Transverse instability of hybrid solitons in the strong light-matter coupling regime

TL;DR

This work analyzes the transverse stability of two-component polariton solitons in a planar waveguide under strong light-matter coupling. By formulating a conservative two-field model for photons and excitons, it derives a spectral problem coupling transverse diffraction to nonlinear exciton dynamics and obtains long-wavelength asymptotics for bright solitons, supported by numerical eigenvalue calculations. The study shows that bright solitons exhibit a finite-wavelength instability with growth that increases with soliton amplitude, while gray-dark and gray-gray solitons are unstable in a bounded $k_x$ range, producing spontaneous vortex-antivortex nucleation in both fields. Dynamical simulations illustrate the development of instability into high-intensity spots for bright pulses and transient vortex lattices for gray solitons, offering insight into the 2D behavior of polariton solitons and guiding future explorations of dissipative effects and structured waveguides.

Abstract

We investigate the transverse instability of two-component solitons forming in a planar waveguide operating in the regime of strong light-matter coupling. The instability emerges as a result of the coupling between transverse diffraction of the photonic component and nonlinearity of the material excitations. Solutions of three different forms are addressed which include bright, gray-dark, and gray-gray solitons. In the limit of long-wavelength transverse perturbations, the instability is described with an asymptotic expansion whose predictions agree with the results of numerical simulations. The dynamic development of instability of initially perturbed bright solitons leads to the formation of high-intensity spots in the photonic component. For gray-dark and dark-dark solitons, the transverse instability leads to the spontaneous nucleation of vortex-antivortex pairs which emerge in both fields as transient patterns.

Figures (9)

• Figure 1: A schematic of the system. A planar waveguide with an embedded layer of quantum wells (QWs) is situated in the $(x,z)$ plane, where $x$ and $z$ correspond to the transverse and longitudinal directions, respectively. The waveguide is pumped through the input grating with a pulse whose spatial aperture is wide in the transverse direction; the amplitude of the coherent pump is denoted as $|P(t)|$. The pulsed pump leads to the formation of an elongated soliton whose shape is localized in the $z$ direction and does not depend on the transverse coordinate $x$. As the soliton propagates in the longitudinal direction with velocity $v$, its shape becomes modulated due to the transverse instability resulting from the interplay between nonlinearity and diffraction along the $x$-axis.
• Figure 2: Examples of coexisting solutions of different types: bright solitons on zero (a) and nonzero (b) backgrounds, gray-dark soliton (c), gray-gray soliton (d). Black and red curves show moduli of photonic ($A$) and exitonic ($\psi$) fields. Horizontal axes $\zeta$ corresponds to frames moving with velocity $v_s$. For all shown solutions, velocity corresponds to $v_s=0.25$, and frequencies are $\delta_s=-0.5$ (a), $\delta=1.07$ (b,d), $\delta=1$ (c).
• Figure 3: The increments of transverse instability obtained from the truncated asymptotic expansion (solid lines) and from the numerical solution of the spectral problem (asterisks) for fixed frequency $\delta_s$ and changing velocity $v_s$ (a) and for fixed velocity $v_s$ and changing frequency $\delta_s$ (b). In all cases the transverse perturbation wavenumber is set to $k_x=0.1$.
• Figure 4: Instability increments for bright solitons plotted as functions of the perturbation wave number $k_x$. Dotted lines correspond to the linear dependence predicted by the asymptotic expansions, and red asterisks correspond to the values obtained from the numerical soliton of the eigenvalue problem. Circles corresponds to additional instabilities which emerge with nonzero wavenumbers.
• Figure 5: Decay of a bright-bright soliton with $v=0.25$ and $\delta=-0.5$. Left and right panels show moduli of photonic ($A$) and excitonic ($\psi$) fields. The vertical $\zeta$-axis corresponds to the frame moving in the $z$-direction with velocity $v$. All plots are shown in the windows $(x, \zeta)\in [-63, 63]\times [-5.5,5.5]$.