Abstract

Non-Hermitian characteristics accompany any photonic device incorporating spatial domains of gain and loss. In this work, a one-dimensional beam-forming array playing the role of the active part is disturbed from the scattering losses produced by an obstacle in its vicinity. It is found that the placement of the radiating elements leading to perfect beam shaping is practically not affected by the presence of that jammer. A trial-and-error inverse technique of identifying the features of the obstacle is presented based on the difference between the beam target pattern and the actual one. Such a difference is an analytic function of the position, size, and texture of the object, empowering the designer to find the feeding fields for the lasers giving a perfect beam forming. In this way, an optimal beam-shaping equilibrium is re-established by effectively cloaking the object and nullifying its jamming effect.

© 2018 Chinese Laser Press

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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2017 (6)

T. Komljenovic, R. Helkey, L. Coldren, and J. E. Bowers, “Sparse aperiodic arrays for optical beam forming and LIDAR,” Opt. Express 25, 2511–2528 (2017).
[Crossref]

C. A. Valagiannopoulos and V. Kovanis, “Judicious distribution of laser emitters to shape the desired far-field patterns,” Phys. Rev. A 95, 063806 (2017).
[Crossref]

A. Gao, S. T. M. Fryslie, B. J. Thompson, P. S. Carney, and K. D. Choquette, “Parity-time symmetry in coherently coupled vertical cavity laser arrays,” Optica 4, 323–329 (2017).
[Crossref]

Y. Kominis, V. Kovanis, and T. Bountis, “Controllable asymmetric phase-locked states of the fundamental active photonic dimer,” Phys. Rev. A 96, 043836 (2017).
[Crossref]

W. Liu, M. Li, R. S. Guzzon, E. J. Norberg, J. S. Parker, M. Lu, L. A. Coldren, and J. Yao, “An integrated parity-time symmetric wavelength-tunable single-mode microring laser,” Nat. Commun. 8, 15389 (2017).
[Crossref]

M. H. Teimourpour, A. Rahman, K. Srinivasan, and R. El-Ganainy, “Non-Hermitian engineering of synthetic saturable absorbers for applications in photonics,” Phys. Rev. Appl. 7, 014015 (2017).
[Crossref]

2016 (3)

M. H. Teimourpour, L. Ge, D. N. Christodoulides, and R. El-Ganainy, “Non-Hermitian engineering of single mode two dimensional laser arrays,” Sci. Rep. 6, 33253 (2016).
[Crossref]

A. Andryieuski, A. V. Lavrinenko, M. Petrov, and S. A. Tretyakov, “Homogenization of metasurfaces formed by random resonant particles in periodical lattices,” Phys. Rev. B 93, 205127 (2016).
[Crossref]

J. Zhang, N. Liu, L. Zhang, S. Zhao, and Y. Zhao, “Active jamming suppression based on transmitting array designation for colocated multiple-input multiple-output radar,” IET Radar Sonar Navig. 10, 500–505 (2016).
[Crossref]

2015 (2)

2013 (4)

J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493, 195–199 (2013).
[Crossref]

C. T. DeRose, R. D. Kekatpure, D. C. Trotter, A. Starbuck, J. R. Wendt, A. Yaacobi, M. R. Watts, U. Chettiar, N. Engheta, and P. S. Davids, “Electronically controlled optical beam-steering by an active phased array of metallic nanoantennas,” Opt. Express 21, 5198–5208 (2013).
[Crossref]

M. Selvanayagam and G. V. Eleftheriades, “Experimental demonstration of active electromagnetic cloaking,” Phys. Rev. X 3, 041011 (2013).
[Crossref]

F. Monticone and A. Alù, “Do cloaked objects really scatter less?” Phys. Rev. X 3, 041005 (2013).
[Crossref]

2012 (1)

C. A. Valagiannopoulos and P. Alitalo, “Electromagnetic cloaking of cylindrical objects by multilayer or uniform dielectric claddings,” Phys. Rev. B 85, 115402 (2012).
[Crossref]

2010 (1)

C. A. Valagiannopoulos, “A novel methodology for estimating the permittivity of a specimen rod at low radio frequencies,” J. Electromagn. Waves. Appl. 24, 631–640 (2010).
[Crossref]

2009 (1)

A. Alù and N. Engheta, “Cloaking a sensor,” Phys. Rev. Lett. 102, 233901 (2009).
[Crossref]

2008 (1)

C. A. Valagiannopoulos, “On examining the influence of a thin dielectric strip posed across the diameter of a penetrable radiating cylinder,” Prog. Electromagn. Res. C 3, 203–214 (2008).
[Crossref]

2007 (2)

Y.-C. Xin, Y. Li, V. Kovanis, A. L. Gray, L. Zhang, and L. F. Lester, “Reconfigurable quantum dot monolithic multisection passive mode-locked lasers,” Opt. Express 15, 7623–7633 (2007).
[Crossref]

M. Gustafsson, C. Sohl, and G. Kristensson, “Physical limitations on antennas of arbitrary shape,” Proc. R. Soc. A 463, 2589–2607 (2007).
[Crossref]

2000 (1)

1997 (1)

G. Lythe, T. Erneux, A. Gavrielides, and V. Kovanis, “Low pump limit of the bifurcation to periodic intensities in a semiconductor laser subject to external optical feedback,” Phys. Rev. A 55, 4443–4448 (1997).
[Crossref]

1994 (1)

O. Hess and E. Scholl, “Spatio-temporal dynamics in twin-stripe semiconductor lasers,” Physica D 70, 165–177 (1994).
[Crossref]

1986 (1)

N. Jablon, “Adaptive beamforming with the generalized sidelobe canceller in the presence of array imperfections,” IEEE Trans. Antennas Propag. 34, 996–1012 (1986).
[Crossref]

1982 (1)

B. Widrow, K. M. Duvall, R. P. Gooch, and W. C. Newman, “Signal cancellation phenomena in adaptive antennas: causes and cures,” IEEE Trans. Antennas Propag. 30, 469–478 (1982).
[Crossref]

1980 (1)

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16, 347–355 (1980).
[Crossref]

Abramowitz, M.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (National Bureau of Standards, 1970), pp. 360–361.

Alitalo, P.

C. A. Valagiannopoulos and P. Alitalo, “Electromagnetic cloaking of cylindrical objects by multilayer or uniform dielectric claddings,” Phys. Rev. B 85, 115402 (2012).
[Crossref]

P. Alitalo, C. A. Valagiannopoulos, and S. A. Tretyakov, “Simple cloak for antenna blockage reduction,” in IEEE International Symposium on Antennas and Propagation (2011).

Alù, A.

F. Monticone and A. Alù, “Do cloaked objects really scatter less?” Phys. Rev. X 3, 041005 (2013).
[Crossref]

A. Alù and N. Engheta, “Cloaking a sensor,” Phys. Rev. Lett. 102, 233901 (2009).
[Crossref]

Andryieuski, A.

A. Andryieuski, A. V. Lavrinenko, M. Petrov, and S. A. Tretyakov, “Homogenization of metasurfaces formed by random resonant particles in periodical lattices,” Phys. Rev. B 93, 205127 (2016).
[Crossref]

Bandres, M. A.

M. Parto, S. Wittek, H. Hodaei, G. Harari, M. A. Bandres, J. Ren, M. C. Rechtsman, M. Segev, D. N. Christodoulides, and M. Khajavikhan, “Complex edge-state phase transitions in 1D topological laser arrays,” arXiv: 1709.00523 (2017).

Bountis, T.

Y. Kominis, V. Kovanis, and T. Bountis, “Controllable asymmetric phase-locked states of the fundamental active photonic dimer,” Phys. Rev. A 96, 043836 (2017).
[Crossref]

Bowers, J. E.

T. Komljenovic, R. Helkey, L. Coldren, and J. E. Bowers, “Sparse aperiodic arrays for optical beam forming and LIDAR,” Opt. Express 25, 2511–2528 (2017).
[Crossref]

J. E. Bowers, “Evolution of photonic integrated circuits,” in 75th Annual Device Research Conference (2017).

Carney, P. S.

Chettiar, U.

Choquette, K. D.

Christodoulides, D. N.

M. H. Teimourpour, L. Ge, D. N. Christodoulides, and R. El-Ganainy, “Non-Hermitian engineering of single mode two dimensional laser arrays,” Sci. Rep. 6, 33253 (2016).
[Crossref]

K. G. Makris, Z. H. Musslimani, D. N. Christodoulides, and S. Rotter, “Constant-intensity waves and their modulation instability in non-Hermitian potentials,” Nat. Commun. 6, 7257 (2015).
[Crossref]

M. Parto, S. Wittek, H. Hodaei, G. Harari, M. A. Bandres, J. Ren, M. C. Rechtsman, M. Segev, D. N. Christodoulides, and M. Khajavikhan, “Complex edge-state phase transitions in 1D topological laser arrays,” arXiv: 1709.00523 (2017).

Coldren, L.

Coldren, L. A.

W. Liu, M. Li, R. S. Guzzon, E. J. Norberg, J. S. Parker, M. Lu, L. A. Coldren, and J. Yao, “An integrated parity-time symmetric wavelength-tunable single-mode microring laser,” Nat. Commun. 8, 15389 (2017).
[Crossref]

Davids, P. S.

DeRose, C. T.

Duvall, K. M.

B. Widrow, K. M. Duvall, R. P. Gooch, and W. C. Newman, “Signal cancellation phenomena in adaptive antennas: causes and cures,” IEEE Trans. Antennas Propag. 30, 469–478 (1982).
[Crossref]

Efimov, O.

Eleftheriades, G. V.

M. Selvanayagam and G. V. Eleftheriades, “Experimental demonstration of active electromagnetic cloaking,” Phys. Rev. X 3, 041011 (2013).
[Crossref]

El-Ganainy, R.

M. H. Teimourpour, A. Rahman, K. Srinivasan, and R. El-Ganainy, “Non-Hermitian engineering of synthetic saturable absorbers for applications in photonics,” Phys. Rev. Appl. 7, 014015 (2017).
[Crossref]

M. H. Teimourpour, L. Ge, D. N. Christodoulides, and R. El-Ganainy, “Non-Hermitian engineering of single mode two dimensional laser arrays,” Sci. Rep. 6, 33253 (2016).
[Crossref]

Engheta, N.

Erneux, T.

G. Lythe, T. Erneux, A. Gavrielides, and V. Kovanis, “Low pump limit of the bifurcation to periodic intensities in a semiconductor laser subject to external optical feedback,” Phys. Rev. A 55, 4443–4448 (1997).
[Crossref]

Fedkiw, R.

S. Osher and R. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces (Springer, 2003).

Fryslie, S. T. M.

Gao, A.

Gavrielides, A.

G. Lythe, T. Erneux, A. Gavrielides, and V. Kovanis, “Low pump limit of the bifurcation to periodic intensities in a semiconductor laser subject to external optical feedback,” Phys. Rev. A 55, 4443–4448 (1997).
[Crossref]

Ge, L.

M. H. Teimourpour, L. Ge, D. N. Christodoulides, and R. El-Ganainy, “Non-Hermitian engineering of single mode two dimensional laser arrays,” Sci. Rep. 6, 33253 (2016).
[Crossref]

Gooch, R. P.

B. Widrow, K. M. Duvall, R. P. Gooch, and W. C. Newman, “Signal cancellation phenomena in adaptive antennas: causes and cures,” IEEE Trans. Antennas Propag. 30, 469–478 (1982).
[Crossref]

Gray, A. L.

Griffiths, L.

Gustafsson, M.

M. Gustafsson, C. Sohl, and G. Kristensson, “Physical limitations on antennas of arbitrary shape,” Proc. R. Soc. A 463, 2589–2607 (2007).
[Crossref]

Guzzon, R. S.

W. Liu, M. Li, R. S. Guzzon, E. J. Norberg, J. S. Parker, M. Lu, L. A. Coldren, and J. Yao, “An integrated parity-time symmetric wavelength-tunable single-mode microring laser,” Nat. Commun. 8, 15389 (2017).
[Crossref]

Harari, G.

M. Parto, S. Wittek, H. Hodaei, G. Harari, M. A. Bandres, J. Ren, M. C. Rechtsman, M. Segev, D. N. Christodoulides, and M. Khajavikhan, “Complex edge-state phase transitions in 1D topological laser arrays,” arXiv: 1709.00523 (2017).

Helkey, R.

Hess, O.

O. Hess and E. Scholl, “Spatio-temporal dynamics in twin-stripe semiconductor lasers,” Physica D 70, 165–177 (1994).
[Crossref]

Hodaei, H.

M. Parto, S. Wittek, H. Hodaei, G. Harari, M. A. Bandres, J. Ren, M. C. Rechtsman, M. Segev, D. N. Christodoulides, and M. Khajavikhan, “Complex edge-state phase transitions in 1D topological laser arrays,” arXiv: 1709.00523 (2017).

Hosseini, E. S.

J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493, 195–199 (2013).
[Crossref]

Jablon, N.

N. Jablon, “Adaptive beamforming with the generalized sidelobe canceller in the presence of array imperfections,” IEEE Trans. Antennas Propag. 34, 996–1012 (1986).
[Crossref]

Jones, D. S.

D. S. Jones, Theory of Electromagnetism (Pergamon, 1964), pp. 269–271.

Kekatpure, R. D.

Khajavikhan, M.

M. Parto, S. Wittek, H. Hodaei, G. Harari, M. A. Bandres, J. Ren, M. C. Rechtsman, M. Segev, D. N. Christodoulides, and M. Khajavikhan, “Complex edge-state phase transitions in 1D topological laser arrays,” arXiv: 1709.00523 (2017).

Kiruluta, A.

Kobayashi, K.

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16, 347–355 (1980).
[Crossref]

Kominis, Y.

Y. Kominis, V. Kovanis, and T. Bountis, “Controllable asymmetric phase-locked states of the fundamental active photonic dimer,” Phys. Rev. A 96, 043836 (2017).
[Crossref]

Komljenovic, T.

Kovanis, V.

C. A. Valagiannopoulos and V. Kovanis, “Judicious distribution of laser emitters to shape the desired far-field patterns,” Phys. Rev. A 95, 063806 (2017).
[Crossref]

Y. Kominis, V. Kovanis, and T. Bountis, “Controllable asymmetric phase-locked states of the fundamental active photonic dimer,” Phys. Rev. A 96, 043836 (2017).
[Crossref]

Y.-C. Xin, Y. Li, V. Kovanis, A. L. Gray, L. Zhang, and L. F. Lester, “Reconfigurable quantum dot monolithic multisection passive mode-locked lasers,” Opt. Express 15, 7623–7633 (2007).
[Crossref]

G. Lythe, T. Erneux, A. Gavrielides, and V. Kovanis, “Low pump limit of the bifurcation to periodic intensities in a semiconductor laser subject to external optical feedback,” Phys. Rev. A 55, 4443–4448 (1997).
[Crossref]

Kraut, S.

Kriehn, G.

Kristensson, G.

M. Gustafsson, C. Sohl, and G. Kristensson, “Physical limitations on antennas of arbitrary shape,” Proc. R. Soc. A 463, 2589–2607 (2007).
[Crossref]

Lang, R.

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16, 347–355 (1980).
[Crossref]

Lavrinenko, A. V.

A. Andryieuski, A. V. Lavrinenko, M. Petrov, and S. A. Tretyakov, “Homogenization of metasurfaces formed by random resonant particles in periodical lattices,” Phys. Rev. B 93, 205127 (2016).
[Crossref]

Lester, L. F.

Li, M.

W. Liu, M. Li, R. S. Guzzon, E. J. Norberg, J. S. Parker, M. Lu, L. A. Coldren, and J. Yao, “An integrated parity-time symmetric wavelength-tunable single-mode microring laser,” Nat. Commun. 8, 15389 (2017).
[Crossref]

Li, Y.

Liu, N.

J. Zhang, N. Liu, L. Zhang, S. Zhao, and Y. Zhao, “Active jamming suppression based on transmitting array designation for colocated multiple-input multiple-output radar,” IET Radar Sonar Navig. 10, 500–505 (2016).
[Crossref]

Liu, W.

W. Liu, M. Li, R. S. Guzzon, E. J. Norberg, J. S. Parker, M. Lu, L. A. Coldren, and J. Yao, “An integrated parity-time symmetric wavelength-tunable single-mode microring laser,” Nat. Commun. 8, 15389 (2017).
[Crossref]

Lu, M.

W. Liu, M. Li, R. S. Guzzon, E. J. Norberg, J. S. Parker, M. Lu, L. A. Coldren, and J. Yao, “An integrated parity-time symmetric wavelength-tunable single-mode microring laser,” Nat. Commun. 8, 15389 (2017).
[Crossref]

Lythe, G.

G. Lythe, T. Erneux, A. Gavrielides, and V. Kovanis, “Low pump limit of the bifurcation to periodic intensities in a semiconductor laser subject to external optical feedback,” Phys. Rev. A 55, 4443–4448 (1997).
[Crossref]

Makris, K. G.

K. G. Makris, Z. H. Musslimani, D. N. Christodoulides, and S. Rotter, “Constant-intensity waves and their modulation instability in non-Hermitian potentials,” Nat. Commun. 6, 7257 (2015).
[Crossref]

Miglo, A.

Miller, O.

O. Miller, “Photonic design: from fundamental solar cell physics to computational inverse design,” Ph.D. thesis (University of California, 2013).

Monticone, F.

F. Monticone and A. Alù, “Do cloaked objects really scatter less?” Phys. Rev. X 3, 041005 (2013).
[Crossref]

Musslimani, Z. H.

K. G. Makris, Z. H. Musslimani, D. N. Christodoulides, and S. Rotter, “Constant-intensity waves and their modulation instability in non-Hermitian potentials,” Nat. Commun. 6, 7257 (2015).
[Crossref]

Newman, W. C.

B. Widrow, K. M. Duvall, R. P. Gooch, and W. C. Newman, “Signal cancellation phenomena in adaptive antennas: causes and cures,” IEEE Trans. Antennas Propag. 30, 469–478 (1982).
[Crossref]

Norberg, E. J.

W. Liu, M. Li, R. S. Guzzon, E. J. Norberg, J. S. Parker, M. Lu, L. A. Coldren, and J. Yao, “An integrated parity-time symmetric wavelength-tunable single-mode microring laser,” Nat. Commun. 8, 15389 (2017).
[Crossref]

Osher, S.

S. Osher and R. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces (Springer, 2003).

Parker, J. S.

W. Liu, M. Li, R. S. Guzzon, E. J. Norberg, J. S. Parker, M. Lu, L. A. Coldren, and J. Yao, “An integrated parity-time symmetric wavelength-tunable single-mode microring laser,” Nat. Commun. 8, 15389 (2017).
[Crossref]

Parto, M.

M. Parto, S. Wittek, H. Hodaei, G. Harari, M. A. Bandres, J. Ren, M. C. Rechtsman, M. Segev, D. N. Christodoulides, and M. Khajavikhan, “Complex edge-state phase transitions in 1D topological laser arrays,” arXiv: 1709.00523 (2017).

Patterson, P.

Petrov, M.

A. Andryieuski, A. V. Lavrinenko, M. Petrov, and S. A. Tretyakov, “Homogenization of metasurfaces formed by random resonant particles in periodical lattices,” Phys. Rev. B 93, 205127 (2016).
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M. H. Teimourpour, A. Rahman, K. Srinivasan, and R. El-Ganainy, “Non-Hermitian engineering of synthetic saturable absorbers for applications in photonics,” Phys. Rev. Appl. 7, 014015 (2017).
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M. Parto, S. Wittek, H. Hodaei, G. Harari, M. A. Bandres, J. Ren, M. C. Rechtsman, M. Segev, D. N. Christodoulides, and M. Khajavikhan, “Complex edge-state phase transitions in 1D topological laser arrays,” arXiv: 1709.00523 (2017).

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M. Parto, S. Wittek, H. Hodaei, G. Harari, M. A. Bandres, J. Ren, M. C. Rechtsman, M. Segev, D. N. Christodoulides, and M. Khajavikhan, “Complex edge-state phase transitions in 1D topological laser arrays,” arXiv: 1709.00523 (2017).

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M. Selvanayagam and G. V. Eleftheriades, “Experimental demonstration of active electromagnetic cloaking,” Phys. Rev. X 3, 041011 (2013).
[Crossref]

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Silveira, P. E.

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M. Gustafsson, C. Sohl, and G. Kristensson, “Physical limitations on antennas of arbitrary shape,” Proc. R. Soc. A 463, 2589–2607 (2007).
[Crossref]

Srinivasan, K.

M. H. Teimourpour, A. Rahman, K. Srinivasan, and R. El-Ganainy, “Non-Hermitian engineering of synthetic saturable absorbers for applications in photonics,” Phys. Rev. Appl. 7, 014015 (2017).
[Crossref]

Starbuck, A.

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M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (National Bureau of Standards, 1970), pp. 360–361.

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J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493, 195–199 (2013).
[Crossref]

Teimourpour, M. H.

M. H. Teimourpour, A. Rahman, K. Srinivasan, and R. El-Ganainy, “Non-Hermitian engineering of synthetic saturable absorbers for applications in photonics,” Phys. Rev. Appl. 7, 014015 (2017).
[Crossref]

M. H. Teimourpour, L. Ge, D. N. Christodoulides, and R. El-Ganainy, “Non-Hermitian engineering of single mode two dimensional laser arrays,” Sci. Rep. 6, 33253 (2016).
[Crossref]

Thompson, B. J.

Timurdogan, E.

J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493, 195–199 (2013).
[Crossref]

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A. Andryieuski, A. V. Lavrinenko, M. Petrov, and S. A. Tretyakov, “Homogenization of metasurfaces formed by random resonant particles in periodical lattices,” Phys. Rev. B 93, 205127 (2016).
[Crossref]

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M. Parto, S. Wittek, H. Hodaei, G. Harari, M. A. Bandres, J. Ren, M. C. Rechtsman, M. Segev, D. N. Christodoulides, and M. Khajavikhan, “Complex edge-state phase transitions in 1D topological laser arrays,” arXiv: 1709.00523 (2017).

Xin, Y.-C.

Xu, G.

Yaacobi, A.

Yao, J.

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J. Zhang, N. Liu, L. Zhang, S. Zhao, and Y. Zhao, “Active jamming suppression based on transmitting array designation for colocated multiple-input multiple-output radar,” IET Radar Sonar Navig. 10, 500–505 (2016).
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J. Zhang, N. Liu, L. Zhang, S. Zhao, and Y. Zhao, “Active jamming suppression based on transmitting array designation for colocated multiple-input multiple-output radar,” IET Radar Sonar Navig. 10, 500–505 (2016).
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J. Zhang, N. Liu, L. Zhang, S. Zhao, and Y. Zhao, “Active jamming suppression based on transmitting array designation for colocated multiple-input multiple-output radar,” IET Radar Sonar Navig. 10, 500–505 (2016).
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N. Jablon, “Adaptive beamforming with the generalized sidelobe canceller in the presence of array imperfections,” IEEE Trans. Antennas Propag. 34, 996–1012 (1986).
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B. Widrow, K. M. Duvall, R. P. Gooch, and W. C. Newman, “Signal cancellation phenomena in adaptive antennas: causes and cures,” IEEE Trans. Antennas Propag. 30, 469–478 (1982).
[Crossref]

IET Radar Sonar Navig. (1)

J. Zhang, N. Liu, L. Zhang, S. Zhao, and Y. Zhao, “Active jamming suppression based on transmitting array designation for colocated multiple-input multiple-output radar,” IET Radar Sonar Navig. 10, 500–505 (2016).
[Crossref]

J. Electromagn. Waves. Appl. (1)

C. A. Valagiannopoulos, “A novel methodology for estimating the permittivity of a specimen rod at low radio frequencies,” J. Electromagn. Waves. Appl. 24, 631–640 (2010).
[Crossref]

Nat. Commun. (2)

K. G. Makris, Z. H. Musslimani, D. N. Christodoulides, and S. Rotter, “Constant-intensity waves and their modulation instability in non-Hermitian potentials,” Nat. Commun. 6, 7257 (2015).
[Crossref]

W. Liu, M. Li, R. S. Guzzon, E. J. Norberg, J. S. Parker, M. Lu, L. A. Coldren, and J. Yao, “An integrated parity-time symmetric wavelength-tunable single-mode microring laser,” Nat. Commun. 8, 15389 (2017).
[Crossref]

Nature (1)

J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493, 195–199 (2013).
[Crossref]

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Optica (1)

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Y. Kominis, V. Kovanis, and T. Bountis, “Controllable asymmetric phase-locked states of the fundamental active photonic dimer,” Phys. Rev. A 96, 043836 (2017).
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C. A. Valagiannopoulos and V. Kovanis, “Judicious distribution of laser emitters to shape the desired far-field patterns,” Phys. Rev. A 95, 063806 (2017).
[Crossref]

Phys. Rev. Appl. (1)

M. H. Teimourpour, A. Rahman, K. Srinivasan, and R. El-Ganainy, “Non-Hermitian engineering of synthetic saturable absorbers for applications in photonics,” Phys. Rev. Appl. 7, 014015 (2017).
[Crossref]

Phys. Rev. B (2)

C. A. Valagiannopoulos and P. Alitalo, “Electromagnetic cloaking of cylindrical objects by multilayer or uniform dielectric claddings,” Phys. Rev. B 85, 115402 (2012).
[Crossref]

A. Andryieuski, A. V. Lavrinenko, M. Petrov, and S. A. Tretyakov, “Homogenization of metasurfaces formed by random resonant particles in periodical lattices,” Phys. Rev. B 93, 205127 (2016).
[Crossref]

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A. Alù and N. Engheta, “Cloaking a sensor,” Phys. Rev. Lett. 102, 233901 (2009).
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M. Selvanayagam and G. V. Eleftheriades, “Experimental demonstration of active electromagnetic cloaking,” Phys. Rev. X 3, 041011 (2013).
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F. Monticone and A. Alù, “Do cloaked objects really scatter less?” Phys. Rev. X 3, 041005 (2013).
[Crossref]

Physica D (1)

O. Hess and E. Scholl, “Spatio-temporal dynamics in twin-stripe semiconductor lasers,” Physica D 70, 165–177 (1994).
[Crossref]

Proc. R. Soc. A (1)

M. Gustafsson, C. Sohl, and G. Kristensson, “Physical limitations on antennas of arbitrary shape,” Proc. R. Soc. A 463, 2589–2607 (2007).
[Crossref]

Prog. Electromagn. Res. C (1)

C. A. Valagiannopoulos, “On examining the influence of a thin dielectric strip posed across the diameter of a penetrable radiating cylinder,” Prog. Electromagn. Res. C 3, 203–214 (2008).
[Crossref]

Sci. Rep. (1)

M. H. Teimourpour, L. Ge, D. N. Christodoulides, and R. El-Ganainy, “Non-Hermitian engineering of single mode two dimensional laser arrays,” Sci. Rep. 6, 33253 (2016).
[Crossref]

Other (7)

M. Parto, S. Wittek, H. Hodaei, G. Harari, M. A. Bandres, J. Ren, M. C. Rechtsman, M. Segev, D. N. Christodoulides, and M. Khajavikhan, “Complex edge-state phase transitions in 1D topological laser arrays,” arXiv: 1709.00523 (2017).

P. Alitalo, C. A. Valagiannopoulos, and S. A. Tretyakov, “Simple cloak for antenna blockage reduction,” in IEEE International Symposium on Antennas and Propagation (2011).

O. Miller, “Photonic design: from fundamental solar cell physics to computational inverse design,” Ph.D. thesis (University of California, 2013).

S. Osher and R. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces (Springer, 2003).

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (National Bureau of Standards, 1970), pp. 360–361.

D. S. Jones, Theory of Electromagnetism (Pergamon, 1964), pp. 269–271.

J. E. Bowers, “Evolution of photonic integrated circuits,” in 75th Annual Device Research Conference (2017).

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Figures (8)

Fig. 1.
Fig. 1. Schematic of the regarded configuration. The aggregate field of an active laser array is perturbed by a passive cylindrical obstacle.
Fig. 2.
Fig. 2. Percent error of the obstacle-free optimal solution as functions of: (a) radius of the obstacle b/λ0 (ϵ=2) and (b) relative permittivity of the obstacle ϵ (b=λ0/4) for several vertical positions yb. Plot parameters: G˜(φ)=eγ(φϑ)2, ϑ=90°, γ=10, k0L=0.1, M=80, U=12, xb=0.
Fig. 3.
Fig. 3. Percent error of the obstacle-free optimal solution as a function of the horizontal position of the obstacle xb/D=xb/(ML) for several (a) radii b/λ0 (ϵ=2) and (b) permittivities ϵ (b=λ0/4). Plot parameters: yb=2λ0, and the remaining ones the same as in Fig. 2.
Fig. 4.
Fig. 4. Percent error of the obstacle-free optimal solution in contour plot of the permittivity ϵ and the electrical radius of the cylinder b/λ0 for (a) centered obstacle (xb=0) and (b) off-centered obstacle (xb=ML=D=4λ0/π). Plot parameters: yb=2λ0 and the remaining ones the same as in Fig. 2.
Fig. 5.
Fig. 5. Ideal target G˜(φ) and the optimal actual pattern G(φ) (both real and imaginary parts) as functions of azimuthal angle φ for the obstacle-free solution of Ref. [5] with (a) b=λ0/8, (b) b=λ0/4, (c) b=λ0/2, and (d) for the solution of Section 2 of this study and the worst case b=λ0/2. Plot parameters: ϵ=2, xb=0, yb=2λ0, and the remaining ones the same as in Fig. 2.
Fig. 6.
Fig. 6. (a) Percent error of optimal solution without and with the obstacle as a function of the optical distance between two neighboring lasers k0L. (b) Ideal target G˜(φ) and the optimal actual pattern G(φ) (both real and imaginary parts) as functions of azimuthal angle φ for k0L=2.4. The configuration of Fig. 5(c) is considered.
Fig. 7.
Fig. 7. Ideal target G˜(φ) and the optimal actual pattern G(φ) (both real and imaginary parts) as functions of azimuthal angle φ for the obstacle-free solution of Ref. [5] with (a) ϵ=1.5, (b) ϵ=2, (c) ϵ=2.5, and (d) for the solution of Section 2 of this study and the worst case ϵ=2.5. Plot parameters: G˜(φ)=eβφ[1+Acos(αφ)], A=0.7, α=13.5, β=0.2, k0L=1, M=50, U=12, b=λ0/4, xb=0, yb=2λ0.
Fig. 8.
Fig. 8. Block diagram for the introduced processes and presented concepts of the study at hand. A greedy inverse search by trial and error for the actual obstacle; as long as the error is non-negligible, a new trial object is considered.

Equations (9)

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

Eback(x,y)=m=MMFmH0(2)(k0a)H0(2)[k0(xmL)2+y2],
Escat(R,ϕ)=u=UUCuHu(2)(k0R)ejuϕ,
Cu=Bum=MMFmHu(2)(k0Rm)ejuϕm,
G(φ)=m=MMFm[ejk0LmcosφH0(2)(k0a)+u=UUjuBuHu(2)(k0Rm)ejuϕmej(uφ+k0xbcosφ+k0ybsinφ)].
Sbacknm=J0[k0L(mn)],
Sscatnm=H0(2)(k0a)πu=UUHu(2)(k0Rm)ejuϕmQu(n),
Vn=H0(2)(k0a)π0πG˜(φ)ejk0Lncosφdφ,
umaxMk0L3.
error=0π|G˜(φ)G(φ)|dφ0π(|G˜(φ)|+|G(φ)|)dφ.