Abstract

In order to extend the Coherent Perfect Absorption (CPA) phenomenology to broadband operation, the interferometric control of absorption is investigated in two-port systems without port permutation symmetry. Starting from the two-port theory of CPA treated within the Scattering Matrix formalism, we demonstrate that for all linear two-port systems with reciprocity the absorption is represented by an ellipse as function of the relative phase and intensity of the two input beams, and it is uniquely determined by the device single-beam reflectance and transmittance, and by the dephasing of the output beams. The basic properties of the phenomenon in systems without port permutation symmetry show that CPA conditions can still be found in such asymmetric devices, while the asymmetry can be beneficial for broadband operation. As experimental proof, we performed transmission measurements on a metal-semiconductor metamaterial, employing a Mach-Zehnder interferometer. The experimental results clearly evidence the elliptical feature of absorption and trace a route towards broadband operation.

© 2015 Optical Society of America

Full Article  |  PDF Article
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References

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2014 (4)

Y. Sun, W. Tan, H.-q. Li, J. Li, and H. Chen, “Experimental demonstration of a coherent perfect absorber with pt phase transition,” Phys. Rev. Lett. 112, 143903 (2014).
[Crossref] [PubMed]

S. Zanotto, F. P. Mezzapesa, F. Bianco, G. Biasiol, L. Baldacci, M. S. Vitiello, L. Sorba, R. Colombelli, and A. Tredicucci, “Perfect energy-feeding into strongly coupled systems and interferometric control of polariton absorption,” Nature Phys. 10, 830–834 (2014).
[Crossref]

J. A. Giese, J. W. Yoon, B. R. Wenner, J. W. Allen, M. S. Allen, and R. Magnusson, “Guided-mode resonant coherent light absorbers,” Opt. Lett. 39, 486–488 (2014).
[Crossref] [PubMed]

J. R. Piper and S. Fan, “Total absorption in a graphene monolayer in the optical regime by critical coupling with a photonic crystal guided resonance,” ACS Photonics 1, 347–353 (2014).
[Crossref]

2013 (3)

J.-M. Manceau, S. Zanotto, I. Sagnes, G. Beaudoin, and R. Colombelli, “Optical critical coupling into highly confining metal-insulator-metal resonators,” Applied Physics Letters 103, 091110 (2013).
[Crossref]

R. Bruck and O. L. Muskens, “Plasmonic nanoantennas as integrated coherent perfect absorbers on soi waveguides for modulators and all-optical switches,” Opt. Express 21, 27652–27661 (2013).
[Crossref]

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popovic, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is – and what is not – an optical isolator,” Nature Photonics 7, 579–582 (2013).
[Crossref]

2012 (3)

Z. Yu, A. Raman, and S. Fan, “Thermodynamic upper bound on broadband light coupling with photonic structures,” Phys. Rev. Lett. 109, 173901 (2012).
[Crossref] [PubMed]

M. Pu, Q. Feng, M. Wang, C. Hu, C. Huang, X. Ma, Z. Zhao, C. Wang, and X. Luo, “Ultrathin broadband nearly perfect absorber with symmetrical coherent illumination,” Opt. Express 20, 2246–2254 (2012).
[Crossref] [PubMed]

J. W. Yoon, G. M. Koh, S. H. Song, and R. Magnusson, “Measurement and modeling of a complete optical absorption and scattering by coherent surface plasmon-polariton excitation using a silver thin-film grating,” Phys. Rev. Lett. 109, 257402 (2012).
[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] [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, 889–892 (2011).
[Crossref] [PubMed]

2010 (3)

J. Yoon, K. H. Seol, S. H. Song, and R. Magnusson, “Critical coupling in dissipative surface-plasmon resonators with multiple ports,” Opt. Express 18, 25702–25711 (2010).
[Crossref] [PubMed]

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

S. Longhi, “Pt-symmetric laser absorber,” Phys. Rev. A 82, 031801 (2010).
[Crossref]

2000 (2)

M. Cai, O. Painter, and K. J. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett. 85, 74–77 (2000).
[Crossref] [PubMed]

J. Jeffers, “Interference and the lossless lossy beam splitter,” Journal of Modern Optics 47, 1819–1824 (2000).
[Crossref]

1998 (1)

S. M. Barnett, J. Jeffers, A. Gatti, and R. Loudon, “Quantum optics of lossy beam splitters,” Phys. Rev. A 57, 2134–2145 (1998).
[Crossref]

1996 (1)

1983 (1)

D. Aspnes and A. Studna, “Dielectric functions and optical parameters of si, ge, gap, gaas, gasb, inp, inas, and insb from 1.5 to 6.0 ev,” Physical Review B 27, 985 (1983).
[Crossref]

1972 (1)

P. B. Johnson and R.-W. Christy, “Optical constants of the noble metals,” Physical Review B 6, 4370 (1972).
[Crossref]

Agarwal, G.

S. Huang and G. Agarwal, “Coherent perfect absorption of single photons,” arXiv preprint arXiv:1402.7146 (2014).

Allen, J. W.

Allen, M. S.

Aspnes, D.

D. Aspnes and A. Studna, “Dielectric functions and optical parameters of si, ge, gap, gaas, gasb, inp, inas, and insb from 1.5 to 6.0 ev,” Physical Review B 27, 985 (1983).
[Crossref]

Baets, R.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popovic, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is – and what is not – an optical isolator,” Nature Photonics 7, 579–582 (2013).
[Crossref]

Baldacci, L.

S. Zanotto, F. P. Mezzapesa, F. Bianco, G. Biasiol, L. Baldacci, M. S. Vitiello, L. Sorba, R. Colombelli, and A. Tredicucci, “Perfect energy-feeding into strongly coupled systems and interferometric control of polariton absorption,” Nature Phys. 10, 830–834 (2014).
[Crossref]

Barnett, S. M.

S. M. Barnett, J. Jeffers, A. Gatti, and R. Loudon, “Quantum optics of lossy beam splitters,” Phys. Rev. A 57, 2134–2145 (1998).
[Crossref]

Beaudoin, G.

J.-M. Manceau, S. Zanotto, I. Sagnes, G. Beaudoin, and R. Colombelli, “Optical critical coupling into highly confining metal-insulator-metal resonators,” Applied Physics Letters 103, 091110 (2013).
[Crossref]

Bianco, F.

S. Zanotto, F. P. Mezzapesa, F. Bianco, G. Biasiol, L. Baldacci, M. S. Vitiello, L. Sorba, R. Colombelli, and A. Tredicucci, “Perfect energy-feeding into strongly coupled systems and interferometric control of polariton absorption,” Nature Phys. 10, 830–834 (2014).
[Crossref]

Biasiol, G.

S. Zanotto, F. P. Mezzapesa, F. Bianco, G. Biasiol, L. Baldacci, M. S. Vitiello, L. Sorba, R. Colombelli, and A. Tredicucci, “Perfect energy-feeding into strongly coupled systems and interferometric control of polariton absorption,” Nature Phys. 10, 830–834 (2014).
[Crossref]

Bruck, R.

Cai, M.

M. Cai, O. Painter, and K. J. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett. 85, 74–77 (2000).
[Crossref] [PubMed]

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, 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, 053901 (2010).
[Crossref] [PubMed]

Chen, H.

Y. Sun, W. Tan, H.-q. Li, J. Li, and H. Chen, “Experimental demonstration of a coherent perfect absorber with pt phase transition,” Phys. Rev. Lett. 112, 143903 (2014).
[Crossref] [PubMed]

Chew, W. C.

W. C. Chew, Waves and Fields in Inhomogeneous Media, vol. 522 (IEEE, 1995).

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, 889–892 (2011).
[Crossref] [PubMed]

Chong, Y. D.

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

Christy, R.-W.

P. B. Johnson and R.-W. Christy, “Optical constants of the noble metals,” Physical Review B 6, 4370 (1972).
[Crossref]

Colombelli, R.

S. Zanotto, F. P. Mezzapesa, F. Bianco, G. Biasiol, L. Baldacci, M. S. Vitiello, L. Sorba, R. Colombelli, and A. Tredicucci, “Perfect energy-feeding into strongly coupled systems and interferometric control of polariton absorption,” Nature Phys. 10, 830–834 (2014).
[Crossref]

J.-M. Manceau, S. Zanotto, I. Sagnes, G. Beaudoin, and R. Colombelli, “Optical critical coupling into highly confining metal-insulator-metal resonators,” Applied Physics Letters 103, 091110 (2013).
[Crossref]

Doerr, C. R.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popovic, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is – and what is not – an optical isolator,” Nature Photonics 7, 579–582 (2013).
[Crossref]

Eich, M.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popovic, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is – and what is not – an optical isolator,” Nature Photonics 7, 579–582 (2013).
[Crossref]

Fan, S.

J. R. Piper and S. Fan, “Total absorption in a graphene monolayer in the optical regime by critical coupling with a photonic crystal guided resonance,” ACS Photonics 1, 347–353 (2014).
[Crossref]

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popovic, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is – and what is not – an optical isolator,” Nature Photonics 7, 579–582 (2013).
[Crossref]

Z. Yu, A. Raman, and S. Fan, “Thermodynamic upper bound on broadband light coupling with photonic structures,” Phys. Rev. Lett. 109, 173901 (2012).
[Crossref] [PubMed]

Feng, Q.

Freude, W.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popovic, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is – and what is not – an optical isolator,” Nature Photonics 7, 579–582 (2013).
[Crossref]

Gatti, A.

S. M. Barnett, J. Jeffers, A. Gatti, and R. Loudon, “Quantum optics of lossy beam splitters,” Phys. Rev. A 57, 2134–2145 (1998).
[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, 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, 053901 (2010).
[Crossref] [PubMed]

Giese, J. A.

Granet, G.

Guizal, B.

Haus, H. A.

H. A. Haus, Waves and fields in optoelectronics (Prentice-Hall, 1984).

Hu, C.

Huang, C.

Huang, S.

S. Huang and G. Agarwal, “Coherent perfect absorption of single photons,” arXiv preprint arXiv:1402.7146 (2014).

Jalas, D.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popovic, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is – and what is not – an optical isolator,” Nature Photonics 7, 579–582 (2013).
[Crossref]

Jeffers, J.

J. Jeffers, “Interference and the lossless lossy beam splitter,” Journal of Modern Optics 47, 1819–1824 (2000).
[Crossref]

S. M. Barnett, J. Jeffers, A. Gatti, and R. Loudon, “Quantum optics of lossy beam splitters,” Phys. Rev. A 57, 2134–2145 (1998).
[Crossref]

Joannopoulos, J. D.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popovic, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is – and what is not – an optical isolator,” Nature Photonics 7, 579–582 (2013).
[Crossref]

Johnson, P. B.

P. B. Johnson and R.-W. Christy, “Optical constants of the noble metals,” Physical Review B 6, 4370 (1972).
[Crossref]

Jokerst, N. M.

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] [PubMed]

Koh, G. M.

J. W. Yoon, G. M. Koh, S. H. Song, and R. Magnusson, “Measurement and modeling of a complete optical absorption and scattering by coherent surface plasmon-polariton excitation using a silver thin-film grating,” Phys. Rev. Lett. 109, 257402 (2012).
[Crossref]

Li, H.-q.

Y. Sun, W. Tan, H.-q. Li, J. Li, and H. Chen, “Experimental demonstration of a coherent perfect absorber with pt phase transition,” Phys. Rev. Lett. 112, 143903 (2014).
[Crossref] [PubMed]

Li, J.

Y. Sun, W. Tan, H.-q. Li, J. Li, and H. Chen, “Experimental demonstration of a coherent perfect absorber with pt phase transition,” Phys. Rev. Lett. 112, 143903 (2014).
[Crossref] [PubMed]

Liu, X.

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] [PubMed]

Longhi, S.

S. Longhi, “Pt-symmetric laser absorber,” Phys. Rev. A 82, 031801 (2010).
[Crossref]

Loudon, R.

S. M. Barnett, J. Jeffers, A. Gatti, and R. Loudon, “Quantum optics of lossy beam splitters,” Phys. Rev. A 57, 2134–2145 (1998).
[Crossref]

Luo, X.

Ma, X.

Magnusson, R.

Manceau, J.-M.

J.-M. Manceau, S. Zanotto, I. Sagnes, G. Beaudoin, and R. Colombelli, “Optical critical coupling into highly confining metal-insulator-metal resonators,” Applied Physics Letters 103, 091110 (2013).
[Crossref]

Melloni, A.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popovic, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is – and what is not – an optical isolator,” Nature Photonics 7, 579–582 (2013).
[Crossref]

Mezzapesa, F. P.

S. Zanotto, F. P. Mezzapesa, F. Bianco, G. Biasiol, L. Baldacci, M. S. Vitiello, L. Sorba, R. Colombelli, and A. Tredicucci, “Perfect energy-feeding into strongly coupled systems and interferometric control of polariton absorption,” Nature Phys. 10, 830–834 (2014).
[Crossref]

Muskens, O. L.

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, 889–892 (2011).
[Crossref] [PubMed]

Padilla, W. J.

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] [PubMed]

Painter, O.

M. Cai, O. Painter, and K. J. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett. 85, 74–77 (2000).
[Crossref] [PubMed]

Petrov, A.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popovic, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is – and what is not – an optical isolator,” Nature Photonics 7, 579–582 (2013).
[Crossref]

Piper, J. R.

J. R. Piper and S. Fan, “Total absorption in a graphene monolayer in the optical regime by critical coupling with a photonic crystal guided resonance,” ACS Photonics 1, 347–353 (2014).
[Crossref]

Popovic, M.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popovic, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is – and what is not – an optical isolator,” Nature Photonics 7, 579–582 (2013).
[Crossref]

Pu, M.

Raman, A.

Z. Yu, A. Raman, and S. Fan, “Thermodynamic upper bound on broadband light coupling with photonic structures,” Phys. Rev. Lett. 109, 173901 (2012).
[Crossref] [PubMed]

Renner, H.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popovic, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is – and what is not – an optical isolator,” Nature Photonics 7, 579–582 (2013).
[Crossref]

Sagnes, I.

J.-M. Manceau, S. Zanotto, I. Sagnes, G. Beaudoin, and R. Colombelli, “Optical critical coupling into highly confining metal-insulator-metal resonators,” Applied Physics Letters 103, 091110 (2013).
[Crossref]

Seol, K. H.

Song, S. H.

J. W. Yoon, G. M. Koh, S. H. Song, and R. Magnusson, “Measurement and modeling of a complete optical absorption and scattering by coherent surface plasmon-polariton excitation using a silver thin-film grating,” Phys. Rev. Lett. 109, 257402 (2012).
[Crossref]

J. Yoon, K. H. Seol, S. H. Song, and R. Magnusson, “Critical coupling in dissipative surface-plasmon resonators with multiple ports,” Opt. Express 18, 25702–25711 (2010).
[Crossref] [PubMed]

Sorba, L.

S. Zanotto, F. P. Mezzapesa, F. Bianco, G. Biasiol, L. Baldacci, M. S. Vitiello, L. Sorba, R. Colombelli, and A. Tredicucci, “Perfect energy-feeding into strongly coupled systems and interferometric control of polariton absorption,” Nature Phys. 10, 830–834 (2014).
[Crossref]

Starr, A. F.

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] [PubMed]

Starr, T.

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

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Y. Sun, W. Tan, H.-q. Li, J. Li, and H. Chen, “Experimental demonstration of a coherent perfect absorber with pt phase transition,” Phys. Rev. Lett. 112, 143903 (2014).
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Y. Sun, W. Tan, H.-q. Li, J. Li, and H. Chen, “Experimental demonstration of a coherent perfect absorber with pt phase transition,” Phys. Rev. Lett. 112, 143903 (2014).
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S. Zanotto, F. P. Mezzapesa, F. Bianco, G. Biasiol, L. Baldacci, M. S. Vitiello, L. Sorba, R. Colombelli, and A. Tredicucci, “Perfect energy-feeding into strongly coupled systems and interferometric control of polariton absorption,” Nature Phys. 10, 830–834 (2014).
[Crossref]

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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).
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M. Cai, O. Painter, and K. J. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett. 85, 74–77 (2000).
[Crossref] [PubMed]

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D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popovic, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is – and what is not – an optical isolator,” Nature Photonics 7, 579–582 (2013).
[Crossref]

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S. Zanotto, F. P. Mezzapesa, F. Bianco, G. Biasiol, L. Baldacci, M. S. Vitiello, L. Sorba, R. Colombelli, and A. Tredicucci, “Perfect energy-feeding into strongly coupled systems and interferometric control of polariton absorption,” Nature Phys. 10, 830–834 (2014).
[Crossref]

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

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Wang, M.

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D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popovic, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is – and what is not – an optical isolator,” Nature Photonics 7, 579–582 (2013).
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Z. Yu, A. Raman, and S. Fan, “Thermodynamic upper bound on broadband light coupling with photonic structures,” Phys. Rev. Lett. 109, 173901 (2012).
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S. Zanotto, F. P. Mezzapesa, F. Bianco, G. Biasiol, L. Baldacci, M. S. Vitiello, L. Sorba, R. Colombelli, and A. Tredicucci, “Perfect energy-feeding into strongly coupled systems and interferometric control of polariton absorption,” Nature Phys. 10, 830–834 (2014).
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S. Zanotto, F. P. Mezzapesa, F. Bianco, G. Biasiol, L. Baldacci, M. S. Vitiello, L. Sorba, R. Colombelli, and A. Tredicucci, “Perfect energy-feeding into strongly coupled systems and interferometric control of polariton absorption,” Nature Phys. 10, 830–834 (2014).
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Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent perfect absorbers: Time-reversed lasers,” Phys. Rev. Lett. 105, 053901 (2010).
[Crossref] [PubMed]

Y. Sun, W. Tan, H.-q. Li, J. Li, and H. Chen, “Experimental demonstration of a coherent perfect absorber with pt phase transition,” Phys. Rev. Lett. 112, 143903 (2014).
[Crossref] [PubMed]

J. W. Yoon, G. M. Koh, S. H. Song, and R. Magnusson, “Measurement and modeling of a complete optical absorption and scattering by coherent surface plasmon-polariton excitation using a silver thin-film grating,” Phys. Rev. Lett. 109, 257402 (2012).
[Crossref]

M. Cai, O. Painter, and K. J. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett. 85, 74–77 (2000).
[Crossref] [PubMed]

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] [PubMed]

Z. Yu, A. Raman, and S. Fan, “Thermodynamic upper bound on broadband light coupling with photonic structures,” Phys. Rev. Lett. 109, 173901 (2012).
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W. Wan, Y. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science 331, 889–892 (2011).
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Figures (4)

Fig. 1
Fig. 1 Coherent absorption control in a linear two port scattering system with reciprocity. In the upper-left panel a general schematic is presented, with the scattering properties defined by a matrix S. If the two inputs are coherent, the total absorption Aj = 1 − Iout/Iin can be controlled by means of their relative phase γ = arg ( s 2 + / s 1 + ) and access all values delimited by an ellipse as function of their normalized relative intensity x = ( | s 1 + | 2 | s 2 + | 2 ) / ( | s 1 + | 2 + | s 2 + | 2 ), as illustraded by the graph in the upper-right panel. For fixed x, absorption can assume all different values along the vertical line delimited by the ellipse simply varying the phase difference γ. On the contrary, total absorption in the presence of two incoherent inputs is described by a straightline connecting A2 to A1, with no possibility to be controlled by γ.
Fig. 2
Fig. 2 Experimental setup and schematic of the sample. Radiation generated by a tunable diode laser is split in two and focused onto the opposite sides of the sample. The relative phase and intensity of the two input beams are controlled respectively by a neutral density filter wheel and a liquid crystal device driven by a voltage sweep. The total output intensity is then collected by a detector. A HeNe laser is employed for alignment purposes. Lower-right panel: SEM image of a cleaved sample.
Fig. 3
Fig. 3 Maximum and minimum joint absorption as function of input beams relative intensity. The elliptical feature predicted in the general theory (Sect. 2 and Fig. 1) is clearly observed in the experiment. The dashed line is obtained through the rigorous coupled wave analysis (RCWA). The mismatch with the measured set is attributed to the roughness of the interfaces resulting from the etching processes, the bending of the sample due to the strain at the interface between Ti and GaAs, the complex spatial distribution of the incident beams, which RCWA does not account for, in addition to the possible mismatch between the dielectric constants employed, taken from the literature [24, 25], and their actual values.
Fig. 4
Fig. 4 Joint absorption spectrum, experimental results (left) and theoretical predictions (right) obtained through RCWA. Incident beams have fixed equal intensity. In both cases the symmetry predicted in the general two port theory is preserved. The broad operation band is attributed to the plasmonic resonance of the sample. The disagreement between measured and predicted values is due to the back-reflection of signal into the cavity of the laser as the sample is put into the setup.

Equations (11)

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( s 1 s 2 ) = S ( s 1 + s 2 + )
S = e i ϕ ( ρ 1 e i ψ 1 i τ i τ ρ 2 e i ψ 2 )
I out = | s 1 | 2 + | s 2 | 2 = ( ρ 1 2 + τ 2 ) | s 1 + | 2 + ( ρ 2 2 + τ 2 ) | s 2 + | 2 + 2 | s 1 + | | s 2 + | τ ρ 1 2 + ρ 2 2 2 ρ 1 ρ 2 cos ( ψ 1 + ψ 2 ) sin ( γ + δ ) .
tan δ = ρ 2 sin ( ψ 2 ) + ρ 1 sin ( ψ 1 ) ρ 2 cos ( ψ 2 ) ρ 1 cos ( ψ 1 ) .
A j = 1 I out I in = 1 + x 2 A 1 + 1 x 2 A 2 1 x 2 A M sin ( γ + δ ) ,
A M = ( 1 A 1 ) ( 1 A 2 ) | det S | 2
x = | s 1 + | 2 | s 2 + | 2 | s 1 + | 2 + | s 2 + | 2 .
x min = x max x max = ± ( A 1 A 2 ) 2 4 A M 2 + ( A 1 A 2 ) 2
A M = τ ρ 1 2 + ρ 2 2 2 ρ 1 ρ 2 cos ( ψ 1 + ψ 2 ) .
y = ρ 1 2 ρ 2 2 ρ 1 2 + ρ 2 2 ,
cos ( ψ 1 + ψ 2 ) = 1 1 y 2 ,

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