A model for the thermal lens which approximates the refractive shape as a parabola is compared with a model which accounts for the aberrant nature of the lens; both models are tested against experimental results. The comparison suggests how the inaccuracies of the parabolic lens model may be corrected while retaining its mathematical simplicity and better predictive power for stronger thermal lenses.

Fabio Luiz Sant’Anna Cuppo, Antônio Martins Figueiredo Neto, Sergio Leonardo Gómez, and Peter Palffy-Muhoray J. Opt. Soc. Am. B 19(6) 1342-1348 (2002)

References

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P = 220 mW, T = 22°C for first and third entries; P = 225 mW, T = 21.8°C for second entry. A = A_{Co(II)} + A_{H2O}; A_{H2O} = 1.56 × 10^{−4}.18
Values for parameters are measured independently or calculated from the definition. λ = 514.5 nm; see Table V for physical constants of water used in the calculations.

Uncertainties are ±ts//√n, where t is for 95% confidence and n − 1 degrees of freedom, and s is the sample standard deviation of the replicates.21 ω = 1.42 (±0.03) × 10^{−2} cm. See Table V for physical constants.
pH = 2 by addition of H_{2}SO_{4}.

Table IV

From Time-Resolved Thermal Lens Measurements on Aqueous Solutions

First entry is acidified water (pH = 2), remaining entries are COSO_{4} solutions in acidified water.
Uncertainty is ±ts/√n, where t is for 95% confidence and n − 1 degrees of freedom, and s is the sample standard deviation of the replicates.
λ = 514.5 nm; see Table V for physical constants of water used in calculation. P = 220 ± 4 mW; T = 22.4°C.
Ref. 18.

Table V

Physical Constants of Selected Solvents for Prediction of Thermal Lens Parameters

This work using modified parabolic lens model. T = 21.7 − 23.5°C, underlined values of (−dn/dT), k used to find A from measured θ.
For water, (−dn/dT) = 26.2 × 10^{−5} ·{1 − exp[−(T − 2.0°C)/48.5°C]} (±0.5%), Ref. 22 for λ = 632.8 nm, and (−dn/dT)_{514.5 nm} = 1.013 (−dn/dT)_{632.8 nm}. The latter relationship derived from tabulated values of n(λ,T),23 and volume expansion coefficient24 using the Lorentz formula [Eq. (6) of Ref. 22].
Correction to 23°C would decrease (−dn/dT) by ~1%; correction to 514.5 nm would increase (−dn/dT) by 1–2%. Accuracy of the information did not warrant an attempt to correct the values given in the references.
At 632.8 nm.

Tables (5)

Table I

Formulas for the Parabolic and Aberrant Thermal Lens Model a

P = 220 mW, T = 22°C for first and third entries; P = 225 mW, T = 21.8°C for second entry. A = A_{Co(II)} + A_{H2O}; A_{H2O} = 1.56 × 10^{−4}.18
Values for parameters are measured independently or calculated from the definition. λ = 514.5 nm; see Table V for physical constants of water used in the calculations.

Uncertainties are ±ts//√n, where t is for 95% confidence and n − 1 degrees of freedom, and s is the sample standard deviation of the replicates.21 ω = 1.42 (±0.03) × 10^{−2} cm. See Table V for physical constants.
pH = 2 by addition of H_{2}SO_{4}.

Table IV

From Time-Resolved Thermal Lens Measurements on Aqueous Solutions

First entry is acidified water (pH = 2), remaining entries are COSO_{4} solutions in acidified water.
Uncertainty is ±ts/√n, where t is for 95% confidence and n − 1 degrees of freedom, and s is the sample standard deviation of the replicates.
λ = 514.5 nm; see Table V for physical constants of water used in calculation. P = 220 ± 4 mW; T = 22.4°C.
Ref. 18.

Table V

Physical Constants of Selected Solvents for Prediction of Thermal Lens Parameters

This work using modified parabolic lens model. T = 21.7 − 23.5°C, underlined values of (−dn/dT), k used to find A from measured θ.
For water, (−dn/dT) = 26.2 × 10^{−5} ·{1 − exp[−(T − 2.0°C)/48.5°C]} (±0.5%), Ref. 22 for λ = 632.8 nm, and (−dn/dT)_{514.5 nm} = 1.013 (−dn/dT)_{632.8 nm}. The latter relationship derived from tabulated values of n(λ,T),23 and volume expansion coefficient24 using the Lorentz formula [Eq. (6) of Ref. 22].
Correction to 23°C would decrease (−dn/dT) by ~1%; correction to 514.5 nm would increase (−dn/dT) by 1–2%. Accuracy of the information did not warrant an attempt to correct the values given in the references.
At 632.8 nm.