Laser-threshold calculations for lasing of acid–base species in proton-transfer media

R. Weigand; J. M. Guerra

doi:10.1364/AO.33.006352

Applied Optics
Vol. 33,
Issue 27,
pp. 6352-6359
(1994)
•https://doi.org/10.1364/AO.33.006352

Laser-threshold calculations for lasing of acid–base species in proton-transfer media

R. Weigand and J. M. Guerra

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R. Weigand and J. M. Guerra, "Laser-threshold calculations for lasing of acid–base species in proton-transfer media," Appl. Opt. 33, 6352-6359 (1994)

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Abstract

An estimate of laser thresholds for both the acid and the base species of dyes undergoing proton-transfer reactions is given. It is seen how the excited-state kinetic constants and proton concentration affect the laser threshold of each species. Calculations of laser threshold for simultaneous lasing of both species are also carried out. The latter is applied to the simultaneous lasing of neutral and acid forms of the 4-Amino-1,7-dimethylpyrido[2,3-c]-1,2,6-thiadiazine 2,2-dioxide in acetonitrile and corroborates the experimental results.

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Parameter	Value
τ _N = τ _B	3 × 10⁻⁹ s
ɛ _pN = ɛ _pB	5 × 10⁴ mol⁻¹ L cm⁻¹
σ _aN = σ _aB	10⁻²² dm²
σ _eN = σ _eB	10⁻¹⁸ dm²
$k_{B N}^{g}$	10¹² s⁻¹
$k_{N B}^{g}$	10¹³ s⁻¹ mol⁻¹ L
[N] _T	5 × 10⁻³ M
S	2 × 10⁻⁴ dm²
Δt _p	5 × 10⁻⁹ s

Parameter	Value
L	0.1 dm
R ₁	0.9
R ₂	0.2
σ _pN	1.2 × 10⁻¹⁹ dm²
σ _pA	0.22 × 10⁻¹⁸ dm²
σ _aN ~ σ _aA °	~ 0
σ _eN	9.6 × 10⁻¹⁹ dm²
σ _eA	8.5 × 10⁻¹⁹ dm²
τ _N	5.2 × 10⁻⁹ s
τ _A	3.5 × 10⁻⁹ s
pK _a	2 (k _NA ^g = 10¹² s⁻¹ and k _AN ^g = 10¹⁴ s⁻¹ mol⁻¹ L)
pK _a ^*	2.3 (k _NA = 10¹² s⁻¹ and k _AN = 10^14.3 s⁻¹ mol⁻¹ L)
[N] _T	1.1 × 10⁻² M

Parameter	Value
τ _N = τ _B	3 × 10⁻⁹ s
ɛ _pN = ɛ _pB	5 × 10⁴ mol⁻¹ L cm⁻¹
σ _aN = σ _aB	10⁻²² dm²
σ _eN = σ _eB	10⁻¹⁸ dm²
$k_{B N}^{g}$	10¹² s⁻¹
$k_{N B}^{g}$	10¹³ s⁻¹ mol⁻¹ L
[N] _T	5 × 10⁻³ M
S	2 × 10⁻⁴ dm²
Δt _p	5 × 10⁻⁹ s

Parameter	Value
L	0.1 dm
R ₁	0.9
R ₂	0.2
σ _pN	1.2 × 10⁻¹⁹ dm²
σ _pA	0.22 × 10⁻¹⁸ dm²
σ _aN ~ σ _aA °	~ 0
σ _eN	9.6 × 10⁻¹⁹ dm²
σ _eA	8.5 × 10⁻¹⁹ dm²
τ _N	5.2 × 10⁻⁹ s
τ _A	3.5 × 10⁻⁹ s
pK _a	2 (k _NA ^g = 10¹² s⁻¹ and k _AN ^g = 10¹⁴ s⁻¹ mol⁻¹ L)
pK _a ^*	2.3 (k _NA = 10¹² s⁻¹ and k _AN = 10^14.3 s⁻¹ mol⁻¹ L)
[N] _T	1.1 × 10⁻² M

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Equations (58)

Applied Optics