Abstract

A semiclassical model consisting of two noninteracting waveguide arrays along with three side-coupled waveguides is presented to demonstrate the optical analogue of double Fano resonance. The photonic system is configured so that it causes simultaneous cross coupling between two decay channels via one array and another two decay channels via the other array. Owing to the two individual interference effects, the decay-rate profile for the waveguide coupled directly to the continuum exhibits two asymmetric peaks, or dips, or a combination of one peak and one dip in the vicinity of the frequency mismatches. As far as the distribution of optical field amplitudes in the side-coupled waveguides is concerned, the present model also demonstrates the features of optical trapping (optical analogue of coherent population trapping) in side-coupled waveguides under certain symmetric parametric conditions.

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. S. Agarwal and J. Banerji, “Off-resonant pumping for the transition from a continuous to a discrete spectrum and quantum revivals in systems in coherent states,” J. Opt. B 3, S79–S82 (2001).
    [CrossRef]
  2. N. K. Efrimidis and D. N. Christodoulides, “Bloch oscillations in optical dissipative lattices,” Opt. Lett. 29, 2485–2487 (2004).
    [CrossRef]
  3. H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Bruer, and U. Peschel, “Visual observation of Zener tunneling,” Phys. Rev. Lett. 96, 023901 (2006).
    [CrossRef]
  4. R. Khomeriki, “Multiple Landau–Zener tunnelling in two weakly coupled waveguide arrays,” Eur. Phys. J. D 61, 193–197 (2011).
    [CrossRef]
  5. R. Iyer, J. S. Aitchison, J. Wan, M. M. Dignam, and C. M. de Sterke, “Exact dynamic localization in curved AlGaAs optical waveguide arrays,” Opt. Express 15, 3212–3223 (2007).
    [CrossRef]
  6. K. Shandarova, C. E. Ruter, R. Dong, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett. 102, 123905 (2009).
    [CrossRef]
  7. K. G. Makris, D. N. Christodoulides, O. Peleg, M. Segev, and D. Kip, “Optical transitions and Rabi oscillations in waveguide arrays,” Opt. Express 16, 10309–10314 (2008).
    [CrossRef]
  8. G. Della Valle, M. Ornigotti, E. Cianci, V. Foglietti, P. Laporta, and S. Longhi, “Visualization of coherent destruction of tunneling in an optical double well system,” Phys. Rev. Lett. 98, 263601 (2007).
    [CrossRef]
  9. E. Arimondo, Progress in Optics, E. Wolf, ed. (Elsevier, 1996), Vol. 35, pp. 257–354.
  10. K. Bergmann, H. Theuer, and B. W. Shore, “Coherent population transfer among quantum states of atoms and molecules,” Rev. Mod. Phys. 70, 1003–1025 (1998).
    [CrossRef]
  11. S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36–42 (1997).
    [CrossRef]
  12. M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
    [CrossRef]
  13. G. S. Agarwal and W. Harshawardhan, “Inhibition and enhancement of two photon absorption,” Opt. Commun. 77, 1039–1042 (1996).
  14. G. S. Agarwal, “Nature of the quantum interference in electromagnetic-field-induced control of absorption,” Phys. Rev. A 55, 2467–2470 (1997).
    [CrossRef]
  15. X. M. Hu and J. S. Peng, “Quantum interference from spontaneous decay in Lambda systems: realization in the dressed-state picture,” J. Phys. B 33, 921–931 (2000).
    [CrossRef]
  16. B. P. Hou, S. J. Wang, W. L. Yu, and W. L. Sun, “Control of one- and two-photon absorption in a four-level atomic system by changing the amplitude and phase of a driving microwave field,” J. Phys. B 38, 1419–1434 (2005).
    [CrossRef]
  17. B. K. Dutta and P. K. Mahapatra, “Nonlinear optical effects in a doubly driven four-level atom,” Phys. Scr. 75, 345–353 (2007).
    [CrossRef]
  18. S. Ghosh and S. Mandal, “A theoretical analysis on coherent double resonant absorptive lineshape in closely spaced transitions for Λ type five level system,” Opt. Commun. 284, 376–387 (2011).
    [CrossRef]
  19. U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866–1878 (1961).
    [CrossRef]
  20. K. Rzazewski and J. H. Eberly, “Confluence of bound-free coherences in laser-induced autoionization,” Phys. Rev. Lett. 47, 408–412 (1981).
    [CrossRef]
  21. P. L. Knight, M. A. Lauder, and B. J. Dalton, “Laser-induced continuum structure,” Phys. Rep. 190, 1–61 (1990).
    [CrossRef]
  22. H. Schmidt, K. L. Campman, A. C. Gossard, and A. Imamoglu, “Tunneling induced transparency: Fano interference in intersubband transitions,” Appl. Phys. Lett. 70, 3455–3457 (1997).
    [CrossRef]
  23. X. Y. Hao, J. H. Li, X. Y. Lu, and X. Yang, “Controllable amplification and absorption properties in coupled-double-quantum-wells with tunneling-induced interference,” Eur. Phys. J. D 56, 239–246 (2010).
    [CrossRef]
  24. G. S. Agarwal, Quantum Statistical Theories of Spontaneous Emission and Their Relation to Other Approaches, G. Hohler, ed., Vol. 70 of Springer Tracts in Modern Physics (Springer-Verlag, 1974), pp. 88–97.
  25. Z. Ficek and S. Swain, Quantum Interference and Coherence: Theory and Experiments, W. T. Rhodes, ed., Vol. 100 of Springer Series in Optical Sciences (Springer, 2005), pp. 139–177.
  26. Y. S. Joe, A. M. Satanin, and C. S. Kim, “Classical analogy of Fano resonances,” Phys. Scr. 74, 259–266 (2006).
    [CrossRef]
  27. B. Lukyanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
    [CrossRef]
  28. R. A. Vicencio, A. V. Gorbach, and S. Flach, “Fano resonance in two-dimensional optical waveguide arrays with a bi-modal defect,” Phys. Lett. A 354, 210–213 (2006).
    [CrossRef]
  29. A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82, 2257–2298 (2010).
    [CrossRef]
  30. W. Leonski, R. Tanas, and S. Kielich, “Laser-induced autoionization from a double Fano system,” J. Opt. Soc. Am. B 4, 72–77 (1987).
    [CrossRef]
  31. W. Leonski and R. Tanas, “DC-field effects on the photoelectron spectrum from a system with two autoionising levels,” J. Phys. B 21, 2835–2844 (1988).
    [CrossRef]
  32. W. Leonski, R. Tanas, and S. Kielich, “Effect of DC field coupling on the photoelectron spectrum from double auto-ionizing levels,” J. Phys. D 21, S125–S127 (1988).
    [CrossRef]
  33. G. S. Agarwal, S. Ravi, and J. Cooper, “dc-field-coupled autoionizing states for laser action without population inversion,” Phys. Rev. A 41, 4721–4726 (1990).
    [CrossRef]
  34. G. S. Agarwal, S. Ravi, and J. Cooper, “Lasers without inversion: Raman transitions using autoionizing resonances,” Phys. Rev. A 41, 4727–4731 (1990).
    [CrossRef]
  35. J. Mostowski, “Influence of the light statistics on the many photon resonance ionization,” Phys. Lett. A 56, 87–88 (1976).
    [CrossRef]
  36. A. Raczynski, M. Rzepecka, J. Zaremba, and S. Zielinska-Kaniasty, “Electromagnetically induced transparency and light slowdown for Λ-like systems with a structured continuum,” Opt. Commun. 266, 552–557 (2006).
    [CrossRef]
  37. W. Leonski and R. Tanas, “Quantum laser field effect on the photoelectron spectrum for auto-ionizing systems,” J. Mod. Opt. 37, 1923–1934 (1990).
    [CrossRef]
  38. W. Leonski, “Squeezed-state effect on bound-continuum transitions,” J. Opt. Soc. Am. B 10, 244–252 (1993).
    [CrossRef]
  39. G. Shvets, C.-H. Wu, and A. Khanikaev, “Slow light without electromagnetically induced transparency: the double-Fano resonance approach,” in Quantum Electronics and Laser Science Conference, San Jose, California, USA, 2010, paper QThE7.
  40. K. D. Quoc, V. C. Long, and W. Leoski, “A broad-band laser-driven double Fano system—photoelectron spectra,” Phys. Scr. 86, 045301 (2012).
    [CrossRef]
  41. A. M. Kenis, I. Vorobeichik, M. Orenstein, and N. Moiseyev, “Non-evanescent adiabatic directional coupler,” IEEE J. Quantum Electron. 37, 1321–1328 (2001).
    [CrossRef]
  42. M. F. Yanik, W. Suh, Z. Wang, and S. Fan, “Stopping light in a waveguide with an all-optical analog of electromagnetically induced transparency,” Phys. Rev. Lett. 93, 233903 (2004).
    [CrossRef]
  43. Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, “Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency,” Phys. Rev. Lett. 96, 123901 (2006).
    [CrossRef]
  44. P. Ginzburg and M. Orenstein, “Photonic switching in waveguides using spatial concepts inspired by EIT,” Opt. Express 14, 11312–11317 (2006).
    [CrossRef]
  45. P. Biagioni, G. Della Valle, M. Ornigotti, M. Finazzi, L. Du, P. Laporta, and S. Longhi, “Experimental demonstration of the optical Zeno effect by scanning tunneling optical microscopy,” Opt. Express 16, 3762–3767 (2008).
    [CrossRef]
  46. E. Paspalakis, “Adiabatic three-waveguide directional coupler,” Opt. Commun. 258, 30–34 (2006).
    [CrossRef]
  47. G. Della Valle, M. Ornigotti, T. Toney Fernandez, P. Laporta, S. Longhi, A. Coppa, and V. Foglietti, “Adiabatic light transfer via dressed states in optical waveguide arrays,” Appl. Phys. Lett. 92, 011106 (2008).
    [CrossRef]
  48. S. Kazazis and E. Paspalakis, “Effects of nonlinearity in Uasymmetric adiabatic three-waveguide directional couplers,” J. Mod. Opt. 57, 2123–2129 (2010).
    [CrossRef]
  49. S. Longhi, “Decay of a nonlinear impurity in a structured continuum from a nonlinear Fano–Anderson model,” Phys. Rev. B 75, 184306 (2007).
    [CrossRef]
  50. S. Longhi, “Optical analogue of coherent population trapping via a continuum in optical waveguide arrays,” J. Mod. Opt. 56, 729–737 (2009).
    [CrossRef]
  51. S. Longhi, “Optical analog of population trapping in the continuum: classical and quantum interference effects,” Phys. Rev. A 79, 023811 (2009).
    [CrossRef]
  52. F. Dreisow, A. Szameit, M. Heinrich, R. Keil, S. Nolte, A. Tnnermann, and S. Longhi, “Adiabatic transfer of light via a continuum in optical waveguides,” Opt. Lett. 34, 2405–2407 (2009).
    [CrossRef]
  53. I. Bayal, P. Panchadhyayee, B. K. Dutta, and P. K. Mahapattra, “Optical trapping with modified exponential decay in optical waveguides via dressed continuum,” J. Mod. Opt. 59, 226–234 (2012).
    [CrossRef]
  54. I. Bayal, B. K. Dutta, P. Panchadhyayee, and P. K. Mahapattra, “Variable-coupling-induced optical trapping in optical waveguides via dressed continuum,” J. Mod. Opt. 60, 1006–1014 (2013).
    [CrossRef]
  55. S. Longhi, “Nonexponential decay via tunneling in tight-binding lattices and the optical Zeno Effect,” Phys. Rev. Lett. 97, 110402 (2006).
    [CrossRef]
  56. S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, “Ultrafast laser processing: new options for three-dimensional photonic structures,” J. Mod. Opt. 51, 2533–2542 (2004).
    [CrossRef]

2013

I. Bayal, B. K. Dutta, P. Panchadhyayee, and P. K. Mahapattra, “Variable-coupling-induced optical trapping in optical waveguides via dressed continuum,” J. Mod. Opt. 60, 1006–1014 (2013).
[CrossRef]

2012

I. Bayal, P. Panchadhyayee, B. K. Dutta, and P. K. Mahapattra, “Optical trapping with modified exponential decay in optical waveguides via dressed continuum,” J. Mod. Opt. 59, 226–234 (2012).
[CrossRef]

K. D. Quoc, V. C. Long, and W. Leoski, “A broad-band laser-driven double Fano system—photoelectron spectra,” Phys. Scr. 86, 045301 (2012).
[CrossRef]

2011

R. Khomeriki, “Multiple Landau–Zener tunnelling in two weakly coupled waveguide arrays,” Eur. Phys. J. D 61, 193–197 (2011).
[CrossRef]

S. Ghosh and S. Mandal, “A theoretical analysis on coherent double resonant absorptive lineshape in closely spaced transitions for Λ type five level system,” Opt. Commun. 284, 376–387 (2011).
[CrossRef]

2010

X. Y. Hao, J. H. Li, X. Y. Lu, and X. Yang, “Controllable amplification and absorption properties in coupled-double-quantum-wells with tunneling-induced interference,” Eur. Phys. J. D 56, 239–246 (2010).
[CrossRef]

B. Lukyanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
[CrossRef]

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82, 2257–2298 (2010).
[CrossRef]

S. Kazazis and E. Paspalakis, “Effects of nonlinearity in Uasymmetric adiabatic three-waveguide directional couplers,” J. Mod. Opt. 57, 2123–2129 (2010).
[CrossRef]

2009

S. Longhi, “Optical analogue of coherent population trapping via a continuum in optical waveguide arrays,” J. Mod. Opt. 56, 729–737 (2009).
[CrossRef]

S. Longhi, “Optical analog of population trapping in the continuum: classical and quantum interference effects,” Phys. Rev. A 79, 023811 (2009).
[CrossRef]

K. Shandarova, C. E. Ruter, R. Dong, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett. 102, 123905 (2009).
[CrossRef]

F. Dreisow, A. Szameit, M. Heinrich, R. Keil, S. Nolte, A. Tnnermann, and S. Longhi, “Adiabatic transfer of light via a continuum in optical waveguides,” Opt. Lett. 34, 2405–2407 (2009).
[CrossRef]

2008

2007

G. Della Valle, M. Ornigotti, E. Cianci, V. Foglietti, P. Laporta, and S. Longhi, “Visualization of coherent destruction of tunneling in an optical double well system,” Phys. Rev. Lett. 98, 263601 (2007).
[CrossRef]

B. K. Dutta and P. K. Mahapatra, “Nonlinear optical effects in a doubly driven four-level atom,” Phys. Scr. 75, 345–353 (2007).
[CrossRef]

R. Iyer, J. S. Aitchison, J. Wan, M. M. Dignam, and C. M. de Sterke, “Exact dynamic localization in curved AlGaAs optical waveguide arrays,” Opt. Express 15, 3212–3223 (2007).
[CrossRef]

S. Longhi, “Decay of a nonlinear impurity in a structured continuum from a nonlinear Fano–Anderson model,” Phys. Rev. B 75, 184306 (2007).
[CrossRef]

2006

S. Longhi, “Nonexponential decay via tunneling in tight-binding lattices and the optical Zeno Effect,” Phys. Rev. Lett. 97, 110402 (2006).
[CrossRef]

P. Ginzburg and M. Orenstein, “Photonic switching in waveguides using spatial concepts inspired by EIT,” Opt. Express 14, 11312–11317 (2006).
[CrossRef]

R. A. Vicencio, A. V. Gorbach, and S. Flach, “Fano resonance in two-dimensional optical waveguide arrays with a bi-modal defect,” Phys. Lett. A 354, 210–213 (2006).
[CrossRef]

Y. S. Joe, A. M. Satanin, and C. S. Kim, “Classical analogy of Fano resonances,” Phys. Scr. 74, 259–266 (2006).
[CrossRef]

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, “Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency,” Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef]

E. Paspalakis, “Adiabatic three-waveguide directional coupler,” Opt. Commun. 258, 30–34 (2006).
[CrossRef]

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Bruer, and U. Peschel, “Visual observation of Zener tunneling,” Phys. Rev. Lett. 96, 023901 (2006).
[CrossRef]

A. Raczynski, M. Rzepecka, J. Zaremba, and S. Zielinska-Kaniasty, “Electromagnetically induced transparency and light slowdown for Λ-like systems with a structured continuum,” Opt. Commun. 266, 552–557 (2006).
[CrossRef]

2005

B. P. Hou, S. J. Wang, W. L. Yu, and W. L. Sun, “Control of one- and two-photon absorption in a four-level atomic system by changing the amplitude and phase of a driving microwave field,” J. Phys. B 38, 1419–1434 (2005).
[CrossRef]

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[CrossRef]

2004

M. F. Yanik, W. Suh, Z. Wang, and S. Fan, “Stopping light in a waveguide with an all-optical analog of electromagnetically induced transparency,” Phys. Rev. Lett. 93, 233903 (2004).
[CrossRef]

N. K. Efrimidis and D. N. Christodoulides, “Bloch oscillations in optical dissipative lattices,” Opt. Lett. 29, 2485–2487 (2004).
[CrossRef]

S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, “Ultrafast laser processing: new options for three-dimensional photonic structures,” J. Mod. Opt. 51, 2533–2542 (2004).
[CrossRef]

2001

A. M. Kenis, I. Vorobeichik, M. Orenstein, and N. Moiseyev, “Non-evanescent adiabatic directional coupler,” IEEE J. Quantum Electron. 37, 1321–1328 (2001).
[CrossRef]

G. S. Agarwal and J. Banerji, “Off-resonant pumping for the transition from a continuous to a discrete spectrum and quantum revivals in systems in coherent states,” J. Opt. B 3, S79–S82 (2001).
[CrossRef]

2000

X. M. Hu and J. S. Peng, “Quantum interference from spontaneous decay in Lambda systems: realization in the dressed-state picture,” J. Phys. B 33, 921–931 (2000).
[CrossRef]

1998

K. Bergmann, H. Theuer, and B. W. Shore, “Coherent population transfer among quantum states of atoms and molecules,” Rev. Mod. Phys. 70, 1003–1025 (1998).
[CrossRef]

1997

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36–42 (1997).
[CrossRef]

G. S. Agarwal, “Nature of the quantum interference in electromagnetic-field-induced control of absorption,” Phys. Rev. A 55, 2467–2470 (1997).
[CrossRef]

H. Schmidt, K. L. Campman, A. C. Gossard, and A. Imamoglu, “Tunneling induced transparency: Fano interference in intersubband transitions,” Appl. Phys. Lett. 70, 3455–3457 (1997).
[CrossRef]

1996

G. S. Agarwal and W. Harshawardhan, “Inhibition and enhancement of two photon absorption,” Opt. Commun. 77, 1039–1042 (1996).

1993

1990

P. L. Knight, M. A. Lauder, and B. J. Dalton, “Laser-induced continuum structure,” Phys. Rep. 190, 1–61 (1990).
[CrossRef]

W. Leonski and R. Tanas, “Quantum laser field effect on the photoelectron spectrum for auto-ionizing systems,” J. Mod. Opt. 37, 1923–1934 (1990).
[CrossRef]

G. S. Agarwal, S. Ravi, and J. Cooper, “dc-field-coupled autoionizing states for laser action without population inversion,” Phys. Rev. A 41, 4721–4726 (1990).
[CrossRef]

G. S. Agarwal, S. Ravi, and J. Cooper, “Lasers without inversion: Raman transitions using autoionizing resonances,” Phys. Rev. A 41, 4727–4731 (1990).
[CrossRef]

1988

W. Leonski and R. Tanas, “DC-field effects on the photoelectron spectrum from a system with two autoionising levels,” J. Phys. B 21, 2835–2844 (1988).
[CrossRef]

W. Leonski, R. Tanas, and S. Kielich, “Effect of DC field coupling on the photoelectron spectrum from double auto-ionizing levels,” J. Phys. D 21, S125–S127 (1988).
[CrossRef]

1987

1981

K. Rzazewski and J. H. Eberly, “Confluence of bound-free coherences in laser-induced autoionization,” Phys. Rev. Lett. 47, 408–412 (1981).
[CrossRef]

1976

J. Mostowski, “Influence of the light statistics on the many photon resonance ionization,” Phys. Lett. A 56, 87–88 (1976).
[CrossRef]

1961

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866–1878 (1961).
[CrossRef]

Agarwal, G. S.

G. S. Agarwal and J. Banerji, “Off-resonant pumping for the transition from a continuous to a discrete spectrum and quantum revivals in systems in coherent states,” J. Opt. B 3, S79–S82 (2001).
[CrossRef]

G. S. Agarwal, “Nature of the quantum interference in electromagnetic-field-induced control of absorption,” Phys. Rev. A 55, 2467–2470 (1997).
[CrossRef]

G. S. Agarwal and W. Harshawardhan, “Inhibition and enhancement of two photon absorption,” Opt. Commun. 77, 1039–1042 (1996).

G. S. Agarwal, S. Ravi, and J. Cooper, “dc-field-coupled autoionizing states for laser action without population inversion,” Phys. Rev. A 41, 4721–4726 (1990).
[CrossRef]

G. S. Agarwal, S. Ravi, and J. Cooper, “Lasers without inversion: Raman transitions using autoionizing resonances,” Phys. Rev. A 41, 4727–4731 (1990).
[CrossRef]

G. S. Agarwal, Quantum Statistical Theories of Spontaneous Emission and Their Relation to Other Approaches, G. Hohler, ed., Vol. 70 of Springer Tracts in Modern Physics (Springer-Verlag, 1974), pp. 88–97.

Aitchison, J. S.

Arimondo, E.

E. Arimondo, Progress in Optics, E. Wolf, ed. (Elsevier, 1996), Vol. 35, pp. 257–354.

Banerji, J.

G. S. Agarwal and J. Banerji, “Off-resonant pumping for the transition from a continuous to a discrete spectrum and quantum revivals in systems in coherent states,” J. Opt. B 3, S79–S82 (2001).
[CrossRef]

Bayal, I.

I. Bayal, B. K. Dutta, P. Panchadhyayee, and P. K. Mahapattra, “Variable-coupling-induced optical trapping in optical waveguides via dressed continuum,” J. Mod. Opt. 60, 1006–1014 (2013).
[CrossRef]

I. Bayal, P. Panchadhyayee, B. K. Dutta, and P. K. Mahapattra, “Optical trapping with modified exponential decay in optical waveguides via dressed continuum,” J. Mod. Opt. 59, 226–234 (2012).
[CrossRef]

Bergmann, K.

K. Bergmann, H. Theuer, and B. W. Shore, “Coherent population transfer among quantum states of atoms and molecules,” Rev. Mod. Phys. 70, 1003–1025 (1998).
[CrossRef]

Biagioni, P.

Bruer, A.

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Bruer, and U. Peschel, “Visual observation of Zener tunneling,” Phys. Rev. Lett. 96, 023901 (2006).
[CrossRef]

Burghoff, J.

S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, “Ultrafast laser processing: new options for three-dimensional photonic structures,” J. Mod. Opt. 51, 2533–2542 (2004).
[CrossRef]

Campman, K. L.

H. Schmidt, K. L. Campman, A. C. Gossard, and A. Imamoglu, “Tunneling induced transparency: Fano interference in intersubband transitions,” Appl. Phys. Lett. 70, 3455–3457 (1997).
[CrossRef]

Chong, C. T.

B. Lukyanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
[CrossRef]

Christodoulides, D. N.

Cianci, E.

G. Della Valle, M. Ornigotti, E. Cianci, V. Foglietti, P. Laporta, and S. Longhi, “Visualization of coherent destruction of tunneling in an optical double well system,” Phys. Rev. Lett. 98, 263601 (2007).
[CrossRef]

Cooper, J.

G. S. Agarwal, S. Ravi, and J. Cooper, “Lasers without inversion: Raman transitions using autoionizing resonances,” Phys. Rev. A 41, 4727–4731 (1990).
[CrossRef]

G. S. Agarwal, S. Ravi, and J. Cooper, “dc-field-coupled autoionizing states for laser action without population inversion,” Phys. Rev. A 41, 4721–4726 (1990).
[CrossRef]

Coppa, A.

G. Della Valle, M. Ornigotti, T. Toney Fernandez, P. Laporta, S. Longhi, A. Coppa, and V. Foglietti, “Adiabatic light transfer via dressed states in optical waveguide arrays,” Appl. Phys. Lett. 92, 011106 (2008).
[CrossRef]

Dalton, B. J.

P. L. Knight, M. A. Lauder, and B. J. Dalton, “Laser-induced continuum structure,” Phys. Rep. 190, 1–61 (1990).
[CrossRef]

de Sterke, C. M.

Della Valle, G.

P. Biagioni, G. Della Valle, M. Ornigotti, M. Finazzi, L. Du, P. Laporta, and S. Longhi, “Experimental demonstration of the optical Zeno effect by scanning tunneling optical microscopy,” Opt. Express 16, 3762–3767 (2008).
[CrossRef]

G. Della Valle, M. Ornigotti, T. Toney Fernandez, P. Laporta, S. Longhi, A. Coppa, and V. Foglietti, “Adiabatic light transfer via dressed states in optical waveguide arrays,” Appl. Phys. Lett. 92, 011106 (2008).
[CrossRef]

G. Della Valle, M. Ornigotti, E. Cianci, V. Foglietti, P. Laporta, and S. Longhi, “Visualization of coherent destruction of tunneling in an optical double well system,” Phys. Rev. Lett. 98, 263601 (2007).
[CrossRef]

Dignam, M. M.

Dong, R.

K. Shandarova, C. E. Ruter, R. Dong, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett. 102, 123905 (2009).
[CrossRef]

Dreisow, F.

Du, L.

Dutta, B. K.

I. Bayal, B. K. Dutta, P. Panchadhyayee, and P. K. Mahapattra, “Variable-coupling-induced optical trapping in optical waveguides via dressed continuum,” J. Mod. Opt. 60, 1006–1014 (2013).
[CrossRef]

I. Bayal, P. Panchadhyayee, B. K. Dutta, and P. K. Mahapattra, “Optical trapping with modified exponential decay in optical waveguides via dressed continuum,” J. Mod. Opt. 59, 226–234 (2012).
[CrossRef]

B. K. Dutta and P. K. Mahapatra, “Nonlinear optical effects in a doubly driven four-level atom,” Phys. Scr. 75, 345–353 (2007).
[CrossRef]

Eberly, J. H.

K. Rzazewski and J. H. Eberly, “Confluence of bound-free coherences in laser-induced autoionization,” Phys. Rev. Lett. 47, 408–412 (1981).
[CrossRef]

Efrimidis, N. K.

Fan, S.

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, “Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency,” Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef]

M. F. Yanik, W. Suh, Z. Wang, and S. Fan, “Stopping light in a waveguide with an all-optical analog of electromagnetically induced transparency,” Phys. Rev. Lett. 93, 233903 (2004).
[CrossRef]

Fano, U.

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866–1878 (1961).
[CrossRef]

Ficek, Z.

Z. Ficek and S. Swain, Quantum Interference and Coherence: Theory and Experiments, W. T. Rhodes, ed., Vol. 100 of Springer Series in Optical Sciences (Springer, 2005), pp. 139–177.

Finazzi, M.

Flach, S.

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82, 2257–2298 (2010).
[CrossRef]

R. A. Vicencio, A. V. Gorbach, and S. Flach, “Fano resonance in two-dimensional optical waveguide arrays with a bi-modal defect,” Phys. Lett. A 354, 210–213 (2006).
[CrossRef]

Fleischhauer, M.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[CrossRef]

Foglietti, V.

G. Della Valle, M. Ornigotti, T. Toney Fernandez, P. Laporta, S. Longhi, A. Coppa, and V. Foglietti, “Adiabatic light transfer via dressed states in optical waveguide arrays,” Appl. Phys. Lett. 92, 011106 (2008).
[CrossRef]

G. Della Valle, M. Ornigotti, E. Cianci, V. Foglietti, P. Laporta, and S. Longhi, “Visualization of coherent destruction of tunneling in an optical double well system,” Phys. Rev. Lett. 98, 263601 (2007).
[CrossRef]

Ghosh, S.

S. Ghosh and S. Mandal, “A theoretical analysis on coherent double resonant absorptive lineshape in closely spaced transitions for Λ type five level system,” Opt. Commun. 284, 376–387 (2011).
[CrossRef]

Giessen, H.

B. Lukyanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
[CrossRef]

Ginzburg, P.

Gorbach, A. V.

R. A. Vicencio, A. V. Gorbach, and S. Flach, “Fano resonance in two-dimensional optical waveguide arrays with a bi-modal defect,” Phys. Lett. A 354, 210–213 (2006).
[CrossRef]

Gossard, A. C.

H. Schmidt, K. L. Campman, A. C. Gossard, and A. Imamoglu, “Tunneling induced transparency: Fano interference in intersubband transitions,” Appl. Phys. Lett. 70, 3455–3457 (1997).
[CrossRef]

Halas, N. J.

B. Lukyanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
[CrossRef]

Hao, X. Y.

X. Y. Hao, J. H. Li, X. Y. Lu, and X. Yang, “Controllable amplification and absorption properties in coupled-double-quantum-wells with tunneling-induced interference,” Eur. Phys. J. D 56, 239–246 (2010).
[CrossRef]

Harris, S. E.

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36–42 (1997).
[CrossRef]

Harshawardhan, W.

G. S. Agarwal and W. Harshawardhan, “Inhibition and enhancement of two photon absorption,” Opt. Commun. 77, 1039–1042 (1996).

Heinrich, M.

Hou, B. P.

B. P. Hou, S. J. Wang, W. L. Yu, and W. L. Sun, “Control of one- and two-photon absorption in a four-level atomic system by changing the amplitude and phase of a driving microwave field,” J. Phys. B 38, 1419–1434 (2005).
[CrossRef]

Hu, X. M.

X. M. Hu and J. S. Peng, “Quantum interference from spontaneous decay in Lambda systems: realization in the dressed-state picture,” J. Phys. B 33, 921–931 (2000).
[CrossRef]

Imamoglu, A.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[CrossRef]

H. Schmidt, K. L. Campman, A. C. Gossard, and A. Imamoglu, “Tunneling induced transparency: Fano interference in intersubband transitions,” Appl. Phys. Lett. 70, 3455–3457 (1997).
[CrossRef]

Iyer, R.

Joe, Y. S.

Y. S. Joe, A. M. Satanin, and C. S. Kim, “Classical analogy of Fano resonances,” Phys. Scr. 74, 259–266 (2006).
[CrossRef]

Kazazis, S.

S. Kazazis and E. Paspalakis, “Effects of nonlinearity in Uasymmetric adiabatic three-waveguide directional couplers,” J. Mod. Opt. 57, 2123–2129 (2010).
[CrossRef]

Keil, R.

Kenis, A. M.

A. M. Kenis, I. Vorobeichik, M. Orenstein, and N. Moiseyev, “Non-evanescent adiabatic directional coupler,” IEEE J. Quantum Electron. 37, 1321–1328 (2001).
[CrossRef]

Khanikaev, A.

G. Shvets, C.-H. Wu, and A. Khanikaev, “Slow light without electromagnetically induced transparency: the double-Fano resonance approach,” in Quantum Electronics and Laser Science Conference, San Jose, California, USA, 2010, paper QThE7.

Khomeriki, R.

R. Khomeriki, “Multiple Landau–Zener tunnelling in two weakly coupled waveguide arrays,” Eur. Phys. J. D 61, 193–197 (2011).
[CrossRef]

Kielich, S.

W. Leonski, R. Tanas, and S. Kielich, “Effect of DC field coupling on the photoelectron spectrum from double auto-ionizing levels,” J. Phys. D 21, S125–S127 (1988).
[CrossRef]

W. Leonski, R. Tanas, and S. Kielich, “Laser-induced autoionization from a double Fano system,” J. Opt. Soc. Am. B 4, 72–77 (1987).
[CrossRef]

Kim, C. S.

Y. S. Joe, A. M. Satanin, and C. S. Kim, “Classical analogy of Fano resonances,” Phys. Scr. 74, 259–266 (2006).
[CrossRef]

Kip, D.

K. Shandarova, C. E. Ruter, R. Dong, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett. 102, 123905 (2009).
[CrossRef]

K. G. Makris, D. N. Christodoulides, O. Peleg, M. Segev, and D. Kip, “Optical transitions and Rabi oscillations in waveguide arrays,” Opt. Express 16, 10309–10314 (2008).
[CrossRef]

Kivshar, Y. S.

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82, 2257–2298 (2010).
[CrossRef]

Knight, P. L.

P. L. Knight, M. A. Lauder, and B. J. Dalton, “Laser-induced continuum structure,” Phys. Rep. 190, 1–61 (1990).
[CrossRef]

Laporta, P.

G. Della Valle, M. Ornigotti, T. Toney Fernandez, P. Laporta, S. Longhi, A. Coppa, and V. Foglietti, “Adiabatic light transfer via dressed states in optical waveguide arrays,” Appl. Phys. Lett. 92, 011106 (2008).
[CrossRef]

P. Biagioni, G. Della Valle, M. Ornigotti, M. Finazzi, L. Du, P. Laporta, and S. Longhi, “Experimental demonstration of the optical Zeno effect by scanning tunneling optical microscopy,” Opt. Express 16, 3762–3767 (2008).
[CrossRef]

G. Della Valle, M. Ornigotti, E. Cianci, V. Foglietti, P. Laporta, and S. Longhi, “Visualization of coherent destruction of tunneling in an optical double well system,” Phys. Rev. Lett. 98, 263601 (2007).
[CrossRef]

Lauder, M. A.

P. L. Knight, M. A. Lauder, and B. J. Dalton, “Laser-induced continuum structure,” Phys. Rep. 190, 1–61 (1990).
[CrossRef]

Lederer, F.

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Bruer, and U. Peschel, “Visual observation of Zener tunneling,” Phys. Rev. Lett. 96, 023901 (2006).
[CrossRef]

Leonski, W.

W. Leonski, “Squeezed-state effect on bound-continuum transitions,” J. Opt. Soc. Am. B 10, 244–252 (1993).
[CrossRef]

W. Leonski and R. Tanas, “Quantum laser field effect on the photoelectron spectrum for auto-ionizing systems,” J. Mod. Opt. 37, 1923–1934 (1990).
[CrossRef]

W. Leonski and R. Tanas, “DC-field effects on the photoelectron spectrum from a system with two autoionising levels,” J. Phys. B 21, 2835–2844 (1988).
[CrossRef]

W. Leonski, R. Tanas, and S. Kielich, “Effect of DC field coupling on the photoelectron spectrum from double auto-ionizing levels,” J. Phys. D 21, S125–S127 (1988).
[CrossRef]

W. Leonski, R. Tanas, and S. Kielich, “Laser-induced autoionization from a double Fano system,” J. Opt. Soc. Am. B 4, 72–77 (1987).
[CrossRef]

Leoski, W.

K. D. Quoc, V. C. Long, and W. Leoski, “A broad-band laser-driven double Fano system—photoelectron spectra,” Phys. Scr. 86, 045301 (2012).
[CrossRef]

Li, J. H.

X. Y. Hao, J. H. Li, X. Y. Lu, and X. Yang, “Controllable amplification and absorption properties in coupled-double-quantum-wells with tunneling-induced interference,” Eur. Phys. J. D 56, 239–246 (2010).
[CrossRef]

Lipson, M.

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, “Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency,” Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef]

Long, V. C.

K. D. Quoc, V. C. Long, and W. Leoski, “A broad-band laser-driven double Fano system—photoelectron spectra,” Phys. Scr. 86, 045301 (2012).
[CrossRef]

Longhi, S.

S. Longhi, “Optical analogue of coherent population trapping via a continuum in optical waveguide arrays,” J. Mod. Opt. 56, 729–737 (2009).
[CrossRef]

S. Longhi, “Optical analog of population trapping in the continuum: classical and quantum interference effects,” Phys. Rev. A 79, 023811 (2009).
[CrossRef]

F. Dreisow, A. Szameit, M. Heinrich, R. Keil, S. Nolte, A. Tnnermann, and S. Longhi, “Adiabatic transfer of light via a continuum in optical waveguides,” Opt. Lett. 34, 2405–2407 (2009).
[CrossRef]

P. Biagioni, G. Della Valle, M. Ornigotti, M. Finazzi, L. Du, P. Laporta, and S. Longhi, “Experimental demonstration of the optical Zeno effect by scanning tunneling optical microscopy,” Opt. Express 16, 3762–3767 (2008).
[CrossRef]

G. Della Valle, M. Ornigotti, T. Toney Fernandez, P. Laporta, S. Longhi, A. Coppa, and V. Foglietti, “Adiabatic light transfer via dressed states in optical waveguide arrays,” Appl. Phys. Lett. 92, 011106 (2008).
[CrossRef]

S. Longhi, “Decay of a nonlinear impurity in a structured continuum from a nonlinear Fano–Anderson model,” Phys. Rev. B 75, 184306 (2007).
[CrossRef]

G. Della Valle, M. Ornigotti, E. Cianci, V. Foglietti, P. Laporta, and S. Longhi, “Visualization of coherent destruction of tunneling in an optical double well system,” Phys. Rev. Lett. 98, 263601 (2007).
[CrossRef]

S. Longhi, “Nonexponential decay via tunneling in tight-binding lattices and the optical Zeno Effect,” Phys. Rev. Lett. 97, 110402 (2006).
[CrossRef]

Lu, X. Y.

X. Y. Hao, J. H. Li, X. Y. Lu, and X. Yang, “Controllable amplification and absorption properties in coupled-double-quantum-wells with tunneling-induced interference,” Eur. Phys. J. D 56, 239–246 (2010).
[CrossRef]

Lukyanchuk, B.

B. Lukyanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
[CrossRef]

Mahapatra, P. K.

B. K. Dutta and P. K. Mahapatra, “Nonlinear optical effects in a doubly driven four-level atom,” Phys. Scr. 75, 345–353 (2007).
[CrossRef]

Mahapattra, P. K.

I. Bayal, B. K. Dutta, P. Panchadhyayee, and P. K. Mahapattra, “Variable-coupling-induced optical trapping in optical waveguides via dressed continuum,” J. Mod. Opt. 60, 1006–1014 (2013).
[CrossRef]

I. Bayal, P. Panchadhyayee, B. K. Dutta, and P. K. Mahapattra, “Optical trapping with modified exponential decay in optical waveguides via dressed continuum,” J. Mod. Opt. 59, 226–234 (2012).
[CrossRef]

Maier, S. A.

B. Lukyanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
[CrossRef]

Makris, K. G.

K. Shandarova, C. E. Ruter, R. Dong, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett. 102, 123905 (2009).
[CrossRef]

K. G. Makris, D. N. Christodoulides, O. Peleg, M. Segev, and D. Kip, “Optical transitions and Rabi oscillations in waveguide arrays,” Opt. Express 16, 10309–10314 (2008).
[CrossRef]

Mandal, S.

S. Ghosh and S. Mandal, “A theoretical analysis on coherent double resonant absorptive lineshape in closely spaced transitions for Λ type five level system,” Opt. Commun. 284, 376–387 (2011).
[CrossRef]

Marangos, J. P.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[CrossRef]

Michaelis, D.

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Bruer, and U. Peschel, “Visual observation of Zener tunneling,” Phys. Rev. Lett. 96, 023901 (2006).
[CrossRef]

Miroshnichenko, A. E.

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82, 2257–2298 (2010).
[CrossRef]

Moiseyev, N.

A. M. Kenis, I. Vorobeichik, M. Orenstein, and N. Moiseyev, “Non-evanescent adiabatic directional coupler,” IEEE J. Quantum Electron. 37, 1321–1328 (2001).
[CrossRef]

Mostowski, J.

J. Mostowski, “Influence of the light statistics on the many photon resonance ionization,” Phys. Lett. A 56, 87–88 (1976).
[CrossRef]

Nolte, S.

F. Dreisow, A. Szameit, M. Heinrich, R. Keil, S. Nolte, A. Tnnermann, and S. Longhi, “Adiabatic transfer of light via a continuum in optical waveguides,” Opt. Lett. 34, 2405–2407 (2009).
[CrossRef]

S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, “Ultrafast laser processing: new options for three-dimensional photonic structures,” J. Mod. Opt. 51, 2533–2542 (2004).
[CrossRef]

Nordlander, P.

B. Lukyanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
[CrossRef]

Orenstein, M.

P. Ginzburg and M. Orenstein, “Photonic switching in waveguides using spatial concepts inspired by EIT,” Opt. Express 14, 11312–11317 (2006).
[CrossRef]

A. M. Kenis, I. Vorobeichik, M. Orenstein, and N. Moiseyev, “Non-evanescent adiabatic directional coupler,” IEEE J. Quantum Electron. 37, 1321–1328 (2001).
[CrossRef]

Ornigotti, M.

G. Della Valle, M. Ornigotti, T. Toney Fernandez, P. Laporta, S. Longhi, A. Coppa, and V. Foglietti, “Adiabatic light transfer via dressed states in optical waveguide arrays,” Appl. Phys. Lett. 92, 011106 (2008).
[CrossRef]

P. Biagioni, G. Della Valle, M. Ornigotti, M. Finazzi, L. Du, P. Laporta, and S. Longhi, “Experimental demonstration of the optical Zeno effect by scanning tunneling optical microscopy,” Opt. Express 16, 3762–3767 (2008).
[CrossRef]

G. Della Valle, M. Ornigotti, E. Cianci, V. Foglietti, P. Laporta, and S. Longhi, “Visualization of coherent destruction of tunneling in an optical double well system,” Phys. Rev. Lett. 98, 263601 (2007).
[CrossRef]

Panchadhyayee, P.

I. Bayal, B. K. Dutta, P. Panchadhyayee, and P. K. Mahapattra, “Variable-coupling-induced optical trapping in optical waveguides via dressed continuum,” J. Mod. Opt. 60, 1006–1014 (2013).
[CrossRef]

I. Bayal, P. Panchadhyayee, B. K. Dutta, and P. K. Mahapattra, “Optical trapping with modified exponential decay in optical waveguides via dressed continuum,” J. Mod. Opt. 59, 226–234 (2012).
[CrossRef]

Paspalakis, E.

S. Kazazis and E. Paspalakis, “Effects of nonlinearity in Uasymmetric adiabatic three-waveguide directional couplers,” J. Mod. Opt. 57, 2123–2129 (2010).
[CrossRef]

E. Paspalakis, “Adiabatic three-waveguide directional coupler,” Opt. Commun. 258, 30–34 (2006).
[CrossRef]

Peleg, O.

K. Shandarova, C. E. Ruter, R. Dong, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett. 102, 123905 (2009).
[CrossRef]

K. G. Makris, D. N. Christodoulides, O. Peleg, M. Segev, and D. Kip, “Optical transitions and Rabi oscillations in waveguide arrays,” Opt. Express 16, 10309–10314 (2008).
[CrossRef]

Peng, J. S.

X. M. Hu and J. S. Peng, “Quantum interference from spontaneous decay in Lambda systems: realization in the dressed-state picture,” J. Phys. B 33, 921–931 (2000).
[CrossRef]

Pertsch, T.

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Bruer, and U. Peschel, “Visual observation of Zener tunneling,” Phys. Rev. Lett. 96, 023901 (2006).
[CrossRef]

Peschel, U.

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Bruer, and U. Peschel, “Visual observation of Zener tunneling,” Phys. Rev. Lett. 96, 023901 (2006).
[CrossRef]

Povinelli, M. L.

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, “Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency,” Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef]

Quoc, K. D.

K. D. Quoc, V. C. Long, and W. Leoski, “A broad-band laser-driven double Fano system—photoelectron spectra,” Phys. Scr. 86, 045301 (2012).
[CrossRef]

Raczynski, A.

A. Raczynski, M. Rzepecka, J. Zaremba, and S. Zielinska-Kaniasty, “Electromagnetically induced transparency and light slowdown for Λ-like systems with a structured continuum,” Opt. Commun. 266, 552–557 (2006).
[CrossRef]

Ravi, S.

G. S. Agarwal, S. Ravi, and J. Cooper, “Lasers without inversion: Raman transitions using autoionizing resonances,” Phys. Rev. A 41, 4727–4731 (1990).
[CrossRef]

G. S. Agarwal, S. Ravi, and J. Cooper, “dc-field-coupled autoionizing states for laser action without population inversion,” Phys. Rev. A 41, 4721–4726 (1990).
[CrossRef]

Ruter, C. E.

K. Shandarova, C. E. Ruter, R. Dong, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett. 102, 123905 (2009).
[CrossRef]

Rzazewski, K.

K. Rzazewski and J. H. Eberly, “Confluence of bound-free coherences in laser-induced autoionization,” Phys. Rev. Lett. 47, 408–412 (1981).
[CrossRef]

Rzepecka, M.

A. Raczynski, M. Rzepecka, J. Zaremba, and S. Zielinska-Kaniasty, “Electromagnetically induced transparency and light slowdown for Λ-like systems with a structured continuum,” Opt. Commun. 266, 552–557 (2006).
[CrossRef]

Sandhu, S.

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, “Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency,” Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef]

Satanin, A. M.

Y. S. Joe, A. M. Satanin, and C. S. Kim, “Classical analogy of Fano resonances,” Phys. Scr. 74, 259–266 (2006).
[CrossRef]

Schmidt, H.

H. Schmidt, K. L. Campman, A. C. Gossard, and A. Imamoglu, “Tunneling induced transparency: Fano interference in intersubband transitions,” Appl. Phys. Lett. 70, 3455–3457 (1997).
[CrossRef]

Segev, M.

K. Shandarova, C. E. Ruter, R. Dong, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett. 102, 123905 (2009).
[CrossRef]

K. G. Makris, D. N. Christodoulides, O. Peleg, M. Segev, and D. Kip, “Optical transitions and Rabi oscillations in waveguide arrays,” Opt. Express 16, 10309–10314 (2008).
[CrossRef]

Shakya, J.

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, “Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency,” Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef]

Shandarova, K.

K. Shandarova, C. E. Ruter, R. Dong, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett. 102, 123905 (2009).
[CrossRef]

Shore, B. W.

K. Bergmann, H. Theuer, and B. W. Shore, “Coherent population transfer among quantum states of atoms and molecules,” Rev. Mod. Phys. 70, 1003–1025 (1998).
[CrossRef]

Shvets, G.

G. Shvets, C.-H. Wu, and A. Khanikaev, “Slow light without electromagnetically induced transparency: the double-Fano resonance approach,” in Quantum Electronics and Laser Science Conference, San Jose, California, USA, 2010, paper QThE7.

Streppel, U.

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Bruer, and U. Peschel, “Visual observation of Zener tunneling,” Phys. Rev. Lett. 96, 023901 (2006).
[CrossRef]

Suh, W.

M. F. Yanik, W. Suh, Z. Wang, and S. Fan, “Stopping light in a waveguide with an all-optical analog of electromagnetically induced transparency,” Phys. Rev. Lett. 93, 233903 (2004).
[CrossRef]

Sun, W. L.

B. P. Hou, S. J. Wang, W. L. Yu, and W. L. Sun, “Control of one- and two-photon absorption in a four-level atomic system by changing the amplitude and phase of a driving microwave field,” J. Phys. B 38, 1419–1434 (2005).
[CrossRef]

Swain, S.

Z. Ficek and S. Swain, Quantum Interference and Coherence: Theory and Experiments, W. T. Rhodes, ed., Vol. 100 of Springer Series in Optical Sciences (Springer, 2005), pp. 139–177.

Szameit, A.

Tanas, R.

W. Leonski and R. Tanas, “Quantum laser field effect on the photoelectron spectrum for auto-ionizing systems,” J. Mod. Opt. 37, 1923–1934 (1990).
[CrossRef]

W. Leonski, R. Tanas, and S. Kielich, “Effect of DC field coupling on the photoelectron spectrum from double auto-ionizing levels,” J. Phys. D 21, S125–S127 (1988).
[CrossRef]

W. Leonski and R. Tanas, “DC-field effects on the photoelectron spectrum from a system with two autoionising levels,” J. Phys. B 21, 2835–2844 (1988).
[CrossRef]

W. Leonski, R. Tanas, and S. Kielich, “Laser-induced autoionization from a double Fano system,” J. Opt. Soc. Am. B 4, 72–77 (1987).
[CrossRef]

Theuer, H.

K. Bergmann, H. Theuer, and B. W. Shore, “Coherent population transfer among quantum states of atoms and molecules,” Rev. Mod. Phys. 70, 1003–1025 (1998).
[CrossRef]

Tnnermann, A.

Toney Fernandez, T.

G. Della Valle, M. Ornigotti, T. Toney Fernandez, P. Laporta, S. Longhi, A. Coppa, and V. Foglietti, “Adiabatic light transfer via dressed states in optical waveguide arrays,” Appl. Phys. Lett. 92, 011106 (2008).
[CrossRef]

Trompeter, H.

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Bruer, and U. Peschel, “Visual observation of Zener tunneling,” Phys. Rev. Lett. 96, 023901 (2006).
[CrossRef]

Tuennermann, A.

S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, “Ultrafast laser processing: new options for three-dimensional photonic structures,” J. Mod. Opt. 51, 2533–2542 (2004).
[CrossRef]

Vicencio, R. A.

R. A. Vicencio, A. V. Gorbach, and S. Flach, “Fano resonance in two-dimensional optical waveguide arrays with a bi-modal defect,” Phys. Lett. A 354, 210–213 (2006).
[CrossRef]

Vorobeichik, I.

A. M. Kenis, I. Vorobeichik, M. Orenstein, and N. Moiseyev, “Non-evanescent adiabatic directional coupler,” IEEE J. Quantum Electron. 37, 1321–1328 (2001).
[CrossRef]

Wan, J.

Wang, S. J.

B. P. Hou, S. J. Wang, W. L. Yu, and W. L. Sun, “Control of one- and two-photon absorption in a four-level atomic system by changing the amplitude and phase of a driving microwave field,” J. Phys. B 38, 1419–1434 (2005).
[CrossRef]

Wang, Z.

M. F. Yanik, W. Suh, Z. Wang, and S. Fan, “Stopping light in a waveguide with an all-optical analog of electromagnetically induced transparency,” Phys. Rev. Lett. 93, 233903 (2004).
[CrossRef]

Will, M.

S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, “Ultrafast laser processing: new options for three-dimensional photonic structures,” J. Mod. Opt. 51, 2533–2542 (2004).
[CrossRef]

Wu, C.-H.

G. Shvets, C.-H. Wu, and A. Khanikaev, “Slow light without electromagnetically induced transparency: the double-Fano resonance approach,” in Quantum Electronics and Laser Science Conference, San Jose, California, USA, 2010, paper QThE7.

Xu, Q.

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, “Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency,” Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef]

Yang, X.

X. Y. Hao, J. H. Li, X. Y. Lu, and X. Yang, “Controllable amplification and absorption properties in coupled-double-quantum-wells with tunneling-induced interference,” Eur. Phys. J. D 56, 239–246 (2010).
[CrossRef]

Yanik, M. F.

M. F. Yanik, W. Suh, Z. Wang, and S. Fan, “Stopping light in a waveguide with an all-optical analog of electromagnetically induced transparency,” Phys. Rev. Lett. 93, 233903 (2004).
[CrossRef]

Yu, W. L.

B. P. Hou, S. J. Wang, W. L. Yu, and W. L. Sun, “Control of one- and two-photon absorption in a four-level atomic system by changing the amplitude and phase of a driving microwave field,” J. Phys. B 38, 1419–1434 (2005).
[CrossRef]

Zaremba, J.

A. Raczynski, M. Rzepecka, J. Zaremba, and S. Zielinska-Kaniasty, “Electromagnetically induced transparency and light slowdown for Λ-like systems with a structured continuum,” Opt. Commun. 266, 552–557 (2006).
[CrossRef]

Zheludev, N. I.

B. Lukyanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
[CrossRef]

Zielinska-Kaniasty, S.

A. Raczynski, M. Rzepecka, J. Zaremba, and S. Zielinska-Kaniasty, “Electromagnetically induced transparency and light slowdown for Λ-like systems with a structured continuum,” Opt. Commun. 266, 552–557 (2006).
[CrossRef]

Appl. Phys. Lett.

H. Schmidt, K. L. Campman, A. C. Gossard, and A. Imamoglu, “Tunneling induced transparency: Fano interference in intersubband transitions,” Appl. Phys. Lett. 70, 3455–3457 (1997).
[CrossRef]

G. Della Valle, M. Ornigotti, T. Toney Fernandez, P. Laporta, S. Longhi, A. Coppa, and V. Foglietti, “Adiabatic light transfer via dressed states in optical waveguide arrays,” Appl. Phys. Lett. 92, 011106 (2008).
[CrossRef]

Eur. Phys. J. D

X. Y. Hao, J. H. Li, X. Y. Lu, and X. Yang, “Controllable amplification and absorption properties in coupled-double-quantum-wells with tunneling-induced interference,” Eur. Phys. J. D 56, 239–246 (2010).
[CrossRef]

R. Khomeriki, “Multiple Landau–Zener tunnelling in two weakly coupled waveguide arrays,” Eur. Phys. J. D 61, 193–197 (2011).
[CrossRef]

IEEE J. Quantum Electron.

A. M. Kenis, I. Vorobeichik, M. Orenstein, and N. Moiseyev, “Non-evanescent adiabatic directional coupler,” IEEE J. Quantum Electron. 37, 1321–1328 (2001).
[CrossRef]

J. Mod. Opt.

W. Leonski and R. Tanas, “Quantum laser field effect on the photoelectron spectrum for auto-ionizing systems,” J. Mod. Opt. 37, 1923–1934 (1990).
[CrossRef]

S. Kazazis and E. Paspalakis, “Effects of nonlinearity in Uasymmetric adiabatic three-waveguide directional couplers,” J. Mod. Opt. 57, 2123–2129 (2010).
[CrossRef]

S. Longhi, “Optical analogue of coherent population trapping via a continuum in optical waveguide arrays,” J. Mod. Opt. 56, 729–737 (2009).
[CrossRef]

I. Bayal, P. Panchadhyayee, B. K. Dutta, and P. K. Mahapattra, “Optical trapping with modified exponential decay in optical waveguides via dressed continuum,” J. Mod. Opt. 59, 226–234 (2012).
[CrossRef]

I. Bayal, B. K. Dutta, P. Panchadhyayee, and P. K. Mahapattra, “Variable-coupling-induced optical trapping in optical waveguides via dressed continuum,” J. Mod. Opt. 60, 1006–1014 (2013).
[CrossRef]

S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, “Ultrafast laser processing: new options for three-dimensional photonic structures,” J. Mod. Opt. 51, 2533–2542 (2004).
[CrossRef]

J. Opt. B

G. S. Agarwal and J. Banerji, “Off-resonant pumping for the transition from a continuous to a discrete spectrum and quantum revivals in systems in coherent states,” J. Opt. B 3, S79–S82 (2001).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. B

W. Leonski and R. Tanas, “DC-field effects on the photoelectron spectrum from a system with two autoionising levels,” J. Phys. B 21, 2835–2844 (1988).
[CrossRef]

X. M. Hu and J. S. Peng, “Quantum interference from spontaneous decay in Lambda systems: realization in the dressed-state picture,” J. Phys. B 33, 921–931 (2000).
[CrossRef]

B. P. Hou, S. J. Wang, W. L. Yu, and W. L. Sun, “Control of one- and two-photon absorption in a four-level atomic system by changing the amplitude and phase of a driving microwave field,” J. Phys. B 38, 1419–1434 (2005).
[CrossRef]

J. Phys. D

W. Leonski, R. Tanas, and S. Kielich, “Effect of DC field coupling on the photoelectron spectrum from double auto-ionizing levels,” J. Phys. D 21, S125–S127 (1988).
[CrossRef]

Nat. Mater.

B. Lukyanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
[CrossRef]

Opt. Commun.

A. Raczynski, M. Rzepecka, J. Zaremba, and S. Zielinska-Kaniasty, “Electromagnetically induced transparency and light slowdown for Λ-like systems with a structured continuum,” Opt. Commun. 266, 552–557 (2006).
[CrossRef]

G. S. Agarwal and W. Harshawardhan, “Inhibition and enhancement of two photon absorption,” Opt. Commun. 77, 1039–1042 (1996).

S. Ghosh and S. Mandal, “A theoretical analysis on coherent double resonant absorptive lineshape in closely spaced transitions for Λ type five level system,” Opt. Commun. 284, 376–387 (2011).
[CrossRef]

E. Paspalakis, “Adiabatic three-waveguide directional coupler,” Opt. Commun. 258, 30–34 (2006).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Lett. A

R. A. Vicencio, A. V. Gorbach, and S. Flach, “Fano resonance in two-dimensional optical waveguide arrays with a bi-modal defect,” Phys. Lett. A 354, 210–213 (2006).
[CrossRef]

J. Mostowski, “Influence of the light statistics on the many photon resonance ionization,” Phys. Lett. A 56, 87–88 (1976).
[CrossRef]

Phys. Rep.

P. L. Knight, M. A. Lauder, and B. J. Dalton, “Laser-induced continuum structure,” Phys. Rep. 190, 1–61 (1990).
[CrossRef]

Phys. Rev.

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866–1878 (1961).
[CrossRef]

Phys. Rev. A

G. S. Agarwal, “Nature of the quantum interference in electromagnetic-field-induced control of absorption,” Phys. Rev. A 55, 2467–2470 (1997).
[CrossRef]

G. S. Agarwal, S. Ravi, and J. Cooper, “dc-field-coupled autoionizing states for laser action without population inversion,” Phys. Rev. A 41, 4721–4726 (1990).
[CrossRef]

G. S. Agarwal, S. Ravi, and J. Cooper, “Lasers without inversion: Raman transitions using autoionizing resonances,” Phys. Rev. A 41, 4727–4731 (1990).
[CrossRef]

S. Longhi, “Optical analog of population trapping in the continuum: classical and quantum interference effects,” Phys. Rev. A 79, 023811 (2009).
[CrossRef]

Phys. Rev. B

S. Longhi, “Decay of a nonlinear impurity in a structured continuum from a nonlinear Fano–Anderson model,” Phys. Rev. B 75, 184306 (2007).
[CrossRef]

Phys. Rev. Lett.

K. Shandarova, C. E. Ruter, R. Dong, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett. 102, 123905 (2009).
[CrossRef]

S. Longhi, “Nonexponential decay via tunneling in tight-binding lattices and the optical Zeno Effect,” Phys. Rev. Lett. 97, 110402 (2006).
[CrossRef]

M. F. Yanik, W. Suh, Z. Wang, and S. Fan, “Stopping light in a waveguide with an all-optical analog of electromagnetically induced transparency,” Phys. Rev. Lett. 93, 233903 (2004).
[CrossRef]

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, “Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency,” Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef]

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Bruer, and U. Peschel, “Visual observation of Zener tunneling,” Phys. Rev. Lett. 96, 023901 (2006).
[CrossRef]

G. Della Valle, M. Ornigotti, E. Cianci, V. Foglietti, P. Laporta, and S. Longhi, “Visualization of coherent destruction of tunneling in an optical double well system,” Phys. Rev. Lett. 98, 263601 (2007).
[CrossRef]

K. Rzazewski and J. H. Eberly, “Confluence of bound-free coherences in laser-induced autoionization,” Phys. Rev. Lett. 47, 408–412 (1981).
[CrossRef]

Phys. Scr.

B. K. Dutta and P. K. Mahapatra, “Nonlinear optical effects in a doubly driven four-level atom,” Phys. Scr. 75, 345–353 (2007).
[CrossRef]

K. D. Quoc, V. C. Long, and W. Leoski, “A broad-band laser-driven double Fano system—photoelectron spectra,” Phys. Scr. 86, 045301 (2012).
[CrossRef]

Y. S. Joe, A. M. Satanin, and C. S. Kim, “Classical analogy of Fano resonances,” Phys. Scr. 74, 259–266 (2006).
[CrossRef]

Phys. Today

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36–42 (1997).
[CrossRef]

Rev. Mod. Phys.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[CrossRef]

K. Bergmann, H. Theuer, and B. W. Shore, “Coherent population transfer among quantum states of atoms and molecules,” Rev. Mod. Phys. 70, 1003–1025 (1998).
[CrossRef]

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82, 2257–2298 (2010).
[CrossRef]

Other

G. Shvets, C.-H. Wu, and A. Khanikaev, “Slow light without electromagnetically induced transparency: the double-Fano resonance approach,” in Quantum Electronics and Laser Science Conference, San Jose, California, USA, 2010, paper QThE7.

G. S. Agarwal, Quantum Statistical Theories of Spontaneous Emission and Their Relation to Other Approaches, G. Hohler, ed., Vol. 70 of Springer Tracts in Modern Physics (Springer-Verlag, 1974), pp. 88–97.

Z. Ficek and S. Swain, Quantum Interference and Coherence: Theory and Experiments, W. T. Rhodes, ed., Vol. 100 of Springer Series in Optical Sciences (Springer, 2005), pp. 139–177.

E. Arimondo, Progress in Optics, E. Wolf, ed. (Elsevier, 1996), Vol. 35, pp. 257–354.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1.

Schematic diagram of three straight optical waveguides (represented as |1, |2, and |3) side-coupled with two noninteracting linear waveguide arrays.

Fig. 2.
Fig. 2.

Optical analogue of DFR: (a)–(e) show the variation of normalized decay rates with frequency mismatch (ω˜1). System parameters: (a) n0=3, n0=3, ω˜3=0.15; (b) n0=4, n0=4, ω˜3=0.15; (c) n0=3, n0=4, ω˜3=0.15; (d) n0=4, n0=3, ω˜3=0.15; and (e) n0=3, n0=4, ω˜3=0.1; (f) n0=4, n0=3, ω˜3=0.1. For all graphs κ˜1=κ˜2=0.09, κ˜1=κ˜3=0.1, ω˜2=0.1. The initial boundary condition: c1(0)=1, c2(0)=0, c3(0)=0.

Fig. 3.
Fig. 3.

Optical analogue of single Fano resonance: (a) and (b) shows the variation of normalized decay rates with frequency mismatch (ω˜1). System parameters: κ˜1=κ˜2=0.09, κ˜1=κ˜3=0.1, ω˜2=0.1, ω˜3=0.15. The initial boundary condition: c1(0)=0, c2(0)=1, c3(0)=0.

Fig. 4.
Fig. 4.

Occurrence of optical trapping with the initial boundary condition, c1(0)=1, c2(0)=0, c3(0)=0. Fractional powers in side waveguides are plotted against the normalized propagation distance (ξ). Solid, dashed, and dotted curves stand for fractional power in |1, |2, and |3, respectively. System parameters: n0=3, ω˜0=0.5, κ˜0=0.09.

Fig. 5.
Fig. 5.

Occurrence of optical trapping with the initial boundary condition, c1(0)=0, c2(0)=1, c3(0)=0. The system parameters are same as Fig. 4.

Equations (18)

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

H=H0+Hint,
|ψ=nbn|n+mam|m+ρ=1,2,3cρ|ρ.
ib˙n=(bn+1+bn1)ρ=1,2(κ˜1δρ,1+κ˜2δρ,2)δn,nρcρ,
ia˙m=(am+1+am1)ρ=1,3(κ˜1δρ,1+κ˜3δρ,3)δm,mρcρ,
ic˙ρ=(κ˜1δρ,1+κ˜2δρ,2)bnρ(κ˜1δρ,1+κ˜3δρ,3)amρ+2ω˜ρcρ,
c˙1=(Λ˜11+Λ˜11+2iω˜1)c1Λ˜12c2Λ˜13c3,
c˙2=Λ˜21c1(Λ˜22+2iω˜2)c2,
c˙3=Λ˜31c1(Λ˜33+2iω˜3)c3,
Λ˜pq=i|npnq|κ˜pκ˜q2((1ω˜q2)1/2+iω˜q)|npnq|(1ω˜q2)1/2,
Λ˜pq=i|npnq|κ˜pκ˜q2((1ω˜q2)1/2+iω˜q)|npnq|(1ω˜q2)1/2,
ΛN=Re[Λ](Λ˜11+Λ˜11)=1Re[1(Λ˜11+Λ˜11)(Λ˜12Λ˜21Λ˜22+i2(ω˜2ω˜1)+Λ˜13Λ˜31Λ˜33+i2(ω˜3ω˜1))].
ΛN=Re[Λ]Λ˜22=1Re[Λ˜12Λ˜21Λ˜22(δi2ω˜2)],
c1(ξ)=(1/f)exp[(3Λ˜s+4iω˜0)ξ/2][fcosh(Λ˜sfξ/2)sinh(Λ˜sfξ/2)],
c2(ξ)=c3(ξ)=(2f0/f)exp[(3Λ˜s+4iω˜0)ξ/2]sinh(Λ˜sfξ/2).
c1(ξ)=(2f0/f)exp[(3Λ˜s+4iω˜0)ξ/2]sinh(Λ˜sfξ/2),
c2(ξ)=(1/2f)exp[(3Λ˜s+4iω˜0)ξ/2][fcosh(Λ˜sfξ/2)+sinh(Λ˜sfξ/2)]+(1/2)exp[(Λ˜s+2iω˜0)ξ],
c3(ξ)=(1/2f)exp[(3Λ˜s+4iω˜0)ξ/2][fcosh(Λ˜sfξ/2)+sinh(Λ˜sfξ/2)](1/2)exp[(Λ˜s+2iω˜0)ξ],
M¯=(2Λ˜s+i2ω˜0Λ˜mΛ˜mΛ˜mΛ˜s+i2ω˜00Λ˜m0Λ˜s+i2ω˜0)

Metrics