## Bragg solitons in the nonlinear Schrödinger limit: experiment and theory

JOSA B, Vol. 16, Issue 4, pp. 587-599 (1999)

http://dx.doi.org/10.1364/JOSAB.16.000587

Acrobat PDF (318 KB)

### Abstract

We present a detailed experimental and theoretical study of nonlinear pulse propagation in an apodized fiber Bragg grating. In particular, we consider the generation and the propagation of Bragg solitons with a frequency content just outside the grating’s photonic bandgap, where, thanks to the apodization, the transmissivity of the grating is high and the strong grating dispersion dominates. We demonstrate the efficient launching of Bragg solitons with velocities as low as 50% of that in untreated fiber. The experimental results agree well with numerical simulations obtained by solving the full nonlinear coupled-mode equations that govern the experimental geometry. We also show that, for most parameters, the experimental results are in very good agreement with a nonlinear-Schrödinger-equation model. Thus many of the results known for the nonlinear Schrödinger equation can be brought to bear on our results.

© 1999 Optical Society of America

**OCIS Codes**

(060.2340) Fiber optics and optical communications : Fiber optics components

(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers

(060.5530) Fiber optics and optical communications : Pulse propagation and temporal solitons

(190.4370) Nonlinear optics : Nonlinear optics, fibers

(190.5530) Nonlinear optics : Pulse propagation and temporal solitons

(230.1480) Optical devices : Bragg reflectors

(230.4320) Optical devices : Nonlinear optical devices

(250.5530) Optoelectronics : Pulse propagation and temporal solitons

**Citation**

B. J. Eggleton, C. Martijn de Sterke, and R. E. Slusher, "Bragg solitons in the nonlinear Schrödinger limit: experiment and theory," J. Opt. Soc. Am. B **16**, 587-599 (1999)

http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-16-4-587

Sort: Year | Journal | Reset

### References

- G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego, 1995).
- L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095 (1980).
- B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
- B. J. Eggleton, C. M. de Sterke, and R. E. Slusher, “Nonlinear propagation in superstructure Bragg gratings,” Opt. Lett. 21, 1223–1225 (1996).
- B. J. Eggleton, C. M. de Sterke, and R. E. Slusher, “Nonlinear pulse propagation in Bragg gratings,” J. Opt. Soc. Am. B 14, 2980–2993 (1997).
- C. M. de Sterke, B. J. Eggleton, and P. A. Krug, “High-intensity pulse propagation in uniform gratings and grating superstructures,” J. Lightwave Technol. 15, 2908–2993 (1997).
- B. J. Eggleton, C. M. de Sterke, A. B. Aceves, J. E. Sipe, T. A. Strasser, and R. E. Slusher, “Modulational instability and multiple soliton pulse generation in apodized fiber gratings,” Opt. Commun. 149, 267–271 (1998).
- D. Taverner, N. G. R. Broderick, D. J. Richardson, R. I. Laming, and M. Ibsen, “Nonlinear self-switching and multiple-gap soliton formation in a fiber Bragg grating,” Opt. Lett. 23, 328–330 (1998).
- D. Taverner, N. G. R. Broderick, D. J. Richardson, M. Ibsen, and R. I. Laming, “All-optical AND gate based on coupled gap–soliton formation in a fiber Bragg grating,” Opt. Lett. 23, 259–261 (1998).
- H. G. Winful, “Pulse compression in optical fiber filters,” Appl. Phys. Lett. 46, 527–529 (1985).
- D. N. Christodoulides and R. I. Joseph, “Slow Bragg solitons in nonlinear periodic structures,” Phys. Rev. Lett. 62, 1746–1749 (1989).
- A. B. Aceves and S. Wabnitz, “Self-induced transparency solitons in nonlinear refractive periodic media,” Phys. Lett. A 141, 37–42 (1989).
- T. A. Strasser, P. J. Chandonnet, J. DeMarko, C. E. Soccolich, J. R. Pedrazzani, D. J. DiGiovanni, M. J. Andrejco, and D. S. Shenk, in Optical Fiber Communication Conference; Vol. 2 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996); postdeadline paper PD8–1.
- P. S. Cross and H. Kogelnik, “Sidelobe suppression in corrugated-waveguide filters,” Opt. Lett. 1, 43–45 (1977).
- B. Malo, D. C. Johnson, F. Bilodeau, J. Albert, and K. O. Hill, “Apodized in-fibre Bragg grating reflectors photoimprinted using a phase mask,” Electron. Lett. 31, 223–225 (1995).
- H. Haus, “Matching of distributed-feedback structures,” Opt. Lett. 17, 1134–1136 (1992).
- H. G. Winful and G. D. Cooperman, “Self-pulsing and chaos in distributed feedback bistable optical devices,” Appl. Phys. Lett. 40, 298–300 (1982).
- C. M. de Sterke and J. E. Sipe, “Gap solitons,” in Progress in Optics XXXIII, E. Wolf, ed (Elsevier, Amsterdam, 1994), Chap. III.
- C. M. de Sterke and J. E. Sipe, “Coupled modes and the nonlinear Schrödinger equation,” Phys. Rev. A 42, 550–555 (1990).
- C. M. de Sterke and B. J. Eggleton, “Bragg solitons and the nonlinear Schrödinger equation,” Phys. Rev. E 59, 1267–1270 (1999).
- N. M. Litchinitser, B. J. Eggleton, and D. B. Patterson, “Fiber Bragg gratings for dispersion compensation in transmission: theoretical model and design criteria for nearly ideal pulse recompression,” J. Lightwave Technol. 15, 1303–1313 (1997).
- C. M. de Sterke, K. R. Jackson, and B. D. Robert, “Nonlinear coupled mode equations on a finite interval: a numerical procedure,” J. Opt. Soc. Am. B 8, 403–412 (1991).
- M. J. Steel and C. Martijn de Sterke, “Schrödinger description for cross-phase modulation in grating structures,” Phys. Rev. A 49, 5048–5055 (1994).
- P. St. J. Russell, “Bloch wave analysis of dispersion and pulse propagation in pure distributed feedback structures,” J. Mod. Opt. 38, 1599–1619 (1991).
- C. M. de Sterke, “Propagation through nonuniform gratings,” Opt. Express 3, 405–410 (1998).
- D. Von der Linde, “Experimental study of single picosecond light pulses,” IEEE J. Quantum Electron. QE-8, 328–338 (1972).
- B. J. Eggleton, G. Lenz, R. E. Slusher, and N. M. Litchinitser, “Compression of pulses spectrally broadened by self-phase modulation with a fiber Bragg grating in transmission,” Appl. Opt. 37, 7055–7061 (1998).
- K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, “Bragg gratings fabricated in monomode photosensitive optical fiber by exposure through a phase mask,” Appl. Phys. Lett. 62, 1035–1037 (1993).
- J. Martin and F. Ouellette, “Novel writing technique of long and highly reflective in-fibre gratings,” Electron. Lett. 30, 812–813 (1994).
- J. E. Sipe, B. J. Eggleton, and T. A. Strasser, “Dispersion characteristics of nonuniform Bragg gratings: implications for WDM systems,” Opt. Commun. 152, 269–274 (1998).
- K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).
- A. B. Aceves and S. Wabnitz, “Multisoliton-like solutions of wave propagation in periodic nonlinear structures,” in Nonlinear Processes in Physics, A. S. Fokas, D. J. Kaup, A. C. Newell, and V. E. Zakharov, eds. (Springer, New York, 1993), p. 6.
- G. Lenz, B. J. Eggleton, and N. Litchinitser, “Pulse compression using fiber gratings as highly dispersive nonlinear elements,” J. Opt. Soc. Am. B 15, 715–721 (1997).
- R. E. Slusher, B. J. Eggleton, T. A. Strasser, and C. M. de Sterke, “Nonlinear pulse reflections from chirped fiber gratings,” Opt. Express 3, 465–475 (1998).
- G. Lenz and B. J. Eggleton, “Adiabatic compression soliton compression in nonuniform grating structures,” J. Opt. Soc. Am. B 15, 2979–2985 (1998).
- N. M. Litchinitser, G. P. Agrawal, B. J. Eggleton, and G. Lenz, “High repetition-rate soliton-train generation using fiber Bragg gratings,” Opt. Express 3, 411–417 (1998).
- B. J. Eggleton, R. E. Slusher, N. M. Litchinitser, G. P. Agrawal, A. B. Aceves, and C. M. de Sterke, “Experimental observation of interaction between Bragg solitons,” in International Quantum Electronics Conference, Vol. 7 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), paper QTuJ5.
- N. M. Litchinitser, B. J. Eggleton, C. M. de Sterke, A. B. Aceves, and G. P. Agrawal, “Interaction of Bragg solitons in fiber gratings,” J. Opt. Soc. Am. B 16, 18–23 (1998).
- J. P. Gordon, “Interaction forces among solitons in optical fibers,” Opt. Lett. 8, 596–598 (1983).
- S. Wang, H. Erlig, H. Fetterman, V. Grubsky, and J. Feinberg, “One-dimensional photonic crystals for CDMA,” Proc. SPIE 3228, 407–416 (1997).
- M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, J. P. Dowling, and R. P. Leavitt, “Ultrashort pulse propagation at the photonic band edge: large tunable group delay with minimal distortion and loss,” Phys. Rev. E 54, 1078–1081 (1996).

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.