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Abstract
We report a novel modified Gires–Tournois interferometer (MGTI) starting design for high-dispersive mirrors (HDMs). The MGTI structure combines multi-G-T and conjugate cavities and introduces a large amount of dispersion while covering a wide bandwidth. With this MGTI starting design, a pair of positive (PHDM) and negative highly dispersive mirrors (NHDM) providing group delay dispersions of +1000 fs2 and -1000 fs2 in the spectral range of 750 nm to 850 nm is developed. The pulse stretching and compression capabilities of both HDMs are studied theoretically by simulating the pulse envelopes reflected from the HDMs. A near Fourier Transform Limited pulse is obtained after 50 bounces on each positive and negative HDM, which verifies the excellent matching between the PHDM and NHDM. Moreover, the laser-induced damage properties of the HDMs are studied using laser pulses of 800 nm and 40 fs. The damage thresholds of the PHDM and NHDM are approximately 0.22 J/cm2 and 0.11 J/cm2, respectively. The laser-induced blister structure of the HDMs is observed, the formation and evolution processes of the blister are evaluated.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The invention of chirped pulse amplification (CPA) [1] in 1985 broke the nearly 20 year plateau in laser peak power and ushered a new era for super intense ultrafast laser technology, where the peak power of ultrashort pulses has been increasing gradually and has reached the petawatt (PW) [2–4] and 10 PW level [5–9]. Diffraction gratings (DGs) [10] have been extensively used in CPA as key stretching/compressing components. They can provide a large amount of dispersion and easily broaden femtosecond pulses to the nanosecond regime, which is advantageous for the amplification of the pulse energy. However, DGs have the disadvantages of causing high losses and unavoidable third-order dispersion (TOD), as well as higher-order dispersion, which leads to distortion in ultrashort pulses.
Dispersive mirrors (DM, also known as chirped mirrors [11]) with properties of high reflection and precise phase control have been widely used as intracavity dispersion compensation components [12–17] and extra-cavity pulse compressors [18–21] in ultrashort lasers. Among these applications, the extra-cavity pulse compression requires a large amount of group delay dispersion (GDD), which makes the high dispersive mirror (HDM) [14–17,20–23] more desirable. The pursuit of higher GDDs and larger bandwidth is of great interest and importance for the advancement of ultrafast lasers. However, the amount of GDD and working bandwidth contradict each other. The broader the spectrum, the lower the nominal value of GDDs can be achieved. Most HDMs provide a negative GDD, which is referred to as a negative high dispersive mirror (NHDM) because the materials employed in laser systems are in a normal dispersion regime in the visible and near-infrared regions. The largest negative GDDs ever reported at the central wavelength of 800 nm were -1300 fs2 with a bandwidth of 40 nm [21]. Moreover, a positive high dispersive mirror (PHDM) can be used as a pulse stretcher. Compared to DGs, PHDM and NHDM have a higher reflection efficiency and can provide a flatter GDD with considerably lower higher-order dispersion. Additionally, HDMs introduce little spatial chirp, pulse front tilt, and simple implementation in laser systems. Based on these advantages, PHDM and NHDM pairs could be an alternative way to stretch or compress pulses in the CPA technique.
In this study, a pair of PHDM and NHDM, introducing GDDs of +1000 fs2 and -1000 fs2 in the spectral range of 750 nm to 850 nm, was designed, fabricated, and characterized, which are the largest GDDs reported in a bandwidth of 100 nm to the best of our knowledge. A new modified Gires–Tournois interferometer (GTI) with a combination of multi-G–T and conjugate cavities is proposed to design the HDMs. The transmittance and GDD properties were characterized. We also simulated the pulse stretching and compression capabilities of both the PHDM and NHDM, validating the excellent matching between them. The laser-induced damage performance of HDMs and the evolution of the blister structure are also studied.
2. Design and production of positive and negative high dispersive mirror pair
Niobium pentoxide (Nb2O5) and silicon dioxide (SiO2) were chosen as layer materials to design the PHDM and NHDM. The refractive indices of both materials were specified by the Cauchy formula, with the coefficients presented in Table 1.
where λ is in µm and A1 and A2 are in µm2 and µm4, respectively.
Table 1. Cauchy formula coefficients for layer materials
For the PHDM, a novel starting design based on a modified Gires–Tournois interferometer (MGTI) was employed. The MGTI consists of three parts: a high-reflection stack, multi-G-T cavities, and conjugate cavities, which can be expressed as G/(HL)^n(HxL)^m(HyLH)^o(LyHL)^o/A, where G and A are the substrate and air, respectively, and H and L represent the high- and low-index materials (the optical thickness equals the quarter-wave of the reference wavelength). The high-reflection stack, multi-G-T cavities, and conjugate cavities are represented as (HL)^n, (HxL)^m and (HyLH)^o(LyHL)^o, respectively, where n, m, and o correspond to the periodic number of the high-reflection stack, multi-G-T cavities, and conjugate cavities, respectively, and x and y are the thickness coefficients of the G-T and conjugate cavities, respectively. Compared to the standard GTI, the MGTI with a combination of multi-G-T and conjugate cavities provide a larger amount of dispersion and cover a broader spectral range.
Based on the MGTI structure, the initial design of G/(HL)^7(H1.25 L)^16(H1.25LH)^16(L1.25HL)^16/A with the reference wavelength of 800 nm was applied. The PHDM was designed to operate at an angle of incidence (AOI) of 10° and with p-polarization. The GDD and reflectance target were set to +1000 fs2 and 100%, respectively, in the wavelength range of 750 nm to 850 nm. A variable metric algorithm was used to optimize the starting design. A merit function evaluating the discrepancies between the designed spectral characteristics and target specifications is defined as:
The final design of the PHDM consisted of 112 layers with a total physical thickness of 16.5 µm, and the thickness of each layer was between 30 nm and 400 nm, as shown in Fig. 1(a). The PHDM provides a GDD of approximately +1000 fs2 with a GDD oscillation of less than 60 fs2 and minimum reflectance of 99.84% in the wavelength range of 750–850 nm, as shown in Fig. 1(b).
For the NHDM, p-polarized light and an AOI of 10° were also employed. Moreover, it was designed to provide a -1000 fs2 GDD and compensate for the positive GDD introduced by the PHDM in the spectral range of 750 nm to 850 nm. The GD and reflectance were chosen as the target characteristics. The GD target was integrated with the GDD target.
where $GDD(\omega )$ equals -1000 fs2, ${\omega _1}$ and ${\omega _2}$ are the lower and upper limits of the angular frequency corresponding to 850 nm and 750 nm, respectively, and C is an arbitrary constant. The GD difference between 750 nm and 850 nm was approximately 360 fs. The designed reflectance target was set as 100%. Commercial Optilayer software [24] with powerful needle optimization and gradual evolution algorithms was applied to optimize the NHDM. The merit function is defined as follows:Consequently, a 120-layer NHDM design was obtained. The layer thickness ranged between 90 nm and 300 nm, resulting in a total thickness of 15.9 µm, as shown in Fig. 2(a). The NHDM provides a GDD of approximately -1000 fs2 with a minimum reflectance of 99.92% in the spectral range of 750–850 nm, as shown in the theoretical GDD and reflectance curves in Fig. 2(b).
Both the PHDM and NHDM were deposited on fused silica substrates using a Veeco Spector dual-ion beam sputtering plant. The primary ion source was used to generate, accelerate, and extract the ion beam with the help of a three-grid multi-aperture. The assistant ion source directly shining at the substrates can be exploited to pre-clean the substrates and optimize the stoichiometry of the thin films. The pressure in the coating chamber evacuated by a cyro-pump was approximately 1 × 10−6 mbar before deposition and increased to 1 × 10−4 mbar during the coating process owing to the input of the Ar and O2 gases. The Nb2O5 material was deposited on fused silica substrates by sputtering a pure Nb target with a purity of 99.95% and an O2 flow of 65 standard cubic centimeters per minute (sccm), whereas the SiO2 material was formed by sputtering a SiO2 target with a purity of 99.995% and an O2 flow of 40 sccm. Owing to the stable deposition rates, a time-control technique was utilized to monitor the layer thickness. The deposition rates of the Nb2O5 and SiO2 materials were approximately 0.21 nm/s and 0.18 nm/s, respectively.
3. Characterization of positive and negative high dispersive mirrors
3.1 Transmittance and GDD characteristics
The transmittance spectra of both the PHDM and NHDM were measured using a Perkin-Elmer Lambda 1050 spectrophotometer at an AOI of 10° in the wavelength range of 600–1200 nm. The GDDs of both the PHDM and NHDM were characterized at normal incidence with a white light interferometer [25]. The measured transmittance and GDD of the PHDM are shown in Fig. 3. As shown in Fig. 3(a), the measured transmittance spectra fit well with the theoretical spectra and the designed transmittance spikes were reproduced from the theoretical data. There is only a minor difference between the absolute values in the spike areas due to the low resolution of the spectrophotometer. The measured GDD of the PHDM is approximately 1000 fs2 with some oscillations, as shown in Fig. 3(b). These GDD deviations are mainly caused by measurement errors, where the GDD was measured at normal incidence instead of an AOI of 10°, resulting in increased GDD oscillations and spectral shifts. Moreover, because GDD is the second derivative of the phase to the angular frequency, even small errors in the measured phase result in large errors in the measured GDD. However, deposition errors that are inevitable in all coating plants could also play a role in causing GDD deviations. The correspondence between the measured and designed GDD is sufficient if the design sensitivity is considered. The experimental transmittance and GDD of the NHDM versus theoretical data are presented in Fig. 4. A good agreement between the measured and theoretical transmittance spectra is shown in Fig. 4(a). The measured GDD oscillates at approximately -1000 fs2 and fits better with the theoretical GDD at the normal incidence, as illustrated in Fig. 4(b). Even though larger GDD oscillations in measured GDD at the normal incidence were observed, better agreements between the designed and measured GDD at the normal incidence were obtained, as blue and red curves show in Fig. 3(b) and Fig. 4(b), which proved the successful development of both PHDM and NHDM.
Fig. 3. Comparison of theoretical and measured transmittance and GDD of the PHDM. (a) Transmittance spectra (b) GDD
Fig. 4. Comparison of theoretical and measured transmittance and GDD of NHDM. (a) Transmittance spectra (b) GDD
3.2 Pulse stretching and compressing analysis of the positive and negative high dispersive mirrors
Output pulses stretched by the PHDM and recompressed by the NHDM were simulated to study the pulse stretching and compression capabilities of the PHDM and NHDM, respectively. In the simulation process, we assumed that the input pulse was a Fourier-transform-limited Gaussian pulse with a pulse duration of 30 fs and covered a spectrum from 750 to 850 nm, which is the working range of the PHDM and NHDM. The temporal electric field of the input pulses was first converted into the frequency domain using the Fourier transform. Subsequently, the reflectance ${R_1}(\omega )$ and phase ${\varphi _1}(\omega )$ of the PHDM were applied to the spectral intensity and spectral phase of the spectrum, respectively. The temporal shape of the stretched pulses can be obtained by the inverse Fourier transform of the new spectrum. The pulse duration was calculated based on the temporal intensity. Moreover, to estimate the matching effect between the PHDM and NHDM, the stretched pulses were compressed by the NHDM with the same bounces. The spectral amplitude (spectrum) after the application of the PHDM was multiplied by the square root of the reflectance ${R_2}(\omega )\; $ and the spectral phase item ${e^{i{\varphi _2}(\omega )}}$ from the NHDM. The inverse Fourier transformation provided the final compressed pulse shape in the time domain. During the simulations, 50 reflections on both the PHDM and NHDM were employed, providing an absolute GDD of 50000 fs2. The entire calculation process is illustrated as follows.
The simulated input and stretched pulses are shown in Fig. 5(a). The input pulse was broadened to 4.47 ps after 50 bounces on the PHDM, as shown in the inset of Fig. 5(a). A comparison of the Fourier-limited and compressed pulses is shown in Fig. 5(b). The compressed pulse is quite similar to the Fourier limited input pulse, and there are only less than 8% losses in the pulse intensity with 50 reflections on both the PHDM and NHDM. Furthermore, the duration of the compressed pulse is approximately 32.2 fs and close to the Fourier limited pulse duration, which verified the compression capability of the NHDM and great matching between the PHDM and NHDM.
Fig. 5. Pulse analysis of the PHDM and NHMD. (a) Simulated output pulse reflected off the PHDM and input Fourier limited pulse. The inset shows the zoomed pulse shape. (b) Simulated output pulse reflected off the NHDM and input Fourier limited pulse. The pink and black curves represent the output and input pulses, respectively.
3.3 Laser induced damage properties of the positive and negative high dispersive mirrors
Laser-induced damage tests were performed using 40 fs laser pulses with a spectral width of 35 nm centered at 800 nm (full-width at half maximum, FWHM), which were delivered by a commercial Ti: sapphire CPA system operating at a repetition rate of 1 KHz. The HDM samples were irradiated at an AOI of 10° and p-polarized using laser pulses. A 1-on-1 test was performed according to ISO 21254 [26]. Ten sites were individually tested at each energy fluence, whereas 10 sites were tested one by one. The effective area of the laser beam spot focused on the sample surface is approximately 0.34 mm2. The occurrence of damage is determined by the online intensity change of the scattered light, which is then ascertained using an offline Leica polarizing optical microscope. The laser-induced damage thresholds (LIDT) of the HDM samples were determined by the mean value between the highest fluence of 0 damage probability and the lowest fluence of 100% damage probability [27], as shown in Fig. 6. The LIDTs are approximately 0.22 J/cm2 and 0.11 J/cm2 for the PHDM and NHDM, respectively. The lower damage threshold of the NHDM is due to the considerably higher electric field intensity compared to that of the PHDM, as shown in Fig. 7.
Fig. 6. Laser-induced damage threshold determined by the mean value between the highest fluence of zero damage probability and the upper fluence. (a) PHDM, (b) NHDM.
A blister structure was observed over a wide fluence range for both HDMs. Scanning electron microscope (SEM) images of typical blisters and a cross-sectional profile of the blister obtained by focused ion beam (FIB) technology on the PHDM and NHDM are presented in Fig. 8 and 9, respectively. As the fluence increased, the diameter and height of the blisters gradually increased. When the critical fluence was reached, the outermost layer fell off, as shown in Figs. 8(g) and 9(g). Furthermore, the locations where the delamination and bulking occur in the PHDM and NHDM are inside the 6th and 12th layers from the air interface (both are in the Nb2O5 layer and close to the Nb2O5/SiO2 interface, as shown in Fig. 8 (h) and Fig. 9 (h)), corresponding to depths of 1.08 µm and 1.73 µm, respectively, which are determined by the FIB. Although a blister structure appears for both HDMs, there is still a slight difference between them. In the PHDM, a blister structure was observed near the damage threshold. For the NHDM, at lower fluences (near the threshold), a superficial shadow was visible in the optical microscope, but no change in the surface morphology was observed under SEM. The blister structure occurred only after the fluence reached 2.2 times of the threshold. This is probably because buckling occurred at a deeper position in the NHDM than in the PHDM. Moreover, the deeper the position, the more energy required for the swelling of the outer layers.
Fig. 8. SEM images of typical blister in PHDM (a-g) and FIB cross-section picture (h) on the surface of the blister structure at 0.23 J/cm2.
Fig. 9. SEM images of typical blister in NHDM (a-g) and FIB cross-section picture (h) on the surface of the blister structure at 0.25 J/cm2.
The laser-induced blister structure of chirped mirrors was also observed in our previous publications [28,29]. The formation and evolution of the blister are similar to what we observed in this work. In [28,29], the evolution process was analyzed with a linear-elastic buckling model and an adiabatic expansion model of ideal gas. Based on the observed damage morphologies and previous publications, the formation and evolution processes of the blister structure can be summarized in four steps, as illustrated in Fig. 10. (1) Irradiation: the samples were irradiated by a 40-fs laser pulse in the 1-on-1 mode. (2) Absorption and evaporation: Immediately after the irradiation, the pulse energy was absorbed within the absorption length of a few tens of nanometers inside the 6th and 12th layers (Nb2O5 layer) for the PHDM and NHDM (confirmed by the cross-section profile of the blister), transforming a certain volume V1 of solid Nb2O5 material into gaseous Nb2O5. The evaporated Nb2O5 layer with volume V1 has an internal pressure P1, which begins to drive the coatings to swell. (3) Bulging-blister formation: Owing to the evolution of gaseous Nb2O5 from the absorbed pulse energy, the pressure builds up at the location where the Nb2O5 material evaporates, and the outer layers deforms into a blister to accommodate the increasing pressure. (4) Fall-off of the outermost layer: As the laser energy was further enhanced, the blister dimensions (including the height and radius) increased. When the stress limit of the outermost layer is reached, the outermost layer falls off, and the blister feature begins to be destroyed.
Fig. 10. Schematic illustrating the hypothesized blister formation mechanism. (1) Laser irradiation and energy conversion, (2) absorption and material evaporation, (3) internal pressure development in coating driving the bulging formation, and (4) the outermost layer falling off the inner layers. The white and blue bands represent the high refractive index material (Nb2O5) and low refractive index materials (SiO2), respectively.
4. Conclusions
PHDMs and NHDMs providing GDDs of +1000fs2 and -1000fs2 in the wavelength range of 750 nm to 850 nm were successfully designed, produced, and characterized for the first time. A new MGTI structure was applied to the design of the HDMs. Pulse analysis showed a nearly Fourier-limited pulse with only a few percent loss after a total of 100 reflections on the PHDM and NHDM were obtained, which proved the great matching between the PHDM and NHDM. Moreover, the laser-induced damage characteristics were evaluated. A higher damage threshold of the PHDM than that of the NHDM resulting from a lower electric field inside the layer structure, was observed. The formation and evolution of laser-induced blisters were demonstrated. PHDM and NHDM pairs may open a new horizon for simple, alignment-insensitive, compact, and spatially distortion-free pulse stretching and compression schemes in chirped pulse amplification systems. In the next step, we will try to apply the PHDM and NHDM in a Ti: Sapphire chirped pulse amplification system for pulse stretching and compression.
Funding
National Key Research and Development Program of China (2018YFE0118000); National Natural Science Foundation of China (11904376, 11975052, 61805263); China Postdoctoral Science Foundation (2022M723268); International Partnership Program of Chinese Academy of Sciences (181231KYSB20200040); Youth Innovation Promotion Association of the Chinese Academy of Sciences (2017289); Shanghai Sailing Program (18YF1426400); Strategic Priority Research Program of CAS (XDB1603); NSAF Fund Jointly set up by the National Natural Science Foundation of China, and Chinese Academy of Engineering Physics (U1630140).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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