Femtosecond laser ablation of copper at high laser fluence: Modeling and experimental comparison

Applied Surface Science 361 (2016) 41–48

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Femtosecond laser ablation of copper at high laser fluence: Modeling and experimental comparison C.W. Cheng a,∗ , S.Y. Wang b , K.P. Chang b , J.K. Chen c a b c

Department of Mechanical Engineering, National Chiao Tung University, No. 1001, Ta Hsueh Road, Hsinchu 30010, Taiwan ITRI Southern Campus, Industrial Technology Research Institute, No. 8, Gongyan Rd., Liujia District, Tainan City 734, Taiwan Department of Mechanical and Aerospace Engineering, University of Missouri, Columbia, MO 65211, USA

a r t i c l e

i n f o

Article history: Received 13 July 2015 Received in revised form 29 September 2015 Accepted 6 November 2015 Available online 19 November 2015 Keywords: Femtosecond laser Two-temperature model Phase explosion model

a b s t r a c t Thermal ablation of a copper foil surface by a single femtosecond laser pulse of duration 120 fs and wavelength 800 nm was investigated herein both theoretically and experimentally. A 1D two-temperature model with temperature-dependent material properties was considered, including the extended Drude model for dynamic optical properties. The rapid phase change and phase explosion models were incorporated to simulate the material ablation process. The simulated ablation depths agree well with the experimental measurements for the high laser fluence regime ranging from 6.1 to 63.4 J/cm2 . © 2015 Elsevier B.V. All rights reserved.

1. Introduction Femtosecond lasers have been successfully employed in surface structural modification, drilling and cutting because of the minimal heat affected zone [1] and the unique capability to create quasiperiodic nanostructures by single laser beam irradiation [2–4]; thus, they are considered as a promising tool in precise micro/nano material processing. Many theoretical and experimental works on ultrashort (picoor femto-second) laser-material interactions have been reported since the early 1990s. In the theoretical studies on femtosecond laser ablation of copper, most of the works focus on the use of a twotemperature (TTM) model [1,5–7], or a hydrodynamic model [8]. On the other hand, experiments with single- or multi-shot ablation of copper under different laser parameters have also been presented, e.g., laser fluence [1,9–11], incident angle and polarization [12], and pulse duration [13]. Two different ablation regimes are found, and the ablation rates are shown to be dependent on either optical penetration depth or electron heat penetration depth [1]. As most previously-published experimental results for the ablation rate of copper are limited to low laser fluences, i.e. <10 J/cm2 , most theoretical studies have only compared simulation results within this regime of fluence [7,5]. In our previous study, numerical

∗ Corresponding author. Tel.: +886 3 5712121 55126; fax: +886 3 5720634. E-mail address: [email protected] (C.W. Cheng). http://dx.doi.org/10.1016/j.apsusc.2015.11.055 0169-4332/© 2015 Elsevier B.V. All rights reserved.

simulation and experimental comparison were investigated for femtosecond laser ablation of copper by multi-pulses (i.e. grooving) with laser fluence above 10 J/cm2 [14]. However, due to the change in laser intensity distribution over the ablated crater surface of the target as a result of the multi-pulse effect, the discrepancy between simulation and actual experiment was revealed. In this work, a 1D two-temperature model with temperaturedependent material properties, i.e. dynamic optical properties and thermophysical properties was developed. Together with the rapid phase changes, a phase explosion model for ejecting metastable liquid and vapor was considered. A comparison between the simulation and experimental results for ablation of a copper foil surface by a single pulse femtosecond laser with high laser fluence of 6.1–63.4 J/cm2 was carried out.

2. Modeling Considering that a copper foil is normally irradiated by a femtosecond laser pulse on the front surface (z = 0), a 1D twotemperature model can be used in this simulation since the laser spot size is often much larger than the thermally-affected depth. The 1D TTM is given as a coupled set of nonlinear differential equations [15,16]: Ce

∂Te ∂ = ∂t ∂z

 ke

∂Te ∂z

 − G (Te − Tl ) + S

(1)

42

∂Tl ∂ = ∂t ∂z

 kl

∂Tl ∂z

 + G (Te − Tl )

(2)

where the subscript e and l denote electron and lattice, respectively, C is heat capacity, k is thermal conductivity, G is the electron–phonon coupling factor, S is laser heat density, t is time, and z is distance; the laser beam is propagated along the z-axis. For temperature-dependent optical properties, the heat density S can be expressed as [14]: 1 [1 − R(0, t)] Fo S(z, t) = 0.94 tp ı(z, t) + ıb

⎡

z

exp ⎣−

1 dz − 2.77 ı(z, t) + ıb

 2 t tp



1 1/2 f2 (z, t) = √ (ε21 + ε22 ) − ε1 2

⎦

(3)

2kB Te me

(4)

ε(ω) = ε∞ −

−

f˝L2 2 (ω − ˝L2 ) + iAD ω

R(z, t) = ˛(z, t) =

= ε1 + iε2

2ωf2 c

(6)

where Ae represents the material constants for electron relaxation time, and e,p is the electron–phonon collision rate which depends on both electron and lattice temperature. For copper, Ae is 1.75 × 107 K−2 /s and e,p is calculated by the model proposed in [21]. The details of the above parameters in the modified Drude model for copper can be found in reference [14].

(10)

where c indicates light speed in a vacuum. The thermophysical properties of Eqs. (1) and (2), C, k, G, control thermal transport and temperature distributions in the laserirradiated material. In this study, polynomial functions adapted from Lin and Zhigilei [22] are used to describe Ce and G for copper over a range of electron temperature (≤5 × 104 K). Fig. 1 shows

100 Lin and Zhigilei [23] Curve fitted 80

60

40

20

0 0

2

4 6 Temperature [104 K]

8

10

(a) 7

)

3

17

4

G [10

where ε∞ is the dielectric constant, ωp is plasma frequency, ω is laser frequency,  D is the damping coefficient which equals the inverse of electron relaxation time ( e ), ˝L represents the oscillator strength of the Lorentz oscillators, f is a weighting factor and A is a constant. The following values are optimized for copper: ε∞ = 9.4286, ωp = 1.3593 × 1016 Hz, ˝L = 1.7668 × 1015 Hz, f = 3.6355 and A = 44.5275. The  e is expressed in the form: 1

(9)

2

5

Ae Te2 + 1.4144e,p

(8)

(f1 + 1) + f22

6

e =

1/2

(f1 − 1) + f22

(5)

ω(ω + iD )

(7)

Assume the incidence of the laser beam is normal to the material surface; the surface reflectivity R and absorption coefficient ˛ can be determined by Fresnel functions:

where kB is the Boltzmann constant, and me is the mass of an electron. The dynamic optical properties of surface reflectivity and absorption coefficient during laser irradiation could significantly alter the irradiated laser energy absorption and influence the distribution of laser heat density, respectively. Recently, an extended Drude model which accurately characterizes the reflectivity and absorption coefficient for gold film at different temperatures was presented [20]. That model is modified here by taking the interband transition effect into account, as shown below: ωp2

1/2

2

where Fo is the laser peak fluence, R(0, t) is the temperaturedependent surface reflectivity of the material at z = 0, ␦(z, t) = 1/˛(z, t) is the temperature-dependent optical penetration depth, ␦b is the ballistic electron penetration depth, and tp is the full width half maximum (FWHM) of the Gaussian temporal pulse. The lasing starts from t = −2tp , reaches its peak power at t = 0, and ends at t = 2tp . The laser energy outside this time period is ignored because it is too small to significantly alter the results. The ıb is added to take into account the effects of the ballistic motion of photon-excited hot electrons in contributing to penetration depth [6,17]. A constant value of ıb is often computed based on the assumption that the excited, non-equilibrium electrons could penetrate into the non-excited region at Fermi velocity [18]. In this work, it is determined by ıb = ve × tb , where tb = 27 fs is the Drude relaxation time [19], and ve is the electron velocity calculated by:

ve =



1 1/2 f1 (z, t) = √ (ε21 + ε22 ) + ε1 2

⎤

0



With calculated temperature-dependent ε1 and ε2 values from Eq. (5), the normal refractive index (f1 ) and extinction coefficient (f2 ) can be calculated by:

Ce [10 5)

Cl

C.W. Cheng et al. / Applied Surface Science 361 (2016) 41–48

Lin and Zhigilei [23] Curve fitted

2 1 0 0

1

2

3

4

5

4

Temperature [10 K] (b) Fig. 1. Temperature dependent (a) Ce [J/m3 /K] and (b) G [W/m3 /K] of copper.

C.W. Cheng et al. / Applied Surface Science 361 (2016) 41–48

the curve-fitted results. Note that when the electron temperature is higher than 5 × 104 K, the data (Ce and G) were not presented [22]. However, for high fluence machining, the electron temperature is usually higher than 5 × 104 K, and high temperature thermophysical properties are needed. A previous study [1] shows that when electron temperature is less than the Fermi temperature (i.e. 8.16 × 104 K for copper), Ce is proportional to the electron temperature, and Ce is a constant when the electron temperature is higher than the Fermi temperature. In this study, Ce between the temperatures 5 × 104 K and 8.16 × 104 K is assumed to be proportional to the fitting slope of the temperature between 4.5 × 104 K and 5 × 104 K, and Ce higher than the Fermi temperature is assumed to be constant value 77.38 × 105 J/m3 /K at Fermi temperature. For electron temperature higher than 5 × 104 K, a form of the temperaturedependent G is adopted [23]: G = GRT

A

e

Bl



(Te + Tl ) + 1

(11)

where GRT is the G factor at room temperature, Ae (see Eq. (6)) and Bl are material constants for calculating electron relaxation time. For copper, GRT is 0.5551 × 1017 W/m3 /K (see Fig. 1(b)) and Bl is 1.98 × 1011 K−1 /s [5]. The electron thermal conductivity Ke is given by [24]: Ke = 

( e2 + 0.16)

5/4

( e2 + 0.44) e 1/2 ( e2 + 0.092) ( e2 + l )

(12)

where e = Te /TF and l = Tl /TF . TF is Fermi temperature; ␹ and ␰ are constants. For copper, TF = 8.16 × 104 K,  = 377 W/m K, and

= 0.139 [25]. The bulk thermal conductivity, specific heat and mass density of copper in solid and liquid phases can be found in [26]. If the laser fluence of a femtosecond laser pulse is sufficiently high, a solid medium can be melted and ablated through vaporization, and even by phase explosion. To accurately simulate the material removal process, the above 1D TTM was integrated with two phase change models for ultrafast melting/resolidification and evaporation, and a phase explosion model for the ejection of metastable liquid and vapor [27–29]. The details of these models can be found in Ref. [29]; for the sake of brevity, they are not described here. In metals heated by a femtosecond laser pulse, molten material can be heated well beyond the normal boiling point without actually boiling because the time is too short for the necessary heterogeneous nuclei to form. Instead, the subsurface material can be superheated to more or less than the thermodynamic equilibrium critical temperature Ttc . The tensile strength of the superheated, metastable liquid will fall to zero; consequently, homogeneous bubble nucleation occurs at an extremely high rate. As a result, the superheated subsurface material relaxes explosively (or sputters) into a mixture of vapor and equilibrium liquid droplets, and is immediately ejected from the bulk material. In numerical analyses of ultrafast laser ablation, it is frequently assumed that phase explosion takes place when the liquid temperature is about 0.9 Ttc [30]. In this study, vaporization during the superheating, in addition to melting/resolidification, was simulated before and after the phase change occurred. When superheated liquid temperature reaches 0.9 Ttc , that material, including both electrons and lattice, is removed under the assumption of phase explosion. Once phase explosion no longer occurs, vaporization could continue until the temperature drops significantly. Because of the nonlinearity of the coupled heat conduction equations, a finite difference method with uniform mesh was adopted to solve the above equations. A tri-diagonal matrix method was used to solve the Te from Eq. (1). After that, the lattice temperature Tl could be solved from Eq. (2), using the same algorithm with known Te . At the first iteration in each time step, the material

43

properties involved in the equations were updated based on the temperature of the previous time step. After obtaining the electron and lattice temperature field, the solid–liquid interfacial velocity, temperature and location were calculated using the numerical method proposed by [31]. When the calculated liquid lattice temperature at a grid point reached 90% of Ttc , 7696 K for copper [32], the superheated liquid was assumed to have undergone phase explosion. That grid point was then removed from the model. In the numerical simulation, a copper foil with an initial temperature of 300 K was irradiated on the front surface by a laser pulse of tp = 120 fs and a wavelength of 800 nm. A number of 2500 control volumes per ␮m were employed, i.e. the difference of any two consecutive grid sizes is 0.4 nm. The thicknesses of the foils varied from 1 ␮m to 2 ␮m, depending on the laser fluence. 3. Experiment A copper foil was irradiated by a single pulse of Ti:Sapphire femtosecond laser in air with 120 fs in duration (at FWHM) at a wavelength of 800 nm. The laser beam was spatially filtered, resulting in an essentially Gaussian profile with a beam diameter measuring 5.2 mm (at 1/e2 ). The laser beam was passed through a shutter and a series of reflective mirrors, and subsequently entered an objective lens (numerical aperture 0.26, M Plan Apo NIR, Mitutoyo). To make a single shot ablation, the sample was translated using an X–Y motion stage, and the copper foil was then ablated in an array pattern (4 × 4) while subjected to the same laser pulse energy. Crater shapes, including maximum ablation depth and crater profiles were measured using an atomic force microscope (AFM, Veeco 3100). 4. Results and discussion Fig. 2 presents the top view microscopic images of the four craters on a copper foil caused by a single laser pulse with pulse energy levels of 1.0, 3.8, 7.4 and 10.4 ␮J, respectively. It appears that the width of the crater increases as laser pulse energy increases. For a Gaussian incident beam, the effective focused beam diameter can be determined by the approach proposed in reference [33]. In this study, it is approximated to be 6.5 ␮m (at 1/e2 ). Note that because the focused beam diameter is larger at the heat-affected zone size (usually less 1 ␮m) of interest, the use of the simplified 1D TTM approach, as shown in Section 2, is sufficient. Fig. 3 illustrates the variation of the square of the crack diameters with laser peak fluence. The straight lines curve-fitted from the experimental data confirm the logarithmic dependence between the square of the crack diameter and the laser fluence [33]. The ablation threshold fluence can be computed using the fitting equation shown in Fig. 3. The estimated ablation threshold fluence is 3.4 J/cm2 (at the square of crack diameter equal to zero), which is higher than the value 1.7 J/cm2 using femtosecond laser with shorter pulse duration (100 fs) previously reported [34]. From the simulation results (see Fig. 8, and discussed later), the single-shot ablation threshold fluence around 0.5 J/cm2 was obtained. This value was determined by setting the simulated ablation depth near zero, which differs from the above method (i.e. determined by crack diameter). The simulated ablation threshold fluence, 0.5 J/cm2 , is similar to the experimental values determined by the ablation depth technique, e.g. 0.51 J/cm2 [34] or 0.55 J/cm2 [35]. The AFM data of Fig. 2(d) with pulse energy 10.4 ␮J (fluence 63.4 J/cm2 ) are shown in Fig. 4. Compared to the zero height, the measured maximum ablation depth and crater diameter are about 1.126 ␮m and 6.035 ␮m, respectively. The surrounding area of the crater has a trace of molten material that has solidified around the crater, and the crater profile is asymmetrical.

44

C.W. Cheng et al. / Applied Surface Science 361 (2016) 41–48

Fig. 2. Microscopic images of craters on a copper foil caused by a single laser pulse with energy levels of 1.0, 3.8, 7.4 and 10.4 ␮J, respectively.

Fig. 3. The square of crater diameter against laser peak fluence.

Because the irradiated intensity is much higher than the intensity threshold for optical breakdown in air for 800 nm laser pulse at 100 fs, i.e. 6 × 1013 W/cm2 [36], the asymmetrical crater profile was deduced to be caused by the irregular distribution of laser beam energy density as a result of air breakdown by high intensity (e.g. 5.1 × 1014 W/cm2 of 10.4 ␮J) focused femtosecond laser beam. Fig. 5 shows the time dependence of calculated optical properties at the front side surface of the material irradiated by laser fluences of 0.5, 6.1, 63.4 J/cm2 , respectively. In Fig. 5(a), the surface reflectivity R(0, t) decreases quickly during the laser pulse, and then increases at a slower rate as the time is prolonged. The time-resolved reflectivity for copper irradiated by laser intensity

3 × 1015 W/cm2 with femtosecond laser (806 nm, 100 fs) measured by pump-probe technique was presented previously [37]. The temporal reflectivity was decreased from a maximum of about 0.85 to a minimum 0.23, and increased to 0.32, which is similar to our simulation results, i.e. fluence 0.5 J/cm2 of Fig. 5(a). For clarity, the the calculated transient variations of surface reflectivity R(0, t), absorption coefficient ˛(0, t) and ballistic electron penetration depth ıb during the laser irradiation are shown in Fig. 5(b)–(d). The R and ␣ at room temperature (tY=Y−0.24 ps) are 0.962 and 79 ␮m−1 , respectively. For convenience, the normalized temporal Gaussian profile of the laser pulse is also presented in the figures. It can be seen that the transient variation of absorption coefficient ␣ is similar to that of the reflectivity. In Fig. 5(d), as expected, the ballistic electron penetration depth increases due to increased electron temperature (see Fig. 6(a) below). As a result, both surface reflectivity and the absorption coefficient decrease within the pulse duration, and ballistic electron penetration depth increases within the pulse duration. The decrease in R makes the target absorb more laser energy, while the decrease in ˛ and increase in ıb alter the distribution of laser heat density inside the target. It is evident that these properties influence the amount of laser energy deposition and distribution within the pulse duration, and subsequently alter the thermal response and the amount of material ablation. Fig. 6 shows the time histories of the calculated electron and lattice temperatures at the front side surface of the material for different laser fluences. The smooth evolutions of both electron and lattice temperatures with time in Fig. 6(a) for the laser fluence 0.5 J/cm2 are as most simulation results of femtosecond laser heating reported previously. The calculated peak temperature

C.W. Cheng et al. / Applied Surface Science 361 (2016) 41–48

45

Fig. 4. AFM data of the crater in Fig. 2(d) with pulse energy 10.4 ␮J: (a) image of the ablated surface and (b) cross section.

1

1 0.5 J/cm 2

0.5 J/cm 2

6.1 J/cm 2

0.6

0.4

0.2

0

6.1 J/cm 2 63.4 J/cm2 Laser pulse

0.8

63.4 J/cm2

Reflectivity

Reflectivity

0.8

0.6

0.4

0.2

0

2

4 Time (ps)

6

8

0

-0.2

-0.1

0 Time (ps)

(a)

6.1 J/cm 70

2 2

63.4 J/cm Laser pulse

60 50 40 30 20 10 -0.2

-0.1

0 Time (ps)

(c)

0.1

0.2

Ballistic electron penetration depth (nm)

60 0.5 J/cm 2

80 Absorption coefficient (μm-1)

0.2

(b)

90

0

0.1

0.5 J/cm 2 50

6.1 J/cm 2

40

63.4 J/cm2 Laser pulse

30 20 10 0

-0.2

-0.1

0 Time (ps)

0.1

0.2

(d)

Fig. 5. Time dependence of the calculated optical properties, (a) and (b) surface reflectivity, (c) absorption coefficient and (d) ballistic electron penetration depth.

46

C.W. Cheng et al. / Applied Surface Science 361 (2016) 41–48

150

1200 2

0.5 J/cm

2

Tl

2

Te

0.5 J/cm

Temperature (103 K)

6.1 J/cm

2

6.1 J/cm

100

Tl 2

63.4 J/cm Te 2

63.4 J/cm Tl

75 50

63.4 J/cm2

800

750 ps

600 480 ps

400

25 0

1336 ps

11.6 J/cm2 23.2 J/cm2

1000 Ablation depth (nm)

125

6.1 J/cm2

Te

310 ps

200

0

5

10 Time (ps)

15

0 0

20

500

1000

1500

Time (ps)

(a)

(a) 265

8

6

2

0.5 J/cm

Tl

2

6.1 J/cm

5

Tl 2

63.4 J/cm Tl

4 3

Ablation depth (nm)

Temperature (103 K)

7 260

255

2 1 250

0 -0.2

-0.1

0

0.1

0.2

0.3

300

350

400

0.4

550

600

(b)

Time (ps) 7

(b)

6.1 J/cm 2

6

Fig. 6. (a) Time dependence of the calculated electron and lattice temperature and (b) magnification of the lattice temperature.

11.6 J/cm2 23.2 J/cm2

Ablation depth (nm)

5 Te and Tl here are 19,357 K and 5,504 K, respectively. Over the timescale of a few picoseconds, the lattice is heated up via the electron–phonon collisions, and the Te becomes equal to Tl at time 8.2 ps. After that, Te is even lower than Tl and decreases until thermal equilibrium is established at approximately 1 ns (not shown). On the other hand, as shown in Fig. 6(b), the time evolutions of Tl in the 6.1 and 63.4 J/cm2 case are respectively different than those in the 0.5 J/cm2 case. The maximum lattice temperature remains at around 6,926 K, i.e. 90% of the thermodynamic equilibrium critical temperature Ttc (7,696 K), which is attributed to the phase explosion. For the lower laser fluence 0.5 J/cm2 , the maximum Tl is 5,504 K; thus, no phase explosion occurs. The time history of the ablation depth resulting from different fluences is shown in Fig. 7. It is evident that the higher the laser fluence, the later the sputtering is completed and the more the material is ablated, for example, 1336 ps and 1145.3 nm for the fluence 63.4 J/cm2 . The steep occurrences of material ablation result mainly from the phase explosion. The sloping parts are caused by vaporization. As shown in Fig. 7(b), at a laser fluence of 6.1 J/cm2 , the total ablation depth at 600 ps is 264.3 nm, in which the ablation depth by phase explosion and vaporization are 258.4 nm and 5.9 nm (310 ps to 600 ps), respectively. This means that once phase explosion no longer occurs, e.g. 310 ps in this case, vaporization can

450 500 Time (ps)

63.4 J/cm2 4 3 2 1 0 -1

0

2

4 Time (ps)

6

8

(c) Fig. 7. (a) Time dependence of the calculated ablation depth by different fluences, (b) magnification of the fluence 6.1 J/cm2 and (c) magnification during the first few ps.

continue until the temperature drops off significantly. It is shown that phase explosion is the dominating material ablation mechanism in femtosecond laser ablation for high fluences. Fig. 7(c) shows the time history of the ablation depth during the first few ps; it is shown that the phase explosion starts at about 1 ps.

C.W. Cheng et al. / Applied Surface Science 361 (2016) 41–48

Fig. 8. Simulation and experimental ablation depths.

The proposed method was used to predict ablation depths, as well as to compare the results with the experimental measurements by AFM. Fig. 8 shows the comparison between the simulated and experimental ablation depths. Apparently, the experimental ablation depths at high laser fluences of 6.1, 11.6, 23.2, 32.3, 45.1 and 63.4 J/cm2 agree well with those predicted by numerical simulation. The average difference between the simulation and experimental results at the six experiment fluences is 36 nm. It is found that at low fluence (<10 J/cm2 ) regime, the simulated ablation depth may also agree well with the experimental data [34]. In addition, given the simulated ablation depth near zero, the single-shot ablation threshold fluence was determined to be around 0.5 J/cm2 , which is similar to the experimental threshold values, e.g. 0.51 J/cm2 [34] or 0.55 J/cm2 [35]. It is shown that through accurate description, the 1D TTM with temperature-dependent optical properties and thermal properties of materials can accurately predict the ablation depth over a larger scale of laser fluences. The good correlation suggests that the proposed 1D model can be extended to a higher dimensional model (e.g. axisymmetric model) for simultaneously predicting the crater profile and ablation depth. 5. Conclusions This study reports the theoretical and experimental results of thermal ablation of copper foil by a single femtosecond laser pulse of high laser fluences, 6.1–63.4 J/cm2 . To simulate the ultrafast laser heating process, a 1D two-temperature model with temperaturedependent material properties, i.e. dynamic optical properties with extended Drude model and thermo-physical properties, was presented. A phase explosion model along with rapid phase changes was developed to simulate the material ablation process. Using an experimental procedure to determine the effective focused Gaussian incident beam diameter, the peak laser fluence on the material surface was accurately calculated and used in the numerical simulation. The numerical simulation agreed well with the results of the experimental ablation depth, with an average difference between simulation and experimental results being only about 36 nm. Acknowledgements The authors would like to thank the MOST 103-2218-E-009025-MY2 for support of this research. In addition, we thank Dr. Tsung-Wen Tsai at ITRI Taiwan for useful discussions. References [1] S. Nolte, C. Momma, H. Jacobs, A. Tunnermann, B.N. Chichkov, B. Wellegehausen, H. Welling, Ablation of metals by ultrashort laser pulses, J. Opt. Soc. Am. B—Opt. Phys. 14 (1997) 2716–2722.

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