Passive thin-film optical shutters for protecting image ... - OSA Publishing

Passive thin-film optical shutters for protecting image detectors from being blinded V. V. Chesnokov, D. V. Chesnokov,a) and V. B. Shlishevski˘ı Siberian State Geodesic Academy, Novosibirsk

(Submitted November 29, 2010) Opticheski˘ı Zhurnal 78, 39–46 (June 2011) This paper discusses the results of an investigation of the possibility of protecting optical observation facilities from damage by pulsed laser irradiation by using passive optical shutters with a response time no greater than 1 ns. The shutter’s active element is a thin metallic mirror film located at the intermediate focal plane of the system and locally evaporated at the instant of c 2011 Optical Society of America. irradiation.

Work on the creation of means for protecting observational devices and the observer’s eyes from the blinding action of suddenly appearing bright flashes of light has been carried out for a long time. To reduce the intensity of radiation incident on the photosensitive elements of optical systems, one uses photochromic glasses,1 the self-focusing effect of radiation in nonlinear media,2,3 nonlinear scattering of radiation by metallic nanowires,4 Christiansen filters in the form of a suspension of crushed glass in a mixture of acetone and carbon disulfide (picosecond response rate),5 the effects of increased absorption cross section when the nanoparticles make a transition to excited levels, and photoinduced light scattering in suspensions or solid-state arrays (including suspensions of colloidal metals and fullerenes,6 carbon and fullerene nanoparticles,7 and in phthalocyanines8 ), nonlinear effects in polymethine dyes,9 two-photon absorption in semiconductors (amorphous chalcogenide films) with picosecond width of the laser pulses,10 etc. In the cited references, exception for Refs. 5 and 10, it is experimentally shown that the given effect occurs in the visible and IR ranges of the spectrum and that its delay is at the level of tens of nanoseconds or more. In all the cases under consideration, in which the transmitted radiation intensity decreases as a consequence of complete or partial absorption of the incident radiation, this causes thermal energy to accumulate in the active medium, because it is impossible to provide sufficient heat dissipation. This is the fundamental cause of the breakdown of limiters in powerful radiation fluxes. The idea of creating light-attenuating devices based on special two-layer surfaces, smooth and specular, under conditions in which they were illuminated with weak light fluxes was proposed and discussed in Ref. 11. When a pulse of focused laser radiation is received, the layers are locally heated, the lower layer is evaporated at the site of the heating, and the upper layer is deformed by the excess vapor pressure, so that it takes the shape of a bell and scatters the incident flux. After the irradiation pulse finishes acting, the mirror resumes its own original flat shape in a time of the order of microseconds, and all the observation facilities needing to be protected from blinding are again usable. However, it was impossible to investigate such systems under actual conditions and in actual devices. 377

J. Opt. Technol. 78 (6), June 2011

This article presents the results of an investigation of the possibility of effectively suppressing harmful laser radiation in a wide wavelength interval, using a passive light shutter with a nonlinear-optical switching element in the form of a thin metallic mirror film as a means of protection. One version of a schematic diagram of a shutter of the indicated type for the visible and near-IR regions of the spectrum is shown in Fig. 1. The active element of the shutter – a special metallic mirror film 4 – is on transparent substrate 3 and is located in the plane of the intermediate image created by input objective 1. Output objective 10 accordingly transfers the image (depending on the specific application) from film 4 to the optoelectronic device to be protected. When powerful laser radiation enters the system, the mirror film first locally changes its reflectivity only in the region where focusing occurs and to the extent that it is heated. It then begins to vaporize, a hole forms in the film, and reflection from the given section of the mirror surface of the shutter ceases. The useful area of the mirror shows virtually no change in this case, and the shutter remains workable and maintains its protective properties even after a large number of hits, since, after the shutter operates, the radiation is not absorbed by it, but is brought outside the structure of the shutter, for example into a special trap 5. As a result, the shutter can withstand multiple overloads without being damaged as a whole and can control radiations that are significant in energy flux. The action of powerful laser radiation on the surface of a monolithic metal has been investigated in many papers, particularly in Refs. 12 and 13; the breakdown of thin films on substrates by laser radiation was studied in Refs. 12 and 14. Our treatment concerns the behavior of thin semitransparent metallic films on transparent substrates under the action of radiation and is based on an analysis of laser-radiation-induced processes in a solid.12,13 Figure 2 schematically shows the structure and operating process of a light-reflective shutter. For the device to work efficiently, the film thickness l must not be substantially different from the penetration depth of the incident light into it (which equals 50–100 nm for most metals in the spectral range under consideration), since it will then simultaneously be heated by the radiation over the entire thickness and, when the wavelength of the thermal wave in the film is

1070-9762/2011/060377-06/$15.00

c 2011 Optical Society of America

377

1´

1 2

When a metal melts, the absorption coefficient abruptly increases by a factor of 1.5–2, and this is explained by Drude theory by the increase of the resistivity of metals when they melt12,13 and, when they are heated further, can be calculated from Eq. (2), if A0 is understood to be the absorptivity of the melt. To take into account the dependence given in Eq. (2) as applied to the absorptivity of a thin metallic film located on a thermally insulating substrate, the traditional model of a semi-infinite solid1) is used by transforming the well-known expression for the temperature of its irradiated surface12 :

2

3 4 5 FIG. 1. Schematic diagram of passive optical shutter. 1 and 10 —input and output objectives, 2—flat mirrors, 3—transparent substrate, 4—burnt-through mirror film, 5—trap for flux of directed laser radiation transmitted through the shutter.

A0 T(t) = T0 + A1

exp u2 (1 + erfu) −

A0 , A1

(3)

where T0 is the surface temperature before irradiation,

(a)

(b)

3

3

u = A1 I0

2

1

1

l

2

4

5 6

FIG. 2. Structure and functioning of passive optical shutter with evaporated mirror film. (a) Stage of radiation absorption, (b) stage of evaporation of mirror layer. 1—Metallic mirror film, 2—transparent substrate, 3—laser radiation incident on the structure, 4—region of heating of the film–substrate structure, 5—region of heating of the substrate after evaporation of the film, 6—metal vapor diffusing after evaporation.

lT = (at)1/2 > l, can be regarded as being heated uniformly. Here a = kT /cV is the thermal diffusivity of the film, kT and cV are its thermal conductivity and volume heat capacity, and t is the time of action of the radiation. At the first stage of the irradiation (Fig. 2(a)), the intensity of the reflected light is determined by the value and variations of the reflectivity R of the film, which, in accordance with the law of conservation of energy and neglecting its transmission (when l > 50 nm) equals R = 1 − A,

(1)

where A is the absorptivity of the film. According to Drude theory, the change of the absorptivity of metals when the temperature increases by 1T is described by12 A = A0 (1 + α1T) = A0 + A1 1T,

(2)

where A0 is the absorptivity at 20 ◦ C, A1 = αA0 , and α is the thermal coefficient of resistance, which for most metals lies within the limits α ≈ (3–4) × 10−3 deg−1 . This expression is valid only for a bulk material and can be used only in rough calculations in the case of thin films; to obtain accurate values, it is necessary to refine the parameters experimentally. 378


t1 kT cV

1/2

,

(4)

I0 is the intensity of the incident radiation in the surface plane, and t1 is the time to heat the surface to temperature T(t). Function f (u) = exp u2 (1 + erfu) is given in Ref. 12 (p. 56, Fig. 1.25) in the form of a graph. Equations (3) and (4) are not immediately suitable for calculating the temperature of a thin film on a substrate when the film thickness is less than the wavelength of the thermal wave in it. However, if it is recalled that the surface temperature T(t) is determined by the capability of the body to accumulate the heat energy of the absorbed radiation in a near-surface layer of depth lT , Eq. (4) can be reformulated to apply to calculations of thin-film structures. In the case under consideration, the film lies on a heat-insulating substrate with low thermal emissivity, and the heat losses to the substrate are small. Then, with l < lT , as pointed out above, the heating temperature can be considered identical over its entire thickness, and the quantity of heat stored in such a film will equal Q1 = 1T1 cV l, where 1T1 is the temperature change of the film during the irradiation pulse. On the other hand, the heat energy stored in the near-surface layer of a semi-infinite medium made from the same material during the irradiation pulse is Q2 ≈ 1T2 cV

Z

lT

e−x/lT dx = 0.6321T2 cV lT ,

0

where 1T2 is the temperature increment of the surface of the medium, and x is the coordinate of a point of the medium measured down from the surface. The condition for reformulating Eq. (4) is that the surface temperatures of the semi-infinite medium and of the thin-film structure that replaces it, achieved in the same time t1 , are equal: 1T1 = 1T2 . Calling to mind that Q1 = I1 t1 A and Q2 = Ie t1 A, where I1 and Ie are the radiation intensities incident on the film surface Chesnokov et al.

378

and a semi-infinite medium equivalent to it (having the same surface temperature), we have Ie = I1

0.632lT . l

t4 =

Replacing in Eq. (4) the quantity I0 by the equivalent value Ie for irradiation of a film on a transparent substrate, we get u0 = 0.632

A1 I1 lT l

t1 kT cV

1/2

,

or, after substituting lT = (t1 kT /cV )1/2 , u0 = 0.632

A1 I1 t1 . lcV

(5)

The value of function fm (u0 ) corresponding to the melting temperature Tm of the film under the action of radiation can be found from the general expression given by Eq. (2): fm (u0 ) =

Tm + 250 Tm + A0 /A1 ≈ . T0 + A0 /A1 T0 + 250

For the film-heating process, Eq. (5) makes it possible to express how the time interval t1 from the instant the radiation starts to act until the melting temperature is reached depends on the auxiliary quantity u0 . This is given by t1 =

u0 lcV . 0.632A1 Ie

(6)

If the irradiation continues, the film melts after the time t2 =

l ρLm Ie Al

(7)

and then heats up to the temperature T ∗ of intense vaporization, which requires the time t3 =

l 1T ∗ cV,l , Ie Al

(8)

where ρ is the film density, Lm is the specific heat of melting, Al is the absorption index of the melt (for metals, which have A0 ≈ 0.2–0.3, after they are heated to melting and make the transition to the liquid state, the absorption index is Al ≈ 1), 1T ∗ = T ∗ −Tm is the difference of the temperatures of intense vaporization and melting, and cV,l is the bulk heat capacity of the melt. The temperature T ∗ can be found from the approximate formula14 T∗ =

3M , 10RA

(9)

where 3 is the specific heat of vaporization at 0 K, i.e., that quantity of heat that needs to be expended per unit volume of substance in order to successively heat it from 0 K to the melting temperature, to melt it, to heat the melt to the vaporization temperature, and to convert it to vapor; M is the molar mass; and RA is the universal gas constant. Calculations 379


using this formula show that the temperature of intense vaporization is above the boiling temperature. To vaporize the heated film requires the additional time Lvap ρl Ie Al

(10)

where Lvap is the heat of vaporization of the material of the melted film. The last expression was obtained starting from the assumption of free vaporization of the substance, when the vaporization rate is limited only by the rate at which thermal energy reaches the medium. The validity of such an assumption is confirmed by calculations of the velocity at which the vaporization front moves into the depth of the film, carried out in accordance with the analysis given in Ref. 13 and taking into account how the flow of particles being vaporized from the surface depends on the surface temperature: when the power density of the absorbed radiation is about 2 × 1012 W/m2 , velocities within the limits 10–100 m/s are obtained, from which it follows that, at the indicated power densities and above, the time for the vaporization front to move in the film is substantially less than the vaporization time t4 and can therefore be neglected. The second assumption imposed on Eq. (10) consists of neglecting the energy of back-condensation of the particles of vapor that return to the surface of vaporization. Actually, since the vapor molecules are distributed over velocities according to Maxwell’s laws, part of the molecules (according to the data of Ref. 13, as much as 18%) returns to the substrate surface. However, they should not condense on the surface with transfer of heat energy to it (during the entire stage of vaporization and unlike the vaporization of a semi-infinite metal), since the surface temperature does not differ from the vapor temperature (the substrate is thermally insulated), and the adhesion coefficient of the metal atoms to the dielectric is fairly small. Provided that all the stages of the process follow one after the other with no overlap, the total irradiation time required by the film to obtain thermal energy sufficient for vaporization is t6 ≈ t1 + t2 + t3 + t4 . At the stage of widespread vaporization, the optical characteristics of the metal film are affected by a number of processes. The vapor cloud of the metal (Fig. 2(b)) moves as a continuous medium (since the particle density is great and the free path length of the atoms of the vapor is much less than the thickness of the layer of vapor) and is supersaturated. When it expands, it cools and condenses into droplets; taking into account the condensation, the velocity of the vapor flux is determined by U ≈ 0.5 × 1012 (kB T ∗ /AM )1/2 , where kB is Boltzmann’s constant and AM is the atomic weight of the metal. After the substance of the film completely evaporates, the propagation of the flow of vapor into space occurs with a sharp decrease of its density; i.e., the vaporization process cannot be considered steady-state. The critical Chesnokov et al.

379

state of the metal probably cannot be reached with laser heating of a thin film under the conditions considered here, since, until it reaches the necessary temperature and pressure, the absorption of the radiation decreases because it is scattered from the irradiated zone during vaporization. For the same reasons, there is no question of the heated metal being able to pass through the “dielectric-transillumination” phase.12 In the case of a semi-infinite body, irradiation regimes are possible in which there is appreciable absorption of the radiation in the vapors of the evaporated material. The effect is observed in steady-state evaporation regimes when there is intense irradiation of 1012 W/m2 or more.13 The vapor is a two-phase system composed of saturated vapor and particles of the condensed phase, and the greatest role in the absorption of the radiation is played by the condensed phase. When the geometrical thickness of the vapor layer is close to the radius of the irradiation spot (tens of micrometers), its optical thickness2) self- stabilizes equal to unity.13 There is no reflection from the surface of the body in this case. Let us estimate the reflectivity of a thin metal film of the shutter on a dielectric substrate at the instant it vaporizes. When a thin-film structure (of the order of tenths of a micrometer) is irradiated, the substance of the film during the operation of the shutter for t6 ≈ 1 ns becomes a layer of vapor with thickness lv ≈ t6 U ≈ 0.5 µm and is then scattered into space. The maximum optical thickness of this layer is about a factor of 20 less than when the surface of a monolithic body is irradiated. The reflection from the layer of vapor is the “backscattering” of the incident radiation. If it is recalled that the scattering cross section of the particles is much less than the absorption cross section when the size of the particles is as much as 10 µm,13 it can be concluded that there is an insignificant scattering effect and negligible reflectivity of the vapor of the thin film in the case under consideration. The graphs in Fig. 3 show the variation of the temperature and reflectivity of films of magnesium (a) and bismuth (b) of thickness l = 100 nm as a function of irradiation time. The calculations were carried out in accordance with Eqs. (1)–(3) and (5)–(9) for incident radiation intensities of I0 = 1 × 1011 W/m2 (a) and I0 = 5 × 1011 W/m2 (b) with values of the thermophysical constants from Ref. 16 and the following basic parameters: at a wavelength of λ = 1 µm and under normal conditions, the absorption index is A0 = 0.15 for magnesium and A0 = 0.2 for bismuth17 ; in the liquid phase, the calculated absorption index is A0 (Tm ) ≈ 1 for both metals. It can be seen that the reflectivity R of films in the focusing zone of the laser radiation decreases to virtually zero long before they completely evaporate (the instants of evaporation are shown in the form of points at the high-temperature end of the graphs of the time dependences of the temperature of the films). The irradiating radiation pulse can have significant width, but the width of the reflected pulse is substantially less because of the indicated lessening of the reflectivity at the time of complete transition of the film into the melted state. It follows from this that the share of energy of the blinding radiation that enters the detector aperture is proportional to the reflectivity of the film and decreases not only because of the decrease of the reflection intensity, but also because of the shortening of the reflection time, as in Ref. 18. 380


T, K

(a)

R T *(Bi)

2500

1

T *(Mg) 2000

0.8

R Mg (t)

1500

0.6

T Bi (t) T Mg (t)

1000

T m (Mg)

0.4

Tm (Bi)

500

0.2

R Bi (t) 0

2

4

T, K

6

8

10

12 t, ns

T *(Bi)

1

(b)

R

2500

T *(Mg) 2000

0.8

R Mg (t)

1500

0.6

T Bi (t) T Mg (t)

1000

T m (Mg)

0.4

Tm (Bi) 500

0.2

R Bi (t) 0

0.4

0.8

1.2

1.6

2.0

2.4 t, ns

FIG. 3. Graphs of the dependence of the temperature T and reflectance R of magnesium and bismuth films with thickness l = 100 nm on irradiation time t when the incident radiation intensity is I0 = 1 × 1011 W/m2 (a), I0 = 5 × 1011 W/m2 (b).

The graphs shown here make it possible to estimate the minimum energy density of radiation incident on the surface of the mirror film of the shutter that causes it to operate—i.e., the sensitivity of the passive shutter to blinding radiation. Next, going to the dynamic range of operation of the shutter, it should be kept in mind that its mirror film is optically matched with the photodetector array—the surface of each pixel of the array corresponds to some finite section of the sensitive surface of the shutter. This shows why it is important to take into account the reflectance distribution over the spot illuminated by radiation on the mirror film. The lower level of the range is therefore determined not only by the sensitivity of the passive shutter, but also by the nonuniformity of the intensity distribution in the focal spot; it depends on the quality of the image given by the objective and is somewhat higher than the sensitivity of the shutter. The physical causes of the existence of the upper limit of the range are the possibility of optical breakdown of the substrate on which the mirror film of the shutter is formed and the increase of the local damaged region of the film of the shutter as a consequence of illumination nonuniformity in the focal spot. The former cause can be eliminated by design measures18 ; the latter cause is more fundamental—it is mainly results from the diffraction of light at the aperture stop of the objective and, to a lesser extent, by its unavoidable scattering inside the optical system. Chesnokov et al.

380

In order to estimate the influence of diffraction effects, we make the following approximate calculation for a remote radiator, for which the incident wave front can be considered planar. We assume that the diameter of the useful aperture of the shutter equals 10 mm and that the diameter of the burnt-through hole is 10 µm when the irradiation intensity corresponds to the lower limit of the dynamic range of the shutter, with only the central part of the diffraction spot burning through. If it is assumed that the allowable fraction of damaged surface equals 1% of the total surface, the shutter’s lifetime will be at least 104 irradiation pulses. Other things being equal, let the power of the laser radiation be increased so much (by about a factor of 625 by comparison with the preceding case) that breakdown now occurs at the third ring of the diffraction spot. The geometrical region of the operation of the shutter is expanded to the third dark ring of the Airy circle at the focal spot, and the diameter of the shutter’s breakdown region is increased by a factor of 2.65. The array pixels optically matched with this section of the shutter remain undamaged, but the operating lifetime of the shutter decreases by a factor of 2.652 ≈ 7 and is about 1.4 × 103 pulses. A more detailed analysis of the limiting possibilities of this type of device is beyond the framework of this article and requires separate consideration. Experimental checking was carried out on mirror films of magnesium with effective diameter 11.5 mm, irradiated by a focused beam from an LTI-501 solid-state laser with wavelength λ = 1.06 µm, in terms of solving the problem of protecting silicon photodetector arrays in the IR range. CCD arrays were mounted in the focal plane of an objective with a focal length of 50 mm, and the laser radiation was directed into the aperture of the objective, either directly or through the described shutter. The radiation pulses of the laser had a bell-shaped temporal shape with a width at half-height of 16 ns. In the course of the experiment, all the arrays were irreversibly damaged under the direct action of even one radiation pulse with an energy of 2 µJ but remained undamaged for pulse energies up to 1.5 mJ (the limiting irradiation energy, achieved by using a test stand), when the shutter was placed on the radiation path. The actual response-delay time of the shutter was 0.7 ns and was defined as the difference of the widths of two successive laser radiation pulses transmitted through the shutter: the first opened the shutter and was shortened, and the second passed into the opening thus formed and maintained its width. As a result of the action of the pulse, in a time of a fraction of its leading edge, a hole with a diameter of about 40 µm and transparent for the radiation was formed in the film; i.e., about 1/80 000 of the useful surface of the shutter was damaged during the pulse. A reduction of the energy in the radiation pulse incident on the shutter by a factor of 5 reduced the hole diameter by half and increased the response-delay time to 1–1.5 ns. The quality of the image formed by the array–monitor system did not degrade after the action of hundreds of pulses of blinding irradiation. The experiment thus demonstrated reliable suppression of radiation with wavelength 1.06 µm transmitted through the passive shutter to a level that is safe for photodetector 381


arrays with blinding pulses having a width in the 1–16-ns range and an energy density of up to 1 × 106 J/m2 . The experimental results experiment confirm that the assumptions of the proposed theoretical model of the functioning of the passive shutter are correct. The appearance of a shutter-functioning mechanism for response times of the order of a fraction of a nanosecond or a few nanoseconds can also be regarded as an important result—the optical reflection is reduced even at the stage of melting of the shutter film. Further unavoidable evaporation (because of prolonged arrival of the energy) of the shutter material plays a smaller role, especially with short response times, as a consequence of the long lag and large power requirement of the process. The shutter can be effective in protecting virtually all types of radiation detectors from blinding. The principle of the use of the shutter (the detector is located along the path of the light beam reflected from the mirror of the shutter) allows it to be re-used (prospectively up to 104 –105 operations). Because of the spatial distribution of the blinding radiation and the radiation from the observed scene at the time the shutter acts, the “reception” of the image does not cease even during the time of direct blinding. a) Email: [email protected] 1) A body that has only one boundary surface, on the side of which the heat

source acts. 2) By optical thickness is meant the dimensionless quantity D0 that

characterizes the attenuation of the optical radiation in the medium due to absorption and scattering and is defined as D0 = 2.304D, where D is the optical density of the layer.15

1 V. A. Barachevski˘ı, G. I. Lashkov, and V. A. Tsekhomski˘ı, Photochromism

and Its Application (Khimiya, Moscow, 1977). 2 W. Zhang and M. G. Kuzyk, “Optical limiting using Laguerre–Gaussian

beams,” Appl. Phys. Lett. 91, 201110 (2007). L. Justus, A. J. Campillo, and A. L. Huston, “Thermal-defocusing/scattering optical limiter,” Opt. Lett. 19, 673 (1994). 4 H. Pan, W. Chen, Y. P. Feng, W. Ji, and J. Lin, “Optical limiting properties of metal nanowires,” Appl. Phys. Lett. 88, 223106 (2006). 5 G. L. Fischer, R. W. Boyd, T. R. Moore, and J. E. Sipe, “Nonlinear-optical Christiansen filter as an optical power limiter,” Opt. Lett. 21, 1643 (1996). 6 N. V. Kamanina, “Photophysics of fullerene-containing media: limiters of laser radiation, diffraction elements, dispersed liquid-crystal light modulators,” Nanotekhnika No. 1, 86 (2006). 7 I. M. Belousova, V. P. Belousov, O. B. Danilov, N. G. Mironova, T. D. Murav’eva, A. N. Ponomarev, V. V. Ryl’kov, A. G. Skobelev, and M. S. Yur’ev, “Nonlinear-optical limiters of laser radiation based on suspensions of carbon and fulleroid nanoparticles,” Opt. Zh. 71, No. 3, 6 (2004). [J. Opt. Technol. 71, 130 (2004)]. 8 J. W. Perry, K. Mansour, I.-Y. S. Lee, X.-L. Wu, P. V. Bedworth, C.-T. Chen, D. Ng, S. R. Marder, P. Miles, T. Wada, M. Tian, and H. Sasabe, “Organic optical limiter with a strong nonlinear absorptive response,” Science 273, No. 5281, 1533 (1996). 9 T. N. Kopylova, A. P. Lugovski˘ı, V. M. Podgaetski˘ı, O. V. Ponomareva, and V. A. Svetlichny˘ı, “Laser-radiation intensity limiter based on polymethine dyes,” Kvant. Elektron. (Moscow) 36, 274 (2006). [Quantum Electron. 36, 274 (2006)]. 10 R. A. Ganeev, A. I. Ryasnyanski˘ı, and T. Usmanov, “Effect of nonlinear refraction and two-photon absorption on the optical limiting in amorphous chalcogenide films,” Fiz. Tverd. Tela 45, 198 (2003). [Phys. Solid State 45, 201 (2003)]. 3 B.

Chesnokov et al.

381

11 N. V. Prudnikov, V. V. Chesnokov, D. V. Chesnokov, S. L. Shergin, and

V. B. Shlishevski˘ı, “Using thermally induced nanosize surface deformations to attenuate pulsed light fluxes,” Opt. Zh. 76, No. 2, 36 (2009). [J. Opt. Technol. 76, 82 (2009)]. 12 A. M. Prokhorov, V. I. Konov, I. Ursu, and I. N. Mikh´eilesku, Interaction of Laser Radiation with Metals (Nauka, Moscow, 1998). 13 S. I. Anisimov, Ya. A. Imas, G. S. Romanov, and Yu. V. Khodyko, The Action of High-Power Radiation on Metals (Nauka, Moscow, 1970). 14 V. P. Ve˘ıko, Laser Processing of Thin-Film Elements (Mashinostroenie, Leningrad, 1986).

382


15 B. A. Vvedenski˘ı and B. M. Vul, eds., Physical Encyclopedic Dictionary,

´ vol. 3 (Sov. Entsiklopediya, Moscow, 1963). 16 A. Ya. Guva, Brief Thermophysical Handbook (Sibvuzizdat, Novosibirsk,

2002). 17 G. V. Samsonov, ed., Physicochemical Properties of the Elements. A

Handbook (Naukova Dumka, Kiev, 1965). 18 M. P. Vanyukov and V. N. Isaenko, “Formation of powerful pulses with

a steep leading edge in a laser system with passive nonlinear elements,” Kvant. Elektron. (Moscow) No. 1, 35 (1971). [Sov. J. Quantum Electron. 1, 23 (1971)].

Chesnokov et al.

382