Parametric gap solitons in quadratic media
Optics Express, Vol. 3, Issue 11, pp. 389-404 (1998)
http://dx.doi.org/10.1364/OE.3.000389
Acrobat PDF (594 KB)
Abstract
Localized energy states such as two-color gap solitons are theoretically and numerically predicted in a periodic structure in the presence of a frequency doubling nonlinearity. These parametric solitons exhibit appealing features as compared to the Kerr case. Novel effects such as merging and all-optical buffering are envisaged.
© Optical Society of America
1.. Introduction
1. W. Chen and D. L. Mills, “Gap solitons and the nonlinear optical response of superlattices,” Phys. Rev. Lett. 58, 160–163 (1987). [CrossRef] [PubMed]
3. 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). [CrossRef]
4. 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). [CrossRef]
5. Y. Kivshar, “Gap solitons due to cascading,” Phys. Rev. E 51, 1613–1615 (1995). [CrossRef]
6. C. Conti, S. Trillo, and G. Assanto, “Doubly resonant Bragg simultons via second-harmonic generation,” Phys. Rev. Lett. 78, 2341–2344 (1997). [CrossRef]
13. C. Conti, G. Assanto, and S. Trillo, “Excitation of self-transparency Bragg solitons in quadratic media,” Opt. Lett. 22, 1350–1352 (1997). [CrossRef]
14. C. Conti, A. De Rossi, and S. Trillo, “Existence, bistability, and instability of Kerr-like parametric gap solitons in quadratic media,” Opt. Lett. 23, 1265–1267 (1998). [CrossRef]
15. W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995). [CrossRef] [PubMed]
16. R. Schiek, Y. Baek, and G. I. Stegeman, “One-dimensional spatial solitary waves due to cascaded second-order nonlinearities in planar waveguides,” Phys. Rev. E 53, 1138 (1996). [CrossRef]
2.. Derivation of the governing equations
17. C. M. de Sterke, D. G. Salinas, and J. E. Sipe, “Coupled-mode theory for light propagation through deep nonlinear gratings,” Phys. Rev. E 54, 1969–1989 (1996). [CrossRef]
17. C. M. de Sterke, D. G. Salinas, and J. E. Sipe, “Coupled-mode theory for light propagation through deep nonlinear gratings,” Phys. Rev. E 54, 1969–1989 (1996). [CrossRef]
18. J. Söchtiget al., Electron. Lett. 31, 551–552 (1995). [CrossRef]
19. Z. Weissman et al., “Second-harmonic generation in Bragg-resonant quasi-phase-matched periodically segmented waveguide,” Opt. Lett. 20, 674–676 (1995). [CrossRef] [PubMed]
20. P. G. Kazansky and V. Pruneri, “Electric-field poling of quasi-phase-matched optical fibers,” J. Opt. Soc. Am. B , 14, 3170–3179 (1997). [CrossRef]
21. Ch. Becker, A. Greiner, Th. Oesselke, A. Pape, W. Sohler, and H. Suche, “Integrated optical Ti:Er:LiNbO_{3} distribuited Bragg reflector laser with a fixed photorefractive grating,” Opt. Lett. 23, 1195–1197 (1998). [CrossRef]
17. C. M. de Sterke, D. G. Salinas, and J. E. Sipe, “Coupled-mode theory for light propagation through deep nonlinear gratings,” Phys. Rev. E 54, 1969–1989 (1996). [CrossRef]
6. C. Conti, S. Trillo, and G. Assanto, “Doubly resonant Bragg simultons via second-harmonic generation,” Phys. Rev. Lett. 78, 2341–2344 (1997). [CrossRef]
7. H. He and P. D. Drummond, “Ideal soliton environment using parametric band gaps,” Phys. Rev. Lett. 78, 4311–4314 (1997). [CrossRef]
8. T. Peschel, U. Peschel, F. Lederer, and B. Malomed, “Solitary waves in Bragg gratings with a quadratic nonlinearity,” Phys. Rev. E 55, 4730–4739 (1997). [CrossRef]
6. C. Conti, S. Trillo, and G. Assanto, “Doubly resonant Bragg simultons via second-harmonic generation,” Phys. Rev. Lett. 78, 2341–2344 (1997). [CrossRef]
3.. Gap solitons resembling parametric walking solitons in homogeneous media
24. L. Torner, D. Mihalache, D. Mazilu, M. C. Santos, and N. N. Akhmediev, “Walking solitons in quadratic nonlinear media,” J. Opt. Soc. Am. B 15, 1476–1487 (1998). [CrossRef]
25. C. Etrich, U. Peschel, F. Lederer, and B. A. Malomed, “Stability of temporal chirped solitary waves in quadratically nonlinear media,” Phys. Rev. E 55, 6155–6161 (1997). [CrossRef]
24. L. Torner, D. Mihalache, D. Mazilu, M. C. Santos, and N. N. Akhmediev, “Walking solitons in quadratic nonlinear media,” J. Opt. Soc. Am. B 15, 1476–1487 (1998). [CrossRef]
25. C. Etrich, U. Peschel, F. Lederer, and B. A. Malomed, “Stability of temporal chirped solitary waves in quadratically nonlinear media,” Phys. Rev. E 55, 6155–6161 (1997). [CrossRef]
3.1 . Gap solitons with strong group-velocity dispersion
6. C. Conti, S. Trillo, and G. Assanto, “Doubly resonant Bragg simultons via second-harmonic generation,” Phys. Rev. Lett. 78, 2341–2344 (1997). [CrossRef]
11. C. Conti, S. Trillo, and G. Assanto, “Trapping of slowly moving or stationary two-color gap solitons,” Opt. Lett. 23, 334–336 (1998). [CrossRef]
22. A. V. Buryak and Y. S. Kivshar, “Spatial optical solitons governed by quadratic nonlinearity,” Opt. Lett. 19, 1612–1614 (1994). [CrossRef] [PubMed]
6. C. Conti, S. Trillo, and G. Assanto, “Doubly resonant Bragg simultons via second-harmonic generation,” Phys. Rev. Lett. 78, 2341–2344 (1997). [CrossRef]
3.2 . Excitation of slowly moving or still GSs in doubly resonant structures
26. C. Etrich, U. Peschel, F. Lederer, and B. A. Malomed, “Collision of solitary waves in media with a second-order nonlinearity,” Phys. Rev. A 52, R3444–R3447 (1995). [CrossRef] [PubMed]
26. C. Etrich, U. Peschel, F. Lederer, and B. A. Malomed, “Collision of solitary waves in media with a second-order nonlinearity,” Phys. Rev. A 52, R3444–R3447 (1995). [CrossRef] [PubMed]
3.3 . Interrogation process and all optical buffers
4.. Parametric gap solitons in a singly resonant Bragg grating
10. C. Conti, S. Trillo, and G. Assanto, “Optical gap solitons via second-harmonic generation: exact solitary solutions,” Phys. Rev. E , 57, R1251–R1254 (1998). [CrossRef]
13. C. Conti, G. Assanto, and S. Trillo, “Excitation of self-transparency Bragg solitons in quadratic media,” Opt. Lett. 22, 1350–1352 (1997). [CrossRef]
14. C. Conti, A. De Rossi, and S. Trillo, “Existence, bistability, and instability of Kerr-like parametric gap solitons in quadratic media,” Opt. Lett. 23, 1265–1267 (1998). [CrossRef]
14. C. Conti, A. De Rossi, and S. Trillo, “Existence, bistability, and instability of Kerr-like parametric gap solitons in quadratic media,” Opt. Lett. 23, 1265–1267 (1998). [CrossRef]
5.. Conclusions
3. 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). [CrossRef]
4. 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). [CrossRef]
18. J. Söchtiget al., Electron. Lett. 31, 551–552 (1995). [CrossRef]
21. Ch. Becker, A. Greiner, Th. Oesselke, A. Pape, W. Sohler, and H. Suche, “Integrated optical Ti:Er:LiNbO_{3} distribuited Bragg reflector laser with a fixed photorefractive grating,” Opt. Lett. 23, 1195–1197 (1998). [CrossRef]
3. 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). [CrossRef]
4. 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). [CrossRef]
20. P. G. Kazansky and V. Pruneri, “Electric-field poling of quasi-phase-matched optical fibers,” J. Opt. Soc. Am. B , 14, 3170–3179 (1997). [CrossRef]
References
1. | W. Chen and D. L. Mills, “Gap solitons and the nonlinear optical response of superlattices,” Phys. Rev. Lett. 58, 160–163 (1987). [CrossRef] [PubMed] |
2. | C. M. De Sterke and J. E. Sipe, in Progress in Optics XXXIII, E. Wolf ed., (Elsevier, Amsterdam, 1994), Chap. III. |
3. | 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). [CrossRef] |
4. | 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). [CrossRef] |
5. | Y. Kivshar, “Gap solitons due to cascading,” Phys. Rev. E 51, 1613–1615 (1995). [CrossRef] |
6. | C. Conti, S. Trillo, and G. Assanto, “Doubly resonant Bragg simultons via second-harmonic generation,” Phys. Rev. Lett. 78, 2341–2344 (1997). [CrossRef] |
7. | H. He and P. D. Drummond, “Ideal soliton environment using parametric band gaps,” Phys. Rev. Lett. 78, 4311–4314 (1997). [CrossRef] |
8. | T. Peschel, U. Peschel, F. Lederer, and B. Malomed, “Solitary waves in Bragg gratings with a quadratic nonlinearity,” Phys. Rev. E 55, 4730–4739 (1997). [CrossRef] |
9. | C. Conti, S. Trillo, and G. Assanto, “Bloch functions approach for parametric gap solitons,” Opt. Lett. 22, 445–447 (1997). [CrossRef] [PubMed] |
10. | C. Conti, S. Trillo, and G. Assanto, “Optical gap solitons via second-harmonic generation: exact solitary solutions,” Phys. Rev. E , 57, R1251–R1254 (1998). [CrossRef] |
11. | C. Conti, S. Trillo, and G. Assanto, “Trapping of slowly moving or stationary two-color gap solitons,” Opt. Lett. 23, 334–336 (1998). [CrossRef] |
12. | C. Conti, G. Assanto, and S. Trillo, “Read/write all-optical buffer by self trapped gap simultons,” Electron. Lett. 34, 689–690 (1998). [CrossRef] |
13. | C. Conti, G. Assanto, and S. Trillo, “Excitation of self-transparency Bragg solitons in quadratic media,” Opt. Lett. 22, 1350–1352 (1997). [CrossRef] |
14. | C. Conti, A. De Rossi, and S. Trillo, “Existence, bistability, and instability of Kerr-like parametric gap solitons in quadratic media,” Opt. Lett. 23, 1265–1267 (1998). [CrossRef] |
15. | W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995). [CrossRef] [PubMed] |
16. | R. Schiek, Y. Baek, and G. I. Stegeman, “One-dimensional spatial solitary waves due to cascaded second-order nonlinearities in planar waveguides,” Phys. Rev. E 53, 1138 (1996). [CrossRef] |
17. | C. M. de Sterke, D. G. Salinas, and J. E. Sipe, “Coupled-mode theory for light propagation through deep nonlinear gratings,” Phys. Rev. E 54, 1969–1989 (1996). [CrossRef] |
18. | J. Söchtiget al., Electron. Lett. 31, 551–552 (1995). [CrossRef] |
19. | Z. Weissman et al., “Second-harmonic generation in Bragg-resonant quasi-phase-matched periodically segmented waveguide,” Opt. Lett. 20, 674–676 (1995). [CrossRef] [PubMed] |
20. | P. G. Kazansky and V. Pruneri, “Electric-field poling of quasi-phase-matched optical fibers,” J. Opt. Soc. Am. B , 14, 3170–3179 (1997). [CrossRef] |
21. | Ch. Becker, A. Greiner, Th. Oesselke, A. Pape, W. Sohler, and H. Suche, “Integrated optical Ti:Er:LiNbO_{3} distribuited Bragg reflector laser with a fixed photorefractive grating,” Opt. Lett. 23, 1195–1197 (1998). [CrossRef] |
22. | A. V. Buryak and Y. S. Kivshar, “Spatial optical solitons governed by quadratic nonlinearity,” Opt. Lett. 19, 1612–1614 (1994). [CrossRef] [PubMed] |
23. | Guided-Wave Optoelectronic, chapter 2, T. Tamir ed., (Springer, Berlin, 1980). |
24. | L. Torner, D. Mihalache, D. Mazilu, M. C. Santos, and N. N. Akhmediev, “Walking solitons in quadratic nonlinear media,” J. Opt. Soc. Am. B 15, 1476–1487 (1998). [CrossRef] |
25. | C. Etrich, U. Peschel, F. Lederer, and B. A. Malomed, “Stability of temporal chirped solitary waves in quadratically nonlinear media,” Phys. Rev. E 55, 6155–6161 (1997). [CrossRef] |
26. | C. Etrich, U. Peschel, F. Lederer, and B. A. Malomed, “Collision of solitary waves in media with a second-order nonlinearity,” Phys. Rev. A 52, R3444–R3447 (1995). [CrossRef] [PubMed] |
OCIS Codes
(050.2770) Diffraction and gratings : Gratings
(190.2620) Nonlinear optics : Harmonic generation and mixing
(190.4410) Nonlinear optics : Nonlinear optics, parametric processes
(230.1480) Optical devices : Bragg reflectors
ToC Category:
Focus Issue: Bragg solitons and nonlinear optics of periodic structures
History
Original Manuscript: October 19, 1998
Published: November 23, 1998
Citation
Claudio Conti, Gaetano Assanto, and Stefano Trillo, "Parametric gap solitons in quadratic media," Opt. Express 3, 389-404 (1998)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-3-11-389
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References
- W. Chen and D. L. Mills, "Gap solitons and the nonlinear optical response of superlattices," Phys. Rev. Lett. 58, 160-163 (1987). [CrossRef] [PubMed]
- C. M. De Sterke and J. E. Sipe, in Progress in Optics XXXIII, E. Wolf ed., (Elsevier, Amsterdam, 1994), Chap. III.
- 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). [CrossRef]
- 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). [CrossRef]
- Y. Kivshar, "Gap solitons due to cascading," Phys. Rev. E 51, 1613-1615 (1995). [CrossRef]
- C. Conti, S. Trillo, and G. Assanto, "Doubly resonant Bragg simultons via second-harmonic generation," Phys. Rev. Lett. 78, 2341-2344 (1997). [CrossRef]
- H. He and P. D. Drummond, "Ideal soliton environment using parametric band gaps," Phys. Rev. Lett. 78, 4311-4314 (1997). [CrossRef]
- T. Peschel, U. Peschel, F. Lederer, and B. Malomed, "Solitary waves in Bragg gratings with a quadratic nonlinearity," Phys. Rev. E 55, 4730-4739 (1997). [CrossRef]
- C. Conti, S. Trillo, and G. Assanto, "Bloch functions approach for parametric gap solitons," Opt. Lett. 22, 445-447 (1997). [CrossRef] [PubMed]
- C. Conti, S. Trillo, and G. Assanto, "Optical gap solitons via second-harmonic generation: exact solitary solutions," Phys. Rev. E, 57, R1251-R1254 (1998). [CrossRef]
- C. Conti, S. Trillo, and G. Assanto, "Trapping of slowly moving or stationary two-color gap solitons," Opt. Lett. 23, 334-336 (1998). [CrossRef]
- C. Conti, G. Assanto, and S. Trillo, "Read/write all-optical buffer by self trapped gap simultons," Electron. Lett. 34, 689-690 (1998). [CrossRef]
- C. Conti, G. Assanto, and S. Trillo, "Excitation of self-transparency Bragg solitons in quadratic media," Opt. Lett. 22, 1350-1352 (1997). [CrossRef]
- C. Conti, A. De Rossi, and S. Trillo, "Existence, bistability, and instability of Kerr-like parametric gap solitons in quadratic media," Opt. Lett. 23, 1265-1267 (1998). [CrossRef]
- W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, "Observation of two-dimensional spatial solitary waves in a quadratic medium," Phys. Rev. Lett. 74, 5036-5039 (1995). [CrossRef] [PubMed]
- R. Schiek, Y. Baek, G. I. Stegeman, "One-dimensional spatial solitary waves due to cascaded second-order nonlinearities in planar waveguides," Phys. Rev. E 53, 1138 (1996). [CrossRef]
- C. M. de Sterke, D. G. Salinas, J. E. Sipe, "Coupled-mode theory for light propagation through deep nonlinear gratings," Phys. Rev. E 54, 1969-1989 (1996). [CrossRef]
- J. Söchtig et al., Electron. Lett. 31, 551-552 (1995). [CrossRef]
- Z. Weissman et al., "Second-harmonic generation in Bragg-resonant quasi-phase-matched peri- odically segmented waveguide," Opt. Lett. 20, 674-676 (1995). [CrossRef] [PubMed]
- P. G. Kazansky and V. Pruneri, "Electric-field poling of quasi-phase-matched optical fibers," J. Opt. Soc. Am. B, 14, 3170-3179 (1997). [CrossRef]
- Ch. Becker, A. Greiner, Th. Oesselke, A. Pape, W. Sohler, and H. Suche, "Integrated optical Ti:Er:LiNbO3 distribuited Bragg reflector laser with a fixed photorefractive grating," Opt. Lett. 23, 1195-1197 (1998). [CrossRef]
- A. V. Buryak and Y. S. Kivshar, "Spatial optical solitons governed by quadratic nonlinearity," Opt. Lett. 19, 1612-1614 (1994). [CrossRef] [PubMed]
- Guided-Wave Optoelectronic, chapter 2, T. Tamir ed., (Springer, Berlin, 1980).
- L. Torner, D. Mihalache, D. Mazilu, M. C. Santos, and N. N. Akhmediev, "Walking solitons in quadratic nonlinear media," J. Opt. Soc. Am. B 15, 1476-1487 (1998). [CrossRef]
- C. Etrich, U. Peschel, F. Lederer, and B. A. Malomed, "Stability of temporal chirped solitary waves in quadratically nonlinear media," Phys. Rev. E 55, 6155-6161 (1997). [CrossRef]
- C. Etrich, U. Peschel, F. Lederer, and B. A. Malomed, "Collision of solitary waves in media with a second-order nonlinearity," Phys. Rev. A 52, R3444-R3447 (1995). [CrossRef] [PubMed]
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