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

Table of Contents

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

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