Design of high-efficiency ultrabroadband dielectric gratings Zoltán Várallyay1,2 and Péter Dombi2,3,* 1 2 3
FETI Ltd., H-1158 Budapest, Hungary
ELI-HU Nonprofit Kft., H-6720 Szeged, Hungary
MTA “Lendület” Ultrafast Nanooptics Group, Wigner Research Centre for Physics, H-1121 Budapest, Hungary *Corresponding author: [email protected] Received 12 March 2014; revised 28 July 2014; accepted 31 July 2014; posted 1 August 2014 (Doc. ID 208160); published 28 August 2014
We present a design concept of dielectric gratings containing resonant high (TiO2 ) and resonant low (SiO2 ) index dielectric thin-film layers between the grating and the underlying multilayer reflector. We use numerical simulations and the genetic algorithm optimization method to achieve high diffraction efficiency (>97%) in the first diffracted order over a wide wavelength range (∼160 nm) at around 800 nm. The basic concept of the structural optimization contains a high refractive index binary grating with alternating low- and high-index reflector layers, the thicknesses of which are also among the optimization parameters. We introduce two resonant dielectric layers directly below the corrugated TiO2 grating structure and we choose a small (97%) a
Obtained Grating Parameters for Different Model Structuresa
Δλ
Model 1 and Model 2 correspond to Fig. 2, Model 3 and Model 4 to Fig. 3, and Model 5 to Fig. 5.
parameter list shown in Table 1 in the Model 2 column. We lose only a few nanometers of bandwidth with this design and, for an angle of incidence α 40°, it provides over 160 nm bandwidth (from 721 to 882 nm) with higher than 97% DE. This is an almost 1.5 times wider bandwidth than previously reported in ref. [11]. Even though the optimum filling fractions are relatively low in this case, we expect the proposed structures to be within reach (in terms of their fabrication) with further development of reactive ion etching and focused ion beam techniques, which already allow for less than 25% filling fractions to be achieved [18–20]. In Fig. 2, one can see that the aim to obtain broad bandwidth with higher than 97% DE is achieved by three resonant peaks appearing around the 800 nm wavelength range due to the properly adjusted GT layers. These layers allow us to obtain high DE at those regions where the grating alone would not show this behavior. The resonant layers shift the phase of the reflected light in certain wavelength ranges with an amount required so that the grating is able to operate at those shorter and longer wavelengths with high DE, too. The refractive indices of the constituting materials are wavelength-dependent parameters described by an appropriate fitting function to evaluate them for the necessary wavelengths. At 800 nm, the 1
0R, α=39° −1R, α=39° 0R, α=40° −1R, α=40°
0.9 1
0.8 0.995
α=39° α=40°
0.7 0.99
0.6
DE
Diffraction efficiency
nm
0.985
0.5 0.98
0.4 0.975
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0.2
750
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0.1 0 600
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Wavelength [nm] Fig. 2. DE for the dielectric grating having higher than 97% DE over 165 nm (α 39°, Model 1 in Table 1) and 160 nm (α 40°, Model 2) wavelength ranges. Inset zooms to the region where DE is higher than 97% in the -1R direction.
silica and TiO2 have refractive index values of 1.453 and 2.792, respectively. The grating, without any resonant layer, would result in reasonable DE only in a relatively narrow wavelength range at around 800 nm (from 770 to 820 nm). With the introduction of the high-index resonant layer (dGT H ), the grating produces the peak at around 710 nm and the obtainable bandwidth increases to 117 nm with larger than 97% DE (from 716.5 to 833.5 nm). Introducing only the low-index GT resonant layer (dGT L ) without dH , the region at around 850 nm is gained in DE and we may obtain a usable bandwidth between 753 and 840 nm with larger than 97% efficiency. The simultaneous introduction of the two layers will result in the pattern shown in Fig. 2. Without the optimization of the multilayer stack below the grating with the resonant layers, a large number of narrow, low DE regions or leaky modes would appear in the bandgap. As a next step in the parameter study, we also optimize the structure for standardly used CPA grating periods, which are usually 1480 or 1740 lines∕mm. Again, first we start with a Littrow mount. We choose now 1740 lines∕mm, corresponding to a Λ 575 nm grating period. The Littrow angle is 44.1° at 800 nm. We optimized the structure for an incidence angle of 44.1°. In order to check the robustness of the solution against slight deviations in the incidence angle, we also investigate α 45.0° angle of incidence at the same time. We obtain the results shown in Fig. 3 with the parameter list shown in columns Model 3 and Model 4 in Table 1. The obtained bandwidth is 130 nm (from 738 to 868 nm) with larger than 97% grating efficiency. The grating period is far from the ideal for this design, unlike in case in Fig. 2. where Λ is 633 nm and over 160 nm bandwidth is achieved, but still managed to achieve a broad bandwidth. One can see, also, that the TF layer thicknesses are far from the ones obtained in the case of Fig. 2. This shows that the maximum reflectivity of the underlying TF structure highly depends on the properties of the GT layer and the grating structure. This makes it necessary to optimize the layer thicknesses of the dielectric reflector, as well, and not only the parameters of the grating and GT interferometers. 1 September 2014 / Vol. 53, No. 25 / APPLIED OPTICS
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1
0.8 0.995
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Fig. 3. DE for the dielectric grating having higher than 97% DE over a 130 nm wavelength range. Inset zooms to the region where DE is higher than 97%. Two curves are plotted here; they correspond to α 45° (Model 3 in Table 1) and α 44° (Model 4 in Table 1).
We note that a narrow, low DE region can be observed at around 675 nm (Figs. 2 and 3), which reduces the maximum obtainable bandwidth for the investigated dielectric grating structure. By changing the grating period and the thickness of the two GT layers, the low DE region can be shifted to longer or shorter wavelengths, but that way the bandgap is destroyed elsewhere. This typical form appears in a redistribution of energy in the change of the character of a diffracted order from the evanescent to propagating (or vice versa) in the constitutive materials and, therefore, its elimination is not a trivial task. Nevertheless, with the two presented resonant layers, the maximum bandwidth we managed to achieve was more than 160 nm useful bandwidth (with higher than 97% DE) for both angles of incidence, confirming the robustness of the proposed solution. 3. CPA Gratings
In order to simulate a realistic and practical scenario for a CPA system, we need to consider now two criteria. (i) We need to adhere to the standard 1480 or 1740 lines∕mm gratings in order to facilitate an easy exchange of the compressor gratings without having to reconstruct the pulse stretcher/compressor architecture. (ii) This way, we have to set an angle of incidence of some 50° to simulate a typical in-plane compressor where a considerably large off-Littrow angle is used to avoid reflecting the side components of the spectrum back in autocollimation. This criterion will provide an ultrabroad effective compressor bandwidth enabling sub-10-fs pulse production in theory. Results optimized for this scenario are shown in Fig. 4 for a 1740 lines∕mm grating and α 50°. The α 50° angle of incidence is chosen because this Littrow angle corresponds to 881 nm wavelength, thus an ultrabroadband 720–880 nm wavelength range can be transmitted over the compressor made up of the optimized gratings. In the optimized structure in Fig. 4, one still sees a spectral 5772
0R −1R 0R − DM
0.9
Diffraction efficiency
1
Diffraction efficiency
1
0R −1R
0.9
APPLIED OPTICS / Vol. 53, No. 25 / 1 September 2014
0 600
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Wavelength [nm] Fig. 4. DE achieved with a 150 nm bandwidth using 50° angle of incidence and 575 nm grating period (1740 lines∕mm), finding the grating parameters as follows: dH 81 nm, dL 135 nm, GT dGT H 36 nm, dL 0 nm, t 300 nm, and f 7.4%. We added also the reflectance of the dielectric mirror (0R—DM) without the corrugated upper layer.
leakage, but this can be confined to the edge of the useful band. Even with this setup, we achieved more than 150 nm (from 720.5 to 871.5 nm) usable diffraction bandwidth using our standard 97% criteria for determining the bandwidth. Therefore, this offers a viable solution for fully dielectric, ultrabroadband pulse compressor gratings and demonstrates the general applicability of this design approach. Note, however, that the optimization gives zero thickness for the upper silica layer and a reduced thickness for the TiO2 layer, which is the only resonant layer in this structure. The design parameters are listed in the caption of Fig. 4. We plotted also the reflected order from the dielectric mirror without the corrugated top layer in Fig. 4. The reflection bandwidth of the base dielectric mirror with the resonant high-index layer (dH 81 nm, dL 135 nm, dGT H 36 nm) shows a wide high-efficiency region typical for high reflector stacks, which is the basis for obtaining a high DE spectrum for the whole grating structure. 4. Metal–Dielectric Hybrid Gratings
As a further step, we investigated whether the effective bandwidth can be increased by reducing the number of layer pairs in the high reflector stack and introducing a silver substrate at the same time. The TF layer structure and the grating for this study are equivalent with Model 2, in which we used eight periods of high- and low-index layers, from which the upper two layers are the resonant layers as earlier. The refractive index of silver is a wavelengthdependent parameter in the model; its refractive index value at 800 nm is nλ0 0.143 i · 5.323, where λ0 800 nm. The parameters of this grating are listed in Table 1 in column Model 5. Figure 5 shows that the metal substrate with a thinner high reflector stack causes reduction of the bandwidth because, at a few wavelength ranges, the DE suffers
1
which reasonable and high-efficiency diffraction can be reached. Therefore, the proposed dielectric gratings may be recommended for pulse compression purposes, even for ultrashort, high-power pulses in which high DE is required over a broad band. The damage threshold of these types of grating is supposedly lower than that of other types of grating [12] due to the smooth electromagnetic field distribution across the layer structure [7].
0.9
Diffraction efficiency
0.8 0.7 0.6 0.5 8 pairs, −1R 8 pairs, 0R 7 pairs, −1R 7 pairs, 0R 6 pairs, −1R 6 pairs, 0R 5 pairs, −1R 5 pairs, 0R
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Fig. 5. DE in the -1R order for different number of TF layers below the grating using a silver substrate under the same structure, which provided higher than 97% DE over a 160 nm wavelength range (Model 2). We replaced the substrate with a silver one (Model 5) and varied the number of dielectric layer pairs between the grating structure and the substrate without further optimization. With the metal substrate, the bandwidth is reduced to a 129.5 nm wide wavelength range already in the case of eight pairs of layers.
some extra loss compared to the earlier results; for example, at around 870 nm. This effect is more dominant if we use fewer periods of high- and low-index dielectric layers between the corrugated grating and the metal substrate (see Fig. 5). This unfortunate effect is the result of the interference between light reflected from the metal layer and that reflected from the TF layers. As a result, some drop in the DE can be observed at around the 800 and 870 nm wavelengths. This way, we remain with only a 130 nm wavelength range where DE is larger than 97% (between 720 and 850 nm). Executing an optimization for the parameters of the dielectric layer components close to the existing values does not result in a more advantageous DE profile. 5. Conclusion
We showed that using a binary grating made of a high-index dielectric material with an underlying dielectric TF structure may result in more than 160 nm bandwidth with higher than 97% DE by introducing resonant layers in the layer stack design. These resonant layers are, in fact, Gires–Tournois cavities. The overall grating is designed in a way that the high-index grating is followed by a low-index layer, the thickness of which is approximately twice that of the other low-index layers in the Bragg reflector. The next high-index layer is also a resonant layer approximately twice as thick as the other high-index layers in the reflector layers. The optimization parameters contained the low- and high-index layer thicknesses and the grating parameters, such as thickness, filling fraction, and period. The obtained DE shows three well-separated resonances compared to the earlier reported two peaks or hat-shaped DE curves, broadening in this way the spectral range in
P. D. was supported by the Bolyai and Lendület Grants of the Hungarian Academy of Sciences (MTA). This work was supported by project 109257 of the Hungarian Scientific Research Fund and by the European Union with project identification GOP-1.1.1-12B-2012-0001. References 1. 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, Zs. Major, F. Mathieu, T. Metzger, G. Mourou, P. Nickles, K. Osvay, B. Rus, W. Sandner, G. Szabó, D. Ursescu, and K. Varjú, “Extreme light infrastructure: architecture and major challenges,” Proc. SPIE 7721, 77211D (2010). 2. T. Eidam, S. Hanf, E. Seise, T. V. Andersen, T. Gabler, C. Wirth, T. Schreiber, J. Limpert, and A. Tünnermann, “Femtosecond fiber CPA system emitting 830 W average output power,” Opt. Lett. 35, 94–96 (2010). 3. D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985). 4. S. Backus, C. G. Durfee, M. M. Murnane, and H. C. Kapteyn, “High power ultrafast lasers,” Rev. Sci. Instrum. 69, 1207– 1223 (1998). 5. N. Destouches, A. V. Tishchenko, J. C. Pommier, S. Reynaud, O. Parriaux, S. Tonchev, and M. Abdou Ahmed, “99% efficiency measured in the -1st order of a resonant grating,” Opt. Express 13, 3230–3235 (2005). 6. M. Flury, A. V. Tishchenko, and O. Parriaux, “The leaky mode resonance condition ensures 100% diffraction efficiency of mirror-based resonant gratings,” J. Lightwave Technol. 25, 1870–1878 (2007). 7. R. Szipöcs and A. Köházi-Kis, “Theory and design of chirped dielectric laser mirrors,” Appl. Phys. B 65, 115–135 (1997). 8. S. Liu, Y. Jin, Y. Cui, J. Ma, J. Shao, and Z. Fan, “Characteristics of high reflection mirror with an SiO2 top layer for multilayer dielectric grating,” J. Phys. D 40, 3224–3228 (2007). 9. F. Canova, O. Uteza, J.-P. Chambaret, M. Flury, S. Tonchev, R. Fechner, and O. Parriaux, “High-efficiency, broad band, high-damage threshold high-index gratings for femtosecond pulse compression,” Opt. Express 15, 15324–15334 (2007). 10. G. A. Kalinchenko and A. M. Lerer, “Wideband all-dielectric diffraction grating on chirped mirror,” J. Lightwave Technol. 28, 2743–2749 (2010). 11. J. Wang, Y. Jin, J. Shao, and Z. Fan, “Optimization design of an ultrabroadband, high-efficiency, all-dielectric grating,” Opt. Lett. 35, 187–189 (2010). 12. 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, and C. S. Menoni, “Large area high efficiency broad bandwidth 800 nm dielectric gratings for high energy laser pulse compression,” Opt. Express 17, 23809–23816 (2009). 13. J. Fekete, Z. Várallyay, and R. Szipöcs, “Design of highbandwidth one- and two-dimensional photonic bandgap 1 September 2014 / Vol. 53, No. 25 / APPLIED OPTICS
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dielectric structures at grazing incidence of light,” Appl. Opt. 47, 5330–5336 (2008). A. V. Tishchenko and V. A. Sychugov, “High grating efficiency by energy accumulation in a leaky mode,” Opt. Quantum Electron. 32, 1027–1031 (2000). F. Gires and P. Tournois, “Interferometre utilisable pour la compression dimpulsions lumineuses modulees en frequence,” C. R. Acad. Sci. Paris 258, 6112–6115 (1964). Z. Várallyay and K. Saitoh, “Photonic crystal fibre for dispersion control,” in Frontiers in Guided Wave Optics and Optoelectronics, B. Pal, ed. (InTech, 2010), pp. 183–208. http://www.gsolver.com.
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18. S.-S. Kim, Ch. Chun, J.-Ch. Hong, and D.-Y. Kim, “Well-ordered TiO2 nanostructures fabricated using surface relief gratings on polymer films,” J. Mater. Chem. 16, 370–375 (2006). 19. D. Mawet, C. Hanot, C. Lenaerts, P. Riaud, D. Defrère, D. Vandormae, J. Loicq, K. Fleury, J.-Y. Plesseria, J. Surdej, and S. Habraken, “Fresnel rhombs as achromatic phase shifters for infrared nulling interferometry,” Opt. Express 15, 12850–12865 (2007). 20. H. P. H. Liddell, “Enhancing the performance of multilayerdielectric diffraction gratings through cleaning process modifications and defect mitigation,” Ph.D. dissertation (University of Rochester, 2013).
FETI Ltd., H-1158 Budapest, Hungary
ELI-HU Nonprofit Kft., H-6720 Szeged, Hungary
MTA “Lendület” Ultrafast Nanooptics Group, Wigner Research Centre for Physics, H-1121 Budapest, Hungary *Corresponding author: [email protected] Received 12 March 2014; revised 28 July 2014; accepted 31 July 2014; posted 1 August 2014 (Doc. ID 208160); published 28 August 2014
We present a design concept of dielectric gratings containing resonant high (TiO2 ) and resonant low (SiO2 ) index dielectric thin-film layers between the grating and the underlying multilayer reflector. We use numerical simulations and the genetic algorithm optimization method to achieve high diffraction efficiency (>97%) in the first diffracted order over a wide wavelength range (∼160 nm) at around 800 nm. The basic concept of the structural optimization contains a high refractive index binary grating with alternating low- and high-index reflector layers, the thicknesses of which are also among the optimization parameters. We introduce two resonant dielectric layers directly below the corrugated TiO2 grating structure and we choose a small (97%) a
Obtained Grating Parameters for Different Model Structuresa
Δλ
Model 1 and Model 2 correspond to Fig. 2, Model 3 and Model 4 to Fig. 3, and Model 5 to Fig. 5.
parameter list shown in Table 1 in the Model 2 column. We lose only a few nanometers of bandwidth with this design and, for an angle of incidence α 40°, it provides over 160 nm bandwidth (from 721 to 882 nm) with higher than 97% DE. This is an almost 1.5 times wider bandwidth than previously reported in ref. [11]. Even though the optimum filling fractions are relatively low in this case, we expect the proposed structures to be within reach (in terms of their fabrication) with further development of reactive ion etching and focused ion beam techniques, which already allow for less than 25% filling fractions to be achieved [18–20]. In Fig. 2, one can see that the aim to obtain broad bandwidth with higher than 97% DE is achieved by three resonant peaks appearing around the 800 nm wavelength range due to the properly adjusted GT layers. These layers allow us to obtain high DE at those regions where the grating alone would not show this behavior. The resonant layers shift the phase of the reflected light in certain wavelength ranges with an amount required so that the grating is able to operate at those shorter and longer wavelengths with high DE, too. The refractive indices of the constituting materials are wavelength-dependent parameters described by an appropriate fitting function to evaluate them for the necessary wavelengths. At 800 nm, the 1
0R, α=39° −1R, α=39° 0R, α=40° −1R, α=40°
0.9 1
0.8 0.995
α=39° α=40°
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DE
Diffraction efficiency
nm
0.985
0.5 0.98
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0.2
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0.1 0 600
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Wavelength [nm] Fig. 2. DE for the dielectric grating having higher than 97% DE over 165 nm (α 39°, Model 1 in Table 1) and 160 nm (α 40°, Model 2) wavelength ranges. Inset zooms to the region where DE is higher than 97% in the -1R direction.
silica and TiO2 have refractive index values of 1.453 and 2.792, respectively. The grating, without any resonant layer, would result in reasonable DE only in a relatively narrow wavelength range at around 800 nm (from 770 to 820 nm). With the introduction of the high-index resonant layer (dGT H ), the grating produces the peak at around 710 nm and the obtainable bandwidth increases to 117 nm with larger than 97% DE (from 716.5 to 833.5 nm). Introducing only the low-index GT resonant layer (dGT L ) without dH , the region at around 850 nm is gained in DE and we may obtain a usable bandwidth between 753 and 840 nm with larger than 97% efficiency. The simultaneous introduction of the two layers will result in the pattern shown in Fig. 2. Without the optimization of the multilayer stack below the grating with the resonant layers, a large number of narrow, low DE regions or leaky modes would appear in the bandgap. As a next step in the parameter study, we also optimize the structure for standardly used CPA grating periods, which are usually 1480 or 1740 lines∕mm. Again, first we start with a Littrow mount. We choose now 1740 lines∕mm, corresponding to a Λ 575 nm grating period. The Littrow angle is 44.1° at 800 nm. We optimized the structure for an incidence angle of 44.1°. In order to check the robustness of the solution against slight deviations in the incidence angle, we also investigate α 45.0° angle of incidence at the same time. We obtain the results shown in Fig. 3 with the parameter list shown in columns Model 3 and Model 4 in Table 1. The obtained bandwidth is 130 nm (from 738 to 868 nm) with larger than 97% grating efficiency. The grating period is far from the ideal for this design, unlike in case in Fig. 2. where Λ is 633 nm and over 160 nm bandwidth is achieved, but still managed to achieve a broad bandwidth. One can see, also, that the TF layer thicknesses are far from the ones obtained in the case of Fig. 2. This shows that the maximum reflectivity of the underlying TF structure highly depends on the properties of the GT layer and the grating structure. This makes it necessary to optimize the layer thicknesses of the dielectric reflector, as well, and not only the parameters of the grating and GT interferometers. 1 September 2014 / Vol. 53, No. 25 / APPLIED OPTICS
5771
1
0.8 0.995
α=44° α=45°
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DE
0.6 0.985
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Fig. 3. DE for the dielectric grating having higher than 97% DE over a 130 nm wavelength range. Inset zooms to the region where DE is higher than 97%. Two curves are plotted here; they correspond to α 45° (Model 3 in Table 1) and α 44° (Model 4 in Table 1).
We note that a narrow, low DE region can be observed at around 675 nm (Figs. 2 and 3), which reduces the maximum obtainable bandwidth for the investigated dielectric grating structure. By changing the grating period and the thickness of the two GT layers, the low DE region can be shifted to longer or shorter wavelengths, but that way the bandgap is destroyed elsewhere. This typical form appears in a redistribution of energy in the change of the character of a diffracted order from the evanescent to propagating (or vice versa) in the constitutive materials and, therefore, its elimination is not a trivial task. Nevertheless, with the two presented resonant layers, the maximum bandwidth we managed to achieve was more than 160 nm useful bandwidth (with higher than 97% DE) for both angles of incidence, confirming the robustness of the proposed solution. 3. CPA Gratings
In order to simulate a realistic and practical scenario for a CPA system, we need to consider now two criteria. (i) We need to adhere to the standard 1480 or 1740 lines∕mm gratings in order to facilitate an easy exchange of the compressor gratings without having to reconstruct the pulse stretcher/compressor architecture. (ii) This way, we have to set an angle of incidence of some 50° to simulate a typical in-plane compressor where a considerably large off-Littrow angle is used to avoid reflecting the side components of the spectrum back in autocollimation. This criterion will provide an ultrabroad effective compressor bandwidth enabling sub-10-fs pulse production in theory. Results optimized for this scenario are shown in Fig. 4 for a 1740 lines∕mm grating and α 50°. The α 50° angle of incidence is chosen because this Littrow angle corresponds to 881 nm wavelength, thus an ultrabroadband 720–880 nm wavelength range can be transmitted over the compressor made up of the optimized gratings. In the optimized structure in Fig. 4, one still sees a spectral 5772
0R −1R 0R − DM
0.9
Diffraction efficiency
1
Diffraction efficiency
1
0R −1R
0.9
APPLIED OPTICS / Vol. 53, No. 25 / 1 September 2014
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Wavelength [nm] Fig. 4. DE achieved with a 150 nm bandwidth using 50° angle of incidence and 575 nm grating period (1740 lines∕mm), finding the grating parameters as follows: dH 81 nm, dL 135 nm, GT dGT H 36 nm, dL 0 nm, t 300 nm, and f 7.4%. We added also the reflectance of the dielectric mirror (0R—DM) without the corrugated upper layer.
leakage, but this can be confined to the edge of the useful band. Even with this setup, we achieved more than 150 nm (from 720.5 to 871.5 nm) usable diffraction bandwidth using our standard 97% criteria for determining the bandwidth. Therefore, this offers a viable solution for fully dielectric, ultrabroadband pulse compressor gratings and demonstrates the general applicability of this design approach. Note, however, that the optimization gives zero thickness for the upper silica layer and a reduced thickness for the TiO2 layer, which is the only resonant layer in this structure. The design parameters are listed in the caption of Fig. 4. We plotted also the reflected order from the dielectric mirror without the corrugated top layer in Fig. 4. The reflection bandwidth of the base dielectric mirror with the resonant high-index layer (dH 81 nm, dL 135 nm, dGT H 36 nm) shows a wide high-efficiency region typical for high reflector stacks, which is the basis for obtaining a high DE spectrum for the whole grating structure. 4. Metal–Dielectric Hybrid Gratings
As a further step, we investigated whether the effective bandwidth can be increased by reducing the number of layer pairs in the high reflector stack and introducing a silver substrate at the same time. The TF layer structure and the grating for this study are equivalent with Model 2, in which we used eight periods of high- and low-index layers, from which the upper two layers are the resonant layers as earlier. The refractive index of silver is a wavelengthdependent parameter in the model; its refractive index value at 800 nm is nλ0 0.143 i · 5.323, where λ0 800 nm. The parameters of this grating are listed in Table 1 in column Model 5. Figure 5 shows that the metal substrate with a thinner high reflector stack causes reduction of the bandwidth because, at a few wavelength ranges, the DE suffers
1
which reasonable and high-efficiency diffraction can be reached. Therefore, the proposed dielectric gratings may be recommended for pulse compression purposes, even for ultrashort, high-power pulses in which high DE is required over a broad band. The damage threshold of these types of grating is supposedly lower than that of other types of grating [12] due to the smooth electromagnetic field distribution across the layer structure [7].
0.9
Diffraction efficiency
0.8 0.7 0.6 0.5 8 pairs, −1R 8 pairs, 0R 7 pairs, −1R 7 pairs, 0R 6 pairs, −1R 6 pairs, 0R 5 pairs, −1R 5 pairs, 0R
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Fig. 5. DE in the -1R order for different number of TF layers below the grating using a silver substrate under the same structure, which provided higher than 97% DE over a 160 nm wavelength range (Model 2). We replaced the substrate with a silver one (Model 5) and varied the number of dielectric layer pairs between the grating structure and the substrate without further optimization. With the metal substrate, the bandwidth is reduced to a 129.5 nm wide wavelength range already in the case of eight pairs of layers.
some extra loss compared to the earlier results; for example, at around 870 nm. This effect is more dominant if we use fewer periods of high- and low-index dielectric layers between the corrugated grating and the metal substrate (see Fig. 5). This unfortunate effect is the result of the interference between light reflected from the metal layer and that reflected from the TF layers. As a result, some drop in the DE can be observed at around the 800 and 870 nm wavelengths. This way, we remain with only a 130 nm wavelength range where DE is larger than 97% (between 720 and 850 nm). Executing an optimization for the parameters of the dielectric layer components close to the existing values does not result in a more advantageous DE profile. 5. Conclusion
We showed that using a binary grating made of a high-index dielectric material with an underlying dielectric TF structure may result in more than 160 nm bandwidth with higher than 97% DE by introducing resonant layers in the layer stack design. These resonant layers are, in fact, Gires–Tournois cavities. The overall grating is designed in a way that the high-index grating is followed by a low-index layer, the thickness of which is approximately twice that of the other low-index layers in the Bragg reflector. The next high-index layer is also a resonant layer approximately twice as thick as the other high-index layers in the reflector layers. The optimization parameters contained the low- and high-index layer thicknesses and the grating parameters, such as thickness, filling fraction, and period. The obtained DE shows three well-separated resonances compared to the earlier reported two peaks or hat-shaped DE curves, broadening in this way the spectral range in
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