Abstract

We present a two-dimensional photonic crystal design of four defect dielectric rods, which form a microcavity with eigenfrequencies residing in the propagating band of a directional waveguide. In this system, a nonrobust bound state in the continuum (BSC) occurs as a result of full destructive interference of the monopole and quadrupole modes, with the same parity at certain values of the material parameters of the defect rods. Due to the Kerr effect, a robust BSC arises in a self-adaptive way without necessity to tune the material parameters. The absence of the superposition principle in that nonlinear system gives rise to coupling of the BSC with injected light, resulting in a novel transmission resonance.

© 2014 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  12. I. Rotter and A. F. Sadreev, Phys. Rev. E 69, 066201 (2004).
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    [CrossRef]
  18. N. Prodanovic, V. Milanovic, and J. Radovanovic, J. Phys. A 42, 415304 (2009).
    [CrossRef]
  19. C. M. Linton and P. McIver, Wave Motion 45, 16 (2007).
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  20. S. Hein, W. Koch, and L. Nannen, J. Fluid Mech. 692, 257 (2012).
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  21. E. N. Bulgakov, K. N. Pichugin, A. F. Sadreev, and I. Rotter, JETP Lett. 84, 430 (2006).
    [CrossRef]
  22. M. I. Molina, A. E. Miroshnichenko, and Yu. S. Kivshar, Phys. Rev. Lett. 108, 070401 (2012).
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  26. W. Suh, Z. Wang, and S. Fan, IEEE J. Quantum Electron. 40, 1511 (2004).
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  27. E. N. Bulgakov and A. F. Sadreev, Opt. Lett. 39, 1787 (2014).
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2014 (1)

2013 (2)

G. Corrielli, G. Della Valle, A. Crespi, R. Osellame, and S. Longhi, Phys. Rev. Lett. 111, 220403 (2013).
[CrossRef]

C. W. Hsu, B. Zhen, J. Lee, S.-L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, Nature 499, 188 (2013).
[CrossRef]

2012 (3)

S. Hein, W. Koch, and L. Nannen, J. Fluid Mech. 692, 257 (2012).
[CrossRef]

M. I. Molina, A. E. Miroshnichenko, and Yu. S. Kivshar, Phys. Rev. Lett. 108, 070401 (2012).
[CrossRef]

E. N. Bulgakov and A. F. Sadreev, Phys. Rev. B 86, 075125 (2012).
[CrossRef]

2011 (1)

Y. Plotnik, O. Peleg, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, and M. Segev, Phys. Rev. Lett. 107, 183901 (2011).
[CrossRef]

2010 (2)

T. Lepetit, E. Akmansoy, J.-P. Ganne, and J.-M. Lourtioz, Phys. Rev. B 82, 195307 (2010).
[CrossRef]

R. F. Ndangali and S. V. Shabanov, J. Math. Phys. 51, 102901 (2010).
[CrossRef]

2009 (2)

N. Prodanovic, V. Milanovic, and J. Radovanovic, J. Phys. A 42, 415304 (2009).
[CrossRef]

E. N. Bulgakov and A. F. Sadreev, Phys. Rev. B 80, 115308 (2009); ibid 81, 115128 (2010).
[CrossRef]

2008 (2)

E. N. Bulgakov and A. F. Sadreev, Phys. Rev. B 78, 075105 (2008).
[CrossRef]

D. C. Marinica, A. G. Borisov, and S. V. Shabanov, Phys. Rev. Lett. 100, 183902 (2008).
[CrossRef]

2007 (1)

C. M. Linton and P. McIver, Wave Motion 45, 16 (2007).
[CrossRef]

2006 (2)

A. F. Sadreev, E. N. Bulgakov, and I. Rotter, Phys. Rev. B 73, 235342 (2006).
[CrossRef]

E. N. Bulgakov, K. N. Pichugin, A. F. Sadreev, and I. Rotter, JETP Lett. 84, 430 (2006).
[CrossRef]

2005 (2)

S. P. Shipman and S. Venakides, Phys. Rev. E 71, 026611 (2005).
[CrossRef]

I. Rotter and A. F. Sadreev, Phys. Rev. E 71, 046204 (2005).
[CrossRef]

2004 (2)

I. Rotter and A. F. Sadreev, Phys. Rev. E 69, 066201 (2004).
[CrossRef]

W. Suh, Z. Wang, and S. Fan, IEEE J. Quantum Electron. 40, 1511 (2004).
[CrossRef]

2003 (3)

K. Busch, S. F. Mingaleev, A. Garcia-Martin, M. Schillinger, and D. Hermann, J. Phys. Condens. Matter 15, R1233 (2003).
[CrossRef]

A. Volya and V. Zelevinsky, Phys. Rev. C 67, 054322 (2003).
[CrossRef]

M. L. Ladron de Guevara, F. Claro, and P. A. Orellana, Phys. Rev. B 67, 195335 (2003).
[CrossRef]

1999 (2)

C. S. Kim, A. M. Satanin, Y. S. Joe, and R. M. Cosby, Phys. Rev. B 60, 10962 (1999).
[CrossRef]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, Phys. Rev. B 59, 15882 (1999).
[CrossRef]

1985 (1)

H. Friedrich and D. Wintgen, Phys. Rev. A 32, 3231 (1985).
[CrossRef]

1929 (1)

J. von Neumann and E. Wigner, Phys. Z. 30, 465 (1929).

Akmansoy, E.

T. Lepetit, E. Akmansoy, J.-P. Ganne, and J.-M. Lourtioz, Phys. Rev. B 82, 195307 (2010).
[CrossRef]

Borisov, A. G.

D. C. Marinica, A. G. Borisov, and S. V. Shabanov, Phys. Rev. Lett. 100, 183902 (2008).
[CrossRef]

Bulgakov, E. N.

E. N. Bulgakov and A. F. Sadreev, Opt. Lett. 39, 1787 (2014).
[CrossRef]

E. N. Bulgakov and A. F. Sadreev, Phys. Rev. B 86, 075125 (2012).
[CrossRef]

E. N. Bulgakov and A. F. Sadreev, Phys. Rev. B 80, 115308 (2009); ibid 81, 115128 (2010).
[CrossRef]

E. N. Bulgakov and A. F. Sadreev, Phys. Rev. B 78, 075105 (2008).
[CrossRef]

A. F. Sadreev, E. N. Bulgakov, and I. Rotter, Phys. Rev. B 73, 235342 (2006).
[CrossRef]

E. N. Bulgakov, K. N. Pichugin, A. F. Sadreev, and I. Rotter, JETP Lett. 84, 430 (2006).
[CrossRef]

Busch, K.

K. Busch, S. F. Mingaleev, A. Garcia-Martin, M. Schillinger, and D. Hermann, J. Phys. Condens. Matter 15, R1233 (2003).
[CrossRef]

Chua, S.-L.

C. W. Hsu, B. Zhen, J. Lee, S.-L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, Nature 499, 188 (2013).
[CrossRef]

Claro, F.

M. L. Ladron de Guevara, F. Claro, and P. A. Orellana, Phys. Rev. B 67, 195335 (2003).
[CrossRef]

Corrielli, G.

G. Corrielli, G. Della Valle, A. Crespi, R. Osellame, and S. Longhi, Phys. Rev. Lett. 111, 220403 (2013).
[CrossRef]

Cosby, R. M.

C. S. Kim, A. M. Satanin, Y. S. Joe, and R. M. Cosby, Phys. Rev. B 60, 10962 (1999).
[CrossRef]

Crespi, A.

G. Corrielli, G. Della Valle, A. Crespi, R. Osellame, and S. Longhi, Phys. Rev. Lett. 111, 220403 (2013).
[CrossRef]

Della Valle, G.

G. Corrielli, G. Della Valle, A. Crespi, R. Osellame, and S. Longhi, Phys. Rev. Lett. 111, 220403 (2013).
[CrossRef]

Dreisow, F.

Y. Plotnik, O. Peleg, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, and M. Segev, Phys. Rev. Lett. 107, 183901 (2011).
[CrossRef]

Fan, S.

W. Suh, Z. Wang, and S. Fan, IEEE J. Quantum Electron. 40, 1511 (2004).
[CrossRef]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, Phys. Rev. B 59, 15882 (1999).
[CrossRef]

Friedrich, H.

H. Friedrich and D. Wintgen, Phys. Rev. A 32, 3231 (1985).
[CrossRef]

Ganne, J.-P.

T. Lepetit, E. Akmansoy, J.-P. Ganne, and J.-M. Lourtioz, Phys. Rev. B 82, 195307 (2010).
[CrossRef]

Garcia-Martin, A.

K. Busch, S. F. Mingaleev, A. Garcia-Martin, M. Schillinger, and D. Hermann, J. Phys. Condens. Matter 15, R1233 (2003).
[CrossRef]

Haus, H. A.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, Phys. Rev. B 59, 15882 (1999).
[CrossRef]

Hein, S.

S. Hein, W. Koch, and L. Nannen, J. Fluid Mech. 692, 257 (2012).
[CrossRef]

Heinrich, M.

Y. Plotnik, O. Peleg, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, and M. Segev, Phys. Rev. Lett. 107, 183901 (2011).
[CrossRef]

Hermann, D.

K. Busch, S. F. Mingaleev, A. Garcia-Martin, M. Schillinger, and D. Hermann, J. Phys. Condens. Matter 15, R1233 (2003).
[CrossRef]

Hsu, C. W.

C. W. Hsu, B. Zhen, J. Lee, S.-L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, Nature 499, 188 (2013).
[CrossRef]

Joannopoulos, J. D.

C. W. Hsu, B. Zhen, J. Lee, S.-L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, Nature 499, 188 (2013).
[CrossRef]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, Phys. Rev. B 59, 15882 (1999).
[CrossRef]

Joe, Y. S.

C. S. Kim, A. M. Satanin, Y. S. Joe, and R. M. Cosby, Phys. Rev. B 60, 10962 (1999).
[CrossRef]

Johnson, S. G.

C. W. Hsu, B. Zhen, J. Lee, S.-L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, Nature 499, 188 (2013).
[CrossRef]

Khan, M. J.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, Phys. Rev. B 59, 15882 (1999).
[CrossRef]

Kim, C. S.

C. S. Kim, A. M. Satanin, Y. S. Joe, and R. M. Cosby, Phys. Rev. B 60, 10962 (1999).
[CrossRef]

Kivshar, Yu. S.

M. I. Molina, A. E. Miroshnichenko, and Yu. S. Kivshar, Phys. Rev. Lett. 108, 070401 (2012).
[CrossRef]

Koch, W.

S. Hein, W. Koch, and L. Nannen, J. Fluid Mech. 692, 257 (2012).
[CrossRef]

Ladron de Guevara, M. L.

M. L. Ladron de Guevara, F. Claro, and P. A. Orellana, Phys. Rev. B 67, 195335 (2003).
[CrossRef]

Lee, J.

C. W. Hsu, B. Zhen, J. Lee, S.-L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, Nature 499, 188 (2013).
[CrossRef]

Lepetit, T.

T. Lepetit, E. Akmansoy, J.-P. Ganne, and J.-M. Lourtioz, Phys. Rev. B 82, 195307 (2010).
[CrossRef]

Linton, C. M.

C. M. Linton and P. McIver, Wave Motion 45, 16 (2007).
[CrossRef]

Longhi, S.

G. Corrielli, G. Della Valle, A. Crespi, R. Osellame, and S. Longhi, Phys. Rev. Lett. 111, 220403 (2013).
[CrossRef]

Lourtioz, J.-M.

T. Lepetit, E. Akmansoy, J.-P. Ganne, and J.-M. Lourtioz, Phys. Rev. B 82, 195307 (2010).
[CrossRef]

Manolatou, C.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, Phys. Rev. B 59, 15882 (1999).
[CrossRef]

Marinica, D. C.

D. C. Marinica, A. G. Borisov, and S. V. Shabanov, Phys. Rev. Lett. 100, 183902 (2008).
[CrossRef]

McIver, P.

C. M. Linton and P. McIver, Wave Motion 45, 16 (2007).
[CrossRef]

Milanovic, V.

N. Prodanovic, V. Milanovic, and J. Radovanovic, J. Phys. A 42, 415304 (2009).
[CrossRef]

Mingaleev, S. F.

K. Busch, S. F. Mingaleev, A. Garcia-Martin, M. Schillinger, and D. Hermann, J. Phys. Condens. Matter 15, R1233 (2003).
[CrossRef]

Miroshnichenko, A. E.

M. I. Molina, A. E. Miroshnichenko, and Yu. S. Kivshar, Phys. Rev. Lett. 108, 070401 (2012).
[CrossRef]

Molina, M. I.

M. I. Molina, A. E. Miroshnichenko, and Yu. S. Kivshar, Phys. Rev. Lett. 108, 070401 (2012).
[CrossRef]

Nannen, L.

S. Hein, W. Koch, and L. Nannen, J. Fluid Mech. 692, 257 (2012).
[CrossRef]

Ndangali, R. F.

R. F. Ndangali and S. V. Shabanov, J. Math. Phys. 51, 102901 (2010).
[CrossRef]

Nolte, S.

Y. Plotnik, O. Peleg, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, and M. Segev, Phys. Rev. Lett. 107, 183901 (2011).
[CrossRef]

Orellana, P. A.

M. L. Ladron de Guevara, F. Claro, and P. A. Orellana, Phys. Rev. B 67, 195335 (2003).
[CrossRef]

Osellame, R.

G. Corrielli, G. Della Valle, A. Crespi, R. Osellame, and S. Longhi, Phys. Rev. Lett. 111, 220403 (2013).
[CrossRef]

Peleg, O.

Y. Plotnik, O. Peleg, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, and M. Segev, Phys. Rev. Lett. 107, 183901 (2011).
[CrossRef]

Pichugin, K. N.

E. N. Bulgakov, K. N. Pichugin, A. F. Sadreev, and I. Rotter, JETP Lett. 84, 430 (2006).
[CrossRef]

Plotnik, Y.

Y. Plotnik, O. Peleg, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, and M. Segev, Phys. Rev. Lett. 107, 183901 (2011).
[CrossRef]

Prodanovic, N.

N. Prodanovic, V. Milanovic, and J. Radovanovic, J. Phys. A 42, 415304 (2009).
[CrossRef]

Radovanovic, J.

N. Prodanovic, V. Milanovic, and J. Radovanovic, J. Phys. A 42, 415304 (2009).
[CrossRef]

Rotter, I.

E. N. Bulgakov, K. N. Pichugin, A. F. Sadreev, and I. Rotter, JETP Lett. 84, 430 (2006).
[CrossRef]

A. F. Sadreev, E. N. Bulgakov, and I. Rotter, Phys. Rev. B 73, 235342 (2006).
[CrossRef]

I. Rotter and A. F. Sadreev, Phys. Rev. E 71, 046204 (2005).
[CrossRef]

I. Rotter and A. F. Sadreev, Phys. Rev. E 69, 066201 (2004).
[CrossRef]

Sadreev, A. F.

E. N. Bulgakov and A. F. Sadreev, Opt. Lett. 39, 1787 (2014).
[CrossRef]

E. N. Bulgakov and A. F. Sadreev, Phys. Rev. B 86, 075125 (2012).
[CrossRef]

E. N. Bulgakov and A. F. Sadreev, Phys. Rev. B 80, 115308 (2009); ibid 81, 115128 (2010).
[CrossRef]

E. N. Bulgakov and A. F. Sadreev, Phys. Rev. B 78, 075105 (2008).
[CrossRef]

A. F. Sadreev, E. N. Bulgakov, and I. Rotter, Phys. Rev. B 73, 235342 (2006).
[CrossRef]

E. N. Bulgakov, K. N. Pichugin, A. F. Sadreev, and I. Rotter, JETP Lett. 84, 430 (2006).
[CrossRef]

I. Rotter and A. F. Sadreev, Phys. Rev. E 71, 046204 (2005).
[CrossRef]

I. Rotter and A. F. Sadreev, Phys. Rev. E 69, 066201 (2004).
[CrossRef]

Satanin, A. M.

C. S. Kim, A. M. Satanin, Y. S. Joe, and R. M. Cosby, Phys. Rev. B 60, 10962 (1999).
[CrossRef]

Schillinger, M.

K. Busch, S. F. Mingaleev, A. Garcia-Martin, M. Schillinger, and D. Hermann, J. Phys. Condens. Matter 15, R1233 (2003).
[CrossRef]

Segev, M.

Y. Plotnik, O. Peleg, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, and M. Segev, Phys. Rev. Lett. 107, 183901 (2011).
[CrossRef]

Shabanov, S. V.

R. F. Ndangali and S. V. Shabanov, J. Math. Phys. 51, 102901 (2010).
[CrossRef]

D. C. Marinica, A. G. Borisov, and S. V. Shabanov, Phys. Rev. Lett. 100, 183902 (2008).
[CrossRef]

Shipman, S. P.

S. P. Shipman and S. Venakides, Phys. Rev. E 71, 026611 (2005).
[CrossRef]

Soljacic, M.

C. W. Hsu, B. Zhen, J. Lee, S.-L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, Nature 499, 188 (2013).
[CrossRef]

Suh, W.

W. Suh, Z. Wang, and S. Fan, IEEE J. Quantum Electron. 40, 1511 (2004).
[CrossRef]

Szameit, A.

Y. Plotnik, O. Peleg, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, and M. Segev, Phys. Rev. Lett. 107, 183901 (2011).
[CrossRef]

Venakides, S.

S. P. Shipman and S. Venakides, Phys. Rev. E 71, 026611 (2005).
[CrossRef]

Villeneuve, P. R.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, Phys. Rev. B 59, 15882 (1999).
[CrossRef]

Volya, A.

A. Volya and V. Zelevinsky, Phys. Rev. C 67, 054322 (2003).
[CrossRef]

von Neumann, J.

J. von Neumann and E. Wigner, Phys. Z. 30, 465 (1929).

Wang, Z.

W. Suh, Z. Wang, and S. Fan, IEEE J. Quantum Electron. 40, 1511 (2004).
[CrossRef]

Wigner, E.

J. von Neumann and E. Wigner, Phys. Z. 30, 465 (1929).

Wintgen, D.

H. Friedrich and D. Wintgen, Phys. Rev. A 32, 3231 (1985).
[CrossRef]

Zelevinsky, V.

A. Volya and V. Zelevinsky, Phys. Rev. C 67, 054322 (2003).
[CrossRef]

Zhen, B.

C. W. Hsu, B. Zhen, J. Lee, S.-L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, Nature 499, 188 (2013).
[CrossRef]

IEEE J. Quantum Electron. (1)

W. Suh, Z. Wang, and S. Fan, IEEE J. Quantum Electron. 40, 1511 (2004).
[CrossRef]

J. Fluid Mech. (1)

S. Hein, W. Koch, and L. Nannen, J. Fluid Mech. 692, 257 (2012).
[CrossRef]

J. Math. Phys. (1)

R. F. Ndangali and S. V. Shabanov, J. Math. Phys. 51, 102901 (2010).
[CrossRef]

J. Phys. A (1)

N. Prodanovic, V. Milanovic, and J. Radovanovic, J. Phys. A 42, 415304 (2009).
[CrossRef]

J. Phys. Condens. Matter (1)

K. Busch, S. F. Mingaleev, A. Garcia-Martin, M. Schillinger, and D. Hermann, J. Phys. Condens. Matter 15, R1233 (2003).
[CrossRef]

JETP Lett. (1)

E. N. Bulgakov, K. N. Pichugin, A. F. Sadreev, and I. Rotter, JETP Lett. 84, 430 (2006).
[CrossRef]

Nature (1)

C. W. Hsu, B. Zhen, J. Lee, S.-L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, Nature 499, 188 (2013).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (1)

H. Friedrich and D. Wintgen, Phys. Rev. A 32, 3231 (1985).
[CrossRef]

Phys. Rev. B (8)

M. L. Ladron de Guevara, F. Claro, and P. A. Orellana, Phys. Rev. B 67, 195335 (2003).
[CrossRef]

A. F. Sadreev, E. N. Bulgakov, and I. Rotter, Phys. Rev. B 73, 235342 (2006).
[CrossRef]

C. S. Kim, A. M. Satanin, Y. S. Joe, and R. M. Cosby, Phys. Rev. B 60, 10962 (1999).
[CrossRef]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, Phys. Rev. B 59, 15882 (1999).
[CrossRef]

E. N. Bulgakov and A. F. Sadreev, Phys. Rev. B 78, 075105 (2008).
[CrossRef]

T. Lepetit, E. Akmansoy, J.-P. Ganne, and J.-M. Lourtioz, Phys. Rev. B 82, 195307 (2010).
[CrossRef]

E. N. Bulgakov and A. F. Sadreev, Phys. Rev. B 80, 115308 (2009); ibid 81, 115128 (2010).
[CrossRef]

E. N. Bulgakov and A. F. Sadreev, Phys. Rev. B 86, 075125 (2012).
[CrossRef]

Phys. Rev. C (1)

A. Volya and V. Zelevinsky, Phys. Rev. C 67, 054322 (2003).
[CrossRef]

Phys. Rev. E (3)

S. P. Shipman and S. Venakides, Phys. Rev. E 71, 026611 (2005).
[CrossRef]

I. Rotter and A. F. Sadreev, Phys. Rev. E 69, 066201 (2004).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

PhC consists of a square lattice of GaAs rods with a linear refractive index n0=3.4 and nonlinear refractive index n2=1.5×1013cm2/W at λ=1.55mμ and radius 0.18a in air, as shown by blue open circles, where a is the lattice unit. Four linear defect rods of the same radius with dielectric constant ϵ are shown by green circles.

Fig. 2.
Fig. 2.

Eigenfrequencies in units of 2πc/a versus dielectric constant of the microcavity. Insets show profiles of the eigenmodes.

Fig. 3.
Fig. 3.

(a) Transmittance versus frequency of injected light and dielectric constant of the defect rods in the two-level approximation. The BSC point is marked by the white open circle. It is seen that the Kerr effect transforms the BSC point into a line (red). (b) Transmittance versus frequency in the vicinity of the BSC point. The three slices correspond to ϵ=3.03, 3.015, 3.01. Red closed circles mark the BSC frequency. Results of computation based on the Maxwell equations are shown by green open circles, while the CMT results are shown by solid blue lines.

Fig. 4.
Fig. 4.

Solutions of Eq. (1) (real parts) for (a) ϵ=3.01, ω=0.3619 and (b) ϵ=3.01, ω=0.361755. Thin solid lines show the Poynting vector flow lines. (c) BSC.

Fig. 5.
Fig. 5.

(a) Intensities of the monopole mode |A1|2 (blue lines) and quadrupole-diag mode |A2|2 (red lines) for λ11=104 and ϵ=3.1. Thin lines correspond to unstable solutions, while thicker lines show stable solutions. (b) Transmittance versus frequency of injected light with the amplitude ψin=0.0025. Blue dash lines show transmittance found from the nonlinear CMT equations, and red solid lines show transmittance found from nonlinear Maxwell equations.

Equations (8)

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[H^effω2]ψS=Γ^ψin,
[Heff(2)ω](A1A2)=i(γ1γ2)ψin,
Heff(2)=(ω1iγ1uiγ1γ2uiγ1γ2ω2iγ2);
t=ψin+γ1A1+γ2A1
ω2ω1=u(γ2γ1)γ1γ2,ωBSC=ω2+uγ2γ1.
Vmn=n0c2n22(ωm+ωn)16πa2d2r⃗|A1E1(r⃗)+A2E2(r⃗)|2Em(r⃗)En(r⃗)
λ11I1c=λ11|A1|2=ω2ω1u(γ2γ1)γ1γ2,
I2c=|A2c|2=γ1γ2I1c.

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