484 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 46, NO. 4, APRIL /$ IEEE

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1 484 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 46, NO. 4, APRIL 2010 Time-Domain Modeling of Ultralong Semiconductor Optical Amplifiers Patrick Runge, Robert Elschner, Student Member, IEEE, and Klaus Petermann, Fellow, IEEE Abstract An advanced numerical model for simulating ultralong semiconductor optical amplifiers (UL-SOAs) is presented. The model specifically accounts for the very strong gain saturation and the ultrafast gain dynamics in UL-SOAs. Due to the UL-SOA s length, the weak but fast intraband effects can strongly interact with the input signals. For this reason, UL-SOAs have a tremendous four-wave mixing (FWM) efficiency even for large wavelength detunings. Therefore, it is necessary that the UL-SOA model is a time-domain model so that all FWM products and their interaction with other FWM products are automatically calculated. These FWM products need to be considered in simulations, because they contribute to the UL-SOA s saturation in addition to amplified spontaneous emission. Moreover, due to the time-domain modeling, pseudorandom bit sequence signals can be applied to the model for simulating telecommunication applications. Other aspects that should be considered when modeling UL-SOAs are the gain parametrization and the ultrafast gain dynamics. The wavelength-dependent material gain needs to be properly represented close to the transparency, since most of the device is deeply saturated. The gain dynamics have to be dynamically modeled with rate equations automatically incorporating the limited bandwidths of the different nonlinear gain effects. Although usually not considered for short SOAs, the implementation of weak nonlinear effects like free carrier absorption and two-photon absorption is important due to the long interaction length in UL-SOAs. Index Terms Four-wave mixing, simulation model, ultralong semiconductor optical amplifiers (UL-SOA). I. INTRODUCTION T HE increased traffic of communication demands higher data rates in existing optical networks. Because of higher data rates all-optical solutions are needed. For this reason, the research for high-speed devices like quantum-dot (QD) structures is in progress, but there are still problems in the fabrication and with the properties of QD devices. Another of those novel high-speed devices is an ultralong bulk semiconductor optical amplifier (UL-SOA). The first applications with UL-SOAs have been presented. In [1] the decreased effective carrier lifetime in UL-SOAs is used to handle data rates up to 40 Gb/s. Since the decreasing of the carrier lifetime saturates with the length of the SOA [2] this concept is also quickly speed-limited. In [3] a concept is presented where only the fast nonlinear effects of the semiconductor material are used, to make the Manuscript received August 21, 2009; revised October 15, Current version published February 12, This work was supported by the Deutsche Forschungsgemeinschaft (DFG). The authors are with the Fachgebiet Hochfrequenztechnik, Technische Universität Berlin, D Berlin, Germany ( runge@hft.ee.tu-berlin.de; elschner@hft.ee.tu-berlin.de; petermann@tu-berlin.de). Color versions of one or more of the figures in this paper are available online at Digital Object Identifier /JQE UL-SOA capable for high-speed all-optical signal processing (data rates Gb/s). Furthermore, UL-SOAs can generate short pulses because of their tremendous four-wave mixing (FWM) efficiency, also caused by the fast intraband effects [4]. Nevertheless, for modeling some of these applications, the UL-SOA model must be a time-domain model so that it can handle PRBS signals. Moreover, for computing the FWM products, a time-domain model is also of advantage because the interaction of the dynamical gain and index gratings with the signals are modeled automatically. The paper is structured as follows. First, the basic properties of UL-SOAs are discussed in order to figure out which important effects have to be included to the simulation model. In Section III a gain parametrization is presented which gives good results close to the material transparency and how to apply the parametrization on time-domain modeling. The gain dynamics of UL-SOAs are discussed in Section IV where the focus is on the consideration of weak effects like free carrier absorption (FCA) and two-photon absorption (TPA) and on their dynamical implementation with rate equations. II. PROPERTIES OF UL-SOAS The purpose of UL-SOAs is to benefit from the semiconductor s fast nonlinear intraband effects like carrier heating (CH) and spectral hole burning (SHB), while slow interband effects should be suppressed as far as possible, in order to avoid bit pattern effects. Unlike in short SOAs, the main part of UL-SOAs is saturated by the amplified input signals and the amplified spontaneous emission (ASE) noise after a certain length. For this reason, UL-SOAs can be regarded as being divided into an amplifying section and a saturated section. For bulk SOAs with typical dimensions, the transition between these sections takes place after approximately 1 mm of propagation. The amplifying section has the same properties as a short SOA, and the saturated section can be regarded as another device with different properties. Because of the high optical power after the amplifying section, the carrier density in the saturated section is fixed to the net transparency level. In the saturated section only the fast nonlinear intraband effects influence the signals. While for the intraband effects the carrier density distribution inside of a band changes, the overall number of carriers of the band remains unchanged. The response time of these effects is about 1000 times shorter compared to the carrier density pulsation (CDP), but their impact is also weaker. For this reason UL-SOAs have a length of several millimeters. In the gain regime these nonlinear intraband effects are gain suppressing and mainly dependent on the photon density. When injecting multiple copolarized signals at the same time into an UL-SOA, in the UL-SOA s saturated section the signals beating creates dynamic index and gain gratings due to the fast /$ IEEE

2 RUNGE et al.: TIME-DOMAIN MODELING OF ULTRALONG SEMICONDUCTOR OPTICAL AMPLIFIERS 485 Fig. 1. Calculated FWM spectrum at the end of an 8-mm-long UL-SOA caused by two injected copolarized CW signals at and 1560 nm respectively. The FWM products again interact with their neighbor signals so that at the end of the UL-SOA a broad FWM comb can be obtained due to the high FWM efficiency. Because of the broad FWM comb the UL-SOA is mainly saturated by FWM products instead of ASE. For comparison to measurements see [4]. intraband effects. The interaction of the signals with these dynamic gratings generates FWM. Due to the high signals power in the saturated section and the short relaxation times of the intraband effects, FWM can take place over several nanometers. Since there are three main gain mechanism (CDP, CH, and SHB) and each mechanism has another relaxation time constant, their contribution to the FWM efficiency hold for different bandwidths [5]. Furthermore, the FWM products again interact with their neighbor signals (cascaded FWM process) due the good FWM efficiency so that a broad spectral FWM comb can be obtained at the end of the UL-SOA (Fig. 1). Moreover, further FWM-related effects like the Bogatov-like effect occur due to the dynamic gain and index grating [3], [5], [6] also changing the power and the phase of the signals. III. MODELING THE WAVELENGTH-DEPENDENT GAIN In telecommunication applications the input signals can be PRBS signals which have to propagate in time-domain through the UL-SOA [7]. Furthermore, because of the complex FWM interactions, it is nearly impossible to calculate the FWM spectrum in the frequency domain, since even simple FWM processes are complicated to calculate [8]. When modeling in the time domain, the dynamic gain and index gratings causing FWM are automatically created. Hence, all interactions of the signals and the dynamic gratings are inherently included (FWM, Bogatov effect, etc.). On the other hand, when using time-domain modeling, the calculation of the wavelength-dependent gain is complicated because the frequency components of the signals are unknown. For this reason adaptive finite-impulse response (FIR) filters are used for modeling the wavelength-dependent gain in each segment of the UL-SOA [9]. A. Spectral Gain Approximation In [9] the wavelength-dependent gain is fitted to a parabolic gain model which is only accurate for high carrier densities around the gain peak. Since in short SOAs the carrier density is nearly constant and the input signals are launched around Fig. 2. Spectrum of the linear material gain in dependence of the wavelength for different carrier densities according to Table I (dotted lines: parabolic gain approximation [9], dashed lines: cubic gain approximation [10], solid lines: advanced cubic gain approximation). The cubic gain approximation by Leuthold is for N = N around greater than 0. the gain peak into the SOA, the parabolic gain approximation can be used. In UL-SOAs the carrier density is high in the amplifying section and low in the saturated section resulting in a shift of the gain peak by approximately 30 nm so that the parabolic gain approximation can not be used. A cubic parametrization was given in [10] accurately describing the material gain over a broad bandwidth for various carrier densities. Unfortunately, this model does not properly represent the gain spectrum for carrier densities close to the material transparency. Fig. 2 shows that there is still positive gain around for the transparency carrier density, which can be a problem for modeling UL-SOAs since most of the device is saturated. As long as the carrier density for the net transparency is about 1.5 times larger than the material transparency, the cubic model can be used because the error does not carry to much weight. But when optimizing the UL-SOA in terms of increasing the nonlinear gain [11], the net transparency and material transparency level become similar and one obtains unphysical modeling results when using the cubic gain parametrization. Since, except for this problem, the cubic gain model very well matches with measurements of the material gain of InGaAsP semiconductors with of approximately of 1550 nm (see [10]), only two additional boundary conditions are defined in order to resolve this problem: and (1) These two boundary conditions can be included to the model when creating two additional degrees of freedom by extending the cubic gain model from [10] with two further parameters. The advanced cubic gain model is given in (2) (the explanations of the variables are given in Table I, shown later): for and for (2)

3 486 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 46, NO. 4, APRIL 2010 Fig. 3. Schematic description of the material gain model constructed by a quadratic and a cubic polynomial term; the gain starts to be zero for > > because of the spectral lineshape function caused by the carrier relaxation time. with (3a) (3b) (3c) (3d) (3e) For a better understanding Fig. 3 illustrates that the gain model consists of a parabolic and a cubic polynomial term. The idea behind the modifications of the advanced cubic gain model is to make sure that the cubic part of the polynomial in (2) dominates for low carrier densities. Therefore, the exponential terms in (3a) and (3c) that dominate for low are weighted with and.for the exponential terms of (3) vanish and the cubic gain model from [10] and the here presented gain model become equal. As a result, the advanced cubic gain model represents the material gain over a broad bandwidth for very precise and does not suffer from the inaccuracy at low carrier densities (Fig. 2). B. Implementation of the Wavelength Dependence The UL-SOA is divided into segments with the length corresponding to the sampling interval of the input signals Fig. 4. Schematic description of the modeling concept; the SOA is divided into longitudinal segments corresponding to the sampling time of the input signal. The signal E propagates trough the SOA and interacts at each segment with nonlinear medium represented by the carrier density N, the gain g, and the spontaneous emission E. The index x; y denotes the polarization axis, and the superscript 6 denotes the forward and backward traveling field.. The flowchart in Fig. 4 illustrates the interaction between the electric field and the semiconductor material. In order to model the wavelength dependence of the gain, an adaptive FIR filter in each segment is used. To avoid under sampling of the signals, difference signals are used for the propagation in the UL-SOA ( with being the reference frequency). The best approximation of the FIR filters to the advanced cubic gain model will be around the reference frequency. The FIR filters will be of first order so that the propagation equation for the signals can be written as (4), shown at the bottom of the page. is the contribution of the spontaneous emission (SE) of each SOA segment to the propagating field [12]. The noise source in this model is a white noise source getting the spectral shape of ASE due to the convolution with the material gain of each SOA segment when propagating with the signal through the UL-SOA. The implementation of ASE is a very important issue when modeling UL-SOAs because it contributes to the saturation of the UL-SOA. C. Calculation of the FIR Filter s Coefficients In this subsection the complex filter coefficients, that are needed for the signal propagation in (4), are derived. Applying the Fourier transformation on the time-domain propagation equation (4) yields the propagation equation in the frequency domain For the further derivation only one segment of the SOA is regarded exemplarily so that the spatial dependence of the variables can be neglected in order to simplify the equations and make them more clearly. The same calculation can be done in (5) (4)

4 RUNGE et al.: TIME-DOMAIN MODELING OF ULTRALONG SEMICONDUCTOR OPTICAL AMPLIFIERS 487 each segment with the corresponding variables of the segment. The FIR filter s gain function for the field is written as where the filter coefficient is a complex value while is assumed to be real. Relating the FIR filter s gain function (6) to the power, the following equation can be obtained: (6) (7) The advanced cubic material gain approximation is given in (2). Due to the difference frequency concept, the cubic gain model has to be related to. The cubic material gain is needed in order to calculate the power-related net gain of the propagating signals (8) Fig. 5. Wavelength-dependent net gain of one segment of the UL-SOA for different carrier densities (solid lines implementation with the FIR filters, dashed lines reference gain according to (2)). Due to the first-order FIR filter the spectral gain has a periodic shape and does not approximate well the reference gain model for j 0 j > 30 nm. The inset shows spectral gain of interest (70 nm around ) where the FIR very well approximate the gain model. Equating (8) and (7) and expanding both sides with the help of the Taylor series around, a polynomial comparison can be done. After some calculations the FIR coefficients can be obtained (9) with,, and defined as follows: Fig. 6. Carrier density in a 4-mm UL-SOA along the propagation direction. For the cubic gain approximation, the carrier density falls even below the material transparent level (dotted green line) in order to saturate the UL-SOA. (10) According to [13] also the wavelength dependence of SHB can be implemented with these filter coefficients. Fig. 5 shows the gain dispersion created by the FIR filters (7) compared to the reference gain from (8). Depending on the sampling interval, the FIR filter creates a periodicity in frequency domain. For a sampling interval of 25 fs, the periodicity has a spectral repetition rate of approximately 325 nm. For modeling applications, it is important that the gain approximation is accurate in a bandwidth of 30 nm around the reference wavelength. The inset of Fig. 5 gives a detailed view on this bandwidth and an excellent match can be observed. D. Modeling Results The improvements of the simulations due to the advanced cubic gain model are demonstrate with the help of a FWM example. For this reason, two copolarized CW signals with a power of 0 dbm each are injected into the UL-SOA at 1550 and 1552 nm, respectively. The UL-SOA has a length of 4 mm and is pumped with a current of 300 ma/mm. The other SOA parameters are given in Table I. Comparing the advanced cubic gain model with the cubic gain model by Leuthold, the carrier density along the -direction for simulations with the two gain models has to be regarded (Fig. 6). While for the advanced cubic gain model, the carrier density in the saturated section becomes the net transparency carrier density m, the carrier density for the cubic model drops below the material transparency carrier density resulting in an unphysical behaviour since, and are positive values. The effect is caused by the inaccuracy of the cubic gain approximation for low carrier densities as discussed in Section III-A. To show the improvement of the advanced cubic gain model compared to the parabolic gain model, the optical output

5 488 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 46, NO. 4, APRIL 2010 TABLE I TYPICAL PARAMETERS OF BULK SOAS USED FOR THE SIMULATION.THE PARAMETERS HAVE BEEN TAKEN FROM THE LITERATURE [9], [10], [13], [20] Fig. 7. Optical spectrum at the end of a 4-mm UL-SOA for two copolarized CW input signals at 1550 and 1552 nm. According to Fig. 2, the spectrum for the parabolic gain approximation is very narrow. should be considered: First of all, the influence of weak effects like FCA and TPA is not negligible because they can strongly interact with the signals due to the UL-SOA s interaction length. Second, the effects must be modeled with rate equations so that the bandwidth of the effects is included automatically. This allows accurate modeling of pulse propagation with pulse widths in the order of the intraband scattering times for which an instantaneous implementation would be invalid. For this reason, the dynamic rate equations for the nonlinear gain are briefly derived in the Section IV-A. A. Derivation of the Rate Equations The carrier dynamics (11a) spectra of the FWM simulation have to be regarded (Fig. 7). The spectrum generated with the advanced cubic gain model provides a broad FWM comb. With the parabolic gain model a more narrow FWM comb with about 30 db less power is obtained because for carrier densities close to the transparency level, the parabolic gain approximation also becomes narrow (Fig. 2). Moreover, the noise floor for the simulation with the advanced cubic gain model has a nice shape corresponding to the gain spectrum while for the parabolic gain model only a flat noise floor is observable. For the cubic gain model by Leuthold, no FWM spectrum could be obtained from the simulations because the always positive gain around the gain peak results in extremely high photon densities toward the end of the device causing a break down of the simulations. IV. GAIN DYNAMICS IN UL-SOAS Since the applications of UL-SOAs are based on the fast intraband effects, the important aspects of modeling these effects are discussed in this section. There are two major aspects that (11b) (11c) are given by [14] and [15] with being the energy density, the overall carrier density, the local carrier density and and the energy levels for one and two photons respectively. is the frequency related to. is the photon density and is related to the optical field:. is the carrier lifetime which can be calculated with:. The description of the other variables is given in Table I. The index can be replaced by and representing the conduction and valence band respectively. All effects are dominated by the slower conduction band electrons due to their smaller mass. For this reason the calculations only have to be done for the conduction band. Equation (12) (12)

6 RUNGE et al.: TIME-DOMAIN MODELING OF ULTRALONG SEMICONDUCTOR OPTICAL AMPLIFIERS 489 is the linear expansion of the energy density with respect to the carrier density and the carrier temperature [16]. According to [17] the cooling rate can be derived from (11b) and (12) [18] (13) Usually, the contribution of TPA to CH is neglected when modeling SOAs because in short SOAs, TPA has an influence only for very high photon densities, where the carrier temperature is strongly increased. Then the Fermi-distribution approach breaks down and (13) is no more valid [19]. However, due the long interaction length in UL-SOAs, TPA has a non-negligible impact also for moderate carrier temperatures. In this case, (13) can be used. In the style of [20] the gain dynamics in (14) are derived for the wavelength at the gain peak. Opposite to [20] the actual carrier density should be used in (14c) since the carrier density in UL-SOAs strongly varies along the propagation direction. (14a) (14b) (14c) (14d) (14e) Since (14a) is derived from (11a), can be related directly to the carrier density:. Based on [21] the total gain and the induced phase change due to the -factors is calculated as follows at each SOA segment: (15a) (15b) In this approach of modeling the nonlinear gain, the gain suppression factors are empirical parameters that have to be fitted with the help of simulations to experimental results. In reality the gain suppression factors, the alpha-factors and even the time constants of the gain suppression mechanisms are not constant [13], [22], [23]. However, the consideration of several dependencies of these parameters would result in the introduction of several additional parameters which can not be measured directly but have to be fitted to the measurements. The inevitable Fig. 8. FWM efficiency for a 4-mm-long SOA in dependence of the wavelength detuning measured at the conjugated wavelength. When disabling FCA and TPA, the FWM efficiency increases for 1 > 0 in the range of the CH time constant for up to 3 db. inaccuracies in determination of these new parameters would neutralize the additional accuracy of the model. For this reason the dependences of the gain suppressing parameters have been neglected because even without considering these dependences, our simulation model shows a good match with measurements. In [4] it has been demonstrated how well the modeling of the dynamical rate equations in combination with the implementation of the wavelength-dependent gain matches with measurements of FWM. A further example for matching of the modeling results with measurements can be found in [24]. Note that the instantaneous optical absorption due to TPA and FCA and the instantaneous phase change due to the Kerr effect are not included in the model. TPA is considered via its contribution to the change of the carrier density and its contribution to the gain compression by additional carrier heating. FCA is also taken into account via its contribution to carrier heating. The -factors of both effects are related to the phase change due to the carrier heating. B. Modeling Results Fig. 8 shows the FWM efficiency of a 4-mm-long bulk UL-SOA for two copolarized CW signals. The pump was injected at 1560 nm and had an input power of 0 dbm, while the probe s input power is dbm. In order to optimize the FWM efficiency, has been increased to 0.5. When regarding the solid line with the filled squares in Fig. 8, the three FWM regimes related to the different gain relaxation time constants can be observed. Up to 0.2 nm the slow but due to the strong gain change and the big -factor very powerful CDP can still follow the signals beating so that the FWM efficiency is dominated by CDP. From 0.2 nm up to 3 nm, CH dominates the FWM efficiency while from 3 nm up to 10 nm SHB dominates. When disabling FCA and TPA, a difference of up to 3 db compared to a simulation with FCA and TPA for a positive wavelength detuning and 1.25 db for a negative wavelength detuning can be observed. In general, one would have expected that disabling both mechanisms would result in a decreased FWM efficiency because less nonlinear effects contribute to the FWM process but the opposite can be observed. In [5] it has been explained, why additional gain

7 490 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 46, NO. 4, APRIL 2010 mechanisms can decrease the FWM efficiency. The range of this difference takes place in the bandwidth of the CH time constant, since FCA and TPA contribute to CH. In this regime, CH due to stimulated recombination creates the dominating dynamic gain and index gratings. Since the -factors of FCA and TPA differ from, FCA and TPA create dynamic gratings that are not necessarily in phase with the CH grating and therefore can result in destructive interference. Moreover, the phase shift of the dynamic index grating is dependent on the detuning. Hence, for the same positive and negative wavelength detuning, differences in the FWM efficiency of up to 1.5 db can be observed. Although the gain suppression of TPA is small compared to FCA, TPA also contributes opposite to FCA due to its -factor to the nonlinear phase change. Therefore, both FCA and TPA should be considered when modeling UL-SOAs because even these weak effects influence the signals over such a device length. Compared to typical (short) SOAs, only a slight difference can be observed in the FWM efficiency for the positive and negative detuning while in [5] a difference of about 10 db for a detuning of 6 nm is predicted. The reason for this discrepancy is that more than two modes are involved in the generation of the conjugated signal in UL-SOAs. The generated FWM modes can feedback on their parent modes due to the very high FWM efficiency (see for example the spectrum in Fig. 1). When increasing the detuning, the FWM efficiency is reduced as well as the feedback making the FWM process straight forward like in typical (short) SOAs. As a result, a difference between the positive and negative detuning of approximately 10 db around 12 nm can be observed. V. CONCLUSION We here presented a time-domain UL-SOA model which accounts for the important issues of FWM and FWM-related effects. Due to the time-domain modeling and the models simplicity regarding the implementation of the wavelength-dependent gain and the nonlinear effects, it can actually be used for complex engineering applications with PRBS signals [7]. Since the main part of the UL-SOA is deeply saturated it is especially important that the gain model also is exact for carrier densities close to the net transparency. For this reason we presented a gain approximation that properly represents the gain for various carrier densities over a broad bandwidth nm. The bandwidth of the gain model is also an important issue because the gain peak shifts due to the different carrier densities in the UL-SOA s amplifying and saturated section. In addition, the tremendous FWM efficiency of UL-SOAs can create broad FWM spectra up to 30 nm making the bandwidth of the gain model even more important. While FWM for a wavelength detuning above 0.2 nm is mainly created by the dominating fast intraband effects like CH and SHB, the contribution of weaker nonlinear effects like FCA and TPA are not negligeable. Due to the length of the UL-SOA device, FCA and TPA can also strongly interact with the signals. Hence, enabling and disabling FCA and TPA results in a difference of up to 3 db in the FWM efficiency. Furthermore, when modeling the nonlinear gain due to dynamic rate equations, the bandwidth of the effects will be automatically incorporated. REFERENCES [1] J. Slovak, C. Bornholdt, U. Busolt, G. Bramann, C. Schmidt, H. Ehlers, H.-P. Nolting, and B. Sartorius, Optically clocked ultra long SOAs: A novel technique for high speed 3R signal regeneration, in Optical Fiber Commun. Conf., Los Angeles, CA, [2] K. Obermann, T. Liu, K. Petermann, F. Girardin, and G. Guekos, Saturation of semiconductor optical amplifiers due to amplified spontaneous emission, in Proc. 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8 RUNGE et al.: TIME-DOMAIN MODELING OF ULTRALONG SEMICONDUCTOR OPTICAL AMPLIFIERS 491 Patrick Runge was born in Berlin, Germany, in He received the Dipl.-Ing. degree in computer science from the Technische Universität Berlin, in He is currently working toward the Ph.D. degree at the Technische Universität Berlin. His research is on the physics and applications of ultralong semiconductor optical amplifiers. From 2005 to 2007 he was with the Hymite GmbH where he was involved in the design and measurement of optoelectronic packages for optical communication. Robert Elschner (S 06) was born in Eisenhüttenstadt, Germany, in He received the Dipl.-Ing. degree in electrical engineering from the Technische Universität Berlin, Berlin, Germany, in 2006, where he is currently working toward the Ph.D. degree at the Institut für Hochfrequenztechnik und Halbleiter-Systemtechnologien, in the field of all optical wavelength conversion and regeneration. During 2005, he was with the École Nationale Supérieure des Télécommunications, Paris, France, where he was engaged in research on all-optical clock recovery using self-pulsating lasers. Klaus Petermann (M 76 SM 85 F 09) was born in Mannheim, Germany in He received the Dipl.-Ing. degree in 1974 and the Dr.-Ing. degree in 1976, both in electrical engineering from the Technische Universität Braunschweig, Braunschweig, Germany. From 1974 to 1976, he was a Research Associate at the Institut für Hochfrequenztechnik, Technische Universität Braunschweig, where he worked on optical waveguide theory. From 1977 to 1983, he was with AEG-Telefunken, Forschungsinstitut, Ulm, Germany, where he was engaged in research work on semiconductor lasers, optical fibers, and optical fiber sensors. In 1983, he became a Full Professor at the Technische Universität Berlin, Berlin, Germany. His current research interests include optical fiber communications and integrated optics. Dr. Petermann is a member of the Berlin Brandenburg Academy of Science. He is the recipient of the Leibniz Award from the Deutsche Forschungsgemeinschaft in 1993, and the Distinguished Lecturer Award from the IEEE Laser and Electro-Optics Society in 1999/2000. From 1999 to 2004, he was an Associate Editor of the IEEE PHOTONICS TECHNOLOGY LETTERS. From 1996 to 2004, he was a member of the board of the Verband Der Elektrotechnik Elektronik Informationstechnik (VDE). From 2004 to 2006, he was the Vice President for research at the Technische Universität Berlin.