Abstract

We study a critically coupled system [Opt. Lett. 32, 1483 (2007)] with a Kerr nonlinear spacer layer. Nonlinearity is shown to inhibit null scattering in a critically coupled system at low powers. However, a system detuned from critical coupling can exhibit near-complete suppression of scattering by means of nonlinearity-induced changes in refractive index. Our studies reveal clearly an important aspect of critical coupling as a delicate balance in both the amplitude and the phase relations, while a nonlinear resonance in dispersive bistability concerns only the phase.

© 2013 Optical Society of America

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  1. M. Cai, O. Painter, and K. J. Vahala, Phys. Rev. Lett. 85, 74 (2000).
    [CrossRef]
  2. J. R. Tischler, M. S. Bradley, and V. Bulovic, Opt. Lett. 31, 2045 (2006).
    [CrossRef]
  3. S. Dutta Gupta, Opt. Lett. 32, 1483 (2007).
    [CrossRef]
  4. S. Deb, S. Dutta-Gupta, J. Banerji, and S. Dutta Gupta, J. Opt. A 9, 555 (2007).
    [CrossRef]
  5. S. Balci, C. Kocabas, and A. Aydinli, Opt. Lett. 36, 2770 (2011).
    [CrossRef]
  6. W. Wan, Y. D. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, Science 331, 889 (2011).
    [CrossRef]
  7. S. Dutta-Gupta, O. J. F. Martin, S. Dutta Gupta, and G. S. Agarwal, Opt. Express 20, 1330 (2012).
    [CrossRef]
  8. S. Longhi, Phys. Rev. A 82, 031801 (2010).
  9. S. Dutta Gupta, in Guided Wave Optics and Photonic Devices, S. Bhadra and A. Ghatak, eds. (CRC Press, 2013), Chap. 18, pp. 463–482.
  10. M. K. Hedayati, M. Javaherirahim, B. Mozooni, R. Abdelaziz, A. Tavassolizadeh, V. S. K. Chakravadhanula, V. Zaporojtchenko, T. Strunkus, F. Faupel, and M. Elbahri, Adv. Mater. 23, 5410 (2011).
  11. J. H. Chow, M. A. Taylor, T. T.-Y. Lam, J. Knittel, J. D. S. Rickson, D. A. Shaddock, M. B. Gray, D. E. McClelland, and W. P. Bowen, Opt. Express 20, 12622 (2012).
    [CrossRef]
  12. S. Dutta-Gupta, R. Deshmukh, A. V. Gopal, O. J. F. Martin, and S. Dutta Gupta, Opt. Lett. 37, 4452 (2012).
    [CrossRef]
  13. G. S. Agarwal and S. Huang, arXiv:1304.7323 [quant-ph].
  14. J.-T. Shen and S. Fan, Phys. Rev. A 82, 021802 (2010).
  15. S. Longhi, Phys. Rev. A 83, 055804 (2011).
    [CrossRef]
  16. S. Longhi, Phys. Rev. Lett. 107, 033901 (2011).
    [CrossRef]
  17. S. Longhi and G. della Valle, Phys. Rev. A 85, 053838 (2012).
    [CrossRef]
  18. Y. Zheng, H. Ren, W. Wan, and X. Chen, arXiv:1301.2882 [physics.optics].
  19. S. Dutta Gupta, Nonlinear Optics of Stratified Media, E. Wolf, ed., Vol. 38 of Progress in Optics (Elsevier, 1998), p. 1.
  20. S. Dutta Gupta and G. S. Agarwal, J. Opt. Soc. Am. B 4, 691 (1987).
    [CrossRef]
  21. S. Dutta Gupta and G. S. Agarwal, J. Opt. Soc. Am. B 3, 236 (1986).
    [CrossRef]
  22. G. S. Agarwal and S. Dutta Gupta, Phys. Rev. B 34, 5239 (1986).
    [CrossRef]
  23. M. B. Pande and S. Dutta Gupta, Opt. Lett. 15, 944 (1990).
    [CrossRef]
  24. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998), p. 369.
  25. P. B. Johnson and W. Christy, Phys. Rev. B 6, 4370 (1972).
    [CrossRef]
  26. S. Dutta Gupta and D. S. Ray, Phys. Rev. B 41, 8048 (1990).
  27. J. H. Marburger and F. S. Felber, Phys. Rev. A 17, 335 (1978).
    [CrossRef]
  28. M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999), Chap. 1.

2012

2011

S. Balci, C. Kocabas, and A. Aydinli, Opt. Lett. 36, 2770 (2011).
[CrossRef]

W. Wan, Y. D. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, Science 331, 889 (2011).
[CrossRef]

M. K. Hedayati, M. Javaherirahim, B. Mozooni, R. Abdelaziz, A. Tavassolizadeh, V. S. K. Chakravadhanula, V. Zaporojtchenko, T. Strunkus, F. Faupel, and M. Elbahri, Adv. Mater. 23, 5410 (2011).

S. Longhi, Phys. Rev. A 83, 055804 (2011).
[CrossRef]

S. Longhi, Phys. Rev. Lett. 107, 033901 (2011).
[CrossRef]

2010

S. Longhi, Phys. Rev. A 82, 031801 (2010).

J.-T. Shen and S. Fan, Phys. Rev. A 82, 021802 (2010).

2007

S. Deb, S. Dutta-Gupta, J. Banerji, and S. Dutta Gupta, J. Opt. A 9, 555 (2007).
[CrossRef]

S. Dutta Gupta, Opt. Lett. 32, 1483 (2007).
[CrossRef]

2006

2000

M. Cai, O. Painter, and K. J. Vahala, Phys. Rev. Lett. 85, 74 (2000).
[CrossRef]

1990

M. B. Pande and S. Dutta Gupta, Opt. Lett. 15, 944 (1990).
[CrossRef]

S. Dutta Gupta and D. S. Ray, Phys. Rev. B 41, 8048 (1990).

1987

1986

S. Dutta Gupta and G. S. Agarwal, J. Opt. Soc. Am. B 3, 236 (1986).
[CrossRef]

G. S. Agarwal and S. Dutta Gupta, Phys. Rev. B 34, 5239 (1986).
[CrossRef]

1978

J. H. Marburger and F. S. Felber, Phys. Rev. A 17, 335 (1978).
[CrossRef]

1972

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

Abdelaziz, R.

M. K. Hedayati, M. Javaherirahim, B. Mozooni, R. Abdelaziz, A. Tavassolizadeh, V. S. K. Chakravadhanula, V. Zaporojtchenko, T. Strunkus, F. Faupel, and M. Elbahri, Adv. Mater. 23, 5410 (2011).

Agarwal, G. S.

Aydinli, A.

Balci, S.

Banerji, J.

S. Deb, S. Dutta-Gupta, J. Banerji, and S. Dutta Gupta, J. Opt. A 9, 555 (2007).
[CrossRef]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998), p. 369.

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999), Chap. 1.

Bowen, W. P.

Bradley, M. S.

Bulovic, V.

Cai, M.

M. Cai, O. Painter, and K. J. Vahala, Phys. Rev. Lett. 85, 74 (2000).
[CrossRef]

Cao, H.

W. Wan, Y. D. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, Science 331, 889 (2011).
[CrossRef]

Chakravadhanula, V. S. K.

M. K. Hedayati, M. Javaherirahim, B. Mozooni, R. Abdelaziz, A. Tavassolizadeh, V. S. K. Chakravadhanula, V. Zaporojtchenko, T. Strunkus, F. Faupel, and M. Elbahri, Adv. Mater. 23, 5410 (2011).

Chen, X.

Y. Zheng, H. Ren, W. Wan, and X. Chen, arXiv:1301.2882 [physics.optics].

Chong, Y. D.

W. Wan, Y. D. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, Science 331, 889 (2011).
[CrossRef]

Chow, J. H.

Christy, W.

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

Deb, S.

S. Deb, S. Dutta-Gupta, J. Banerji, and S. Dutta Gupta, J. Opt. A 9, 555 (2007).
[CrossRef]

della Valle, G.

S. Longhi and G. della Valle, Phys. Rev. A 85, 053838 (2012).
[CrossRef]

Deshmukh, R.

Dutta Gupta, S.

S. Dutta-Gupta, R. Deshmukh, A. V. Gopal, O. J. F. Martin, and S. Dutta Gupta, Opt. Lett. 37, 4452 (2012).
[CrossRef]

S. Dutta-Gupta, O. J. F. Martin, S. Dutta Gupta, and G. S. Agarwal, Opt. Express 20, 1330 (2012).
[CrossRef]

S. Dutta Gupta, Opt. Lett. 32, 1483 (2007).
[CrossRef]

S. Deb, S. Dutta-Gupta, J. Banerji, and S. Dutta Gupta, J. Opt. A 9, 555 (2007).
[CrossRef]

M. B. Pande and S. Dutta Gupta, Opt. Lett. 15, 944 (1990).
[CrossRef]

S. Dutta Gupta and D. S. Ray, Phys. Rev. B 41, 8048 (1990).

S. Dutta Gupta and G. S. Agarwal, J. Opt. Soc. Am. B 4, 691 (1987).
[CrossRef]

S. Dutta Gupta and G. S. Agarwal, J. Opt. Soc. Am. B 3, 236 (1986).
[CrossRef]

G. S. Agarwal and S. Dutta Gupta, Phys. Rev. B 34, 5239 (1986).
[CrossRef]

S. Dutta Gupta, Nonlinear Optics of Stratified Media, E. Wolf, ed., Vol. 38 of Progress in Optics (Elsevier, 1998), p. 1.

S. Dutta Gupta, in Guided Wave Optics and Photonic Devices, S. Bhadra and A. Ghatak, eds. (CRC Press, 2013), Chap. 18, pp. 463–482.

Dutta-Gupta, S.

Elbahri, M.

M. K. Hedayati, M. Javaherirahim, B. Mozooni, R. Abdelaziz, A. Tavassolizadeh, V. S. K. Chakravadhanula, V. Zaporojtchenko, T. Strunkus, F. Faupel, and M. Elbahri, Adv. Mater. 23, 5410 (2011).

Fan, S.

J.-T. Shen and S. Fan, Phys. Rev. A 82, 021802 (2010).

Faupel, F.

M. K. Hedayati, M. Javaherirahim, B. Mozooni, R. Abdelaziz, A. Tavassolizadeh, V. S. K. Chakravadhanula, V. Zaporojtchenko, T. Strunkus, F. Faupel, and M. Elbahri, Adv. Mater. 23, 5410 (2011).

Felber, F. S.

J. H. Marburger and F. S. Felber, Phys. Rev. A 17, 335 (1978).
[CrossRef]

Ge, L.

W. Wan, Y. D. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, Science 331, 889 (2011).
[CrossRef]

Gopal, A. V.

Gray, M. B.

Hedayati, M. K.

M. K. Hedayati, M. Javaherirahim, B. Mozooni, R. Abdelaziz, A. Tavassolizadeh, V. S. K. Chakravadhanula, V. Zaporojtchenko, T. Strunkus, F. Faupel, and M. Elbahri, Adv. Mater. 23, 5410 (2011).

Huang, S.

G. S. Agarwal and S. Huang, arXiv:1304.7323 [quant-ph].

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998), p. 369.

Javaherirahim, M.

M. K. Hedayati, M. Javaherirahim, B. Mozooni, R. Abdelaziz, A. Tavassolizadeh, V. S. K. Chakravadhanula, V. Zaporojtchenko, T. Strunkus, F. Faupel, and M. Elbahri, Adv. Mater. 23, 5410 (2011).

Johnson, P. B.

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

Knittel, J.

Kocabas, C.

Lam, T. T.-Y.

Longhi, S.

S. Longhi and G. della Valle, Phys. Rev. A 85, 053838 (2012).
[CrossRef]

S. Longhi, Phys. Rev. Lett. 107, 033901 (2011).
[CrossRef]

S. Longhi, Phys. Rev. A 83, 055804 (2011).
[CrossRef]

S. Longhi, Phys. Rev. A 82, 031801 (2010).

Marburger, J. H.

J. H. Marburger and F. S. Felber, Phys. Rev. A 17, 335 (1978).
[CrossRef]

Martin, O. J. F.

McClelland, D. E.

Mozooni, B.

M. K. Hedayati, M. Javaherirahim, B. Mozooni, R. Abdelaziz, A. Tavassolizadeh, V. S. K. Chakravadhanula, V. Zaporojtchenko, T. Strunkus, F. Faupel, and M. Elbahri, Adv. Mater. 23, 5410 (2011).

Noh, H.

W. Wan, Y. D. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, Science 331, 889 (2011).
[CrossRef]

Painter, O.

M. Cai, O. Painter, and K. J. Vahala, Phys. Rev. Lett. 85, 74 (2000).
[CrossRef]

Pande, M. B.

Ray, D. S.

S. Dutta Gupta and D. S. Ray, Phys. Rev. B 41, 8048 (1990).

Ren, H.

Y. Zheng, H. Ren, W. Wan, and X. Chen, arXiv:1301.2882 [physics.optics].

Rickson, J. D. S.

Shaddock, D. A.

Shen, J.-T.

J.-T. Shen and S. Fan, Phys. Rev. A 82, 021802 (2010).

Stone, A. D.

W. Wan, Y. D. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, Science 331, 889 (2011).
[CrossRef]

Strunkus, T.

M. K. Hedayati, M. Javaherirahim, B. Mozooni, R. Abdelaziz, A. Tavassolizadeh, V. S. K. Chakravadhanula, V. Zaporojtchenko, T. Strunkus, F. Faupel, and M. Elbahri, Adv. Mater. 23, 5410 (2011).

Tavassolizadeh, A.

M. K. Hedayati, M. Javaherirahim, B. Mozooni, R. Abdelaziz, A. Tavassolizadeh, V. S. K. Chakravadhanula, V. Zaporojtchenko, T. Strunkus, F. Faupel, and M. Elbahri, Adv. Mater. 23, 5410 (2011).

Taylor, M. A.

Tischler, J. R.

Vahala, K. J.

M. Cai, O. Painter, and K. J. Vahala, Phys. Rev. Lett. 85, 74 (2000).
[CrossRef]

Wan, W.

W. Wan, Y. D. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, Science 331, 889 (2011).
[CrossRef]

Y. Zheng, H. Ren, W. Wan, and X. Chen, arXiv:1301.2882 [physics.optics].

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999), Chap. 1.

Zaporojtchenko, V.

M. K. Hedayati, M. Javaherirahim, B. Mozooni, R. Abdelaziz, A. Tavassolizadeh, V. S. K. Chakravadhanula, V. Zaporojtchenko, T. Strunkus, F. Faupel, and M. Elbahri, Adv. Mater. 23, 5410 (2011).

Zheng, Y.

Y. Zheng, H. Ren, W. Wan, and X. Chen, arXiv:1301.2882 [physics.optics].

Adv. Mater.

M. K. Hedayati, M. Javaherirahim, B. Mozooni, R. Abdelaziz, A. Tavassolizadeh, V. S. K. Chakravadhanula, V. Zaporojtchenko, T. Strunkus, F. Faupel, and M. Elbahri, Adv. Mater. 23, 5410 (2011).

J. Opt. A

S. Deb, S. Dutta-Gupta, J. Banerji, and S. Dutta Gupta, J. Opt. A 9, 555 (2007).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Express

Opt. Lett.

Phys. Rev. A

S. Longhi, Phys. Rev. A 82, 031801 (2010).

J.-T. Shen and S. Fan, Phys. Rev. A 82, 021802 (2010).

S. Longhi, Phys. Rev. A 83, 055804 (2011).
[CrossRef]

S. Longhi and G. della Valle, Phys. Rev. A 85, 053838 (2012).
[CrossRef]

J. H. Marburger and F. S. Felber, Phys. Rev. A 17, 335 (1978).
[CrossRef]

Phys. Rev. B

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

S. Dutta Gupta and D. S. Ray, Phys. Rev. B 41, 8048 (1990).

G. S. Agarwal and S. Dutta Gupta, Phys. Rev. B 34, 5239 (1986).
[CrossRef]

Phys. Rev. Lett.

M. Cai, O. Painter, and K. J. Vahala, Phys. Rev. Lett. 85, 74 (2000).
[CrossRef]

S. Longhi, Phys. Rev. Lett. 107, 033901 (2011).
[CrossRef]

Science

W. Wan, Y. D. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, Science 331, 889 (2011).
[CrossRef]

Other

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998), p. 369.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999), Chap. 1.

Y. Zheng, H. Ren, W. Wan, and X. Chen, arXiv:1301.2882 [physics.optics].

S. Dutta Gupta, Nonlinear Optics of Stratified Media, E. Wolf, ed., Vol. 38 of Progress in Optics (Elsevier, 1998), p. 1.

S. Dutta Gupta, in Guided Wave Optics and Photonic Devices, S. Bhadra and A. Ghatak, eds. (CRC Press, 2013), Chap. 18, pp. 463–482.

G. S. Agarwal and S. Huang, arXiv:1304.7323 [quant-ph].

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Figures (6)

Fig. 1.
Fig. 1.

Schematic view of the layered medium. Background dielectric constant of the nonlinear medium is ϵ2.

Fig. 2.
Fig. 2.

(a) Intensity transmission coefficient T (dashed curve) and total scattering R+T (solid curve) as functions of the wavelength λ for d2=75nm for a linear system. (b) R+T as a function of incident intensity Ui for three different values of λ, namely, 405.5, 407.4, and 409.3 nm, marked by crosses in (a). Corresponding curves are labeled by 1, 2, and 3, respectively. Other parameters are as follows, ϵi=1, ϵh=2.25, f=0.05, d1=10nm, ϵ2=2.6244, N=10, ϵa=5.7121, da=42.88nm, ϵb=2.6244, db=63.72nm, ϵf=2.25.

Fig. 3.
Fig. 3.

(a) Total scattering R+T as a function of λ for d2=165nm (solid curve). (b) R+T as a function of input intensity Ui. Curves labeled by 1, 2, and 3 correspond to increasing wavelengths, namely, 407.4, 414.1, and 420.8 nm, marked by crosses in (a). The dashed curve in (a) is for Ut=1.6×104, which corresponds to the scattering minimum for curve 1 at Ui=0.3292 in (b). Other parameters are as in Fig. 2.

Fig. 4.
Fig. 4.

Same as in Fig. 3 except that now d2=55nm and the system is away from linear CC resonance. The operating wavelengths for curves labeled by 1, 2, and 3 in (b) are now 407.4, 411.2, and 414.9 nm, respectively. The dashed curve in (a) is for Ut=2.93×104, which corresponds to the scattering minimum for curve 1 at Ui=0.5164 in (b).

Fig. 5.
Fig. 5.

(a) Total scattering R+T as a function of λ for f=0.1, d1=60nm, d2=55nm (solid curve). (b) R+T as a function of input intensity Ui. Curves labeled by 1, 2, and 3 correspond to wavelengths 384.0, 393.5, and 427.7 nm, respectively [marked by crosses in the (a)]. The dashed curve in (a) is for Ut=3.6×104, which corresponds to the scattering minimum for curve 2 at Ui=0.1333 in (b). Other parameters are as in Fig. 2.

Fig. 6.
Fig. 6.

Re(E) as a function of z in the composite and the nonlinear layers for two cases of nonlinearity-induced CC, namely (1) minimum of curve 1 in Fig. 4(b) with f=0.05, d1=10nm, d2=55nm, Ui=0.5164 (Ut=2.93×104); (2) minimum of curve 2 in Fig. 5(b) f=0.1, d1=60nm, d2=55nm, Ui=0.1333 (Ut=3.6×104). Vertical lines demarcate the interfaces, dotted (dashed) line for case 1 (case 2). Other parameters are as in Fig. 2.

Equations (5)

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

ϵ1(ω)=ϵh+fx(ϵmϵh)1+f(x1),x=3ϵhϵm+2ϵh,
k±=k0ϵ2(1+U±+2U)1/2,
(U+U)=|(11k+k0kk0)1MDBR(1ϵf)|2Ut,
M=M1×M2×MDBR,
Ui=Ut/T.

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