Abstract

Motivated by the recent observation of periodic filter characteristics of an oval-shaped microcavity, we study the possible interference of multiple beams in the far field of a laser-illuminated quadrupolar glass fiber. From numerical ray-tracing simulations we obtain the interference-relevant length-difference spectrum and compare it with data extracted from the experimental filter results. Our analysis reveals that different polygonal cavity modes that are refractively output coupled in the high-curvature region of the fiber contribute to the observed far-field interference.

© 2001 Optical Society of America

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References

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  1. M. C. Gutzwiller, Chaos and Quantum Physics (Springer, New York, 1990).
  2. J. U. Nöckel and A. D. Stone, Nature 385, 45 (1997).
    [CrossRef]
  3. A. W. Poon, P. A. Tick, D. A. Nolan, and R. K. Chang, “Periodic filter characteristics from an oval-shaped microcavity,” submitted to Opt. Lett.
  4. M. V. Berry, Eur. J. Phys. 2, 91 (1981).
    [CrossRef]
  5. J. A. Lock, C. L. Adler, B. R. Stone, and P. D. Zajak, Appl. Opt. 37, 1527 (1998).
    [CrossRef]
  6. N. S. Kapany, Fiber Optics: Principles and Applications (Academic, New York, 1967).
  7. A. W. Snyder and J. D. Love, IEEE Trans. MTT 23, 134 (1975).
    [CrossRef]

1998 (1)

1997 (1)

J. U. Nöckel and A. D. Stone, Nature 385, 45 (1997).
[CrossRef]

1981 (1)

M. V. Berry, Eur. J. Phys. 2, 91 (1981).
[CrossRef]

1975 (1)

A. W. Snyder and J. D. Love, IEEE Trans. MTT 23, 134 (1975).
[CrossRef]

Adler, C. L.

Berry, M. V.

M. V. Berry, Eur. J. Phys. 2, 91 (1981).
[CrossRef]

Chang, R. K.

A. W. Poon, P. A. Tick, D. A. Nolan, and R. K. Chang, “Periodic filter characteristics from an oval-shaped microcavity,” submitted to Opt. Lett.

Gutzwiller, M. C.

M. C. Gutzwiller, Chaos and Quantum Physics (Springer, New York, 1990).

Kapany, N. S.

N. S. Kapany, Fiber Optics: Principles and Applications (Academic, New York, 1967).

Lock, J. A.

Love, J. D.

A. W. Snyder and J. D. Love, IEEE Trans. MTT 23, 134 (1975).
[CrossRef]

Nöckel, J. U.

J. U. Nöckel and A. D. Stone, Nature 385, 45 (1997).
[CrossRef]

Nolan, D. A.

A. W. Poon, P. A. Tick, D. A. Nolan, and R. K. Chang, “Periodic filter characteristics from an oval-shaped microcavity,” submitted to Opt. Lett.

Poon, A. W.

A. W. Poon, P. A. Tick, D. A. Nolan, and R. K. Chang, “Periodic filter characteristics from an oval-shaped microcavity,” submitted to Opt. Lett.

Snyder, A. W.

A. W. Snyder and J. D. Love, IEEE Trans. MTT 23, 134 (1975).
[CrossRef]

Stone, A. D.

J. U. Nöckel and A. D. Stone, Nature 385, 45 (1997).
[CrossRef]

Stone, B. R.

Tick, P. A.

A. W. Poon, P. A. Tick, D. A. Nolan, and R. K. Chang, “Periodic filter characteristics from an oval-shaped microcavity,” submitted to Opt. Lett.

Zajak, P. D.

Appl. Opt. (1)

Eur. J. Phys. (1)

M. V. Berry, Eur. J. Phys. 2, 91 (1981).
[CrossRef]

IEEE Trans. MTT (1)

A. W. Snyder and J. D. Love, IEEE Trans. MTT 23, 134 (1975).
[CrossRef]

Nature (1)

J. U. Nöckel and A. D. Stone, Nature 385, 45 (1997).
[CrossRef]

Other (3)

A. W. Poon, P. A. Tick, D. A. Nolan, and R. K. Chang, “Periodic filter characteristics from an oval-shaped microcavity,” submitted to Opt. Lett.

M. C. Gutzwiller, Chaos and Quantum Physics (Springer, New York, 1990).

N. S. Kapany, Fiber Optics: Principles and Applications (Academic, New York, 1967).

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Figures (4)

Fig. 1
Fig. 1

(a) Schematic setup3 for the filter experiment. Shown is the cross section of the oval-shaped fiber. θi,o are the input and output angles. (b) Typical orbits that contribute to the far-field response; see text.

Fig. 2
Fig. 2

Representative experimental spectrum of Ref.  3. (a) Raw interference data, Jk, plotted as a function of wave vector k; θi=60° and θo=56°. (b) Fourier transform of Jk corresponding to the length-difference spectrum Sl. The strong decay of the peak intensity for lengths l longer than three or four round trips is a characteristic feature.

Fig. 3
Fig. 3

Results of the ray-tracing simulation. (a) Intensity histograms showing the distribution of orbit lengths L˜ versus output angle θo. The gray scale indicates the intensity (black means maximal). The input angle is fixed at θi=60°. (b) Intensity versus orbit length L˜ at a specific detector position (in the magic window) obtained by integration of this histogram over a narrow interval of output angles, 58°<θo<62°. If we neglect external path differences, this quantity is equivalent to the length distribution TL.

Fig. 4
Fig. 4

Theoretical ray-tracing result for the parameters θi=60°, θo=60°, and ϵ=0.1; for details, see text. The axes are as in Fig.  2.

Equations (2)

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Jk=-dLTLexpikL2dlexp-iklSl.
qr=cosχ-n1-n2sin2χ1/2cosχ+n1-n2sin2χ1/2qt=1-qr2,

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