Leaky modes on circular optical waveguides

Rowland Sammut; Allan W. Snyder

doi:10.1364/AO.15.000477

Applied Optics
Vol. 15,
Issue 2,
pp. 477-482
(1976)
•https://doi.org/10.1364/AO.15.000477

Leaky modes on circular optical waveguides

Rowland Sammut and Allan W. Snyder

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Rowland Sammut and Allan W. Snyder, "Leaky modes on circular optical waveguides," Appl. Opt. 15, 477-482 (1976)

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Abstract

A nonabsorbing optical waveguide of circular cross section supports leaky modes in addition to the well-known bound modes. The detailed properties of these leaky modes are determined by solving the eigenvalue equation for the modes of a circular dielectric cylinder below their cutoff frequency. The purpose of this paper is to present such solutions together with the associated characteristic mode parameters. The results are presented in graphical form for low order modes and asymptotically for higher order modes. The effects of material absorption on the attenuation of leaky modes are also discussed.

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	Tunneling modes Q_lm < l − 1	Near critical angle Q_lm ≈ l − 1	Refracting modes Q_lm > l − 1
α_lm	$\frac{2 {U_{l m}}^{2}}{(ρ β_{l m}) V^{2}} {(l^{2} - {Q_{l m}}^{2})}^{1 / 2} exp [- \frac{2 {(l^{2} - {Q_{l m}}^{2})}^{3 / 2}}{3 {Q_{l m}}^{2}}]$	$1.59 \frac{Q_{l m} {U_{l m}}^{2}}{(ρ β_{l m}) V^{7 / 3}}$	$\frac{2 {U_{l m}}^{2}}{(ρ β_{l m}) V^{2}} {({Q_{l m}}^{2} - l^{2})}^{1 / 2}$
η_lm	$1 - \frac{{U_{l m}}^{2}}{V^{2} {(l^{2} - {Q_{l m}}^{2})}^{1 / 2}}$	$1 - \frac{{U^{2}}_{l m}}{V^{2}} (\frac{l^{2}}{{Q_{l m}}^{2}} - 1)$	1

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Applied Optics