Abstract

As highlighted by recent articles [Phys. Rev. Lett. 105, 053901 (2010) and Science 331, 889-892 (2011)], the coherent control of narrowband perfect absorption in intrinsic silicon slab has attracted much attention. In this paper, we demonstrate that broadband coherent perfect absorber (CPA) can be achieved by heavily doping an ultrathin silicon film. Two distinct perfect absorption regimes are derived with extremely broad and moderately narrow bandwidth under symmetrical coherent illumination. The large enhancement of bandwidth may open up new avenues for broadband applications. Subsequently, interferometric method is used to control the absorption coherently with extremely large contrast between the maximum and minimum absorptance. Compared with the results in literatures, the thin film CPAs proposed here show much more flexibility in both operation frequency and bandwidth.

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References

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  1. Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent perfect absorbers: time-reversed lasers,” Phys. Rev. Lett. 105(5), 053901 (2010).
    [CrossRef] [PubMed]
  2. W. Wan, Y. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science 331(6019), 889–892 (2011).
    [CrossRef] [PubMed]
  3. Y. D. Chong and A. D. Stone, “Hidden black: coherent enhancement of absorption in strongly scattering media,” Phys. Rev. Lett. 107(16), 163901 (2011).
    [CrossRef] [PubMed]
  4. N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
    [CrossRef] [PubMed]
  5. T. V. Teperik, F. J. García de Abajo, A. G. Borisov, M. Abdelsalam, P. N. Bartlett, Y. Sugawara, and J. J. Baumberg, “Omnidirectional absorption in nanostructured metal surfaces,” Nat. Photonics 2(5), 299–301 (2008).
    [CrossRef]
  6. M. Diem, T. Koschny, and C. M. Soukoulis, “Wide-angle perfect absorber/thermal emitter in the terahertz regime,” Phys. Rev. B 79(3), 033101 (2009).
    [CrossRef]
  7. M. Pu, C. Hu, M. Wang, C. Huang, Z. Zhao, C. Wang, Q. Feng, and X. Luo, “Design principles for infrared wide-angle perfect absorber based on plasmonic structure,” Opt. Express 19(18), 17413–17420 (2011).
    [CrossRef] [PubMed]
  8. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd ed., (Wiley, 2007).
  9. S. Nashima, O. Morikawa, K. Takata, and M. Hangyo, “Measurement of optical properties of highly doped silicon by terahertz time domain reflection spectroscopy,” Appl. Phys. Lett. 79(24), 3923–3925 (2001).
    [CrossRef]
  10. R. A. Falk, “Near IR Absorption in Heavily Doped Silicon-An Empirical Approach,” in Proceedings of the 26th ISTFA, 2000.
  11. B. V. Zeghbroeck, Principles of Semiconductor Devices (Boulder, 1997).
  12. W. Woltersdorff, “Über die optischen Konstanten dünner Metallschichten im langwelligen Ultrarot,” Z. Phys. 91(3-4), 230–252 (1934).
    [CrossRef]
  13. M. Dressel and G. Gruner, Electrodynamics of Solids: Optical Properties of Electrons in Matter (Cambridge, New York, 2002).
  14. In the impedance theory, the thin film CPA can be approximated as a resistive sheet with Z=1/(dwσ0)=Z0/2 as the thickness of the slab is much smaller than the skin depth. Here, σ0=ωp2τε0 is the AC conductivity and Z0=μ0/ε0 is the impedance of vacuum. Then consider the radiation property of an infinite oscillating current sheet in xy plane. Assuming that the current is J→=Ksin(ωt)x→, the electric field at z = 0 can be written as: E→=−0.5μ0cKsin(ωt)x→. The effective sheet impedance, defined as E/J, is -Z0/2, which is just in opposite to the thin film CPA condition. Such a radiation can be thought as the time reversed process of the broadband CPA, although the infinite oscillating current sheet is not applicable in practical applications.
  15. Q. L. Zhou, Y. L. Shi, T. Li, B. Jin, D. M. Zhao, and C. L. Zhang, “Carrier dynamics and terahertz photoconductivity of doped silicon measured by femtosecond pump-terahertz probe spectroscopy,” Sci. China, Ser. G 52(12), 1944–1948 (2009).
    [CrossRef]
  16. J. Kim, R. Jonathan, B. V. Sharma, J. G. Fujimoto, F. X. Kärtner, V. Scheuer, and G. Angelow, “Ultrabroadband beam splitter with matched group-delay dispersion,” Opt. Lett. 30(12), 1569–1571 (2005).
    [CrossRef] [PubMed]
  17. E. D. Palik, Handbook of Optical Constants of Solids (Academic, Orlando, Fla., 1985).
  18. G. Nimtz and U. Panten, “Broad band electromagnetic wave absorbers designed with nano-metal films,” Ann. Phys. 19(1-2), 53–59 (2010).
    [CrossRef]

2011 (3)

W. Wan, Y. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science 331(6019), 889–892 (2011).
[CrossRef] [PubMed]

Y. D. Chong and A. D. Stone, “Hidden black: coherent enhancement of absorption in strongly scattering media,” Phys. Rev. Lett. 107(16), 163901 (2011).
[CrossRef] [PubMed]

M. Pu, C. Hu, M. Wang, C. Huang, Z. Zhao, C. Wang, Q. Feng, and X. Luo, “Design principles for infrared wide-angle perfect absorber based on plasmonic structure,” Opt. Express 19(18), 17413–17420 (2011).
[CrossRef] [PubMed]

2010 (2)

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent perfect absorbers: time-reversed lasers,” Phys. Rev. Lett. 105(5), 053901 (2010).
[CrossRef] [PubMed]

G. Nimtz and U. Panten, “Broad band electromagnetic wave absorbers designed with nano-metal films,” Ann. Phys. 19(1-2), 53–59 (2010).
[CrossRef]

2009 (2)

Q. L. Zhou, Y. L. Shi, T. Li, B. Jin, D. M. Zhao, and C. L. Zhang, “Carrier dynamics and terahertz photoconductivity of doped silicon measured by femtosecond pump-terahertz probe spectroscopy,” Sci. China, Ser. G 52(12), 1944–1948 (2009).
[CrossRef]

M. Diem, T. Koschny, and C. M. Soukoulis, “Wide-angle perfect absorber/thermal emitter in the terahertz regime,” Phys. Rev. B 79(3), 033101 (2009).
[CrossRef]

2008 (2)

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
[CrossRef] [PubMed]

T. V. Teperik, F. J. García de Abajo, A. G. Borisov, M. Abdelsalam, P. N. Bartlett, Y. Sugawara, and J. J. Baumberg, “Omnidirectional absorption in nanostructured metal surfaces,” Nat. Photonics 2(5), 299–301 (2008).
[CrossRef]

2005 (1)

2001 (1)

S. Nashima, O. Morikawa, K. Takata, and M. Hangyo, “Measurement of optical properties of highly doped silicon by terahertz time domain reflection spectroscopy,” Appl. Phys. Lett. 79(24), 3923–3925 (2001).
[CrossRef]

1934 (1)

W. Woltersdorff, “Über die optischen Konstanten dünner Metallschichten im langwelligen Ultrarot,” Z. Phys. 91(3-4), 230–252 (1934).
[CrossRef]

Abdelsalam, M.

T. V. Teperik, F. J. García de Abajo, A. G. Borisov, M. Abdelsalam, P. N. Bartlett, Y. Sugawara, and J. J. Baumberg, “Omnidirectional absorption in nanostructured metal surfaces,” Nat. Photonics 2(5), 299–301 (2008).
[CrossRef]

Angelow, G.

Bartlett, P. N.

T. V. Teperik, F. J. García de Abajo, A. G. Borisov, M. Abdelsalam, P. N. Bartlett, Y. Sugawara, and J. J. Baumberg, “Omnidirectional absorption in nanostructured metal surfaces,” Nat. Photonics 2(5), 299–301 (2008).
[CrossRef]

Baumberg, J. J.

T. V. Teperik, F. J. García de Abajo, A. G. Borisov, M. Abdelsalam, P. N. Bartlett, Y. Sugawara, and J. J. Baumberg, “Omnidirectional absorption in nanostructured metal surfaces,” Nat. Photonics 2(5), 299–301 (2008).
[CrossRef]

Borisov, A. G.

T. V. Teperik, F. J. García de Abajo, A. G. Borisov, M. Abdelsalam, P. N. Bartlett, Y. Sugawara, and J. J. Baumberg, “Omnidirectional absorption in nanostructured metal surfaces,” Nat. Photonics 2(5), 299–301 (2008).
[CrossRef]

Cao, H.

W. Wan, Y. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science 331(6019), 889–892 (2011).
[CrossRef] [PubMed]

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent perfect absorbers: time-reversed lasers,” Phys. Rev. Lett. 105(5), 053901 (2010).
[CrossRef] [PubMed]

Chong, Y.

W. Wan, Y. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science 331(6019), 889–892 (2011).
[CrossRef] [PubMed]

Chong, Y. D.

Y. D. Chong and A. D. Stone, “Hidden black: coherent enhancement of absorption in strongly scattering media,” Phys. Rev. Lett. 107(16), 163901 (2011).
[CrossRef] [PubMed]

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent perfect absorbers: time-reversed lasers,” Phys. Rev. Lett. 105(5), 053901 (2010).
[CrossRef] [PubMed]

Diem, M.

M. Diem, T. Koschny, and C. M. Soukoulis, “Wide-angle perfect absorber/thermal emitter in the terahertz regime,” Phys. Rev. B 79(3), 033101 (2009).
[CrossRef]

Feng, Q.

Fujimoto, J. G.

García de Abajo, F. J.

T. V. Teperik, F. J. García de Abajo, A. G. Borisov, M. Abdelsalam, P. N. Bartlett, Y. Sugawara, and J. J. Baumberg, “Omnidirectional absorption in nanostructured metal surfaces,” Nat. Photonics 2(5), 299–301 (2008).
[CrossRef]

Ge, L.

W. Wan, Y. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science 331(6019), 889–892 (2011).
[CrossRef] [PubMed]

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent perfect absorbers: time-reversed lasers,” Phys. Rev. Lett. 105(5), 053901 (2010).
[CrossRef] [PubMed]

Hangyo, M.

S. Nashima, O. Morikawa, K. Takata, and M. Hangyo, “Measurement of optical properties of highly doped silicon by terahertz time domain reflection spectroscopy,” Appl. Phys. Lett. 79(24), 3923–3925 (2001).
[CrossRef]

Hu, C.

Huang, C.

Jin, B.

Q. L. Zhou, Y. L. Shi, T. Li, B. Jin, D. M. Zhao, and C. L. Zhang, “Carrier dynamics and terahertz photoconductivity of doped silicon measured by femtosecond pump-terahertz probe spectroscopy,” Sci. China, Ser. G 52(12), 1944–1948 (2009).
[CrossRef]

Jonathan, R.

Kärtner, F. X.

Kim, J.

Koschny, T.

M. Diem, T. Koschny, and C. M. Soukoulis, “Wide-angle perfect absorber/thermal emitter in the terahertz regime,” Phys. Rev. B 79(3), 033101 (2009).
[CrossRef]

Landy, N. I.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
[CrossRef] [PubMed]

Li, T.

Q. L. Zhou, Y. L. Shi, T. Li, B. Jin, D. M. Zhao, and C. L. Zhang, “Carrier dynamics and terahertz photoconductivity of doped silicon measured by femtosecond pump-terahertz probe spectroscopy,” Sci. China, Ser. G 52(12), 1944–1948 (2009).
[CrossRef]

Luo, X.

Mock, J. J.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
[CrossRef] [PubMed]

Morikawa, O.

S. Nashima, O. Morikawa, K. Takata, and M. Hangyo, “Measurement of optical properties of highly doped silicon by terahertz time domain reflection spectroscopy,” Appl. Phys. Lett. 79(24), 3923–3925 (2001).
[CrossRef]

Nashima, S.

S. Nashima, O. Morikawa, K. Takata, and M. Hangyo, “Measurement of optical properties of highly doped silicon by terahertz time domain reflection spectroscopy,” Appl. Phys. Lett. 79(24), 3923–3925 (2001).
[CrossRef]

Nimtz, G.

G. Nimtz and U. Panten, “Broad band electromagnetic wave absorbers designed with nano-metal films,” Ann. Phys. 19(1-2), 53–59 (2010).
[CrossRef]

Noh, H.

W. Wan, Y. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science 331(6019), 889–892 (2011).
[CrossRef] [PubMed]

Padilla, W. J.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
[CrossRef] [PubMed]

Panten, U.

G. Nimtz and U. Panten, “Broad band electromagnetic wave absorbers designed with nano-metal films,” Ann. Phys. 19(1-2), 53–59 (2010).
[CrossRef]

Pu, M.

Sajuyigbe, S.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
[CrossRef] [PubMed]

Scheuer, V.

Sharma, B. V.

Shi, Y. L.

Q. L. Zhou, Y. L. Shi, T. Li, B. Jin, D. M. Zhao, and C. L. Zhang, “Carrier dynamics and terahertz photoconductivity of doped silicon measured by femtosecond pump-terahertz probe spectroscopy,” Sci. China, Ser. G 52(12), 1944–1948 (2009).
[CrossRef]

Smith, D. R.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
[CrossRef] [PubMed]

Soukoulis, C. M.

M. Diem, T. Koschny, and C. M. Soukoulis, “Wide-angle perfect absorber/thermal emitter in the terahertz regime,” Phys. Rev. B 79(3), 033101 (2009).
[CrossRef]

Stone, A. D.

Y. D. Chong and A. D. Stone, “Hidden black: coherent enhancement of absorption in strongly scattering media,” Phys. Rev. Lett. 107(16), 163901 (2011).
[CrossRef] [PubMed]

W. Wan, Y. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science 331(6019), 889–892 (2011).
[CrossRef] [PubMed]

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent perfect absorbers: time-reversed lasers,” Phys. Rev. Lett. 105(5), 053901 (2010).
[CrossRef] [PubMed]

Sugawara, Y.

T. V. Teperik, F. J. García de Abajo, A. G. Borisov, M. Abdelsalam, P. N. Bartlett, Y. Sugawara, and J. J. Baumberg, “Omnidirectional absorption in nanostructured metal surfaces,” Nat. Photonics 2(5), 299–301 (2008).
[CrossRef]

Takata, K.

S. Nashima, O. Morikawa, K. Takata, and M. Hangyo, “Measurement of optical properties of highly doped silicon by terahertz time domain reflection spectroscopy,” Appl. Phys. Lett. 79(24), 3923–3925 (2001).
[CrossRef]

Teperik, T. V.

T. V. Teperik, F. J. García de Abajo, A. G. Borisov, M. Abdelsalam, P. N. Bartlett, Y. Sugawara, and J. J. Baumberg, “Omnidirectional absorption in nanostructured metal surfaces,” Nat. Photonics 2(5), 299–301 (2008).
[CrossRef]

Wan, W.

W. Wan, Y. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science 331(6019), 889–892 (2011).
[CrossRef] [PubMed]

Wang, C.

Wang, M.

Woltersdorff, W.

W. Woltersdorff, “Über die optischen Konstanten dünner Metallschichten im langwelligen Ultrarot,” Z. Phys. 91(3-4), 230–252 (1934).
[CrossRef]

Zhang, C. L.

Q. L. Zhou, Y. L. Shi, T. Li, B. Jin, D. M. Zhao, and C. L. Zhang, “Carrier dynamics and terahertz photoconductivity of doped silicon measured by femtosecond pump-terahertz probe spectroscopy,” Sci. China, Ser. G 52(12), 1944–1948 (2009).
[CrossRef]

Zhao, D. M.

Q. L. Zhou, Y. L. Shi, T. Li, B. Jin, D. M. Zhao, and C. L. Zhang, “Carrier dynamics and terahertz photoconductivity of doped silicon measured by femtosecond pump-terahertz probe spectroscopy,” Sci. China, Ser. G 52(12), 1944–1948 (2009).
[CrossRef]

Zhao, Z.

Zhou, Q. L.

Q. L. Zhou, Y. L. Shi, T. Li, B. Jin, D. M. Zhao, and C. L. Zhang, “Carrier dynamics and terahertz photoconductivity of doped silicon measured by femtosecond pump-terahertz probe spectroscopy,” Sci. China, Ser. G 52(12), 1944–1948 (2009).
[CrossRef]

Ann. Phys. (1)

G. Nimtz and U. Panten, “Broad band electromagnetic wave absorbers designed with nano-metal films,” Ann. Phys. 19(1-2), 53–59 (2010).
[CrossRef]

Appl. Phys. Lett. (1)

S. Nashima, O. Morikawa, K. Takata, and M. Hangyo, “Measurement of optical properties of highly doped silicon by terahertz time domain reflection spectroscopy,” Appl. Phys. Lett. 79(24), 3923–3925 (2001).
[CrossRef]

Nat. Photonics (1)

T. V. Teperik, F. J. García de Abajo, A. G. Borisov, M. Abdelsalam, P. N. Bartlett, Y. Sugawara, and J. J. Baumberg, “Omnidirectional absorption in nanostructured metal surfaces,” Nat. Photonics 2(5), 299–301 (2008).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. B (1)

M. Diem, T. Koschny, and C. M. Soukoulis, “Wide-angle perfect absorber/thermal emitter in the terahertz regime,” Phys. Rev. B 79(3), 033101 (2009).
[CrossRef]

Phys. Rev. Lett. (3)

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent perfect absorbers: time-reversed lasers,” Phys. Rev. Lett. 105(5), 053901 (2010).
[CrossRef] [PubMed]

Y. D. Chong and A. D. Stone, “Hidden black: coherent enhancement of absorption in strongly scattering media,” Phys. Rev. Lett. 107(16), 163901 (2011).
[CrossRef] [PubMed]

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
[CrossRef] [PubMed]

Sci. China, Ser. G (1)

Q. L. Zhou, Y. L. Shi, T. Li, B. Jin, D. M. Zhao, and C. L. Zhang, “Carrier dynamics and terahertz photoconductivity of doped silicon measured by femtosecond pump-terahertz probe spectroscopy,” Sci. China, Ser. G 52(12), 1944–1948 (2009).
[CrossRef]

Science (1)

W. Wan, Y. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science 331(6019), 889–892 (2011).
[CrossRef] [PubMed]

Z. Phys. (1)

W. Woltersdorff, “Über die optischen Konstanten dünner Metallschichten im langwelligen Ultrarot,” Z. Phys. 91(3-4), 230–252 (1934).
[CrossRef]

Other (6)

M. Dressel and G. Gruner, Electrodynamics of Solids: Optical Properties of Electrons in Matter (Cambridge, New York, 2002).

In the impedance theory, the thin film CPA can be approximated as a resistive sheet with Z=1/(dwσ0)=Z0/2 as the thickness of the slab is much smaller than the skin depth. Here, σ0=ωp2τε0 is the AC conductivity and Z0=μ0/ε0 is the impedance of vacuum. Then consider the radiation property of an infinite oscillating current sheet in xy plane. Assuming that the current is J→=Ksin(ωt)x→, the electric field at z = 0 can be written as: E→=−0.5μ0cKsin(ωt)x→. The effective sheet impedance, defined as E/J, is -Z0/2, which is just in opposite to the thin film CPA condition. Such a radiation can be thought as the time reversed process of the broadband CPA, although the infinite oscillating current sheet is not applicable in practical applications.

R. A. Falk, “Near IR Absorption in Heavily Doped Silicon-An Empirical Approach,” in Proceedings of the 26th ISTFA, 2000.

B. V. Zeghbroeck, Principles of Semiconductor Devices (Boulder, 1997).

E. D. Palik, Handbook of Optical Constants of Solids (Academic, Orlando, Fla., 1985).

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd ed., (Wiley, 2007).

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Figures (6)

Fig. 1
Fig. 1

Schematic of the coherent perfect absorber. The thickness of the slab is d and refractive index is n. A and B denote the input beams, while C and D denote the output beams. When d, n, A, and B is correctly designed, all incident energy could be perfectly absorbed and the output C and D vanish.

Fig. 2
Fig. 2

(a) Absorption as a function of the frequency and the thickness of the doped silicon film. The dashed lines illustrate the absorption at two different characteristic thicknesses. (b) Refractive index described by Drude model and the absorption curves extracted from (a) for different thicknesses. The two absorption regimes are highlighted as ZoneI and ZoneII, where the real and imaginary parts of n become nearly equal. The theoretical refractive indexes are calculated using Eqs. (11) and (13) for 5THz and 27 THz, respectively.

Fig. 3
Fig. 3

Coherent absorption of a 450nm thick doped silicon film for different doping concentrations. The red-solid curve shows the absorption when the Plasmon thickness is equal to the Woltersdorff thickness and the two absorption couple together. As the increase of doping concentration, the absorption peak shifts to higher frequency. The shaded area around 40THz illustrates the tunability of absorption provided by varying of doping concentration.

Fig. 4
Fig. 4

Coherent absorption of 150nm thick doped silicon for different Δl varying from 0 to 60μm. The symmetrical and antisymmetrical absorption curves are near unit and zero, respectively.

Fig. 5
Fig. 5

Coherent absorption of a 450nm thick doped silicon film. The yellow dashed (green dot) line shows the absorption bound where in-phase (out-of-phase) condition is obtained at respective frequency point. Inset: the absorption in a short range of frequency near 27THz. Red and green solid lines show the absorption for Δl equal 500 and 505.56μm, respectively. Gray dotted line shows the absorption for incoherent inputs.

Fig. 6
Fig. 6

Coherent absorption of 17nm thick tungsten for symmetrical and antisymmetrical inputs. The absorption peak is around 940nm. The two curves act as the upper and lower bounds of absorption when Δl is changed. The absorption curve for a specific Δl is not given here for simplicity.

Equations (15)

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

[ C D ]=S[ A B ]=[ t r r t ][ A B ],
r= ( n 2 1 )( 1+ e i2nkd ) ( n+1 ) 2 ( n1 ) 2 e i2nkd ,
t= 4n e inkd ( n+1 ) 2 ( n1 ) 2 e i2nkd .
exp(inkd)=± n1 n+1 .
r s = 1 2 ( n 2 1 n 2 +1 ),
t s =± 1 2 ( n 2 1 n 2 +1 ).
n n 1 kd = c ωd .
n 2 = ε 1 +i ε 2 = ε ω p 2 ω(ω+iΓ) ,
ε 1 = ε ω p 2 τ 2 1+ ω 2 τ 2 , ε 2 = ω p 2 τ ω(1+ ω 2 τ 2 ) ,
ν= ν min + ν max ν min 1+ ( N c N r ) α .
n n ε 2 2 = τ ω p 2 2ω .
d w 2c ω p 2 τ ,
n = n = ε 2 2 = ε 2ωτ .
d p 2cτ ε .
I= I 0 sin 2 ( ϕ 2 ),

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