Abstract

A polarization-based tunable interferometric filter essentially consisting of a two-beam interferometer with birefringence elements is described. The analysis of the filter is done through the concept of a geometric phase in optics—namely, the Pancharatnam phase. The transmission characteristics of the filter can be controlled through three parameters: the thickness of the birefringent elements, the optical path difference, and the orientation angle of an analyzer placed at the interferometer output. It is demonstrated theoretically that, with a particular choice of these parameters, the chromatic dispersion of the filter is compensated in a given spectral range. Some properties of the device are confirmed by an experimental demonstration.

© 1998 Optical Society of America

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References

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  1. Y. Bao, K. Hsu, C. M. Miller, “Polarization-maintaining fiber Fabry–Perot tunable filters,” Opt. Lett. 19, 2098–2100 (1994).
    [CrossRef] [PubMed]
  2. H. D. Ford, R. P. Tatam, “Polarization-based optical fiber wavelength filters,” J. Lightwave Technol. 13, 1435–1444 (1995).
    [CrossRef]
  3. A. Ezbiri, R. P. Tatam, “Passive signal processing for a miniature Fabry–Perot interferometric sensor with a multimode laser-diode source,” Opt. Lett. 20, 1818–1820 (1995).
    [CrossRef] [PubMed]
  4. H. D. Ford, R. P. Tatam, “Multiplexed sensor network employing birefringent-fibre WDMs,” Opt. Commun. 131, 290–294 (1996).
    [CrossRef]
  5. Yu. V. Troitski, “Dispersion-free, multiple beam interferometer,” Appl. Opt. 34, 4717–4722 (1995).
    [CrossRef] [PubMed]
  6. H. Haidner, “Artificial dielectrics designed as wavelength filters,” Opt. Commun. 130, 219–224 (1996).
    [CrossRef]
  7. S. S. Wang, R. Magnusson, “Design of waveguide-grating filters with symmetrical line shapes and low sidebands,” Opt. Lett. 19, 919–921 (1994).
    [CrossRef] [PubMed]
  8. L. B. Jeunhomme, Single-mode Fiber Optics (Dekker, New York, 1990), p. 7.
  9. S. Pancharatnam, “Generalized theory of interference, and its applications,” Proc. Ind. Acad. Sci. A44, 247–262 (1956).
  10. B. Hils, E. Frins, W. Dultz, W. Martienssen, “A polarizing interferometer with wide range varying dispersion due to Pancharatnam’s geometrical phase,” in 17th Congress of the International Commission for Optics: Optics for Science and New Technology, J.-S. Chang, J.-H. Lee, C.-H. Nam, eds., Proc. SPIE2778, 769–770 (1996).
  11. W. G. Driscoll, ed., Handbook of Optics (McGraw-Hill, New York, 1978), Table 15.
  12. H. Schmitzer, S. Klein, W. Dultz, “Nonlinearity of Pancharatnam’s topological phase,” Phys. Rev. Lett. 71, 1530–1533 (1993).
    [CrossRef] [PubMed]
  13. S. Klein, H. H. Wills Laboratory, Bristol University, UK (personal communication, 1996).

1996 (2)

H. D. Ford, R. P. Tatam, “Multiplexed sensor network employing birefringent-fibre WDMs,” Opt. Commun. 131, 290–294 (1996).
[CrossRef]

H. Haidner, “Artificial dielectrics designed as wavelength filters,” Opt. Commun. 130, 219–224 (1996).
[CrossRef]

1995 (3)

1994 (2)

1993 (1)

H. Schmitzer, S. Klein, W. Dultz, “Nonlinearity of Pancharatnam’s topological phase,” Phys. Rev. Lett. 71, 1530–1533 (1993).
[CrossRef] [PubMed]

1956 (1)

S. Pancharatnam, “Generalized theory of interference, and its applications,” Proc. Ind. Acad. Sci. A44, 247–262 (1956).

Bao, Y.

Dultz, W.

H. Schmitzer, S. Klein, W. Dultz, “Nonlinearity of Pancharatnam’s topological phase,” Phys. Rev. Lett. 71, 1530–1533 (1993).
[CrossRef] [PubMed]

B. Hils, E. Frins, W. Dultz, W. Martienssen, “A polarizing interferometer with wide range varying dispersion due to Pancharatnam’s geometrical phase,” in 17th Congress of the International Commission for Optics: Optics for Science and New Technology, J.-S. Chang, J.-H. Lee, C.-H. Nam, eds., Proc. SPIE2778, 769–770 (1996).

Ezbiri, A.

Ford, H. D.

H. D. Ford, R. P. Tatam, “Multiplexed sensor network employing birefringent-fibre WDMs,” Opt. Commun. 131, 290–294 (1996).
[CrossRef]

H. D. Ford, R. P. Tatam, “Polarization-based optical fiber wavelength filters,” J. Lightwave Technol. 13, 1435–1444 (1995).
[CrossRef]

Frins, E.

B. Hils, E. Frins, W. Dultz, W. Martienssen, “A polarizing interferometer with wide range varying dispersion due to Pancharatnam’s geometrical phase,” in 17th Congress of the International Commission for Optics: Optics for Science and New Technology, J.-S. Chang, J.-H. Lee, C.-H. Nam, eds., Proc. SPIE2778, 769–770 (1996).

Haidner, H.

H. Haidner, “Artificial dielectrics designed as wavelength filters,” Opt. Commun. 130, 219–224 (1996).
[CrossRef]

Hils, B.

B. Hils, E. Frins, W. Dultz, W. Martienssen, “A polarizing interferometer with wide range varying dispersion due to Pancharatnam’s geometrical phase,” in 17th Congress of the International Commission for Optics: Optics for Science and New Technology, J.-S. Chang, J.-H. Lee, C.-H. Nam, eds., Proc. SPIE2778, 769–770 (1996).

Hsu, K.

Jeunhomme, L. B.

L. B. Jeunhomme, Single-mode Fiber Optics (Dekker, New York, 1990), p. 7.

Klein, S.

H. Schmitzer, S. Klein, W. Dultz, “Nonlinearity of Pancharatnam’s topological phase,” Phys. Rev. Lett. 71, 1530–1533 (1993).
[CrossRef] [PubMed]

S. Klein, H. H. Wills Laboratory, Bristol University, UK (personal communication, 1996).

Magnusson, R.

Martienssen, W.

B. Hils, E. Frins, W. Dultz, W. Martienssen, “A polarizing interferometer with wide range varying dispersion due to Pancharatnam’s geometrical phase,” in 17th Congress of the International Commission for Optics: Optics for Science and New Technology, J.-S. Chang, J.-H. Lee, C.-H. Nam, eds., Proc. SPIE2778, 769–770 (1996).

Miller, C. M.

Pancharatnam, S.

S. Pancharatnam, “Generalized theory of interference, and its applications,” Proc. Ind. Acad. Sci. A44, 247–262 (1956).

Schmitzer, H.

H. Schmitzer, S. Klein, W. Dultz, “Nonlinearity of Pancharatnam’s topological phase,” Phys. Rev. Lett. 71, 1530–1533 (1993).
[CrossRef] [PubMed]

Tatam, R. P.

H. D. Ford, R. P. Tatam, “Multiplexed sensor network employing birefringent-fibre WDMs,” Opt. Commun. 131, 290–294 (1996).
[CrossRef]

A. Ezbiri, R. P. Tatam, “Passive signal processing for a miniature Fabry–Perot interferometric sensor with a multimode laser-diode source,” Opt. Lett. 20, 1818–1820 (1995).
[CrossRef] [PubMed]

H. D. Ford, R. P. Tatam, “Polarization-based optical fiber wavelength filters,” J. Lightwave Technol. 13, 1435–1444 (1995).
[CrossRef]

Troitski, Yu. V.

Wang, S. S.

Appl. Opt. (1)

J. Lightwave Technol. (1)

H. D. Ford, R. P. Tatam, “Polarization-based optical fiber wavelength filters,” J. Lightwave Technol. 13, 1435–1444 (1995).
[CrossRef]

Opt. Commun. (2)

H. D. Ford, R. P. Tatam, “Multiplexed sensor network employing birefringent-fibre WDMs,” Opt. Commun. 131, 290–294 (1996).
[CrossRef]

H. Haidner, “Artificial dielectrics designed as wavelength filters,” Opt. Commun. 130, 219–224 (1996).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. Lett. (1)

H. Schmitzer, S. Klein, W. Dultz, “Nonlinearity of Pancharatnam’s topological phase,” Phys. Rev. Lett. 71, 1530–1533 (1993).
[CrossRef] [PubMed]

Proc. Ind. Acad. Sci. (1)

S. Pancharatnam, “Generalized theory of interference, and its applications,” Proc. Ind. Acad. Sci. A44, 247–262 (1956).

Other (4)

B. Hils, E. Frins, W. Dultz, W. Martienssen, “A polarizing interferometer with wide range varying dispersion due to Pancharatnam’s geometrical phase,” in 17th Congress of the International Commission for Optics: Optics for Science and New Technology, J.-S. Chang, J.-H. Lee, C.-H. Nam, eds., Proc. SPIE2778, 769–770 (1996).

W. G. Driscoll, ed., Handbook of Optics (McGraw-Hill, New York, 1978), Table 15.

S. Klein, H. H. Wills Laboratory, Bristol University, UK (personal communication, 1996).

L. B. Jeunhomme, Single-mode Fiber Optics (Dekker, New York, 1990), p. 7.

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Figures (6)

Fig. 1
Fig. 1

Top view of the proposed filter: LS, white-light source; L, lenses; S, rectangular slit; POL, linear polarizer with a horizontal transmission direction; BS, polarization-maintaining beam splitter; BP, birefringent wave plates; M, mirrors; AN, rotatable analyzer; AP, Amici-type direct-vision dispersion prism; C, CCD camera.

Fig. 2
Fig. 2

Representation of the polarization states on the Poincaré sphere. The shaded area is the solid angle Ω. The unit vectors ê 1,2 are parallel to the direction of the fast axes of the birefringent plates.

Fig. 3
Fig. 3

Dependence of the Pancharatnam phase on the angle of the analyzer with respect to the horizontal direction for λ = 490, 514, 530 nm and a plate thickness of D = 125.3 μm.

Fig. 4
Fig. 4

Plots of the transfer functions calculated with Eq. (8) by use of Δl = 12.1 μm and D = 600 μm. At ψ = 0° the transfer function behaves as expected in white-light interference (i.e., a sequence of wavelength-dependent maxima and minima). At ψ = 45° the transfer function is quite flat over a wide region of the spectrum.

Fig. 5
Fig. 5

(a) Evolution of the measured interference pattern when the analyzer is rotated. The picture was constructed from parts (strips) of the interference patterns obtained when the analyzer was rotated by steps of 10° as a function of the wavelength. (b) Predicted evolution of the interference pattern calculated with Eq. (8) by use of Δl = 13.5 μm and D = 125.3 μm.

Fig. 6
Fig. 6

Cuts of Fig. 5(a) at ψ = -90° and at ψ = 0° in the region between 560 and 620 nm. At ψ = -90° band-stop behavior is observed over a relatively wide part of this spectral region, whereas at ψ = 0° the filter behaves as a bandpass filter.

Equations (11)

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

I = I 0 1 + V   cos Δ ϕ ,
c Δ l ,   λ = Δ ϕ + γ λ = 2 π n Δ l λ + γ λ .
γ λ c Δ l - 2 π n Δ l λ 0 + 2 π n Δ l λ 0 2 λ - λ 0 + .
2 ω = 2 π 2 D Δ n λ ,
γ λ ,   2 ψ = - 1 2   Ω ( P ,   P 1 λ ,   P 2 λ ) ,
Ω = - 2   arccos sin 2 2 ω cos 2 ψ + sin 2 2 ψ cos 2 ω 1 - cos 2 2 ψ cos 2 2 ω .
I = I 0 2 1 + cos 2 ψ cos 2 ω 1 + cos Δ ϕ + γ ,
I = I 0 2 1 + cos 2 ψ cos 2 ω + cos Δ ϕ cos 2 ψ + cos 2 ω + sin Δ ϕ sin 2 ω sin 2 ψ .
I = I 0 2 1 + cos Δ ϕ - 2 ω .
Δ ϕ - 2 ω 2 π Δ l - 2 π 2 D B λ - 2 π 2 D A .
Δ l B 2 D ,

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