Temperature distributions in semi-infinite and finite-thickness media as a result of absorption of laser light

M. K. Loze; C. D. Wright

doi:10.1364/AO.36.000494

Temperature distributions in semi-infinite and finite-thickness media as a result of absorption of laser light

M. K. Loze and C. D. Wright

Applied Optics
Vol. 36,
Issue 2,
pp. 494-507
(1997)
•https://doi.org/10.1364/AO.36.000494

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M. K. Loze and C. D. Wright, "Temperature distributions in semi-infinite and finite-thickness media as a result of absorption of laser light," Appl. Opt. 36, 494-507 (1997)

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History
- Original Manuscript: April 9, 1996
- Revised Manuscript: August 16, 1996
- Published: January 10, 1997

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Abstract

A time-domain method is used to derive simple expressions for temperature distributions within media heated by a moving laser beam with a Gaussian power density profile. Various medium-absorption functions are considered. The solutions are given as single integrals with respect to time of simple functions. The expressions can be applied to multilayer media consisting of layers with different optical (light-absorbing) properties, provided that the layers have similar thermal properties. A number of optical recording examples have been examined in detail, and the results compared with those obtained by use of a more general (fast-Fourier-transform-based) approach.

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Corrections

M. K. Loze and C. D. Wright, "Temperature distributions in semi-infinite and finite-thickness media as a result of absorption of laser light: erratum," Appl. Opt. 36, 4890-4890 (1997)
https://www.osapublishing.org/ao/abstract.cfm?uri=ao-36-20-4890

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Laser Parameter	Value
Wavelength λ	780 nm
Beam 1/e radius r	1 µm
Scanning speed v
Static	0 m/s
Moving	0.5 m/s
Pulse length T _p	5 µs
Incident power P ₀	1 mW
Objective-lens numerical aperture NA	0.4
Medium thickness d
Semi-infinite	Semi-infinite
Finite	2 µm
Medium absorption coefficient γ	1 µm^-1
Medium thermal conductivity K	0.3 J m^-1 s^-1
	°C^-1
Medium specific heat ρ C	3 MJ m^-3 °C^-1

Laser Parameter	Value
Wavelength λ	450 nm
Beam 1/e radius r	0.5 µm
Scanning speed v	20 m/s
Pulse length T _p	0.1 µsa
Power absorbed by the Te layer	1 mW
Medium Layers
Material
Top layer	Tellurium
Bottom layer 1	PMMA
Bottom layer 2	2P glass
Thickness d
Top layer	0.015 µm
Bottom layer 1	Semi-infinite
Bottom layer 2	Semi-infinite
Refractive index n
Top layer	3.3– j 3.9
Bottom layer 1	1.5
Bottom layer 2	1.5
Thermal conductivity K
Top layer	1.5 J m^-1 s^-1 °C^-1
Bottom layer 1	0.2 J m^-1 s^-1 °C^-1
Bottom layer 2	1.5 J m^-1 s^-1 °C^-1
Specific heat ρ C
Top layer	1.5 MJ m^-3 °C^-1
Bottom layer 1	1.5 MJ m^-3 °C^-1
Bottom layer 2	2 MJ m^-3 °C^-1

Medium	Peak Temparature (°C/mW)	Method Used for Solution
Te: isolated layer, no substrate	1915	TDM, Eq. (34)
Te: thick substrate	135	TDM, Eq. (29)
Te: isolated layer, no substance	1915	FFT
Te: PMMA substrate	360	FFT
Te: PMMA substrate with Al layer	315	FFT
Te: 2P glass substrate	130	FFT
Te: 2P glass substrate with Al layer	75	FFT

Laser Parameter	Value
Wavelength λ	830 nm
Beam 1/e radius r	0.6 µm
Scanning Speed v
Static	0 m/s
Moving	20 m/s
Pulse length T _p	0.1 µs
Power absorbed by the dye layer	1 mW
Medium layers
Material
Top layer	Glass
Middle layer	Dye
Bottom layer	Glass
Thickness d
Top layer	0.05 µm
Middle layer	0.1 µm
Bottom layer	0.25 µm
Refractive index n
Top layer	1.5
Middle layer	2- j 0.7
Bottom layer	1.5
Thermal conductivity K
Top layer	0.19 J m^-1 s^-1 °C^-1
Middle layer	0.2 J m^-1 s^-1 °C^-1
Bottom layer	0.19 J m^-1 s^-1 °C^-1
Specific heat ρ C
Top layer	1.51 MJ m^-3 °C^-1
Middle layer	2.25 MJ m^-3 °C^-1
Bottom layer	1.51 MJ m^-3 °C^-1

Heat Generation Model	Peak Temparature (°C/mW)	Method Used for Solution
δ function	275	TDM, Eq. (21)
Constant	200	TDM, Eq. (32)
Linear	220	TDM, Eq. (34)
Exponential (Lambert-Beer)	210	TDM, Eq. (34)
Poynting vector (Ref. 11)	215	FFT
Poynting vector (Ref. 11) for an Al layer under the trilayer	260	FFT

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