Abstract

Berry showed that a quantum system, upon an excursion around a closed path in phase space, can lead to a geometric phase. The polarization state of light in a fiber is a classical analog that is called the Pancharantnam phase. While most experiments have focused on esoteric issues, I show that, in theory, Berry’s phase (or Pancharantnam’s phase) can be used to make a position-sensitive acoustical or stress sensor.

© 2002 Optical Society of America

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References

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  1. P. Senthilkumaran, G. Thursby, and B. Culshaw, “Fiber-optic tunable loop mirror using Berry’s geometric phase,” Opt. Lett. 25, 533–535 (2000).
    [CrossRef]
  2. P. Senthilkumaran, G. Thursby, and B. Culshaw, “Fiber-optic Sagnac interferometer for the observation of Berry’s topological phase,” J. Opt. Soc. Am. B 17, 1914–1919 (2000).
    [CrossRef]
  3. M. V. Berry, “Quantal phase factors accompanying adiabatic changes,” Proc. R. Soc. London Ser. A 392, 45–57 (1984).
    [CrossRef]
  4. A. Tomita, “Observation of Berry’s topological phase by use of an optical fiber,” Phys. Rev. Lett. 57, 937–940 (1986).
    [CrossRef] [PubMed]
  5. S. G. Lipson, “Berry’s phase in optical interferometry: a simple derivation,” Opt. Lett. 15, 154–155 (1990).
    [CrossRef] [PubMed]

2000 (2)

1990 (1)

1986 (1)

A. Tomita, “Observation of Berry’s topological phase by use of an optical fiber,” Phys. Rev. Lett. 57, 937–940 (1986).
[CrossRef] [PubMed]

1984 (1)

M. V. Berry, “Quantal phase factors accompanying adiabatic changes,” Proc. R. Soc. London Ser. A 392, 45–57 (1984).
[CrossRef]

Berry, M. V.

M. V. Berry, “Quantal phase factors accompanying adiabatic changes,” Proc. R. Soc. London Ser. A 392, 45–57 (1984).
[CrossRef]

Culshaw, B.

Lipson, S. G.

Senthilkumaran, P.

Thursby, G.

Tomita, A.

A. Tomita, “Observation of Berry’s topological phase by use of an optical fiber,” Phys. Rev. Lett. 57, 937–940 (1986).
[CrossRef] [PubMed]

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Figures (2)

Fig. 1
Fig. 1

(a) Schematic of a double-wound cylinder geometry used for stress detection; (b) parameters used to calculate the response of such a detector.

Fig. 2
Fig. 2

Signal as a function of frequency.

Equations (19)

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r=(ρ cos t)xˆ+(ρ sin t)yˆ+(ηt)zˆ.
dr=[(-ρ sin t)xˆ+(ρ cos t)yˆ+ηzˆ]dt.
γ=-2πN1-η(ρ2+η2)1/2.
dγ=-2πNηρ(ρ2+η2)3/2 dρ-ρ2(ρ2+η2)3/2 dη.
I=I0 cos2(ϕ+dγ).
I=I0[cos2 ϕ-sin(2ϕ)dγ-cos(2ϕ)(dγ)2].
nΛc2πΩ.
dγ=dγ0{sin[Ω(t-τ1)]-sin[Ω(t-τ2)]},
I=I02 1+2γ0 sinΩΔτ2cosΩt-τ2.
IΩ=I0γ0 sinΩΔτ2.
x=L+l2-πncΩn,
dγ|dη=0=-2πN n/ρ[1+(η/ρ)2]3/2 dρρ,
dγ|dρ=0=2πN η/ρ[1+(η/ρ)2]3/2 dηη;
s(ξ)=ξ(1+ξ2)3/2,
smax=s(1/2)=239=0.385.
dγmax|dη=0=-2πN 239 dρρ
Λ=2πηN=2πρξN.
dγmax|dη=0=Λρ dρρ.
ηρ=12.

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