Excitation temporal pulse shape and probe beam size effect on pulsed photothermal lens of single particle

Marta Andika; George Chung Kit Chen; Srivathsan Vasudevan

doi:10.1364/JOSAB.27.000796

Journal of the Optical Society of America B
Vol. 27,
Issue 4,
pp. 796-805
(2010)
•https://doi.org/10.1364/JOSAB.27.000796

Excitation temporal pulse shape and probe beam size effect on pulsed photothermal lens of single particle

Marta Andika, George Chung Kit Chen, and Srivathsan Vasudevan

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Marta Andika, George Chung Kit Chen, and Srivathsan Vasudevan, "Excitation temporal pulse shape and probe beam size effect on pulsed photothermal lens of single particle," J. Opt. Soc. Am. B 27, 796-805 (2010)

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Abstract

We developed the theoretical model of the time-resolved thermal lens spectroscopy of a single particle with various pulse shape optical excitations. To account for the pulse shape optical excitation in the model, a heat diffusion equation of two media (the particle and liquid solvent) is solved using the numerical Laplace transform method. The model also incorporates the propagation of a diffracted Gaussian probe beam due to the thermal lens effect. Numerical results are presented to illustrate the effects of the excitation pulse shape and probe beam size on the evolution of the photothermal lens signal. The developed model is utilized for the thermal diffusivity and size extraction of a red polystyrene particle.

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Pulse Shape	$φ (t)$	$\bar{φ} (s)$
Delta	$δ (t)$	1
Rectangular (step function)	$\frac{μ (t) - μ (t - t_{m})}{t_{m}}$	$\frac{1 - exp (- s t_{m})}{s t_{m}}$
Gaussian	$\frac{1}{t_{m} \sqrt{2 π}} exp [- \frac{1}{2} {(\frac{t - t_{p}}{t_{m}})}^{2}]$	$\frac{1}{2} [1 + erf (\frac{1}{\sqrt{2}} (\frac{t_{p}}{t_{m} - t_{m} s}))] exp [- t_{p} s + \frac{t_{m}^{2} s}{2}]$
Exponential	$\frac{t}{t_{m}^{2}} exp (- \frac{t}{t_{m}})$	$\frac{1}{t_{m}^{2} {(s + t_{m}^{- 1})}^{2}}$


Density $(g {cm}^{- 3})$	1.047
Specific heat (J/g K)	1.2
Refractive index	1.59
Absorption coefficient $({cm}^{- 1})$	0.06
Thermal expansion coefficient $(K^{- 1})$	$90 - 150 \times 10^{- 6}$

Pulse Shape	Thermal Diffusivity $({cm}^{2} / s)$	Size $(μ m)$	Discrepancy
Gaussian	$1.23 \times 10^{- 3} \pm 0.125 \times 10^{- 3}$	$2.54 \pm 0.1633$	$3.86 \times 10^{- 2}$
Rectangular	$1.242 \times 10^{- 3} \pm 0.129 \times 10^{- 3}$	$2.55 \pm 0.1582$	$3.88 \times 10^{- 2}$
Dirac delta	$1.264 \times 10^{- 3} \pm 0.134 \times 10^{- 3}$	$2.562 \pm 0.1722$	$3.92 \times 10^{- 2}$

Pulse Shape	$φ (t)$	$\bar{φ} (s)$
Delta	$δ (t)$	1
Rectangular (step function)	$\frac{μ (t) - μ (t - t_{m})}{t_{m}}$	$\frac{1 - exp (- s t_{m})}{s t_{m}}$
Gaussian	$\frac{1}{t_{m} \sqrt{2 π}} exp [- \frac{1}{2} {(\frac{t - t_{p}}{t_{m}})}^{2}]$	$\frac{1}{2} [1 + erf (\frac{1}{\sqrt{2}} (\frac{t_{p}}{t_{m} - t_{m} s}))] exp [- t_{p} s + \frac{t_{m}^{2} s}{2}]$
Exponential	$\frac{t}{t_{m}^{2}} exp (- \frac{t}{t_{m}})$	$\frac{1}{t_{m}^{2} {(s + t_{m}^{- 1})}^{2}}$


Density $(g {cm}^{- 3})$	1.047
Specific heat (J/g K)	1.2
Refractive index	1.59
Absorption coefficient $({cm}^{- 1})$	0.06
Thermal expansion coefficient $(K^{- 1})$	$90 - 150 \times 10^{- 6}$

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Journal of the Optical Society of America B