Third harmonic generation in the field of a backward pump wave

Abstract

Third harmonic generation in a nonlinear medium the refractive index of which is negative at the pump frequency and positive at the harmonic frequency with allowance for self action effects is considered theoretically. An exact solution of equations that describe the parametric interaction of continuous waves has been obtained analytically. The behavior of the solution is analyzed depending on the degree of violation of the phase matching condition. It is shown that, in a definite domain of values of nonlinear susceptibilities of the third order, there exists a critical value of the phase detuning at which the monotonic transform of the pump into the harmonic is changed by a periodical one. This phenomenon does not occur when the third har monic is generated in ordinary media with a positive refractive index.

Modulation instability in a triangular three-core coupler with a negative-index material channel

“…Numerous analytical and numerical studies have been devoted to exploring the various properties associated with devices based on PIM and NIM channels. For instance, solitary wave propagation in a nonlinear oppositely directed coupler was studied in [20,21], a waveguide amplifier based on a counter-directional coupler was studied in [22], thirdharmonic generation in the context of NIMs can be seen in [23]. Litchinister et al predicted that PIM-NIM couplers exhibit optical bistability and also admit gap solitons, a feature which is peculiar to periodic structures [24].…”

Interaction of forward and backward waves in a Kerr medium

“…The third-harmonic generation is described by equations that are similar to (1), but with 2ω replaced by 3ω. The corresponding expressions for nonlinear polarizations are also more complex [38][39][40].…”

Discrete gap solitons in binary positive-negative index nonlinear waveguide arrays with strong second-order couplings

“…Nonlinear response of such negative index metamaterials (NIM) to electromagnetic waves propagation leads to novel optical phenomena and is studied thoroughly in the last decade [17][18][19]. In particular, new regimes of nonlinear wave mixing between forward and backward waves can be brought about in NIM [20][21][22][23][24][25][26][27][28] (for more examples of studies, see the review papers of Ref. [27,28]).…”

“…In particular, new regimes of nonlinear wave mixing between forward and backward waves can be brought about in NIM [20][21][22][23][24][25][26][27][28] (for more examples of studies, see the review papers of Ref. [27,28]). Also, the interface between NIM and positive index media (PIM) presents new features of refraction or localization of electromagnetic waves [29][30][31][32][33].…”