Novel multioscillator approach to the problem of locking in two-mode ring-laser gyros

Marlan O. Scully; Virgil Sanders; Murray Sargent

doi:10.1364/OL.3.000043

Optics Letters
Vol. 3,
Issue 2,
pp. 43-45
(1978)
•https://doi.org/10.1364/OL.3.000043

Novel multioscillator approach to the problem of locking in two-mode ring-laser gyros

Marlan O. Scully, Virgil Sanders, and Murray Sargent

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Marlan O. Scully, Virgil Sanders, and Murray Sargent, "Novel multioscillator approach to the problem of locking in two-mode ring-laser gyros," Opt. Lett. 3, 43-45 (1978)

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Abstract

We show theoretically that ring-laser locking between counterrunning waves can be avoided by an internally generated dither effect. Specifically, a barely oscillating detuned mode pair dithers the primary mode pair through coupling in the nonlinear medium. Experimental evidence supporting this result is presented.

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	Physical Content

Coefficient
ν_μ	Lasing frequency of the μth mode
Ω_ν	Empty cavity eigenfrequency
ω	Atomic frequency
γ	Polarisation decay rate constant
$σ_{n} = Z_{r} [γ + i (ω - ν_{n})] F_{1} / \sqrt{π}$	Linear mode pulling
$τ_{i j} = F_{1} {[ω - \frac{1}{2} (ν_{i} + ν_{j})] / γ} L [ω - \frac{1}{2} (ν_{i} + ν_{j})] \times exp [- {(ν_{i} - ω)}^{2} / {(K u)}^{2}] γ_{a b} / γ$	Mode pulsing(j on i)
$θ_{n μ ρ σ} = F (ν_{ρ} - ν_{σ}) [N_{2 (ρ -, σ)} / \bar{N}] \times D (ω - \frac{1}{2} ν_{μ} + \frac{1}{2} ν_{ρ} - ν_{σ})$	Complex coupling coefficient (in Doppler limit) for the cases θ₃₄₁₂, θ₂₃₄₁, and θ₃₂₁₄, ≅ 0
Quantities Appearing in Above Coefficients
Z_r	Real part of plasma dispersion function5
$F_{1} = \frac{\sqrt{π}}{2} ν P^{2} \bar{N} {(ℏ K u ∊_{0})}^{- 1} = \frac{ν}{2 Q} N$	First-order factor (the relative excitation N = $\bar{N}$ / ${\bar{N}}_{t}$ )
L(x) = γ²/(γ² + x²)	Dimensionless Lorentzian
$F (ν_{ρ} - ν_{σ}) = i {(\frac{1}{2} P / ℏ)}^{2} [D_{a} (ν_{ρ} - ν_{σ}) + D_{b} (ν_{ρ} - ν_{σ})] F_{1}$	factor appering in θ_nμρσ
D_α(x) = 1/(γ_α + ix)	α = a,b for upper or lower lasing levels
$N_{2 (ρ - σ)} = (1 / L) \int_{0}^{L} d s N (s, t) exp [- 2 (ρ - σ) π s / L]$	Excitation integral
$\bar{N} = (1 / L) \int_{0}^{L} d s N (s, t)$	Excitation density

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Optics Letters