Abstract
Coupled nonlinear Schrödinger equations (CNLS) very often represent wave propagation in optical media such as multicore fibers, photorefractive materials and so on. We consider specifically the pulse propagation in integrable CNLS equations (generalized Manakov systems). We point out that these systems possess novel exact soliton type pulses which are shape changing under collision leading to an intensity redistribution. The shape changes correspond to linear fractional transformations allowing for the possibility of construction of logic gates and Turing equivalent all optical computers in homogeneous bulk media as shown by Steiglitz recently. Special cases of such solitons correspond to the recently much discussed partially coherent stationary solitons (PCS). In this paper, we review critically the recent developments regarding the above properties with particular reference to 2-CNLS.
Similar content being viewed by others
References
See for example, several articles in the Focus Issue on “Optical Solitons — Perspectives and Applications” in Chaos 10(3) (2000)
M Segev and G Stegeman, Phys. Today 8, 43 (1998)
A Hasegawa, Chaos 10, 475 (2000)
G P Agrawal, Nonlinear fiber optics, second edition (Academic Press, New York, 1995)
S Chakravarty, M J Ablowitz, J R Sauer and R B Jenkins, Opt. Lett. 20, 136 (1995)
C Yeh and L Bergman, Phys. Rev. E57, 2398 (1998)
A C Scott, Phys. Scr. 29, 279 (1984)
M Mitchell, Z Chen, M F Shih and M Segev, Phys. Rev. Lett. 77, 490 (1996)
M Mitchell and M Segev, Nature 387, 880 (1997)
D N Christodoulides, T H Coskun, M Mitchell and M Segev, Phys. Rev. Lett. 78, 646 (1997)
D N Christodoulides, T H Coskun and R I Joseph, Opt. Lett. 22, 1080 (1997)
A W Snyder and D J Mitchell, Phys. Rev. Lett. 80, 1422 (1998)
A Ankiewicz, W Krolikowski and N N Akhmediev, Phys. Rev. E59, 6079 (1999)
N Akhmediev, W Krolikowski and A W Snyder, Phys. Rev. Lett. 81, 4632 (1998)
N Akhmediev and A Ankiewicz, Chaos 10, 600 (2000)
S V Manakov, Zh. Eksp. Teor. Fiz. 65, 505 (1973); Sov. Phys. JETP 38, 248 (1974)
R Radhakrishnan, M Lakshmanan and J Hietarinta, Phys. Rev. E56, 2213 (1997)
T Kanna and M Lakshmanan, Phys. Rev. Lett. 86, 5043 (2001)
M H Jakubowski, K Steiglitz and R Squier, Phys. Rev. E58, 6752 (1998)
K Steiglitz, Phys. Rev. E63, 016608 (2000)
R Radhakrishnan, R Sahadevan and M Lakshmanan, Chaos, Solitons and Fractals 5, 2315 (1995)
R Sahadevan, K M Tamizhmani and M Lakshmanan, J. Phys. A19, 1783 (1986)
V G Makhan’kov and O K Pashaev, Theor. Math. Phys. 53, 979 (1982)
K Nakkeeran, Phys. Rev. E62, 1313 (2000)
D N Christodoulides and M I Carvalho, J. Opt. Soc. Am. B12, 1628 (1995)
N Kukhtarev, V B Markov, S G Odulov, M S Soskin and V L Vinetskii, Ferroelectrics 22, 949 (1979)
M J Ablowitz and H Segur, Solitons and the inverse scattering transform (Siam, Philadelphia, 1981)
R Hirota, J. Math. Phys. (N.Y.) 14, 805 (1973)
M Lakshmanan, T Kanna and R Radhakrishnan, Rep. Math. Phys. 46, 143 (2000)
T Kanna and M Lakshmanan (to be published)
M J Ablowitz and A S Fokas, Complex variables, Cambridge texts in applied mathematics, (Cambridge University Press, 1997)
J U Kang, G I Stegeman, J S Aitchison and N Akhmediev, Phys. Rev. Lett. 76, 3699 (1996)
C Anastassiou, M Segev, K Steiglitz, J A Giordmaime, M Mitchell, Ming-fong Shih, S Lan and J Martin, Phys. Rev. Lett. 83, 2332 (1999)
W Krolikowski, N Akhmediev and B Luther-Davies, Phys. Rev. E59, 4654 (1999)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Lakshmanan, M., Kanna, T. Shape changing collisions of optical solitons, universal logic gates and partially coherent solitons in coupled nonlinear Schrödinger equations. Pramana - J Phys 57, 885–916 (2001). https://doi.org/10.1007/s12043-001-0005-0
Issue Date:
DOI: https://doi.org/10.1007/s12043-001-0005-0