Optimization of a perfect absorber multilayer structure by genetic algorithms
Abstract
Background
An increasing interest has been recently grown in the development of nearly perfect absorber materials for solar energy collectors and more in general for all the thermophotovoltaic applications.
Methods
Wide angle and broadband perfect absorbers with compact multilayer structures made of a sequence of ITO and TiN layers are here studied to develop new devices for solar thermal energy harvesting. Genetic Algorithms are introduced for searching the optimal thicknesses of the layers so to design a perfect broadband absorber in the visible range, for a wide range of angles of incidence from 0° to 50°, and for both polarizations.
Results
Genetic Algorithms allow to design several optimized structures with 6, 8, and 10 layers reaching a very high average absorbance of 97%, 99% and 99.5% respectively together with a low hemispherical total emissivity (<20%) from 200 °C till 400 °C.
Conclusions
The proposed multilayer structures use materials with high thermal stability, and high melting temperature, can be fabricated with simple thin film deposition techniques, appearing to have very promising applications in solar thermal energy harvesting.
Keywords
Optical materials and properties Perfect absorber Multilayer structure Thermophotovoltaic Solar energy collectorsAbbreviations
 A_{av}
Absorbance averaged in the wavelength range 400 nm – 750 nm, and in the angular range from 0° to 50°
 A_{o}
Absorbance for normal incidence averaged in the wavelength range 400 nm – 750 nm
 ɛ_{IR}
hemispherical total emissivity
 f
Fitness function of the Genetic Algorithms
 GAs
Genetic Algorithms
 ITO
Indium Tin Oxide
 M
Number of layers of the structure
 N_{pop}
Size of the population of the Genetic Algorithms
 P_{m}
Probability of mutation
 SiO_{2}
silica
 TiN
Titanium Nitride
Background
During last decade a huge interest has been grown in the development of nearly perfect absorber materials for applications as solar energy collectors, and, more in general, for all the thermophotovoltaic applications (TPV), so to increase the absorbed power for energy harvesting, storage and conversion as well as for the reprocessing of wasted heat in industrial processes [1, 2].
The use of carbon nanotube technology improved a lot the performance of the absorbing materials. In 2009 nanomaterials based on vertically aligned singlewalled carbon nanotubes shown an absorbance of about 98% of the incoming light in a wide spectral range UVVISNIR [3]. But despite recent advances in the development of carbon nanotubes (CNT) purity assessment tools, the macroscale assessment of the overall surface qualities of commercial CNT materials remains a great challenge, bringing negative impacts on the reliable and consistent nanomanufacturing of CNT products [4, 5].
A new concept of perfect absorber is now based on metamaterials where the enhancement of the absorption can be obtained thanks to the excitation of the surface plasmon resonance for example in gold and silver [6, 7, 8, 9, 10, 11, 12, 13]. This can be achieved with structured metallic surfaces [14], microcavities [15], subwavelength hole arrays and opals [16, 17]. Alternatively structured phase change materials [18, 19, 20, 21, 22, 23] and chiral metamaterials [24, 25, 26, 27] have been recently used so to obtain an active switching of the absorption properties thanks to the metalinsulator transition in one case, or to intrinsic/extrinsic dichroism in the other case. However, the realisation of broadband absorber metamaterials requires long and expensive procedures with multiple steps of film deposition, photoresist coating, etching and photoresist removing [28].
It should be underlined that the design and realisation of perfect absorbers with multilayers can be more technically and economically convenient [29]. The multilayer structure can be easily theoretically tested by numerical simulations, and optimized so to obtain broadband absorbers for a wide range of angles of incidence by using several standard search methods (Genetic Algorithms [30], Neural Network [31, 32, 33], Singular Value Decomposition [34, 35, 36], Steepest Descent Methods [37, 38], etc.…). In addition the multilayered opaque structures are also easy to be characterized by using many different diagnostic techniques: photothermal, photoacoustic, photopyroelectric, and thermographic techniques [39, 40, 41, 42, 43, 44, 45].
Concerning the materials, an increasing interest is for the inorganic ceramic materials such as semiconductorbased oxides and transitionmetal nitrides (TiN) which represent the alternative plasmonic materials in the visible frequencies [46, 47, 48, 49, 50], with a good thermal stability [51, 52].
Other common materials for optical electronic device applications and solar cells are the transparent conducting oxides (i.e. ITO) which can support surface plasmon polariton excitations [53, 54].
In this paper we study and optimize a multilayer structure based on a stack of ITO/TiN layers deposited onto a silver thick layer so to design the coating of a solar thermal collector. The idea of such a structure has been recently proposed in Ref. [49]. The authors designed an ITO/TiN multilayer finding an average absorbance of 90% in the visible for a wide range of incidence angle with 7 layers but without studying the infrared emissivity. Our purpose is to optimize this configuration by introducing a silica top layer in order to reach a higher average absorbance and by analysing the low thermal emissivity properties of the structure at different temperatures. We performed numerical simulations by changing the number of layers, and the layer thicknesses, and we applied the Genetic Algorithms to find the optimal thicknesses of the multilayer structure.
Methods
In this section we discuss the approach to design a ITO/TiN multilayered structure to be an efficient coating for solar thermal collectors. The structure will be designed so to exhibit the highest average absorbance in the spectral range from 400 nm to 750 nm (visible window) for a wide range of incidence angles from 0° to 50°, but also satisfying the requirement on a low thermal emissivity (< 20%) in the infrared, so to minimize the radiative losses of the solar collector.
Starting from this state of the art, we want to show that it is possible to achieve better results by replacing the metal layers with Titanium Nitride layers (TiN) [50].
An earlier study concerning the combination of these two materials has already shown how the average absorbance can reach 90% in the visible and for a wide range of incidence angles by using only 7 layers [49]. However we show here that this scheme can be further improved by introducing a silica top layer which acts as an additional antireflection coating (being \( {n}_{SiO2}\cong \sqrt{n_{ITO}\cdot {n}_{air}} \)), without any relevant increase of the thermal emissivity, (see Fig. 1b), and by searching the optimal thicknesses of the whole structure with Genetic Algorithms (GAs).
GAs have been introduced in the 60s by John Holland for two purposes [65]: to explain the adaptive processes of natural systems, and to design artificial systems software capable to emulate the mechanisms of natural systems. For many years GAs have been applied to solve both optimization and inverse problems in many different scientific fields: in biology [66, 67] in computer science [68, 69], in engineering and physics for adaptive filter design [70], in the synthesis of fiber gratings, in thin film metrology [71], in image processing [72], and in metallurgy for the nondestructive testing (NDT) of materials [73, 74, 75].
Adopting the terminology of the biological sciences, GAs evaluate, process and manipulate a population of chromosomes that represent possible solutions in the research space. In our case the chromosome is a string containing the values of the layer thicknesses of the ITO/TiN structure: for example for M layers, the chromosome is a string containing M genes {d_{1}, d_{2}, d_{3}, d_{4}, …, d_{M}} where d_{i} is the thickness of the generic ith layer (from top to bottom) (see Fig. 2). For each chromosome, a numerical simulation should be performed to calculate the absorbance of the multilayer by using the transfermatrix method [76], and to quantify how much the absorbance is close to the ideal case of 100% through the fitness of the chromosome. Each chromosome belongs to the population of N_{pop} individuals. Thanks to the mutual interactions among individuals and to the natural selection mechanisms, the population can evolve and adapt to the environment (research domain), increasing the fitness of all individuals, and eventually finding the best chromosome representing the optimal ITO/TiN multilayer structure.
 a)
The structure is made of a sequence of ITO and TiN layers. The thickness for each ITO layer should be searched by GAs in the range [5 nm – 100 nm], thinner than λ/2 so to avoid internal interference effects. Each TiN layer should be searched by GAs in the interval [5 nm – 60 nm] so to play with its transparency/opaqueness.
 b)
A silica top layer can be optionally inserted as additional antireflection coating. Its thickness should be searched by GAs in the range [5 nm – 150 nm], without causing a relevant change of the IR emissivity.
 c)
The last 200 nm thick silver layer absorbs and stops the residual radiation. Therefore the results of the numerical simulations and optimizations are general and independent on the choice of the substrate.
 d)
The total number of layers M ranges from 3 to 10. The silica top layer is inserted only when M is an even number (see Fig. 2). The optimized multilayers found by GAs for different values of M, will be discussed and compared.
 e)
The objective to be maximized is the absorbance A_{av} averaged in the visible range from λ_{min} = 400 nm to λ_{max} = 750 nm, and averaged for a wide range of angles of incidence from 0° to λ_{max} = 50°, for unpolarised light. It is calculated as follows
where R(λ,θ) is the reflectance for unpolarised light at the wavelength λ, and at the incident angle θ and is calculated by using the transfermatrix method. Note that transmittance is neglected due to the thick silver layer. A_{av} well represents the figure of merit of the perfect absorber.
 f)
The hemispherical total emissivity of the whole structure is also calculated as ɛ_{IR} = 1R_{IR} in the infrared range from 1 μm to 10 μm, averaged over the solid angle and over the Planck blackbody radiation spectrum for 200 °C and for 400 °C, which is the typical temperature range for most solar collectors. The hemispherical total emissivity should be kept as small as possible (< 0.2) to minimize the radiation losses. The calculation is done by using the literature values for the infrared properties of TiN, ITO, SiO_{2}, and silver [61, 62, 63, 64].
 g)
Many parameters of the GAs has to be set, controlled or adjusted (as will be clear in the next section):

M is the number of genes (coincident with the number of layers). It will be selected in the range from 3 to 10 so to design a realistic and sustainable structure;

N_{pop} is the size of the population used for searching the maximum of A_{av}. It is an even number to be adjusted in the range from 8 to 14;

f is the fitness function of each individual and is the quantity to be maximized. It also rules the selection for the reproduction process. In order to enhance the sensitivity we implemented “ad hoc” GAs by using the fitness function f = 1/(1A_{av})^{4} which is more appropriate to distinguish the difference among highly absorbing structures (with A_{av} around unity). This choice allows to reach an optimal solution already after 1000 generations with a run of a few of minutes on a standard PC, giving in general better results with respect to commercial software;

P_{m} is the probability of mutation of each gene in the GAs. It is kept constant to 5%; This choice is driven by a previous study [30].
Results and discussions
In this section we show how Genetic Algorithms (GAs) represent a useful tool to find an optimal ITO/TiN multilayer coating for heat solar collectors, giving some examples which demonstrate how the mechanic of the GAs is surprisingly simple and efficient.
According to the methods described in the previous section, the figure of merit of the multilayer coating has been identified in the average absorbance A_{av} or better in the fitness function f = 1/(1A_{av})^{4} which is more appropriate to enhance the differences among quasi perfect absorbers (when A_{av} ≈ 1).
Initial population processed by the GAs. Number of layer M = 6. Size of the population N_{pop} = 8
As said each chromosome identifies a specific individual who belongs to the population of N_{pop} individuals. As a result of mutual interactions among individuals, the population can evolve and adapt to the environment, increasing the fitness of all individuals.
Table 1 shows the initial population of N_{pop} = 8 chromosomes. Each chromosome is made of M = 6 genes (rows from 6 to 11). All genes are randomly chosen within the ranges described in section 2.
Both absorbances A_{o}, and A_{av} are calculated for each chromosome, and shown in rows 2, and 3 respectively. The corresponding fitness function f = 1/(1A_{av})^{4} is shown in row 4. Looking at the fitness the best chromosome of the population is found to be the N.6 (the column is highlighted in black in Table 1).
Results after the selection procedure applied to the initial population in Table 1
Results after the crossover procedure applied to the population in Table 2
Results after the mutation procedure applied to the population in Table 3
Last mechanism of GAs is the elitism, which allows to clone the best chromosome of the previous generation and keep it unchanged for the next generation so to avoid a possible regression of the evolutionary process that might statistically occur: for example chromosome N.1 in Table 4 is the clone of the best chromosome in Table 1.
In synthesis the new generation is formed from the previous one by applying the sequence of the following procedures: selection, reproduction, mutation, and elitism. By iterating these procedures it has been demonstrated that the fitness of the population increases, generation by generation, and that the best chromosome slowly tends to the solution of the optimization problem [65, 30].
Optimized structures found by GAs for different number of layers M
Conclusions
The design of quasi perfect absorbers based on ITO/TiN multilayered structures is here discussed. The practical purpose is to find new optimized coatings for solar thermal collectors with the highest achievable absorbance in the visible range from 400 nm to 750 nm, working for a wide range of angles of incidence from 0° to 50°, for both polarizations, and with a low hemispherical total emissivity, so to minimize the radiative losses. Genetic Algorithms are introduced and adjusted for searching the optimal thicknesses for several ITO/TiN multilayered structures with 6, 8, 10 layers reaching a very high average absorbance of 97%, 99% and 99.5% respectively and a low hemispherical total emissivity (< 20%) from 200 °C till 400 °C. The proposed multilayer structures use materials with high thermal stability, and high melting temperature, can be fabricated with simple thin film deposition techniques, appearing to have very promising applications in solar thermal energy harvesting.
Notes
Acknowledgements
This author is indebted with Mario Bertolotti and Joseph Haus for useful discussions.
Funding
This work has been done in the framework of the project “optical metamaterial” funded by Sapienza University of Rome, and “Scherma” cofinanced by Italian Ministry of Defence.
Availability of data and materials
The numerical results and data can be reproduced by applying the optical method in Ref. [71], by using the Genetic Algorithms described in Ref. [60], and by taking the optical properties of the materials found in Refs. [47, 61, 62, 63, 64]. No additional supporting information or data are necessary.
Author's contributions
The author read and approved the final manuscript.
Author’s information
Roberto Li Voti is associate professor in Applied Physics at Sapienza University of Rome, Italy. He is author of more than 150 publications in the field of optics, photohermal and photoacoustic techniques for nondestructive testing of materials.
Competing interests
The author declares that he has no competing interests.
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
References
 1.Siegel, R., Howell, J.R.: Thermal Radiation Heat Transfer, vol. 1, 4th edn, p. 7. Taylor & Francis (2002) ISBN 1560328398.Google Scholar
 2.Nam, Y., Xiang Yeng, Y., Lenert, A., Bermel, P., Celanovic, I., Soljačić, M., Wang, E.N.: Solar thermophotovoltaic energy conversion systems with twodimensional tantalum photonic crystal absorbers and emitters. Sol. Energy Mater. Sol. Cells. 122, 287–296 (2014)Google Scholar
 3.Mizuno, K., et al.: A black body absorber from vertically aligned singlewalled carbon nanotubes. Proc Natl Acad Sci. 106, 6044–6077 (2009). https://doi.org/10.1073/pnas.0900155106 ADSCrossRefGoogle Scholar
 4.Tune, D.D., Flavel, B.S., Krupke, R., Shapter, J.G.: Solar Cells: Carbon NanotubeSilicon Solar Cells. Advanced Energy Materials. 2, 1043–1055 (2012). https://doi.org/10.1002/aenm.201290045 CrossRefGoogle Scholar
 5.Leahu, G., Li Voti, R., Larciprete, M.C., Sibilia, C., Bertolotti, M., Nefedov, I., Anoshkin, I.V.: Thermal Characterization of Carbon Nanotubes by Photothermal Techniques. Int. J. Thermophys. 36, 1349–1357 (2015)ADSCrossRefGoogle Scholar
 6.Cao, T., Wei, C.W., Simpson, R.E., Zhang, L., Cryan, M.J.: Broadband PolarizationIndependent Perfect Absorber Using a PhaseChange Metamaterial at Visible Frequencies. Sci. Rep. 4, 3955 (2014)CrossRefGoogle Scholar
 7.Wang, W., Wu, S., Reinhardt, K., Lu, Y., Chen, S.: Broadband Light Absorption Enhancement in ThinFilm Silicon Solar Cells. Nano Lett. 10, 2012 (2010)ADSCrossRefGoogle Scholar
 8.Aydin, K., Ferry, V.E., Briggs, R.M., Atwater, H.A.: Broadband polarizationindependent resonant light absorption using ultrathin plasmonic super absorbers. Nat. Commun. 2, 517 (2011)ADSCrossRefGoogle Scholar
 9.Teperik, T.V., De Abajo, F.G., Borisov, A., Abdelsalam, M., Bartlett, P., Sugawara, Y., Baumberg, J.: Omnidirectional absorption in nanostructured metal surfaces. Nat. Photonics. 2, 299 (2008)CrossRefGoogle Scholar
 10.Cheng, C.W., Abbas, M.N., Chiu, C.W., Lai, K.T., Shih, M.H., Chang, Y.C.: Wideangle polarization independent infrared broadband absorbers based on metallic multisized disk arrays. Opt. Express. 20, 10376 (2012)ADSCrossRefGoogle Scholar
 11.Centini, M., Benedetti, A., Larciprete, M.C., Belardini, A., Li Voti, R., Bertolotti, M., Sibilia, C.: Midinfrared thermal emission properties of finite arrays of gold dipole nanoantennas. Phys. Rev. B. 92, 205411 (2015)ADSCrossRefGoogle Scholar
 12.Li Voti, R., Leahu, G., Larciprete, M.C., Sibilia, C., Bertolotti, M., Nefedov, I., Anoshkin, I.V.: Photoacoustic Characterization of Randomly Oriented Silver Nanowire Films. Int. J. Thermophys. 36, 1342–1348 (2015)ADSCrossRefGoogle Scholar
 13.Belardini, A., Pannone, F., Leahu, G., Larciprete, M.C., Centini, M., Sibilia, C., Martella, C., Giordano, M., Chiappe, D., Buatier de Mongeot, F.: Evidence of anomalous refraction of selfassembled curved gold nanowires. Appl. Phys. Lett. 100(25), 251109 (2012)ADSCrossRefGoogle Scholar
 14.Laroche, M., Carminati, R., Greffet, J.J.: Coherent Thermal Antenna Using a Photonic Crystal Slab. Phys. Rev. Lett. 96, 123903 (2006)ADSCrossRefGoogle Scholar
 15.Celanovic, I., Perreault, D., Kassakian: Resonantcavity enhanced thermal emission. J. Phys. Rev. B. 72, 075127 (2005)ADSCrossRefGoogle Scholar
 16.Hu, C.G., Liu, L.Y., Chen, X.N., Luo, X.G.: Mixed plasmons coupling for expanding the bandwidth of nearperfect absorption at visible frequencies. Opt. Express. 17, 16745 (2009)ADSCrossRefGoogle Scholar
 17.Leahu, G., Voti, R.L., Sibilia, C., Bertolotti, M., Golubev, V., Kurdyukov, D.A.: Study of thermal and optical properties of SiO_{2}/GaN opals by photothermal deflection technique. Opt. Quant. Electron. 39, 305–310 (2007)CrossRefGoogle Scholar
 18.Kats, M.A., Blanchard, R., Zhang, S., Genevet, P., Ko, C., Ramanathan, S., Capasso, F.: Vanadium Dioxide as a Natural Disordered Metamaterial: Perfect Thermal Emission and Large Broadband Negative Differential Thermal Emittance. Physical Review X. 3, 041004 (2013)ADSCrossRefGoogle Scholar
 19.Paonea, M., Geiger, R., Sanjines, A., Schüler: Thermal solar collector with VO_{2} absorber coating and thermochromic glazing – Temperature matching and triggering. Sol. Energy. 110, 151–159 (2014)ADSCrossRefGoogle Scholar
 20.Leahu, G., Li Voti, R., Sibilia, C., Bertolotti, M.: Anomalous optical switching and thermal hysteresis during semiconductormetal phase transition of VO2 films on Si substrate. Appl. Phys. Lett. 103, 231114 (2013)ADSCrossRefGoogle Scholar
 21.Voti, R.L., Larciprete, M.C., Leahu, G., Sibilia, C., Bertolotti, M.: Optimization of thermochromic VO 2 based structures with tunable thermal emissivity. J. Appl. Phys. 112, 034305 (2012)ADSCrossRefGoogle Scholar
 22.Mercuri, F., Zammit, U., Scudieri, F., Marinelli, M.: Thermal and optical study of the kinetics of the nematicisotropic transition in octylcyanobiphenyl. Phys. Rev. E. 68, 041708 (2003)ADSCrossRefGoogle Scholar
 23.Zammit, U., Marinelli, M., Mercuri, F., Paoloni, S.: Effect of Confinement and Strain on the Specific Heat and Latent Heat over the Nematic−Isotropic Phase Transition of 8CB Liquid Crystal. J. Phys. Chem. B. 113, 14315–14322 (2009)CrossRefGoogle Scholar
 24.Wang, B., Koschny, T., Soukoulis, C.M.: Wideangle and polarizationindependent chiral metamaterial absorber. Phys. Rev. B. 80(033108), (2009)Google Scholar
 25.Plum, E., Zheludev, N.I.: Chiral mirrors. Appl. Phys. Lett. 106(221901), (2015)Google Scholar
 26.Belardini, A., Centini, M., Leahu, G., Hooper, D.C., Li Voti, R., Fazio, E., Haus, J.W., Sibilia, C.: Chiral light intrinsically couples to extrinsic/pseudochiral metasurfaces made of tilted gold nanowires. Sci. Rep. 6, 31796 (2016)ADSCrossRefGoogle Scholar
 27.Benedetti, A., Alam, B., Esposito, M., Tasco, V., Leahu, G., Belardini, A., Li Voti, R., Passaseo, A., Sibilia, C.: Precise detection of circular dichroism in a cluster of nanohelices by photoacoustic measurements. Sci. Rep. 7, 5257 (2017)ADSCrossRefGoogle Scholar
 28.Wu, J., Zhou, C.Z., Cao, H.C., Hu, A.D.: Polarizationdependent and independent spectrum selective absorption based on a metallic grating structure. Opt. Comm. 309, 57 (2013)ADSCrossRefGoogle Scholar
 29.Chen, H.T., Zhou, J., O’Hara, J.F., Chen, F., Azad, A.K., Taylor, A.J.: Antireflection Coating Using Metamaterials and Identification of Its Mechanism. Phys. Rev. Lett. 105(073901), (2010)Google Scholar
 30.Li Voti, R.: Optimization of transparent metal structures by genetic algorithms. Romanian Reports in Physics. 64, 446–466 (2012)Google Scholar
 31.Glorieux, C., Thoen, J.: Thermal depth profile reconstruction by neural network recognition of the photothermal frequency spectrum. J. Appl. Phys. 80, 6510 (1996)ADSCrossRefGoogle Scholar
 32.Glorieux, R., Thoen, L.V.J., Bertolotti, M., Sibilia, C.: Depth profiling of thermally inhomogeneous materials by neural network recognition of photothermal time domain data. J. Appl. Phys. 85, 7059–7063 (1999)ADSCrossRefGoogle Scholar
 33.Glorieux, C., Li Voti, R., Thoen, J., Bertolotti, M., Sibilia, C.: Photothermal depth profiling: Analysis of reconstruction errors. Inverse Problems. 15, 1149–1163 (1999)ADSCrossRefzbMATHGoogle Scholar
 34.Tomoda, M., Li Voti, R., Matsuda, O., Wright, O.B.: Tomographic reconstruction of picosecond acoustic strain propagation. Appl. Phys. Lett. 90, 041114 (2007)ADSCrossRefGoogle Scholar
 35.Krapez, J.C., Li Voti, R.: Effusivity Depth Profiling from Pulsed Radiometry Data: Comparison of Different Reconstruction Algorithms. Anal. Sci. 17, s417–s418 (2001). https://doi.org/10.14891/analscisp.17icpp.0.s417.0 CrossRefGoogle Scholar
 36.Li Voti, R., Leahu, G.L., Gaetani, S., Sibilia, C., Violante, V., Castagna, E., Bertolotti, M.: Light scattering from a rough metal surface: Theory and experiment. J. Opt. Soc. Am. B. 26, 1585–1593 (2009)ADSCrossRefGoogle Scholar
 37.Larciprete, M.C., Belardini, A., Voti, R.L., Sibilia, C.: Prefractal multilayer structure for polarizationinsensitive temporally and spatially coherent thermal emitter. Opt. Express. 21, A576–A584 (2013)ADSCrossRefGoogle Scholar
 38.Larciprete, M.C., Centini, M., Voti, R.L., Bertolotti, M., Sibilia, C.: Polarization insensitive infrared absorbing behaviour of onedimensional multilayer stack: A fractal approach. Opt. Express. 22, A1547–A1552 (2014)ADSCrossRefGoogle Scholar
 39.Melnikov, A., Mandelis, A., Tolev, J., Chen, P., Huq, S.: Infrared lockin carrierography (photocarrier radiometric imaging) of Si solar cells. J. Appl. Phys. 107, 114513 (2010)ADSCrossRefGoogle Scholar
 40.Sun, Q.M., Melnikov, A., Mandelis, A.: Quantitative Carrier Density Wave Imaging in Silicon Solar Cells Using Photocarrier Radiometry and Lockin Carrierography. Int. J. Thermophys. 37, 45 (2016)ADSCrossRefGoogle Scholar
 41.Matsuda, O., Larciprete, M.C., Li Voti, R., Wright, O.B.: Fundamentals of picosecond laser ultrasonics. Ultrasonics. 56, 3–20 (2015)CrossRefGoogle Scholar
 42.Dehoux, T., Wright, O.B., Voti, R.L.: Picosecond time scale imaging of mechanical contacts. Ultrasonics. 50, 197–201 (2010)CrossRefGoogle Scholar
 43.Tomoda, M., Wright, O.B., Li Voti, R.: Nanoscale thermoelastic probing of megahertz thermal diffusion. Appl. Phys. Lett. 91, 071911 (2007)ADSCrossRefGoogle Scholar
 44.Zammit, U., Mercuri, F., Paoloni, S., Marinelli, M., Pizzoferrato, R.: Simultaneous absolute measurements of the thermal diffusivity and the thermal effusivity in solids and liquids using photopyroelectric calorimetry. J. Appl. Phys. 117, 105104 (2015)Google Scholar
 45.Zammit, U., Paoloni, S., Mercuri, F., Marinelli, M., Scudieri, F.: Self consistently calibrated photopyroelectric calorimeter for the high resolution simultaneous absolute measurement of the specific heat and of the thermal conductivity. AIP Advances. 2, 012135 (2012)ADSCrossRefGoogle Scholar
 46.Naik, G.V., Kim, J., Boltasseva, A.: Oxides and nitrides as alternative plasmonic materials in the optical range. Opt. Mater. Express. 1, 1090 (2011)CrossRefGoogle Scholar
 47.Naik, G.V., Schroeder, J.L., Ni, X., Kildishev, A.V., Sands, T.D., Boltasseva, A.: Titanium nitride as a plasmonic material for visible and nearinfrared wavelengths. Opt. Mater. Express. 2, 478 (2012)CrossRefGoogle Scholar
 48.Naik, G.V., Shalaev, V.M., Boltasseva, A.: Alternative Plasmonic Materials: Beyond Gold and Silver. Adv. Mater. 25, 3264 (2013)CrossRefGoogle Scholar
 49.Wang, J., Yin, C., Zhu, M., Sun, J., Yi, K., Shao, J.: Wide angle and broadband perfect absorber with compact multilayer structures. Mod. Phys. Lett. B. 31, 1750136 (2017)Google Scholar
 50.Venugopal, N., Gerasimov, V.S., Ershov, A.E., Karpov, S.V., Polyutov, S.P.: Titanium nitride as light trapping plasmonic material in silicon solar cell. Opt. Mater. 72, 397–402 (2017)ADSCrossRefGoogle Scholar
 51.Yu, H., Tan, T., Wu, W., Tian, C., An, Y., Sun, F.: Thermal stability of titanium nitride coatings prepared by the mixing technology with laser and plasma. Curr. Appl. Phys. 12, 152–154 (2012)Google Scholar
 52.Liu, Y., Mandelis, A., Choy, M., Wang, C., Lee, S.: Remote quantitative temperature and thickness measurements of plasmadeposited titanium nitride thin coatings on steel using a laser interferometric thermoreflectance optical thermometer. Rev. Sci. Instrum. 76, 084902 (2005)ADSCrossRefGoogle Scholar
 53.Abb, M., Sepu’lveda, B., Chong, M.H., Muskens, O.L.: Transparent conducting oxides for active hybrid metamaterial devices. J. Opt. 14, 114007–114001 (2012)ADSCrossRefGoogle Scholar
 54.Rajak, S., Ray, M.: Comparative study of plasmonic resonance in transparent conducting oxides: ITO and AZO. J. Opt. 43, 231 (2014)CrossRefGoogle Scholar
 55.You, J.B., Lee, W.J., Won, D., Yu, K.: Multiband perfect absorbers using metaldielectric films with optically dense medium for angle and polarization insensitive operation. OPTICS EXPRESS. 22, 8339 (2014)ADSCrossRefGoogle Scholar
 56.Kuo, C.C.: International Scholarly and Scientific Research & Innovation. 7, 570–572 (2013)Google Scholar
 57.Scalora, M., Bloemer, M.J., Pethel, A.S., Dowling, J.P., Bowden, C.M., Manka, A.S.: Transparent, metallodielectric, onedimensional, photonic bandgap structures. J. Appl. Phys. 83, 2377 (1998)ADSCrossRefGoogle Scholar
 58.Sarto, M.S., Li Voti, R., Sarto, F., Larciprete, M.C.: Nanolayered lightweight flexible shields with multidirectional optical transparency. IEEE Transactions on Electromagnetic Compatibility. 47, 602–611 (2005)CrossRefGoogle Scholar
 59.Li Voti, R., Larciprete, M.C., Leahu, G., Sibilia, C., Bertolotti, M.: Optical response of multilayer thermochromic VO2based structures. Journal of Nanophotonics. 6, 061601 (2012)ADSCrossRefGoogle Scholar
 60.Cesarini, G., Leahu, G., Grilli, M.L., Sytchkova, A., Sibilia, C., Voti, R.L.: Optical and photoacoustic investigation of AZO/Ag/AZO transparent conductive coating for solar cells. Phys. Status Solidi C. 13, 998–1001 (2016)Google Scholar
 61.Pflüger, J., Fink, J., Weber, W., Bohnen, K.P., Crecelius, G.: Dielectric properties of TiCx, TiNx, VCx, and VNx from 1.5 to 40 eV determined by electronenergyloss spectroscopy. Phys. Rev. B. 30, 1155–1163 (1984)ADSCrossRefGoogle Scholar
 62.Yuste, M., Escobar Galindo, R., Sánchez, O., Cano, D., Casasola, R., Albella, J.M.: Correlation between structure and optical properties in low emissivity coatings for solar thermal collectors. Thin Solid Films. 518, 5720 (2010)ADSCrossRefGoogle Scholar
 63.Briggs, J.A., Naik, G.V., Yang, Z., Petach, T.A., Sahasrabuddhe, K., Gordon, D.G., Melosh, N.A., Dionne, J.A.: Temperaturedependent optical properties of titanium nitride. Appl. Phys. Lett. 110, 101901 (2017)ADSCrossRefGoogle Scholar
 64.Palik, E.D.: Handbook of Optical Constants of Solids. Academic Press, New York (1985)Google Scholar
 65.Holland, J.H.: Outline for a Logical Theory of Adaptive Systems. J. Assoc. Comput. Mach. 3, 297–314 (1962)Google Scholar
 66.Rosenberg, R.S.: Simulation of genetic populations with biochemical properties : I. The model. Math. Biosci. 7, 223–257 (1970)Google Scholar
 67.Rosenberg, R.S.: Simulation of genetic populations with biochemical properties: II. Selection of crossover probabilities. Math. Biosci. 8, 1–37 (1970)CrossRefGoogle Scholar
 68.David Edward Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning, Publisher: AddisonWesley Professional; 1 edition (Jan. 1 1989) ISBN10: 0201157675, ISBN13: 9780201157673.Google Scholar
 69.Etter, D.M., Hicks, M.J., Cho, K.H.: Recursive adaptive filter design using an adaptive genetic algorithm. IEEE Int Conference Acoustics Speech Signal Proc. 2, 635–638 (1982)CrossRefGoogle Scholar
 70.Goldberg D.E., “Computeraided gas pipeline operation using genetic algorithms and rule learning”, Dissertation Abstracts International 44 (10) 3174b (1983). DOI (doi: https://doi.org/10.1234/12345678). or a PubMed ID (pmid:12345678).
 71.Skaar, J., Risvik, K.M.: A Genetic Algorithm for the Inverse Problem in Synthesis of Fiber Gratings. J. Lightwave Technol. 16, 1928–1932 (1998)Google Scholar
 72.Lienert, B.R., Porter, J.N., Sharma, S.K.: Repetitive genetic inversion of optical extinction data. Appl. Opt. 40, 3476–3482 (2001)ADSCrossRefGoogle Scholar
 73.Li Voti, R.: Inverse problems by Genetic Algorithms: application to the photothermal depth profiling. In: Maldague, X., ASNT (eds.) IV International Workshop  Advances in Signal Processing for Nondestructive Evaluation of Materials, vol. 6, pp. 31–41. Published by The American Society Nondestructive Testing Inc. (2002) ISBN: 157117091XGoogle Scholar
 74.Li Voti, R., Melchiorri, C., Sibilia, C., Bertolotti, M.: Use of the Genetic Algorithms in the Photothermal Depth Profiling. Anal. Sci. 17, s410–s413 (2001). https://doi.org/10.14891/analscisp.17icpp.0.s410.0
 75.Li Voti, R., Sibilia, C., Bertolotti, M.: Photothermal depth profiling by thermal wave backscattering and genetic algorithms. Int. J. Thermophys. 26, 1833–1848 (2005)Google Scholar
 76.Born, M., Wolf, E.: Principles of optics: electromagnetic theory of propagation, interference and diffraction of light. Pergamon Press, Oxford (1964)zbMATHGoogle Scholar
 77.Leahu, G., Petronijevic, E., Belardini, A., Centini, M., Li Voti, R., Hakkarainen, T., Koivusalo, E., Guina, M., Sibilia, C.: Photoacoustic spectroscopy revealing resonant absorption of selfassembled GaAsbased nanowires. Sci. Rep. 7, 2833 (2017)Google Scholar
Copyright information
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.