and calculated versus the wavelength separation of F1A from the gain peak wavelength The FWM output power (PF1A) experimental results are shown in the second column. OSNR and PF1A are measured for two ( in Fig. 15): 1 and 2 nm. wavelength separations The experimental results, particularly for nm, show many ripples. For the two first cases the modulated signal is particularly close to the peak causing significant gain modulation. Considering the separation of 1 nm, the two first cases are very similar. Starting from the output power the main mechanism M1 results in a decrease in the output power toward low wavelengths. There is a process that enhances this behavior especially for the first nanometer of down shifts and creates the difference in the output power between the Case 1 and 2: this is related to the gain and explained through the , where G is the saturated model where unsaturated gain of the amplifier [33]. and gain of the and both decrease for short wavelengths while decreases increases for increasingly longer wavelengths. This is and reflected in a less steeper curve slope toward the bandgap in comparison to the other side of the curve; the OSNR curve
exhibits a different behavior. ASE is proportional to so OSNR is expected to behave similarly to the efficiency. However for very small detunings the ASE is low, especially for up conversion. This is due to the gain asymmetry when the signal is close to the pump. For the case of a 2-nm separation, the same arguments hold, however the general efficiency is lower, as M1 is less efficient. , CH starts to dominate that exhibits This is because for this low efficiency. The same effects dominate in Cases 3 and 4. The interplay and , and the nature of between the relative magnitude of the interferences that is imposed by the responsible mechanisms defines the shape of the curve. For wavelengths lower than the both decrease and more than . peak wavelength, and This, combined with the enhanced down conversion efficiency of M2 makes Case 4 very appealing. Although there is a significant decrease of the output power, the OSNR remains almost constant and of a very high value over a wide range of wavelengths. This is in contrast with Case 3 where the up conversion characteristics of M2 dictate lower efficiency and OSNR. Given the choice, in a system that deploys a FITO converter, the SOA should be chosen in a way that the peak gain wavelength is lower than the fixed wavelength of the input, so that the converter will benefit from the down conversion, so that the systems is configured like in Case 4 before. C. Tunable Input/Fixed Output Wavelength Converter (TIFO) The opposite problem exists for the TIFO: the output signal is placed at one of the four following positions: P2 is placed at the peak wavelength (Case 1 in Fig. 16), F1A is at the gain peak (Case 2), F1A is at the longer wavelength side (Case 3) or F1A close to bandgap (Case 4). The converter is now configured as a TIFO. In Fig. 17 where the dashed line shows the gain peak wavelength, Case 1 assumes that the FO is positioned close to the gain peak wavelength, and the pump wavelength coincides with the peak wavelength; and Case 2 that F1A is exactly at peak wavelength. In both cases, the TI may be positioned at any possible wavelength. In Case 3, the FO is at a low wavelength and all TI are at any other higher wavelength, while the opposite occurs in Case 4. The nm experimental results are illustrated in Fig. 17 for and 2 nm. The modeling results are for the 1-nm case and for the output OSNR only (first column). The second column illustrates the output power. The axis shows the wavelength of the TI S1.
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1 1=1
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Fig. 15. First column: OSNR for nm (experiment and modeling) and nm (experiment) for the cases shown in Fig. 14. Second column: PF1A nm and the dashed (—) its position when nm. experimentally measured for both cases. The dashed (- -) line shows the position of the FI when
The interpretation of the results is based on the previous discussion. Since F1A is at a specific wavelength, is constant.
1 1=1
1 1=2
In the two first cases, F1A is in the peak region. In contrast with the FITO, here when the procedure is down conver-
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Fig. 16. Four cases for which the TIFO is investigated, with respect to the wavelength placement of the F1A. The FO position is in the circles. There are two examples of TI (P1 and S1) indicated for each case to illustrate the tunability of the input.
sion while when is up. Thus, when the S1 wavelength is lower than that of the F1A case, the main mechanism M1 results in a decrease in the output power toward longer wavelengths. While the S1 wavelength is close to the gain peak, M1 and M2 are enhanced. Case 3 bears all the characteristics of up-conversion with very low efficiency and OSNR, while Case 4 exhibits very good OSNR output over a wide wavelength range. Furthermore, the fact that the modulation grating due to carrier heating and CPP is enhanced toward lower wavelengths, assists this later case [32]. For the case of 2-nm, the case is equivalent as both procedures affect the gain modulation with bandgapthe sane trend, i.e., CH and CPP. Given the choice, in a system that deploys a TIFO converter, the configuration should be similar to Case 4. The SOA should be chosen in a way that the peak wavelength is higher than the fixed wavelength of the output F1A, so that the converter will benefit from the down conversion. VI. DISCUSSION In this work, FWM has been used for a simple WC, a TWC and ER enhancement. The dynamic effects that characterize FWM converters have been accounted for by the numerical model. The model predicts well the performance of the WC as far as modulation effects and wavelength dependence is concerned. Regarding the generation of ER, this can take place only in a simple WC. In the conventional FWM configuration, ER cannot be enhanced. If however the pump is modulated instead of the signal and the parameter takes values between 0.67 and 1, ER enhancement can occur. The rule for the specific SOA used, is experimentally validated. Enhancement is limited by saturation effects. ER enhancement, and format conversion can also take place if instead of a CW S1, a pulsed one is used. This method is more efficient and can potentially be used for retiming of the signal. As far as the performance of a FITO dual-pump converter is concerned, wavelength down conversion is preferable. The FI signal wavelength should be close to the SOA bandgap. This is a useful rule if the converter is to be used for a wavelength-routed switch. If a converter is combined with an AWG for example switch, an SOA must be [1], for the implementation of a chosen in a way that the input wavelength is close to the SOA bandgap for maximum OSNR output. Nevertheless, optimized OSNR solely cannot guarantee optimized performance of the converter. For that reason effects like GM ISI must be taken
into consideration. As two pumps are now involved, the rules for optimized performance assumed in the previous chapter are now relaxed by 3 dB. For the TIFO configuration the discussion yields the same results. The spectral distance between the wavelength of the FO and the bandgap needs to be as large as possible, so that down conversion is ensured. In practice and in order to enhance the performance of a TWC, RZ pulses instead of NRZ signals must be used for high-speed operation. Assuming that the ASE contribution is the same for the two cases, the performance is enhanced, because the efficiency is much better for the RZ case and also the GM effects on the pump is reduced [15]. This provides an extra argument in favor of high speed FWM. For systems operating at 160 Gb/s, the requirement for sufficient OSNR may lead in avoiding this method. For example even 28-dB OSNR is not sufficient for this high speed operation. However when operating with RZ pulses, demultiplexing to 10 Gb/s before the receiver provides a useful means of relaxing the requirements for high OSNR. Numerous conversion techniques have been proposed and implemented to date based on different nonlinear materials [34]–[39]. Non-linear coefficients in fibers and waveguides are low, requiring long lengths and high powers for the required degree of nonlinearity; although such devices are promising in terms of modulation bandwidth. SOAs were initially rejected for use as in-line amplifiers due to their inherit nonlinearities, but it is now exactly this feature that presents them as interesting devices for all-optical processing; they can also be integrated, but are limited in response times. Cross-gain modulation and especially cross-phase modulation (XPM) in SOAs are promising techniques, exhibiting regenerative characteristics with exceptional concatenation performance at low bit rates. However for higher bit rates XPM requires specific configurations with bit level phase control that supports only RZ format. Enhanced modulations formats cannot be translated by push pull configurations in any interferometers. FWM in SOAs has been suggested as a wavelength conversion technique, supporting bit rates higher than 100 Gb/s. Its unique characteristics, like phase conjugation and multiwavelength translation, have attracted much attention recently and numerous publications have focused on investigating specific features like efficiency, OSNR and pulse conversion. In this paper therefore, FWM is investigated with respect to its feasibility as a WC when deployed in realistic optical communication systems.
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nm (experiment and modeling) and nm (experiment) for the cases shown in Fig. 16. Second column: PF1A Fig. 17. First column: OSNR for nm. nm and the dashed (—) its position when experimentally measured for both cases. The dotted ( ) line shows the position of the FO when
...
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Fig. 18. Spectral arrangement at the output of a TWC based on FWM in SOAs with parallel-polarized pumps P 1 P 2.
?
VII. CONCLUSION It is expected that in future optical networks wavelength converters will be deployed in a tunable mode. Their tunability and dynamic physical performance may have a large impact on the design of the associated optical network. Especially when FWM wavelength converters are concerned dual-pump configurations should be implemented in order to achieve wide tunability. In this paper the physical performance of a FITO and TIFO was discussed and explained, and possible effects on the design of the node were studied. Other than that, simple wavelength converters based on FWM were investigated as far as static and dynamic behavior is concerned and as ER regenerative devices. In all the above cases results are discussed by means of experiment, numerical simulation and analytical modeling. APPENDIX A THE ANALYTICAL MODEL The output FWM power pected to be [25]
at frequency
is ex-
(A.1) is the SOA gain assumed spectrally flat and is the relative conversion efficiency function as defined [25]. Theoretical investigation of (A.1) has already been published in [25]. Here, the experimentally determined is used [25] (A.2) where is the total input power. We will assume that is independent of power [25]. The ASE is given by the formula [25] (A.3) By means of comparison with the experimentally achieved amplifier gain and ASE, the parameters , , and were obtained. The parameters that gave a good matching for a power and spanning from 15 to 0 dBm are: for the gain while and for the ASE. The analytical results are expected to be reliable for the range of total optical power [ 15 dBm, 3 dBm]; this yields from direct comparison of gain and ASE measurements with the specific amplifier used in the experiments.
P1
k P 2 and orthogonally polarized pumps
APPENDIX B DUAL-PUMP CONFIGURATIONS The two pumps are either copolarized or orthogonally polarized. In Fig. 18, the first case is illustrated with solid lines and the second with dashed ones. Both techniques feature characteristics that arise from different mechanisms. Pump P1 and signal . S1 are polarized in parallel and it is assumed that Hence, production of F1 is enhanced by means of up (frequency) conversion. When a second pump, say P2 at , enters the SOA the configuration is different. Mixing between the pumps and and F1A at . If P2 is the signal will produce F1A at parallel polarized with P1, there are two different mechanisms that contribute to the generation of each product. F1A has the same properties as F1, i.e., is the phase conjugate of S1, and is generated by the beating of S1 with P1 that scatters P2 (M1) and by a second mechanism (M2) where the beating between S1 and P2 scatters P1. In that way the product is generated at . F1A is a replica but not conjugate of S1 and the mechanisms are, respectively, the beating of P1 with S1 that scatters P2 (M1) and the second mechanism (M2) when the beating between P1 and P2 scatters S1. The product is thus gen. Both products are an aggregate of erated at a frequency spacing dependent term (due to M2) and a term that . Furthermore, depends on the fixed frequency spacing the sign of this spacing will determine whether the contributing effects are in phase and thus constructive interference enhances their performance. By using the lumped model the above configuration can be described as in [25]. The electric field is given by the summation of the two electric fields that are generated by the two mech, and anisms. By setting , one can derive the following relation for output powers:
(B.1) The equivalent function is now given by the summation of two squared functions. The magnitude of the first term de(or ) and pends on the (fixed) frequency spacing (M1). thus this term is independent of the frequency shift
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The magnitude of the second term depends on the spacing and thus PF1 is considered frequency dependent. Dual-pump configurations that allow both these mechanisms, as in the case of parallel pumps, do not have a constant efficiency over the is of the order of whole spectrum. Especially if spacing , both mechanisms are of the same magnitude. The orthogonal pump configuration could lead to almost flat conversion efficiency. In order to apply the above in the case of orthogonal polarized pumps (see Fig. 18) one has to assume that the gain is isotropic. In the case where P1 is orthogonal to the P2 and thus M2 does not contribute to the efficiency. In that case, the powers would be
(B.2) , It must be noted that the gain here is actually given by due to the different polarization of the pumps [32]. But the . This SOA is considered polarization insensitive and method, has several advantages with respect to the previous one, other than uniform performance with respect to efficiency and OSNR, see Fig. 13. In this scheme the output signal, FA1, is orthogonally polarized to the input signal S1, and to other products for example (F1). This implies that other crosstalk producing spurious products and ASE may be potentially reduced by means of polarization filtering. Most importantly it allows for spectral inversion without frequency shift. REFERENCES [1] F. Matera, “ATLAS Consortium, Final Project Report,” IST1999–10626, Feb. 2003. [2] D. Klonidis et al., “Fast and widely tunable optical packet switching scheme based on tunable laser and dual-pump four-wave mixing,” IEEE Photon. Technol. Lett., vol. 16, no. 5, pp. 1412–1414, May 2004. [3] G. Guekos, Ed., Photonic Devices for Telecommunications: Springer Co., 1998. [4] S. Diez et al., “Four wave mixing in semiconductor optical amplifiers for frequency conversion and fast optical switching,” IEEE J. Sel. Topics Quantum Electron., vol. 3, no. 5, pp. 1131–1145, May 1997. [5] A. D’Ottavi et al., “Four-wave mixing in semiconductor optical amplifiers: a practical tool for wavelength conversion,” IEEE J. Sel. Topics Quantum Electron., vol. 3, no. 4, pp. 522–528, Apr. 1997. [6] A. Girardin et al., “Low-noise and very high-efficiency four-wave mixing in 1.5-mm-long semiconductor optical amplifiers,” IEEE Photon. Technol. Lett., vol. 9, no. 6, pp. 746–748, Jun. 1997. [7] S.-L. Lee, P.-M. Gong, and C.-T. Yang, “Performance enhancement on SOA-based four-wave-mixing wavelength conversion using an assisted beam,” IEEE Photon. Technol. Lett., vol. 14, no. 12, pp. 1713–1715, Dec. 2002. [8] T. Hasegawa, K. Inoue, and K. Oda, “Polarization independent frequency conversion by fiber four -wave-mixing with a polarization diversity technique,” IEEE Photon. Technol. Lett., vol. 5, no. 8, pp. 945–948, Oct. 1993. [9] M. W. K. Mak, H. K. Tsang, and K. Chan, “Widely tunable polarization independent all-optical wavelength converter using a semiconductor optical amplifier,” IEEE Photon. Technol. Lett., vol. 12, pp. 525–528, May 2000. [10] T. Morgan et al., “All optical wavelength translation over 80 nm at 2.5 Gb/s using four wave mixing in a semiconductor optical amplifier,” IEEE Photon. Technol. Lett., vol. 11, no. 8, pp. 982–985, Aug. 1999. [11] A. E. Kelly et al., “100 Gbit/s wavelength conversion using FWM in an MQW semiconductor optical amplifier,” Electron. Lett., vol. 34, pp. 1955–1957, 1998. [12] S. Arahira and Y. Ogawa, “160-Gb/s all-optical encoding experiments by four-wave mixing in a gain-clamped SOA with assist-light injection,” IEEE Photon. Technol. Lett., vol. 16, no. 2, pp. 653–655, Feb. 2004.
[13] Z. Li et al., “Cascaded all-optical wavelength conversion for RZ-DPSK signal based on four-wave mixing in semiconductor optical amplifier,” IEEE Photon. Technol. Lett., vol. 16, no. 7, pp. 1685–1687, Jul. 2004. [14] G. P. Agrawal, Fiber Optic Communication Systems. New York: Wiley, 1997. [15] M. Shtaif and G. Eisenstein, “Calculation of bit error rates in all-optical signal processing applications exploiting nondegenerate four wave mixing in semiconductor optical amplifier,” J. Lightw. Technol., vol. 14, no. 9, pp. 2069–2077, Sep. 1996. [16] Y. Kim et al., “Analysis of frequency chirping and extinction ratio of optical phase conjugate signals by four wave mixing in SOAs,” J. Sel. Topics Quantum Electron., vol. 5, no. 3, pp. 267–280, May/Jun. 1999. [17] H. Simos et al., “Regenerative properties of wavelength converters based on FWM in a semiconductor optical amplifier,” IEEE Photon. Technol. Lett., vol. 15, no. 4, pp. 566–568, Apr. 2003. [18] H. Simos, A. Bogris, and D. Syvridis, “Investigation of a 2R all-optical regenerator based on four-wave mixing in a semiconductor optical amplifier,” J. Lightw. Technol., vol. 22, no. 2, pp. 595–604, Feb. 2004. [19] M. Summerfield and R. Tucker, “Frequency domain model of multiwave mixing in bulk semiconductor optical amplifiers,” IEEE J. Sel. Topics Quantum Electron., vol. 5, no. 3, pp. 839–850, Mar. 1999. [20] G. P. Agrawal, “Population pulsations and nondegenerate four-wave mixing in semiconductor lasers and amplifiers,” J. Opt. Soc. Amer. B, vol. 5, pp. 147–159, 1998. [21] A. Tzanakaki and M. O’Mahony, “Analysis of tunable wavelength converters based on cross-gain modulation in semiconductor optical amplifiers operating in the counter propagating mode,” Proc. IEE Optoelectronics, vol. 147, pp. 49–55, 2000. [22] G. Lindfield and J. Penny, Numerical Methods Using Matlab. Englewood Cliffs, NJ: Prentice Hall, 1999. [23] D. Alexandropoulos and M. Adams, “Theoretical study of GaInNAsGaAs-based semiconductor optical amplifiers,” IEEE J. Quantum Electron., vol. 39, no. 5, pp. 647–655, May 2003. [24] A. Mecozzi and J. Mork, “Saturation induced by picosecond pulses in semiconductor optical amplifiers,” J. Opt. Soc. Amer. B, vol. 14, pp. 761–775, 1997. [25] J. P. R. Lacey, M. Summerfield, and S. J. Madden, “Tunability of polarization insensitive wavelength converters based on four wave mixing in semiconductor optical amplifiers,” J. Lightw. Technol., vol. 16, no. 12, pp. 2419–2427, Dec. 1998. [26] L. Lu et al., “Bit-error-rate performance dependence on pump and signal powers of the wavelength converter based on FWM in semiconductor optical amplifiers,” IEEE Photon. Technol. Lett., vol. 12, no. 7, pp. 855–857, Jul. 2000. [27] C. Gosset and G.-H. Duan, “Extinction ratio improvement and wavelength conversion based on four-wave mixing in semiconductor optical amplifiers,” IEEE Photon. Technol. Lett., vol. 13, no. 2, pp. 139–141, Feb. 2001. [28] G. Contestabile et al., “Efficiency flattening and equalization of frequency up- and down-conversion using four-wave mixing in semiconductor optical amplifiers,” IEEE Photon. Technol. Lett., vol. 10, no. 10, pp. 1398–1400, Oct. 1998. [29] J. Zhou et al., “Efficiency of broad-band four-wave mixing wavelength conversion using semiconductor travelling-wave amplifiers,” IEEE Photon. Technol. Lett., vol. 6, no. 1, pp. 50–52, Jan. 1994. [30] T. J. Morgan, J. P. R. Lacey, and R. S. Tucker, “Widely tunable four-wave mixing in semiconductor optical amplifiers with constant conversion efficiency,” IEEE Photon. Technol. Lett., vol. 10, no. 10, pp. 1401–1403, Oct. 1998. [31] T. J. Morgan, R. S. Tucker, and J. P. R. Lacey, “All-optical wavelength translation over 80 nm at 2.5 Gb/s using four-wave mixing in a semiconductor optical amplifier,” IEEE Photon. Technol. Lett., vol. 11, no. 8, pp. 982–984, Aug. 1999. [32] A. Mecozzi, “Applications of four-wave mixing in semiconductor optical amplifiers,” in Proc. ECOC, 1998, pp. 647–648. [33] , “Analytical theory of four-wave mixing in semiconductor amplifiers,” Opt. Lett., vol. 19, pp. 892–894, 1994. [34] B. Ramamurthy and B. Mukherjee, “Wavelength conversion in WDM networking,” IEEE J. Sel. Areas Commun., vol. 16, no. 7, pp. 1061–1078, Jul. 1998. [35] R. Sabella and E. Iannone, “Wavelength conversion in optical transport networks,” Fiber Integr. Opt., vol. 15, pp. 167–179, 1996. [36] T. Durhuus et al., “All-optical wavelength conversion by semiconductor optical amplifiers,” J. Lightw. Technol., vol. 14, no. 6, pp. 942–956, Jun. 1996.
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[37] S. J. B. Yoo, “Wavelength conversion technologies for WDM network applications,” J. Lightw. Technol., vol. 14, no. 6, pp. 955–966, Jun. 1996. [38] M. Asghari, I. H. White, and R. V. Penty, “Wavelength conversion using semiconductor optical amplifiers,” J. Lightw. Technol., vol. 15, no. 7, pp. 1181–1190, Jul. 1997. [39] K. E. Stubkjaer et al., “Wavelength converter technology,” IEICE Trans. Electron., vol. E82-C, no. 2, pp. 338–346, 1999.
Christina (Tanya) Politi received the B.Sc. degree in physics from the University of Athens, Athens, Greece, in 1998, and the M.Sc. degree in the “physics of laser communications” from the University of Essex, Colchester, U.K., in 2000. Subsequently, she joined the Photonic Network Research Group in the Department of Electronic Systems Engineering at the University of Essex. She was involved in various projects including the IST-OPTIMIST and IST-BREAD projects and received her Ph.D. in 2005. She has recently joint the Optical Networks Group, National Technical University of Athens. Her research interests include optical packet and circuit switched networks, high speed optical networks and optical wavelength converters.
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Dimitrios Klonidis was received the B.S. degree in electrical and computer engineering from Aristotle University of Thessalonica, Greece, in 1998 and the M.Sc. degree in Telecommunication and Information Systems from the University of Essex, Colchester, U.K., in 2001. He worked on high-speed networks while he participated in various national and EU projects. In September 2005, he joined the High-Speed Networks and Optical Communications (NOC) Group in AIT, Greece. His main research interests are in the area of ultrafast photonic networks, including optical transmission and modulation, fast switching, high speed optical processing and fast node control. Considered networking applications include high capacity SONET/SDH, optical packet/burst switched, and grid computing networks.
Mike J. O’Mahony (M’88–SM’94) graduated from Essex University, Colchester, U.K., in 1974 and received the Ph.D. degree for research in digital transmission systems in 1977. In 1979, he joined the Optical System Research Division of British Telecom working on research into fiber-optic systems for undersea systems, in particular, experimental and theoretical studies of receiver and transmitter design. In 1984, he became a Group Leader responsible for the study and application of optical amplifiers to transmission systems. In 1988, he became Head of Section responsible for 50 graduates researching terrestrial long haul optical systems and networks. In 1991, he joined the Department of Electronic Systems Engineering, University of Essex, as Professor of Communication Networks. He was Head of Department from 1996 to 1999. His current research is related to the study of future network infrastructures and technologies. He is principal investigator for grants supported by industry, national research councils, and the European Union. He is the author of over 200 papers relating to optical communications. Prof. O’Mahony is a member of the Institute of Electrical Engineers (IEE), U.K.
