Effect of Electric Field Regulation on Laser Damage of Composite Low-Dispersion Mirrors

: Low dispersion mirrors are important because of their potential use in petawatt (PW) laser systems. The following two methods are known to increase the laser-induced damage threshold of low dispersion optical components: use of a wide-bandgap-material protective layer and control of electric ﬁeld distribution. By controlling the electric ﬁeld distribution of composite low-dispersion mirrors (CLDM), we shift the electric ﬁeld peaks from the material interface into the wide-bandgap material. However, the damage threshold of modiﬁed-electric-ﬁeld composite low dispersion mirror (E-CLDM) does not increase. Damage morphology shows that the initial damaged layer is Ta 2 O 5 . An immediate cause is the enhancement of the electric ﬁeld in internal layers caused by surface electric ﬁeld regulation. Theoretical calculations show that the damage threshold of CLDM or E-CLDM is determined by the competition results of bandgap and the electric ﬁeld of layer materials. The CLDM with different materials or different protective layer periods can be optimally designed according to the electric ﬁeld competition effect in the future. The theoretical results show that the enhancement of the electric ﬁeld in internal layers, caused by surface electric ﬁeld regulation, is an immediate cause of the threshold to decrease. These data suggest that the method of shifting the electric ﬁeld to wide-bandgap-material is no longer suitable for CLDM. The competitive effect between layer materials must be considered in the new electric ﬁeld modulation method. The competition effect can help us to obtain the best electric ﬁeld control results for CLDM with different material combinations and different protective layer periods. This study contributes to ﬁnding new ways to improve the LIDT of low-dispersion mirrors.


Introduction
The development of high-power petawatt (PW) laser promotes the development of physics, medicine, biology and materials science [1][2][3][4][5]. However, the generation of high-power pulses is constrained by the laser-induced damage threshold (LIDT) of optical elements. In particular, the LIDT of a low-dispersion mirror (LDM) is a weak point in the development of high-power ultrafast systems [6]. LDMs that can afford a broadband high-reflection (HR) spectrum, high LIDT, and stable group delay dispersion (GDD) play an essential role for PW lasers with pulses in the femtosecond regime [7]. However, reflection bandwidth, dispersion and damage threshold are interdependent, restricting each other [8]. Thereby, the LIDT of broad-bandwidth, low-dispersion mirrors have become a recognized research focus [8][9][10][11][12][13][14][15][16].
Quarter-wave optical thickness (QWOT) mirrors are the most commonly used low dispersion mirrors. The current work to raise the threshold is based on QWOT mirrors. Therefore, how to raise the threshold without sacrificing bandwidth and dispersion is very meaningful. Several researchers have reported experimental results for LDMs [17]. Such studies on a large number of samples are known [16,18]. Several methods are recognized to be effective in increasing the threshold of QWOT [19]. The first method is to increase the damage resistance by using wide-bandgap-material protective layers. Depositing a highly damaged resistant layer stack on a conventional quarter-wave mirror (composite low dispersion mirrors, CLDM) overcomes the tradeoff between LIDT and bandwidth. Takada et al. proposed a broadband mirror with high damage fluence for chirped-pulsed amplification of 10 fs pulses. This mirror consists of broadband TiO 2 /SiO 2 coatings and optimized high-damage-threshold ZrO 2 /SiO 2 coatings [7]. Patel et al. demonstrated that a modified Ta 2 O 5 /SiO 2 structure in which the high index layer is replaced by either HfO 2 or Y 2 O 3 for the three uppermost high-index layers results in an increase of 50% in LIDT when measured at 1 µm using 350 ps laser pulses [15]. The second method to increase the damage threshold is electric field regulation. According to previous research, the damage caused to optical elements occurs at a laser power that yields a critical electric field intensity in the coating material [20]. Apfel et al. derived a mirror structure with thinner high-index layers, reducing the peak electric field in the high-index material by 33% and shifting the peak electric field away from the interface [21]. Bellum et al. used a similar method, where at an angle of incidence of 45 • both the threshold of s-and p-polarization increased. [13]. Schiltz et al. observed that a modified-electric-field composite low dispersion mirror (E-CLDM) does not offer any definite damage performance advantages over the standard CLDM when tested for a 4 ns source and a 0.19 ns source [11]. However, the reason was not given in his report.
Compared with QWOT, the CLDM can increase the threshold without sacrificing the bandwidth by using wide-bandgap-material protective layers, and the method of electric field regulation can shift the peak electric field to the low-index material. Furthermore, the damage threshold in the femtosecond regime is more dependent on the electric field [12]. Therefore, we believe that combining the two methods can further increase the threshold in the femtosecond regime.

Materials, Design and Methods
We aim to design high-damage-threshold mirrors that meet a minimum reflectivity of 99.5% at a 45 • incidence angle for p-polarization with GDD < ±300 fs 2 over a spectral range of 750-850 nm. We choose SiO 2 as a low-index material (~1.46), which is well-known for exhibiting high resistance to femtosecond laser damage. And Ta 2 O 5 and Al 2 O 3 is as a high-index material. In this study, we choose Al 2 O 3 as the top high-index material which has a wide bandgap of 6.5 eV. The layer stack is represented by the formula G|(HL) m (XL) n−1 X|Air, where m is the periods of Ta 2 O 5 /SiO 2 stack; n is the periods of Al 2 O 3 layer, and H, L, and X denote Ta 2 O 5 , SiO 2 , and Al 2 O 3 , respectively, G is substrate. Figure 1a shows the calculated electric field distribution of CLDM for different protective layers. As the number of Al 2 O 3 periods increases, the electric field in the narrowbandgap material decreases. Meanwhile, the peak electric field intensity in Al 2 O 3 remains constant. To ensure that the protective layer work, we need as many protective layers (Al 2 O 3 ) as possible. However, different periods of the Al 2 O 3 protective layer significantly impact the GDD performance, as shown in Figure 2a. The calculated GDDs of CLDM and E-CLDM are obtained by the film design software TFCalc. As the number of Al 2 O 3 periods increases, GDD increases. When the number of periods n is 5, the maximum GDD ripple is just under ±300 fs 2 . Considering the electric field and dispersion, we replace Ta 2 O 5 with Al 2 O 3 in the five uppermost high-index layers. The layer stack is represented by the formula G|HL) 16 (XL) 4 X|Air. The initial design is a Ta 2 O 5 -Al 2 O 3 /SiO 2 composite mirror with 41 layers. This design combines the superior optical properties of Ta 2 O 5 and the higher damage threshold of Al 2 O 3 . The layer structure of the quarter-wave opticalthickness composite mirror is shown in Figure 3a and the electric field intensity distribution in the proximity of the Ta 2 O 5 -Al 2 O 3 interface is shown in Figure 1a (n = 5). The electric field distribution shows that the peaks' electric fields are located at the material interfaces, which can easily lead to damage, and that the maximum field intensities at the Al 2 O 3 and Ta 2 O 5 interfaces are 1.2 and 0.33, respectively.  When n > 5, the GDD ripple does not meet the requirements; (b) E-CLDM, when n = 5, the modified design has a superior dispersion value of ±175 fs 2 , compared to the value of ±300 fs 2 for the CLDM stack. However, for n > 5, the GDD ripple does not meet the requirements.
The design E-CLDM, based on the initial design, is optimized such that the electric field is shifted away from the material interfaces and into the low-index high-damage threshold material (SiO 2 ). The electric field distribution of E-CLDM for different n is shown in Figure 1b. We keep the electric field in Al 2 O 3 and SiO 2 constant for different n. As the number of Al 2 O 3 periods increases, the electric field in the Ta 2 O 5 decreases. However, compared with the electric field in CLDM, the electric field in Ta 2 O 5 of E-CLDM is higher. The layer profile of E-CLDM (n = 5) is shown in Figure 3b. It is obvious that the thickness of the Al 2 O 3 is decreased, while that of the low-index material is increased [21]. The electric field distribution is shown in Figure 1b    The modified design has superior dispersion value of ±175 fs 2 , compared to the value of ±300 fs 2 for the CLDM stack. However, for n > 5, neither CLDM nor E-CLDM meets the requirements of dispersion.

Fabrication
Mirrors based on Figure 3a,b were fabricated by dual-ion-beam sputtering technique (Spector, Veeco) with two ion sources (16 cm main source and 12 cm assistant source). The high-energy argon ions produced by 16 cm main source bombard the target (Ta, Al, SiO 2 ). The main function of the 12 cm assistant ion source is the pre-cleaning of the substrate and the improvement the coating absorption, making the coating more dense and bonding with the substrate stronger. The background pressure is 10 −4 Pa and the substrate baking temperature is 120 • C.

Reflectivity
The reflection spectrum was measured with a Perkin-Elmer (Lambda 1050) spectrophotometer. The reflectivities of the two sample types for p-polarization at 45 • AOI are shown in Figure 4. This is consistent with that expected for the E-CLDM stack, which performs similarly to the CLDM stack. Both E-CLDM and CLDM stacks provide a reflectivity of 99.5% over a spectral range of 750-850 nm.

Damage Threshold
A laser damage test for two types of samples was performed in the 1-on-1 mode [22]. Pulses were generated by a Ti:sapphire laser system with an 800 nm central wavelength and a pulse duration of 30 fs, and were p-polarized and incident at 45 • . The spectral range is 800 (±35 nm). The measurement spot area is 0.221 mm 2 and the error range is 3%. The experimental setup is shown in Figure 5. A CCD camera was used to observe the damage in real time. Firstly, we measured the damage threshold of three low-dispersion mirrors, including CLDM, E-CLDM and 41 layers quarter-wave optical thickness mirror (Ta 2 O 5 /SiO 2 ), as shown in Figure 6. Compared to QWOT, which comprises a Ta 2 O 5 /SiO 2 stack and has a low damage threshold of 0.32 J/cm 2 , the damage threshold was increased by 50% to 0.48 J/cm 2 for CLDM. However, contrary to our expectations, the damage threshold of E-CLDM was found to be lower than that of CLDM at only 0.41 J/cm 2 . In other words, electric field regulation did not increase the damage threshold of the composite mirror. However, the damage thresholds of both CLDM and E-CLDM were higher than that of QWOT.

Damage Morphology
To explain why electric field regulation would decrease the damage threshold of a composite mirror, the damage morphology of the E-CLDM stack was observed by scanning electron microscopy. As shown in Figure 7, the SEM results suggest that while the initial damage morphology (Figure 7a) occurred at a laser pulse fluence of 0.43 J/cm 2 , the other two damage morphologies (Figure 7c,d) occurred at higher fluences. The beam is incident obliquely from the right side of the picture. Firstly, at a laser fluence of 0.43 J/cm 2 , an inner layer material was melted and gasified, and the resulting gas pressure deformed the outer layer, forming a protrusion. At a fluence of 0.45 J/cm 2 , the internal pressure exceeded the limit stress of the layer, and thus, damaged the protrusion structure. As the fluence was further increased to 0.5 J/cm 2 , the bulge structure was detached and exposed to a damage pit. (e) diagrammatic sketch of (d). At a laser fluence of 0.43 J/cm 2 , an inner layer material was melted and gasified, and the resulting gas pressure deformed the outer layer, forming a protrusion. At a fluence of 0.45 J/cm 2 , the internal pressure exceeded the limit stress of the layer, and thus, damaged the protrusion structure. As the fluence was further increased to 0.5 J/cm 2 , the bulge structure was detached and exposed to a damage pit. The real thickness of Al 2 O 3 /SiO 2 stack is consistent with the design thickness. The initial damage layer is located in the Ta 2 O 5 layer.
To demonstrate the initial damage layer, we further observed the cross-sectional morphology after focused-ion-beam sectioning. The cross-sectional morphology of region 1 of the protrusion is shown in Figure 7d and the diagrammatic sketch of Figure 7d is shown in Figure 7e. Because the atomic number of Al is close to that of Si, the Al 2 O 3 /SiO 2 stack layer cannot be clearly observed. However, the first Al 2 O 3 layer and Ta 2 O 5 layer can be observed. A precise measurement shows that the distance between the first Al 2 O 3 layer and the Ta 2 O 5 layer is 1535 nm, and the design distance is 1542 nm. These data suggest that the position of the layer is accurate. The white layers are Ta 2 O 5 and black layers are SiO 2 .
It is unexpected that the initial damage site is located in the Ta 2 O 5 layer. Taken together, these results suggest that the wide-bandgap material Al 2 O 3 has no protective effect on the narrow-bandgap material Ta 2 O 5 . This causes the damage threshold of E-CLDM to be lower than that of CLDM.

Discussion
We next consider why the initial damage layer is Ta 2 O 5 . The threshold values presented in Section 4.2 were calculated without considering the electric field distribution. If the distribution is considered, internal thresholds that are characteristic for the layers will be obtained. Therefore, if the initial damage layer for different coatings is made of the same material, we can calculate the relations among damage thresholds of different designs from the electric field distribution. Thus, the theoretical damage threshold can be calculated according to Equation (1) [16,23].
Here F t is the theoretical damage threshold of the front surface of the sample, F int is the internal threshold of layer X, E inc is the magnitude of the incident electric field, and E max is the magnitude of the electric field inside layer X.
The internal threshold of a Ta 2 O 5 layer can be calculated from the damage threshold of Ta 2 O 5 /SiO 2 , as shown in Figure 6. The damage threshold of SiO 2 and Al 2 O 3 layers can be obtained from the previous work of our group [24,25]. Thus, the internal thresholds of Ta 2 O 5 , Al 2 O 3 , and SiO 2 layers are 0.101, 0.337, and 0.430 J/cm 2 , respectively. Figure 8 shows theoretical damage thresholds of CLDM or E-CLDM with different numbers of Al 2 O 3 periods. The threshold of CLDM or E-CLDM is decided by the lowest threshold value in layer materials. From Figure 8a, a competitive relationship exists between Ta 2 O 5 and SiO 2 in CLDM. We find that the threshold in Ta 2 O 5 layer increases with the number of Al 2 O 3 layer periods, because at different Al 2 O 3 periods, the electric field in Ta 2 O 5 decreases as shown in Figure 1b. So, if n < 5, the threshold in Ta 2 O 5 layer is always the lowest value, that is, the damage source is in internal layer Ta 2 O 5 . In the case of n = 5 or n > 5, the electric field in Ta 2 O 5 is at a very low level resulting in the threshold in Ta 2 O 5 exceeds that in Al 2 O 3 . The damage source is in surface Al 2 O 3 layer. The electric field distribution of E-CLDM for different n is shown in Figure 1b. Compared with the electric field intensity of Ta 2 O 5 in CLDM, the stack of E-CLDM has a higher intensity in Ta 2 O 5 . It implies that the surface electric field regulation causes the enhancement of the electric field in narrow band material Ta 2 O 5 . The threshold of E-CLDM with different numbers of Al 2 O 3 periods is shown in Figure 8b. Compared with Figure 8a, the competitive relationship exists between Ta 2 O 5 and SiO 2 . If n < 9, the threshold of E-CLDM decreased because of the enhancement of the electric field in Ta 2 O 5 . n = 9 is an inflection point and the electric field in Ta 2 O 5 is at a low level resulting in the threshold in Ta 2 O 5 layer exceeds that of SiO 2 . In the case of n > 9, the damage source is in SiO 2 , and the threshold of E-CLDM keeps constant. So the optimal n for E-CLDM is 9. The threshold of E-CLDM for n > 9 has no significant increase compared with CLDM. And considering the GDD, n = 9 is not a good choice. In summary, the method of shifting the electric field to wide-bandgap-material is no longer suitable for CLDM.
The competition effect can help us to obtain the best electric field control results for CLDM with different material combinations and different protective layer periods. We need to control the electric field according to the competition results of bandgap and the electric field of layer materials.
According to the electric field distribution shown in Figure 1 (n = 5), we calculate the theoretical threshold in Ta 2 O 5 , Al 2 O 3 , and SiO 2 layers of E-CLDM are 0.50, 1.20, and 0.84 J/cm 2 , respectively. Clearly, the theoretical threshold of E-CLDM is 0.50 J/cm 2 and the initial damage layer is Ta 2 O 5 . The measured threshold is 0.41 J/cm 2 . These data are consistent with the cross-sectional morphology, as shown in Figure 7d. Similarly, the theoretical thresholds in Ta 2 O 5 , Al 2 O 3 , and SiO 2 layer of CLDM for n = 5 are 0.86, 0.78, and 0.94 J/cm 2 . The theoretical threshold of CLDM is 0.78 J/cm 2 and the measured threshold is 0.48 J/cm 2 . Both the calculated damage thresholds are higher than the corresponding experimental thresholds. We attribute this discrepancy to low adhesion at the layer interfaces and residual stress that lower the threshold.
The internal threshold of Al 2 O 3 is calculated through a single Al 2 O 3 layer and that of Ta 2 O 5 is calculated through Ta 2 O 5 /SiO 2 . So this is the reason why there is a large deviation between the calculated result of CLDM and the experimental result. The relation between the calculated damage thresholds of the two samples (CLDM and E-CLDM) agrees with the experimental results.

Conclusions
In summary, we combined the methods of electric field regulation and wide-bandgap protective layers in the femtosecond regime. The damage threshold of two types of composite low-dispersion mirrors, with and without electric field regulation, are investigated using femtosecond laser pulses. The results show that the damage threshold of E-CLDM is lower than that of CLDM. The internal threshold is used to calculate the theoretical threshold of all samples. The damage threshold of CLDM or E-CLDM is determined by the competition results of bandgap and the electric field. The damage properties of layer materials are determined by bandgap and electric field distribution. The theoretical results show that the enhancement of the electric field in internal layers, caused by surface electric field regulation, is an immediate cause of the threshold to decrease. These data suggest that the method of shifting the electric field to wide-bandgap-material is no longer suitable for CLDM. The competitive effect between layer materials must be considered in the new electric field modulation method. The competition effect can help us to obtain the best electric field control results for CLDM with different material combinations and different protective layer periods. This study contributes to finding new ways to improve the LIDT of low-dispersion mirrors.  Informed Consent Statement: Informed consent was obtained from all subjects involved in the study.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy and secret.

Conflicts of Interest:
The authors declare no conflict of interest.