1. Introduction

Dispersive multilayer dielectric coatings have been developed for the past two decades since their invention in 1995 [1]. A range of applications for various pulse compression tasks has been demonstrated [2,3]. Different designs of dispersive mirrors, such as double-chirped mirrors [4,5], back-side-coated chirped mirrors [6], complementary chirped mirror pairs [2], high dispersion Gires-Tournois interferometer (GTI) type mirrors [7,8] and others [9] were created to meet the highly demanding requirements for the group delay dispersion versus bandwidth performance. The progress in the chirped mirror design and manufacturing allowed dispersion compensation up to −10000 fs² [10] or up to 1.5 octave bandwidth [2]. Such a bandwidth permits pulse compression up to a single cycle of the electric field oscillation [2]. Large optical systems developed by international teams (FEL, ELI, LMJ, NIF, PETAL) as well as smaller commercial laser systems operating in the ultrashort regime, allow development of modern analysis tools in spectroscopy, medicine, material processing and other fields. As a rule of thumb chirped mirrors feature lower LIDT if compared to standard Bragg mirrors [11]. Such LIDT behaviour is strongly related to the complicated design of multilayer structure and resonant origin of delay characteristics [12]. Since materials used for chirped mirror coatings have been extensively studied by the means of femtosecond pulse resistance [13,14], multilayer coatings require additional exploration as only several papers are addressing this topic. Optimization of inner EFI distribution was performed by several groups for high reflectors [15–17] and diffraction gratings [18]. Multilayer chirped mirror optical resistance studies were only performed in recent years [11,19–21]. To our best knowledge, only theoretical optimization of electric field distribution in chirped mirror structure was made [19]. It has been also shown that electric field distribution and resulting peak intensity inside chirped mirror can induce negative nonlinear effects in the fluence regime close to the LIDT value [21]. Despite these results, a clear experimental demonstration of the relation between the electric field intensity and LIDT values for chirped mirrors was never performed. To fill this gap we carried out an experimental study to optimize electric field intensity inside highly dispersive GTI and narrow band CM coatings.

2. Sample preparation

In this paper two GTI type multilayer coatings, as well as a pair of similar narrow band chirped mirrors, were designed with Optilayer software package [22]. The GTI-like interferometric structures with the electric field variation according to the angle of incidence (AOI) were designed using Ta₂O₅(H) and SiO₂(L) materials and consisted of the quarter wave of optical thickness (QWOT) or double QWOT layers at the wavelength of 1030 nm. Coating samples were deposited with the CEC IBS@lab ion beam sputtering (IBS) coating system with a zone target configuration. The optical broadband monitoring system with the spectral range of 400-1600 nm was used as a high-accuracy tool to control layer thickness. The dependence of the electric field strength on AOI inside a multilayer structure enabled us to change and control it accurately [23] while neglecting the influence of small manufacturing errors: as they change only the absolute values and keep the tendency of \E²\ versus AOI the same. Both designs and the resulting electric field distributions are shown in Fig. 1. For the first GTI structure [Fig. 1 (a)] electric field changes its amplitude as AOI is increased but the position of maximum electric field peak and distribution within a structure is maintained. GTI-1 structure with a double SiO₂ layer enhances electric field by a factor of 3.7-3.8 inside the structure at the AOI of 29 degrees for TE polarization in comparison to incident field amplitude. In this particular case changing the AOI enables us to analyse the LIDT behaviour in accordance with the electric field. Meanwhile, inside the GTI-2 structure the electric field distribution changes as the maximum at the Ta₂O₅/SiO₂ layer interfaces shifts to SiO₂ when the AOI changes from 0 to 40 degrees. This electric field behaviour enables us to study the LIDT at the interfaces of high and low refractive index materials and to compare the LIDT while relocating the maxima of the electric field from the layer interface to pure SiO₂ still keeping the same sample. For both aforementioned structures, the reflection curve shifts to the shorter wavelength as the AOI is increased but values of reflection vary by few percent in the range of interest – from 1010 to 1050 nm [Figs. 1(c) and 1(d)].

 

Fig. 1 Reflectance coefficient (a,c) and squared electric field distribution at 1030 nm wavelength (b,d) of GTI-1 (a,b) and GTI-2 (c,d) coatings.

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3. Experimental setup

Reflectance coefficient was measured with spectrophotometer Perkin Elmer “Lambda 950”, while GDD was measured with the white-light interferometer [24]. Both of these measurements confirmed negligible layer optical thickness error during sample preparation. Laser-induced damage threshold was measured at Vilnius University Laser Research Center (VULRC). Test samples were irradiated with 1030 nm, 180 fs (~11 nm spectral bandwidth at FWHM) laser pulses at 50 kHz repetition rate. Gaussian-like laser beam was focused down to 47.8 ± 0.13 µm (1/e² level of peak intensity) on the focal plane. LIDT testing was performed in accordance with 1-on-1 and S-on-1 test protocols [25,26]. Single pulses are extracted by using built in electro optical modulator, namely fast Pockels cell in combination with appropriate TTL signal control. Approximately from 600 to 800 sites have been tested on each sample. The uncertainty of laser-induced damage threshold measurements has been considered [27]. For morphological and structural analysis of the damaged sites analytic tools were used, including a scanning electron microscope (SEM) Helios Nanolab 650, a contact profilometer Veeco Dektak 150 and an optical microscope Olympus BX51. SEM measurements were chosen particularly to determine the cross-sections of the damaged sites for various samples corresponding to irradiation levels exceeding damaging fluence by few percent. Therefore, additional preparation of samples was needed before post-mortem morphology analysis. Sample coatings were additionally covered by conductive chromium layer of a thickness not exceeding several tens of nanometers. Furthermore, inspected damage locations were covered with a platinum layer in order to preserve damaged site structure from a mechanical influence of scattered ions. A microscopical cuboid piece of sample intersecting with particular damage site was etched using focussed ion beam (FIB) technology in order to observe its cross section. Such approach allowed us to correlate damage initiation layers within investigated coatings with electric field intensity of standing waves.

4. Results

The measured LIDTs for GTI-1 and GTI-2 are depicted in Figs. 2(a) and 2(b) respectively. A clear interdependence of maximum electric field and LIDT is observed for both 1-on-1 and 1000-on-1 measurement regimes, while latter being a less apparent due to so-called fatigue effect [28]. For the GTI-1 structure the LIDT values range from approximately 0.1 J/cm² to 0.36 J/cm² as the electric field intensity is reduced by a factor of 7. GTI-2 also exhibits the same tendency in the LIDT values with respect to AOI or the electric field strength. In this case absolute values of the electric field are twice lower due to much higher refractive index of Ta₂O₅ as compared to SiO₂ [Figs. 1(b)-1(d)]. However, at 40° AOI the distribution of the electric field is changed so that its maximum of electric field is positioned in the SiO₂ layer [Fig. 1(b)]. This fact does not change the LIDT and electric field interdependence as depicted in Fig. 2(b), which is still governed by the electric field strength in the high index layer.

 

Fig. 2 LIDT and theoretical electric field dependence on measurement angle (AOI) for GTI-1 (a) and GTI-2 (b) coatings.

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Several damaged sites of GTI-1 and GTI-2 coatings were inspected in detail with an optical microscope, a contact profilometer and a SEM. Both the contact profilometer and the optical microscope analyses have shown that the damage morphology is of a blister form with minor discrepancies from spherical shape [Figs. 3(a), 3(b), 3(d), 3(e), 3(g) and 3(h)]. In GTI-2 optical microscope images [Figs. 3(d) and 3(g)] complex shaped structures in the central zone of the damaged site are visible which are not observed with contact profilometer [Figs. 3(e) and 3(h)]. It may be explained that these structures are formed inside the coating beneath the surface. This fact indicates that the damage most likely was initiated inside the coating structure. For a further analysis of damaged sites SEM measurements of damage sites cross-sections were performed. Three measured cross-sections are displayed in Figs. 3(c), 3(f) and 3(i). It is possible in this way to indicate the exact layers and interfaces in which the damage initiation occurred. For all cases in Fig. 3, only the highly refractive index material Ta₂O₅ layers or interfaces with the highest electric field strength were damaged. In the case of GTI-1 the AOI = 0° damage site [Fig. 3(c)], even approximately double electric field strength in the SiO₂ layer did not inflict a bulk damage or any visible modification, while the nearby Ta₂O₅ layers were damaged. Based on the obtained results and observations, a strategy for a chirped mirror electric field optimization was formed: the electric field target was added in the last optimization step, considering the electric field strength in the Ta₂O₅ layers. Meanwhile, electric field strength in SiO₂ layers was allowed to grow without any limitations [see below].

 

Fig. 3 Damage morphology measured by dark field optical microscopy (a, d, g), transversal surface scan measurements by contact profilometer (b, e, h) and SEM cross section of the damaged sites (c, f, i); a-c GTI-1 sample AOI = 0°; d-f GTI-2 sample AOI = 0°; g-i GTI-2 sample AOI = 27°. Light and dark colour layers in SEM measurements indicate Ta₂O₅ and SiO₂ layers respectively. White and black dotted lines mark Ta₂O₅ and SiO₂ layers of maximum electric field intensity respectively. Platinum (Pt) layer overcoated just before SEM measurement is also designated in SEM scans.

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By considering the results and observations mentioned above, two additional chirped mirrors featuring different electric field distribution were designed. The first one was without electric field optimization (CM-1) and the second one - with electric field optimization (CM-2). The resulting coating designs are depicted in Figs. 4(a) and 4(b). Both designs are constructed of several parts: high reflection mirror (1-24 layers) and chirped structure. CM-2 is specific for the optimized design, because a tendency to increase thickness for the lower refractive index layers is observed. However, the both designs result in GDD = - 600 ± 100 fs² in the range from 1025 to 1055 nm and the reflectivity larger than 99.5% [Figs. 4(c) and 4(d)], though some minor difference in the GDD oscillations and the position of reflection spectra exists.

 

Fig. 4 Designs (a, b) and spectral parameters (c, d) of CM-1 (a) and CM-2 (b) chirped mirrors.

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While spectral performance and phase characteristics are similar, electric field distribution is considerably different as depicted in Fig. 5. For CM-1 chirped mirror the electric field maxima are distributed almost only on the high refractive index material layers and interfaces among the layers. Meanwhile, for CM-2 mirror electric field peaks are shifted to the SiO₂ layers while maintaining the electric field amplitude on the H layers as low as possible. For the CM-2 design the maximum electric field intensity is almost two times larger on the SiO₂ layers than on interfaces among different layers.

 

Fig. 5 Squared electric field distribution at 1030 nm wavelength for CM-1 (a) and CM-2 (b) mirrors.

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As expected, the measured LIDT for the electric-field-optimized CM-2 was approximately two times larger than for standard CM-1 for both used measurement regimes: in case of 1-on-1 measurement it was increased from 0.13 ± 0.01 J/cm2 (CM-1) to 0.28 ± 0.02 J/cm2 (CM-2) and in case of 1000-on-1 measurement: from 0.12 ± 0.01 J/cm2 (CM-1) to 0.26 ± 0.02 J/cm2 (CM-2). The increase in LIDT was expected as the electric field intensity was reduced nearly twice on Ta₂O₅ layers and interfaces for the CM-2 design as compared to the CM-1 design. The morphological analysis with a profilometer and an optical microscope indicates that the damage location is again inside the coating structure for both designs – no craters while observing the damage sites were noticed [Figs. 6(a), 6(b), 6(d) and 6(e)]. The SEM cross-sections analysis indicates damaged layers in coatings [Figs. 6(c) and 6(f)]. Selected sites were damaged at fluences approximately 20% higher than the LIDT values for both mirrors at S-on-1 regime. In the case of the CM-1, a damaged layer coincides with the layer of the largest electric field intensity [Fig. 6(c)]. In the CM-2 mirror [Fig. 6(f)] two layers were heavily damaged, and both of them slightly deviated from the maximum electric field intensity. In the first damaged layer (6-th layer from the air side i.e. top of the image), the electric field intensity reached 200%. In the second damaged layer (10-th layer from the air side i.e. top of the image), the electric field intensity was below 100% and was several times smaller than in the nearby layers. The reasons for the damage of this layer cannot be explained by the LIDT dependence on the static electric field enhancement calculated using the plane wave model. As laser damage is dynamic process, most likely electric field intensity is redistributed in time due to nonlinear laser matter interaction effects (Kerr effect [21] and free electron generation [29]). Further research must be done in order to validate either of them.

 

Fig. 6 Damage morphology measured by dark field optical microscopy (a, d), transversal surface scan measurements by contact profilometer (b, e) and SEM cross-section of the damaged sites (c, f); a-c CM-1 sample AOI = 0°; d-f CM-2 sample AOI = 0°. Light and dark colour layers in SEM measurements indicate Ta₂O₅ and SiO₂ layers respectively. White and black dotted lines mark Ta₂O₅ and SiO₂ layers of maximum electric field intensity respectively. Platinum (Pt) layer overcoated just before SEM measurement is also designated in SEM scans.

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In several previous publications [13], it has been shown that the LIDT for ultrashort pulses scales linearly according to a material band-gap to a certain extent [15] where the electric field intensity should be taken into account. In Fig. 7, a summary of the obtained results is presented. A clear interdependence between the electric field amplitude on the H layer and the LIDT values for both GTI and chirped mirrors can be noticed. A saturation in LIDT, limited by a combination of electric field intensity and the material “internal” damage threshold can be expected [30].

 

Fig. 7 LIDT dependence on the maximum squared electric field in damaged layers (H layers).

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5. Conclusions

We have examined LIDT behaviour as a function of electric field distribution inside chirped multilayer coatings such as GTI and CM. It was experimentally demonstrated that in most of the cases damage initiation position inside the multilayer stack correlates with electric field intensity maxima in high refractive index layers. Moreover, it was also demonstrated that shifting electric field intensity peaks from high refractive index layers to low refractive index layers leads to higher LIDT values of the coating. Specifically, CM with coating design optimized by redistribution of the electric field in multilayer stack showed two times higher LIDT value compared to a CM with the unoptimized design. Such an increase in resistance to laser radiation is of a crucial importance in ultrashort pulse generation and applications.