Solitary electromagnetic wave propagation in the asymmetric oppositely directed coupler

Abstract

We consider the electromagnetic waves propagating in the system of coupled waveguides. One of the system components is a standard waveguide fabricated from nonlinear medium having positive refraction and another component is a waveguide produced from an artificial material having negative refraction. The metamaterial constituting the second waveguide has linear characteristics and a wave propagating in the waveguide of this type propagates in the direction opposite to direction of energy flux. It is found that the coupled nonlinear solitary waves propagating both in the same direction are exist in this oppositely-directed coupler due to linear coupling between nonlinear positive refractive waveguide and linear negative refractive waveguide. The corresponding analytical solution is found and it is used for numerical simulation to illustrate that the results of the solitary wave collisions are sensible to the relative velocity of the colliding solitary waves.

Oppositely Directional Coupler: Example of the Forward Backward Waves Interaction in the Metamaterials

“…This expression shows that (a) the forbidden zone (gap) in spectrum of the linear waves exist | | 2 1 γ = ω ∆ , (b) spectrum is shifted along both frequency axis and wave numbers axis, (c) the form of spectrum likes the spectrum for linear oppositely-directional coupler [17,21,22]. The gapless spectrum appears only when condition 2 / π = ϕ is hold.…”

Third harmonic generation in the field of a backward pump wave

“…Passage through the inter face between nonlinear media with NR and positive refraction (PR), surface waves at such interface [11][12][13], periodic structures [14][15][16][17], and waveguide arrays [18][19][20] with alternating NR and PR are some exam ples in which new nonlinear optical effects arise. In addition, NR features manifest themselves in the interaction of wave packets with carrier frequencies related to spectral regions in which the refractive index has different signs [21][22][23][24][25][26][27][28][29][30][31].…”

Discrete solitons in arrays of positive and negative index waveguides

“…The phenomenon is related to a gap in the linear spectrum and is originated by the effective feedback due to opposite Poynting vectors in the coupler arms. As further developments, solitons [5][6][7], modulational instability [8], amplification [9] in such opposite directional couplers were investigated.…”

“…1) and z is the propagation distance. The stationary field distribution in the array can be described by the system [4,6] i _ u n νu n κv n−1 v n χ 1 ju n j 2 u n 0;…”