The Nonlinear Analytical Envelope Equation in quadratic nonlinear crystals
Abstract
We here derive the socalled Nonlinear Analytical Envelope Equation (NAEE) inspired by the work of Conforti et al. [M. Conforti, A. Marini, T. X. Tran, D. Faccio, and F. Biancalana, "Interaction between optical fields and their conjugates in nonlinear media," Opt. Express 21, 3123931252 (2013)], whose notation we follow. We present a complete model that includes $\chi^{(2)}$ terms [M. Conforti, F. Baronio, and C. De Angelis, "Nonlinear envelope equation for broadband optical pulses in quadratic media," Phys. Rev. A 81, 053841 (2010)], $\chi^{(3)}$ terms, and then extend the model to delayed Raman effects in the $\chi^{(3)}$ term. We therefore get a complete model for ultrafast pulse propagation in quadratic nonlinear crystals similar to the Nonlinear Wave Equation in Frequency domain [H. Guo, X. Zeng, B. Zhou, and M. Bache, "Nonlinear wave equation in frequency domain: accurate modeling of ultrafast interaction in anisotropic nonlinear media," J. Opt. Soc. Am. B 30, 494504 (2013)], but where the envelope is modelled rather than the electrical field while still keeping a subcarrier level resolution. The advantage of the envelope formation is that the physical origin of the additional terms that are included to model the physics at the carrier level becomes more clear, in contrast to the electric field equations that are more "black box" expansions of the electrical field. We also point out that by comparing our results to a very similar model and widely used model [G. Genty, P. Kinsler, B. Kibler, and J. M. Dudley, "Nonlinear envelope equation modeling of subcycle dynamics and harmonic generation in nonlinear waveguides," Opt. Express 15, 53825387 (2007)], the Raman terms presented there will most likely lead to an artificially lower Raman effect.
 Publication:

arXiv eprints
 Pub Date:
 March 2016
 arXiv:
 arXiv:1603.00188
 Bibcode:
 2016arXiv160300188B
 Keywords:

 Physics  Optics