Abstract

Emission of thermal radiation from periodically patterned surfaces that support surface phonon polaritons has always been into two symmetric emission angles. This is because of the nature of randomness in the thermal spectrum of a hot body that symmetrically distributes the heat into counterpropagating surface waves. Here we demonstrate the design method of metasurfaces with unconventional unit cell dimension and internal structure to direct the thermal radiation into a single specific emission angle. We utilize a combination of diffraction order engineering and numerical optimization techniques for the design process of an ultra-thin metasurface to couple counterpropagating surface waves into a single emission direction. In addition, we compute the near-field incoherent thermal emission intensity from the metasurface by combining the concepts of fluctuation dissipation theorem with solutions of Maxwell’s equations based on rigorous coupled-wave analysis and demonstrate unidirectional phaseless thermal radiation emission. The developed approach serves as a tool to design metasurfaces for manipulation of light sources with more complex nature than a plane wave.

© 2017 Optical Society of America

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References

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2017 (8)

B. Liu, W. Gong, B. Yu, P. Li, and S. Shen, “Perfect thermal emission by nanoscale transmission line resonators,” Nano Lett. 17, 666–672 (2017).
[Crossref]

T. Inoue, T. Asano, and S. Noda, “Near-field thermal radiation transfer between semiconductors based on thickness control and introduction of photonic crystals,” Phys. Rev. B 95, 125307 (2017).
[Crossref]

E. Sakr and P. Bermel, “Angle-selective reflective filters for exclusion of background thermal emission,” Phys. Rev. Appl. 7, 044020 (2017).
[Crossref]

S. Jafar-Zanjani, M. M. Salary, and H. Mosallaei, “Metafabrics for thermoregulation and energy-harvesting applications,” ACS Photon. 4, 915–927 (2017).
[Crossref]

J. van Schoot and H. Schift, “Next-generation lithography-an outlook on EUV projection and nanoimprint,” Adv. Opt. Technol. 6, 159–162 (2017).

D. J. Resnick and J. Choi, “A review of nanoimprint lithography for high-volume semiconductor device manufacturing,” Adv. Opt. Technol. 6, 229–241 (2017).
[Crossref]

D. A. Miller, L. Zhu, and S. Fan, “Universal modal radiation laws for all thermal emitters,” Proc. Natl. Acad. Sci. USA 114, 4336–4341 (2017).
[Crossref]

S. Inampudi and H. Mosallaei, “Tunable wideband-directive thermal emission from SiC surface using bundled graphene sheets,” Phys. Rev. B 96, 125407 (2017).
[Crossref]

2016 (11)

S.-A. Biehs and P. Ben-Abdallah, “Revisiting super-Planckian thermal emission in the far-field regime,” Phys. Rev. B 93, 165405 (2016).
[Crossref]

S. Inampudi and H. Mosallaei, “Fresnel refraction and diffraction of surface plasmon polaritons in two-dimensional conducting sheets,” ACS Omega 1, 843–853 (2016).
[Crossref]

S. Inampudi, M. Nazari, A. Forouzmand, and H. Mosallaei, “Manipulation of surface plasmon polariton propagation on isotropic and anisotropic two-dimensional materials coupled to boron nitride heterostructures,” J. Appl. Phys. 119, 025301 (2016).
[Crossref]

Y. Guo and S. Fan, “Narrowband thermal emission from a uniform tungsten surface critically coupled with a photonic crystal guided resonance,” Opt. Express 24, 29896–29907 (2016).
[Crossref]

K. Ito and H. Iizuka, “Directional thermal emission control by coupling between guided mode resonances and tunable plasmons in multilayered graphene,” J. Appl. Phys. 120, 163105 (2016).
[Crossref]

E. Sakr, S. Dhaka, and P. Bermel, “Asymmetric angular-selective thermal emission,” Proc. SPIE 9743, 97431D (2016).
[Crossref]

H. Chalabi, A. Alù, and M. L. Brongersma, “Focused thermal emission from a nanostructured SiC surface,” Phys. Rev. B 94, 094307 (2016).
[Crossref]

K. Ito, H. Toshiyoshi, and H. Iizuka, “Densely-tiled metal-insulator-metal metamaterial resonators with quasi-monochromatic thermal emission,” Opt. Express 24, 12803–12811 (2016).
[Crossref]

H.-T. Chen, A. J. Taylor, and N. Yu, “A review of metasurfaces: physics and applications,” Rep. Prog. Phys. 79, 076401 (2016).
[Crossref]

S. B. Glybovski, S. A. Tretyakov, P. A. Belov, Y. S. Kivshar, and C. R. Simovski, “Metasurfaces: from microwaves to visible,” Phys. Rep. 634, 1–72 (2016).
[Crossref]

Y. Shen, C. W. Hsu, Y. X. Yeng, J. D. Joannopoulos, and M. Soljačić, “Broadband angular selectivity of light at the nanoscale: progress, applications, and outlook,” Appl. Phys. Rev. 3, 011103 (2016).
[Crossref]

2015 (5)

D. Costantini, A. Lefebvre, A.-L. Coutrot, I. Moldovan-Doyen, J.-P. Hugonin, S. Boutami, F. Marquier, H. Benisty, and J.-J. Greffet, “Plasmonic metasurface for directional and frequency-selective thermal emission,” Phys. Rev. Appl. 4, 014023 (2015).
[Crossref]

E. C. Kinzel, J. C. Ginn, L. A. Florence, B. A. Lail, and G. D. Boreman, “Directional thermal emission from a leaky-wave frequency-selective surface,” J. Nanophoton. 9, 093040 (2015).
[Crossref]

F. Marquier, D. Costantini, A. Lefebvre, A.-L. Coutrot, I. Moldovan-Doyen, J.-P. Hugonin, S. Boutami, H. Benisty, and J.-J. Greffet, “Metallic metasurface as a directional and monochromatic thermal emitter,” Proc. SPIE 9370, 937004 (2015).
[Crossref]

H. Chalabi, E. Hasman, and M. L. Brongersma, “Near-field radiative thermal transfer between a nanostructured periodic material and a planar substrate,” Phys. Rev. B 91, 014302 (2015).
[Crossref]

C. M. Roberts, S. Inampudi, and V. A. Podolskiy, “Diffractive interface theory: nonlocal susceptibility approach to the optics of metasurfaces,” Opt. Express 23, 2764–2776 (2015).
[Crossref]

2014 (3)

K. Ito, T. Matsui, and H. Iizuka, “Thermal emission control by evanescent wave coupling between guided mode of resonant grating and surface phonon polariton on silicon carbide plate,” Appl. Phys. Lett. 104, 051127 (2014).
[Crossref]

J. Cheng, D. Ansari-Oghol-Beig, and H. Mosallaei, “Wave manipulation with designer dielectric metasurfaces,” Opt. Lett. 39, 6285–6288 (2014).
[Crossref]

H. Miyazaki, T. Kasaya, M. Iwanaga, B. Choi, Y. Sugimoto, and K. Sakoda, “Dual-band infrared metasurface thermal emitter for CO2 sensing,” Appl. Phys. Lett. 105, 121107 (2014).
[Crossref]

2013 (4)

Z. Yu, N. P. Sergeant, T. Skauli, G. Zhang, H. Wang, and S. Fan, “Enhancing far-field thermal emission with thermal extraction,” Nat. Commun. 4, 1730 (2013).
[Crossref]

Y. Guo and Z. Jacob, “Thermal hyperbolic metamaterials,” Opt. Express 21, 15014–15019 (2013).
[Crossref]

S. Molesky, C. J. Dewalt, and Z. Jacob, “High temperature epsilon-near-zero and epsilon-near-pole metamaterial emitters for thermophotovoltaics,” Opt. Express 21, A96–A110 (2013).
[Crossref]

T. Inoue, M. De Zoysa, T. Asano, and S. Noda, “Single-peak narrow-bandwidth mid-infrared thermal emitters based on quantum wells and photonic crystals,” Appl. Phys. Lett. 102, 191110 (2013).
[Crossref]

2011 (2)

X. Liu, T. Tyler, T. Starr, A. F. Starr, N. M. Jokerst, and W. J. Padilla, “Taming the blackbody with infrared metamaterials as selective thermal emitters,” Phys. Rev. Lett. 107, 045901 (2011).
[Crossref]

A. W. Rodriguez, O. Ilic, P. Bermel, I. Celanovic, J. D. Joannopoulos, M. Soljačić, and S. G. Johnson, “Frequency-selective near-field radiative heat transfer between photonic crystal slabs: a computational approach for arbitrary geometries and materials,” Phys. Rev. Lett. 107, 114302 (2011).
[Crossref]

2010 (1)

2009 (3)

E. Rephaeli and S. Fan, “Absorber and emitter for solar thermo-photovoltaic systems to achieve efficiency exceeding the Shockley-Queisser limit,” Opt. Express 17, 15145–15159 (2009).
[Crossref]

J. A. Schuller, T. Taubner, and M. L. Brongersma, “Optical antenna thermal emitters,” Nat. Photonics 3, 658–661 (2009).
[Crossref]

A. Narayanaswamy, S. Shen, L. Hu, X. Chen, and G. Chen, “Breakdown of the Planck blackbody radiation law at nanoscale gaps,” Appl. Phys. A 96, 357–362 (2009).
[Crossref]

2008 (2)

J. Elser and V. A. Podolskiy, “Scattering-free plasmonic optics with anisotropic metamaterials,” Phys. Rev. Lett. 100, 066402 (2008).
[Crossref]

I. Puscasu and W. L. Schaich, “Narrow-band, tunable infrared emission from arrays of microstrip patches,” Appl. Phys. Lett. 92, 233102 (2008).
[Crossref]

2007 (1)

N. Dahan, A. Niv, G. Biener, Y. Gorodetski, V. Kleiner, and E. Hasman, “Enhanced coherency of thermal emission: beyond the limitation imposed by delocalized surface waves,” Phys. Rev. B 76, 045427 (2007).
[Crossref]

2006 (2)

A. Battula and S. Chen, “Monochromatic polarized coherent emitter enhanced by surface plasmons and a cavity resonance,” Phys. Rev. B 74, 245407 (2006).
[Crossref]

R. A. Waltz, J. L. Morales, J. Nocedal, and D. Orban, “An interior algorithm for nonlinear optimization that combines line search and trust region steps,” Math. Program. 107, 391–408 (2006).
[Crossref]

2005 (3)

I. Celanovic, D. Perreault, and J. Kassakian, “Resonant-cavity enhanced thermal emission,” Phys. Rev. B 72, 075127 (2005).
[Crossref]

M. Laroche, C. Arnold, F. Marquier, R. Carminati, J.-J. Greffet, S. Collin, N. Bardou, and J.-L. Pelouard, “Highly directional radiation generated by a tungsten thermal source,” Opt. Lett. 30, 2623–2625 (2005).
[Crossref]

K. Joulain, J.-P. Mulet, F. Marquier, R. Carminati, and J.-J. Greffet, “Surface electromagnetic waves thermally excited: radiative heat transfer, coherence properties and Casimir forces revisited in the near field,” Surf. Sci. Rep. 57, 59–112 (2005).
[Crossref]

2004 (2)

H. Sai and H. Yugami, “Thermophotovoltaic generation with selective radiators based on tungsten surface gratings,” Appl. Phys. Lett. 85, 3399–3401 (2004).
[Crossref]

F. Marquier, K. Joulain, J.-P. Mulet, R. Carminati, J.-J. Greffet, and Y. Chen, “Coherent spontaneous emission of light by thermal sources,” Phys. Rev. B 69, 155412 (2004).
[Crossref]

2002 (2)

J.-J. Greffet, R. Carminati, K. Joulain, J.-P. Mulet, S. Mainguy, and Y. Chen, “Coherent emission of light by thermal sources,” Nature 416, 61–64 (2002).
[Crossref]

J.-P. Mulet, K. Joulain, R. Carminati, and J.-J. Greffet, “Enhanced radiative heat transfer at nanometric distances,” Microscale Thermophys. Eng. 6, 209–222 (2002).
[Crossref]

2000 (3)

S.-Y. Lin, J. Fleming, E. Chow, J. Bur, K. Choi, and A. Goldberg, “Enhancement and suppression of thermal emission by a three-dimensional photonic crystal,” Phys. Rev. B 62, R2243(R) (2000).
[Crossref]

C. Henkel, K. Joulain, R. Carminati, and J.-J. Greffet, “Spatial coherence of thermal near fields,” Opt. Commun. 186, 57–67 (2000).
[Crossref]

A. V. Shchegrov, K. Joulain, R. Carminati, and J.-J. Greffet, “Near-field spectral effects due to electromagnetic surface excitations,” Phys. Rev. Lett. 85, 1548–1551 (2000).
[Crossref]

1999 (1)

R. Carminati and J.-J. Greffet, “Near-field effects in spatial coherence of thermal sources,” Phys. Rev. Lett. 82, 1660–1663 (1999).
[Crossref]

1998 (1)

1997 (1)

1995 (2)

M. Moharam, T. Gaylord, E. B. Grann, and D. A. Pommet, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12, 1068–1076 (1995).
[Crossref]

C. A. Palmer, J. L. Olson, and M. M. Dunn, “Blazed diffraction gratings obtained by ion-milling sinusoidal photoresist gratings,” Proc. SPIE 2622, 112–121 (1995).
[Crossref]

1993 (1)

R. Bräuer and O. Bryngdahl, “Electromagnetic diffraction analysis of two-dimensional gratings,” Opt. Commun. 100, 1–5 (1993).
[Crossref]

1992 (1)

E. Ishiguro, K. Yamashita, H. Ohashi, M. Sakurai, O. Aita, M. Watanabe, K. Sano, M. Koeda, and T. Nagano, “Fabrication and characterization of reactive ion beam etched sic gratings,” Rev. Sci. Instrum. 63, 1439–1442 (1992).
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Figures (6)

Fig. 1.
Fig. 1. (a) Schematic representation of unidirectional thermal emission from SiC bars. (b) Optical parameters of SiC (left axis) and blackbody radiation curve at 315°K (right axis) as a function of frequency. Shaded region represents the SPhPs regime. (c) Thermal emission intensity from a planar semi-infinite SiC slab calculated using the integral in Eq. (1). Highly (3 orders of magnitude) localized thermal emission is observed around 1.66 × 10 14    rad / s . (d) The integrand of Eq. (1) at peak emission frequency demonstrating the wave vector resolved variation of thermal radiation intensity. The red colored peak emission positions represent the surface phonon polariton resonances. The central low magnitude blue region is the contribution of the propagation spectrum.
Fig. 2.
Fig. 2. (a) Schematic representation of coupling of SPhP waves to an obtuse angle. (b) Schematic representation of the same phenomenon in the wave vector domain. Red and blue peaks represent the locations of high-intensity SPhP waves. Arrows represent the coupling direction. (c) Schematic of the aim of the paper representing the coupling of the counterpropagating SPhP waves to one emission angle.
Fig. 3.
Fig. 3. (a) The index of diffraction orders with respect to k x θ to support coupling of both ± k spp to one direction (with a restriction of m 1 , m 2 10 ). (b) Comparison of emissivity from binary diffraction grating of various heights ( Λ = 6.1    μm , 50% duty cycle) and the optimized metasurface ( Λ = 63.8    μm ) designed for λ 0 = 11.36    μm . The green dashed line represents simplified optimized grating of same height where blocks and gaps of widths less than 50 nm and 200 nm, respectively, are removed from the grating.
Fig. 4.
Fig. 4. (a) Cross-sectional view of the optimized unit cell structure. (b) and (c) represent normal electric field component pattern in the unit cell when the system is excited by SPhP waves propagating in the ( + x ) and ( x ) directions, respectively. (d) and (e) represent the transmission function matrices of binary grating and optimized metasurface, respectively. The height of both systems is 0.82 μm.
Fig. 5.
Fig. 5. Computed intensity of thermal radiation using Eq. (6) at λ 0 = 11.36    μm . The source of radiation is a semi-infinite SiC slab from z = to z = 0 . While binary grating in (a) emits into two symmetric angles the optimized metasurface emission, (b) is dominated on to one side. Both systems are of the same height ( h = 0.82    μm ).
Fig. 6.
Fig. 6. Computed emissivity of the designed optimized metasurface as a function of wavelength and emission angle in the SPhP region of SiC demonstrating both narrow frequency band and narrow angular emission.

Equations (14)

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I ( ω , z , T ) = k 0 Θ ( ω , T ) 64 π 5 d k x d k y e 2 k z t z μ = s , p | t μ | 2 [ E x μ H y μ * E y μ H x μ * ] M μ ,
Λ = m 2 π | Re ( k x ; spp ) k x ; θ | ,
k x ; θ < Re ( k x ; spp ) k 0 2 .
f = Re ( k x ; spp ) k x ; θ Re ( k x ; spp ) + k x ; θ = m 2 m 1
Obj = p = q = | T p ; q ( Aim ) | t p ; q ( calc ) | | 2 min .
I ( ω , r , T ) = k 0 3 Θ ( ω , T ) 64 π 5 d k x d k y μ 1 , μ 2 = s , p [ m E x μ 2 ( m ) m H y μ 2 ( m ) * m E y μ 2 ( m ) m H x μ 2 ( m ) * ] M μ 1 ,
( E x E y H x H y ) = ϕ x y ( W p W p V p V p ) ( ϕ z ; p + 0 0 ϕ z ; p ) ( i p r p ) ,
W p = [ k y ( n ) ( k x ( n ) ) 2 + ( k y ( n ) ) 2 k x ( n ) k z ; p ( n ) k 0 ε p ( k x ( n ) ) 2 + ( k y ( n ) ) 2 k x ( n ) ( k x ( n ) ) 2 + ( k y ( n ) ) 2 k y ( n ) k z ; p ( n ) k 0 ε p ( k x ( n ) ) 2 + ( k y ( n ) ) 2 ] ,
V p = [ k x ( n ) k z ; p ( n ) k 0 ( k x ( n ) ) 2 + ( k y ( n ) ) 2 k y ( n ) ( k x ( n ) ) 2 + ( k y ( n ) ) 2 k y ( n ) k z ; p ( n ) k 0 ( k x ( n ) ) 2 + ( k y ( n ) ) 2 k x ( n ) ( k x ( n ) ) 2 + ( k y ( n ) ) 2 ] .
A = [ A 11 A 12 A 21 A 22 ] ,
A 11 = K x E 1 K y K x K y + ( I K x E 1 K x ) K x K y , A 12 = ( K x E 1 K y ) ( K x 2 E ) + ( I K x E 1 K x ) K x K y , A 21 = ( I K x E 1 K x ) K x K y ( K y E 1 K x ) ( K y 2 + E ) , A 22 = ( K x E 1 K x I ) ( K x 2 E ) ( K y E 1 K x ) K x K y .
E ( m , n ) = Λ x / 2 Λ x / 2 Λ y / 2 Λ y / 2 d x d y ε p ( x , y ) exp ( i ( q x ( m ) q x ( n ) ) x + i ( q y ( m ) q y ( n ) ) y ) ,
V p = [ K x K y ( K x 2 E ) ( K y 2 + E ) K x K y ] W p K z ; p 1 ,
T = ( T s , s T s , p T p , s T p , p ) .

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