Modeling the effect of nanosecond laser conditioning on the femtosecond laser-induced damage of optical films

Zehan Li; Juan Du; Yuanan Zhao; Yueliang Wang; Yuxin Leng; Jianda Shao

doi:10.1364/OE.23.014774

1. Introduction

Improving the performance and increasing the laser-induced damage threshold (LIDT) of thin film components have been key issues in laser industry for many years [1,2]. In the nanosecond regime, laser conditioning has been confirmed as an effective method for improving the LIDT of the optical coatings [3–8], which is due to the desorption of contaminants [4,5] or the elimination of the defects and absorbers in subsurface [6–8] to avoid the occurrence of catastrophic damage. However, in our previous work [9], we found the femtosecond LIDT of Ta₂O₅/SiO₂ high reflectors were decreased after nanosecond laser conditioning and supposed that some irreversible changes had occurred in the host medium after conditioning, but direct experimental proof and appropriate model were lacking at that time. It has been found by Mero et al. that the damage threshold of dielectric films will be reduced when it is exposed to multiple femtosecond pulses [10], so it is meaningful to investigate whether the improvement in the nanosecond laser damage tests would transfer to the femtosecond regime.

Recently, with the help of UV femtosecond laser spectroscopy, ultrafast dynamics of laser-excited carriers in Al₂O₃/SiO₂ high reflectors before and after nanosecond laser conditioning are investigated by our group. A permanent mid-gap defect state is discovered, and the experimental result directly provides the decay lifetime constants of carrier population as the relaxation time of electrons. The aim of this paper is to evaluate the effect of nanosecond laser conditioning on the femtosecond laser-induced damage of optical films systematically. A theoretical model including MPI, AI and decays of electrons with one defect state is built to simulate the evolution of electron density in the conduction band. Series of thin films (Al₂O₃, HfO₂, SiO₂ films, 400 nm 30° AOI Al₂O₃/SiO₂ high reflectors) after nanosecond laser conditioning by Raster-scanning have been investigated. Both the experimental result and theoretical calculation agree very well with each other. By comparing the LIDT results of our samples to the model, the corresponding values of the absorption cross section of electrons in defect state after laser conditioning have been calculated. To the best of our knowledge, this is the first study on modeling the effect of nanosecond laser conditioning on the femtosecond laser-induced damage with clear experimental evidence.

2. Experimental details

2.1. Fabrication of samples

We prepare four kinds of optical films as samples, namely HfO₂, Al₂O₃, SiO₂ single layers and Al₂O₃/SiO₂ HR. The reference wavelength of Al₂O₃/SiO₂ HR is 400 nm with the incidence angles of 30°. The coating design of reflectors is G|(LH)³⁰ 4L|A, where H and L denote the high-refractive index material Al₂O₃ and the low-refractive index material SiO₂, respectively, with one quarter wavelength optical thickness (QWOT), G represents the K9 substrate (Φ50mm × 5mm), and A is the incident medium (air). The samples are prepared by dual-ion beam sputtering (DIBS) in Veeco coating equipment. All of them are used the same deposition parameters.

2.2. Nanosecond laser conditioning

The nanosecond laser conditioning of samples is performed by a 8 ns, 30 Hz, 355 nm Nd:YAG laser system, which operates at the TEM₀₀ mode and generates linearly polarized Gaussian spatial beam profile laser pulses focused on the target plane with 1.3 mm spot size. According to ISO 21254 [11], we obtain the nanosecond LIDT of samples, referring that, four kinds of energy steps (20%, 40%, 60%, 80% of the LIDT) are chosen to modify the reflector surface by the style of Raster-scanning [12] in the mode of 1-on-1 (each sample site is irradiated by a single shot under one fixed fluence step). The scanning velocity is controlled to fulfill a beam overlap at 90% of the peak fluence. The fluence we used for laser conditioning is sub-threshold and the conditioning process is undamaged.

2.3. Femtosecond laser damage experiments

In femtosecond LIDT test, a commercial Ti:sapphire laser system is utilized as the laser source, UV femtosecond laser pulses centered at 400 nm with pulse duration of 70 fs are used in LIDT test (see Fig. 1). The samples are mounted on a motorized x-y translation stage and positioned in the focal plane of lens with a focal length of 1.5 m. The effective area of the focal spot of laser beam achieved on the specimen surface is 3.05 × 10⁴ μm². 1-on-1 test is made according to ISO 21254 [11], The occurrence of damage origination is judged by the on-line intensity change of scattered light, then ascertained by off-line Leica polarizing optical microscope.

Fig. 1 Schematic drawing of the experimental set-ups for the femtosecond and nanosecond measurements.

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In nanosecond measurement, a half-wave plate and a polarizing beam splitter combination worked as a variable attenuator for varying the laser energy. In femtosecond measurement, a pair of circular variable filters worked as attenuator. The pulse energy is measured by an energy meter from a split-off portion of the beam, and the effective area of the focal spot of laser beam is measured by a beam profiler from a split-off portion of the beam. The energy meter and the beam profiler are connected to the computer, during LIDT measurement, the pulse energy and the effective area can be monitored simultaneously, respectively. So we can control the incident fluence precisely and real-timely.

In this experiment, the LIDTs of samples are determined by the maximum value of all the laser fluence with 0% damage probability. The experimental LIDTs of samples before and after laser conditioning are listed in Table 1. It can be seen that the LIDTs of the samples after laser conditioning are lower than the one before conditioning slightly. That means the nanosecond laser conditioning has negative effects on enhancing the laser resistance of samples in the femtosecond region. The LIDTs are determined by the relation of the pulse energy and the effective area of laser beam’s focal spot, which are given by averaging the data of 20 sites under irradiation at each fluence step. Because the fluctuation of laser energy ∆x is about 2.7% in femtosecond measurement (4.8% in nanosecond measurement) and the fluctuation of the effective area ∆y is about 2% in femtosecond measurement (3.1% in nanosecond measurement), so the uncertainty of the LIDT ∆ ( $Δ = \sqrt{Δ x^{2} + Δ y^{2}}$ ) is about 3.7% (5.7% in nanosecond measurement) as the error budget of the fluence shown in Fig. 2. Although the reduction of femtosecond LIDT is quite smaller than the increase of nanosecond LIDT, but the overall reducing trend of LIDT after conditioning can’t be neglected.

Table 1. The 8 ns and 70 fs LIDT of samples before and after laser conditioning.

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Fig. 2 The damage probability curve of Al₂O₃/SiO₂ reflectors before (a) and after (b) laser conditioning.

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We take the damage probability curve of Al₂O₃/SiO₂ reflectors before and after laser conditioning for example. It should be noted that, after nanosecond laser conditioning, the femtosecond damage of samples are less deterministic then before. The reflectors after conditioning have a wider range of fluence interval with damage probability between 0% and 100% as shown in Fig. 2. The phenomenon may reveal that the laser conditioning process increases the defect density of samples, and that is the presentation of the increase of the absorption cross section of electrons in defect state (σ) which we will discuss in section 3.

2.4. Damage morphology analysis

The fine morphologies and corresponding depth information of damage craters are characterized by Auriga scanning electron microscope (SEM) and Dektak surface profiler. In 1-on-1 damage test, the typical damage craters of all samples before and after laser conditioning present similar flat bottom morphologies with delaminating feature of the outer layers flake off from inner materials as shown in Fig. 3(c) and 3(a), which is believed to be associated with the step decrease characteristic of the normalized electric field intensity (NEFI) from the outer to the inner interfaces of Al₂O₃ and SiO₂ materials.

Fig. 3 The typical damage craters of Al₂O₃/SiO₂ reflectors after (a) and before (c) laser conditioning; the crater depth information after laser conditioning (b); NEFI distribution in the outer fifteen layers of Al₂O₃/SiO₂ reflectors irradiated by 400 nm laser (d). The area in blue ellipse in (d) represents the weakest position vulnerable to ablation.

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Obviously, the crater depth closely corresponds to the NEFI distribution in the outer four layers of the Al₂O₃/SiO₂ reflector. The strongest NEFI is located in 351 nm as depicted by dashed ellipse in Fig. 3(d), namely, in the second interface of 2H|3L (the second layer Al₂O₃ and third layer SiO₂) layers. From the Fig. 3(b), we know that the crater depth after laser conditioning is 335 nm. The depth of the first Al₂O₃ layer is from 286 nm to 351 nm. That means the laser ablation first occurs in the Al₂O₃ layer, the 2H layer near the interface of 2H and 3L, which is identified with subsequent theoretical calculation.

3. Theoretical analysis

According to our previous work [9], the reduction of the femtosecond LIDT of Ta₂O₅/SiO₂ high reflectors was due to the irreversible change occurred in the host medium after conditioning, and we detected a mid-gap defect state by UV femtosecond laser spectroscopy in Al₂O₃/SiO₂ HR after nanosecond laser conditioning. So we bring a mid-gap defect state in our theoretical model, which is based on MPI, AI, and decays with one laser-induced defect state, to simulate the evolution process of the electron density in the conduction band; a simplified energy diagram is shown in Fig. 4. Both the native and laser-induced defects can contribute the seed electrons in the conduction band and then the electrons are heated rapidly by the pulse resulting in further collision ionization. When the electron density in the conduction band reaches the critical plasma density N_cr, which is generally considered as the damage criterion, the respective plasma wave resonates with the incident laser wavelength. After that, the material absorbs laser radiation strongly through the process of inverse bremsstrahlung resulting in permanent structural changes and damage occurs. It should be noted that, after laser conditioning, the amount of initial seed electron which can be ionized to the conduction band has been observed to be increased in ultrafast laser spectroscopy experiment, as compared with the one without laser conditioning. And the absorption feature of these extra seed electrons is different from those contributed from valence band, but similar with those at the mid-gap state. It means that the mid-gap electronic defect inside the films, provide additional initial electrons to the conduction band, and hence promote the evolution process of femtosecond laser damage in the fs range. The relaxation time of electrons in UV Al₂O₃/SiO₂ reflectors from conduction band to valence band (T_cv = 12 ps) and to the defect state (T_cd = 2.5 ps) are determined, and the one from the defect state to valence band is expected to be T_dv = 100 ps. The parameters in SiO₂ have also been detected in our previous work [13].

Fig. 4 Simplified energy diagram for electron excitation and relaxation in HfO₂, Al₂O₃ or SiO₂ after nanosecond laser conditioning.

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We choose Keldysh’s photon ionization model [14,15] and Drude’s avalanche ionization model [16–18] as the basic electron excitation process, and refer to the similar study about the defect state [10,19,20], we make the corresponding kinetic rate equations for the CB electron density n and the defect state electron density n_d as follows:

\frac{d n}{d t} = W_{M P I} (I (t)) + W_{A I} (I (t)) \cdot n (t) - \frac{n (t)}{T_{c v}} + σ n_{d} (t) \cdot \frac{I (t)}{ℏ ω} - \frac{n (t)}{T_{c d}} (1 - \frac{n_{d} (t)}{n_{d, \max}})

\frac{d n_{d}}{d t} = \frac{n (t)}{T_{c d}} (1 - \frac{n_{d} (t)}{n_{d, \max}}) - σ n_{d} (t) \cdot \frac{I (t)}{ℏ ω} - \frac{n_{d} (t)}{T_{d v}}

Where W_MPI(I(t)) is the MPI rate described by the Keldysh theory [14,15]:

\begin{array}{l} W_{M P I} (I (t)) = \frac{2 ω}{9 π} (^{\frac{m_{e}^{*} ω}{ℏ}) \frac{3}{2}} Φ (\sqrt{2 〈 {E^{'}}_{g} / ℏ ω + 1 〉 - 2 {E^{'}}_{g} / ℏ ω}) \\ \times \exp {2 〈 {E^{'}}_{g} / ℏ ω + 1 〉 (1 - \frac{1}{4 γ^{2}})} {(\frac{1}{16 γ^{2}})}^{〈 {E^{'}}_{g} / ℏ ω + 1 〉} \end{array}

The Keldysh parameter (adiabaticity parameter) for solid medium is

γ = ω \sqrt{m_{e}^{*} E_{g}} / e E

, at two extreme limits of the field (γ >> 1 and γ << 1), Keldysh’s photon ionization (PI) rate asymptotically approaches multiphoton ionization and tunneling ionization as might be expected from an analogy with the atomic case. In our situation, for example in Al₂O₃, the value of γ is greater than 196, it is reasonable to use such MPI formula as an approximation of the Keldysh’s PI rate. W_AI(I(t)) denotes the AI rate calculated according to Drude’s ionization model [16–18]:

W_{A I} (I (t)) = \frac{I (t)}{E_{g}} \cdot \frac{e^{2}}{c ε_{0} n_{0} m_{e}^{*}} \cdot \frac{τ_{c}}{1 + ω^{2} τ_{c}^{2}}

Where τ_c means the resulting collision time reciprocal to the electron density:

τ_{c} = \frac{16 π ε_{0}^{2} \sqrt{m_{e}^{*} {(0.1 E_{g})}^{3}}}{\sqrt{2} e^{4} n (t)}

The critical electron density is given by [16]

n_{c r} = ε_{0} m_{e}^{*} ω^{2} / e^{2}

The power density of laser pulse can be written as

I (t) = \frac{1}{2} c n_{0} ε_{0} {| E (t) |}^{2}

A Gaussian temporal pulse shape is given by

I = I_{0} \exp [- 4 \ln (2) {(t / τ_{p})}^{2}]

The pulse fluence is

F_{i} = {(π / \ln 2)}^{1 / 2} I_{0} τ_{p} / 2

In Eqs. (1)-(9), σ means one photon absorption cross section of electrons in defect state; ħ is the reduced Planck constant, and ω is the incident laser frequency;

m_{e}^{*}

is the reduced effective mass of the conduction electron and the valence hole shown by

m_{e}^{*} = m_{e} m_{h} / (m_{e} + m_{h}) \approx 0.5 m_{e}

, m_e (9.10938215 × 10⁻³¹ Kg) and m_h are effective conductivity masses of electrons and holes, respectively. Φ describes the Dawson function. E_g means the intrinsic material band-gap, and

{E^{'}}_{g}

represents the material effective band-gap when irradiated by laser pluses and shown by

{E^{'}}_{g} = E_{g} [1 + (1 / 4 γ^{2})]

. The notation

〈 〉

means the integer part of the argument. e stands for the electron mass, and E denotes the electric field amplitude of the incident laser. c and ε₀ mean the velocity of light and the permittivity of free space, respectively. n₀ denotes the medium refractive index and τ_p is the incident laser pulse duration.

A suitable model should not only include necessary physical process, but also have similar results with experiments. In our model, by giving a pulse fluence F_i, we could solve the CB electron density n. Then increase the pulse fluence gradually until the CB electron density can reach the critical electron density, we can get the breakdown threshold fluence F_th. In the process of our calculations, all the parameters we used in Eqs. (1)-(9) can be determined by references or experimental results. Some important parameters are listed in Table 2, with that we get our theoretical simulation results listed in Table 3. Comparing the experimental results listed in Table 1, the simulation LIDT values agree quite well with the experimental ones. The reduction of the LIDT indicates that irreversible changes occurred in the host medium after laser conditioning. Hence, we attribute the LIDT reduction to the role of the electronic defect state, which directly provided initial seed electrons from the defect state into the conduction band [20]. In the following, we will discuss the role of the initial density of the defect state electrons n_d0 and the absorption cross section of electrons in defect state σ.

Table 2. List of parameters used in the theoretical calculation

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Table 3. The theoretical and experimental femtosecond LIDT of samples.

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The Fig. 5(a) displays the evolution of the breakdown threshold fluence (F_th) with different values of n_d0. It can be seen that, when n_d0 < 1 × 10¹⁹ cm⁻³, the F_th approaches the maximum value, the exact value of n_d0 has no influence to the results. When n_d0 > 1 × 10¹⁹ cm⁻³, the F_th of Al₂O₃ or SiO₂ decreases quickly,the more n_d0 is, the less the F_th will be. So we choose the value of 1 × 10¹⁷ cm⁻³ is suitable, which is also picked by Emmert et al. [20].

Fig. 5 Calculated breakdown threshold as a function of the initial density (a) and the absorption cross section (b) of the defect state electrons.

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Consequently, when we ascertain the value of n_d0, the role of σ could be discussed. We put different values of σ into our model and get corresponding F_th as shown in Fig. 5(b). Obviously, when the value of σ is smaller than 1 × 10⁻²⁰ m², the F_th of all samples approach the corresponding maximum values, which is very close to the threshold without laser conditioning. When σ > 5 × 10⁻²⁰ m² (6.3 × 10⁻²⁰ m² for Al₂O₃, 1.1 × 10⁻¹⁹ m² for HfO₂), the F_th of SiO₂ decreases sharply, Emmert et al. have got the similar result in multiple-pulse breakdown threshold [20]. By comparing the experimental LIDT of samples after laser conditioning listed in Table 1 to the F_th of Fig. 5(b), we get the certain corresponding σ of all samples as listed in Table 2. It is logical to make the interpretation that, as long as σ is smaller than 1 × 10⁻²⁰ m², the LIDT will be a constant, no matter the σ of native defect (maybe introduced by coating process) is increasing or decreasing. After nanosecond laser conditioning process, the value of σ increases to a certain value (1.26 × 10⁻¹⁹ m² for HfO₂, 6.65 × 10⁻²⁰ m² for Al₂O₃ and 5.65 × 10⁻²⁰ m² for SiO₂), the initial electrons in the laser induced defects will contribute seed electrons to the conduction band and hence decrease the laser induced damage threshold. Kozlowski [21] had used electron paramagnetic resonance (EPR) to study the electronic defect such as E' and oxygen hole centers in HfO₂/SiO₂ multilayer films after laser conditioning. Emmert [20] also reported that the existence of electronic trapping states (native or laser-induced defects) could obviously decrease the LIDT of oxide films in the femtosecond pulse regime. Therefore, we hold the opinion that the concentration of native electronic defects was elevated after laser conditioning, and hence accelerated the damage evolution process. In our future work, we will explore different laser conditioning processes including different laser fluence and repetition rate to find that whether the nanosecond irradiation conditions could affect the effect of the decrease in femtosecond LIDT.

4. Summary

In the present study, the effect of nanosecond laser conditioning on the femtosecond laser-induced damage behaviors of Al₂O₃, HfO₂, SiO₂, Al₂O₃/SiO₂ HR fabricated by DIBS has been studied. The results indicate that nanosecond laser conditioning reduces the femtosecond LIDT of optical thin films by 5%~10%. To explain this phenomenon, a theoretical model including MPI, AI, and relaxation of electrons in conduction band to the valence band and the one to the defect state generated by nanosecond laser conditioning, which is revealed by previous ultrafast time-resolved laser spectroscopy, is built to simulate the evolution of electron density in the conduction band. The decrease of LIDTs of samples is elucidated reasonably by the seed electron contribution from this electronic defect state in the band gap to conduction band, which could enhance the initial seed electron density in the conduction band for MPI and AI processes and accelerate the final breakdown. We calculate the values of the absorption cross section of electrons in defect state of our films after laser conditioning. In the nanosecond regime, the defects such as nodulars will absorb the laser energy intensively to cause the final breakdown, eliminating such absorbers will improve the films capability in laser resistance. However, in the femtosecond regime, the intrinsic field ionization mechanism dominates the damage process of optical thin films, if the nanosecond laser conditioning induces mid-gap electronic defects inside the films, as the one introduced in our theoretical model, it will promote the evolution process of femtosecond laser damage by increasing the initial seed electron in the ionization process. Hence, LIDT will be decreased in the femtosecond range. This is why the conditioning has different effect in both regimes.

Acknowledgments

This work is partly financially supported by 100 Talents Program of CAS, the National Basic Research Program of China (Grant No. 2011CB808101), and National Natural Science Foundation of China (Grant No. 61475169, 61221064).

References and links

1. T. W. Walker, A. H. Guenther, and P. E. Nielsen, “Pulsed laser-induced damage to thin-film optical coatings - part I: experimental,” IEEE J. Quantum Electron. 17(10), 2041–2052 (1981). [CrossRef]

2. J. Jasapara, A. V. V. Nampoothiri, W. Rudolph, D. Ristau, and K. Starke, “Femtosecond laser pulse induced breakdown in dielectric thin films,” Phys. Rev. B 63(4), 045117 (2001). [CrossRef]

3. M. E. Frink, J. W. Arenberg, D. W. Mordaunt, S. C. Seitel, M. T. Babb, and E. A. Teppo, “Temporary laser damage threshold enhancement by laser conditioning of antireflection-coated glass,” Appl. Phys. Lett. 51(6), 415–417 (1987). [CrossRef]

4. S. D. Allen, J. O. Porteus, and W. N. Faith, “Infrared laser-induced desorption of H₂O and hydrocarbons from optical-surfaces,” Appl. Phys. Lett. 41(5), 416–418 (1982). [CrossRef]

5. J. W. Arenberg and M. E. Frink, “On the role of water in the laser conditioning effect,” Proc. SPIE 756, 430–439 (1988).

6. A. B. Papandrew, C. J. Stolz, Z. Wu, G. E. Loomis, and S. Falabella, “Laser conditioning characterization and damage threshold prediction of hafnia/silica multilayer mirrors by photothermal microscopy,” Proc. SPIE 4347, 53–61 (2001). [CrossRef]

7. C. R. Wolfe, M. R. Kozlowski, J. H. Campbell, F. Rainer, A. J. Morgan, and R. P. Gonzales, “Laser conditioning of optical thin films,” Proc. SPIE 1438, 360–375 (1989).

8. Y. Zhao, T. Wang, D. Zhang, S. Fan, J. Shao, and Z. Fan, “Laser conditioning of ZrO₂:Y₂O₃/SiO₂ mirror coatings prepared by E-beam evaporation,” Appl. Surf. Sci. 239(2), 171–175 (2005). [CrossRef]

9. S. Chen, Y. Zhao, D. Li, H. He, and J. Shao, “Effect of nanosecond laser pre-irradiation on the femtosecond laser-induced damage of Ta₂O₅/SiO₂ high reflector,” Appl. Opt. 51(10), 1495–1502 (2012). [PubMed]

10. M. Mero, B. Clapp, J. C. Jasapara, W. Rudolph, D. Ristau, K. Starke, J. Kruger, S. Martin, and W. Kautek, “On the damage behavior of dielectric films when illuminated with multiple femtosecond laser pulses,” Opt. Eng. 44(5), 051107 (2005). [CrossRef]

11. ISO 21254, Laser and laser-related equipment—Test methods for laser-induced damage threshold, (2011).

12. L. M. Sheehan, M. R. Kozlowski, F. Rainer, and M. C. Staggs, “Large area conditioning of optics for high-power laser systems,” Proc. SPIE 2114, 559–568 (1994). [CrossRef]

13. J. Du, Z. Li, T. Kobayashi, Y. Zhao, and Y. Leng, “Ultrafast UV laser induced dynamics in dielectric coating materials before laser damage,” Proc. SPIE 9238, 923805 (2014).

14. L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP 20, 1307–1314 (1965).

15. A.-C. Tien, S. Backus, H. Kapteyn, M. Murnane, and G. Mourou, “Short-pulse laser damage in transparent materials as a function of pulse duration,” Phys. Rev. Lett. 82(19), 3883–3886 (1999). [CrossRef]

16. K. Starke, D. Ristau, H. Welling, T. V. Amotchkina, M. Trubetskov, A. A. Tikhonravov, and A. S. Chirkin, “Investigations in the nonlinear behavior of dielectrics by using ultrashort pulses,” Proc. SPIE 5273, 501–514 (2004). [CrossRef]

17. M. Jupé, L. Jensen, A. Melninkaitis, V. Sirutkaitis, and D. Ristau, “Calculations and experimental demonstration of multi-photon absorption governing fs laser-induced damage in titania,” Opt. Express 17(15), 12269–12278 (2009). [CrossRef] [PubMed]

18. X. Jing, Y. Tian, J. Zhang, S. Chen, Y. Jin, J. Shao, and Z. Fan, “Modeling validity of femtosecond laser breakdown in wide bandgap dielectrics,” Appl. Surf. Sci. 258(10), 4741–4749 (2012). [CrossRef]

19. D. N. Nguyen, L. A. Emmert, D. Patel, C. S. Menoni, and W. Rudolph, “Transient phenomena in the dielectric breakdown of HfO₂ optical films probed by ultrafast laser pulse pairs,” Appl. Phys. Lett. 97(19), 191909 (2010). [CrossRef]

20. L. A. Emmert, M. Mero, and W. Rudolph, “Modeling the effect of native and laser-induced states on the dielectric breakdown of wide band gap optical materials by multiple subpicosecond laser pulses,” J. Appl. Phys. 108(4), 043523 (2010). [CrossRef]

21. M. R. Kozlowski, M. Staggs, F. Rainer, and J. H. Stathis, “Laser conditioning and electronic defect measurements of HfO₂ and SiO₂ thin films,” Proc. SPIE 1441, 269–282 (1991). [CrossRef]

22. M. Mero, J. Liu, W. Rudolph, D. Ristau, and K. Starke, “Scaling laws of femtosecond laser pulse induced breakdown in oxide films,” Phys. Rev. B 71(11), 115109 (2005). [CrossRef]

23. M. Mero, A. J. Sabbah, J. Zeller, and W. Rudolph, “Femtosecond dynamics of dielectric films in the pre-ablation regime,” Appl. Phys., A Mater. Sci. Process. 81(2), 317–324 (2005). [CrossRef]

Material	HfO₂ (J/cm²)	Al₂O₃ (J/cm²)	Al₂O₃/SiO₂ HR (J/cm²)	SiO₂ (J/cm²)
70 fs LIDT before conditioning	0.37 ± 0.01	0.68 ± 0.02	0.69 ± 0.02	0.80 ± 0.03
70 fs LIDT after conditioning	0.34 ± 0.01	0.64 ± 0.02	0.65 ± 0.02	0.76 ± 0.03
Decrease of fs LIDT	8.1%	5.9%	5.8%	5.0%
8 ns LIDT before conditioning	8.5 ± 0.5	7.5 ± 0.4	15.2 ± 0.9	19.4 ± 1.1
8 ns LIDT after conditioning	11.4 ± 0.7	10.8 ± 0.6	29.5 ± 1.7	22.6 ± 1.3
Increase of ns LIDT	34%	44%	94%	16%

		HfO₂	Al₂O₃	SiO₂
λ	Incident laser wavelength	400 nm
τ_p	Incident laser pulse duration	70 fs
n₀	Medium refractive index	1.95	1.63	1.46
E_g	Intrinsic material band-gap	5.1 eV	6.5 eV	8.3 eV
σ	absorption cross section of electrons in defect state	1.26 × 10⁻¹⁹ m²	6.65 × 10⁻²⁰ m²	5.65 × 10⁻²⁰ m²
T_cv	Relaxation time from CB to VB	1 ps [22]	12 ps	1 ps [22]
T_cd	Relaxation time from CB to the defect state	3.9 ps [23]	2.5 ps	0.3 ps [13]
T_dv	Relaxation time from the defect state to VB	100 ps
n_d0	Initial density of the defect state electrons	1 × 10¹⁷ cm⁻³
n_dmax	Maximum density of the defect state electrons	1 × 10²⁰ cm⁻³ [20]

Material		HfO₂ (J/cm²)	Al₂O₃ or Al₂O₃/SiO₂ HR (J/cm²)	SiO₂ (J/cm²)
Theoretical	70 fs LIDT before conditioning	0.380	0.686	0.777
	70 fs LIDT after conditioning	0.341	0.651	0.760
	Decrease of fs LIDT	10.3%	5.1%	2.2%
Experimental	70 fs LIDT before conditioning	0.37 ± 0.01	0.69 ± 0.02	0.80 ± 0.03
	70 fs LIDT after conditioning	0.34 ± 0.01	0.65 ± 0.02	0.76 ± 0.03
	Decrease of fs LIDT	8.1%	5.8%	5.0%

Material	HfO₂ (J/cm²)	Al₂O₃ (J/cm²)	Al₂O₃/SiO₂ HR (J/cm²)	SiO₂ (J/cm²)
70 fs LIDT before conditioning	0.37 ± 0.01	0.68 ± 0.02	0.69 ± 0.02	0.80 ± 0.03
70 fs LIDT after conditioning	0.34 ± 0.01	0.64 ± 0.02	0.65 ± 0.02	0.76 ± 0.03
Decrease of fs LIDT	8.1%	5.9%	5.8%	5.0%
8 ns LIDT before conditioning	8.5 ± 0.5	7.5 ± 0.4	15.2 ± 0.9	19.4 ± 1.1
8 ns LIDT after conditioning	11.4 ± 0.7	10.8 ± 0.6	29.5 ± 1.7	22.6 ± 1.3
Increase of ns LIDT	34%	44%	94%	16%

		HfO₂	Al₂O₃	SiO₂
λ	Incident laser wavelength	400 nm
τ_p	Incident laser pulse duration	70 fs
n₀	Medium refractive index	1.95	1.63	1.46
E_g	Intrinsic material band-gap	5.1 eV	6.5 eV	8.3 eV
σ	absorption cross section of electrons in defect state	1.26 × 10⁻¹⁹ m²	6.65 × 10⁻²⁰ m²	5.65 × 10⁻²⁰ m²
T_cv	Relaxation time from CB to VB	1 ps [22]	12 ps	1 ps [22]
T_cd	Relaxation time from CB to the defect state	3.9 ps [23]	2.5 ps	0.3 ps [13]
T_dv	Relaxation time from the defect state to VB	100 ps
n_d0	Initial density of the defect state electrons	1 × 10¹⁷ cm⁻³
n_dmax	Maximum density of the defect state electrons	1 × 10²⁰ cm⁻³ [20]

Modeling the effect of nanosecond laser conditioning on the femtosecond laser-induced damage of optical films

Abstract

1. Introduction

2. Experimental details

2.1. Fabrication of samples

2.2. Nanosecond laser conditioning

2.3. Femtosecond laser damage experiments

2.4. Damage morphology analysis

3. Theoretical analysis

4. Summary

Acknowledgments

References and links

Cited By

Figures (5)

Tables (3)

Equations (9)

Optics Express