Exact analytical solutions and their applications for interacting waves in quadratic nonlinear medium

doi:10.1364/OE.10.000083

Optics Express

Editor: Michael Duncan
Vol. 10, Iss. 1 — Jan. 14, 2002
pp: 83–97

Exact analytical solutions and their applications for interacting waves in quadratic nonlinear medium

Xueming Liu, Hanyi Zhang, and Mingde Zhang »View Author Affiliations

Optics Express, Vol. 10, Issue 1, pp. 83-97 (2002)
http://dx.doi.org/10.1364/OE.10.000083

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Abstract

The exact analytical solutions for the interacting waves in the quadratic nonlinear medium with the periodic structure are detailedly derived and obtained, and the properties of solutions are analyzed. Three applicable examples employing the exact solutions in the all-optical processing are given and analyzed. The optimized results show that the phase of signal can obviously be increased by proper choosing Δk, and that the intensity of pump can greatly be decreased in the all-optical switching by means of optimizing Δk, increasing medium length, and choosing sum-frequency generation.

[Optical Society of America ]

OCIS Codes
(060.2630) Fiber optics and optical communications : Frequency modulation
(190.0190) Nonlinear optics : Nonlinear optics
(190.2620) Nonlinear optics : Harmonic generation and mixing
(230.1150) Optical devices : All-optical devices

ToC Category:
Research Papers

History
Original Manuscript: December 21, 2001
Published: January 14, 2002

Citation
Xueming Liu, Hanyi Zhang, and Mingde Zhang, "Exact analytical solutions and their applications for interacting waves in quadratic nonlinear medium," Opt. Express 10, 83-97 (2002)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-10-1-83

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References

G. I. Stegeman, D. J. Hagan, L. Torner, "?(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse, compression and solitions," Opt. Quantum Electron. 28, 1691-1740 (1996). [CrossRef]
S. J. B. Yoo, "Wavelength conversion technologies for WDM network applications," J. Lightwave Technol. 14, 955-966 (1996). [CrossRef]
G. P. Banfi, P. K. Datta, V. Degiorgio, D. Fortusini, "Wavelength shifting and amplification of optical pulses through cascaded second-order processes in periodically poled lithium niobate," Appl. Phys. Lett. 73, 136-138 (1998). [CrossRef]
G. Assanto and I. Torelli, "Cascading effects in type II second-harmonic generation: application to all-optical processing," Opt. Commun. 119, 143-148 (1995). [CrossRef]
J. Leuthold, P. A. Besse, E. Gamper, M. Dulk, S. Fischer, G. Guekos, H. Melchior,, "All-optical Mach-Zehnder interferometer wavelength converters and switches with integrated data- and control-signal separation scheme," J. lightwave Technol. 17, 1056-1065 (1999). [CrossRef]
G. S. Kanter and P. Kumar, "Optical devices based on internally seeded cascaded nonlinearities," IEEE. J. Quantum Elecron. 35, 891-896 (1999). [CrossRef]
J. A. Armstrong, N. Bloembergen N, J. Ducuing, et al. "Interaction between light waves in a nonlinear dielectric," Phys. Rev. 127, 1918-1939 (1962). [CrossRef]
A. Kobyakov and F. Lederer, "Cascading of quadratic nonlinearities: an analytical study," Phys. Rev. A 54, 3455-3471 (1996). [CrossRef] [PubMed]
M. Asghari, I. H. White, R. V. Penty, "Wavelength conversion using semiconductor optical amplifiers," J. Lighteave Technol. 15, 1181-1190 (1997). [CrossRef]
R. W. Boyd, Nonlinear Optics (Academic Press, San Diego, 1992), Chap.2.
M. J. T. Milton, "General expressions for the efficiency of phase-matched and nonphase-matched second-order nonlinear interactions between plane waves," IEEE. J. Quantum Elecron. 28, 739-749 (1992). [CrossRef]
Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984), Chap.6-7.
A. R. C. Sibilia, E. Fazio, M. Bertolotti, "Field dependent effect in a quadratic nonlinear medium," J. Mod. Opt. 42, 823-839 (1995). [CrossRef]
C. N. Ironside, J. S. Aitchison, J. M. Arnold, "An all-optical switch employing the cascaded second-order nonlinear effect," IEEE. J. Quantum Elecron. 29, 2650-2654 (1993). [CrossRef]
A. Kobyakov, U. Peschel, F. Lederer, "Vectorial type-II interaction in cascaded quadratic nonlinearities-an analytical approach," Opt. Commun. 124, 184-194 (1996). [CrossRef]
G. D'Aguanno, C. Sibilia, E. Fazio, M. Bertolotti, "Three-wave mixing in a quadratic material under perfect phase-matching,"Opt. Commun. 142, 75-78 (1997). [CrossRef]
X. -M. Liu, H. -Y. Zhang, Y. -L. Guo, "Theoretical analyses and optimizations for wavelength conversion by quasi-phase-matching difference-frequency generation," J. Lightwave Technol. 19, 1785-1792 (2001). [CrossRef]
T. Suhara, H. Nishihara, "Theoretical analysis of waveguide second-harmonic generation phase matched with uniform and chirped gratings," IEEE. J. Quantum Elecron. 26, 1265-1270 (1990). [CrossRef]
X. -M. Liu and M. -D. Zhang, "Theoretical studies for the special states of the cascaded quadratic nonlinear effects", J. Opt. Soc. Am. B 18, 1659-1666 (2001). [CrossRef]
[USA] G. A. Kehen, T. M. Kehen, Handbook of Mathematics (Worker Press, Beijing, 1987), (in Chinese).
M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (Dover Publications, Dover, 1965), Chap. 16-17.
H. Kanbara, H. Itoh, M. Asobe, K. Noguchi, H. Miyazawa, T. Yanagawa, I. Yokohama, "All-optical switching based on cascading of second-order nonlinearities in a periodically poled titanium-diffused lithium niobate waveguide," IEEE. Photon. Technol. Lett. 11, 328-330 (1999). [CrossRef]
C. Q. Xu, H. Okayama, M. Kawahara, "Optical frequency conversions in nonlinear medium with periodically modulated linear and nonlinear optical parameters," IEEE. J. Quantum Elecron. 31, 981-987 (1995). [CrossRef]
X. -M. Liu, H. -Y. Zhang, Y. -H Li, "Optimal design for the quasi-phase-matching three-wave mixing," Opt. Express 9, 631-636 (2001), <a href="http://www.opticsexpress.org/oearchive/source/37804.htm">http://www.opticsexpress.org/oearchive/source/37804.htm</a> [CrossRef] [PubMed]

Opt. Express

X. -M. Liu, H. -Y. Zhang, Y. -H Li, "Optimal design for the quasi-phase-matching three-wave mixing," Opt. Express 9, 631-636 (2001), <a href="http://www.opticsexpress.org/oearchive/source/37804.htm">http://www.opticsexpress.org/oearchive/source/37804.htm</a> [CrossRef] [PubMed]

Other

G. I. Stegeman, D. J. Hagan, L. Torner, "?(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse, compression and solitions," Opt. Quantum Electron. 28, 1691-1740 (1996). [CrossRef]
S. J. B. Yoo, "Wavelength conversion technologies for WDM network applications," J. Lightwave Technol. 14, 955-966 (1996). [CrossRef]
G. P. Banfi, P. K. Datta, V. Degiorgio, D. Fortusini, "Wavelength shifting and amplification of optical pulses through cascaded second-order processes in periodically poled lithium niobate," Appl. Phys. Lett. 73, 136-138 (1998). [CrossRef]
G. Assanto and I. Torelli, "Cascading effects in type II second-harmonic generation: application to all-optical processing," Opt. Commun. 119, 143-148 (1995). [CrossRef]
J. Leuthold, P. A. Besse, E. Gamper, M. Dulk, S. Fischer, G. Guekos, H. Melchior,, "All-optical Mach-Zehnder interferometer wavelength converters and switches with integrated data- and control-signal separation scheme," J. lightwave Technol. 17, 1056-1065 (1999). [CrossRef]
G. S. Kanter and P. Kumar, "Optical devices based on internally seeded cascaded nonlinearities," IEEE. J. Quantum Elecron. 35, 891-896 (1999). [CrossRef]
J. A. Armstrong, N. Bloembergen N, J. Ducuing, et al. "Interaction between light waves in a nonlinear dielectric," Phys. Rev. 127, 1918-1939 (1962). [CrossRef]
A. Kobyakov and F. Lederer, "Cascading of quadratic nonlinearities: an analytical study," Phys. Rev. A 54, 3455-3471 (1996). [CrossRef] [PubMed]
M. Asghari, I. H. White, R. V. Penty, "Wavelength conversion using semiconductor optical amplifiers," J. Lighteave Technol. 15, 1181-1190 (1997). [CrossRef]
R. W. Boyd, Nonlinear Optics (Academic Press, San Diego, 1992), Chap.2.
M. J. T. Milton, "General expressions for the efficiency of phase-matched and nonphase-matched second-order nonlinear interactions between plane waves," IEEE. J. Quantum Elecron. 28, 739-749 (1992). [CrossRef]
Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984), Chap.6-7.
A. R. C. Sibilia, E. Fazio, M. Bertolotti, "Field dependent effect in a quadratic nonlinear medium," J. Mod. Opt. 42, 823-839 (1995). [CrossRef]
C. N. Ironside, J. S. Aitchison, J. M. Arnold, "An all-optical switch employing the cascaded second-order nonlinear effect," IEEE. J. Quantum Elecron. 29, 2650-2654 (1993). [CrossRef]
A. Kobyakov, U. Peschel, F. Lederer, "Vectorial type-II interaction in cascaded quadratic nonlinearities-an analytical approach," Opt. Commun. 124, 184-194 (1996). [CrossRef]
G. D'Aguanno, C. Sibilia, E. Fazio, M. Bertolotti, "Three-wave mixing in a quadratic material under perfect phase-matching,"Opt. Commun. 142, 75-78 (1997). [CrossRef]
X. -M. Liu, H. -Y. Zhang, Y. -L. Guo, "Theoretical analyses and optimizations for wavelength conversion by quasi-phase-matching difference-frequency generation," J. Lightwave Technol. 19, 1785-1792 (2001). [CrossRef]
T. Suhara, H. Nishihara, "Theoretical analysis of waveguide second-harmonic generation phase matched with uniform and chirped gratings," IEEE. J. Quantum Elecron. 26, 1265-1270 (1990). [CrossRef]
X. -M. Liu and M. -D. Zhang, "Theoretical studies for the special states of the cascaded quadratic nonlinear effects", J. Opt. Soc. Am. B 18, 1659-1666 (2001). [CrossRef]
[USA] G. A. Kehen, T. M. Kehen, Handbook of Mathematics (Worker Press, Beijing, 1987), (in Chinese).
M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (Dover Publications, Dover, 1965), Chap. 16-17.
H. Kanbara, H. Itoh, M. Asobe, K. Noguchi, H. Miyazawa, T. Yanagawa, I. Yokohama, "All-optical switching based on cascading of second-order nonlinearities in a periodically poled titanium-diffused lithium niobate waveguide," IEEE. Photon. Technol. Lett. 11, 328-330 (1999). [CrossRef]
C. Q. Xu, H. Okayama, M. Kawahara, "Optical frequency conversions in nonlinear medium with periodically modulated linear and nonlinear optical parameters," IEEE. J. Quantum Elecron. 31, 981-987 (1995). [CrossRef]

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