Symmetry breaking in binary chains with nonlinear sites

Abstract

We consider a system of two or four nonlinear sites coupled with binary chain waveguides. When a monochromatic wave is injected into the first (symmetric) propagation channel the presence of cubic nonlinearity can lead to symmetry breaking giving rise to emission of antisymmetric wave into the second (antisymmetric) propagation channel of the waveguides. We found that in the case of nonlinear plaquette there is a domain in the parameter space where neither symmetry preserving nor symmetry breaking stable stationary solutions exit. As a result injection of a monochromatic symmetric wave gives rise to emission of nonsymmetric satellite waves with energies different from the energy of the incident wave. Thus, the response exhibits nonmonochromatic behavior.

Excitation of a bound state in the continuum via spontaneous symmetry breaking

“…It worth mentioning that similar equations were used in other works for describing the interaction of the incident electromagnetic field with nonlinear photonic structures (see, e.g., Refs. [66,67]). The absence of pump term in the equation for the BIC clearly indicates that it is decoupled from the far-field.…”

Frequency comb generation for wave transmission through the nonlinear dimer

“…As the input amplitude E in increases the system bifurcates from the symmetry preserving solution a 10 = a 20 to the symmetry breaking solution I 1 = I 2 , θ 1 − θ 2 = 0, π where a j0 = I j exp(iθ j ), j = 1, 2 similar to the closed nonlinear dimer [1,3,5]. However in contrast to the closed nonlinear dimer the open dimer can also transit into the phase symmetry breaking solution with I 1 = I 2 but θ 1 − θ 2 = 0, π [15,20].…”

“…As dependent on the way of opening the transmission through nonlinear dimer was studied in Refs. [12][13][14][15][16][17][18][19][20][21][22] where the phenomenon of symmetry breaking was reported. What is interesting there is a domain in the space of frequency and amplitude of injected wave where stable stationary solutions of the temporal equations do not exist [15,20].…”

“…[12][13][14][15][16][17][18][19][20][21][22] where the phenomenon of symmetry breaking was reported. What is interesting there is a domain in the space of frequency and amplitude of injected wave where stable stationary solutions of the temporal equations do not exist [15,20]. Thus one can expect that the dynamical response of the nonlinear dimer will display features which can not be described by the stationary scattering theory.…”

“…Thus one can expect that the dynamical response of the nonlinear dimer will display features which can not be described by the stationary scattering theory. In particular injection of a monochromatic symmetric wave into the nonlinear plaquette gives rise to emission of anti-symmetric satellite waves with frequencies different from the frequency of the incident wave [20]. This phenomenon is known as frequency comb (FC) generation and is widely studied in various linear and nonlinear systems [23][24][25].…”