Ultra-Broadband Infrared Absorption by Tapered Hyperbolic Multilayer Waveguides

Transcription

1 Missouri Universiy of Science and Technology Scholars' Mine Mechanical and Aerospace Engineering Faculy Research & Creaive Works Mechanical and Aerospace Engineering Ulra-Broadband Infrared Absorpion by Tapered Hyperbolic Mulilayer Waveguides Huixu Deng Cherian J. Mahai Shubhra Gangopadhyay Jie Gao Missouri Universiy of Science and Technology, e. al. For a complee lis of auhors, see hp://scholarsmine.ms.edu/mec_aereng_facwork/4178 Follow his and addiional works a: hp://scholarsmine.ms.edu/mec_aereng_facwork Par of he Aerospace Engineering Commons Recommended Ciaion H. Deng e al., "Ulra-Broadband Infrared Absorpion by Tapered Hyperbolic Mulilayer Waveguides," Opics Express, vol. 26, no. 5, pp , Opical Sociey of America (OSA), Mar The definiive version is available a hps://doi.org/ /oe This Aricle - Journal is brough o you for free and open access by Scholars' Mine. I has been acceped for inclusion in Mechanical and Aerospace Engineering Faculy Research & Creaive Works by an auhorized adminisraor of Scholars' Mine. This work is proeced by U. S. Copyrigh Law. Unauhorized use including reproducion for redisribuion requires he permission of he copyrigh holder. For more informaion, please conac scholarsmine@ms.edu.

2 Vol. 26, No. 5 5 Mar 2018 OPTICS EXPRESS 6360 Ulra-broadband infrared absorpion by apered hyperbolic mulilayer waveguides HUIXU DENG,1 CHERIAN J. MATHAI,2 SHUBHRA GANGOPADHYAY,2 JIE GAO,1,3 AND XIAODONG YANG1,* 1Deparmen of Mechanical and Aerospace Engineering, Missouri Universiy of Science and Technology, Rolla, MO 65409, USA 2Deparmen of Elecrical and Compuer Engineering, Universiy of Missouri, Columbia, Missouri 65211, USA 3gaojie@ms.edu *yangxia@ms.edu Absrac: Ulra-broadband srong absorpion over 92% covering he infrared wavelengh range of 1 ~ 6μm is demonsraed by using he apered hyperbolic Au-SiO2 mulilayer waveguides on glass subsraes. Such broadband absorpion is formed by he sop-ligh modes a various wavelenghs locaed a differen waveguide widhs. A planar hyperbolic waveguide model is buil o deermine he sop-ligh modes by considering boh forward and backward guided modes. The sop-ligh modes locaed inside he Au-SiO2 mulilayer waveguide are simulaed a he absorpion peaks by reducing he Au loss. Tapered mulilayer waveguides wih varying op widhs are furher simulaed, fabricaed and measured, indicaing he almos linear relaion beween he waveguide widh and he sop-ligh wavelengh. Moreover, he broadband absorpion of apered waveguide is proved o be angle-insensiive and polarizaion-independen, and he hea generaion and emperaure increase are also discussed Opical Sociey of America under he erms of he OSA Open Access Publishing Agreemen OCIS codes: ( ) Absorpion; ( ) Energy ransfer; ( ) Meamaerials; ( ) Infrared. References and links Y. Cui, Y. He, Y. Jin, F. Ding, L. Yang, Y. Ye, S. Zhong, Y. Lin, and S. He, Plasmonic and meamaerial srucures as elecromagneic absorbers, Laser Phoonics Rev. 8(4), (2014). C. M. Was, X. Liu, and W. J. Padilla, Meamaerial Elecromagneic Wave Absorbers, Adv. Maer. 24(23), OP98 (2012). N. P. Sergean, O. Pincon, M. Agrawal, and P. Peumans, Design of wide-angle solar-selecive absorbers using aperiodic meal-dielecric sacks, Op. Express 17(25), (2009). H. Wang and L. Wang, Perfec selecive meamaerial solar absorbers, Op. Express 21(S6 Suppl 6), A1078 A1093 (2013). H. Deng, T. Wang, J. Gao, and X. Yang, Meamaerial hermal emiers based on nanowire caviies for highefficiency hermophoovolaics, J. Op. 16(3), (2014). X. Liu, T. Tyler, T. Sarr, A. F. Sarr, N. M. Jokers, and W. J. Padilla, Taming he Blackbody wih Infrared Meamaerials as Selecive Thermal Emiers, Phys. Rev. Le. 107(4), (2011). N. I. Landy, C. M. Bingham, T. Tyler, N. Jokers, D. R. Smih, and W. J. Padilla, Design, heory, and measuremen of a polarizaion-insensiive absorber for eraherz imaging, Phys. Rev. B 79(12), (2009). K. Aydin, V. E. Ferry, R. M. Briggs, and H. A. Awaer, Broadband polarizaion-independen resonan ligh absorpion using ulrahin plasmonic super absorbers, Na. Commun. 2, 517 (2011). H. Deng, L. San, D. A. Czaplewski, J. Gao, and X. Yang, Broadband infrared absorbers wih sacked double chromium ring resonaors, Op. Express 25(23), (2017). W. Wang, Y. Cui, Y. He, Y. Hao, Y. Lin, X. Tian, T. Ji, and S. He, Efficien muliband absorber based on onedimensional periodic meal-dielecric phoonic crysal wih a reflecive subsrae, Op. Le. 39(2), (2014). J. W. Dong, G. Q. Liang, Y. H. Chen, and H. Z. Wang, Robus absorpion broadband in one-dimensional meallic-dielecric quasi-periodic srucure, Op. Express 14(5), (2006). N. Maiucci, M. J. Bloemer, N. Aközbek, and G. D Aguanno, Impedance mached hin meamaerials make meals absorbing, Sci. Rep. 3(1), 3203 (2013). H. Deng, Z. Li, L. San, D. Rosenmann, D. Czaplewski, J. Gao, and X. Yang, Broadband perfec absorber based on one ulrahin layer of refracory meal, Op. Le. 40(11), (2015). Y. Cui, K. H. Fung, J. Xu, H. Ma, Y. Jin, S. He, and N. X. Fang, Ulrabroadband Ligh Absorpion by a Sawooh Anisoropic Meamaerial Slab, Nano Le. 12(3), (2012). # Journal 2018 hps://doi.org/ /oe Received 10 Jan 2018; revised 22 Feb 2018; acceped 27 Feb 2018; published 1 Mar 2018

3 Vol. 26, No. 5 5 Mar 2018 OPTICS EXPRESS F. Ding, Y. Jin, B. Li, H. Cheng, L. Mo, and S. He, Ulrabroadband srong ligh absorpion based on hin mulilayered meamaerials, Laser Phoonics Rev. 8(6), (2014). 16. D. Ji, H. Song, X. Zeng, H. Hu, K. Liu, N. Zhang, and Q. Gan, Broadband absorpion engineering of hyperbolic meafilm paerns, Sci. Rep. 4(1), 4498 (2014). 17. H. Hu, D. Ji, X. Zeng, K. Liu, and Q. Gan, Rainbow Trapping in Hyperbolic Meamaerial Waveguide, Sci. Rep. 3(1), 1249 (2013). 18. J. Zhou, A. F. Kaplan, L. Chen, and L. J. Guo, Experimen and Theory of he Broadband Absorpion by a Tapered Hyperbolic Meamaerial Array, ACS Phoonics 1(7), (2014). 19. O. Kidwai, S. V. Zhukovsky, and J. E. Sipe, Dipole radiaion near hyperbolic meamaerials: applicabiliy of effecive-medium approximaion, Op. Le. 36(13), (2011). 20. C. Guclu, S. Campione, and F. Capolino, Hyperbolic meamaerial as super absorber for scaered fields generaed a is surface, Phys. Rev. B 86(20), (2012). 21. G. Xu, T. Pan, T. Zang, and J. Sun, Characerisics of guided waves in indefinie-medium waveguides, Op. Commun. 281(10), (2008). 1. Inroducion Broadband infrared absorpion has been sudied widely [1,2] for advancing many applicaions in solar cells [3,4], hermophoovolaics [5], hermal radiaors [6] and infrared imaging [7]. Several differen mechanisms have been used o obain broadband absorpion such ashe combinaion of muliple resonances in one measurface [4,8,9], he exciaion of inerferences in meal-dielecric sacks [10,11], he design of impedance mach for mulilayers [12,13], and he sop-ligh effecs in apered hyperbolic waveguides [14 18]. Cui e al. [14] demonsraed he ulra-broadband absorpion o be higher han 95% in λ = 3 ~ 5.5μm in heory and simulaion. Ding e al. [15] achieved broadband absorpion over 90% in λ = 0.4 ~ 3.6μm by uilizing he high loss meal of Chromium (Cr) in experimen. Zhou e al. [18] also fabricaed a 9-sack Au-Al 2 O 3 apered srucure resuling in absorpion in λ = 1.5 ~ 3μm and an 11-sack Au-Ge apered srucure giving absorpion in λ = 2.5 ~ 6μm. All hese works proved ha sop ligh in apered hyperbolic waveguide is a robus way o ge ulra-broadband absorpion. In he previous works wih apered hyperbolic waveguides [14 18], he sop-ligh effecs are no fully uilized ye and ulra-broadband srong absorpion is no realized by using meal wih relaively low loss. In his paper, ulra-broadband absorpion covering he wavelengh range from 1 μm o 6 μm wih absorpion over 92% is realized by he designed apered hyperbolic meal-dielecric mulilayer waveguide made of 13-pair Au-SiO 2 mulilayer on a glass subsrae. I is revealed ha he ulra-broadband absorpion response of he apered hyperbolic waveguide is due o he combinaion of he sop-ligh modes a differen wavelenghs locaed a differen waveguide widhs, which is confirmed wih a planar hyperbolic waveguide model by considering boh forward and backward guided modes. The sop-ligh modes a differen wavelenghs suppored inside he Au-SiO 2 mulilayer waveguide are visualized by simulaion a he corresponding absorpion peaks by reducing he Au loss. Six apered mulilayer waveguides wih differen op widhs are furher sudied and characerized. The relaion beween he waveguide widh and he sop-ligh wavelengh urns ou o be almos linear from all he resuls in heory, simulaion and experimen. Finally, in order o show he demonsraed apered hyperbolic waveguide absorbers are pracical in he applicaions of solar and hermal energy harvesing, he angleinsensiive and polarizaion-independen absorpion properies, as well as he hea generaion and emperaure increase in he apered mulilayer waveguide are simulaed. 2. Tapered waveguide design and sop-ligh mode analysis The schemaic of he apered mulilayer waveguide consising of 13-pair Au and SiO 2 layers on a glass subsrae is shown in Fig. 1(a). The Au layer hickness is m = 20nm and he SiO 2 layer hickness is d = 80n m. The uni cell period is P = 1500nm, he op widh of he apered waveguide is W = 250nm and he boom widh is he same as he period P. The

4 Vol. 26, No. 5 5 Mar 2018 OPTICS EXPRESS 6362 permiiviy of SiO 2 is a consan ε d = 2.1, while he permiiviy of Au is from he Drude 2 16 model εm = 1 ωp / ω( ω+ iγ) where ω is he frequency, ω p = rad / s is he 13 plasma frequency and γ = rad / s is he bulk collision frequency which is hree imes of he original value γ 0 [5]. The 13-pair Au-SiO 2 mulilayer is deposied wih he magneron spuering sysem (AJA Inernaional). Au is deposied a 4 m Torr wih 20 sccm of Ar gas flow a 30 W DC power, while SiO 2 is deposied a 4 mtorr wih 20 sccm of Ar gas flow as well as 5 sccm of O 2 gas a 250 W RF power. The apered mulilayer waveguide is fabricaed using Focused Ion Beam (FIB) sysem (Helios Nanolab 600) by conrolling he dwell ime of he ion beam milling a differen milling deph along he apered side wall. From he SEM image shown in Fig. 1(b), he Au-SiO 2 layer pairs in he fabricaed apered waveguide can be clearly seen, while here is fabricaion defec such as he coaings on boh sides of he waveguide which are due o he Ga polluion during he long ime ion beam milling. Differen from mos of oher ligh absorber designs where a hick meal mirror is included as a ground plane o eliminae ransmission, he curren apered mulilayer waveguide absorber sands on a glass subsrae so ha sligh ransmission is allowed. Thus, he specra of boh ransmission T (in cyan) and reflecion R (in red) are measured using Fourier ransform infrared specroscopy (FTIR), and he absorpion can be calculaed as A= 1 T R (in blue),which are shown in Fig. 1(c). Since he ransmission is close o zero due o he srong absorpion of sop-ligh modes, he absorpion is more han 92% in he wavelengh range of λ = 1~6μm. The simulaed specra (dashed curves) calculaed by COMSOL Muliphysics are also shown in Fig. 1(c) and in good agreemen wih he measured resuls (solid curves)under normal incidence. Fig. 1. (a) Schemaic of he apered mulilayer waveguide consising of 13 pairs of Au-SiO 2 layers. (b) SEM image of he fabricaed apered waveguide wih P = 1500 nm and W = 250 nm. (c) Measured (solid curves) and simulaed (dashed curves) specra of absorpion A (in blue), reflecion R (in red) and ransmission T (in cyan)under normal incidence. A cladding/core/cladding planar waveguide model is buil in order o explain he ulrabroadband absorpion achieved in he apered mulilayer waveguide. Due o he symmery in x and y direcions, he apered Au-SiO 2 mulilayer waveguide can be regarded as a 2D apered waveguide wih varying widh along he z direcion and infinie long in y direcion. As ligh propagaes in he waveguide along z direcion, he change of waveguide widh will lead o he variaion of waveguide mode. Thus, he whole apered waveguide can be reaed as he combinaion of infinie slices of waveguides wih differen widhs sacked along z direcion, and each slice of waveguide wih widh W is illusraed in Fig. 2(a). The core represens he hyperbolic waveguide wih permiiviy ensor of ε = εx + εy + εz, and he claddings on he wo sides are air wih permiiviy of ε 1 = 1. The core permiiviy can be evaluaed via he

5 Vol. 26, No. 5 5 Mar 2018 OPTICS EXPRESS 6363 effecive medium heory [19,20] for he Au-SiO 2 mulilayer as ε = f ε + ( 1 f ) ε, ε = 1/ f / ε + ( 1 f ) / ε in which f m is he volume filling raio ( ) x m m m d z m m m d of meal. Since he Au-SiO 2 mulilayer is symmeric in x and y direcions, ε x is equal o ε y. I can be seen from Fig. 2(b) ha he waveguide is hyperbolic since ε x is negaive and ε z is posiive. Fig. 2. (a) Schemaic of he 2D waveguide model where he core represens he hyperbolic waveguide based on he Au-SiO 2 mulilayer and he claddings represen he air. (b) Effecive permiiviy of he Au-SiO 2 mulilayer in x direcion ε (in blue) and z direcion ε (in red). In order o illusrae he formaion of sop-ligh modes, he forward and backward guided modes inside he hyperbolic waveguide are solved by considering he coninuous boundary condiion a x = ± W /2 (Eq. (1)) and he dispersion relaion (Eq. (2)) [21]: x z ± 1 ε1 αw = ± αw κ1w an ε 2 z (1) ε + = (2) ( ) 2 x κw ( αw) 2 κ 2 W 2 ( ε ε ) 1 0 x 1 ε z where κ0 = 2 π / λ is he wave vecor of he inciden ligh in vacuum, κ 2 = β 2 κε 2 and 2 2 ( 0 x ) z α β κε ε x ε =. is he wave vecor in z direcion and should be equal in boh he waveguide core and he air claddings. However, he wave vecor in x direcion would be differen: κ 1 in he air claddings and α in he waveguide core. Afer solving hese wo equaions, he wave vecors can be go and hus he effecive index of he waveguide can be ' '' calculaed by neff = neff + ineff = β / κ0. Since here are wo roos found during solving he equaions, i indicaes ha he hyperbolic waveguide can suppor wo guided modes a he same ime: he forward guided mode where he phase velociy direcion is he same as he group velociy direcion and he backward guided mode where hese wo velociy direcions are opposie. As shown in Figs. 3(a) and 3(b), he real and imaginary pars of he effecive index are ploed as a funcion of he waveguide widh W a differen wavelenghs of λ = 1, 3 and 5μm. The blue curves indicae ha he effecive indices of forward guided modes ge higher as he waveguide widh becomes larger. On he oher hand, he effecive

6 Vol. 26, No. 5 5 Mar 2018 OPTICS EXPRESS 6364 indices of backward guided modes ge decreased as he waveguide widh becomes larger. As a resul, he effecive indices of boh he forward and backward modes will finally merge a a proper waveguide widh. In his way, he sop-ligh mode is formed wih zero group velociy and ligh will be absorbed. For insance, a λ = 5μm, he sop-ligh mode is locaed around W 1340nm as he green region shown in Figs. 3(a) and 3(b). The relaion beween he sopligh wavelengh and he waveguide widh urns ou o be almos linear as shown in he magena line of Fig. 3(c). As he wavelengh increases, he waveguide widh where he sopligh mode is locaed will also increase. ' '' Fig. 3. (a) and (b) The effecive index ( n = n + in ) of he forward (in blue) and backward (in red) guided modes a shows he sop-ligh mode a eff eff eff λ = 1, 3, and 5 μm, respecively. The green region λ = 5 μm where he forward and backward guided modes W 1340nm. (c) Relaion beween he sop-ligh merge a he same waveguide widh wavelengh and he corresponding waveguide widh based on heory (in magena), simulaion (in blue) and experimen (in red), respecively. In order o visualize he sop-ligh modes in he apered mulilayer waveguide in deails, he loss of Au is reduced manually o γ = γ0 and he absorpion specrum is recalculaed for he waveguide wih P = 1500nm and W = 250nm. The specra of ransmission (in cyan), reflecion (in red) and absorpion (in blue) for boh γ = 3γ0 and γ = γ0 are shown in Fig. 4(a), respecively. I is seen ha he absorpion peaks for he apered waveguide wih Au loss of γ = γ0 represen he sop-ligh modes localized a differen waveguide widhs. As shown in Fig. 4(b), he sop-ligh modes are mosly confined beween neighboring meal layers. Specifically, for he absorpion peak a λ = 6.0μm, he sop-ligh mode is confined beween he boom hree meal layers, as he magneic field H shown in Fig. 4(b). As he meal layer widh becomes smaller from boom o op, he sop-ligh wavelengh ges shorer. Consequenly, he absorpion of he whole apered mulilayer waveguide is ulrabroad covering he wavelengh range of λ = 1~6μm wih absorpion higher han 92%. However, for he sop-ligh mode locaed a he boom wo meal layers when λ = 6.52μm, is corresponding absorpion peak is hidden in he declined par of he absorpion specrum. This is because he guided modes are weak a he very boom of waveguide since he boom meal layer is in he end of he hyperbolic waveguide and here is no mirror subsrae in below. I is also hard o deermine he absorpion peak a λ = 1.68μm for he sop-ligh mode a he op meal layer in he absorpion specrum since here are many sharp peaks in he range of λ = 1~2μm. These sharp peaks are caused by he high-order modes a he waveguide boom where he waveguide widh is large. The relaion beween he sop-ligh wavelengh and he waveguide widh can be evaluaed from he simulaion resul as shown in he blue curve of Fig. 3(c). Each blue do represens he absorpion peak wavelengh and is corresponding waveguide widh where he sop-ligh mode is locaed. I can be seen ha he simulaion resuls are very close o he heoreical predicions (magena line in Fig. 3(c))

7 Vol. 26, No. 5 5 Mar 2018 OPTICS EXPRESS 6365 when he waveguide widh is much smaller han he srucure period P = 1500 nm, bu ge away from ha when he waveguide widh approaches o P = 1500 nm. This is because when he waveguide widh is close o he period, here exiss he Bloch mode due o he overlap of he evanescen fields beween neighboring apered waveguides [15,17]. Fig. 4. (a) Simulaed specra of absorpion A (in blue), reflecion R (in red) and ransmission T (in cyan) for he apered mulilayer waveguide wih P = 1500 nm, W = 250 nm and Au loss of γ = 3γ0 (solid curves) and γ = γ0 (dashed curves), respecively. (b) Magneic field H disribuions of he sop-ligh modes in he y-z plane for he apered mulilayer waveguide wih γ = 3γ0 a he absorpion peaks. 3. Tapered waveguides wih varying op widhs and furher analysis The relaion beween he absorpion wavelengh range and he waveguide widh is also proved in experimen by changing he waveguide op widh W. As shown in Figs. 5(a)-5(f), six apered waveguides are fabricaed wih P = 1500 nm and W = 250, 400, 550, 750, 900 and 1050 nm, respecively. The measured specra (solid curves) of absorpion A (in blue), reflecion R (in red) and ransmission T (in cyan) for each fabricaed waveguide sample are shown in Figs. 6(a)-6(f), which mach he simulaed specra (dashed curves). As he op widh is increased, he absorpion wavelengh range shrinks due o he red shif of he absorpion peak deermined by he op widh, while he absorpion peak deermined by he boom widh remains a he same wavelengh. The relaion beween he waveguide widh where he sop-ligh mode obained a he waveguide op and is measured corresponding sop-ligh wavelengh (or he absorpion wavelengh range) is summarized as he red curve shown in Fig. 3(c). Each red do on he red curve represens he sop-ligh mode a he waveguide op of each waveguide sample excep for he las red do a W = 1465 nm which represens he sop-ligh mode a he boom meal layer shared by all he samples. For example, for he sample wih W = 1050 nm as shown in

8 Vol. 26, No. 5 5 Mar 2018 OPTICS EXPRESS 6366 Fig. 5(f), he waveguide widh is W = 1085 nm where he sop-ligh mode is achieved a he op, and i leads o he sop-ligh wavelengh of λ = 4.4 μm. And he waveguide widh where he sop-ligh mode is achieved a he waveguide boom is W = 1465 nm resuling in he sop-ligh wavelengh a λ = 6.0 μm. Thus, he absorpion wavelengh range of his sample λ = 4.4 ~ 6.0 μm And he poins of ( 1085 nm is. W =, λ = 4.4 μm ) and ( W = 1465 nm, λ = 6.0 μm ) are ploed in Fig. 3(c).The absorpion wavelengh ranges of all he oher waveguides are measured in he same way wih respec o he waveguide widh where he sop-ligh mode is locaed a he waveguide op, and all he red dos can be conneced o an almos linear curve close o he simulaion resuls (blue curve in Fig. 3(c)) and he heoreical predicions (magena curve in Fig. 3(c)). Fig. 5. (a)-(f) The SEM images of he fabricaed apered mulilayer waveguides wih P = 1500 nm and W = 250, 400, 550, 750, 900 and 1050 nm, respecively. Scale bar:1 μm.

9 Vol. 26, No. 5 5 Mar 2018 OPTICS EXPRESS 6367 Fig. 6. (a)-(f) Measured (solid curves) and simulaed (dashed curves) specra of absorpion A (in blue), reflecion R (in red) and ransmission T (in cyan) for he apered mulilayer waveguides wih P = 1500 nm and W = 250, 400, 550, 750, 900 and 1050 nm, respecively. In order o collec more ligh in pracical applicaions, he absorpion under oblique incidence is considered. As shown in Fig. 7(a), when he ligh is inciden wih an angle θ under TE polarizaion, he magneic field H is iled and he elecric field E is always unchanged and perpendicular o he cross-secion plane. The TM polarizaion case is vice versa as shown in Fig. 7(b). Since he waveguide propagaion modes are mainly dominaed by he elecric field (seen from Eqs. (1) and (2)), he absorpion for TE polarizaion can be kep in he wavelengh range of λ = 1~7μm wih absorpion more han 80% even a high inciden angles, while he absorpion for TM polarizaion is no as good as TE bu sill remains in he range of λ = 1~6μm a high inciden angles. In consequence, he designed apered waveguide absorber is angle-insensiive and polarizaion-independen and hus useful in he applicaions of solar and hermal energy harvesing.

10 Vol. 26, No. 5 5 Mar 2018 OPTICS EXPRESS 6368 Fig. 7. (a), (b) Configuraions of TE polarizaion and TM polarizaion, respecively. (c), (d) Simulaed absorpion specra of he apered mulilayer waveguide wih P = 1500 nm and W = 250 nm under oblique incidence for TE polarizaion and TM polarizaion, respecively. The emperaure disribuion field is imporan o know in some applicaion siuaions o preven high emperaure damage and ensure he absorber performance, as well as in he hermophoovolaic devices where he emperaures of absorber and emier are crucial parameers. In order o invesigae he emperaure disribuion T in he apered waveguide, k T = q is solved, where k is he hermal conduciviy and he hea ransfer equaion ( ) q is he hea generaion densiy in he lossy meal, ( ) ( ) ( ) ( ) 2 q r = ω/ 2 Im ε ω ε E r. As 0 shown in Fig. 8, he hea generaion densiy is locaed where he E field is concenraed in he meal since q is proporional o ( ) ( ) 2 ~ Im ε ω E r. Paricularly, wih an inciden ligh 2 power of 10 μw ono one uni cell (corresponding o 4.44μW / μm ), he hea generaion densiy can be ~ W / m a differen meal layers where he sop-ligh mode is locaed a differen wavelenghs.

11 Vol. 26, No. 5 5 Mar 2018 OPTICS EXPRESS 6369 Fig. 8. Simulaed hea generaion densiy q disribuion in he x-z plane for he apered mulilayer waveguide wih wavelengh. P = 1500 nm, W = 250 nm and γ 3γ0 = a each sop-ligh Correspondingly, he highes emperaure is always found a he place where he hea is generaed. As shown in Fig. 9, he emperaure disribuions a differen sop-ligh wavelenghs are ploed. The emperaure disribuion fields are calculaed based on he following maerial hermal properies a nanoscale as: hermal conduciviy of Au and SiO 2, k Au = 58.88W / ( m K), k SiO2 = 0.2W / ( m K) ; hermal capaciy of Au and SiO 2, C = 136.8J / ( kg K), ( ) Au C SiO2 = 200J / kg K.When he wavelengh is shor and he sopligh mode is obained a he op of he apered waveguide, he highes emperaure is also a he op and ges lower quickly o he boom. However, when he wavelengh is long and he highes emperaure is locaed a he waveguide boom, he whole waveguide is warmed up and he emperaure gradien along z direcion is small. This is because air has a much lower hermal conduciviy compared wih he glass subsrae, and o conduc he same amoun of hea away, i needs a larger emperaure gradien inside he waveguide.

12 Vol. 26, No. 5 5 Mar 2018 OPTICS EXPRESS 6370 Fig. 9. Simulaed emperaure T disribuion in he x-z plane for he apered mulilayer waveguide wih P = 1500 nm, 250 nm γ = 3γ a each sop-ligh wavelengh. 4. Conclusion W = and 0 Tapered mulilayer waveguides made of 13-pair Au-SiO 2 mulilayer has been designed and demonsraed o realize ulra-broadband absorpion in infrared wavelengh range of 1~6 μm due o sop-ligh phenomenon. A cladding/core/cladding planar hyperbolic waveguide model is used o explore he relaion beween he sop-ligh wavelengh and he waveguide widh. The sop-ligh mode can be achieved a a proper waveguide widh where he forward and backward guided modes have he same effecive index. And i urns ou ha he sop-ligh wavelengh increases linearly wih he waveguide widh. Such linear relaion is shown in simulaion by ploing he sop-ligh mode a each absorpion peak wavelengh, and i is also observed in experimen by measuring he absorpion wavelengh range of apered waveguides wih differen op widhs. The apered mulilayer waveguide absorber is proved o be angle-insensiive and polarizaion-independen by simulaing he absorpion specra under angled incidence for boh TE and TM polarizaions. The hea generaion densiy and emperaure fields are also analyzed. The demonsraed ulra-broadband apered mulilayer waveguide absorbers in infrared will advance many imporan applicaions in solar cells, hermophoovolaics, hermoelecrics, and infrared imaging. Funding Naional Science Foundaion (NSF) (DMR , ECCS ); Office of Naval Research (ONR) (N ). Acknowledgmen The auhors acknowledge he faciliy suppor from he Maerials Research Cener a Missouri S&T.