Abstract

We present theoretical and numerical results for a new method of obtaining hotspots that relies on nonreciprocal “one-way” propagation as opposed to the well-known case of resonance-based hotspots. The nonreciprocal propagation is achieved by the breaking of time-reversal symmetry through the use of magnetically biased medium. The location and existence of the hotspots depends on the magnetic bias that results in the breaking of the time-reversal symmetry. This results in the intriguing possibility of switching and spatial control of the hotspots through the magnetic bias.

© 2014 Optical Society of America

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  34. J. Pendry, A. Holden, W. Stewart, and I. Youngs, Phys. Rev. Lett. 76, 4773 (1996).
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2013

J. Y. Chin, T. Steinle, T. Wehlus, D. Dregely, T. Weiss, V. I. Belotelov, B. Stritzker, and H. Giessen, Nat. Commun. 4, 1599 (2013).
[CrossRef]

A. R. Davoyan and N. Engheta, New J. Phys. 15, 083054 (2013).
[CrossRef]

Y. Hadad, Y. Mazor, and B. Z. Steinberg, Phys. Rev. B 87, 035130 (2013).
[CrossRef]

2012

O. Luukkonen, U. K. Chettiar, and N. Engheta, IEEE Antennas Wireless Propag. Lett. 11, 1398 (2012).
[CrossRef]

U. K. Chettiar and N. Engheta, Phys. Rev. B 86, 075405 (2012).
[CrossRef]

D. C. Marinica, A. K. Kazansky, P. Nordlander, J. Aizpurua, and A. G. Borisov, Nano Lett. 12, 1333 (2012).
[CrossRef]

2011

I. V. Shadrivov, V. A. Fedotov, D. A. Powell, Y. S. Kivshar, and N. I. Zheludev, New J. Phys. 13, 033025 (2011).
[CrossRef]

A. Manjavacas, F. J. García de Abajo, and P. Nordlander, Nano Lett. 11, 2318 (2011).
[CrossRef]

W. Qiu, Z. Wang, and M. Soljačić, Opt. Express 19, 22248 (2011).
[CrossRef]

2010

Y. Hadad and B. Z. Steinberg, Phys. Rev. Lett. 105, 233904 (2010).
[CrossRef]

A. B. Khanikaev, S. H. Mousavi, G. Shvets, and Y. S. Kivshar, Phys. Rev. Lett. 105, 126804 (2010).
[CrossRef]

A. E. Miroshnichenko, E. Brasselet, and Y. S. Kivshar, Appl. Phys. Lett. 96, 063302 (2010).
[CrossRef]

2009

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacić, Nature 461, 772 (2009).
[CrossRef]

2008

Z. Wang, Y. Chong, J. Joannopoulos, and M. Soljačić, Phys. Rev. Lett. 100, 013905 (2008).
[CrossRef]

F. Haldane and S. Raghu, Phys. Rev. Lett. 100, 013904 (2008).
[CrossRef]

Z. Yu, G. Veronis, Z. Wang, and S. Fan, Phys. Rev. Lett. 100, 023902 (2008).
[CrossRef]

A. Alberucci and G. Assanto, Opt. Lett. 33, 1641 (2008).
[CrossRef]

2007

Z. Yu, Z. Wang, and S. Fan, Appl. Phys. Lett. 90, 121133 (2007).
[CrossRef]

M. Danckwerts and L. Novotny, Phys. Rev. Lett. 98, 026104 (2007).
[CrossRef]

2006

P. Anger, P. Bharadwaj, and L. Novotny, Phys. Rev. Lett. 96, 113002 (2006).
[CrossRef]

A. Sundaramurthy, P. J. Schuck, N. R. Conley, D. P. Fromm, G. S. Kino, and W. E. Moerner, Nano Lett. 6, 355 (2006).
[CrossRef]

2005

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, Science 308, 1607 (2005).
[CrossRef]

A. Sundaramurthy, K. Crozier, G. Kino, D. Fromm, P. Schuck, and W. Moerner, Phys. Rev. B 72, 165409 (2005).
[CrossRef]

2004

T. Atay, J.-H. Song, and A. V. Nurmikko, Nano Lett. 4, 1627 (2004).
[CrossRef]

2003

A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, Phys. Rev. Lett. 90, 013903 (2003).
[CrossRef]

2002

C. D. Geddes and J. R. Lakowicz, J. Fluoresc. 12, 121 (2002).
[CrossRef]

1998

A. Campion and P. Kambhampati, Chem. Soc. Rev. 27, 241 (1998).
[CrossRef]

1997

K. Kneipp, Y. Wang, H. Kneipp, L. Perelman, I. Itzkan, R. Dasari, and M. Feld, Phys. Rev. Lett. 78, 1667 (1997).
[CrossRef]

1996

J. Pendry, A. Holden, W. Stewart, and I. Youngs, Phys. Rev. Lett. 76, 4773 (1996).
[CrossRef]

1987

R. E. Camley, Surf. Sci. Rep. 7, 103 (1987).
[CrossRef]

1972

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Aizpurua, J.

D. C. Marinica, A. K. Kazansky, P. Nordlander, J. Aizpurua, and A. G. Borisov, Nano Lett. 12, 1333 (2012).
[CrossRef]

Alberucci, A.

Anger, P.

P. Anger, P. Bharadwaj, and L. Novotny, Phys. Rev. Lett. 96, 113002 (2006).
[CrossRef]

Assanto, G.

Atay, T.

T. Atay, J.-H. Song, and A. V. Nurmikko, Nano Lett. 4, 1627 (2004).
[CrossRef]

Balanis, C. A.

C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, 1989).

Belotelov, V. I.

J. Y. Chin, T. Steinle, T. Wehlus, D. Dregely, T. Weiss, V. I. Belotelov, B. Stritzker, and H. Giessen, Nat. Commun. 4, 1599 (2013).
[CrossRef]

Beversluis, M.

A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, Phys. Rev. Lett. 90, 013903 (2003).
[CrossRef]

Bharadwaj, P.

P. Anger, P. Bharadwaj, and L. Novotny, Phys. Rev. Lett. 96, 113002 (2006).
[CrossRef]

Borisov, A. G.

D. C. Marinica, A. K. Kazansky, P. Nordlander, J. Aizpurua, and A. G. Borisov, Nano Lett. 12, 1333 (2012).
[CrossRef]

Bouhelier, A.

A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, Phys. Rev. Lett. 90, 013903 (2003).
[CrossRef]

Brasselet, E.

A. E. Miroshnichenko, E. Brasselet, and Y. S. Kivshar, Appl. Phys. Lett. 96, 063302 (2010).
[CrossRef]

Camley, R. E.

R. E. Camley, Surf. Sci. Rep. 7, 103 (1987).
[CrossRef]

Campion, A.

A. Campion and P. Kambhampati, Chem. Soc. Rev. 27, 241 (1998).
[CrossRef]

Chettiar, U. K.

U. K. Chettiar and N. Engheta, Phys. Rev. B 86, 075405 (2012).
[CrossRef]

O. Luukkonen, U. K. Chettiar, and N. Engheta, IEEE Antennas Wireless Propag. Lett. 11, 1398 (2012).
[CrossRef]

Chin, J. Y.

J. Y. Chin, T. Steinle, T. Wehlus, D. Dregely, T. Weiss, V. I. Belotelov, B. Stritzker, and H. Giessen, Nat. Commun. 4, 1599 (2013).
[CrossRef]

Chong, Y.

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacić, Nature 461, 772 (2009).
[CrossRef]

Z. Wang, Y. Chong, J. Joannopoulos, and M. Soljačić, Phys. Rev. Lett. 100, 013905 (2008).
[CrossRef]

Christy, R. W.

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Conley, N. R.

A. Sundaramurthy, P. J. Schuck, N. R. Conley, D. P. Fromm, G. S. Kino, and W. E. Moerner, Nano Lett. 6, 355 (2006).
[CrossRef]

Crozier, K.

A. Sundaramurthy, K. Crozier, G. Kino, D. Fromm, P. Schuck, and W. Moerner, Phys. Rev. B 72, 165409 (2005).
[CrossRef]

Danckwerts, M.

M. Danckwerts and L. Novotny, Phys. Rev. Lett. 98, 026104 (2007).
[CrossRef]

Dasari, R.

K. Kneipp, Y. Wang, H. Kneipp, L. Perelman, I. Itzkan, R. Dasari, and M. Feld, Phys. Rev. Lett. 78, 1667 (1997).
[CrossRef]

Davoyan, A. R.

A. R. Davoyan and N. Engheta, New J. Phys. 15, 083054 (2013).
[CrossRef]

Dregely, D.

J. Y. Chin, T. Steinle, T. Wehlus, D. Dregely, T. Weiss, V. I. Belotelov, B. Stritzker, and H. Giessen, Nat. Commun. 4, 1599 (2013).
[CrossRef]

Eisler, H.-J.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, Science 308, 1607 (2005).
[CrossRef]

Engheta, N.

A. R. Davoyan and N. Engheta, New J. Phys. 15, 083054 (2013).
[CrossRef]

O. Luukkonen, U. K. Chettiar, and N. Engheta, IEEE Antennas Wireless Propag. Lett. 11, 1398 (2012).
[CrossRef]

U. K. Chettiar and N. Engheta, Phys. Rev. B 86, 075405 (2012).
[CrossRef]

Fan, S.

Z. Yu, G. Veronis, Z. Wang, and S. Fan, Phys. Rev. Lett. 100, 023902 (2008).
[CrossRef]

Z. Yu, Z. Wang, and S. Fan, Appl. Phys. Lett. 90, 121133 (2007).
[CrossRef]

Fedotov, V. A.

I. V. Shadrivov, V. A. Fedotov, D. A. Powell, Y. S. Kivshar, and N. I. Zheludev, New J. Phys. 13, 033025 (2011).
[CrossRef]

Feld, M.

K. Kneipp, Y. Wang, H. Kneipp, L. Perelman, I. Itzkan, R. Dasari, and M. Feld, Phys. Rev. Lett. 78, 1667 (1997).
[CrossRef]

Fromm, D.

A. Sundaramurthy, K. Crozier, G. Kino, D. Fromm, P. Schuck, and W. Moerner, Phys. Rev. B 72, 165409 (2005).
[CrossRef]

Fromm, D. P.

A. Sundaramurthy, P. J. Schuck, N. R. Conley, D. P. Fromm, G. S. Kino, and W. E. Moerner, Nano Lett. 6, 355 (2006).
[CrossRef]

García de Abajo, F. J.

A. Manjavacas, F. J. García de Abajo, and P. Nordlander, Nano Lett. 11, 2318 (2011).
[CrossRef]

Geddes, C. D.

C. D. Geddes and J. R. Lakowicz, J. Fluoresc. 12, 121 (2002).
[CrossRef]

Giessen, H.

J. Y. Chin, T. Steinle, T. Wehlus, D. Dregely, T. Weiss, V. I. Belotelov, B. Stritzker, and H. Giessen, Nat. Commun. 4, 1599 (2013).
[CrossRef]

Hadad, Y.

Y. Hadad, Y. Mazor, and B. Z. Steinberg, Phys. Rev. B 87, 035130 (2013).
[CrossRef]

Y. Hadad and B. Z. Steinberg, Phys. Rev. Lett. 105, 233904 (2010).
[CrossRef]

Haldane, F.

F. Haldane and S. Raghu, Phys. Rev. Lett. 100, 013904 (2008).
[CrossRef]

Hartschuh, A.

A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, Phys. Rev. Lett. 90, 013903 (2003).
[CrossRef]

Hecht, B.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, Science 308, 1607 (2005).
[CrossRef]

Holden, A.

J. Pendry, A. Holden, W. Stewart, and I. Youngs, Phys. Rev. Lett. 76, 4773 (1996).
[CrossRef]

Itzkan, I.

K. Kneipp, Y. Wang, H. Kneipp, L. Perelman, I. Itzkan, R. Dasari, and M. Feld, Phys. Rev. Lett. 78, 1667 (1997).
[CrossRef]

Joannopoulos, J.

Z. Wang, Y. Chong, J. Joannopoulos, and M. Soljačić, Phys. Rev. Lett. 100, 013905 (2008).
[CrossRef]

Joannopoulos, J. D.

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacić, Nature 461, 772 (2009).
[CrossRef]

Johnson, P. B.

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Kambhampati, P.

A. Campion and P. Kambhampati, Chem. Soc. Rev. 27, 241 (1998).
[CrossRef]

Kazansky, A. K.

D. C. Marinica, A. K. Kazansky, P. Nordlander, J. Aizpurua, and A. G. Borisov, Nano Lett. 12, 1333 (2012).
[CrossRef]

Khanikaev, A. B.

A. B. Khanikaev, S. H. Mousavi, G. Shvets, and Y. S. Kivshar, Phys. Rev. Lett. 105, 126804 (2010).
[CrossRef]

Kino, G.

A. Sundaramurthy, K. Crozier, G. Kino, D. Fromm, P. Schuck, and W. Moerner, Phys. Rev. B 72, 165409 (2005).
[CrossRef]

Kino, G. S.

A. Sundaramurthy, P. J. Schuck, N. R. Conley, D. P. Fromm, G. S. Kino, and W. E. Moerner, Nano Lett. 6, 355 (2006).
[CrossRef]

Kivshar, Y. S.

I. V. Shadrivov, V. A. Fedotov, D. A. Powell, Y. S. Kivshar, and N. I. Zheludev, New J. Phys. 13, 033025 (2011).
[CrossRef]

A. E. Miroshnichenko, E. Brasselet, and Y. S. Kivshar, Appl. Phys. Lett. 96, 063302 (2010).
[CrossRef]

A. B. Khanikaev, S. H. Mousavi, G. Shvets, and Y. S. Kivshar, Phys. Rev. Lett. 105, 126804 (2010).
[CrossRef]

Kneipp, H.

K. Kneipp, Y. Wang, H. Kneipp, L. Perelman, I. Itzkan, R. Dasari, and M. Feld, Phys. Rev. Lett. 78, 1667 (1997).
[CrossRef]

Kneipp, K.

K. Kneipp, Y. Wang, H. Kneipp, L. Perelman, I. Itzkan, R. Dasari, and M. Feld, Phys. Rev. Lett. 78, 1667 (1997).
[CrossRef]

Lakowicz, J. R.

C. D. Geddes and J. R. Lakowicz, J. Fluoresc. 12, 121 (2002).
[CrossRef]

Luukkonen, O.

O. Luukkonen, U. K. Chettiar, and N. Engheta, IEEE Antennas Wireless Propag. Lett. 11, 1398 (2012).
[CrossRef]

Manjavacas, A.

A. Manjavacas, F. J. García de Abajo, and P. Nordlander, Nano Lett. 11, 2318 (2011).
[CrossRef]

Marinica, D. C.

D. C. Marinica, A. K. Kazansky, P. Nordlander, J. Aizpurua, and A. G. Borisov, Nano Lett. 12, 1333 (2012).
[CrossRef]

Martin, O. J. F.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, Science 308, 1607 (2005).
[CrossRef]

Mazor, Y.

Y. Hadad, Y. Mazor, and B. Z. Steinberg, Phys. Rev. B 87, 035130 (2013).
[CrossRef]

Miroshnichenko, A. E.

A. E. Miroshnichenko, E. Brasselet, and Y. S. Kivshar, Appl. Phys. Lett. 96, 063302 (2010).
[CrossRef]

Moerner, W.

A. Sundaramurthy, K. Crozier, G. Kino, D. Fromm, P. Schuck, and W. Moerner, Phys. Rev. B 72, 165409 (2005).
[CrossRef]

Moerner, W. E.

A. Sundaramurthy, P. J. Schuck, N. R. Conley, D. P. Fromm, G. S. Kino, and W. E. Moerner, Nano Lett. 6, 355 (2006).
[CrossRef]

Mousavi, S. H.

A. B. Khanikaev, S. H. Mousavi, G. Shvets, and Y. S. Kivshar, Phys. Rev. Lett. 105, 126804 (2010).
[CrossRef]

Mühlschlegel, P.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, Science 308, 1607 (2005).
[CrossRef]

Nordlander, P.

D. C. Marinica, A. K. Kazansky, P. Nordlander, J. Aizpurua, and A. G. Borisov, Nano Lett. 12, 1333 (2012).
[CrossRef]

A. Manjavacas, F. J. García de Abajo, and P. Nordlander, Nano Lett. 11, 2318 (2011).
[CrossRef]

Novotny, L.

M. Danckwerts and L. Novotny, Phys. Rev. Lett. 98, 026104 (2007).
[CrossRef]

P. Anger, P. Bharadwaj, and L. Novotny, Phys. Rev. Lett. 96, 113002 (2006).
[CrossRef]

A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, Phys. Rev. Lett. 90, 013903 (2003).
[CrossRef]

Nurmikko, A. V.

T. Atay, J.-H. Song, and A. V. Nurmikko, Nano Lett. 4, 1627 (2004).
[CrossRef]

Pendry, J.

J. Pendry, A. Holden, W. Stewart, and I. Youngs, Phys. Rev. Lett. 76, 4773 (1996).
[CrossRef]

Perelman, L.

K. Kneipp, Y. Wang, H. Kneipp, L. Perelman, I. Itzkan, R. Dasari, and M. Feld, Phys. Rev. Lett. 78, 1667 (1997).
[CrossRef]

Pohl, D. W.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, Science 308, 1607 (2005).
[CrossRef]

Powell, D. A.

I. V. Shadrivov, V. A. Fedotov, D. A. Powell, Y. S. Kivshar, and N. I. Zheludev, New J. Phys. 13, 033025 (2011).
[CrossRef]

Pozar, D. M.

D. M. Pozar, Microwave Engineering, 3rd ed. (Wiley, 2005).

Qiu, W.

Raghu, S.

F. Haldane and S. Raghu, Phys. Rev. Lett. 100, 013904 (2008).
[CrossRef]

Schuck, P.

A. Sundaramurthy, K. Crozier, G. Kino, D. Fromm, P. Schuck, and W. Moerner, Phys. Rev. B 72, 165409 (2005).
[CrossRef]

Schuck, P. J.

A. Sundaramurthy, P. J. Schuck, N. R. Conley, D. P. Fromm, G. S. Kino, and W. E. Moerner, Nano Lett. 6, 355 (2006).
[CrossRef]

Shadrivov, I. V.

I. V. Shadrivov, V. A. Fedotov, D. A. Powell, Y. S. Kivshar, and N. I. Zheludev, New J. Phys. 13, 033025 (2011).
[CrossRef]

Shalaev, V. M.

V. M. Shalaev, Nonlinear Optics of Random Media: Fractal Composites and Metal-Dielectric Films (Springer, 2000).

Shvets, G.

A. B. Khanikaev, S. H. Mousavi, G. Shvets, and Y. S. Kivshar, Phys. Rev. Lett. 105, 126804 (2010).
[CrossRef]

Soljacic, M.

W. Qiu, Z. Wang, and M. Soljačić, Opt. Express 19, 22248 (2011).
[CrossRef]

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacić, Nature 461, 772 (2009).
[CrossRef]

Z. Wang, Y. Chong, J. Joannopoulos, and M. Soljačić, Phys. Rev. Lett. 100, 013905 (2008).
[CrossRef]

Song, J.-H.

T. Atay, J.-H. Song, and A. V. Nurmikko, Nano Lett. 4, 1627 (2004).
[CrossRef]

Steinberg, B. Z.

Y. Hadad, Y. Mazor, and B. Z. Steinberg, Phys. Rev. B 87, 035130 (2013).
[CrossRef]

Y. Hadad and B. Z. Steinberg, Phys. Rev. Lett. 105, 233904 (2010).
[CrossRef]

Steinle, T.

J. Y. Chin, T. Steinle, T. Wehlus, D. Dregely, T. Weiss, V. I. Belotelov, B. Stritzker, and H. Giessen, Nat. Commun. 4, 1599 (2013).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

(a) Schematic. (b) Dispersion diagram without (dashed blue) and with (solid red) magnetic bias.

Fig. 2.
Fig. 2.

Different regions in the permittivity space and the corresponding surface plasmon modes. The arrows indicate whether the permittivity supports positive, negative, both, or neither surface plasmon modes.

Fig. 3.
Fig. 3.

(a) Schematic of the structure used in the full wave simulation. (b)–(d) Surface plots of the normalized electric field (y component) in log scale for three different cyclotron frequencies, (b) ωg=0, (c) ωg=0.04ωp, (d) ωg=0.06ωp. The electric fields in all the plots were normalized with respect to the electric field at the junction of the three materials under zero magnetic bias condition.

Fig. 4.
Fig. 4.

(a) Plot of the magnitude of the y component of the electric field along a cross section near the interface for various values of ωg. The cross section was parallel to the air–plasmonic interface and 0.005λp into the air region. The end of the interface corresponds to x=0, which is also the location of the hotspot. (b) Plot of the normalized value of the electric field at the junction between the three materials for various values of collision frequency of the plasmonic material.

Equations (3)

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ε¯¯=ε0(εtiεg0iεgεt000εn).
εvβ2k02εd+εdβ2k02εv+βεgεdεt=0
εt=1ωp2(ω+iγ)ω((ω+iγ)2ωg2)εg=ωp2ωgω((ω+iγ)2ωg2)εn=1ωp2ω(ω+iγ),

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