Nonlinear Fiber Optics - 4 ed. Agrawal

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References 363 9.4 Estimate SBS threshold at 1.55 μm for a 40-km-long fiber with 8-μm core diameter. How much does it change at 1.3 μm? Use g B = 5 ×10 −11 m/W and loss values of 0.5 and 0.2 dB/km at 1.3 and 1.55 μm, respectively. 9.5 Solve Eqs. (9.2.1) and (9.2.2) after neglecting pump deletion. Use the solution to derive the threshold condition for SBS. 9.6 Explain how a Bragg grating can be used to increase the pump power at which SBS reaches its threshold. What other techniques can be used for this purpose? 9.7 Solve Eqs. (9.2.1) and (9.2.2) including pump deletion. Neglect fiber losses by setting α = 0. Plot I p and I s as a function of z/L when g 0 L = 12. Assume that the injected Stokes power at z = L is 0.1, 1, and 10% of the input pump power. 9.8 Solve Eqs. (9.2.1) and (9.2.2) numerically for a 20-km-long fiber using g B I p (0)= 1km −1 and α = 0.2 dB/km. Plot I p and I s along the fiber length assuming I p (0)=2 MW/cm 2 and I s (L)=1 kW/cm 2 . 9.9 Solve Eqs. (9.4.10) and (9.4.11) numerically assuming that both pump and Stokes pulses are Gaussian in shape initially with a FWHM of 1 μs. Plot output pulse shapes when SBS occurs in a 10-m-long fiber assuming g B I p (0)=1m −1 . 9.10 Write a computer code for solving Eqs. (9.4.5)–(9.4.7). You can neglect the z derivative in Eq. (9.4.7). Use the parameters from Ref. [93] and reproduce the curves given in Figures 9.9 and 9.10. 9.11 Verify by direct substitution that the soliton solution given in Eqs. (9.4.16) and (9.4.17) indeed satisfies Eqs. (9.4.13)–(9.4.15). 9.12 Use Eqs. (9.4.5)–(9.4.7) to show that the SBS gain modifies the effective refractive index seen by the Stokes wave. Derive an expression for the transit time through a fiber of length L in terms of the detuning parameter defined as δ = 2(Ω − Ω B )/Γ B , where Ω = ω p − ω s . 9.13 Follow the analysis of Reference [150] and derive the inequality given in Eq. (9.5.3). References [1] R. Y. Chiao, C. H. Townes, and B. P. Stoicheff, Phys. Rev. Lett. 12, 592 (1964). [2] E. Garmire and C. H. Townes, Appl. Phys. Lett. 5, 84 (1964). [3] N. M. Kroll, J. Appl. Phys. 36, 34 (1965). [4] C. L. Tang, J. Appl. Phys. 37, 2945 (1966). [5] W. Kaiser and M. Maier, in Laser Handbook, Vol. 2, F. T. Arecchi and E. O. Schulz- Dubois, Eds. (North-Holland, Amsterdam, 1972), Chap. E2. [6] E. P. Ippen and R. H. Stolen, Appl. Phys. Lett. 21, 539 (1972). [7] R. G. Smith, Appl. Opt. 11, 2489 (1972). [8] D. Cotter, J. Opt. Commun. 4, 10 (1983). [9] Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984), Chap. 11. [10] R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic Press, San Diego, 2003), Chap. 9. [11] R. M. Shelby, M. D. Levenson, and P. W. Bayer, Phys. Rev. Lett. 54, 939 (1985); Phys. Rev. B 31, 5244 (1985).
364 Chapter 9. Stimulated Brillouin Scattering [12] A. Melloni, M. Frasca, A. Garavaglia, A. Tonini, M. Martinelli, Opt. Lett. 23, 691 (1998). [13] R. S. Krishnan, Nature 165, 933 (1950). [14] D. Heiman, D. S. Hamilton, and R. W. Hellwarth, Phys. Rev. B 19, 6583 (1979). [15] P. J. Thomas, N. L. Rowell, H. M. van Driel, and G. I. Stegeman, Phys. Rev. B 19, 4986 (1979). [16] J. Stone and A. R. Chraplyvy, Electron. Lett. 19, 275 (1983). [17] R. W. Tkach, A. R. Chraplyvy, and R. M. Derosier, Electron. Lett. 22, 1011 (1986). [18] N. Shibata, R. G. Waarts, and R. P. Braun, Opt. Lett. 12, 269 (1987). [19] Y. Azuma, N. Shibata, T. Horiguchi, and M. Tateda, Electron. Lett. 24, 250 (1988). [20] N. Shibata, K. Okamoto, and Y. Azuma, J. Opt. Soc. Am. B 6, 1167 (1989). [21] T.-O. Sun, A. Wada, T. Sakai, and R. Yamuchi, Electron. Lett. 28, 247 (1992). [22] A. Yeniay, J.-M. Delavaux, and J. Toulouse, J. Lightwave Technol. 20, 1425 (2002). [23] Y. Koyamada, S. Sato, S. Nakamura, H. Sotobayashi, and W. Chujo, J. Lightwave Technol. 22, 631 (2004). [24] J. H. Lee, T. Tanemura, K. Kikuchi, T. Nagashima, T. Hasegawa, S. Ohara, and N. Sugimoto, Opt. Lett. 30, 1698 (2005). [25] V. I. Kovalev and R. G. Harrison, Opt. Lett. 27, 2022 (2002). [26] G. C. Valley, IEEE J. Quantum Electron. 22, 704 (1986). [27] P. Narum, M. D. Skeldon, and R. W. Boyd, IEEE J. Quantum Electron. 22, 2161 (1986). [28] E. Lichtman, A. A. Friesem, R. G. Waarts, and H. H. Yaffe, J. Opt. Soc. Am. B 4, 1397 (1987). [29] R. H. Stolen, IEEE J. Quantum Electron. 15, 1157 (1979). [30] M. O. van Deventer and A. J. Boot, J. Lightwave Technol. 12, 585 (1994). [31] J. Botineau, E. Picholle, and D. Bahloul, Electron. Lett. 31, 2032 (1995). [32] A. Kobyakov, S. Kumar, D. Q. Chowdhury, A. Boh Ruffin, M. Sauer, S. R. Bickham, and R. Mishra, Opt. Express 13, 5338 (2005). [33] Y. Imai and N. Shimada IEEE Photon. Technol. Lett. 5, 1335 (1993). [34] N. Yoshizawa and T. Imai, J. Lightwave Technol. 11, 1518 (1993). [35] K. Shiraki, M. Ohashi, and M. Tateda, Electron. Lett. 31, 668 (1995). [36] K. Shiraki, M. Ohashi, and M. Tateda, J. Lightwave Technol. 14, 50 (1996); J. Lightwave Technol. 14, 549 (1996). [37] K. Tsujikawa, K. Nakajima, Y. Miyajima, and M. Ohashi, IEEE Photon. Technol. Lett. 10, 1139 (1998). [38] J. Hansryd, F. Dross, M. Westlund, P. A. Andrekson, and S. N. Knudsen, J. Lightwave Technol. 19, 1691 (2001). [39] E. M. Dianov, B. Y. Zeldovich, A. Y. Karasik, and A. N. Pilipetskii, Sov. J. Quantum Electron. 19, 1051 (1989). [40] A. Hirose, Y. Takushima and T. Okoshi, J. Opt. Commun. 12, 82 (1991). [41] K. Kikuchi and C. Lorattanasane, IEEE Photon. Technol. Lett. 6, 992 (1994). [42] M. E. Marhic, F. S. Yang, and L.G. Kazovsky, Electron. Lett. 32, 2336 (1994). [43] J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, IEEE J. Sel. Topics Quantum Electron. 8, 506 (2002). [44] M. M. Howerton, W. K. Burns, and G. K. Gopalakrishnan, J. Lightwave Technol. 14, 417 (1996). [45] S. S. Lee, H. J. Lee, W. Seo, and S. G. Lee, IEEE Photon. Technol. Lett. 13, 741 (2001). [46] H. Lee and G. P. Agrawal, Opt. Express 11, 3467 (2003).
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Preface Since the publication of th
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Chapter 1 Introduction This introdu
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1.2. Fiber Characteristics 3 Figure
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1.2. Fiber Characteristics 7 1.49 1
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1.2. Fiber Characteristics 11 faste
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1.3. Fiber Nonlinearities 13 Figure
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1.3. Fiber Nonlinearities 15 Sectio
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1.3. Fiber Nonlinearities 17 1.3.3
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1.4. Overview 19 briefly. The last
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References 21 1.11 Equation (1.3.2)
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References 23 [63] M. Ibanescu, Y.
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Chapter 2 Pulse Propagation in Fibe
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2.2. Fiber Modes 27 where Ẽ(r,ω)
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2.2. Fiber Modes 29 across the core
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2.3. Pulse-Propagation Equation 31
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2.4. Numerical Methods 41 Equation
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2.4. Numerical Methods 43 Figure 2.
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2.4. Numerical Methods 45 the basic
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References 47 2.5 Derive an express
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References 49 [44] V. I. Karpman an
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Chapter 3 Group-Velocity Dispersion
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3.2. Dispersion-Induced Pulse Broad
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3.3. Third-Order Dispersion 63 This
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3.3. Third-Order Dispersion 65 Figu
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3.3. Third-Order Dispersion 67 6 5
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3.3. Third-Order Dispersion 69 Noti
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3.4. Dispersion Management 71 Figur
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3.4. Dispersion Management 73 10 3
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3.4. Dispersion Management 75 Figur
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References 77 3.10 An optical commu
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Chapter 4 Self-Phase Modulation An
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4.1. SPM-Induced Spectral Changes 8
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4.2. Effect of Group-Velocity Dispe
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4.3. Semianalytic Techniques 103 In
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4.3. Semianalytic Techniques 105 (1
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4.4. Higher-Order Nonlinear Effects
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Problems 115 4.2 Plot the spectrum
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References 117 [40] D. Marcuse, J.
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References 119 [109] J. Santhanam a
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5.1. Modulation Instability 121 of
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5.1. Modulation Instability 123 2 L
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5.1. Modulation Instability 125 Fig
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5.1. Modulation Instability 127 Fig
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5.2. Fiber Solitons 129 Figure 5.5:
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5.2. Fiber Solitons 131 and write i
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5.2. Fiber Solitons 133 Physically,
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5.3. Other Types of Solitons 141 1
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5.3. Other Types of Solitons 143 pr
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5.3. Other Types of Solitons 145 Th
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5.4. Perturbation of Solitons 147 w
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5.4. Perturbation of Solitons 149 w
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5.4. Perturbation of Solitons 151 t
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5.4. Perturbation of Solitons 153 b
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5.4. Perturbation of Solitons 155 F
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5.5. Higher-Order Effects 157 where
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5.5. Higher-Order Effects 159 Figur
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5.5. Higher-Order Effects 161 1 N =
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5.5. Higher-Order Effects 163 Integ
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5.5. Higher-Order Effects 165 Figur
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5.5. Higher-Order Effects 167 that
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Problems 169 Problems 5.1 Solve Eq.
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References 171 [27] E. Brainis, D.
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References 173 [93] L. F. Mollenaue
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References 175 [165] V. V. Afanasje
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Chapter 6 Polarization Effects As d
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6.1. Nonlinear Birefringence 179 wh
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6.1. Nonlinear Birefringence 181 re
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6.2. Nonlinear Phase Shift 183 dA y
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6.2. Nonlinear Phase Shift 185 wher
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6.2. Nonlinear Phase Shift 187 side
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6.3. Evolution of Polarization Stat
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6.4. Vector Modulation Instability
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6.5. Birefringence and Solitons 207
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6.6. Random Birefringence 213 where
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6.6. Random Birefringence 215 PMD,
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6.6. Random Birefringence 217 As in
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6.6. Random Birefringence 219 Figur
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References 221 6.9 Derive the dispe
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References 223 [63] P. Kockaert, M.
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References 225 [140] A. El Amari, N
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7.1. XPM-Induced Nonlinear Coupling
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7.2. XPM-Induced Modulation Instabi
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7.2. XPM-Induced Modulation Instabi
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7.3. XPM-Paired Solitons 233 This t
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7.3. XPM-Paired Solitons 235 The co
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7.3. XPM-Paired Solitons 237 It is
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7.4. Spectral and Temporal Effects
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7.5. Applications of XPM 249 Probe
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7.5. Applications of XPM 251 by hig
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7.5. Applications of XPM 253 Figure
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7.6. Polarization Effects 255 where
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7.6. Polarization Effects 257 Figur
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7.6. Polarization Effects 259 1 0.8
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7.6. Polarization Effects 261 4 Pum
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7.6. Polarization Effects 263 Figur
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7.7. XPM Effects in Birefringent Fi
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7.7. XPM Effects in Birefringent Fi
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Problems 269 7.2 Derive the dispers
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References 271 [33] M. Lisak, A. H
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References 273 [105] B. V. Vu, A. S
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8.1. Basic Concepts 275 Figure 8.1:
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8.1. Basic Concepts 277 set of two
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8.1. Basic Concepts 279 10 mW. Howe
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8.1. Basic Concepts 281 0.5 Raman R
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8.2. Quasi-Continuous SRS 283 four
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8.2. Quasi-Continuous SRS 285 Figur
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8.2. Quasi-Continuous SRS 291 wavel
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8.2. Quasi-Continuous SRS 293 1 0.8
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8.3. SRS with Short Pump Pulses 295
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8.4. Soliton Effects 307 Figure 8.1
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Page 334 and 335: Chapter 9 Stimulated Brillouin Scat
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10.6. Applications of Four-Wave Mix
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10.6. Applications of Four-Wave Mix
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Problems 417 Figure 10.24: Output s
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References 419 [5] R. W. Boyd, Nonl
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References 421 [79] A. Durécu-Legr
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References 423 [140] M. D. Levenson
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11.1. Nonlinear Parameter 425 11.1.
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11.1. Nonlinear Parameter 427 Figur
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11.1. Nonlinear Parameter 433 when
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11.2. Fibers with Silica Cladding 4
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11.3. Tapered Fibers with Air Cladd
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11.3. Tapered Fibers with Air Cladd
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11.4. Microstructured Fibers 441 he
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11.4. Microstructured Fibers 443 Ef
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11.5. Non-Silica Fibers 445 0.05 0.
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11.5. Non-Silica Fibers 447 Figure
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References 449 wavelength range of
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References 451 [57] H. Yokota, E. S
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Chapter 12 Novel Nonlinear Phenomen
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12.1. Intrapulse Raman Scattering 4
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12.2. Four-Wave Mixing 465 Figure 1
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12.2. Four-Wave Mixing 467 Figure 1
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12.3. Supercontinuum Generation 469
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12.4. Temporal and Spectral Evoluti
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12.5. Harmonic Generation 495 Figur
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12.5. Harmonic Generation 497 traps
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12.5. Harmonic Generation 501 analy
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12.5. Harmonic Generation 505 The p
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References 507 12.6 Derive an expre
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References 509 [45] J. E. Sharping,
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References 511 [111] J. Y. Y. Leong
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References 513 [180] A. L. Calvez,
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Appendix A 515 converted into decib
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Appendix B 517 % This code solves t
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Appendix C List of Acronyms Each sc
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Index acoustic response function, 4
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Index 523 distributed fiber sensors
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Index 525 four-photon, 412 gain-swi
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Index 527 Raman amplification with,
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Index 529 spectral hole burning, 36
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Nonlinear Fiber Optics - 4 ed. Agrawal

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