Transverse instability in a diffraction-management structure consisting of negative-index and positive-index materials

Jinggui Zhang

doi:10.1364/JOSAB.33.001702

Journal of the Optical Society of America B
Vol. 33,
Issue 8,
pp. 1702-1708
(2016)
•https://doi.org/10.1364/JOSAB.33.001702

Transverse instability in a diffraction-management structure consisting of negative-index and positive-index materials

Jinggui Zhang

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Jinggui Zhang, "Transverse instability in a diffraction-management structure consisting of negative-index and positive-index materials," J. Opt. Soc. Am. B 33, 1702-1708 (2016)

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Abstract

In this paper, we propose a scheme consisting of alternating layers of a slab of a negative-index material and a slab of positive-index material. By employing the mean-field theory, we show that the sign of standard diffraction can be made either positive or negative, or even zero, in this layered structure. Subsequently, we demonstrate that close to the zero-diffraction regime, the high-order diffraction (HOD) strongly affects the dynamical behavior of the transverse instability, just like the corresponding high-order dispersion in optical fibers. Specifically speaking, HOD not only deforms the original instability regions in the positive-diffraction regime with focusing nonlinearity, but also may lead to the appearance of new instability regions even in the negative-diffraction regime with focusing nonlinearity or in the zero-diffraction regime. Meanwhile, we also disclose some novel features of the transverse instability for defocusing Kerr nonlinearity as well as non-Kerr nonlinearity. Our findings denote that the temporal modulation instability induced by high-order dispersion in optical fibers can find its transverse instability counterpart resulting from HOD in such a diffraction-management structure.

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Equations (7)

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$δ$	$σ$	Condition
$δ > 0$	$σ > 0$	$k_{P} / \| k_{N} \| < l_{P} / l_{N} < k_{P}^{3} / \| k_{N}^{3} \|$
$δ > 0$	$σ < 0$	$l_{P} / l_{N} > \max (k_{P} / \| k_{N} \|, k_{P}^{3} / \| k_{N}^{3} \|)$
$δ < 0$	$σ > 0$	$l_{P} / l_{N} < \min (k_{P} / \| k_{N} \|, k_{P}^{3} / \| k_{N}^{3} \|)$
$δ < 0$	$σ < 0$	$k_{P} / \| k_{N} \| > l_{P} / l_{N} > k_{P}^{3} / \| k_{N}^{3} \|$
$δ = 0$	$σ > 0$	$k_{P} / \| k_{N} \| = l_{P} / l_{N} < k_{P}^{3} / \| k_{N}^{3} \|$
$δ = 0$	$σ < 0$	$k_{P} / \| k_{N} \| = l_{P} / l_{N} > k_{P}^{3} / \| k_{N}^{3} \|$

$δ$	$Ω$	$q$
$δ > 0$	$Ω^{2} < (1 - \sqrt{1 - 8 p q I_{0}}) / 2 q$	$q < 0$
	$(1 + \sqrt{1 - 8 p q I_{0}}) / 2 q < Ω^{2} < 1 / q$	$0 < q < 1 / 8 p I_{0}$
	$Ω^{2} < (1 - \sqrt{1 - 8 p q I_{0}}) / 2 q$	$0 < q < 1 / 8 p I_{0}$
	$Ω^{2} < 1 / q$	$q > 1 / 8 p I_{0}$
$δ < 0$	$- 1 / q < Ω^{2} < (- 1 - \sqrt{1 - 8 p q I_{0}}) / 2 q$	$q < 0$
$δ = 0$	$Ω^{2} < \sqrt{- 2 p I_{0} / q}$	$q < 0$

$δ$	$Ω$	$q$
$δ < 0$	$Ω^{2} < (- 1 + \sqrt{1 - 8 p q I_{0}}) / 2 q$	$q > 0$
	$- (1 + \sqrt{1 - 8 p q I_{0}}) / 2 q < Ω^{2} < - 1 / q$	$0 > q > 1 / 8 p I_{0}$
	$Ω^{2} < (- 1 + \sqrt{1 - 8 p q I_{0}}) / 2 q$	$0 > q > 1 / 8 p I_{0}$
	$Ω^{2} < - 1 / q$	$q < 1 / 8 p I_{0}$
$δ > 0$	$1 / q < Ω^{2} < (1 + \sqrt{1 - 8 p q I_{0}}) / 2 q$	$q > 0$
$δ = 0$	$Ω^{2} < \sqrt{- 2 p I_{0} / q}$	$q > 0$

$δ$	$σ$	Condition
$δ > 0$	$σ > 0$	$k_{P} / \| k_{N} \| < l_{P} / l_{N} < k_{P}^{3} / \| k_{N}^{3} \|$
$δ > 0$	$σ < 0$	$l_{P} / l_{N} > \max (k_{P} / \| k_{N} \|, k_{P}^{3} / \| k_{N}^{3} \|)$
$δ < 0$	$σ > 0$	$l_{P} / l_{N} < \min (k_{P} / \| k_{N} \|, k_{P}^{3} / \| k_{N}^{3} \|)$
$δ < 0$	$σ < 0$	$k_{P} / \| k_{N} \| > l_{P} / l_{N} > k_{P}^{3} / \| k_{N}^{3} \|$
$δ = 0$	$σ > 0$	$k_{P} / \| k_{N} \| = l_{P} / l_{N} < k_{P}^{3} / \| k_{N}^{3} \|$
$δ = 0$	$σ < 0$	$k_{P} / \| k_{N} \| = l_{P} / l_{N} > k_{P}^{3} / \| k_{N}^{3} \|$

$δ$	$Ω$	$q$
$δ > 0$	$Ω^{2} < (1 - \sqrt{1 - 8 p q I_{0}}) / 2 q$	$q < 0$
	$(1 + \sqrt{1 - 8 p q I_{0}}) / 2 q < Ω^{2} < 1 / q$	$0 < q < 1 / 8 p I_{0}$
	$Ω^{2} < (1 - \sqrt{1 - 8 p q I_{0}}) / 2 q$	$0 < q < 1 / 8 p I_{0}$
	$Ω^{2} < 1 / q$	$q > 1 / 8 p I_{0}$
$δ < 0$	$- 1 / q < Ω^{2} < (- 1 - \sqrt{1 - 8 p q I_{0}}) / 2 q$	$q < 0$
$δ = 0$	$Ω^{2} < \sqrt{- 2 p I_{0} / q}$	$q < 0$

Abstract

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Equations (7)

Journal of the Optical Society of America B