Figure 4a. Isometric view of spatial profile of laser pulse at output of LP-140 pulse laser amplifier.

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Figure 4b. Slice of data from above view. Solid line is actual data, the dotted line is a fitted Gaussian curve showing good argument.

1 mm

Figure 5a. One type of damage seen. Damage site is small compared to laser beam diameter and penetrates little or none into substrate.

Figure 5b. Substrate damage. Occurs on output surface of sample and extends into substrate. Note nearly same size as laser beam diameter.

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Figure 6. Occurrence of photomultiplier signal (top row) versus time corresponding to laser pulse shape in time; (a) corresponds to coating damage, (b) corresponds to substrate damage.

Figure 7. Laser induced damage thresholds of CdTe samples versus laser pulse width

Figure 8. Plot showing temperature use of sample relative to single shot heating versus number of laser pulses for different pulse repetition frequencies.

Figure 9. LIPT of AR-coated CdTe versus number of laser pulses, theoretical curves show four different PRF's starting at a mean LIDT of 37J/cm2. The different symbols denote different beam sizes and PRF's. All work was done at 1Hz except those noted at 5Hz.

Manuscript Received

1-12-89

Microcomputer Finite Difference Modeling of Laser Heating and Melting*

J. O. Porteus

Physics Division, Research Department

Naval Weapons Center, China Lake, CA 93555-6001

An existing method of microcomputer finite difference modeling has been
adapted to laser-heating and melt-threshold computations. Versatility compared
to exact-solution methods permits various applications of moderate complexity
with arbitrary pulse waveform and an optional axisymmetric or one-
dimensional spatial profile. Thermal diffusion is modeled in two dimensions
based on optical and thermal transport properties that can vary with
temperature, time, and space. Simplicity and freedom from mainframe
requirements make the method accessible, flexible,
method accessible, flexible, and easily learned.
Examples presented here were performed on XT- and AT-type PC-compatible
computers equipped with floating-point math coprocessor running Turbo Pascal
4.0. Comparisons are given with previously reported surface melt thresholds of
diamond-turned Cu and Au measured and calculated by earlier methods. Other
examples are pulsed-laser bulk heating of semiconductors, including a GaAs
coating on a quartz substrate and a comparison of flashlamp heating of laser
glass in rod and slab configurations.

Key words: diffusion; GaAs; heating; laser damage; melting; metal mirror;
thermal model.

1. Introduction

Calculation of temperatures produced by laser heating of optical materials is a common requirement in damage testing and other areas of laser technology. Simple analytic thermal models such as those provided in Carslaw and Jaeger [1] are capable of representing only the most elementary experimental situations. On the other hand, more powerful numerical models such as SINDA [2] are often too formidable for the casual user, or may not be readily available. This paper presents examples of a very capable microcomputer finite-difference modeling (MFDM) method [3] that offers a compromise between these two extremes. The new method is applied to melt thresholds of Cu and Au surfaces with intrinsic properties. Comparisons are made with previously computed results and laboratory measurements on essentially defect-free samples. Other examples include laser damage of a highly absorbing semiconductor, bulk heating of a semiconductor film, and flashlamp heating of laser glass. Computations were performed on XT- and AT-type PC-compatible computers equipped with floating-point math coprocessors. The typical computation time for heating a Cu surface to melt by single-pulse absorption, using 12x12 nodes, is about 5 minutes.

The mathematical basis for the method and the general finite-difference code in BASIC is available in a monograph and on disk [3]. The computations performed for this paper were

*This work was supported in part by Navy Independent Research funds. 1Numbers in brackets indicate the literature references at the end of the paper.