非局域非線性光學系統

Nonlocal Nonlinear Optical System

林元堯(Yuan-Yao Lin)

《光學工程》 105期 (2009/04) Pp. 1-6

https://doi.org/10.30011/OE.200904.0001

摘要

本論文主要的目的在探討孤立波在非局域非線性介質中的巨觀特性。這些性質預期可以在非線性光學系統及原子光學系統中發現並扮演重要的角色，改變該系統特性並增加系統的可控制性。非局域非線性反應存在於熱－光學物質、光折變晶體、液晶、電漿以及玻色凝態中，已知具有降低非線性維度，穩定非線性孤立波的作用。本研究在不失一般性並兼具不同系統之獨特性的前提下深入非局域非線性介質孤立波的分又點性質及各項穩定度。在非局域非線性效應下，向量式耦合亮－暗光孤子對中的亮光孤子形成所需要的能量會因非局域強度變大而減少。對於在週期性光晶格下的純量波動，非局域非線性則提供了對能帶的可操控性及波動在晶格中的可移動性。此外非局域非線性對所有對稱破壞不穩定度，包含調製不穩定度、振盪不穩定度、橫向調製不穩定度具有明顯的抑制作用。這樣效應是來自於非局域反應使介質中的折射率對波動強度的穩態反應緩慢，造成系統中的微小擾動不容易成長，尤其對於較高頻的微擾，壓制的程度更甚。因此在這個類似“低通瀘波器”效果的系統中所有的嗓音，微擾在各個方向上（空間及時間上）的成長受到限制，導致等效非線性維度下降，有助於孤立波在介質中的穩定存在。

關鍵字

非局域非線性 ； 非局域孤子 ； 對稱性破壞不穩定 ； 橫向調製不穩定度

並列摘要

The focus of this work is to explore the macroscopic property of solitary waves in nonlocal nonlinear materials which extend to nonlinear optical systems and atomic systems. Nonlocal nonlinearity are known to improve the stability of solitary waves by reducing the nonlinear power. This work reveals insights to bifurcate behavior and instability nature of solitary waves in nonlocal nonlinearity in general aspects as well as in specific details. Nonlocal nonlinear response reduces the formation power a guided bright soliton in a dark-bright vector soliton pair, providing controllability over the band structure of scalar waves and enhance the mobility of wave packets in periodic potential; also the symmetry-breaking instabilities are remarkably suppressed ascribable to the fact that nonlocal response exhibits slow steady-state spatial response to the noise spectrum. Such a ”low pass filter” effect restricts the noise to grow in all the transverse dimensions and results in the reduction of the effective order of nonlinearity in the system.

並列關鍵字

nonlocal nonlinear ； nonlocal soliton ； symmetry-breaking instability ； transverse instability