Abstract

A finite-difference time-domain (FDTD) method is used to model thermal radiative properties of vertical arrays of multi-walled carbon nanotubes (MWCNT). Individual CNTs are treated as solid circular cylinders with an effective dielectric tensor. Consistent with experiments, the results confirm that CNT arrays are highly absorptive. Compared with the commonly used Maxwell-Garnett theory, the FDTD calculations generally predict larger reflectance and absorbance, and smaller transmittance, which are attributed to the diffraction and scattering within the cylinder array structure. The effects of volume fraction, tube length, tube distance, and incident angle on radiative properties are investigated systematically. Low volume fraction and long tubes are more favorable to achieve low reflectance and high absorbance. For a fixed volume fraction and finite tube length, larger periodicity results in larger reflectance and absorbance. The angular dependence studies reveal an optimum incident angle at which the reflectance can be minimized. The results also suggest that an even darker material could be achieved by using CNTs with good alignment on the top surface.

©2010 Optical Society of America

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2009 (6)

E. Lidorikis and A. C. Ferrari, “Photonics with multiwall carbon nanotube arrays,” ACS Nano 3, 1238–1248 (2009).
[Crossref] [PubMed]

X. J. Wang, J. D. Flicker, B. J. Lee, W. J. Ready, and Z. M. Zhang, “Visible and near-infrared radiative properties of vertically aligned multi-walled carbon nanotubes,” Nanotechnology 20, 215704 (2009).
[Crossref] [PubMed]

Z. Fan, H. Razavi, J. Do, A. Moriwaki, O. Ergen, Y. Chueh, P. W. Leu, J. C. Ho, T. Takahashi, L. A. Reichertz, S. Neale, K. Yu, M. Wu, J. W. Ager, and A. Javey, “Three-dimensional nanopillar-array photovoltaics on low-cost and flexible substrates,” Nat. Mater. 8, 648–653 (2009).
[Crossref] [PubMed]

J. Zhu, Z. Yu, G. F. Burkhard, C. M. Hsu, S. T. Connor, Y. Xu, Q. Wang, M. McGehee, S. Fan, and Y. Cui, “Optical absorption enhancement in amorphous silicon nanowire and nanocone arrays,” Nano Lett. 9, 279–282 (2009).
[Crossref]

J. Li, H. Yu, S. M. Wong, G. Zhang, X. Sun, P. G. Lo, and D. Kwong, “Si nanopillar array optimization on Si thin films for solar energy harvesting,” Appl. Phys. Lett. 95, 033102 (2009).
[Crossref]

C. Lin and M. L. Povinelli, “Optical absorption enhancement in silicon nanowire arrays with a large lattice constant for photovoltaic applications,” Opt. Express 17, 19371 (2009).
[Crossref] [PubMed]

2008 (6)

O. L. Muskens, J. G. Rivas, R. E. Algra, E. P. A. A. Bakkers, and A. Lagendijk, “Design of light scattering in nanowire materials for photovoltaic applications,” Nano Lett. 8, 2638–2642 (2008).
[Crossref] [PubMed]

R. A. Street, P. Qi, R. Lujan, and W. S. Wong, “Reflectivity of disordered silicon nanowires,” Appl. Phys. Lett. 93, 163109 (2008).
[Crossref]

G. Chen, J. Wu, Q. Lu, H. R. Gutierrez, Q. Xiong, M. E. Pellen, J. S. Petko, D. H. Werner, and P. C. Eklund, “Optical antenna effect in semiconducting nanowires,” Nano Lett. 8, 1341–1346 (2008).
[Crossref] [PubMed]

S. Shoji, H. Suzuki, R. P. Zaccaria, Z. Sekkat, and S. Kawata, “Optical polarizer made of uniaxially aligned short single-wall carbon nanotubes embedded in a polymer film,” Phys. Rev. B,153407 (2008).
[Crossref]

Z.-P. Yang, L. Ci, J. A. Bur, S.-Y. Lin, and P. M. Ajayan, “Experimental observation of extremely dark material made by a low-density nanotube array,” Nano Lett. 8, 446 (2008).
[Crossref] [PubMed]

K. Mizuno, J. Ishii, H. Kishida, Y. Hayamizu, S. Yasuda, D. N. Futaba, M. Yumura, and K. Hata, “A black body absorber from vertically aligned single-walled carbon nanotubes,” Proc. Natl. Acad. Sci. USA 106, 6044–6047 (2008).
[Crossref]

2007 (5)

L. Tsakalakos, J. Balch, J. Fronheiser, B. A. Korevaar, O. Sulima, and J. Rand, “Silicon nanowire solar cells,” Appl. Phys. Lett. 91, 233117 (2007).
[Crossref]

K. Kempa, J. Ryhczynski, Z. P. Huang, K. Gregorczyk, A. Vidan, B. Kimball, J. Carlson, G. Benham, Y. Wang, A. Herczynski, and Z. F. Ren, “Carbon nanotubes as optical antennae,” Adv. Mater. 19, 421–426 (2007).
[Crossref]

L. Hu and G. Chen, “Analysis of optical absorption in silicon nanowire arrays for photovoltatic applications,” Nano Lett. 7, 3249–3252 (2007).
[Crossref] [PubMed]

R. E. Camacho, A. R. Morgan, M. C. Flores, T. A. McLeod, V. S. Kumsomboone, B. J. Mordecai, R. Bhat-tacharjea, W. Tong, B. K. Wagner, J. D. Flicker, S. P. Turano, and W. J. Ready, “Carbon nanotube arrays for photovoltaic applications,” JOM 59, 39–42 (2007).
[Crossref]

T. Xu, S. Yang, S. V. Nair, and H. E. Ruda, “Nanowire-array-based photonic crystal cavity by finite-difference time-domain-calculations,” Phy. Rev. B 75, 125104 (2007).
[Crossref]

2006 (3)

G. Y. Slepyan, M. V. Shuba, and S. A. Maksimenko, “Theory of optical scattering by achiral carbon nanotubes and their potential as optical nanoantennas,” Phys. Rev. B 73, 195416 (2006).
[Crossref]

G. L. Zhao, D. Bagayoko, and L. Yang, “Optical properties of aligned carbon nanotube mats for photonic applications,” J. Appl. Phys. 99, 114311 (2006).
[Crossref]

A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joanopoulos, S. G. Johnson, and G. Burr, “Improving accuracy by subpixel smoothing in FDTD,” Opt. Lett. 31, 2972–2974 (2006).
[Crossref] [PubMed]

2005 (2)

X. Ruan and M. Kaviany, “Photon localization and electromagnetic field enhancement in laser irradiated, random porous media,” Microscale Thermophys. Eng. 9, 63–84 (2005).
[Crossref]

X. Ruan and M. Kaviany, “Enhanced nonradiative relaxation and photoluminescence quenching in random, doped nanocrystalline powders,” J. Appl. Phys. 97, 104331-1–8) (2005).
[Crossref]

2004 (4)

S. Yamashita, Y. Inoue, S. Maruyama, Y. Murakami, H. Yaguchi, M. Jablonski, and S. Y. Set, “Saturable absorbers incorporating carbon nanotubes directly synthesized onto substrates and fibers and their applications to mode-locked fiber lasers,” Opt. Lett. 29, 1581–1583 (2004).
[Crossref] [PubMed]

S. Redmond, S. Rand, X. Ruan, and M. Kaviany, “Multiple scattering and nonlinear thermal emission of Yb3+,Er3+:Y2O3 nanopowders,” J. Appl. Phys. 95, 4069–4077 (2004).
[Crossref]

Y. Wang, K. Kempa, B. Kimball, J. B. Carlson, G. Benham, W. Z. Li, T. Kempa, J. Rybczynski, A. Herczynski, and Z. F. Ren, “Receiving and transmitting light-like radio waves: Antenna effect in arrays of aligned carbon nanotubes,” Appl. Phys. Lett. 85, 2607 (2004).
[Crossref]

G. Y. Guo, K. C. Chu, D. S. Wang, and C. G. Duan, “Linear and nonlinear optical properites of carbon nanotubes from first-principles calculations,” Phys. Rev. B 69, 205416 (2004).
[Crossref]

2003 (1)

K. Kempa, B. Kimball, J. Ryhczynski, Z. P. Huang, P. F. Wu, D. Steeves, M. Sennett, M. Giersig, D. V. G. L. N. Rao, D. Carnahan, D. Z. Wang, J. Y. Lao, W. Z. Li, and Z. F. Ren, “Photonic crystals based on periodic arrays of aligned carbon nanotubes,” Nano Lett. 3, 13–18 (2003).
[Crossref]

2002 (1)

S. M. Bachilo, M. S. Strano, C. Kittrell, R. H. Hauge, R. E. Smalley, and R. B. Weisman, “Structure-assigned optical spectra of single-walled carbon nanotubes,” Science 298, 2361–2366 (2002).
[Crossref] [PubMed]

2000 (2)

M. F. Lin, “Optical spectra of single-wall carbon nanotube bundles,” Phys. Rev. B 62, 13153 (2000).
[Crossref]

W. L, J. Dong, and Z. Li, “Optical properties of aligned carbon nanotube systems studied by the effective-medium approximation method,” Phys. Rev. B 63, 033401 (2000).
[Crossref]

1998 (1)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[Crossref]

1997 (1)

F. J. Garcia-Vidal, J. M. Pitarke, and J. B. Pendry, “Effective medium theory of the optical properties of aligned carbon nanotubes,” Phys. Rev. Lett. 78, 4289–4292 (1997).
[Crossref]

1996 (2)

L. Henrard and P. Lambin, “Calculation of energy loss for an electron passing near giant fullerenes,” J. Phys. B 29, 5127 (1996).
[Crossref]

W. Z. Li, S. S. Xie, L. X. Qian, B. H. Chang, B. S. Zou, W. Y. Zhou, R. A. Zhao, and G. Wang, “Large-scale synthesis of aligned carbon nanotubes,” Science 274, 1701–1703 (1996).
[Crossref] [PubMed]

1994 (1)

M. F. Lin, “Plasmons and optical properties of carbon nanotubes,” Phys. Rev. B 50, 17744 (1994).
[Crossref]

1973 (1)

L. G. Johnson and G. Dresselhaus, “Optical properties of graphite,” Phys. Rev. B 7, 2275 (1973).
[Crossref]

1904 (1)

J. Maxwell-Garnett, “Colours in metal glasses and in metallic films,” Philos. Trans. R. Soc. London, Ser. A 203, 385–420 (1904).
[Crossref]

Ager, J. W.

Z. Fan, H. Razavi, J. Do, A. Moriwaki, O. Ergen, Y. Chueh, P. W. Leu, J. C. Ho, T. Takahashi, L. A. Reichertz, S. Neale, K. Yu, M. Wu, J. W. Ager, and A. Javey, “Three-dimensional nanopillar-array photovoltaics on low-cost and flexible substrates,” Nat. Mater. 8, 648–653 (2009).
[Crossref] [PubMed]

Ajayan, P. M.

Z.-P. Yang, L. Ci, J. A. Bur, S.-Y. Lin, and P. M. Ajayan, “Experimental observation of extremely dark material made by a low-density nanotube array,” Nano Lett. 8, 446 (2008).
[Crossref] [PubMed]

Algra, R. E.

O. L. Muskens, J. G. Rivas, R. E. Algra, E. P. A. A. Bakkers, and A. Lagendijk, “Design of light scattering in nanowire materials for photovoltaic applications,” Nano Lett. 8, 2638–2642 (2008).
[Crossref] [PubMed]

Bachilo, S. M.

S. M. Bachilo, M. S. Strano, C. Kittrell, R. H. Hauge, R. E. Smalley, and R. B. Weisman, “Structure-assigned optical spectra of single-walled carbon nanotubes,” Science 298, 2361–2366 (2002).
[Crossref] [PubMed]

Bagayoko, D.

G. L. Zhao, D. Bagayoko, and L. Yang, “Optical properties of aligned carbon nanotube mats for photonic applications,” J. Appl. Phys. 99, 114311 (2006).
[Crossref]

Bakkers, E. P. A. A.

O. L. Muskens, J. G. Rivas, R. E. Algra, E. P. A. A. Bakkers, and A. Lagendijk, “Design of light scattering in nanowire materials for photovoltaic applications,” Nano Lett. 8, 2638–2642 (2008).
[Crossref] [PubMed]

Balch, J.

L. Tsakalakos, J. Balch, J. Fronheiser, B. A. Korevaar, O. Sulima, and J. Rand, “Silicon nanowire solar cells,” Appl. Phys. Lett. 91, 233117 (2007).
[Crossref]

Benham, G.

K. Kempa, J. Ryhczynski, Z. P. Huang, K. Gregorczyk, A. Vidan, B. Kimball, J. Carlson, G. Benham, Y. Wang, A. Herczynski, and Z. F. Ren, “Carbon nanotubes as optical antennae,” Adv. Mater. 19, 421–426 (2007).
[Crossref]

Y. Wang, K. Kempa, B. Kimball, J. B. Carlson, G. Benham, W. Z. Li, T. Kempa, J. Rybczynski, A. Herczynski, and Z. F. Ren, “Receiving and transmitting light-like radio waves: Antenna effect in arrays of aligned carbon nanotubes,” Appl. Phys. Lett. 85, 2607 (2004).
[Crossref]

Bermel, P.

Bhat-tacharjea, R.

R. E. Camacho, A. R. Morgan, M. C. Flores, T. A. McLeod, V. S. Kumsomboone, B. J. Mordecai, R. Bhat-tacharjea, W. Tong, B. K. Wagner, J. D. Flicker, S. P. Turano, and W. J. Ready, “Carbon nanotube arrays for photovoltaic applications,” JOM 59, 39–42 (2007).
[Crossref]

Bur, J. A.

Z.-P. Yang, L. Ci, J. A. Bur, S.-Y. Lin, and P. M. Ajayan, “Experimental observation of extremely dark material made by a low-density nanotube array,” Nano Lett. 8, 446 (2008).
[Crossref] [PubMed]

Burkhard, G. F.

J. Zhu, Z. Yu, G. F. Burkhard, C. M. Hsu, S. T. Connor, Y. Xu, Q. Wang, M. McGehee, S. Fan, and Y. Cui, “Optical absorption enhancement in amorphous silicon nanowire and nanocone arrays,” Nano Lett. 9, 279–282 (2009).
[Crossref]

Burr, G.

Camacho, R. E.

R. E. Camacho, A. R. Morgan, M. C. Flores, T. A. McLeod, V. S. Kumsomboone, B. J. Mordecai, R. Bhat-tacharjea, W. Tong, B. K. Wagner, J. D. Flicker, S. P. Turano, and W. J. Ready, “Carbon nanotube arrays for photovoltaic applications,” JOM 59, 39–42 (2007).
[Crossref]

Carlson, J.

K. Kempa, J. Ryhczynski, Z. P. Huang, K. Gregorczyk, A. Vidan, B. Kimball, J. Carlson, G. Benham, Y. Wang, A. Herczynski, and Z. F. Ren, “Carbon nanotubes as optical antennae,” Adv. Mater. 19, 421–426 (2007).
[Crossref]

Carlson, J. B.

Y. Wang, K. Kempa, B. Kimball, J. B. Carlson, G. Benham, W. Z. Li, T. Kempa, J. Rybczynski, A. Herczynski, and Z. F. Ren, “Receiving and transmitting light-like radio waves: Antenna effect in arrays of aligned carbon nanotubes,” Appl. Phys. Lett. 85, 2607 (2004).
[Crossref]

Carnahan, D.

K. Kempa, B. Kimball, J. Ryhczynski, Z. P. Huang, P. F. Wu, D. Steeves, M. Sennett, M. Giersig, D. V. G. L. N. Rao, D. Carnahan, D. Z. Wang, J. Y. Lao, W. Z. Li, and Z. F. Ren, “Photonic crystals based on periodic arrays of aligned carbon nanotubes,” Nano Lett. 3, 13–18 (2003).
[Crossref]

Chang, B. H.

W. Z. Li, S. S. Xie, L. X. Qian, B. H. Chang, B. S. Zou, W. Y. Zhou, R. A. Zhao, and G. Wang, “Large-scale synthesis of aligned carbon nanotubes,” Science 274, 1701–1703 (1996).
[Crossref] [PubMed]

Chen, G.

G. Chen, J. Wu, Q. Lu, H. R. Gutierrez, Q. Xiong, M. E. Pellen, J. S. Petko, D. H. Werner, and P. C. Eklund, “Optical antenna effect in semiconducting nanowires,” Nano Lett. 8, 1341–1346 (2008).
[Crossref] [PubMed]

L. Hu and G. Chen, “Analysis of optical absorption in silicon nanowire arrays for photovoltatic applications,” Nano Lett. 7, 3249–3252 (2007).
[Crossref] [PubMed]

Chu, K. C.

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Figures (7)

Fig. 1.
Fig. 1. (Color online) Left: A sketch of a CNT array subject to normal incidence. Upper right: single layer graphite and the anisotropic dielectric tensor. Lower right: MWCNT as a roll of multilayer graphite.

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Fig. 2.
Fig. 2. (Color online) Effective dielectric function of an individual CNT.

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Fig. 3.
Fig. 3. (Color online) (a) Reflectance and transmittance and (b) absorbance of the CNT array from FDTD calculation and MGT with different volume fractions. The reflectance and transmittance are shown in a log scale plot. Insert: an instant electric field distribution of the cross sections of the simulation domain with 500 nm incident wavelength and 0.126 volume fraction. The upper figure is scaled in the vertical direction for clarity.

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Fig. 4.
Fig. 4. (Color online) (a) Reflectance and (b) absorbance of CNTs with different lengths. “Inf” indicates that the back tip of CNT extends into a PML, which approximates semi-infinite CNTs.

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Fig. 5.
Fig. 5. (Color online) (a) Reflectance and (b) absorbance of CNT arrays with different periodicity. The volume fractions are fixed as 0.126. “Inf” denotes the semi-infinite reflectance or absorbance.

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Fig. 6.
Fig. 6. (Color online) (a) Reflectance and (b) absorbance of CNTs at different incident angle. Insert: an instant field distribution for TE wave under 20° oblique incidence. The figure is scaled in the vertical direction for clarity.

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Fig. 7.
Fig. 7. A sketch of surface roughness of CNT array. (a): aligned CNT array with random tube length. (b): aligned CNT array with tip bending.

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Equations (7)

Equations on this page are rendered with MathJax. Learn more.

ε r ̂ ϕ ̂ z ̂ = ε e r ̂ r ̂ + ε o ( z ̂ z ̂ + ϕ ̂ ϕ ̂ ) ,
ε ∥ = ε o
ε ⊥ = ε e ε o .
ε eff ∥ = 1 + f ( ε ∥ − 1 )
ε eff ⊥ = 1 + f ( ε ⊥ − 1 ) 1 + 1 2 ( ε ⊥ − 1 ) ( 1 − f )
α = 4 π κ λ .
κ = ε 1 2 + ε 2 2 − ε 1 2 ,

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