Active Localization in Planar Tapered Waveguideswith Random Index of Refraction Fluctuations and Saturable Gain Nonlinearity

Abstract

Physical Picture(s)

Axial Propagation Model for a Nonlinear Waveguide

Axial Index, Source,Gain,Absorption & Damping Profiles

Illustrating Random Index Fluctuations: Single Carrier

Illustrating Random Index Fluctuations: Double Carrier

3 Split-Steps SolutionScheme ABCCBA

Split Step (A) Is Standard Fare: Just use FFTs

In Split Step (B), Is a Constant of the Motion

In Split Step (C) treat SaturableGain & Absorption Exactly

Changes in the Saturation LevelRatios Affect Split Step (C)

Changes in the Saturation LevelRatios Affect Split Step (C)

Simulation Results IncludingGain & 20% Index Fluctuations

Simulation Results IncludingGain & 40% Index Fluctuations

Planar Tapered Waveguide Model with Continuous Index Variation

2D Index, Taper and Source Profiles

Summary