Mode-coupling analysis of bending losses in IR metallic waveguides

Michel E. Marhic

doi:10.1364/AO.20.003436

Applied Optics
Vol. 20,
Issue 19,
pp. 3436-3441
(1981)
•https://doi.org/10.1364/AO.20.003436

Mode-coupling analysis of bending losses in IR metallic waveguides

Michel E. Marhic

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Michel E. Marhic, "Mode-coupling analysis of bending losses in IR metallic waveguides," Appl. Opt. 20, 3436-3441 (1981)

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Abstract

The bending losses of infrared metallic waveguides are studied by a mode-coupling analysis. Previous results obtained for slab waveguides are confirmed. The high losses observed in practice with circular guides are explained by the near degeneracy between the TE₀₁ and TM₁₁ modes. The method is also used to study losses due to nonsteady-state propagation, such as caused by input mismatch or varying bend radii. Circular metallic waveguides with a thin dielectric lining on the inside could perform better than unlined guides, from the points of view of uniform bending losses and single-mode propagation under arbitrary bends.

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Mode	r_pq or $r_{p q}^{'}$	α (m⁻¹)	β − β₀ (m⁻¹)	$Δ α = α - α_{01}^{TE}$	$Δ β = β - β_{01}^{TE}$	C″	R_c (m)
TE₀₁	3.832	9.69 × 10⁻³	−198	—	—	—	—
TM₁₁	3.832	14.5	−198	14.5	0	0.185	73
TE₁₁	1.841	6.07	−45.7	6.07	152	0.186	4.05
TE₁₂	5.331	0.55	−383	0.54	−184	0.311	1.88

Mode	$\frac{δ α}{β_{0}}$	$\frac{δ β}{β_{0}}$
TM_pq	$\frac{∊^{″}}{{(∊^{'})}^{2}} ζ$	$\frac{∊^{'} - 1}{∊^{'}} ζ$
TE_pq	$\frac{p^{2}}{{(r_{p q}^{'})}^{2} - p^{2}} \frac{∊^{″}}{{(∊^{'})}^{2}} ζ$	$\frac{p^{2}}{{(r_{p q}^{'})}^{2} - p^{2}} \frac{∊^{'} - 1}{∊^{'}} ζ$
p ≠ 0
TE_oq	$\frac{{(r_{o q}^{'})}^{2}}{3} ∊^{″} ζ^{3}$	$\frac{{(r_{o q}^{'})}^{2}}{3} (∊^{'} - 1) ζ^{3}$

Mode	β′ − β₀ (m⁻¹)	$Δ β^{'} = β^{'} - {(β^{'})}_{01}^{TE}$	Rc (m)
TE₀₁	−198	—	—
TM₁₁	−31	167	3.24
TE₁₁	24.2	222	2.94
TE₁₂	−377	−179	1.93

Mode	r_pq or $r_{p q}^{'}$	α (m⁻¹)	β − β₀ (m⁻¹)	$Δ α = α - α_{01}^{TE}$	$Δ β = β - β_{01}^{TE}$	C″	R_c (m)
TE₀₁	3.832	9.69 × 10⁻³	−198	—	—	—	—
TM₁₁	3.832	14.5	−198	14.5	0	0.185	73
TE₁₁	1.841	6.07	−45.7	6.07	152	0.186	4.05
TE₁₂	5.331	0.55	−383	0.54	−184	0.311	1.88

Mode	$\frac{δ α}{β_{0}}$	$\frac{δ β}{β_{0}}$
TM_pq	$\frac{∊^{″}}{{(∊^{'})}^{2}} ζ$	$\frac{∊^{'} - 1}{∊^{'}} ζ$
TE_pq	$\frac{p^{2}}{{(r_{p q}^{'})}^{2} - p^{2}} \frac{∊^{″}}{{(∊^{'})}^{2}} ζ$	$\frac{p^{2}}{{(r_{p q}^{'})}^{2} - p^{2}} \frac{∊^{'} - 1}{∊^{'}} ζ$
p ≠ 0
TE_oq	$\frac{{(r_{o q}^{'})}^{2}}{3} ∊^{″} ζ^{3}$	$\frac{{(r_{o q}^{'})}^{2}}{3} (∊^{'} - 1) ζ^{3}$

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Equations (46)

Applied Optics