Abstract

We report the realization of a three-path Mach–Zehnder interferometer using single-mode fibers and two integrated 3 × 3 fiber couplers. We observed enhanced phase sensitivity, as compared with two-path interferometers, with a visibility of the interference pattern of more than 97%. This interferometer has an analog in two-photon interferometry, and we believe it to be the first nontrivial example of N × N multiport interferometers.

© 1996 Optical Society of America

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  1. M. Reck, A. Zeilinger, H. Bernstein, P. BertaniPhys. Rev. Lett. 73, 58 (1994).
    [CrossRef] [PubMed]
  2. P. D. Townsend, J. G. Rarity, P. R. TapsterElectron. Lett. 29, 634 (1993);P. R. Tapster, J. G. Rarity, P. C. M. OwensPhys. Rev. Lett. 73, 1923 (1994).
    [CrossRef]
  3. P. HariharanOptical Interferometry (Academic, San Diego, Calif., 1985).
  4. 3 × 3 couplers have been used for the demodulation of orthogonal interferometer signals in fiber gyros [Ref. 7 and J. H. JaJ. Mod. Opt. 42, 117 (1995)]and some other sensor applications [R. FuestTech. Messen 58152 (1991);O. B. WrightOpt. Lett. 16, 56 (1991)].
    [CrossRef]
  5. K. Mattle, M. Michler, H. Weinfurter, A. Zeilinger, M. ZukowskiAppl. Phys. B 60, S111 (1995).
  6. A. Zeilinger, M. Zukowski, M. A. Horne, H. J. Bernstein, D. M. Greenbergerin Proceedings of the Adriatico Workshop on Quantum Interferometry,F. De Martini, G. Denardo, A. Zeilinger, eds. (World Scientific, Singapore, 1993), p. 159 ; M. Reck, A. Zeilingerin Proceedings of the Adriatico Workshop on Quantum Interferometry, F. De Martini, G. Denardo, A. Zeilinger, eds. (World Scientific, Singapore, 1993), p. 170.
  7. S. K. SheemJ. Appl. Phys. 52, 3865 (1981).
    [CrossRef]
  8. R. Ulrich, S. C. Rashleigh, W. EickhoffOpt. Lett. 5, 273 (1980).
    [CrossRef] [PubMed]
  9. R. M. A. Azzam, N. M. BasharaEllipsometry and Polarized Light (North-Holland, Amsterdam, 1977).

1995

3 × 3 couplers have been used for the demodulation of orthogonal interferometer signals in fiber gyros [Ref. 7 and J. H. JaJ. Mod. Opt. 42, 117 (1995)]and some other sensor applications [R. FuestTech. Messen 58152 (1991);O. B. WrightOpt. Lett. 16, 56 (1991)].
[CrossRef]

K. Mattle, M. Michler, H. Weinfurter, A. Zeilinger, M. ZukowskiAppl. Phys. B 60, S111 (1995).

1994

M. Reck, A. Zeilinger, H. Bernstein, P. BertaniPhys. Rev. Lett. 73, 58 (1994).
[CrossRef] [PubMed]

1993

P. D. Townsend, J. G. Rarity, P. R. TapsterElectron. Lett. 29, 634 (1993);P. R. Tapster, J. G. Rarity, P. C. M. OwensPhys. Rev. Lett. 73, 1923 (1994).
[CrossRef]

1981

S. K. SheemJ. Appl. Phys. 52, 3865 (1981).
[CrossRef]

1980

Azzam, R. M. A.

R. M. A. Azzam, N. M. BasharaEllipsometry and Polarized Light (North-Holland, Amsterdam, 1977).

Bashara, N. M.

R. M. A. Azzam, N. M. BasharaEllipsometry and Polarized Light (North-Holland, Amsterdam, 1977).

Bernstein, H.

M. Reck, A. Zeilinger, H. Bernstein, P. BertaniPhys. Rev. Lett. 73, 58 (1994).
[CrossRef] [PubMed]

Bernstein, H. J.

A. Zeilinger, M. Zukowski, M. A. Horne, H. J. Bernstein, D. M. Greenbergerin Proceedings of the Adriatico Workshop on Quantum Interferometry,F. De Martini, G. Denardo, A. Zeilinger, eds. (World Scientific, Singapore, 1993), p. 159 ; M. Reck, A. Zeilingerin Proceedings of the Adriatico Workshop on Quantum Interferometry, F. De Martini, G. Denardo, A. Zeilinger, eds. (World Scientific, Singapore, 1993), p. 170.

Bertani, P.

M. Reck, A. Zeilinger, H. Bernstein, P. BertaniPhys. Rev. Lett. 73, 58 (1994).
[CrossRef] [PubMed]

Eickhoff, W.

Greenberger, D. M.

A. Zeilinger, M. Zukowski, M. A. Horne, H. J. Bernstein, D. M. Greenbergerin Proceedings of the Adriatico Workshop on Quantum Interferometry,F. De Martini, G. Denardo, A. Zeilinger, eds. (World Scientific, Singapore, 1993), p. 159 ; M. Reck, A. Zeilingerin Proceedings of the Adriatico Workshop on Quantum Interferometry, F. De Martini, G. Denardo, A. Zeilinger, eds. (World Scientific, Singapore, 1993), p. 170.

Hariharan, P.

P. HariharanOptical Interferometry (Academic, San Diego, Calif., 1985).

Horne, M. A.

A. Zeilinger, M. Zukowski, M. A. Horne, H. J. Bernstein, D. M. Greenbergerin Proceedings of the Adriatico Workshop on Quantum Interferometry,F. De Martini, G. Denardo, A. Zeilinger, eds. (World Scientific, Singapore, 1993), p. 159 ; M. Reck, A. Zeilingerin Proceedings of the Adriatico Workshop on Quantum Interferometry, F. De Martini, G. Denardo, A. Zeilinger, eds. (World Scientific, Singapore, 1993), p. 170.

Ja, J. H.

3 × 3 couplers have been used for the demodulation of orthogonal interferometer signals in fiber gyros [Ref. 7 and J. H. JaJ. Mod. Opt. 42, 117 (1995)]and some other sensor applications [R. FuestTech. Messen 58152 (1991);O. B. WrightOpt. Lett. 16, 56 (1991)].
[CrossRef]

Mattle, K.

K. Mattle, M. Michler, H. Weinfurter, A. Zeilinger, M. ZukowskiAppl. Phys. B 60, S111 (1995).

Michler, M.

K. Mattle, M. Michler, H. Weinfurter, A. Zeilinger, M. ZukowskiAppl. Phys. B 60, S111 (1995).

Rarity, J. G.

P. D. Townsend, J. G. Rarity, P. R. TapsterElectron. Lett. 29, 634 (1993);P. R. Tapster, J. G. Rarity, P. C. M. OwensPhys. Rev. Lett. 73, 1923 (1994).
[CrossRef]

Rashleigh, S. C.

Reck, M.

M. Reck, A. Zeilinger, H. Bernstein, P. BertaniPhys. Rev. Lett. 73, 58 (1994).
[CrossRef] [PubMed]

Sheem, S. K.

S. K. SheemJ. Appl. Phys. 52, 3865 (1981).
[CrossRef]

Tapster, P. R.

P. D. Townsend, J. G. Rarity, P. R. TapsterElectron. Lett. 29, 634 (1993);P. R. Tapster, J. G. Rarity, P. C. M. OwensPhys. Rev. Lett. 73, 1923 (1994).
[CrossRef]

Townsend, P. D.

P. D. Townsend, J. G. Rarity, P. R. TapsterElectron. Lett. 29, 634 (1993);P. R. Tapster, J. G. Rarity, P. C. M. OwensPhys. Rev. Lett. 73, 1923 (1994).
[CrossRef]

Ulrich, R.

Weinfurter, H.

K. Mattle, M. Michler, H. Weinfurter, A. Zeilinger, M. ZukowskiAppl. Phys. B 60, S111 (1995).

Zeilinger, A.

K. Mattle, M. Michler, H. Weinfurter, A. Zeilinger, M. ZukowskiAppl. Phys. B 60, S111 (1995).

M. Reck, A. Zeilinger, H. Bernstein, P. BertaniPhys. Rev. Lett. 73, 58 (1994).
[CrossRef] [PubMed]

A. Zeilinger, M. Zukowski, M. A. Horne, H. J. Bernstein, D. M. Greenbergerin Proceedings of the Adriatico Workshop on Quantum Interferometry,F. De Martini, G. Denardo, A. Zeilinger, eds. (World Scientific, Singapore, 1993), p. 159 ; M. Reck, A. Zeilingerin Proceedings of the Adriatico Workshop on Quantum Interferometry, F. De Martini, G. Denardo, A. Zeilinger, eds. (World Scientific, Singapore, 1993), p. 170.

Zukowski, M.

K. Mattle, M. Michler, H. Weinfurter, A. Zeilinger, M. ZukowskiAppl. Phys. B 60, S111 (1995).

A. Zeilinger, M. Zukowski, M. A. Horne, H. J. Bernstein, D. M. Greenbergerin Proceedings of the Adriatico Workshop on Quantum Interferometry,F. De Martini, G. Denardo, A. Zeilinger, eds. (World Scientific, Singapore, 1993), p. 159 ; M. Reck, A. Zeilingerin Proceedings of the Adriatico Workshop on Quantum Interferometry, F. De Martini, G. Denardo, A. Zeilinger, eds. (World Scientific, Singapore, 1993), p. 170.

Appl. Phys. B

K. Mattle, M. Michler, H. Weinfurter, A. Zeilinger, M. ZukowskiAppl. Phys. B 60, S111 (1995).

Electron. Lett.

P. D. Townsend, J. G. Rarity, P. R. TapsterElectron. Lett. 29, 634 (1993);P. R. Tapster, J. G. Rarity, P. C. M. OwensPhys. Rev. Lett. 73, 1923 (1994).
[CrossRef]

J. Appl. Phys.

S. K. SheemJ. Appl. Phys. 52, 3865 (1981).
[CrossRef]

J. Mod. Opt.

3 × 3 couplers have been used for the demodulation of orthogonal interferometer signals in fiber gyros [Ref. 7 and J. H. JaJ. Mod. Opt. 42, 117 (1995)]and some other sensor applications [R. FuestTech. Messen 58152 (1991);O. B. WrightOpt. Lett. 16, 56 (1991)].
[CrossRef]

Opt. Lett.

Phys. Rev. Lett.

M. Reck, A. Zeilinger, H. Bernstein, P. BertaniPhys. Rev. Lett. 73, 58 (1994).
[CrossRef] [PubMed]

Other

P. HariharanOptical Interferometry (Academic, San Diego, Calif., 1985).

R. M. A. Azzam, N. M. BasharaEllipsometry and Polarized Light (North-Holland, Amsterdam, 1977).

A. Zeilinger, M. Zukowski, M. A. Horne, H. J. Bernstein, D. M. Greenbergerin Proceedings of the Adriatico Workshop on Quantum Interferometry,F. De Martini, G. Denardo, A. Zeilinger, eds. (World Scientific, Singapore, 1993), p. 159 ; M. Reck, A. Zeilingerin Proceedings of the Adriatico Workshop on Quantum Interferometry, F. De Martini, G. Denardo, A. Zeilinger, eds. (World Scientific, Singapore, 1993), p. 170.

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Figures (4)

Fig. 1
Fig. 1

Schematic of an N-path interferometer. ( E 1 in , E 2 in , E N in ) are the electric-field amplitudes at the input modes of the first N × N beam splitter (multiport), and ( E 1 out , E 2 out , E N out ) are the output amplitudes of the second one. The multiports are described by the matrices T N ( 1 ) and T N ( 2 ). ϕ1, ϕ2, … ϕN are the phases accumulated by the fields on their paths between the multiports.

Fig. 2
Fig. 2

Schematic of our three-path interferometer setup. The tritters are three-way integrated fiber couplers. Polarization controllers were used to adjust the polarization manually in all three arms for maximal visibility. Piezo tubes were used to modulate the interferometer phases ϕ and χ in two of the three interferometer arms. The pho-todiode signals and the driving signals were recorded in a digital storage oscilloscope.

Fig. 3
Fig. 3

Experimental data as gray-scale plots (minimum, white; maximum, black) of the measured intensities I1I3 (see Fig. 2) as functions of the voltages applied to the phase shifters (left column). The corresponding theoretical functions given by Eq. (3) are shown in the right column. The phase axes were calibrated by separate measurements with one arm of the interferometer disconnected. The experimental data show only slightly reduced visibility, resulting in smaller white areas in the plot compared with the theoretical calculation.

Fig. 4
Fig. 4

Diagonal cut through the three-dimensional plots reveals the typical structure of a three-path interferometer with two peaks in each 2π phase interval. The higher phase sensitivity stems from the fact that the resulting peaks are thus steeper than the sinusoidal signal of a two-path interferometer. The diagonal phase-space cuts show a lower visibility than the total interference patterns since the absolute minima and maxima are not exactly on the diagonal line (see Fig. 3). This is due to slight differences in the transmissions of the three interferometer arms. Again, the experimental data compare well with theoretical predictions.

Equations (6)

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T = 1 3 [ 1 1 1 1 exp ( i 2 π 3 ) exp ( i 4 π 3 ) 1 exp ( i 4 π 3 ) exp ( i 2 π 3 ) ] .
M = T P T = T [ exp ( i ϕ 1 ) 0 0 0 exp ( i ϕ 2 ) 0 0 0 exp ( i ϕ 3 ) ] T .
I n = | E n out | 2 = I 0 / 9 [ 3 + 2 cos ( ϕ 1 ϕ 2 + θ n ) + 2 cos ( ϕ 2 ϕ 3 + θ n ) + 2 cos ( ϕ 3 ϕ 1 + θ n ) ] ,
P = [ t 1 0 0 0 t 2 exp ( i φ ) 0 0 0 t 3 exp ( i χ ) ] ,
I n = I 0 / 9 [ t 1 2 + t 2 2 + t 3 2 + 2 t 2 cos ( φ + θ n ) + 2 t 3 cos ( χ + θ n ) + 2 t 2 t 3 cos ( φ χ + θ n ) ] .
S = 1 I 0 | d I d φ | ,

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