Four-Wave Mixing in Optical Fibers and Development of Its Applications

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1 Four-Wave Mixing in Optical Fibers and Development of Its Applications * * * Osamu Aso Masateru Tadakuma Shu Namiki FWMDWDM FWM FWM 23.3 nm FWM 1. 1),2) FWM, Four-Wave Mixing FWM idlerfwm DWDM, Dense Wavelength Division Multiplexing FWM 2 DWDM FWM FWMFWM FWM 2 FWM 3 FWM FWM HNL-DSF, High NonLinearity Dispersion Shifted Fiber, HNL-DSF 4 HNL-DSF 5 DMDispersion Managed 6 RDFReverse Dispersion Fiber 7 2. FWM 1 1 f probe f p1 f p2 1 1),2) DFWM, Degenerated Four-Wave Mixing DFWM1 2 * WP 46

2 WDM XPM, Cross Phase Modulation DFWM α=0jacobi 45 3 DFWM 67 1 (a)2 (b)1 A schematic of four-wave mixing in the frequency domain. (a) case of 2 channel pump waves (b) case of the 1 channel pump wave (degenerated four wave mixing) f p cw continuous wavedfwm 1 3. FWM 3.1 8)~13 FWM α γ γ β α γ γ β 3 α γ γ β z α E p, E probe, E idler γ 1 π γ 4 n 2 A eff c 3 β π β = β β β 5 D β 0 FWM FWM 3 3 SPM, Self Phase Modulation a b 11 c 6),7) DFWM 6),7) f DFWM L π 6 β π L coh 6 f 47

3 b cpmf, Polarization Maintaining Fiber n 7 f n 12 PMF DFWM n nm L n (%) 1 π φ SiO (µm) HNL-DSF Refractive index profile of the HNL-DSF + = 2.75% - = -0.55% HNL-DSF Transmission characteristics of the HNL-DSF HNL-DSF 4. HNL-DSF 2 HNL-DSF 1 VAD Vapor phase Axial Deposition = 13.8 W -1 km cw EDFAErbium Doped Fiber Amplifier10 db HNL-DSF OSAOptical Spectrum Analyzer G c km1.2 km0.2 km 100 mw20 dbm 1 mw0 dbm 4 HNL-DSF 0.2 km 23.3 nm 13 (db) L = 24.5km L = 1.2km L = 200m 3 Setup for the wavelength conversion experiment λ idler - λ p (nm) km, 1.2 km, 200 m Measured conversion efficiency. Each fiber length is, 24.5 km, 1.2 km, 200 m respectively. 48

4 WDM DWDMEDFA 14 EDFA FWMDM 15 RDFReverse Dispersion Fiber SMFSingle-Mode Fiber 16 RDF1550 nm SMF SMF+RDFDM WDM 17),18) γspm 19 XPM 20 FWM 21),22) 23),24) DMRDF 5.2 StolenBjorkholm 1),7) pump undepleted DFWM γ γ γ β γ γ β 9 3α 0 DFWM DFWM G c 1 EDFA PC 3dB (RDF) γ g β β γ P p L γ β P p G c γ β P p G c Levenberg- Marquardt 25 γ β 6. RDF EDFA ASEAmplified Spontaneous Emission 15 db PC, Polarization ControllerEDFA attenuator 3 1 nmosa D (ps/nm/km) λ(nm) n 2 /A elf (10-9 ) (W -1 ) 5 Setup for the simultaneous measurement of the nonlinear coefficient and chromatic dispersion 6 10 km, nm Result of the measurements. Fiber length is 10 km and pump wavelength is 1553 nm. represents the chromatic dispersion and is nonlinear coefficient, n 2. 49

5 (dbm) Relation of the idler power with probe wavelength. Measurement was made with the same condition as shown in Fig γ β SBS 25 db 9DFWM 10 kmrdf 1553 nm4γn 2 5 β D 6 λ 6 n 2 D λ λ=0.22 nm D (ps/nm/km) λ p - λ probe (nm) WAVELENGTH (nm) RDF 830 m n 2 Result of the chromatic dispersion and n 2. RDF length is 830 m n 2 /A elf (10-9 ) (W -1 ) 1553 nm ps/nm/km λ>0.22 nm 10 7 λ λ=0.22 nm λ 0.22 nm 6 λ 0.21 nm λ 7 λ λ RDF 6.3 RDF 4 RDF 0.83 km5 km10 km20 km 3 nm 8 4 RDFn 2 XPM 2 n 2 α 9 2 RDFn 2 n 2 XPMn 2 Result of the simultaneous measurement of the n 2 and chromatic dispersion of some RDFs. Comparison of the results from the measured n 2 from the XPM method. Chromatic dispersion characteristics is compared with the results obtained by phase shift method. 50

6 WDM 6.4 DFWM γ α β β γ α n 2 XPM FWM HNL-DSF 23.3 nm DFWM XPM HNL-DSF RFD 1) G.P.Agrawal, "Nonlinear Fiber Optics-Second Edition", Academic Press, San Diego, CA, USA, (1995) Chap ) ) C. Lin, W. A. Reed, A. D. Pearson and H. -T. Shang, Opt. Lett., 6, 10, (1981) ) ) G. Cappelini and S. Trillo, J. Opt. Soc. Am. B, 8, 4, (1991) ) K. O. Hill, D. C. Johnson, B. S. Kawasaki and R. I. MacDonald, J. Appl.Phys., 49, 10, (1978) ) R. H. Stolen and J. E. Bjorkholm, J. Quantum Electron., QE-18, 7,(1982) ) S. J. B. Yoo, J. Lightwave Technol., 14, 6, (1996) ) K. E. Stubjaer, A. Kloch, P. B. Hansen, H. N. Poulsen, D. Wolfson, K. S. Jepsen, A.T. Clausen, E. Limal and A. Buxens, IEICE Trans. Electron., E82-C, 2, (1999) ) N. Antoniades, S. J. B. Yoo, K. Bala, G. Ellinas and T. E. Stern, J. Lightwave Technol., 17, 7, (1999) ) S. Watanabe, S. Takeda, G. Ishikawa, H. Ooi, J. G. Nielsen and C. Sonne, European Conference on Optical Communication(ECOC) 97, post-deadline paper TH3A, (1997) 1. 12) S. Watanabe, S. Takeda and T. Chikama, ECOC' 98, post-deadline paper (1998) ) O. Aso, M. Tadakuma and S. Namiki, Proc. ECOC'99, vol. II, (1999), ) 82,7(1999)718 15) A. R. Chraplyvy and R. W. Tkach, J. Quantum Electron., 34, 11, (1998) ) K. Mukasa, Y. Akasaka, Y. Suzuki and T. Kamiya, ECOC'97, (1997) ) Y. Miyamoto, K. Yonenaga, A. Hirano, N. Shimizu, M. Yoneyama, H. Tanaka, K. Noguchi and K. Tsuzuki, ECOC' 98, post-deadline, (1998) 55 18) M. Murakami, T. Matsuda and T. Imai, ibid., (1998) ) R. H. Stolen and C. Lin, Phys. Rev. A, 17, 4, (1992) ) A. Wada, T. O. Tsun, and R. Yamauchi, ECOC' 92, (1992) 71 21) S. V. Chernikov and J. R. Taylor, Opt. Lett., 21, 24, (1996) ) S. Bigo and M. W. Chbat, Symposium on Optical Fiber Measurement, (1998), p.77 23) M. Tadakuma, O. Aso and S. Namiki, Proc. ECOC'99, vol. II, (1999), ) ibid, Optical Fiber Measurement Conference Program, (1999), ) W. H. Press, S. A. Teukolsky, W. T. Vertterling and B. P. Flannery, " Numerical Receipes in C, Second Edition", Cambridge University Press, N.Y., USA (1992) Chap ) L. F. Mollenauer, P. V. Mamyshev and M. J. Neubelt, Opt. Lett., 21, 21, (1996)

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