Self-Induced Diffusion in Disordered Nonlinear Photonic Media

Yonatan Sharabi, Hanan Herzig Sheinfux, Yoav Sagi, Gadi Eisenstein, and Mordechai Segev

Phys. Rev. Lett. 121, 233901 – Published 7 December 2018

Abstract

We find that waves propagating in a 1D medium that is homogeneous in its linear properties but spatially disordered in its nonlinear coefficients undergo diffusive transport, instead of being Anderson localized as always occurs for linear disordered media. Specifically, electromagnetic waves in a multilayer structure with random nonlinear coefficients exhibit diffusion with features fundamentally different from the traditional diffusion in linear noninteracting systems. This unique transport, which stems from the nonlinear interaction between the waves and the disordered medium, displays anomalous statistical behavior where the fields in multiple different realizations converge to the same intensity value as they penetrate deeper into the medium.

Received 24 May 2018

DOI:https://doi.org/10.1103/PhysRevLett.121.233901

Physics Subject Headings (PhySH)

Classical optics Nonlinear optics

Random & disordered media

Kerr effect

Atomic, Molecular & Optical

Authors & Affiliations

Yonatan Sharabi¹, Hanan Herzig Sheinfux¹, Yoav Sagi¹, Gadi Eisenstein², and Mordechai Segev¹

¹Solid State Institute, Technion—Israel Institute of Technology, Haifa 32000, Israel and Department of Physics, Technion-Israel Institute of Technology, Haifa 32000, Israel
²Department of Electric Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel

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Issue

Vol. 121, Iss. 23 — 7 December 2018

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Images

Figure 1
(a) The 1D dielectric multilayer system and the electric field therein. The nonlinear $n_{2}$ coefficient of each layer (black) varies randomly, inducing a random change in the refractive index proportional to the local intensity. This nonlinear disorder induces decay in the field amplitude (red). (b) 3D illustration of the system with the light (red) incident at an angle slightly below the critical angle for total internal reflection.
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Figure 2
Propagation of waves in multilayer structures with disorder in their nonlinear properties results in evolution strikingly different than in linear disordered systems. This figure shows the evolution of waves in (a) linear and (b) nonlinear disordered systems, for waves entering from the left. Red and blue lines: light intensity as a function of propagation distance $z$ for two specific realizations of disorder. Black line: ensemble-averaged intensity. Yellow line: power-law fit to the ensemble-average results. The decay of the ensemble-averaged intensity in the linear system (a) is exponential, conforming to Anderson localization, whereas the decay in the nonlinear system (b) is of a power law. The nonlinear system is also different than linear diffusive systems [purple dashed line in (b)].
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Figure 3
(a),(b) Histogram of $\log_{10} (Transmission)$ , for an ensemble of linear and nonlinear (respectively) disordered multilayer structures of different lengths $L$ . For both the linear and the NL cases, the histograms are Gaussian, and their centers shift to lower values as the structure becomes longer. However, in the linear case the distribution becomes wider as $L$ increases (a), whereas in the NL case it becomes narrower (b). (c),(d) Variance of $\log_{10} (Transmission)$ (red) and intensity (blue) as a function of $L$ , for linear (c) and nonlinear (d) disorder. For linear disorder the variance increases linearly, whereas for NL disorder the variance first jumps from 0 to 0.08 very close to the entrance face, but then starts to decrease, reaching zero asymptotically. Consequently, the intensities of the optical field in all realizations of NL disorder coalesce to a single value asymptotically.
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Figure 4
(a) Decay length as a function of wavelength (for layer width of 250 nm) found from simulations (red points) showing best fit to a power-law dependence (blue), $L (λ) \approx A λ^{1.2}$ , near the critical angle. (b) Decay length as a function of initial light intensity. As the initial light intensity increases, the magnitude of disorder increases as well, and the scattering process becomes more prominent.
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