Optics & Laser Technology; Vol. 29, No. 8, pp. 517±522, 1997 # 1998 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0030-3992/97 $17.00 + 0.00 PII: S0030-3992(97)00054-6
Laser induced damage thresholds and laser safety levels. Do the units of measurement matter? R. M. WOOD The commonly used units of measurement for laser induced damage are those of peak energy or power density. However, the laser induced damage thresholds, LIDT, of all materials are well known to be absorption, wavelength, spot size and pulse length dependent. As workers using these values become divorced from the theory it becomes increasingly important to use the correct units and to understand the correct scaling factors. This paper summarizes the theory and highlights the danger of using the wrong LIDT units in the context of potentially hazardous materials, laser safety eyewear and laser safety screens. ß 1998 Elsevier Science Ltd. All rights reserved. KEYWORDS: lasers, laser induced damage thresholds (LIDT), laser safety
the irradiation, J cmÿ2, W cmÿ2, W or W cmÿ1. The subject is now mature enough both to set out the dierent regimes, and to require this setting out because of the confusion that can occur. The following treatment sets out the three main cases and then discusses the diculties that can occur if the `wrong' units are used.
Introduction There is a common misconception that the laser induced damage threshold, LIDT, for a particular material, optical component, laser safety eyewear or laser safety screen can be de®ned in terms of constant energy or power density. This has mainly come about since, in practice, the easiest units to measure the laser intensity or irradiance levels are those of energy density, J cmÿ2, or power density, W cmÿ2.
The three main cases
Whilst it is self-obvious that the `safe levels' and the LIDTs of materials and components are wavelength dependent through the absorption, the variation with pulse length and spot size is not so well understood or so well documented. However, it has long been known that there are dierent values for damage threshold measurements depending on the materials, the laser wavelength and pulse length and the focusing arrangements.1±7 The practical problem has historically been that there are three clear cut damage mechanism regimes (those for absorbing materials, semitransparent materials and transmitting materials) with two, three and four time-dependent sub-regimes, respectively. In addition there are a series of modifying mechanisms, e.g. non-linear absorption, electro-optic processes and self-focusing, which modify the basic mechanisms. Each of these mechanisms and submechanisms may be dependent on dierent units of
Absorbing materials When a laser beam is incident on a non-transmitting surface a small amount of energy penetrates it to a distance, termed the skin depthÐa function of the electrical conductivity. Subsequent absorption of this radiation raises the temperature of the surface. It is possible to de®ne a thermal diusion length, L, such that: L2 4Dt
1
where: D = k/rC; and t, laser pulse duration; k, thermal conductivity; r, density; C, heat capacity. While the laser spot radius, r, is much larger than the diusion length, L, there will be negligible spread of the absorbed energy out of the irradiated area during the pulse duration. As the irradiation energy increases the material at the centre of the laser beam will rise in temperature and eventually catastrophic damage will occur due to melting of the surface.
The author is at Cosolas Ltd, Bromsberrow Heath, Herefordshire, HR8 1PF, UK. Received 30 September 1997. Revised 29 October 1997. Accepted 12 November 1997.
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Laser induced damage thresholds and safety levels: R. M. Wood
The temperature rise due to the absorption of this energy may be calculated using a one-dimensional heat ¯ow equation Tm ÿ Ta dT
E a J
t p pr2 2 prkC
2
where J(t) is a function of the temporal shape of the laser pulse, i.e. in this case the LIDT is a constant value if measured in terms of J cmÿ2. In the case of longer irradiation times the whole component warms up and the equation for the temperature of the centre of the component at the time of damage reduces to Pa Pa Tm ÿ Ta dT 2rprCD 2rpk
3
Similarly a threshold for catastrophic cracking can be de®ned
i.e. in this case the LIDT is a constant value if measured in terms of W cmÿ1. The variation of the LIDT with pulse length and focused spot size for a typical absorbing metal surface, diamond turned OFHC copper, at 10.6 mm is shown in Fig. 1, plotted in terms of J cmÿ2, and in Fig. 2, in terms of W cmÿ1.
ED CkS=ab
5
i.e. in this case the LIDT is a constant value if expressed in terms of J cmÿ2. When the thermal conduction out of the irradiated area becomes non-negligible, i.e. when r2 << D << R2 t t
Semi-transparent materials Many materials used with lasers at particular wavelengths are transparent enough to be used as laser windows whilst still being absorbent enough for their LIDT to be dominated by thermal absorption (e.g. Ge, ZnS, ZnSe, GaAs at 10.6 mm). In a transparent material the laser radiation is absorbed in a cylinder and causes both a temperature rise along the axis of the cylinder and a radical strain. As in the case of absorbing substrates, as long as the beam radius, r, is larger than the diusion length, L, there will be negligible spread of the absorbed energy during the pulse duration and the material, and the material on the axis of the beam reaches its melting point when ED CdT=a
Fig. 2. Laser induced damage threshold, LIDT W cmÿ1 versus pulse length and spot size. OFHC Copper at 10.6 mm.
4
where R is the component radius the illuminated region can be treated as a continuous line source.8 In this case the expressions for the LIDT are ED 4CDdT=aIn
4Dt=r2 t=r2
6
and ED
4CkDS=ba
t=r2
7
In the case of long irradiation times (whether long pulse, multiple pulsing or cw irradiation) the component temperature rises to a uniform maximum and the equation again reduces to Tm ÿ Ta dT
Pa 2rpk
8
which is the steady state pro®le in a semi-in®nite solid, i.e. in this case the LIDT is a constant if expressed in terms of W cmÿ1. It must be noted that thermal runaway occurs at fairly low temperatures for all semi-conducting materials. The value for Tm in the above equation should therefore be the value at which non-linear absorption starts in preference to the melting point of the material. The variation of the LIDT with pulse duration and focused spot size for a ZnSe substrate irradiated at 10.6 mm is shown in Fig. 3, plotted in terms of J cmÿ2, and in Fig. 4, plotted in terms of W cmÿ1.
Transparent materials Fig. 1. Laser induced damage threshold, LIDT J cmÿ2 versus pulse length and spot size. OFHC copper at 10.6 mm.
For transparent materials (i.e. materials operating in their spectral transmission range with a << 10ÿ6 cmÿ1) the on-axis temperature rise dT, as de®ned in the
Laser induced damage thresholds and safety levels: R. M. Wood
Fig. 5. Laser induced damage threshold, LIDT J cmÿ2 versus pulse length and spot size. Fused silica at 1.064 mm.
Fig. 3. Laser induced damage threshold, LIDT J cmÿ2 versus pulse length and spot size. ZnSe at 10.6 mm.
ionization rate is proportional to the induced dielectric ®eld and the build up of electrons is given by
previous section, is not enough to cause excessive strain or to reach the melting point of the material except under cw irradiation conditions.
N N0 exp
VB2 t exp
ÿte
For pulsed operation there are four dierent interaction times that have to be considered (1) At ultra short pulse duration (t < 10ÿ13 s) multiphoton avalanche absorption can occur even if there is only one free electron present. The interaction occurs so quickly that the same free electron absorbs energy from several incident photons without having time to move spatially. i.e. in this case the LIDT is constant if expressed in terms of W. (2) For extremely short pulse durations (ti
Fig. 4. Laser induced damage threshold, LIDT W cmÿ1 versus pulse length and spot size. ZnSe at 10.6 mm.
10
where te is the ¯uorescence lifetime of the electron in the excited state, i.e. in this case the LIDT is proportional to tÿ1/2 if expressed in terms of W cmÿ1. If expressed in terms of the more usually quoted terms of peak energy density the LIDT is proportional to t1/2 r ÿ1. (4) For long pulse and cw irradiation (t >> 5te) the component temperature again rises to a uniform maximum value and damage occurs due to a thermal mechanism. Failure in the case of many materials comes about due to migration of defects, dislocations and grain boundaries with a subsequent change in the eective thermal conductivity, i.e. in this case the LIDT is a constant if expressed in terms of W cmÿ1. The variation of the LIDT with pulse length and focused spot size for fused silica at 1.064 mm is shown in Fig. 5, in terms of J cmÿ2, and in Fig. 6, in terms of W cmÿ1, and in Fig. 7 in terms of W.
9
i.e. in this case the LIDT is an exponential function of the pulse length and is proportional to r ÿ1. (3) For normal short pulse duration (5ti
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Discussion It will be realized, from the previous section, that although there are several regions where the LIDTs of speci®c materials can be quoted as being a constant,
Fig. 6. Laser induced damage threshold, LIDT W cmÿ1 versus pulse length and spot size. Fused silica at 1.064 mm.
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Laser induced damage thresholds and safety levels: R. M. Wood materials using 10.6 mm, CO2, cw laser radiation.10 This was literally one of the ®rst attempts to measure the cw LIDTs for a range of materials since most previous work has been done for one material or for pulsed laser system components.
Fig. 7. Laser induced damage threshold, W versus pulse length and spot size. Fused silica at 1.064 mm.
the user has to be aware of all the measurement and application constraintsÐin particular the wavelength, spot size and pulse length used for the measurements. It will also be realized that if the right units for the LIDT are used it is possible to quote constant value LIDTs over speci®c pulse length and/or spot size ranges. It is important to emphasize at this point that although there are regimes for materials where the LIDT is thermally dominated that can correctly be expressed in terms of J cmÿ2 there are no regimes where it can be expressed in terms of a constant W cmÿ2 irrespective of laser spot size. The problem with trying to rationalize the units of measurement is that of inertia because all the previous measurements have been made using a dierent system. It is also true that it is perfectly possible to test materials and to make relevant comparisons using any of the aforementioned units for any particular laser system. However, it has long been realized that it should be easier to scale between measurements made at particular wavelengths, spot sizes and pulse lengths to any other combination. The inertia has come about since many workers have not been able or interested (for reasons of commercial rather than scienti®c interest) in making measurements at other wavelengths, spot sizes or pulse lengths. Where this has been done, good correlation has been found (e.g. Ref. 9 where the pulsed LIDTs for single crystal and CVD grown diamond were collated from several dierent measurement laboratories). It is, however, recommended that designers of high power laser systems do not attempt to extrapolate measurements gained using laser operating conditions that are substantially dierent from those of the laser under design. The reasons behind the writing of this paper in an attempt to rationalize the use of the units of measurement are threefold. 1. The recent paper describing the attempt by an EU CRAFT consortium to look at the factors aecting the LIDTs of standard window and mirror
2. Since, for long pulse and cw irradiation, the damage threshold (or the power handling capability) of the components under test, for any particular laser focused to a common spot size, becomes a constant value, many component manufacturers have taken to marketing their products on their ability to handle high peak-power densities (irrespective of wavelength, spot size or pulse length). One reason for this is that now the laser industry is more mature and no longer `a solution looking for an application', the laser component suppliers are no longer on the fringe of the research ®eld but exist as standard laser component manufacturers. The problem with this approach is illustrated later and is directly related to the safety problems existing with damaging speci®c materials. 3. The realization that in certain pulse length, spot size combinations the protection given by laser eyewear and laser safety screens may not be adequate even though laser safety standards11, 12 are in the process of formulation. This aspect is further discussed later.
LIDTs of hazardous materials It is obviously dangerous to irradiate some materials with power levels such that laser damage is induced. Speci®c examples of this are thorium ¯uoride windows and coatings (slight radioactive dust problem), and gallium arsenide and zinc selenide (arsenic and zinc are not good for the health). The most dangerous material that has been projected onto the laser market is, however, berylium. Berylium has long been known as a particularly useful material from an engineering viewpoint since its density and thermal properties enable potentially lightweight scanning mirrors to be deployed with a consequent low electrical power drive requirement. However, since the TLV of berylium oxide is so extremely low it has also been realized that extreme care must be taken not to vaporize the berylium surface. It has recently been claimed that a berylium mirror could withstand a power density level of 65 W cmÿ2 with the implication that as long as this power density loading was never exceeded no danger would be encountered. On asking the conditions of test it was stated that no damage was encountered when a 56 W cw CO2 laser beam was focused down to a 0.33 mm square top spot diameter. Table 1 illustrates the predicament the user would ®nd himself in if this were the LIDT and he allowed himself the luxury of using the maximum power density of 65 W cmÿ2 to be the limit of use rather than the `true' value of 1700 W cmÿ1.
Laser induced damage thresholds and safety levels: R. M. Wood
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Table 1. Example of how the wrong use of units can lead to unacceptably high LIDTs being quoted Spot diameter mm
Maximum safe power W, using 1700 W cmÿ1
0.33 0.5 1.0 5.0 10.0
Maximum safe power W, using 65 W cmÿ2
56 85 170 850 1700
Threshold
56 127 510 12763 51050
1 1.5 3 15 30
Beryllium mirrors have been measured as being able to withstand 56 W of 10.6 mm cw power in a 0.33 mm, `top hat' CO2 laser pulse Laser safety considerations It should be self-evident that not only should laser safety eyewear and safety screens provide sucient attenuation so as to protect eyes, personnel and ¯ammable surrounds but they should also have adequately high LIDTs in their own right to prevent the laser drilling or burning a hole through them. In short, a screen can only be useful below an irradiation level de®ned by its own LIDT. Laser safety eyewear is mandatory for personnel working with exposed laser beams.11 Similarly, the use of laser guards and screens has been strongly encouraged12 to protect personnel from the eect of stray and re¯ected beams. The level of protection has been discussed at length for many years and standards are in the process of promulgation. Unfortunately although these standards outline the hazards, the attenuation levels necessary and even the methods of measuring the LIDT of the eyewear and screen material, the LIDTs are still expressed in terms of power or energy density. The laser eyewear standard11 states that the testing should be carried out with a focused spot size of at least 0.1 mm. The use of smaller spot sizes is not considered sensible particularly in the case of spectral rejection coatings where there may be weak coating defects. However, in the case of highly transparent coating materials the only constant irradiation limit that can be speci®ed is that measured in terms of
W cmÿ1 (see earlier and Figs 5±7). In the case of absorbing ®lters, unless the pulse duration is below the `thermal diusion break point' the use of a small spot measurement will lead to a high LIDT (in terms of J cmÿ2) which may not give adequate safety protection if higher total power beams are subsequently used. The proposed laser screen standard12 requires screens to be tested with laser spot sizes of not less than 1 mm. This is of course slightly better but again may not be adequate, particularly if the measurement is expressed in terms of power density. Once again the problem is compounded if the laser measurement duration is above the thermal break point. The problem for both the eyewear and the screen safety levels is much the same and can be illustrated in a general way by inspection of Table 2. This table indicates the risk of using the wrong units based on a measured cw threshold of X W in a 0.3 mm diameter focused spot. The calculation shows that using a `safe' power density of 1170X W cmÿ2 (X Watts in a 0.33 mm diameter spot) promulgates a decided risk when larger and more powerful beams are used. The table also indicates the variation in the `real' safe power density values indicating that the larger the beam (expanded or diverging case) the lower is the safe power density level. Reference to Fig. 3 indicates the values of an approximate thermal diusion time versus spot size and when these are applied it is seen that the real safe energy density level is a constant
Table 2. Calculation of the LIDT of a typical absorption dominated material
Spot diameter (mm) 0.1 0.33 1.0 10 100
Maximum safe power, W, using 30X W cmÿ1 0.3X X 3X 30X 300X
Approx. Real safe thermal Real safe Safe power W, Col 3/ power density diffusion limit energy density using 1170X 2 Threshold (W cmÿ2) seconds (s) (J cmÿ2) W cmÿ2 0.092X X 9.2X 920X 92,000X
0.3 1 3 30 300
3820X 1170X 382X 38X 3.8X
ÿ4
10 3.3 10ÿ4 10ÿ3 10ÿ2 10ÿ1
0.38X 0.38X 0.38X 0.38X 0.38X
Safe energy 3 10ÿ5X 3.3 10ÿ4X 3 10ÿ3X 3 10ÿ1X 30X
Based on a measured cw threshold of is X W in a 0.33 mm diameter focused spot. Note: Column 6. These are approximate thermal diffusion limits for the purposes of this calculation. Thermal diffusion limits are material dependent and will vary even between samples of the same material. All the figures in this table are only valid for square top or perfect Gaussian beams. The minimum damage threshold or level of irradiation below which no damage should occur to the material is shown to be 30X W cmÿ1 for pulses longer than the thermal diffusion limit and 0.38X J cmÿ2 for pulse durations lower than the thermal diffusion limit.
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Laser induced damage thresholds and safety levels: R. M. Wood
(and that the energy per pulse danger level rises as expected as the spot size increases).
Conclusions Although the units of peak power or energy density are nearly universally used for the measurement and publication of the laser induced damage thresholds of optical components and materials used with laser systems it has been shown that this can be misleading and even lead to a safety hazard. This paper sets out the scaling factors for the comparison of damage threshold data gained at dierent wavelengths, spot sizes and pulse lengths. The analysis shows that although peak energy density, expressed in terms of J cmÿ2, is a constant value for the damage threshold of absorbing components used with short pulse lasers a more universal unit is that of W cmÿ1. Measurements expressed in this unit are more likely to be constant values than those expressed in any other unit. It is still recommended that it is a good principle not to extrapolate or scale values measured using measuring conditions substantially dierent from those of the application. References
1 Bliss, E. S. Pulse duration dependence of laser damage mechanisms, Optoelectronics, 3 (1971) 99±107 2 Davit, J. Mechanism for laser surface damage of glass, J.A.P., 39(13) (1968) 6052±6056 3 Wood, R. M. Laser Damage in Optical Materials, Adam Hilger Press, Bristol (1986) 4 Wood, R. M. Pulse duration dependence of laser damage mechanisms revisited. Proceedings, Boulder Damage Symposium. SPIE 2428 (1994) pp. 531±545 5 Du, D., Liu, X., Squier, J., Mourou, G. Laser induced breakdown as a function of pulse duration: from 7 ns to 150 fs, Proceedings, Boulder Damage Symposium SPIE, 2428 (1994) 422±434 6 Stuart, B. C., Herman, S., Perry, M. D. Laser induced damage in dielectrics with nanosecond to sub-picosecond pulses, Proceedings, Boulder Damage Symposium SPIE, 2428 (1994) 568±578 7 Wood, R. M. The in¯uence of the laser beam characteristics and the sample properties on the power handling characteristics of optical and laser components. Third International Workshop on Laser Beam and Optics Characterisation. Quebec. SPIE 2870 (1996) pp. 428±438 8 Carslaw, H. S., Jaegar, J. C. Conduction of Heat in Solids, Clarendon Press, Oxford (1947) 9 Wood, R. M. Summary of laser damage data for diamond, Proceedings, Boulder Damage Symposium SPIE, 2428 (1994) 594±604 10 Greening, D. Test rig sets parameters of laser damage to optics, OLE, June (1997) 41±43 11 Laser Safety Eyewear Standard, EN 207, 199 12 Laser Safety Screens Standard, PrEn 12254, 199
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