Kafes Frekansının Kuadratik Ortamda Üretilen Kusurlu Kafes Solitonlari Üzerindeki Etkileri

Yıl 2022, , 344 - 351, 24.03.2022

Mahmut Bağcı

https://doi.org/10.17798/bitlisfen.1024502

Öz

Kafes frekansının kusurlu kafes solitonları üzerindeki etkisi doğrusal olmayan ikinci derece (kuadratik) etkilerin olduğu ortamda araştırılmıştır. NLSM denklem sistemine bir harici kafes eklenerek optik sistemin yönetici denklemi oluşturulmuş ve sistemin soliton çözümleri kare operatör yöntemi ile hesaplanmıştır. Ayrıca, elde edilen solitonların kararlılığı, solitonların doğrusal özdeğer spektrumları ve doğrusal olmayan evolüsyonu ile test edilmiştir. Daha yüksek kafes frekansının, kuadratik ortamda kusurlu kafes solitonlarının varlık alanını genişletse de, solitonların kararlılık dinamiklerini olumsuz etkilediği gösterilmiştir.

Anahtar Kelimeler

Optik kafesler, Kafes solitonları, Soliton kararlılığı, Kuadratik etkiler

Effects of Lattice Frequency on Vacancy Defect Solitons in a Medium with Quadratic Nonlinear Response

Öz

The impact of lattice frequency on the defect lattice solitons have been investigated in a medium with quadratic nonlinear response. Governing equation of the optical system has been formed by adding an external lattice to the NLSM system, and soliton solutions of the system were calculated by the squared operator method. Moreover, stability of the fundamental solitons have been examined by the linear stability spectra and nonlinear evolution of the solitons. It has been demonstrated that although higher lattice frequency extends the existence domain of defective lattice solitons in a quadratic nonlinear medium, it negatively effects the stability dynamics of the solitons.

Anahtar Kelimeler

Optical lattices, Lattice solitons, Soliton stability, Quadratic response

Kaynakça

• [1] Ablowitz M. J. 2011. Nonlinear Dispersive Waves: Asymptotic Analysis and Solitons. Cambridge University Press, Cambridge, 1-345.
• [2] Torruellas W. E., Wang Z., Hagan D. J., VanStryland E. W., Stegeman G. I., Torner L., Menyuk C. R. 1995. Observation of two-dimensional spatial solitary waves in a quadratic medium. Physical Review Letter, 74: 5036-5040.
• [3] Hayata K., Koshiba M. 1993. Multidimensional solitons in quadratic nonlinear media. Physical Review Letters, 71(20): 3275-3278.
• [4] Torner L. and Sukhorukov A. P. 2002. Quadratic solitons. Optics and Photonics News, 13(2): 42-47.
• [5] Bağcı M., Bakırtaş İ., Antar N. 2017. Lattice solitons in nonlinear Schrödinger equation with coupling-to-a-mean-term. Optics Communications, 383: 330-340.
• [6] Bağcı M., Kutz J. N. 2020. Spatiotemporal mode locking in quadratic nonlinear media. Physical Review E, 102(2): 022205.
• [7] Ablowitz M. J., Biondini G., Blair S. 2001. Localized multi-dimensional optical pulses in non-resonant quadratic materials. Mathematics and Computers in Simulation, 56: 511-519.
• [8] Ablowitz M. J., Biondini G., Blair S. 2001. Nonlinear Schrödinger equations with mean terms in nonresonant multidimensional quadratic materials. Physical Review E, 63(4): 046605.
• [9] Ablowitz M. J., Bakırtaş İ., Ilan B. 2005. Wave collapse in a class of nonlocal nonlinear Schrödinger equations. Physica D: Nonlinear Phenomena, 207(3): 230-253.
• [10] Gatz S., Herrmann J. 1991. Soliton propagation in materials with saturable nonlinearity. Journal of Optical Society of America B 8(11): 2296-2302.
• [11] Göksel İ., Bakırtaş İ., Antar N. 2015. Nonlinear lattice solitons in saturable media. Applied Mathematics & Information Sciences 9(1): 377-385.
• [12] Ablowitz M. J., Antar N., Bakırtaş İ, Ilan B. 2010. Band-gap boundaries and fundamental solitons in complex two-dimensional nonlinear lattices. Physical Review A 81(3): 033834.
• [13] Kartashov Y. V., Malomed B. A., Torner L. 2011. Solitons in nonlinear lattices. Review of Modern Physics 83(1): 247-305.
• [14] Fleischer J. W., Segev M., Efremidis N. K., Christodoulides D. N. 2003. Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices. Nature, 422: 147-150.
• [15] Baizakov B. B., Malomed B. A., Salerno M. 2003. Multi-dimensional solitons in periodic potentials. Europhysics Letters, 63(5): 642-648.
• [16] Sakaguchi H., Malomed B. A. 2006. Gap solitons in quasiperiodic optical lattices. Physical Review E, 74(2): 026601.
• [17] Ablowitz M. J., Antar N., Bakırtaş İ., Ilan B. 2012. Vortex and dipole solitons in complex two-dimensional nonlinear lattices. Physical Review A, 86(3): 033804.
• [18] Bağcı M. 2021. Soliton dynamics in quadratic nonlinear media with two-dimensional pythagorean aperiodic lattices. Journal of Optical Society of America B, 38(4): 1276-1282.
• [19] Nixon S., Lijuan G., Yang, J. 2012. Stability analysis for solitons in PT-symmetric optical lattices. Physical Review A, 85(2): 023822.
• [20] Moreira F.C., Konotop V. V., Malomed B. A. 2013. Solitons in PT-symmetric periodic systems with the quadratic nonlinearity. Physical Review A 87(1): 013832.
• [21] Göksel İ., Antar N., Bakırtaş İ. 2018. Two-dimensional solitons in PT-symmetric optical media with competing nonlinearity. Optik, 156: 470-478.
• [22] Bağcı M. 2021. Partially PT-symmetric lattice solitons in quadratic nonlinear media. Physical Review A, 103(2): 023530.
• [23] Ablowitz M. J., Ilan B., Schonbrun E., Piestun R. 2006. Solitons in two-dimensional lattices possessing defects, dislocations, and quasicrystal structures. Physical Review E, 74(3): 035601.
• [24] Sivan Y., Fibich G., Ilan B., Weinstein M. I. 2008. Qualitative and quantitative analysis of stability and instability dynamics of positive lattice solitons. Physical Review E, 78(4): 046602.
• [25] Bağcı M., Bakırtaş İ., Antar N. 2014. Vortex and dipole solitons in lattices possessing defects and dislocations. Optics Communications, 331: 204-218.
• [26] Bağcı M., Bakırtaş İ., Antar N. 2015, Fundamental solitons in parity-time symmetric lattice with a vacancy defect. Optics Communications, 356: 472-481.
• [27] Braun P. V., Rinne S. A., Garcia-Santamaria F. 2006. Introducing defects in 3d photonic crystals: state of the art. Advanced Materials, 18(20): 2665-2678.
• [28] Yang J., Lakoba T. I. 2007. Universally-convergent squared-operator iteration methods for solitary waves in general nonlinear wave equations. Studies in Applied Mathematics, 118(2): 153-197.
• [29] Yang J. 2010. Nonlinear Waves in Integrable and Nonintegrable Systems. SIAM, Philadelphia, 1-454.
• [30] Crasovan L. C., Torres J. P., Mihalache D., Torner L. 2003. Arresting wave collapse by wave self-rectification. Physical Review Letters, 91(6): 063904.
• [31] Vakhitov N.G., Kolokolov A. A. 1973. Stationary solutions of the wave equation in a medium with nonlinearity saturation. Radiophysics and Quantum Electronics, 16: 783-789