In this paper we review our works in the field of nonlinear optics in waveguide arrays (WAs) and photonic nanowires. We first focus on the new equation governing light propagation in optical fibers with sub-wavelength cores which simultaneously takes into account (i) the vector nature of the electromagnetic modes inside fibers, (ii) the strong dispersion of the nonlinearity inside the spectral body of the pulse, (iii) and the full variations of the vector mode profiles with frequency. | Communications in Physics, Vol. 27, No. 1 (2017), pp. 1-22 DOI: Review NONLINEAR OPTICS IN WAVEGUIDE ARRAYS AND PHOTONIC NANOWIRES TRAN XUAN TRUONG † Department of Physics, Le Quy Don University, 236 Hoang Quoc Viet, Hanoi, Vietnam † E-mail: tranxtr@ Received 13 December 2016 Accepted for publication 03 January 2017 Abstract. In this paper we review our works in the field of nonlinear optics in waveguide arrays (WAs) and photonic nanowires. We first focus on the new equation governing light propagation in optical fibers with sub-wavelength cores which simultaneously takes into account (i) the vector nature of the electromagnetic modes inside fibers, (ii) the strong dispersion of the nonlinearity inside the spectral body of the pulse, (iii) and the full variations of the vector mode profiles with frequency. From this equation we have shown that a new kind of nonlinearity emerges in subwavelength-core fibers which can suppress the Raman self-frequency shift of solitons. We then discuss some nonlinear phenomena in WAs such as the emission of the diffractive resonant radiation from spatial discrete solitons and the anomalous recoil effect. Finally, we review our works on the optical analogues of Dirac solitons in quantum relativistic physics in binary waveguide arrays for both fundamental and higher-order solitons, and its interaction. Keywords: nonlinear optics, waveguide array, photonic nanowire, soliton, diffractive resonant radiation, Dirac soliton. Classification numbers: , , . I. INTRODUCTION Optical fibers [1, 2] and waveguide arrays (WAs) [3, 4] are optical systems exhibiting many important and interesting nonlinear phenomena, and are fundamental components of the modern optical technologies from both the fundamental and practical viewpoints. Evolution equations that accurately describe the propagation of short pulses in nonlinear media are extremely valuable tools in modern nonlinear optics, .
