Perturbed Gaussian modes of an unbalanced antiresonant-ring laser cavity*

Shinan-Chur Sheng; A. E. Siegman

doi:10.1364/JOSA.66.001032

Journal of the Optical Society of America
Vol. 66,
Issue 10,
pp. 1032-1036
(1976)
•https://doi.org/10.1364/JOSA.66.001032

Perturbed Gaussian modes of an unbalanced antiresonant-ring laser cavity

Shinan-Chur Sheng and A. E. Siegman

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Shinan-Chur Sheng and A. E. Siegman, "Perturbed Gaussian modes of an unbalanced antiresonant-ring laser cavity*," J. Opt. Soc. Am. 66, 1032-1036 (1976)

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Abstract

We present an analysis of the perturbed Gaussian transverse modes of an antiresonant-ring laser cavity useful for cavity dumping, mode locking, and other applications. A plane-wave analysis of the antiresonant ring with a 50-50 beam splitter indicates that the coupling out the output port of the ring should be identically zero. A perturbed Gaussian mode analysis of a stable antiresonant-ring cavity shows, however, that if the ring is not optically symmetric (in the sense that the paraxial ray matrix is not symmetric in the two directions around the ring) then the modes of the cavity consist of a perturbed mixture of stable Gaussian modes, with a significant interference output or leakage from the output port of the ring. The existence of this leakage output has also been confirmed experimentally and by numerical Fox and Li calculation of the lowest mode of the unbalanced ring. This represents an unusual situation in which there is transverse mode discrimination without there being any diffractive output coupling.

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	${\tilde{Δ}}^{2}$ ≡ Δ²/sinϕ
$γ_{0}^{'} = {\tilde{A}}^{- 1 / 2}$	$\begin{array}{l} ∊_{0}^{'} = ∊_{0} - j [{\frac{1}{8}}^{1 / 2} {\tilde{A}}^{- 3 / 2} / (γ_{0} - γ_{2})] {\tilde{Δ}}^{2} ∊_{2} \\ + [{\frac{3}{8}}^{1 / 2} {\tilde{A}}^{- 5 / 2} / (γ_{0} - γ_{4})] (Δ^{2} - 1 / 4 {\tilde{Δ}}^{4}) ∊_{4} + \dots \end{array}$
$γ_{1}^{'} = {\tilde{A}}^{- 3 / 2}$	$\begin{array}{l} ∊_{1}^{'} = ∊_{1} - j [{\frac{3}{8}}^{1 / 2} {\tilde{A}}^{- 5 / 2} / (γ_{1} - γ_{3})] {\tilde{Δ}}^{2} ∊_{3} \\ + [{\frac{15}{8}}^{1 / 2} {\tilde{A}}^{- 7 / 2} / (γ_{1} - γ_{5})] (Δ^{2} - 1 / 4 {\tilde{Δ}}^{4}) ∊_{5} + \dots \end{array}$
$γ_{2}^{'} = 2^{- 1} (3 - ∣ \tilde{A} ∣^{2}) {\tilde{A}}^{- 5 / 2}$	$\begin{array}{l} ∊_{2}^{'} = ∊_{2} + j [{\frac{1}{8}}^{1 / 2} {\tilde{A}}^{- 3 / 2} / (γ_{0} - γ_{2})] {\tilde{Δ}}^{2} ∊_{0} \\ - j [{\frac{3}{64}}^{1 / 2} (5 - ∣ \tilde{A} ∣^{2}) {\tilde{A}}^{- 7 / 2} / (γ_{2} - γ_{4})] {\tilde{Δ}}^{2} ∊_{4} \\ + [{\frac{45}{8}}^{1 / 2} {\tilde{A}}^{- 9 / 2} / (γ_{2} - γ_{6})] (Δ^{2} - 1 / 4 {\tilde{Δ}}^{4}) ∊_{6} + \dots \end{array}$
$γ_{3}^{'} = 2^{- 1} (5 - 3 ∣ \tilde{A} ∣^{2}) {\tilde{A}}^{- 7 / 2}$	$\begin{array}{l} ∊_{3}^{'} = ∊_{3} + j [{\frac{3}{8}}^{1 / 2} {\tilde{A}}^{- 5 / 2} / (γ_{1} - γ_{3})] {\tilde{Δ}}^{2} ∊_{1} \\ - j [{\frac{5}{64}}^{1 / 2} (7 - 3 ∣ \tilde{A} ∣^{2}) {\tilde{A}}^{- 9 / 2} / (γ_{3} - γ_{5})] {\tilde{Δ}}^{2} ∊_{5} \\ + [{\frac{105}{8}}^{1 / 2} {\tilde{A}}^{- 11 / 2} / (γ_{3} - γ_{7})] (Δ^{2} - 1 / 4 {\tilde{Δ}}^{4}) ∊_{7} + \dots \end{array}$

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Journal of the Optical Society of America