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200-nm-Bandwidth Fiber Optical Amplifier Combining Parametric and Raman Gain Min-Chen Ho, Student Member, IEEE, Katsumi Uesaka, Michel Marhic, Senior Member, IEEE, Member, OSA, Youichi Akasaka, and Leonid G. Kazovsky, Fellow, IEEE, Fellow, OSA
Abstract—Theory shows that the gain bandwidth of a one-pump fiber optical parametric amplifier (OPA) using highly nonlinear fiber (HNLF) could be more than 200 nm. Under these circumstances, the OPA gain would overlap the pump-induced Raman gain. We have studied the combined effects of OPA and Raman gain theoretically and experimentally. The experimental results demonstrate a 200-nm bandwidth from a single fiber-optical amplifier and also verify that the influence of the Raman effect is relatively small, as predicted by the theory. Index Terms—Optical fiber amplifier, optical fiber communication.
I. INTRODUCTION
E
ARLY work with fiber optical parametric amplifiers (OPAs) demonstrated relatively small bandwidths, on the order of 1 nm [1]–[3]. More recently, we have shown that under certain circumstances, fiber OPAs could in principle exhibit bandwidths as large as several hundred nanometers [4], and we have experimentally demonstrated a 120-nm bandwidth [5]. Here, we study theoretically and experimentally fiber OPAs with a bandwidth on the order of 200 nm. Under these circumstances, the OPA gain significantly overlaps the pump-induced Raman gain, which peaks at about 110 nm from the pump, on the long wavelength side. It then becomes necessary to study the combined effect of the two separate gain mechanisms. In Section II, we review the theory applicable to this regime. We have performed experiments to verify the theoretical predictions, and we have obtained good agreement between the two. The experimental results are presented in Section III.
Consider three waves of (radian) frequencies and . They are coupropagation constants pled by four-wave mixing, and the frequencies satisfy is the frequency deviation. Wave 1 corresponds to a strong pump, 3 is the signal, and 4 the idler. The fields are studied by means of their slowly , where and varying envelopes are the power and phase of the th wave at along the . We assume that the fiber is lossless; fiber. We let the pump is much stronger than the signal and idler and is not depleted; all the waves have the same linear polarization; and the non-Raman nonlinear interactions are described by a single nonlinearity coefficient , which is independent of frequency. The Raman interactions are described by the , where is the refractive function is the mode effective area, and is index of the core, the imaginary part of the third-order susceptibility. is an odd function of . With these assumptions, we obtain a set of coupled differenand similar to [6, eq. (3)], namely tial equations for
(1) where
II. THEORY The form of the basic differential equations describing the combined effects of parametric and Raman gain in optical fibers is known [6]. Solutions have been provided in [7] and [8]. Here, we provide the solution of these equations in the case of most interest to us, i.e., when no idler is present at the input. Our starting point is a set of equations with the same form as in [6]; we have adopted notations similar to [9] for the sake of convenience. Manuscript received March 9, 2000; revised April 10, 2001. M.-C. Ho, M. E. Marhic, and L. G. Kazovsky are with the Optical Communication Research Laboratory, Department of Electrical Engineering, Stanford University, Stanford, CA 94305 USA (e-mail:
[email protected]). K. Uesaka is on leave from Sumitomo Electric Industries, Ltd., Yokohama 244-0844 Japan. Y. Akasaka is with Furukawa Electric Co., Ltd., Tokyo 100–8322 Japan. Publisher Item Identifier S 0733-8724(01)05306-3.
Assuming that there is no idler at the input , which corresponds to our experimental conditions, we solve this set of equations as in [8], with the result
(2) where
is such that (3)
is an even function of [4], while is odd, Because the power conversion efficiency from the signal to the idler,
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Fig. 2. Raman gain spectrum. The frequency shift is defined as pump frequency minus signal frequency. Fig. 1.
Setup for Raman gain spectrum measurement.
, is an even function of . In general, however, is asymmetric, and the the signal power gain degree of asymmetry increases as the Raman gain is relatively large compared to the parametric gain. Because gain flatness is a concern in the design of optical amplifiers, it is worth investigating this feature in detail. , measuring the Because the Raman gain vanishes as signal power gain near the pump allows us to measure , since (4) By tuning the pump far from , we essentially eliminate parametric gain, and we can measure the Raman gain spectrum only. This is equivalent to keeping only the Raman term in (1) (5) Upon integration, this yields (6) (7) , we can calculate Hence, by measuring duce the dimensionless parameter , such that
. We intro-
(8) characterizes the relative strength of the Raman and para, the Raman gain has little effect on the metric gains: if usual OPA gain spectrum. However, if is of order 1, the Raman contribution may strongly disturb the OPA gain spectrum. , where With , we may then rewrite as is the normalized Raman gain coefficient (such that ). These considerations will help us to investigate experimentally the relationship between parametric and Raman gain in the following section. III. EXPERIMENTS A. Raman Gain Spectrum Measurement The Raman gain spectrum is required for the theoretical calculation of the combined (OPA Raman) gain spectrum. The gain medium for our OPA experiment was a highly nonlinear fiber (HNLF) provided by Furukawa Electric [10]. To measure
the Raman gain in this HNLF, the experiment shown in Fig. 1 was conducted. The Raman gain was measured under continuous-wave conditions by using a low-power pump. The pump wavelength was chosen to be far away ( 60 nm separation) from . This way, the OPA gain was limited to a small bandwidth near the pump. The Raman gain, which peaks at about 110 nm away from the pump, could be clearly measured. A 1.9-km-long HNLF was used as the gain medium; it is of the same type as the fiber used for the OPA experiment of Section III-B, as both were taken from the same spool. A Furukawa high-power pumping unit (HPU) was used as the pump source. HPU consists of five pump diodes, but only two 1480-nm diodes were used in this experiment. The two diodes were polarization-combined to avoid polarization-dependent gain. However, a polarization controller was still inserted in the signal path to ensure that maximum gain was obtained. The input pump power to the HNLF was 107 mW, after subtracting connector and splice loss. The net gain was measured by comparing the signal output power at the optical spectrum analyzer, with and without pump. can be The raw experimental data are shown in Fig. 2. obtained by normalizing this curve by its maximum value. B. Experimental Setup for OPA Gain Measurements OPA experiments were conducted to verify the theoretical analysis developed in Section II. The setup is shown in Fig. 3. The pump is a 13-dBm output power, fixed-wavelength disnm), amplified by tributed feedback (DFB) laser ( two cascaded erbium-doped fiber amplifiers (EDFAs)( was to optimize the gain bandwidth). It is chosen slightly above pulse-modulated to provide about 10-W peak power. Two different types of lasers were used as signal sources. An external cavity tunable laser provided wavelengths ranging from 1511 to 1593 nm, and discrete DFB lasers, with wavelengths at 1443, 1466, 1495, and 1651 nm, were used elsewhere. Signals were modulated sinusoidally at 1 GHz to allow ac gain measurement. An eight-wavelength planar lightwave circuit Mach–Zehnder interferometer (PLC-MZI) multiplexer [11] was used to combine pump and signal. It provided 1–2-dB loss for both pump and signal. The gain medium, as mentioned in Section III-A, was an HNLF. The fiber parameters are listed in Table I. Because the dispersion varied longitudinally for this particular fiber, the efwas obtained by fitting the experimental fective value of
HO et al.: 200-nm-BANDWIDTH FIBER OPTICAL AMPLIFIER
Fig. 3.
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Experimental setup for OPA gain measurements. TABLE I HNLF PARAMETERS
Fig. 4. Experimental results. The dots are experimental data, and the solid and dashed lines are theoretical curves obtained by setting = 0:15 and = 0 in (2), respectively.
OPA gain data. was estimated from measurements on a calculation are in 1.9-km-long HNLF. (The details of the Appendix A.) Two cascaded tunable optical filters were used to extract the signal at the HNLF output. The gain was measured by comparing the ac amplitude of the signal during the “on” and “off” portions of the pump pulses, as shown at the bottom left of Fig. 3. C. Results of OPA Gain Measurements The experimental results are shown by the dots in Fig. 4. Gain greater than 10 dB is present over wavelengths ranging from 1443 to 1651 nm. To compare the experimental results with theoretical predictions, the ratio of Raman gain over OPA gain was required. It was calculated as follows. The Raman gain spectrum obtained in Section III-A was first converted to parameters (pump wavelength, pump power, and fiber length) equivalent to an OPA experiment; then was determined by (8). The OPA experimental data we used were from [5] because more points were measured near the pump wavelength in that set of data, so that can be determined more precisely. The parameters of that OPA experi-nm pump wavelength, W, mental data were
and m. By fitting OPA gain near pump wavelength, we and . Subobtained . stituting the numbers into (8), we obtained The dashed curve marked “OPA only” is plotted with the exin (2). This curve perimental parameters and by setting shows the hypothetical pure OPA gain without Raman contribution. Compared to this symmetric curve, the experimental data exhibit asymmetry, with higher gain on the longer wavelength side, a feature clearly attributable to the Raman gain. A solid curve marked as “OPA Raman” is also shown in Fig. 4, using . The experimental data are in good agreement (2) and with this curve, indicating the validity of the model developed in Section II. We also note that the two curves (“OPA only” and “OPA Raman”) confirm that the pump-induced Raman gain contribution is relatively small compared to the OPA gain. IV. CONCLUSION We have theoretically investigated the influence of the Raman gain on a broadband fiber OPA. We found that for a high-gain amplifier, the Raman effect should introduce only a relatively small distortion of the pure OPA gain spectrum in the form of an increase (decrease) on the long (short) wavelength side. We have performed experiments to verify these predictions, with an HNLF and a pulsed 10-W pump. We have obtained
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gain in excess of 10 dB over a 208-nm bandwidth, which to our knowledge is the largest to date for any type of fiber amplifier. The shape of the overall gain spectrum is in good agreement with the theoretical predictions. This confirms that for a well-phase-matched broadband fiber OPA, the Raman gain provides only a relatively small perturbation for the broader and stronger OPA gain.
TABLE II DISPERSION PARAMETERS OF HNLF
APPENDIX A The theoretical gain spectrum of fiber OPAs can be expressed , the fourth derivative of with respect to , in terms of , however, cannot directly be at the pump frequency [4]. obtained from dispersion measurements. It is thus convenient to to , the usual chromatic dispersion coefficient, and relate its derivatives as follows:
nm
s
m
(14)
ACKNOWLEDGMENT The authors would like to thank Furukawa Electric Co., Ltd., Tokyo, Japan, and Dr. P. Vujkovic-Cvijin of SRI International for loaning equipment. REFERENCES
(9) It can also be shown that
(10)
(11) can be expressed as a Substituting (10) and (11) into (9), , and function of dispersion coefficient , dispersion slope as follows:
(12) , often available from manufacturers, Given a graph of . one can then easily calculate The measured dispersion and dispersion slope of the HNLF around the pump wavelength (1542.4 nm) are given in Table II. and subUsing interpolation to calculate stituting these numbers, we obtain nm nm nm
ps nm ps nm
km km
ps nm
km
(13)
[1] K. Washio, K. Inoue, and S. Kishida, “Efficient large-frequency-shifted three-wave mixing in low dispersion wavelength region in single-mode optical fiber,” Electron. Lett., vol. 16, no. 17, pp. 658–660, 1980. [2] M. Ohashi, K. Kitayama, Y. Ishida, and N. Uchida, “Phase-matched light amplification by three-wave mixing process in a birefringent fiber due to externally applied stress,” Appl. Phys. Lett., vol. 41, no. 12, pp. 1111–1113, 1982. [3] J. P. Pocholle, J. Raffy, M. Papuchon, and E. Desurvire, “Raman and four photon mixing amplification in single mode fibers,” Opt. Eng., vol. 24, no. 4, pp. 600–608, 1985. [4] M. E. Marhic, N. Kagi, T.-K. Chiang, and L. G. Kazovsky, “Broadband fiber optical parametric amplifiers,” Opt. Lett., vol. 21, no. 8, pp. 573–575, 1996. [5] M.-C. Ho, M. E. Marhic, Y. Akasaka, F. S. Yang, and L. G. Kazovsky, “Fiber optical parametric amplifier with 120 nm bandwidth,” in Proc. NLGW’99, Dijon, France, 1999, pp. 39–41. [6] R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron., vol. QE-18, no. 7, pp. 1062–1072, 1982. [7] Y. R. Shen, The Principles of Nonlinear Optics. New York: Wiley, 1984. [8] R. W. Boyd, Nonlinear Optics. Boston, MA: Academic, 1992. [9] G. P. Agrawal, Nonlinear Fiber Optics. San Diego, CA: Academic, 1995. [10] O. Aso, S.-I. Arai, T. Yagi, M. Tadakuma, Y. Suzuki, and S. Namiki, “Broadband wavelength conversion using a short high-nonlinearity nonpolarization-maintaining fiber,” in Proc. ECOC’99, vol. 2, Nice, France, 1999, pp. 226–227. [11] K. Tanaka, K. Iwashita, Y. Tashiro, S. Namiki, and S. Ozawa, “Low loss integrated Mach-Zehnder-interferometer-type eight-wavelength multiplexer for 1480 nm band pumping,” in Tech. Dig. OFC’99, vol. 1, San Diego, CA, 1999, TuH5, pp. 88–90.
Min-Chen Ho (S’96) received the B.S. degree in electrical engineering from National Taiwan University, Taipei, Taiwan, R.O.C., in 1995 and the M.S. and Ph.D. degrees in electrical engineering from Stanford University, Stanford, CA, in 1998 and 2001, respectively. From 1996 to 2001, she worked for the Optical Comunication Research Laboratory at Stanford University, primarily on the fiber nonlinearities and their applications in WDM optical networks. Since 2001, she has been with Onetta, Inc., San Jose, CA.
HO et al.: 200-nm-BANDWIDTH FIBER OPTICAL AMPLIFIER
Katsumi Uesaka received the B.S. and M.S. degrees in electrical engineering from Tokyo Institute of Technology, Tokyo, Japan, in 1987 and 1989, respectively. He joined the Sumitomo Electric Industries, Ltd., in 1989. He has been engaged in research and development of optical components. Since August 2000, he has been a visiting scholar at Optical Communications Research Laboratory (OCRL), Stanford University, Stanford, CA.
Michel Marhic (M’79–SM’89) received the Diplome D’Ingenieur, the M.S., and Ph.D. degrees in electrical engineering from l’Ecole Superieure d’Electricite, Gif-sur-Yvette, France, Case Western Reserve University, Cleveland, OH, and the University of California, Los Angeles, CA, respectively. He was on the faculty of the Department of Electrical Engineering at Northwestern University, Evanston, IL, from 1974 to 1988, and on sabbatical leaves at the University of Southern California, Los Angeles, from 1979 to 1989, and at Stanford University, Stanford, CA, from 1984 to 1985 and 1993 to 1994. He is currently a Consulting Professor in the Department of Electrical Engineering at Stanford University. He cofounded Holicom, Holographic Industries, and OPAL Laboratories. He is the author or coauthor of many journal and conference papers, and has been awarded eight patents. Over the past 25 years, his research has been in several areas of applied optics, including nonliniear interactions in plasmas, optical fiber measurements, hollow infrared waveguides, holography and phase conjugation, and fiber networks. In the past 10 years, his emphasis has been on optical communication systems and nonlinear optical interactions in fibers. Dr. Marhic is a member of the Optical Society of America (OSA) and an eminent member of Tau Beta Pi. He was the recipient of the Ameritech Research Professorship from the Institute for Modern Communications from 1990 to 1991.
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Youichi Akasaka received the B.S. degree in synthetic chemistry from Kyoto University, Kyoto, Japan, in 1988, and the M.S. and Ph.D. degrees in industrial chemistry from University of Tokyo, Tokyo, Japan, in 1990 and 1993, respectively. In 1993, he joined the research and development group of Furukawa Electric Co., Ltd., Tokyo, Japan. From 1993 to 1998, he was engaged in research and development of new optical fiber design and nonlinear optical amplifier design. From 1998 to 200, he was a visiting scholar in the Department of Electrical Engineering at Stanford University, Stanford, CA, where he researched new components for future transmission systems. Since 2001, he has been a Senior Research Engineer at Sprint Advanced Technology Labs, Burlingame, CA. Dr. Akasaka is a member of the Institute of Electronics, Information and Communication Engineers (IEICE) of Japan and he was the recipient of the Young Engineer Award from IEICE of Japan in 1995. He is also a member of the IEEE Lasers and Electro-Optics Society (LEOS).
Leonid G. Kazovsky (M’80–SM’83–F’91) was born in Leningrad, U.S.S.R., in 1947. He received the M.Sc. and Ph.D. degrees in electrical engineering from the Leningrad Electrotechnical Institute of Communications in 1969 and 1972, respectively. From 1974 to 1984, with a one-year interruption for active military service in Israel, he taught and performed research at universities in Israel and the United States. From 1984 to 1990, he was with Bellcore (now Telcordia), Red Bank, NJ, researching WDM, high-speed and coherent optical fiber communication systems. Since 1990, he has been a Professor of Electrical Engineering at Stanford University, Stanford, CA. After joining Stanford, he founded the Optical Communication Research Laboratory, OCRL (http://ocrl.stanford.edu), which he still leads. While on Bellcore assignments or Stanford sabbaticals, he worked at the Heinrich Hertz Institute, Berlin, Germany; Hewlett-Packard Research Laboratories, Bristol, England; and the Technical University of Eindhoven, The Netherlands. Through research contracts, consulting engagements, and other arrangements, he worked with many industrial companies and U.S. government agencies, including Sprint, DEC, GTE, AT&T, IVP, Lucent, Hitachi, KDD, Furukawa, Fujitsu, Optivision, and Perimeter on the industrial side; and NSF, DARPA, Air Force, Navy, Army, and BMDO on the government side. From 1998 to 1999, he took a one-year leave from Stanford University and launched a start-up company now known as Alidian Networks (http://www.alidian.com). He serves on the Board of Directors of that company. Dr. Kazovsky has served on the editorial boards of the IEEE TRANSACTIONS ON COMMUNICATIONS, the IEEE PHOTONICS TECHNOLOGY LETTERS, and Wireless Networks , and on the program committees of the OFC, CLEO, LEOS, SPIE, and GLOBECOM conferences. He has also served as a reviewer for various IEEE and IEE conference proceedings and journals, funding agencies (NSF, OFC, ERC, NRC), and publishers (Wiley and MacMillan). He has authored and coauthored two books and many journal technical papers and conference papers. He is a Fellow of the Optical Society of American (OSA).
