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Dispersion tailoring and compensation by modal interactions in OmniGuide fibers

Torkel D. Engeness, Mihai Ibanescu, Steven G. Johnson, Ori Weisberg, Maksim Skorobogatiy, Steven Jacobs, and Yoel Fink

Open Access Open Access

Abstract

We present a method for dispersion-tailoring of OmniGuide and other photonic band-gap guided fibers based on weak interactions (“anticrossings”) between the core-guided mode and a mode localized in an intentionally introduced defect of the crystal. Because the core mode can be guided in air and the defect mode in a much higher-index material, we are able to obtain dispersion parameters in excess of 500,000 ps/nm-km. Furthermore, because the dispersion is controlled entirely by geometric parameters and not by material dispersion, it is easily tunable by structural choices and fiber-drawing speed. So, for example, we demonstrate how the large dispersion can be made to coincide with a dispersion slope that matches commercial silica fibers to better than 1%, promising efficient compensation. Other parameters are shown to yield dispersion-free transmission in a hollow OmniGuide fiber that also maintains low losses and negligible nonlinearities, with a nondegenerate TE01 mode immune to polarization-mode dispersion (PMD). We present theoretical calculations for a chalcogenide-based material system that has recently been experimentally drawn.

©2003 Optical Society of America

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Figures (15)
Fig. 1.
Fig. 1. (a) Defect-free OmniGuide fiber and (b) OmniGuide dispersion-compensating fiber. (Not to scale.) The defect-free (“long-haul”) fiber consists of an air core (R=15.35 µm) surrounded by consecutive layers of refractive index=1.5 (blue) and refractive index=2.8 (red) materials. In this fiber, all the high-index layers have the same thickness (0.153 µm) and all the low-index layers have the same thickness (0.358 µm). The outermost region is a thick layer that provides structural stability. The actual number of layers used is larger than in this figure; in order to minimize radiation losses one would use 20 layers or more. The OmniGuide dispersion-compensating fiber is a modified structure that includes a defect, i.e. the thickness of one of the dielectric layers has been altered.

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Fig. 2.
Fig. 2. Nomenclature: “Layer 1” denotes the material layer closest to the air core, the next-closest material layer is “layer 2,” etc. “Core” means the air core inside the dielectric mirror and “cladding” means all layers outside the core. This figure is not drawn to scale and includes a reduced number of layers.

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Fig. 3.
Fig. 3. (a) Band gaps and light line for OmniGuide long-haul fiber and (b) dispersion relations for the lowest-order modes.

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Fig. 4.
Fig. 4. Fraction of energy in the TE01 mode that is not confined in the core. The entire line shows the degree of confinement across the TE band gap, while the solid part of the curve indicate the part that is within the TM band gap (1430–1830nm) as well as the TE gap.

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Fig. 5.
Fig. 5. Dispersion parameter for the TE01 mode in the OmniGuide long-haul fiber, where the solid part of the curve indicates the range that is within the TM band gap. Within the TM band gap the dispersion parameter D ranges from 7.5 to 11.4 ps/nm-km.

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Fig. 6.
Fig. 6. Schematic representation of the effect of interaction between defect and core modes. Panel (a) shows the dispersion relations for the two modes without interaction and panel (b) shows how modal interaction changes the dispersion relations.

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Fig. 7.
Fig. 7. Schematic representation of the effect of varying strengths of modal interaction. The modal interaction is weaker in panel (a) than in panel (b), resulting in a sharper “kink” in (a) and therefore a larger value of the dispersion parameter over a more narrow wavelength range.

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Fig. 8.
Fig. 8. Schematic representation of the interaction between a defect mode and multiple core modes. Panel (a) shows the defect mode (blue) and the core modes (red) separately, while panel (b) shows the resulting modal structure when the modes interact.

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Fig. 9.
Fig. 9. Dispersion relation (a) and dispersion curve (b) for four different locations of the defect. Both curves show that the transition from core-confined mode to the defect mode takes place more rapidly when the defect is located far from the core which results in a large negative dispersion parameter over a narrower band. The point ofminimumdispersion parameter is indicated with a dot on the dispersion relations.

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Fig. 10.
Fig. 10. Dispersion curve for two slightly different sizes of the defect. The defect for the red curve is 1.5% larger than the defect for the blue curve.

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Fig. 11.
Fig. 11. Dispersion curve for two different core sizes, the large core (red) having a core radius of 14.8 µm and the small core (blue) having a radius of 2.98 µm.

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Fig. 12.
Fig. 12. Panel (a) shows the energy density of the operating mode as a function of distance from core center at two different wavelengths. The solid (blue) line represents the energy distribution at 1.55 µm, which is in the center of the operating band and the dotted (red) line represents a wavelength on the other side of the anticrossing. The vertical black line represents the core radius. Panel (b) shows the dispersion curve with dots signaling the two wavelengths for which the energy distributions can be found in panel 9a).

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Fig. 13.
Fig. 13. Dispersion curves for OmniGuide zero dispersion fiber. Panel (a) shows the dispersion of the zero dispersion fiber together with the OmniGuide long haul fiber over a broad wavelength range. Panel (b) zooms in on the dispersion properties for the zero dispersion fiber over a 20 nm band.

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Fig. 14.
Fig. 14. Schematic representation of the interaction between multiple defect modes and multiple core-confined modes.Panel (a) shows three defect modes (blue) and the coreconfined modes (red) separately, while panel (b) shows the resulting modal structure when the modes interact.

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Fig. 15.
Fig. 15. Dispersion curve for the OmniGuide multiple zero dispersion fiber.

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Tables (1)

Tables Icon

Table 1. The dispersion increase at an anticrossing is roughly proportional to the amplitude of the exponential field tails as a function of defect location, causing the product of the two to be roughly constant (with some oscillation).

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Equations (11)

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D = − 2 π c λ 2 · d 2 β d ω 2 ,
L d · D d + L t · D t = 0
L d · δ D d δ λ + L t · δ D t δ λ = 0
R = 1 D · δ D δ λ
F → ( r ) e i ( β z − ω t + m ϕ ) ,
H z = AJ + BY
E z = CJ + DY
d hi d lo = n lo 2 − 1 n hi 2 − 1
A = ∫ 1 2 Dd λ = ∫ 1 2 ∂ ∂ λ ( 1 ν g ) d λ = Δ ( 1 ν g ) = 1 ν g , 1 − 1 ν g , 2
Δ ω ~ ℜ 〈 ψ 1 ∣ H ̂ ∣ ψ 2 〉
B 2 · D · L < 2 · 10 5
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