An experimental method for identifying nonlinear phenomena intervening in a FWM process developed in a semiconductor optical amplifier

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IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 34, NO. 11, NOVEMBER 1998

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An Experimental Method for Identifying Nonlinear Phenomena Intervening in a FWM Process Developed in a Semiconductor Optical Amplifier Horacio Soto and Didier Erasme

Abstract— The new experimental research on the four-wave mixing (FWM) phenomena described here consists in launching three optical waves (pump, probe, and test) into a semiconductor optical amplifier and measuring the test beam transmission and the conversion efficiency of the new wave generated to one side of the test beam. It allows for an excellent identification of the nonlinear phenomena involved in the FWM process. The analysis principle is based on the modulation of the gain curve for each of the three effects considered: spectral hole burning, carrier heating, and carrier density pulsation. Experimental and theoretical results are presented. Index Terms—Four-wave mixing in semiconductor optical amplifiers, nonlinear phenomena identification.

I. INTRODUCTION

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EMICONDUCTOR optical amplifiers (SOA’s) are expected to play an important role in future broad-band multichannel lightwave systems. Several mechanisms, interand intraband, acting in the SOA’s allow the conception of diverse optoelectronics functions such as wavelength conversion [1], chromatic dispersion compensation [2], and clock recovery [3]. Particularly these functions can be achieved using a fourwave mixing (FWM) process within an SOA. Therefore, it is very important to know which are the physical phenomena intervening in the FWM process, and to determine how they relate with each other. With this information, one should be able to find out the application best suited to the SOA tested. Eventually, new applications can be found. Several papers have already been devoted to the identification of the nonlinear effects acting on the dynamics of SOA’s. Among these phenomena, carrier density pulsation, carrier heating, and spectral hole burning have been recognized as the major contributors to the FWM interaction. Some studies are developed in the frequency domain through FWM [4]–[12]. Other works are realized in the time domain via the pump-probe technique [13]–[17]. In the frequency domain, the observation typically consists of finding the evolution of the FWM conversion efficiency versus pump and probe detuning Manuscript received November 26, 1997; revised June 22, 1998. This work was supported in part by Consejo Nacional de Ciencia y Tecnolog´ıa de M´exico and by Conseil National de la Recherche Scientifique de France. H. Soto is with CICESE, Fisica Aplicada, Ensenada 22860, Baja California, Mexico. ´ D. Erasme is with D´epartement Communications, Ecole Nationale Sup´erieure des T´el´ecommunications (CNRS URA 820), 75634 Paris cedex 13, France. Publisher Item Identifier S 0018-9197(98)08088-9.

frequency. In order to identify the different phenomena, characteristic detuning frequencies in the response are compared with the cut-off frequencies for the nonlinear mechanisms of interest. However, since the observation is realized in precise detuning frequencies, phenomenological amplitude variations in the evolution of the FWM conversion efficiency can be misinterpreted for variations due to the measurement noise. This disadvantage is emphasized when the actual nonlinear phenomenon is weak due to the amplifier characteristics or to the experiment design, leading to contradictory interpretations. The pump-probe technique consists of launching two ultrashort optical pulses (some femtosecond) successively into the amplifier. The transmission of the probe beam is measured versus the pump-probe delay. This measurement reveals the gain suppression generated by the pump pulse through various nonlinear effects. The relaxation time can be derived. The first difficulty with this technique is in generating short optical pulses with a duration shorter than the constant time for faster nonlinear phenomena such as spectral hole burning. Another disadvantage for this technique is that amplitude variations on the probe signal occur at precise delays. Thus, phenomenological amplitude variations can be confounded with variations due to the measurement noise. In this paper, we propose a new experimental identification method. CW pump and probe optical beams are injected into the SOA creating FWM. A third codirectional weak test beam is added in the SOA. The experiment consists of tuning the test beam wavelength and observing, for each wavelength, its transmission and the FWM conversion efficiency between the test beam and a new generated beam of frequency where , and are the optical frequencies of the test, pump, and probe beams, respectively (see Fig. 1). The major difference with the previous methods is that, for one given frequency detuning between the pump and the probe characteristic of nonlinear processes, two complete response curves can be obtained. This represents much more information than that obtained previously from a single point. The manifestations of the nonlinear phenomena will be present in each detuning frequency for a large number of test beam wavelengths, hence the interpretation can be more precise. II. EXPERIMENT The SOA under test is an InGaAsP–InP double heterostructure amplifier manufactured by Alcatel Alstom Recherche.

0018–9197/98$10.00  1998 IEEE

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Fig. 1. SOA output spectrum. The spectrum is obtained when a weak test beam is injected into the amplifier when it develops a 3-THz detuning frequency FWM process. The pump, probe, and test beam are placed at 1531.2, 1555, and 1495 nm, respectively.

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Fig. 2. Setup used for the determination of the conversion efficiency for the first modulation harmonic of the test beam. The powers of the pump, probe, and test signals in the input of the SOA are estimated to be about 2, 1, and 20 dBm, respectively. The bias current is fixed to 120 mA.

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The active waveguide includes a 260- m-long central region with a square section, 0.5 m wide, narrowing linearly as a lateral taper of 70 m long at each end. The setup is shown in Fig. 2. The lightwave is launched into and received out of the amplifier using lensed optical fibers. An imperfect DFB semiconductor laser emitting two modes generates the pump ( ) and the probe ( ) signals simultaneously. The probe signal is centered around 1555 nm, and the pump signal can have three different stable wavelengths, depending on the bias current, leading to three detuning frequencies of 90, 250, and 3000 GHz. In order to maintain stable behavior, a 55-dB fiber optic isolator is placed after the DFB laser output. For ensuring saturation of the semiconductor amplifier medium, the pump and the probe signals are amplified in an Er-doped fiber amplifier before being launched into the SOA through a 90%–10% fiber optic coupler. The branch of low transmission of the coupler is connected to an external cavity tunable laser, which generates the wavelength tunable test signal. The powers of the pump, probe, and test signals in the input of the amplifier are estimated to be of about 2, 1, and 20 dBm, respectively, and their polarizations are set in coincidence with the TE fundamental mode of the amplifier. The bias current is fixed at 120 mA. In order to avoid the constitution of an external cavity, a 60-dB fiber optic isolator is placed at

Fig. 3. Measured (o), calculated (solid lines), and linearly interpolated (break lines) values of the generated wave conversion efficiency for three detuning frequencies, ! = 90, 250, and 3000 GHz, corresponding to a probe placed at 1555 nm and to a pump placed at 1554.3, 1553, and 1531.2 nm, respectively. The test beam is tuned from 1530 to 1480 nm.

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the output of the amplifier. The isolator output is coupled to an optical spectrum analyzer and the data are captured and processed. The conversion efficiency of the first modulation harmonic produced by the test beam, and the test beam intensity throughput for the three detuning frequencies, are derived. In order to carry out systematic measurements, the test beam is always tuned from 1530 to 1480 nm, that is, toward wavelengths shorter than the pump wavelengths. III. RESULTS

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DISCUSSION

Fig. 3 shows the conversion efficiency for the first modulation harmonic (generated wave) of the test beam as a function of the test wavelength for a 1555-nm probe wavelength , 90, 250, and three different detuning frequencies and 3000 GHz, i.e., for a pump placed at 1554.3, 1553, and 1531.2 nm, respectively. The experimental results are compared to the theoretical results of an analysis based on density matrix theory [11], [18]. The amplifier is supposed to be fully saturated by the pump and probe power. The slowly , and in the medium varying wave envelopes for the pump, probe, test, and generated waves are given, respectively, by (1) (2) (3) (4) is the longitudinal coordinate, is the where is the effective index, is confinement factor, the first-order susceptibility at frequency , and using Uskov’s (with ) notation [11], are the parameters responsible for FWM. These are quasi-

SOTO AND ERASME: IDENTIFYING NONLINEAR PHENOMENA

independent of due to the strong gain saturation obtained by the pump and probe. In order to validate this assumption, we have calculated the carrier density distribution along the active region using a model presented in [19]. The model has analyzed the SOA as a succession of 10 sections where m on all the carrier density was of sections for a current of 120 mA and an input power of 2 dBm (corresponding to the pump power), demonstrating the quasiuniformity of the carrier density distribution. However, for the long amplifiers with a strong bias current, the model presented here for the analysis of the FWM process does not give precise results and it is necessary to consider the nonuniformity of the carrier density along the active region. In the calculations, we have used the following material parameters: intraband carrier–carrier scattering time fs, intraband carrier–phonon scattering time fs and fs, relaxation time of the dipole fs, carrier lifetime ps, free-carrier absorption cross m and , group refractive sections , bandgap energy eV, and spinindex eV where indexes “ ” and “ ” orbit splitting denote electrons and holes in the conduction and valence band, respectively. These values were taken from [4] and [11]. In order to simplify the explanation, in the next analysis we will simply refer to the conversion efficiency of the first modulation harmonic of the test beam as the conversion efficiency. Thus, Fig. 3 shows that the conversion efficiency for a 3-THz detuning frequency increases as the test beam wavelength decreases toward the pump wavelength (placed at 1531.2 nm). Inversely, the conversion efficiencies for 90and 250-GHz detunings decrease as the wavelength of the test beam is increased. The results can be explained in terms of the modulation index acting on the test wave created by pumpprobe beating. In fact, the modulation index depends strongly on the test wavelength, and its evolution is influenced in a particular way by each nonlinear phenomenon. Thus, in a FWM process carried out with a high detuning THz) and a powerful pump, the spectral frequency ( hole burning (SHB) is the mechanism which, in theory, imposes its dynamics on the process [11], [12]. Due to pumpprobe beating, the presence of electrons in the conduction band fluctuates in time at frequency ; thus, the waves introduced into the amplifier are intensity modulated. Particularly, the intensity variation of the pump wave acts on the depth of the “spectral hole” created by this wave in the carrier energy distribution through stimulated emission. A local modulation on the gain curve is produced, creating a dynamic spectral hole. The center of the spectral hole corresponds to maximum modulation. As the test beam moves away from the spectral hole center, the gain modulation decreases. Fig. 4 outlines this fact, showing the evolution of the gain curve during gain modulation. When the test wavelength is tuned toward the pump wavelength for a 3-THz detuning frequency, the test wave modulation increases as consequently does the conversion efficiency (see Fig. 3). When the FWM process is carried out with a detuning frequency between 200 and 650 GHz and a powerful pump, carrier heating (CH) is the mechanism which, in theory, im-

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Fig. 4. Representation of the gain material excursion induced by the suppression gain modulation (at 3-THz detuning frequency) produced by the SHB mechanism. The visualization is realized for the extreme values of the depth ( 1 and 2 ) and the width ( 1 and 2 ) of the gain suppression. In the representation, the probe and pump are placed at 1555 and 1531.2 nm, respectively.

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Fig. 5. Representation of the gain material excursion induced by the quasi-equilibrium temperature and the Fermi quasi-level modulations (at 250-GHz detuning frequency). The visualization is realized for the extreme values of the quasi-equilibrium temperature ( 1 and 2 ) and the Fermi quasi-level ( 1 and 2 ) excursions. In the representation, the probe and pump are placed at 1555 and 1553 nm, respectively.

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T

T

poses its dynamics on the process [11], [12]. In these detuning frequencies, carrier consumption by stimulated emission (due to the pump and probe beams), and subsequent carrier–phonon scattering, produce a modulation of the quasi-Fermi level and the carrier energy distribution temperature [7], [11], [12]. These fluctuations modulate the gain curve, outlined in Fig. 5. Near the gap energy wavelength (1576 nm), the gain is almost insensitive to the variation of these parameters. However, as the observation moves toward moderately shorter wavelengths (i.e., toward the wavelength where the absorption turns up), the excursion of the gain curve is larger. The modulation acting on the test wave increases as the test is shifted toward wavelengths shorter than that of the energy gap. Consequently, the amplitude of the generated wave and the conversion efficiency for the 250-GHz detuning frequency in Fig. 3 increase. This analysis is possible assuming that the time constants of carrier–carrier and carrier–phonon scatterings are very dif-

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IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 34, NO. 11, NOVEMBER 1998

Fig. 6. Representation of the gain material excursion induced by carrier density pulsation (at 90-GHz detuning frequency). The visualization is realized for the extreme values of the carrier density excursion (N1 and N2 ). In the representation, the probe and pump are placed at 1555 and 1554.3 nm, respectively.

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ferent, therefore, for the detuning frequencies considered here, one can assume that the SHB is totally relaxed. The last case occurs when the FWM process is carried out with a detuning frequency smaller than 100 GHz. The pumpprobe beating creates a carrier density pulsation (CDP) whose dynamics dominate the FWM process [20]. Fig. 6 outlines the evolution of the gain curve during this pulsation. One can observe that the excursion in the curve increases as the test wave is tuned toward wavelengths smaller than the gap-equivalent wavelength. Therefore, in Fig. 3, when the test wave is tuned in this direction for 90-GHz detuning frequency, the test wave modulation increases gradually, leading to increased conversion efficiency. The above analysis allows us to establish the “signature” that each of the nonlinear phenomena studied leaves on the generated wave conversion efficiency. There is a clear difference between the SHB signature and those of CH and of CDP, allowing an easy identification of SHB. On the other hand, the evolutions governed by CH and CDP increase in the same direction. In order to identify the CDP relative to CH, the evolution of the test beam throughput can be tested. In Fig. 7, the test wave transmissions for a FWM process developed with 90- and 250-GHz detuning frequencies are shown. For 250 GHz, short wavelengths are less amplified than for 90 GHz. This performance predicts the strong CH influence on the transmission obtained with the 250-GHz detuning frequency: CH makes use of highenergy carriers when the carrier–phonon scattering produces the carrier energy distribution relaxation which generates a gain suppression at high energies affecting the test transmission. Typically for the pump power used here, the gain suppression produced by CH has the form of a “dipper” with a full width at half maximum (FWHM) of about two hundred nanometers, starting a few nanometers before the pump position [21]–[23]. This phenomenon is sketched in Fig. 7 around 1484 nm where the average gain suppression affecting the transmission for 250-GHz detuning frequency begins to decrease.

Fig. 7. Test wave average transmission developed for two detuning frequencies ! = 90 and 250 GHz, corresponding to a probe placed at 1555 nm and to a pump placed at 1554.3 and 1553 nm, respectively. The test beam is tuned from 1530 to 1480 nm.

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Fig. 8. Theoretical generated signal conversion efficiency for the 90-GHz detuning frequency. The contributions of CDP, CH, and SHB are calculated separately. In the calculation, the probe and pump are placed at 1555 and 1554.3 nm, respectively. The test beam is tuned from 1530 to 1480 nm.

In order to better understand the results, we have plotted in Figs. 8–10 the theoretical conversion efficiency for each single effect studied here. The calculation is realized for 90, 250, and 3000 GHz, respectively. It is quite clear that the trend of the evolution of the conversion efficiency versus the test wavelength (Fig. 8) for a detuning frequency of 90 GHz is dictated by the CDP, because in spite of the fact that CH and SHB contributions depend on the test wavelength, they have a very weak magnitude. For a detuning of 250 GHz (Fig. 9), the SHB contribution is sensitive to the value of the test wavelength, but its magnitude is very small in comparison with the CDP and CH contributions. The CDP contribution is the most significant, but it is insensitive to the test wavelength. Consequently, the CH contribution, in spite of its relative weakness, governs the evolution trend of the conversion efficiency for this detuning. For a detuning of 3 THz (Fig. 10), all phenomena considered produce an equivalent

SOTO AND ERASME: IDENTIFYING NONLINEAR PHENOMENA

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Fig. 9. Theoretical generated signal conversion efficiency for the 250-GHz detuning frequency. The contributions of the CDP, CH, and SHB are calculated separately. In the calculation, the probe and pump are placed at 1555 and 1553 nm, respectively. The test beam is tuned from 1530 to 1480 nm.

frequencies) the test transmission and the conversion efficiency dependence on the test wavelength. Thus, the dominant presence of CDP and CH mechanisms produces a conversion efficiency increasing when the test wavelength decreases. However, the test wave transmission presents a gain suppression for short test wavelengths when CH is the dominant mechanism, allowing the identification of the CDP mechanism. When the dominant mechanism is SHB, the conversion efficiency increases as the test wavelength approaches the pump wavelength. On the other hand, the analysis has shown that when the action produced by a nonlinear phenomenon on the gain curve modulation index begins to be negligible, it produces a conversion efficiency independent on the test wavelength. One can predict that, if for very large detuning frequencies, when the SHB contribution becomes negligible, a new slope change in the conversion efficiency is observed, it has to be attributed to a new nonlinear phenomenon. This is being investigated at present.

REFERENCES

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Fig. 10. Theoretical generated signal conversion efficiency for the 3-THz detuning frequency. The contributions of the CDP, CH, and SHB are calculated separately. In the calculation, the probe and pump are placed at 1555 and 1531.2 nm, respectively. The test beam is tuned from 1530 to 1480 nm.

contribution to the conversion efficiency. Nevertheless, the CDP and CH contributions are notably less dependent on the test wavelength than the SHB contribution. As seen from Fig. 10, the conversion efficiency is also sensitive to the test wavelength, and practically follows the SHB evolution trend; therefore it is possible to conclude that the SHB contribution governs the evolution trend of the conversion efficiency for this detuning.

IV. CONCLUSION A new experimental method for identifying the nonlinear phenomena intervening in a FWM process in an SOA has been developed. The method is based on the material gain and index modulation produced by the FWM process through the diverse nonlinear mechanisms. The modulated medium gives rise to a new signal when a test beam is launched into the SOA. The method consists of analyzing (for various detuning

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[14] K. L. Hall, G. Lens, A. M. Darwish, and E. P. Ippen, “Subpicosecond gain and index nonlinearities in InGaAsP diode lasers,” Opt. Commun., vol. 111, pp. 589–612, Oct. 1994. [15] C. K. Sun, H. K. Choi, C. A. Wang, and J. G. Fujimoto, “Femtosecond gain dynamics in InGaAs/AlGaAs strained-layer single-quantum-well diode lasers,” Appl. Phys. Lett., vol. 63, pp. 96–98, July 1993. [16] J. Mørk and A. Mecozzi, “Response function for gain and refractive index dynamics in active semiconductor waveguides,” Appl. Phys. Lett., vol. 65, pp. 1736–1738, Oct. 1994. [17] J. Mørk and J. Mark, “Carrier heating in InGaAsP laser amplifiers due to two-photon absorption,” Appl. Phys. Lett., vol. 64, pp. 1736–1738, Apr. 1994. [18] H. Soto and D. Erasme, “Investigation of non degenerate four wave mixing in semiconductor optical amplifier through bias current modulation,” Appl. Phys. Lett., vol. 68, pp. 3698–3700, June 1996. , “Modeling and experimental measurements of the switching [19] behavior of semiconductor optical amplifiers,” Opt. Quantum Electron., vol. 28, pp. 669–681, June 1996. [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, Jan. 1988. [21] M. Willatzen, A. Uskov, J. Mørk, H. Olesen, B Tromborg, and A. P. Jauho, “Nonlinear gain suppression in semiconductor lasers due to carrier heating,” IEEE Photon. Technol. Lett., vol. 3, pp. 606–609, July 1991. [22] M. Willatzen, T. Takahashi, and Y. Arakawa, “Nonlinear gain effects due to carrier heating and spectral hole burning in strained-quantum-well lasers,” IEEE Photon. Technol. Lett., vol. 4, pp. 682–685, July 1992. [23] M. Willatzen, J. Mørk, H. Olesen, J. Mark, and A. Uskov, “Influence of carrier heating on gain dynamics in semiconductor lasers,” in Tech. Dig. Quantum Electronics Lasers Science Conf. (QELS’91), Baltimore, MD, May 1991, paper QThD4.

Horacio Soto received the B.S. degree in biomedical engineering from Universidad Autonoma Metropolitana, Mexico, in 1984, the M.S. degree from Centro de Investigaci´on Cient´ıfica y Educaci´on Superior de Ensenada (CICESE), Mexico, in 1990, and the Dipl. Mast`ere and Ph.D. degree in optoelectronics from Ecole Nationale Sup`erieure des T´el´ecommunications de Paris, France, in 1992 and 1996, respectively. From 1983 to 1985, he worked on detection of electrical activity of the human heart at the Centro de Desarrollo y Aplicaciones Technol´ogicas de la Secretaria de Salud de M´exico. From 1987 to 1991, he worked on design of industrial electronic systems at the Instituto de Investigaciones Electricas de Mexico, SINTEX electronica, AUGEN WECKEN and CICESE. In 1996, he joined the Electronics and Telecommunications Department at CICESE. Since then, he has been engaged in research on photonic functional devices. Recent activities include research on semiconductor photonic devices.

Didier Erasme was born in Paris, France, in 1960. He received a “D iplˆome d’Ing´enieur” in physical engineering from the Ecole Nationale Sup´erieure d’Ing´enieurs Electriciens de Grenoble (INPG) in 1983 and the Ph.D. degree for his work on LiNbO3 high-frequency integrated-optic modulators from the Electrical and Electronic Engineering Department of University College London (UCL), U.K., in 1987. After a two-year post-doctoral appointment working on electrooptic sampling of GaAS integrated circuits at UCL, he joined the Ecole Nationale Sup´erieure des T´el´ecommunications, T´el´ecom Paris, in 1990 as an Assistant Professor of Optoelectronics. In 1995, he obtained an “Habilitation diriger des Recherches.” His current research interests are in the area of quantumwell modulators, semiconductor laser amplifiers, and electrooptic probing of GaAS microwave integrated circuits.

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