Dynamics of femtosecond laser pulse induced damage in multilayers

Optical Materials 28 (2006) 1372–1376 www.elsevier.com/locate/optmat

Dynamics of femtosecond laser pulse induced damage in multilayers Haiyi Sun a,*, Tianqing Jia a, Zhongchao Wei b, Jianrong Qiu a,c, Xiaoxi Li a, Chengbin Li a, Shizhen Xu a, Donghai Feng a, Hezhou Wang b, Zhizhan Xu a a

b

State Key Laboratory of High Field Laser Physics, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, P.O. Box 800-211, Shanghai 201800, PR China State Key Laboratory of Ultrafast Laser Spectroscopy, Zhongshan University, Guangzhou 510275, PR China c Photon Craft Project, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, and Japan Science and Technology Corporation, Shanghai 201800, PR China Received 20 April 2005; accepted 15 August 2005 Available online 26 September 2005

Abstract We report the single-shot damage thresholds of MgF2/ZnS omnidirectional reflector for laser pulse durations from 50 fs to 900 fs. A coupled dynamic model is applied to study the damage mechanisms, in which we consider not only the electronic excitation of the material, but also the influence of this excitation-induced changes in the complex refractive index of material on the laser pulse itself. The results indicate that this feedback effect plays a very important role during the damage of material. Based on this model, we calculate the threshold fluences and the time-resolved excitation process of the multiplayer. The theoretical calculations agree well with our experimental results.  2005 Elsevier B.V. All rights reserved. PACS: 42.62.b; 77.55.+f Keywords: MgF2/ZnS omnidirectional reflector; Damage threshold; Damage mechanism; Localized dynamics

1. Introduction Laser-induced damage in optical materials is always a limiting factor in the development of high-power laser systems. Since the invention of laser, laser-induced damage has been extensively studied [1–4], such as damage morphology, threshold fluence and mechanisms, etc. Recent work has concentrated on the damage of bulk dielectric materials with femtosecond pulses, and only a few studied on the multilayers [5]. Dielectric damage in the femtosecond regime can be described as three major processes: (i) the excitation of conduction-band electrons (CBE); (ii) deposition of laser energy in the CBE gas, namely, the heating of CBE; (iii)

*

Corresponding author. Fax: +086 69918021. E-mail address: [email protected] (H. Sun).

0925-3467/$ - see front matter  2005 Elsevier B.V. All rights reserved. doi:10.1016/j.optmat.2005.08.011

transferring the CBE kinetic energy to the lattice [6,7]. A lot of studies have investigated the first process, but only considered the electronic excitation of material by laser and ignored the counteraction of this excitation to the laser pulse itself [8–11]. In fact, this is an interactional process. During the irradiating of laser, the refractive index and extinction coefficient of materials change with the CBE number density, which leads to the changes of reflectivity, transmissivity and distribution of laser intensity in materials. Many experiments about dielectric materials and semiconductors have testified these changes using the pump-probe technique [12–17]. Our recent experiments on another optic films (SiO2/TiO2) also observed the related phenomenon [18]. The change of reflectivity is related to the material and pump laser intensity, which mainly results from the CBE excitation, that is, plasma formation. Generally, high pump laser intensity leads to the great change of reflectivity. Inversely, this change may further

H. Sun et al. / Optical Materials 28 (2006) 1372–1376

affect the excitation of electrons to conduction band. However, no detailed theoretical investigation was reported on this feedback effect. In this paper, we measured the dependence of damage thresholds on the pulse durations for MgF2/ZnS omnidirectional reflector. A coupled dynamic model was used to investigate the damage process. We explored the influence of the single-pulse laser-induced changes in complex refractive index of material on the laser pulse itself. The results show this feedback effect plays a very important role during the damage of material. Using this model, we calculated the threshold fluences and the ultrafast excitation process of the multilayer. The theoretical results were in good agreement to the experimental measurements. 2. Experiments and results Experiments were carried out using a Ti: sapphire laser (k = 800 nm) with 50 fs full width at half maximum pulse duration. The highest output energy is 0.6 mJ. With a half wave plate and a polarizer, we could vary the pulse energy continuously. The pump pulse was focused on the front surface of material with a biconvex lens with 150 mm focal length. The diameter of focused spot was measured to be around 30 lm. We utilized dispersive materials (ZF6 glasses) to adjust the pulse duration sp from 50 fs to 900 fs. MgF2/ZnS omnidirectional reflector was studied in the experiment, and its reflectivity is more than 99% for incident angles of 0–75 at the wavelength of 800 nm. It is deposited by heat evaporation technique on silica substrate. Its construction is S(HL)11(HL)13, where S indicates substrate, (HL) are made from high and low refractive materials (ZnS/MgF2). Their refractive indexes are 2.38 and 1.35, respectively. The optical thickness of each layer is a quarter-wave, and the peak wavelength of the 11 and 13 pairs of layers is 880 and 1040 nm, respectively. The

sample was set on a three-dimensional precision stage, and damaged at normal angle. Each location on the sample was irradiated by only one laser pulse. Fig. 1 shows the process of calculating the threshold fluences, and the method used in our work is adopted from Refs. [12,19] and [20]. This method determines both the threshold energy Eth and the e2-beam radius x0, and Eth thus the damage threshold F th ¼ px 2 . The empty circles in 0

Fig. 2 indicate the threshold fluences of omnidirectional reflector irradiated by 800 nm laser, which are about 0.30 J/cm2. 3. Theory In the bulk dielectric materials, it is proposed the damage is induced by electron avalanche. About the damage threshold, this theory has successfully explained various experimental results [21–23]. A recent report about Ta2O5/SiO2 multilayer also utilized electron avalanche model to explain the dependence of the threshold fluences on the pulse widths, and their theoretical results agree well with the experimental measurements [5]. Additionally, we find that the damage thresholds (Fig. 2) dont increase so fast as those expected from the photo-ionization alone. Considering all these results, we calculate the threshold fluences of the reflector based on electron avalanche model. In this model, the feedback effects of the excitation of CBE on the laser are also calculated. Fig. 3 indicates the flow chart of this feedback model. During the calculation, each layer of the sample is divided into 10 thin layers. At a time t, the laser intensity distribution, CBE density and dielectric constant at a specific location in each thin layer are first calculated. Then adding a temporal step Dt, the above process is cycled using the results obtained at the previous time as the initial condition. The temporal step Dt is 2 fs.

0.40

Laser pulse energy (μJ)

1500

1

10

100 Threshold fluence (J/cm2)

Squared diameters of spots (μm2)

2000

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τp=50 fs

1000

0.35 0.30 0.25 0.20 0.15

500 0.10 100 0 0.1

1000

Pulse duration (fs) 1 Laser fluence (J/cm2)

10

Fig. 1. Squared diameters of the ablation spots as a function of laser pulse energy and laser fluence.

Fig. 2. Threshold fluences vs. pulse durations. The empty circles represent our experimental results with error of ±20%. The solid and dotted lines are theoretical results simulated by the models with and without the feedback effects, respectively.

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H. Sun et al. / Optical Materials 28 (2006) 1372–1376

Fig. 3. The flow chart of the feedback model.

where " # l11 l12 l21 r¼

l22

¼

k Y m¼0

"

expðjdm Þ

rm expðjdm Þ

rm expðjdm Þ

expðjdm Þ

E l 0 ¼ 21 ; Eþ l11 0

;

ð3Þ ð4Þ

N m  N mþ1 ; N m þ N mþ1 2N k tk ¼ . N k þ N kþ1

rm ¼

Fig. 4. The amplitudes of electric fields in multilayer for the normal incidence.

#

ð5Þ ð6Þ

Here r is the reflection coefficient of the multiplayer. rm and tk are corresponding to the reflection and transmission coefficients at a specific interface. dm = 2pNmdm/k is the phase change, and dm is the thickness of each thin-film. Nk = nk + j Æ kk is the complex refractive index, and related by refractive index nk and extinction coefficient kk. The laser intensity distribution Ik(t) can be calculated by [26] "  2 # t k I k ðtÞ ¼ I 0  I max ðtÞ exp ð4 ln 2Þ ; ð7Þ tp 2

The distribution of laser intensity with the thickness of reflector is calculated with the theories in thin-film optics [3,24,25]. Fig. 4 shows the amplitudes (possibly complex) of electric fields in multilayer for the normal incidence. The subscripts from 1 to k + 1 quantities refer to the k + 1 interfaces. Let the beams with positive and inverse amplitudes of electric fields at a specific interface be Eþ k and E k , and those with positive and inverse amplitudes  of electric fields at the incidence surface be Eþ 0 and E0 ,  respectively. Using the boundary condition E0 ¼ r  Eþ 0 we obtain #  þ   " l11 l12 Eþ E0 1 kþ1 ¼ ; ð1Þ t0 t1    tk l21 l22 E r  E kþ1 0 Let the incidence amplitude of electric field be Eþ 0 ¼1; then E ¼ r, and Eq. (1) can be simplified to 0    l11 1 1 ¼ t0 t1    tk l21 r

l12 l22

"

Eþ kþ1 E kþ1

# ;

ð2Þ

 where I kmax ¼ jEþ k þ Ek j , I0 is the incident laser peak intensity. The total reflectivity of the reflector R takes the form

R ¼ r  r ¼

l21  l21 . l11  l11

ð8Þ

Based on avalanche model, the evolution equation of CBE density nke ðtÞ at a specific location can be written as [6,23]   onke ðtÞ nk ðtÞ ¼ ðRPI ðI k Þ þ RP ðI k Þ  ne Þ 1  e ; ð9Þ ot N0 where the photoionization rate RPI can be calculated by Keldysh theory [27]. The factor 1  Nne0 is introduced for the consideration of the exhaust of valence band electron (VBE). We consider that only one VBE in a molecule is excited to the conduction-band, hence the initial number of VBE (N0) is equal to that of molecule in the material [6]. The initial densities N0 of MgF2 and ZnS are 3.2 · 1022 and 2.2 · 1022 cm3, respectively. The impact ionization rates RP are calculated by using a flux-doubling model [21,28].

H. Sun et al. / Optical Materials 28 (2006) 1372–1376

ek ð hxÞ ¼ 1 þ ½ek ð hxÞ  1

N 0  nke nke e2 1  ; N0 e0 mopt me x2 1 þ i xs1D

50 fs, 0.21J/cm

1.5

1.0

2

1

n1

21

-3

n e (10 cm )

Reflectivity (R)

0.5

1

ð10Þ

2.0

n e / Reflectivity / n1 / k1

In order to consider the feedback effects of the excitation of CBE on the laser, the relation between the dielectric constant ek ¼ N 2k and CBE density of the material nke must be given. We use the equation [29]

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where e0, me, e and x are the vacuum dielectric constant, free electron mass, electric charge of electron and optical frequency, respectively. ek( hx) is the dielectric constant of 1 the unexcited material. mopt ¼ ðm1 þ m1 represents e h Þ the optical effective mass of the carriers (me and mh are the effective masses of electrons and holes). sD is the Drude damping time. For the last two parameters we choose mopt ¼ 1:0 for MgF2 and 0.128 for ZnS, and sD = 1 fs for both of them. After solving Eqs. (1)–(10), we obtain a series of results. Fig. 5 shows the distribution of laser intensity I in the first layer. Fig. 6 indicates the evolution of CBE density, refractive index n1, extinction coefficient k1 in the surface layer and total reflectivity R(t)/R0 of the film. R0 is the initial reflectivity of the mirror at 800 nm, and R(t) corresponds to the reflectivity at time t. When t = 2 fs, the number of CBE reaches 1020 cm3, n1 begins to decrease and k1 rises obviously. As a result, the reflectivity and distribution of laser intensity also start to change evidently. When t = 30 fs, CBE density reaches the order of magnitude of 1021 cm3, n1 and k1 begin to change slowly. At last, they reach the value of 1.1 and 0.23, respectively. The final laser intensity decreases to less than one half of the initial value (Fig. 5), and the reflectivity down to 38%. Our calculations also indicate that this dynamic process will become more evident with increasing laser fluence [18]. Using this model, we calculated the damage threshold of the film using the critical plasma density of ncr = 1021 cm3 as the damage criterion. The theoretical results are shown in Fig. 2 (solid line), which agrees well to the experimental

-40

-20

0

20

40

60

Time (fs) Fig. 6. The evolution of CBE density, refractive index n1, extinction coefficient k1 in the surface layer and total reflectivity R(t)/R0 of the film.

measurements. If not considering the feedback effects of the excitation of CBE on the laser (Eq. (10)), the simulated thresholds (dotted line in Fig. 2) are much lower and decrease faster. This indicates that it is necessary to consider this feedback effect. We also simulated the time-resolved excitation process in our pump-probe reflectivity by means of this feedback model, and the theoretical calculation is in good agreement to the experiments [18]. 4. Conclusions The damage thresholds for pulse durations ranging from 50 fs to 900 fs were measured for MgF2/ZnS omnidirectional reflector. We established a coupled dynamic model to study the damage mechanisms, in which not only was the electronic excitation of the material by single-pulse laser considered, but the influence of the laser-induced changes in complex refractive index of material on the laser pulse itself was also included. The results indicate that it is very important to considering this feedback effect during the damage of material. By means of this model, we calculated the threshold fluences of the film and time-resolved excitation process in our pump-probe reflectivity. The theoretical results were in good agreement with the experimental measurements. Acknowledgements

4

pulse width: 50 fs -50 fs +2 fs +50 fs

2

This work was supported by the Chinese National Natural Science Foundation (No. 60108002) and Chinese National Major Basic Research Project (No. G1999075200). The authors thank Xuejun Zha for the program assistance.

1

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3

I/I0

k1

0.0

0

0

1 Optic depth (μm)

Fig. 5. The distribution of laser intensity.

2

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