Abstract

We report Fano resonances in a multimode square glass micropillar resonator; the resonances were obtained by using angle-resolved prism coupling. Our experiments reveal characteristically asymmetric line shapes of high-Q resonances and of detuned low-Q resonances in multimode reflection spectra. The asymmetric resonance line shapes evolve for an approximately π phase within a 0.5° range of reflection angles. We model our observed asymmetric multimode resonances by the far-field interference between a light wave that is evanescently coupled with a high-Q mode orbit and a coherent light wave that is refractively coupled with a detuned low-Q mode orbit.

© 2005 Optical Society of America

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References

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  1. K. J. Vahala, Nature 424, 839 (2003).
    [CrossRef] [PubMed]
  2. A. W. Poon, F. Courvoisier, and R. K. Chang, Opt. Lett. 26, 632 (2001).
    [CrossRef]
  3. H. T. Lee and A. W. Poon, Opt. Lett. 29, 5 (2004).
    [CrossRef] [PubMed]
  4. N. Ma, C. Li, and A. W. Poon, IEEE Photonics Technol. Lett. 16, 2487 (2004).
    [CrossRef]
  5. C. Li and A. W. Poon, Opt. Lett. 30, 546 (2005).
    [CrossRef] [PubMed]
  6. U. Fano, Phys. Rev. 124, 1866 (1961).
    [CrossRef]
  7. S. Fan, Appl. Phys. Lett. 80, 908 (2002).
    [CrossRef]
  8. C. Y. Chao and L. J. Guo, Appl. Phys. Lett. 83, 1527 (2003).
    [CrossRef]
  9. V. Lousse and J. P. Vigneron, Phys. Rev. B 69, 155106 (2004).
    [CrossRef]
  10. W. Liang, Y. Xu, Y. Huang, A. Yariv, J. G. Fleming, and S. Y. Lin, Opt. Express 12, 657 (2004).
    [CrossRef] [PubMed]
  11. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, UK, 1999).
    [CrossRef]

2005 (1)

2004 (4)

N. Ma, C. Li, and A. W. Poon, IEEE Photonics Technol. Lett. 16, 2487 (2004).
[CrossRef]

V. Lousse and J. P. Vigneron, Phys. Rev. B 69, 155106 (2004).
[CrossRef]

H. T. Lee and A. W. Poon, Opt. Lett. 29, 5 (2004).
[CrossRef] [PubMed]

W. Liang, Y. Xu, Y. Huang, A. Yariv, J. G. Fleming, and S. Y. Lin, Opt. Express 12, 657 (2004).
[CrossRef] [PubMed]

2003 (2)

K. J. Vahala, Nature 424, 839 (2003).
[CrossRef] [PubMed]

C. Y. Chao and L. J. Guo, Appl. Phys. Lett. 83, 1527 (2003).
[CrossRef]

2002 (1)

S. Fan, Appl. Phys. Lett. 80, 908 (2002).
[CrossRef]

2001 (1)

1961 (1)

U. Fano, Phys. Rev. 124, 1866 (1961).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, UK, 1999).
[CrossRef]

Chang, R. K.

Chao, C. Y.

C. Y. Chao and L. J. Guo, Appl. Phys. Lett. 83, 1527 (2003).
[CrossRef]

Courvoisier, F.

Fan, S.

S. Fan, Appl. Phys. Lett. 80, 908 (2002).
[CrossRef]

Fano, U.

U. Fano, Phys. Rev. 124, 1866 (1961).
[CrossRef]

Fleming, J. G.

Guo, L. J.

C. Y. Chao and L. J. Guo, Appl. Phys. Lett. 83, 1527 (2003).
[CrossRef]

Huang, Y.

Lee, H. T.

Li, C.

C. Li and A. W. Poon, Opt. Lett. 30, 546 (2005).
[CrossRef] [PubMed]

N. Ma, C. Li, and A. W. Poon, IEEE Photonics Technol. Lett. 16, 2487 (2004).
[CrossRef]

Liang, W.

Lin, S. Y.

Lousse, V.

V. Lousse and J. P. Vigneron, Phys. Rev. B 69, 155106 (2004).
[CrossRef]

Ma, N.

N. Ma, C. Li, and A. W. Poon, IEEE Photonics Technol. Lett. 16, 2487 (2004).
[CrossRef]

Poon, A. W.

Vahala, K. J.

K. J. Vahala, Nature 424, 839 (2003).
[CrossRef] [PubMed]

Vigneron, J. P.

V. Lousse and J. P. Vigneron, Phys. Rev. B 69, 155106 (2004).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, UK, 1999).
[CrossRef]

Xu, Y.

Yariv, A.

Appl. Phys. Lett. (2)

S. Fan, Appl. Phys. Lett. 80, 908 (2002).
[CrossRef]

C. Y. Chao and L. J. Guo, Appl. Phys. Lett. 83, 1527 (2003).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

N. Ma, C. Li, and A. W. Poon, IEEE Photonics Technol. Lett. 16, 2487 (2004).
[CrossRef]

Nature (1)

K. J. Vahala, Nature 424, 839 (2003).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. (1)

U. Fano, Phys. Rev. 124, 1866 (1961).
[CrossRef]

Phys. Rev. B (1)

V. Lousse and J. P. Vigneron, Phys. Rev. B 69, 155106 (2004).
[CrossRef]

Other (1)

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, UK, 1999).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Schematic of the experimental setup: The inset shows two coherently prism-coupled four-bounce ray orbits of a square μ-pillar resonator. n a , air refractive index; n m , dielectric medium refractive index; HWP, half-wave plate; Pol., polarizer; MM Fiber, multimode fiber; Z, MM fiber scanning direction.

Fig. 2
Fig. 2

Measured MM asymmetric resonance line shapes of θ ( a ) 43.98°, (b) 43.84°, (c) 43.80°, (d) 43.68°, (e) 43.48°. int., intensity.

Fig. 3
Fig. 3

(a) Schematic of an evanescently coupled four-bounce ray orbit in a square μ-pillar resonator. The dashed line represents wave-front matching upon a round trip. The dashed arrow represents the surface wave leakage along the resonator sidewall. (b) Schematic of a refractively coupled four-bounce ray orbit in a square μ-pillar resonator.

Fig. 4
Fig. 4

Modeled MM asymmetric resonance line shapes: (a) Φ A Φ B = 0 , (b) Φ A Φ B = 0.5 π , (c) Φ A Φ B = 0.7 π , (d) Φ A Φ B = π , (e) Φ A Φ B = 1.1 π .

Equations (3)

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E A E 0 = r FTIR + ( t FTIR ) 2 exp ( i ϕ A ) exp ( α L ) 1 r FTIR exp ( i ϕ A ) exp ( α L ) ,
E B E 0 = r FP + ( t FP ) 2 r ma exp ( i ϕ B ) exp ( α L ) 1 r FP r ma exp ( i ϕ B ) exp ( α L ) ,
I I 0 = E A E 0 2 + f 2 E B E 0 2 + 2 f E A E 0 E B E 0 cos ( Φ A Φ B ) ,

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