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Diffraction efficiency optimization of multilayer dielectric mirror-based gratings for 1030 nm femtosecond lasers
Optics and Laser Technology 126 (2020) 106071
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Diffraction efficiency optimization of multilayer dielectric mirror-based gratings for 1030 nm femtosecond lasers
T
Lukas Stankevičiusa, Tomas Tamulevičiusa,b, , Andrius Žutautasa,b, Mindaugas Juodėnasa, Kęstutis Juškevičiusc, Ramutis Drazdysc, Sigitas Tamulevičiusa,b ⁎
a
Institute of Materials Science, Kaunas University of Technology, K. Baršausko St. 59, 51423 Kaunas, Lithuania Department of Physics, Kaunas University of Technology, Studentų St. 50, 51368 Kaunas, Lithuania c State Research Institute Center for Physical Sciences and Technology, Savanorių Ave. 231, 02300 Vilnius, Lithuania b
HIGHLIGHTS
unity efficiency was achieved in dielectric mirror-based diffraction grating. • Nearly grating profile scenarios provided 0.99 diffraction efficiencies. • Multiple control of the filling factor allows for etching depth errors. • Fine control of the groove depth offer flexibility in the filing factor. • Precise • > 99% efficiency spanning over 68 nm wavelength range was achieved. ARTICLE INFO
ABSTRACT
Keywords: Multilayered diffraction grating Diffraction efficiency Littrow angle Rigorous coupled wave analysis Spectral response
Diffraction gratings that do not reach > 99% diffraction efficiency (DE) are a major source of losses in chirped pulse amplification systems in current ultrashort pulse lasers. Here, we suggest an optimization route for diffraction gratings based on a commercially available, 1064 nm laser line high reflectivity (HR) multilayer-dielectric mirror. We modeled optical response of 1700 lines/mm gratings in Littrow configuration imposed on this typical quarter wavelength-based stack structure. We demonstrate that theoretically DE of 99.995% at a single wavelength and > 99% in 1003–1034 nm wavelength range can be achieved using the original dielectric mirror layer setup. The high DE spectral range could be broadened up to 992–1060 nm while still maintaining > 99% DE, when the dielectric stack with a thinner topmost layer is considered. In both cases the diffraction grating grooves must span the two topmost layers, including a higher refractive index material, i.e. Nb2O5. Alternatively, > 99% DE in 1009–1033 nm wavelength range can be also obtained using a thicker topmost layer. In this case, the grating groove spanning just the SiO2 layer is sufficient. However, twice as deep grooves and an accurate control of the filing factor is required. We show through numerical simulations that this structure is more sensitive to angular positioning error. The modelled electric field distributions showed reduced laser damage probability in the latter case. All investigated structures can sustain the bandwidth of sub-100 fs pulse length laser pulses. The proposed optimization route can serve as a guideline to design any diffraction grating based on commercially available dielectric mirrors.
1. Introduction Rapid progress in the achievable power of ultra-short pulse lasers is mainly limited by the damage thresholds and losses of the optical components. Unprecedented exawatt (1018 W) peak powers and intensity levels of 1025 W cm−2 that are expected to be achieved in ongoing projects such as Extreme Light Infrastructure in Europe [1]
⁎
stimulate the development of diffraction gratings that are used in compressors of chirped pulse amplification (CPA) systems [2]. The main parameters that describe such gratings are: a uniform, nearly 100% diffraction efficiency (DE) over the full aperture and at the same time in a broad spectral range of the ultra-short pulse laser; optical damage threshold above the used intensities [3]. Historically, gold coated reflection gratings were the first choice in CPA systems [4] but
Corresponding author at: Institute of Materials Science, Kaunas University of Technology, K. Baršausko St. 59, 51423 Kaunas, Lithuania. E-mail address: [email protected] (T. Tamulevičius).
https://doi.org/10.1016/j.optlastec.2020.106071 Received 15 July 2019; Received in revised form 25 October 2019; Accepted 11 January 2020 0030-3992/ © 2020 Elsevier Ltd. All rights reserved.
Optics and Laser Technology 126 (2020) 106071
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Fig. 1. (a) Model of the multilayer dielectric diffraction grating structure used in the simulations. The structure is composed of periodically stacked low (thickness dL, SiO2) and high (thickness dH, Nb2O5) refractive index layers. The thickness of the top layer is indicated as dLT. Various groove depths dG were simulated. The grating pitch, ridge widths and fill factor depicted in the inset are denoted Λ, R, f respectively. The red arrow indicates the incident TE polarized light (point indicates the orientation of the electric field vector). The reflected laser beam is denoted as 0R (specular reflection) and nearly back diffracted −1 order is denoted as −1R; (b) Representation of the multilayer stack thicknesses (light and dark blue colors represent low and high refractive index layers respectively, values on top indicate thicknesses of the layers). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
due to low optical damage threshold, which is 10 times lower than intensities reached in the amplifier [3], they were outclassed by dielectric gratings in most of the high energy density applications [5]. Diffraction gratings used in CPA often require a relatively big area ranging from tens of square centimeters in standard lasers up to square meters in high intensity systems [2,6,7], where expanded laser beams are used in order to avoid optical damage. Holographic lithography (HL) has been one of the most exploited techniques to pattern high area gratings for many years [8,9]. Applications that demand a nearly 100% DE, especially four pass CPA systems where a single transmission diffraction grating is used [3,9], require a precise control of grating filling factor and profile shape [10]. In such cases electron beam lithography (EBL) [10,11] and diffractive proximity photolithography [12] are the most exploited techniques. Similar multilayer dielectric grating structures can serve for spectral filtering of longitudinal modes as well as polarization filters in laser resonator systems when used at normal incidence [13]. As a rule of thumb, TE polarization and minus first order (−1R) diffraction near the Littrow angle is used in transmission or reflection diffraction gratings providing a single propagating diffraction order [14]. The remaining specular reflectance (zero order diffraction) or transmittance along the laser beam can be diminished by rigorous modeling of the grating profile and multilayer stack [14–17]. So far, the highest transmission DE has been achieved by employing volume holographic gratings [18]; rectangular grooves etched in a transparent substrate [9,12,19]; Bragg gratings [20,21]; encapsulated etched groove gratings [11]; and dielectric multilayer stack gratings [3,10,22]. The latter provides a high reflectivity that in turn allows to reach the highest DE. Diffraction in such case is achieved by imposing a lateral periodic groove structure in an additional top layer [10] or a layer stack [23]. In [24] it was demonstrated that by using a chirped mirror, instead of a conventional dielectric one, it is possible to make the high DE zone of the spectrum 20–30 nm wider. In general, the groove depth for high DE is inversely proportional to the refraction of the material comprising the grating layer. The latter could be high or low refractive index layer or may be some third material deposited as the top layer [8,25]. One of the ways to precisely control the grating groove depth is to use an etch stop layer [22] or to control the speed and duration of dry etching accurately [26]. Dry etching through both, high [3,8,9,14] and low [7,8,10] refractive index materials, namely metal oxides and silica respectively, has been demonstrated separately and even in combination where grooves were spanning through multiple layers of different
materials [23,27]. HL, when used as a grating origination technique, may require the use of an antireflective coating in order to isolate the resist layer from back reflections [3]. Addition of supplementary optical layers have to be considered in the multilayer stack design. In this work we present an optimization route of a high DE multilayered-dielectric diffraction grating using rigorous coupled wave analysis simulations. We optimized the diffraction grating structure for standard and modified commercially available multilayer stacks to achieve the highest DE for 1030 nm central wavelength, < 300 fs pulse length and 10 nm spectral width femtosecond laser. Our results showcase how accurately selected properties of a diffraction grating profile and multilayer dielectric stack can ensure nearly unity DE over relatively broad ranges of angle of incidence and wavelength. The benefits and drawbacks of three different structures are discussed in the frame of easiness of production, sensitivity to positioning errors, high DE wavelength range, and electric field distributions that can be directly related to optical damage probability. Furthermore, we compare our theoretical calculations to other authors’ findings and illustrate that suggested optimized high DE structures can be actually realized. 2. Methods 2.1. Grating structure and its profile simulations The optical response of a multilayer-dielectric mirror with a grating profile in its top layer was simulated employing commercial software GSolver V5.2 [28] which is based on the Rigorous Coupled Wave Analysis (RCWA) method. We aimed to achieve a high DE at λ = 1030 nm, which is the central wavelength emitted by Yb:KGW femtosecond laser (τ = 270 fs), and used a 1700 line/mm groove density (grating pitch Λ = 588 nm, see Fig. 1a) diffraction grating that is commonly used in commercial CPA systems. We focused on the Littrow angle configuration that allows for a high DE at α = 61.146° angle of incidence. We based our investigation on a commercially available high reflectivity (HR) quarter wavelength-based stack multi-layer dielectric mirror. It is composed of high (Nb2O5, n1030 nm = 2.23) and low (SiO2, n1030 nm = 1.48) refractive index layers periodically stacked on a fused silica substrate. This mirror is optimized for reflectance of 1064 nm wavelength light at 0° angle of incidence. It is commercially available at Altechna Coatings (for 99.9% reflection within 146 nm wavelength spectral range at normal incidence, which covers the bandwidth of the 2
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Yb:KGW laser). The stack consists of 22 high/low refractive index layers with the topmost layer being SiO2. The thicknesses of the individual layers are provided in Fig. 1b. We investigated the original structure first and then modified it by altering the thickness of the topmost low refractive index layer. The optimization of high DE diffraction gratings involved parameters such as: filling factor f (the ratio of ridge width R to the grating pitch Λ, i.e. the filling factor of the grating, see inset in Fig. 1a), thicknesses d of the multilayered mirror stack (see Fig. 1, dLT, dL and dH, where L stands for low refractive index, H – high refractive index, T – top layer), groove depth dG, angle of incidence α, optical properties of the used materials, i.e. the dispersion curve of refractive index, and polarization of impinging light. It should be noted that DE of such structure in the used configuration is very sensitive to the polarization of light. Preliminary simulations showed that using transverse magnetic polarization (TM), f = 0.5 filling factor, and various groove depths within the thickness of the first layer, DE of just 0.09 can be achieved. In contrast, transverse electric (TE) polarization models showed DE > 0.9. Following these findings that are in line with the observations described in [14,29], in further simulations we focused on TE polarization only. The optimization of the grating parameters (groove depth dG, filling factor f, and top layer height dLT) was performed in order to achieve the highest efficiency of the −1 diffraction order in reflectance (−1R). Finally, electrical field distributions in the multilayered diffraction grating structures were simulated employing Comsol Multiphysics V5.3 suite. Electric field simulations were carried out using alternative software because of the limitations of the commercial implementation of RCWA. Standard 2D electromagnetic modeling was used along with a periodic boundary condition. A plane, TE polarized wave was launched towards the structure and the resulting transmitted and reflected diffraction orders were collected. The dielectric functions of materials were taken from the built-in library. The optimized geometrical parameters were taken from the RCWA simulations and the simulation was parametrized by the angle of incidence.
Fig. 2. DE of the −1R diffraction order: (a) dependence on the groove depth; (b) dependence on the angle of incidence for one particular structure indicated above the graph (dL = 357 nm, dG = 422 nm, f = 0.5).
3.2. Optimization of the diffraction grating profile for a highest DE Based on the preliminary simulation results depicted in Fig. 2 and assuming that the grating has rectangular profile shape, we involved a full range of possible parameters in the simulation, including: already used groove depth dG varied from 0 nm to no more than 3 layers deep with a step of 1 nm; top low refractive index layer height dLT varied from 0 to 784 nm with a step of 1 nm; filling factor f varied from 0.01 to 0.99 relative units (r.u.) with a step of 0.01. −1R DE dependence on these parameters is summarized in Fig. 3. Evolution of the DE at different top layer thicknesses, groove depths and filing factors is depicted in the Supplementary movie 1. The red color surface in Fig. 3, indicating a DE above 0.99 r.u., spans the whole parameter space (f, dLT, dG). In order to ensure the DE in the necessary wavelength range, the DE was calculated for 1020–1040 nm wavelengths. The high DE surfaces (DE−1R > 0.99, see Fig. 3) can be sliced at different dLT values and investigated in more details. Two datasets were chosen, i.e. (i) dLT = 231 nm providing the highest achievable DE with the thinner top SiO2 layer than standard mirror structure, and (ii) dLT = 777 nm providing the highest DE with a thicker topmost layer. Spectral and angular DE dependencies of such grating structures are summarized in Supplementary movies 2 and 3. These datasets are analyzed in more detail in Fig. 4. For the first structure, high DE was obtained with groove depths above 350 nm and corresponding to filling factor values f = 0.14 and f = 0.42 (see Fig. 4a). Also, a range of filling factors 0.14–0.42 providing the same high DE was obtained at 342 nm groove depth. More DE > 0.99 cases along the dashed dotted line are provided in Supplementary movie 2. For the second structure, a high DE plateau was obtained in a much wider range of filing factors (see Fig. 4c). The depths between 480 and 520 nm with a filling factor varying from 0.28 to 0.7 and depths exceeding 520 nm with filling factor values of f = 0.28 and 0.73 also yielded high DE. More DE > 0.99 cases for the latter multi-layer stack are provided in Supplementary movie 3. In order to find the best structure parameters, we took coordinate
3. Results 3.1. Optimization of the diffraction grating profile depth First, we performed simulations on the original 1064 nm HR dielectric mirror stack by varying the groove depth (dG) from 0 nm (plain mirror) through the whole mirror structure down to the substrate with a step of 1 nm (see Fig. 2a). The pitch of the modeled structure was 588 nm, 0.5 filling factor, 1030 nm wavelength, TE polarization, 61.14° angle of incidence (Littrow angle). It is hard to realize such high aspect ratio structures in practice, but the simulation results provided us with a good starting point for further optimization and allowed us to get a preliminary idea about the dependence of the DE on the groove depth. The DE dependence on the angle of incidence for 422 nm groove depth is depicted in Fig. 2b. Fig. 2a clearly demonstrates that the DE can be varied by increasing the grating groove depth and can reach almost 100% at several dG values that repeat with some periodicity. One can also see that all 4 expressed DE maximum values are obtained when the bottom of the groove is situated in the material with a higher refractive index, i.e. Nb2O5. The maximum theoretical diffraction efficiency (DE−1R = 0.9995 @1030 nm) was obtained for a 422 nm deep structure, but the groove in that case goes through the whole thickness of the top SiO2 layer and 85 nm of the Nb2O5 layer. By varying the angle of incidence slightly in the range of 58.8–63.6°, or approx. 2° mounting errors that can be introduced in practice, we found that DE does not go below 0.99 at central wavelength of 1030 nm (see Fig. 2b). 3
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whole spectral band and angles of incidence down to 55.2°, i.e. 6° angle off of the Littrow mount geometry. Such structure inevitably requires the grooves to go through the top two layers. In order to avoid the possible difficulties of dry plasma etching of two different oxides, we suggest the optimized multi-layer stack structure parameters, where etching of only one layer is necessary (Fig. 4c, d). In this case the simulated DE dependences on wavelength and angle of incidence show that such model allows only a 0.6° mounting error of the grating for the selected wavelength range while preserving DE > 0.99 (see Fig. 4d). To sum up, the choice of a single material for grating etching requires the use of a dedicated dielectric mirror structure that in the end requires higher grating positioning accuracy compared to structures etched through several layers. Two-dimensional electric field intensity distributions (see Fig. 5) were simulated for three multilayered diffraction grating structures and their respective dielectric mirror stacks without the grating structures discussed earlier. It is clearly seen that the electric field only marginally penetrates the multilayer structure. The most intensive electric field was found within the groove, which is important for high intensity laser beam applications and suggests higher damage thresholds. Moreover, numerical simulations of diffraction efficiency of the structures at different angles of incidence revealed that high DE can be obtained not only for the Littrow mounting geometry. In Fig. 6 we show that by varying the angle of incidence, high DE values are also inherent for different spectral bands.
Fig. 3. First order (−1R) DE dependence on the top layer thickness (dLT), filing factor (f) and groove depth (dG). The grating was simulated in Littrow configuration for 1030 nm wavelength. Red color surface indicates DE above 0.99 r.u. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
sets belonging to DE > 0.99 at 1030 nm 61.14° incidence angle (Littrow) and simulated DE at 950–1100 nm wavelengths. This was performed for two distinguished planes f × dG at dLT = 231 nm and dLT = 777 nm. The simulated spectral and angular dependencies for the two cases are depicted in Fig. 4(b, d). These simulations led to detection of the parameters providing a widest DE > 0.99 spectrum of 67 nm bandwidth (Fig. 4b). The obtained grating profile parameters: dLT = 231 nm, dG = 486 nm and f = 0.42 ensures DE > 0.99 for the
4. Discussion After the sweep of multiple grating profile parameters, three different high DE structures were selected and investigated in more details (Fig. 7). The maximum DE achieved for 1020–1040 nm wavelength range was 0.999. These theoretical results surpass the declared values of commercially available diffraction gratings [30]. The majority of completed computer simulations revealed that a Fig. 4. Two characteristic multilayered diffraction grating profile cases providing high DE with a thinner topmost layer (a, b) and a thicker topmost layer (c, d). Vertical solid lines in (a) and (c) represent interfaces between two different oxides. Solid (a–d) and dash dotted contour lines (in a, c) are following the conditions DE > 0.99 r.u. and DE > 0.999 r.u. at 1030 nm wavelength respectively. Spectral and angular DE dependence of the two optimized grating structures: (b) dLT = 231 nm with optimized grating groove (dG > dLT) and filing factor indicated above, (d) dLT = 777 nm with a grating groove depth almost equal to the topmost layer (dLT ≈ dG) and a respective filing factor indicated above. More spectral and angular dependencies of structures with parameters along the dashed dotted line are provided in supplementary movies 1 and 2. Dashed rectangular box with the center identified with a cross in (b) and (d) indicates the range of desired α and λ combinations with nearly unity DE.
4
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Fig. 5. Electric field intensity distributions in three optimized dielectric diffraction grating structures and their respective dielectric mirrors (on the right): (a) top layer of 357 nm thickness, groove depth of 422 nm and 0.5 fill factor; (b) dLT = 231 nm, dG = 486 nm and f = 0.42; (c) dLT = 777 nm, dG = 770 nm, f = 0.28.
Fig. 6. Simulation results identifying 0.99 DE zones for the corresponding wavelength and angle of incidence range for different groove depths identified in color. The solid black line depicts Littrow mount configuration for the investigated wavelength range.
Fig. 7. Spectral DE dependence of the three investigated dielectric mirror-based diffraction gratings.
grating groove that goes through several layers provides periodically repeated high DEs along the periodicity of high refractive index layers (see Fig. 2a). It was shown that the highest DE values can be reached when the structure passes the first low refractive index layer and stops within the high refractive index layer. When the structure passes more layers, the DE values vary periodically with the thickness, depending on which layer is at the bottom of the grating groove, and gradually decrease. For example, the best value of DE of > 0.99 was obtained when the calculated structure had a depth of two first layers of Nb2O5 and SiO2 and stopped only in the third SiO2 layer (see Fig. 3). In [23] it was demonstrated that it is feasible to make similar structures experimentally and they have demonstrated very competitive results,
including > 96% DE, that are summarized in Table 1. Multilayer stacks with high refractive index material in the topmost layer [3,5,8,9,14,25] that were not considered in our work could also have nearly unity DE and they are mainly chosen because in this case much lower diffraction grating grooves (100–400 nm, see Table 1 for more details) are necessary, although more complex dry etching chemistries are required. Electrical field simulations of our structures (see Fig. 5a, b) indicate that there is some electrical field concentration in the sandwiched Nb2O3 layer and therefore this structure might be less resistant to optical damage, which was actually measured by others experimentally [23]. Another possibility for achieving high DE structure without the need 5
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Table 1 Properties of the experimentally realized multilayer dielectric diffraction gratings described in literature. No.
Multilayer stack structure
1 1.1
Filing factor, f (r.u.)
Groove depth, dG (nm); thickness of the top layer dT (nm)
DE
Laser damage threshold (J/cm2), angle of incidence, pulse length
Groove in a low refractive index layer SiO2 (nL)/Al2O3 (nH) 1800
< 0.35
700 nm (dG = dT)
> 99% λ = 1030 nm
–
1.2
SiO2 (nL)/HfO2 (nH); 20 layers
1480
0.37
600 nm; 735 nm
94% λ = 1064 nm
–
1.3
SiO2 (nL)/Nb2O3 (nH); 21 layers
2564
0.5
190 nm; 210 nm
97% λ = 532 nm
4.4 (45°, 5 ns); 0.18 (45°, 1 ps)
2 2.1
Groove in a high refractive index layer ZnS (nH)/ThF4 (nL) 1550
~0.8
~100 nm
> 96% λ = 1053 nm
–
2.2
1250
0.25
284 nm; dG = dT
99.7% 1060 nm, (> 99% λ = 1025 – 1070 nm)
2.95 (12 ns, ISO 21254–2)
2.3
Ta2O5 (nH)/SiO2 (nL); 25 layers (mirror) + 4 layers (grating) HfO2 (nH)/SiO2 (nL); 20 layers
1480
0.44
165 nm
95% λ = 1064 nm
1.25 (300 fs)
2.4
HfO2 (nH)/Al2O3 (nL)
1724
0.38
123 nm
96% λ = 777–815 nm
1.1 (57°, 50 fs)
2.5
HfO2 (nH)/SiO2 (nL); 15 layers (mirror) + 1 SiO2(nL) (grating) Ta2O5 (nH)/SiO2 (nL)
1780
0.32
396 nm
96.2% λ = 1053 nm
2.1 (72.5°, 500 fs)
1786
0.5
52 nm; 70 nm
99% λ = 1064 nm
–
0.3
270 nm
97.3% λ = 800 nm (> 96% λ = 820–780 nm)
0.18 (55°, 120 fs); 0.37 (55°, 1 ps); 0.74 (55°, 10 ps); 1.76 (55°, 120 ps)
2.6 3 3.1
Line density (l/mm)
Groove etched through multiple layers (Nb0.5Ta0.5)2O5 (nH)/SiO2 1740 (nL); 20 layers
of etching through Nb2O5 layer is to form a thicker topmost layer of low refractive index. Fig. 3 shows that DE−1R > 0.99 values are obtained only when the thickness of the top layer in the simulated structure reaches 706 nm. Based on the DE−1R > 0.99 surface evolution (see Fig. 3 and Supplementary movie 1) for the analyzed parameter range, it can be seen that for 1030 nm wavelength for every structure that has a top layer thicker than 706 nm DE−1R will be higher than 0.99. Very similar structures were described in [7,8] where 99% DE was experimentally obtained. On the other hand, angular spectral analysis shows (see Fig. 4b, Fig. 7) that DE−1R > 0.99 value using the thicker topmost layer setup is ensured for a significantly narrower range of wavelengths and incidence angles compared to a thinner topmost layer setup (see Fig. 4a, Fig. 7), where grooves are etched through more than one layer. Also, simulations of electric field distribution in the dielectric mirror stack indicate that the electric field does not penetrate deep into the stack and is concentrated between the grating ridges when a thicker top layer is used (see Fig. 5c). This indicates a lower probability of damaging the structure under intensive laser light. It is in agreement with the findings reported in literature and summarized in Table 1. The structure with the topmost low refractive index possessed the highest damage threshold of 4.4 J/cm2 that was obtained with a nanosecond laser [10]. The high DE bandwidths ensured by the three investigated diffraction grating structures (Fig. 7) were converted into available pulse durations. Calculations were carried out by using = 0.44· 02 /c· equation ( 0 – central wavelength; c – speed of light; – spectral width for DE > 0.99) [31]. It was obtained that down to 50 fs pulse duration can be achieved for the diffraction grating based on the 1064 nm dielectric mirror which demonstrated DE > 0.99 in the spectral range of 1003–1034 nm (Fig. 7, solid black line). The shortest pulse length of 23 fs could be maintained with the DE > 0.99 using a diffraction grating with a groove spanning trough two layers of the dielectric stack because it ensures high DE over 992–1060 nm bandwidth (Fig. 7, red dotted line). Pulse with the longest duration of 65 fs corresponds to the highest aspect ratio that maintains smallest DE > 0.99 bandwidth of 1009–1033 nm (Fig. 7, blue dashed line). The
Grating fabrication technology
HL HL EBL
HL HL HL HL –
HL
HL
Ref.
[7] [8] [10]
[14] [9] [8] [3] [5] [25]
[23]
results of maintained pulse length are promising because there are many high intensity commercial laser systems that have longer pulses, i.e. narrower line widths. The high DE regions that were identified by the suggested optimization route would not have been revealed by simple optimization methods, such as the genetic algorithm available in GSolver. Therefore, a full sweep over the parameter space allowed for a selection of parameter sets that not only yield a sufficiently high DE but also have additional fabrication or optical setup related merits. The presented route of simulation can be treated as a possible grating optimization recipe prior to the fabrication of the actual structure. By analyzing the three-dimensional DE data depicted in Fig. 3 in f × dG planes at different top layer thicknesses we showed that there are several high DE zones. One of these zones (Fig. 4c) shows that the DE can be constant at various fill factor values or at a constant groove depth. It is a very promising result regarding the fabrication of the structure because maintaining a required filling factor value is quite a complicated task in lithography processes [10]. The opposite case depicted in Fig. 4d, allows for errors in the dry etching phase because a varying groove depth between 350 and 550 nm (but constant filling factor of 0.14 or 0.42) maintains the same high DE. Similar filing factor having diffraction gratings assuring nearly unity DE were described in [7,8] and are summarized in Table 1. Based on these observations, one can choose the grating profile parameter that is easier to control (f or dG) with the capabilities of the machinery used in the technological formation process, i.e. the type of lithography technology and recipe of the dry etching process. Further investigation showed that high DE values for certain wavelengths can be achieved for a much wider range of angles and not only those that are close to the Littrow condition. From the DE− 1R > 0.99 areas in the DE dependency on angle of incidence and groove depth (Fig. 6) one can see that there are three characteristic conditions ensuring high DE values. One of these areas corresponds to the already discussed Littrow angle curve (Fig. 6, solid black line) that is the usually used configuration [10,29]. The graph suggests that for 6
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shallow grooves (dG 130–350 nm), high DE values are mainly reached at angles 32–45° and 80–88° in the wavelength range of 900–1050 nm, i.e. not for the Littrow angle configuration. On the other hand, the selectivity strongly depends on the groove depth, i.e. when the grating groove reaches Nb2O5 layer, only then Littrow angle allows to achieve high DE−1R > 0.99 values. Using Littrow configuration, broad high DE value contours are achieved in the desired wavelength range—but only for the deeper structures with dG values in the vicinity of the ones summarized in Fig. 6. Another high DE configuration that can be obtained at 84° angle might also have practical applications because at a higher incidence angle the beam interacts with a much bigger surface area of the diffractive structure, thus lowering the energy fluence and possibly damage threshold. Using this kind of angular configuration with bigger aperture gratings, a higher energy chirped pulse amplification might be achieved using the same beam expansion levels. For the full potential understanding of these illumination conditions further investigation is necessary.
Appendix A. Supplementary material Supplementary data to this article can be found online at https:// doi.org/10.1016/j.optlastec.2020.106071. References [1] https://eli-laser.eu/media/1019/eli-whitebook.pdf; the ELI Whitebook. [2] J.P. Chambaret, O. Chekhlov, G. Cheriaux, J. Collier, R. Dabu, P. Dombi, A.M. Dunne, K. Ertel, P. Georges, J. Hebling, J. Hein, C. Hernandez-Gomez, C. Hooker, S. Karsch, G. Korn, F. Krausz, C. Le Blanc, Z. Major, F. Mathieu, T. Metzger, G. Mourou, P. Nickles, K. Osvay, B. Rus, W. Sandner, G. Szabo, D. Ursescu, K. Varju, Extreme Light Infrastructure: architecture and major challenges, in: Conference on Solid State Lasers and Amplifiers III and High-Power Lasers, Brussels, BELGIUM, 2010. [3] F. Canova, O. Uteza, J.-P. Chambaret, M. Flury, S. Tonchev, R. Fechner, O. Parriaux, High-efficiency, broad band, high-damage threshold high-index gratings for femtosecond pulse compression, Opt. Express 15 (2007) 15324–15334. [4] D. Strickland, G. Mourou, Compression of amplified chirped optical pulses, Opt. Commun. 56 (1985) 219–221. [5] J. Neauport, E. Lavastre, G. Raze, G. Dupuy, N. Bonod, M. Balas, G. de Villele, J. Flamand, S. Kaladgew, F. Desserouer, Effect of electric field on laser induced damage threshold of multilayer dielectric gratings, Opt. Express 15 (2007) 12508–12522. [6] I. Richter, P.C. Sun, F. Xu, Y. Fainman, Design considerations of form birefringent microstructures, Appl. Opt. 34 (1995) 2421–2429. [7] J.A. Britten, S.J. Bryan, L.J. Summers, H.T. Nguyen, B.W. Shore, O. Lyngnes, Large aperture, high-efficiency multilayer dielectric reflection gratings, in: Lasers and Electro-Optics, 2002. CLEO '02. Technical Digest. Summaries of Papers Presented at the, 2002, pp. CPDB7–CPDB7. [8] B.W. Shore, M.D. Perry, J.A. Britten, R.D. Boyd, M.D. Feit, H.T. Nguyen, R. Chow, G.E. Loomis, L.F. Li, Design of high-efficiency dielectric reflection gratings, J. Opt. Soc. Am. A – Opt. Image Sci. Vision 14 (1997) 1124–1136. [9] M. Rumpel, M. Moeller, C. Moormann, T. Graf, M.A. Ahmed, Broadband pulse compression gratings with measured 99.7% diffraction efficiency, Opt. Lett. 39 (2014) 323–326. [10] K. Hehl, J. Bischoff, U. Mohaupt, M. Palme, B. Schnabel, L. Wenke, R. Bodefeld, W. Theobald, E. Welsch, R. Sauerbrey, H. Heyer, High-efficiency dielectric reflection gratings: design, fabrication, and analysis, Appl. Opt. 38 (1999) 6257–6271. [11] S. Ratzsch, E.-B. Kley, A. Tuennermann, A. Szeghalmi, Encapsulation process for diffraction gratings, Opt. Express 23 (2015) 17955–17965. [12] L. Stuerzebecher, F. Fuchs, T. Harzendorf, U.D. Zeitner, Pulse compression grating fabrication by diffractive proximity photolithography, Opt. Lett. 39 (2014) 1042–1045. [13] N. Destouches, J.C. Pommier, O. Parriaux, T. Clausnitzer, Narrow band resonant grating of 100% reflection under normal incidence, Opt. Express 14 (2006) 12613–12622. [14] M.D. Perry, R.D. Boyd, J.A. Britten, D. Decker, B.W. Shore, C. Shannon, E. Shults, High-efficiency multilayer dielectric diffraction gratings, Opt. Lett. 20 (1995) 940–942. [15] G. Kalinchenko, S. Vyhlidka, D. Kramer, A. Lerer, B. Rus, High reflective diffraction grating for ultrafast pulse compression, in: Conference on High-Power, HighEnergy, and High-Intensity Laser Technology II, Spie-Int Soc Optical Engineering, Prague, CZECH REPUBLIC, 2015. [16] H.B. Wei, L.F. Li, All-dielectric reflection gratings: a study of the physical mechanism for achieving high efficiency, Appl. Opt. 42 (2003) 6255–6260. [17] Z. Varallyay, P. Dombi, Design of high-efficiency ultrabroadband dielectric gratings, Appl. Opt. 53 (2014) 5769–5774. [18] P.A. Blanche, P. Gailly, S. Habraken, P. Lemaire, C. Jamar, Volume phase holographic gratings: large size and high diffraction efficiency, Opt. Eng. 43 (2004) 2603–2612. [19] C. Zhou, T. Seki, T. Kitamura, Y. Kuramoto, T. Sukegawa, N. Ishii, T. Kanai, J. Itatani, Y. Kobayashi, S. Watanabe, Wavefront analysis of high-efficiency, largescale, thin transmission gratings, Opt. Express 22 (2014) 5995–6008. [20] G. Sobon, K. Krzempek, J. Taka, J. Sotor, Compact, all-PM fiber-CPA system based on a chirped volume Bragg grating, Laser Phys. 26 (2016). [21] M. Nejbauer, T.M. Kardaś, Y. Stepanenko, C. Radzewicz, Spectral compression of femtosecond pulses using chirped volume Bragg gratings, Opt. Lett. 41 (2016) 2394–2397. [22] J.A. Britten, H.T. Nguyen, S.F. Falabella, B.W. Shore, M.D. Perry, D.H. Raguin, Etchstop characteristics of Sc2O3 and HfO2 films for multilayer dielectric grating applications, J. Vacuum Sci. Technol. A – Vacuum Surf. Films 14 (1996) 2973–2975. [23] D.H. Martz, H.T. Nguyen, D. Patel, J.A. Britten, D. Alessi, E. Krous, Y. Wang, M.A. Larotonda, J. George, B. Knollenberg, B.M. Luther, J.J. Rocca, C.S. Menoni, Large area high efficiency broad bandwidth 800 nm dielectric gratings for high energy laser pulse compression, Opt. Express 17 (2009) 23809–23816. [24] G.A. Kalinchenko, A.M. Lerer, Wideband all-dielectric diffraction grating on chirped mirror, J. Lightwave Technol. 28 (2010) 2743–2749. [25] N. Destouches, A.V. Tishchenko, J.C. Pommier, S. Reynaud, O. Parriaux, S. Tonchev, M.A. Ahmed, 99% efficiency measured in the -1st order of a resonant grating, Opt. Express 13 (2005) 3230–3235. [26] T. Tamulevicius, I. Grazuleviciute, A. Jurkeviciute, S. Tamulevicius, The calculation, fabrication and verification of diffraction grating based on laser beam splitters employing a white light scatterometry technique, Opt. Lasers Eng. 51 (2013)
5. Conclusions We have demonstrated that a high diffraction efficiency (DE > 0.99) reflection diffraction grating can be realized in a standard, commercially available, high reflectivity laser line dielectric mirror. Theoretical simulations showed that using a conventional mirror structure, several grating profile scenarios provide 0.99 diffraction efficiencies for TE polarized light in Littrow mount configuration: some require a fine control of the filling factor but allows for etching depth errors, others require the opposite—a precise control of the groove depth but offer more flexibility in the filing factor. In most cases, etching through multiple layers is necessary. We proposed multilayer stack structure with a thicker top SiO2 layer (dLT = 777 nm), which ensures diffraction efficiencies above 0.99 for 1030 nm wavelength in Littrow configuration. Grating profile with a filling factor f = 0.28 and groove depth of dG = 770 nm proved to be promising because the grating grooves spanned through only one material. Theoretically, nearly unity diffraction efficiencies (more than 0.999) for 1030 nm wavelength in Littrow configuration could be achieved by etching a dielectric mirror through several material layers. Especially broad DE > 0.99 spectrum of 68 nm could be maintained using a thinner topmost layer of 231 nm and groove depth of 486 nm. Finite element method simulations suggested that structures with thicker dielectric top layer promise reduced laser damage possibility due to the electric field concentrating in air between the grating ridges. Simulation of various diffraction grating groove depths in multilayered dielectric structure at various illumination angles showed that the same structure can be applied in at least three mounting angles and still have a spectral band with a near unity diffraction efficiency. Based on the bandwidth it was estimated that all investigated structures are capable to maintain DE > 0.99 of a sub 100 fs laser pulse. Main practical limitation is that the spectral band of the high diffraction efficiency is also varying with the mounting angle. Funding This research was funded by the Research, Development and Innovation Fund of Kaunas University of Technology (project grant No. PP35/161). Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. 7
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L. Stankevičius, et al. 1185–1191. [27] H.Y. Guan, H. Chen, J.B. Wu, Y.X. Jin, F.Y. Kong, S.J. Liu, K. Yi, J.D. Shao, Highefficiency, broad-bandwidth metal/multilayerdielectric gratings, Opt. Lett. 39 (2014) 170–173. [28] The “GSolver” software is available from Grating Solver Development Co. https:// www.gsolver.com/.
[29] N. Bonod, J. Neauport, Diffraction gratings: from principles to applications in highintensity lasers, Adv. Opt. Photon. 8 (2016) 156–199. [30] Specification for High Efficiency Transmission Grating, T-1702-1030s Series, LightSmyth Technologies, n.d. http://www.lightsmyth.com/wp-content/uploads/ DS-High-E-Trans-Grating-T-1702-1030s.pdf. [31] E.A.S. Bahaa, C.T. Malvin, Fundamentals of Photonics, Wiley, 2007.
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Optics and Laser Technology journal homepage: www.elsevier.com/locate/optlastec
Diffraction efficiency optimization of multilayer dielectric mirror-based gratings for 1030 nm femtosecond lasers
T
Lukas Stankevičiusa, Tomas Tamulevičiusa,b, , Andrius Žutautasa,b, Mindaugas Juodėnasa, Kęstutis Juškevičiusc, Ramutis Drazdysc, Sigitas Tamulevičiusa,b ⁎
a
Institute of Materials Science, Kaunas University of Technology, K. Baršausko St. 59, 51423 Kaunas, Lithuania Department of Physics, Kaunas University of Technology, Studentų St. 50, 51368 Kaunas, Lithuania c State Research Institute Center for Physical Sciences and Technology, Savanorių Ave. 231, 02300 Vilnius, Lithuania b
HIGHLIGHTS
unity efficiency was achieved in dielectric mirror-based diffraction grating. • Nearly grating profile scenarios provided 0.99 diffraction efficiencies. • Multiple control of the filling factor allows for etching depth errors. • Fine control of the groove depth offer flexibility in the filing factor. • Precise • > 99% efficiency spanning over 68 nm wavelength range was achieved. ARTICLE INFO
ABSTRACT
Keywords: Multilayered diffraction grating Diffraction efficiency Littrow angle Rigorous coupled wave analysis Spectral response
Diffraction gratings that do not reach > 99% diffraction efficiency (DE) are a major source of losses in chirped pulse amplification systems in current ultrashort pulse lasers. Here, we suggest an optimization route for diffraction gratings based on a commercially available, 1064 nm laser line high reflectivity (HR) multilayer-dielectric mirror. We modeled optical response of 1700 lines/mm gratings in Littrow configuration imposed on this typical quarter wavelength-based stack structure. We demonstrate that theoretically DE of 99.995% at a single wavelength and > 99% in 1003–1034 nm wavelength range can be achieved using the original dielectric mirror layer setup. The high DE spectral range could be broadened up to 992–1060 nm while still maintaining > 99% DE, when the dielectric stack with a thinner topmost layer is considered. In both cases the diffraction grating grooves must span the two topmost layers, including a higher refractive index material, i.e. Nb2O5. Alternatively, > 99% DE in 1009–1033 nm wavelength range can be also obtained using a thicker topmost layer. In this case, the grating groove spanning just the SiO2 layer is sufficient. However, twice as deep grooves and an accurate control of the filing factor is required. We show through numerical simulations that this structure is more sensitive to angular positioning error. The modelled electric field distributions showed reduced laser damage probability in the latter case. All investigated structures can sustain the bandwidth of sub-100 fs pulse length laser pulses. The proposed optimization route can serve as a guideline to design any diffraction grating based on commercially available dielectric mirrors.
1. Introduction Rapid progress in the achievable power of ultra-short pulse lasers is mainly limited by the damage thresholds and losses of the optical components. Unprecedented exawatt (1018 W) peak powers and intensity levels of 1025 W cm−2 that are expected to be achieved in ongoing projects such as Extreme Light Infrastructure in Europe [1]
⁎
stimulate the development of diffraction gratings that are used in compressors of chirped pulse amplification (CPA) systems [2]. The main parameters that describe such gratings are: a uniform, nearly 100% diffraction efficiency (DE) over the full aperture and at the same time in a broad spectral range of the ultra-short pulse laser; optical damage threshold above the used intensities [3]. Historically, gold coated reflection gratings were the first choice in CPA systems [4] but
Corresponding author at: Institute of Materials Science, Kaunas University of Technology, K. Baršausko St. 59, 51423 Kaunas, Lithuania. E-mail address: [email protected] (T. Tamulevičius).
https://doi.org/10.1016/j.optlastec.2020.106071 Received 15 July 2019; Received in revised form 25 October 2019; Accepted 11 January 2020 0030-3992/ © 2020 Elsevier Ltd. All rights reserved.
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Fig. 1. (a) Model of the multilayer dielectric diffraction grating structure used in the simulations. The structure is composed of periodically stacked low (thickness dL, SiO2) and high (thickness dH, Nb2O5) refractive index layers. The thickness of the top layer is indicated as dLT. Various groove depths dG were simulated. The grating pitch, ridge widths and fill factor depicted in the inset are denoted Λ, R, f respectively. The red arrow indicates the incident TE polarized light (point indicates the orientation of the electric field vector). The reflected laser beam is denoted as 0R (specular reflection) and nearly back diffracted −1 order is denoted as −1R; (b) Representation of the multilayer stack thicknesses (light and dark blue colors represent low and high refractive index layers respectively, values on top indicate thicknesses of the layers). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
due to low optical damage threshold, which is 10 times lower than intensities reached in the amplifier [3], they were outclassed by dielectric gratings in most of the high energy density applications [5]. Diffraction gratings used in CPA often require a relatively big area ranging from tens of square centimeters in standard lasers up to square meters in high intensity systems [2,6,7], where expanded laser beams are used in order to avoid optical damage. Holographic lithography (HL) has been one of the most exploited techniques to pattern high area gratings for many years [8,9]. Applications that demand a nearly 100% DE, especially four pass CPA systems where a single transmission diffraction grating is used [3,9], require a precise control of grating filling factor and profile shape [10]. In such cases electron beam lithography (EBL) [10,11] and diffractive proximity photolithography [12] are the most exploited techniques. Similar multilayer dielectric grating structures can serve for spectral filtering of longitudinal modes as well as polarization filters in laser resonator systems when used at normal incidence [13]. As a rule of thumb, TE polarization and minus first order (−1R) diffraction near the Littrow angle is used in transmission or reflection diffraction gratings providing a single propagating diffraction order [14]. The remaining specular reflectance (zero order diffraction) or transmittance along the laser beam can be diminished by rigorous modeling of the grating profile and multilayer stack [14–17]. So far, the highest transmission DE has been achieved by employing volume holographic gratings [18]; rectangular grooves etched in a transparent substrate [9,12,19]; Bragg gratings [20,21]; encapsulated etched groove gratings [11]; and dielectric multilayer stack gratings [3,10,22]. The latter provides a high reflectivity that in turn allows to reach the highest DE. Diffraction in such case is achieved by imposing a lateral periodic groove structure in an additional top layer [10] or a layer stack [23]. In [24] it was demonstrated that by using a chirped mirror, instead of a conventional dielectric one, it is possible to make the high DE zone of the spectrum 20–30 nm wider. In general, the groove depth for high DE is inversely proportional to the refraction of the material comprising the grating layer. The latter could be high or low refractive index layer or may be some third material deposited as the top layer [8,25]. One of the ways to precisely control the grating groove depth is to use an etch stop layer [22] or to control the speed and duration of dry etching accurately [26]. Dry etching through both, high [3,8,9,14] and low [7,8,10] refractive index materials, namely metal oxides and silica respectively, has been demonstrated separately and even in combination where grooves were spanning through multiple layers of different
materials [23,27]. HL, when used as a grating origination technique, may require the use of an antireflective coating in order to isolate the resist layer from back reflections [3]. Addition of supplementary optical layers have to be considered in the multilayer stack design. In this work we present an optimization route of a high DE multilayered-dielectric diffraction grating using rigorous coupled wave analysis simulations. We optimized the diffraction grating structure for standard and modified commercially available multilayer stacks to achieve the highest DE for 1030 nm central wavelength, < 300 fs pulse length and 10 nm spectral width femtosecond laser. Our results showcase how accurately selected properties of a diffraction grating profile and multilayer dielectric stack can ensure nearly unity DE over relatively broad ranges of angle of incidence and wavelength. The benefits and drawbacks of three different structures are discussed in the frame of easiness of production, sensitivity to positioning errors, high DE wavelength range, and electric field distributions that can be directly related to optical damage probability. Furthermore, we compare our theoretical calculations to other authors’ findings and illustrate that suggested optimized high DE structures can be actually realized. 2. Methods 2.1. Grating structure and its profile simulations The optical response of a multilayer-dielectric mirror with a grating profile in its top layer was simulated employing commercial software GSolver V5.2 [28] which is based on the Rigorous Coupled Wave Analysis (RCWA) method. We aimed to achieve a high DE at λ = 1030 nm, which is the central wavelength emitted by Yb:KGW femtosecond laser (τ = 270 fs), and used a 1700 line/mm groove density (grating pitch Λ = 588 nm, see Fig. 1a) diffraction grating that is commonly used in commercial CPA systems. We focused on the Littrow angle configuration that allows for a high DE at α = 61.146° angle of incidence. We based our investigation on a commercially available high reflectivity (HR) quarter wavelength-based stack multi-layer dielectric mirror. It is composed of high (Nb2O5, n1030 nm = 2.23) and low (SiO2, n1030 nm = 1.48) refractive index layers periodically stacked on a fused silica substrate. This mirror is optimized for reflectance of 1064 nm wavelength light at 0° angle of incidence. It is commercially available at Altechna Coatings (for 99.9% reflection within 146 nm wavelength spectral range at normal incidence, which covers the bandwidth of the 2
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Yb:KGW laser). The stack consists of 22 high/low refractive index layers with the topmost layer being SiO2. The thicknesses of the individual layers are provided in Fig. 1b. We investigated the original structure first and then modified it by altering the thickness of the topmost low refractive index layer. The optimization of high DE diffraction gratings involved parameters such as: filling factor f (the ratio of ridge width R to the grating pitch Λ, i.e. the filling factor of the grating, see inset in Fig. 1a), thicknesses d of the multilayered mirror stack (see Fig. 1, dLT, dL and dH, where L stands for low refractive index, H – high refractive index, T – top layer), groove depth dG, angle of incidence α, optical properties of the used materials, i.e. the dispersion curve of refractive index, and polarization of impinging light. It should be noted that DE of such structure in the used configuration is very sensitive to the polarization of light. Preliminary simulations showed that using transverse magnetic polarization (TM), f = 0.5 filling factor, and various groove depths within the thickness of the first layer, DE of just 0.09 can be achieved. In contrast, transverse electric (TE) polarization models showed DE > 0.9. Following these findings that are in line with the observations described in [14,29], in further simulations we focused on TE polarization only. The optimization of the grating parameters (groove depth dG, filling factor f, and top layer height dLT) was performed in order to achieve the highest efficiency of the −1 diffraction order in reflectance (−1R). Finally, electrical field distributions in the multilayered diffraction grating structures were simulated employing Comsol Multiphysics V5.3 suite. Electric field simulations were carried out using alternative software because of the limitations of the commercial implementation of RCWA. Standard 2D electromagnetic modeling was used along with a periodic boundary condition. A plane, TE polarized wave was launched towards the structure and the resulting transmitted and reflected diffraction orders were collected. The dielectric functions of materials were taken from the built-in library. The optimized geometrical parameters were taken from the RCWA simulations and the simulation was parametrized by the angle of incidence.
Fig. 2. DE of the −1R diffraction order: (a) dependence on the groove depth; (b) dependence on the angle of incidence for one particular structure indicated above the graph (dL = 357 nm, dG = 422 nm, f = 0.5).
3.2. Optimization of the diffraction grating profile for a highest DE Based on the preliminary simulation results depicted in Fig. 2 and assuming that the grating has rectangular profile shape, we involved a full range of possible parameters in the simulation, including: already used groove depth dG varied from 0 nm to no more than 3 layers deep with a step of 1 nm; top low refractive index layer height dLT varied from 0 to 784 nm with a step of 1 nm; filling factor f varied from 0.01 to 0.99 relative units (r.u.) with a step of 0.01. −1R DE dependence on these parameters is summarized in Fig. 3. Evolution of the DE at different top layer thicknesses, groove depths and filing factors is depicted in the Supplementary movie 1. The red color surface in Fig. 3, indicating a DE above 0.99 r.u., spans the whole parameter space (f, dLT, dG). In order to ensure the DE in the necessary wavelength range, the DE was calculated for 1020–1040 nm wavelengths. The high DE surfaces (DE−1R > 0.99, see Fig. 3) can be sliced at different dLT values and investigated in more details. Two datasets were chosen, i.e. (i) dLT = 231 nm providing the highest achievable DE with the thinner top SiO2 layer than standard mirror structure, and (ii) dLT = 777 nm providing the highest DE with a thicker topmost layer. Spectral and angular DE dependencies of such grating structures are summarized in Supplementary movies 2 and 3. These datasets are analyzed in more detail in Fig. 4. For the first structure, high DE was obtained with groove depths above 350 nm and corresponding to filling factor values f = 0.14 and f = 0.42 (see Fig. 4a). Also, a range of filling factors 0.14–0.42 providing the same high DE was obtained at 342 nm groove depth. More DE > 0.99 cases along the dashed dotted line are provided in Supplementary movie 2. For the second structure, a high DE plateau was obtained in a much wider range of filing factors (see Fig. 4c). The depths between 480 and 520 nm with a filling factor varying from 0.28 to 0.7 and depths exceeding 520 nm with filling factor values of f = 0.28 and 0.73 also yielded high DE. More DE > 0.99 cases for the latter multi-layer stack are provided in Supplementary movie 3. In order to find the best structure parameters, we took coordinate
3. Results 3.1. Optimization of the diffraction grating profile depth First, we performed simulations on the original 1064 nm HR dielectric mirror stack by varying the groove depth (dG) from 0 nm (plain mirror) through the whole mirror structure down to the substrate with a step of 1 nm (see Fig. 2a). The pitch of the modeled structure was 588 nm, 0.5 filling factor, 1030 nm wavelength, TE polarization, 61.14° angle of incidence (Littrow angle). It is hard to realize such high aspect ratio structures in practice, but the simulation results provided us with a good starting point for further optimization and allowed us to get a preliminary idea about the dependence of the DE on the groove depth. The DE dependence on the angle of incidence for 422 nm groove depth is depicted in Fig. 2b. Fig. 2a clearly demonstrates that the DE can be varied by increasing the grating groove depth and can reach almost 100% at several dG values that repeat with some periodicity. One can also see that all 4 expressed DE maximum values are obtained when the bottom of the groove is situated in the material with a higher refractive index, i.e. Nb2O5. The maximum theoretical diffraction efficiency (DE−1R = 0.9995 @1030 nm) was obtained for a 422 nm deep structure, but the groove in that case goes through the whole thickness of the top SiO2 layer and 85 nm of the Nb2O5 layer. By varying the angle of incidence slightly in the range of 58.8–63.6°, or approx. 2° mounting errors that can be introduced in practice, we found that DE does not go below 0.99 at central wavelength of 1030 nm (see Fig. 2b). 3
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whole spectral band and angles of incidence down to 55.2°, i.e. 6° angle off of the Littrow mount geometry. Such structure inevitably requires the grooves to go through the top two layers. In order to avoid the possible difficulties of dry plasma etching of two different oxides, we suggest the optimized multi-layer stack structure parameters, where etching of only one layer is necessary (Fig. 4c, d). In this case the simulated DE dependences on wavelength and angle of incidence show that such model allows only a 0.6° mounting error of the grating for the selected wavelength range while preserving DE > 0.99 (see Fig. 4d). To sum up, the choice of a single material for grating etching requires the use of a dedicated dielectric mirror structure that in the end requires higher grating positioning accuracy compared to structures etched through several layers. Two-dimensional electric field intensity distributions (see Fig. 5) were simulated for three multilayered diffraction grating structures and their respective dielectric mirror stacks without the grating structures discussed earlier. It is clearly seen that the electric field only marginally penetrates the multilayer structure. The most intensive electric field was found within the groove, which is important for high intensity laser beam applications and suggests higher damage thresholds. Moreover, numerical simulations of diffraction efficiency of the structures at different angles of incidence revealed that high DE can be obtained not only for the Littrow mounting geometry. In Fig. 6 we show that by varying the angle of incidence, high DE values are also inherent for different spectral bands.
Fig. 3. First order (−1R) DE dependence on the top layer thickness (dLT), filing factor (f) and groove depth (dG). The grating was simulated in Littrow configuration for 1030 nm wavelength. Red color surface indicates DE above 0.99 r.u. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
sets belonging to DE > 0.99 at 1030 nm 61.14° incidence angle (Littrow) and simulated DE at 950–1100 nm wavelengths. This was performed for two distinguished planes f × dG at dLT = 231 nm and dLT = 777 nm. The simulated spectral and angular dependencies for the two cases are depicted in Fig. 4(b, d). These simulations led to detection of the parameters providing a widest DE > 0.99 spectrum of 67 nm bandwidth (Fig. 4b). The obtained grating profile parameters: dLT = 231 nm, dG = 486 nm and f = 0.42 ensures DE > 0.99 for the
4. Discussion After the sweep of multiple grating profile parameters, three different high DE structures were selected and investigated in more details (Fig. 7). The maximum DE achieved for 1020–1040 nm wavelength range was 0.999. These theoretical results surpass the declared values of commercially available diffraction gratings [30]. The majority of completed computer simulations revealed that a Fig. 4. Two characteristic multilayered diffraction grating profile cases providing high DE with a thinner topmost layer (a, b) and a thicker topmost layer (c, d). Vertical solid lines in (a) and (c) represent interfaces between two different oxides. Solid (a–d) and dash dotted contour lines (in a, c) are following the conditions DE > 0.99 r.u. and DE > 0.999 r.u. at 1030 nm wavelength respectively. Spectral and angular DE dependence of the two optimized grating structures: (b) dLT = 231 nm with optimized grating groove (dG > dLT) and filing factor indicated above, (d) dLT = 777 nm with a grating groove depth almost equal to the topmost layer (dLT ≈ dG) and a respective filing factor indicated above. More spectral and angular dependencies of structures with parameters along the dashed dotted line are provided in supplementary movies 1 and 2. Dashed rectangular box with the center identified with a cross in (b) and (d) indicates the range of desired α and λ combinations with nearly unity DE.
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Fig. 5. Electric field intensity distributions in three optimized dielectric diffraction grating structures and their respective dielectric mirrors (on the right): (a) top layer of 357 nm thickness, groove depth of 422 nm and 0.5 fill factor; (b) dLT = 231 nm, dG = 486 nm and f = 0.42; (c) dLT = 777 nm, dG = 770 nm, f = 0.28.
Fig. 6. Simulation results identifying 0.99 DE zones for the corresponding wavelength and angle of incidence range for different groove depths identified in color. The solid black line depicts Littrow mount configuration for the investigated wavelength range.
Fig. 7. Spectral DE dependence of the three investigated dielectric mirror-based diffraction gratings.
grating groove that goes through several layers provides periodically repeated high DEs along the periodicity of high refractive index layers (see Fig. 2a). It was shown that the highest DE values can be reached when the structure passes the first low refractive index layer and stops within the high refractive index layer. When the structure passes more layers, the DE values vary periodically with the thickness, depending on which layer is at the bottom of the grating groove, and gradually decrease. For example, the best value of DE of > 0.99 was obtained when the calculated structure had a depth of two first layers of Nb2O5 and SiO2 and stopped only in the third SiO2 layer (see Fig. 3). In [23] it was demonstrated that it is feasible to make similar structures experimentally and they have demonstrated very competitive results,
including > 96% DE, that are summarized in Table 1. Multilayer stacks with high refractive index material in the topmost layer [3,5,8,9,14,25] that were not considered in our work could also have nearly unity DE and they are mainly chosen because in this case much lower diffraction grating grooves (100–400 nm, see Table 1 for more details) are necessary, although more complex dry etching chemistries are required. Electrical field simulations of our structures (see Fig. 5a, b) indicate that there is some electrical field concentration in the sandwiched Nb2O3 layer and therefore this structure might be less resistant to optical damage, which was actually measured by others experimentally [23]. Another possibility for achieving high DE structure without the need 5
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Table 1 Properties of the experimentally realized multilayer dielectric diffraction gratings described in literature. No.
Multilayer stack structure
1 1.1
Filing factor, f (r.u.)
Groove depth, dG (nm); thickness of the top layer dT (nm)
DE
Laser damage threshold (J/cm2), angle of incidence, pulse length
Groove in a low refractive index layer SiO2 (nL)/Al2O3 (nH) 1800
< 0.35
700 nm (dG = dT)
> 99% λ = 1030 nm
–
1.2
SiO2 (nL)/HfO2 (nH); 20 layers
1480
0.37
600 nm; 735 nm
94% λ = 1064 nm
–
1.3
SiO2 (nL)/Nb2O3 (nH); 21 layers
2564
0.5
190 nm; 210 nm
97% λ = 532 nm
4.4 (45°, 5 ns); 0.18 (45°, 1 ps)
2 2.1
Groove in a high refractive index layer ZnS (nH)/ThF4 (nL) 1550
~0.8
~100 nm
> 96% λ = 1053 nm
–
2.2
1250
0.25
284 nm; dG = dT
99.7% 1060 nm, (> 99% λ = 1025 – 1070 nm)
2.95 (12 ns, ISO 21254–2)
2.3
Ta2O5 (nH)/SiO2 (nL); 25 layers (mirror) + 4 layers (grating) HfO2 (nH)/SiO2 (nL); 20 layers
1480
0.44
165 nm
95% λ = 1064 nm
1.25 (300 fs)
2.4
HfO2 (nH)/Al2O3 (nL)
1724
0.38
123 nm
96% λ = 777–815 nm
1.1 (57°, 50 fs)
2.5
HfO2 (nH)/SiO2 (nL); 15 layers (mirror) + 1 SiO2(nL) (grating) Ta2O5 (nH)/SiO2 (nL)
1780
0.32
396 nm
96.2% λ = 1053 nm
2.1 (72.5°, 500 fs)
1786
0.5
52 nm; 70 nm
99% λ = 1064 nm
–
0.3
270 nm
97.3% λ = 800 nm (> 96% λ = 820–780 nm)
0.18 (55°, 120 fs); 0.37 (55°, 1 ps); 0.74 (55°, 10 ps); 1.76 (55°, 120 ps)
2.6 3 3.1
Line density (l/mm)
Groove etched through multiple layers (Nb0.5Ta0.5)2O5 (nH)/SiO2 1740 (nL); 20 layers
of etching through Nb2O5 layer is to form a thicker topmost layer of low refractive index. Fig. 3 shows that DE−1R > 0.99 values are obtained only when the thickness of the top layer in the simulated structure reaches 706 nm. Based on the DE−1R > 0.99 surface evolution (see Fig. 3 and Supplementary movie 1) for the analyzed parameter range, it can be seen that for 1030 nm wavelength for every structure that has a top layer thicker than 706 nm DE−1R will be higher than 0.99. Very similar structures were described in [7,8] where 99% DE was experimentally obtained. On the other hand, angular spectral analysis shows (see Fig. 4b, Fig. 7) that DE−1R > 0.99 value using the thicker topmost layer setup is ensured for a significantly narrower range of wavelengths and incidence angles compared to a thinner topmost layer setup (see Fig. 4a, Fig. 7), where grooves are etched through more than one layer. Also, simulations of electric field distribution in the dielectric mirror stack indicate that the electric field does not penetrate deep into the stack and is concentrated between the grating ridges when a thicker top layer is used (see Fig. 5c). This indicates a lower probability of damaging the structure under intensive laser light. It is in agreement with the findings reported in literature and summarized in Table 1. The structure with the topmost low refractive index possessed the highest damage threshold of 4.4 J/cm2 that was obtained with a nanosecond laser [10]. The high DE bandwidths ensured by the three investigated diffraction grating structures (Fig. 7) were converted into available pulse durations. Calculations were carried out by using = 0.44· 02 /c· equation ( 0 – central wavelength; c – speed of light; – spectral width for DE > 0.99) [31]. It was obtained that down to 50 fs pulse duration can be achieved for the diffraction grating based on the 1064 nm dielectric mirror which demonstrated DE > 0.99 in the spectral range of 1003–1034 nm (Fig. 7, solid black line). The shortest pulse length of 23 fs could be maintained with the DE > 0.99 using a diffraction grating with a groove spanning trough two layers of the dielectric stack because it ensures high DE over 992–1060 nm bandwidth (Fig. 7, red dotted line). Pulse with the longest duration of 65 fs corresponds to the highest aspect ratio that maintains smallest DE > 0.99 bandwidth of 1009–1033 nm (Fig. 7, blue dashed line). The
Grating fabrication technology
HL HL EBL
HL HL HL HL –
HL
HL
Ref.
[7] [8] [10]
[14] [9] [8] [3] [5] [25]
[23]
results of maintained pulse length are promising because there are many high intensity commercial laser systems that have longer pulses, i.e. narrower line widths. The high DE regions that were identified by the suggested optimization route would not have been revealed by simple optimization methods, such as the genetic algorithm available in GSolver. Therefore, a full sweep over the parameter space allowed for a selection of parameter sets that not only yield a sufficiently high DE but also have additional fabrication or optical setup related merits. The presented route of simulation can be treated as a possible grating optimization recipe prior to the fabrication of the actual structure. By analyzing the three-dimensional DE data depicted in Fig. 3 in f × dG planes at different top layer thicknesses we showed that there are several high DE zones. One of these zones (Fig. 4c) shows that the DE can be constant at various fill factor values or at a constant groove depth. It is a very promising result regarding the fabrication of the structure because maintaining a required filling factor value is quite a complicated task in lithography processes [10]. The opposite case depicted in Fig. 4d, allows for errors in the dry etching phase because a varying groove depth between 350 and 550 nm (but constant filling factor of 0.14 or 0.42) maintains the same high DE. Similar filing factor having diffraction gratings assuring nearly unity DE were described in [7,8] and are summarized in Table 1. Based on these observations, one can choose the grating profile parameter that is easier to control (f or dG) with the capabilities of the machinery used in the technological formation process, i.e. the type of lithography technology and recipe of the dry etching process. Further investigation showed that high DE values for certain wavelengths can be achieved for a much wider range of angles and not only those that are close to the Littrow condition. From the DE− 1R > 0.99 areas in the DE dependency on angle of incidence and groove depth (Fig. 6) one can see that there are three characteristic conditions ensuring high DE values. One of these areas corresponds to the already discussed Littrow angle curve (Fig. 6, solid black line) that is the usually used configuration [10,29]. The graph suggests that for 6
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shallow grooves (dG 130–350 nm), high DE values are mainly reached at angles 32–45° and 80–88° in the wavelength range of 900–1050 nm, i.e. not for the Littrow angle configuration. On the other hand, the selectivity strongly depends on the groove depth, i.e. when the grating groove reaches Nb2O5 layer, only then Littrow angle allows to achieve high DE−1R > 0.99 values. Using Littrow configuration, broad high DE value contours are achieved in the desired wavelength range—but only for the deeper structures with dG values in the vicinity of the ones summarized in Fig. 6. Another high DE configuration that can be obtained at 84° angle might also have practical applications because at a higher incidence angle the beam interacts with a much bigger surface area of the diffractive structure, thus lowering the energy fluence and possibly damage threshold. Using this kind of angular configuration with bigger aperture gratings, a higher energy chirped pulse amplification might be achieved using the same beam expansion levels. For the full potential understanding of these illumination conditions further investigation is necessary.
Appendix A. Supplementary material Supplementary data to this article can be found online at https:// doi.org/10.1016/j.optlastec.2020.106071. References [1] https://eli-laser.eu/media/1019/eli-whitebook.pdf; the ELI Whitebook. [2] J.P. Chambaret, O. Chekhlov, G. Cheriaux, J. Collier, R. Dabu, P. Dombi, A.M. Dunne, K. Ertel, P. Georges, J. Hebling, J. Hein, C. Hernandez-Gomez, C. Hooker, S. Karsch, G. Korn, F. Krausz, C. Le Blanc, Z. Major, F. Mathieu, T. Metzger, G. Mourou, P. Nickles, K. Osvay, B. Rus, W. Sandner, G. Szabo, D. Ursescu, K. Varju, Extreme Light Infrastructure: architecture and major challenges, in: Conference on Solid State Lasers and Amplifiers III and High-Power Lasers, Brussels, BELGIUM, 2010. [3] F. Canova, O. Uteza, J.-P. Chambaret, M. Flury, S. Tonchev, R. Fechner, O. Parriaux, High-efficiency, broad band, high-damage threshold high-index gratings for femtosecond pulse compression, Opt. Express 15 (2007) 15324–15334. [4] D. Strickland, G. Mourou, Compression of amplified chirped optical pulses, Opt. Commun. 56 (1985) 219–221. [5] J. Neauport, E. Lavastre, G. Raze, G. Dupuy, N. Bonod, M. Balas, G. de Villele, J. Flamand, S. Kaladgew, F. Desserouer, Effect of electric field on laser induced damage threshold of multilayer dielectric gratings, Opt. Express 15 (2007) 12508–12522. [6] I. Richter, P.C. Sun, F. Xu, Y. Fainman, Design considerations of form birefringent microstructures, Appl. Opt. 34 (1995) 2421–2429. [7] J.A. Britten, S.J. Bryan, L.J. Summers, H.T. Nguyen, B.W. Shore, O. Lyngnes, Large aperture, high-efficiency multilayer dielectric reflection gratings, in: Lasers and Electro-Optics, 2002. CLEO '02. Technical Digest. Summaries of Papers Presented at the, 2002, pp. CPDB7–CPDB7. [8] B.W. Shore, M.D. Perry, J.A. Britten, R.D. Boyd, M.D. Feit, H.T. Nguyen, R. Chow, G.E. Loomis, L.F. Li, Design of high-efficiency dielectric reflection gratings, J. Opt. Soc. Am. A – Opt. Image Sci. Vision 14 (1997) 1124–1136. [9] M. Rumpel, M. Moeller, C. Moormann, T. Graf, M.A. Ahmed, Broadband pulse compression gratings with measured 99.7% diffraction efficiency, Opt. Lett. 39 (2014) 323–326. [10] K. Hehl, J. Bischoff, U. Mohaupt, M. Palme, B. Schnabel, L. Wenke, R. Bodefeld, W. Theobald, E. Welsch, R. Sauerbrey, H. Heyer, High-efficiency dielectric reflection gratings: design, fabrication, and analysis, Appl. Opt. 38 (1999) 6257–6271. [11] S. Ratzsch, E.-B. Kley, A. Tuennermann, A. Szeghalmi, Encapsulation process for diffraction gratings, Opt. Express 23 (2015) 17955–17965. [12] L. Stuerzebecher, F. Fuchs, T. Harzendorf, U.D. Zeitner, Pulse compression grating fabrication by diffractive proximity photolithography, Opt. Lett. 39 (2014) 1042–1045. [13] N. Destouches, J.C. Pommier, O. Parriaux, T. Clausnitzer, Narrow band resonant grating of 100% reflection under normal incidence, Opt. Express 14 (2006) 12613–12622. [14] M.D. Perry, R.D. Boyd, J.A. Britten, D. Decker, B.W. Shore, C. Shannon, E. Shults, High-efficiency multilayer dielectric diffraction gratings, Opt. Lett. 20 (1995) 940–942. [15] G. Kalinchenko, S. Vyhlidka, D. Kramer, A. Lerer, B. Rus, High reflective diffraction grating for ultrafast pulse compression, in: Conference on High-Power, HighEnergy, and High-Intensity Laser Technology II, Spie-Int Soc Optical Engineering, Prague, CZECH REPUBLIC, 2015. [16] H.B. Wei, L.F. Li, All-dielectric reflection gratings: a study of the physical mechanism for achieving high efficiency, Appl. Opt. 42 (2003) 6255–6260. [17] Z. Varallyay, P. Dombi, Design of high-efficiency ultrabroadband dielectric gratings, Appl. Opt. 53 (2014) 5769–5774. [18] P.A. Blanche, P. Gailly, S. Habraken, P. Lemaire, C. Jamar, Volume phase holographic gratings: large size and high diffraction efficiency, Opt. Eng. 43 (2004) 2603–2612. [19] C. Zhou, T. Seki, T. Kitamura, Y. Kuramoto, T. Sukegawa, N. Ishii, T. Kanai, J. Itatani, Y. Kobayashi, S. Watanabe, Wavefront analysis of high-efficiency, largescale, thin transmission gratings, Opt. Express 22 (2014) 5995–6008. [20] G. Sobon, K. Krzempek, J. Taka, J. Sotor, Compact, all-PM fiber-CPA system based on a chirped volume Bragg grating, Laser Phys. 26 (2016). [21] M. Nejbauer, T.M. Kardaś, Y. Stepanenko, C. Radzewicz, Spectral compression of femtosecond pulses using chirped volume Bragg gratings, Opt. Lett. 41 (2016) 2394–2397. [22] J.A. Britten, H.T. Nguyen, S.F. Falabella, B.W. Shore, M.D. Perry, D.H. Raguin, Etchstop characteristics of Sc2O3 and HfO2 films for multilayer dielectric grating applications, J. Vacuum Sci. Technol. A – Vacuum Surf. Films 14 (1996) 2973–2975. [23] D.H. Martz, H.T. Nguyen, D. Patel, J.A. Britten, D. Alessi, E. Krous, Y. Wang, M.A. Larotonda, J. George, B. Knollenberg, B.M. Luther, J.J. Rocca, C.S. Menoni, Large area high efficiency broad bandwidth 800 nm dielectric gratings for high energy laser pulse compression, Opt. 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5. Conclusions We have demonstrated that a high diffraction efficiency (DE > 0.99) reflection diffraction grating can be realized in a standard, commercially available, high reflectivity laser line dielectric mirror. Theoretical simulations showed that using a conventional mirror structure, several grating profile scenarios provide 0.99 diffraction efficiencies for TE polarized light in Littrow mount configuration: some require a fine control of the filling factor but allows for etching depth errors, others require the opposite—a precise control of the groove depth but offer more flexibility in the filing factor. In most cases, etching through multiple layers is necessary. We proposed multilayer stack structure with a thicker top SiO2 layer (dLT = 777 nm), which ensures diffraction efficiencies above 0.99 for 1030 nm wavelength in Littrow configuration. Grating profile with a filling factor f = 0.28 and groove depth of dG = 770 nm proved to be promising because the grating grooves spanned through only one material. Theoretically, nearly unity diffraction efficiencies (more than 0.999) for 1030 nm wavelength in Littrow configuration could be achieved by etching a dielectric mirror through several material layers. Especially broad DE > 0.99 spectrum of 68 nm could be maintained using a thinner topmost layer of 231 nm and groove depth of 486 nm. Finite element method simulations suggested that structures with thicker dielectric top layer promise reduced laser damage possibility due to the electric field concentrating in air between the grating ridges. Simulation of various diffraction grating groove depths in multilayered dielectric structure at various illumination angles showed that the same structure can be applied in at least three mounting angles and still have a spectral band with a near unity diffraction efficiency. Based on the bandwidth it was estimated that all investigated structures are capable to maintain DE > 0.99 of a sub 100 fs laser pulse. Main practical limitation is that the spectral band of the high diffraction efficiency is also varying with the mounting angle. Funding This research was funded by the Research, Development and Innovation Fund of Kaunas University of Technology (project grant No. PP35/161). Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. 7
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[29] N. Bonod, J. Neauport, Diffraction gratings: from principles to applications in highintensity lasers, Adv. Opt. Photon. 8 (2016) 156–199. [30] Specification for High Efficiency Transmission Grating, T-1702-1030s Series, LightSmyth Technologies, n.d. http://www.lightsmyth.com/wp-content/uploads/ DS-High-E-Trans-Grating-T-1702-1030s.pdf. [31] E.A.S. Bahaa, C.T. Malvin, Fundamentals of Photonics, Wiley, 2007.
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