Abstract

A differential-phase decoder (DPD) together with a polarization common-path optical heterodyne interferometer is set up. Based on this interferometric configuration and a novel balanced-detector scheme, the performance of the quantum-noise-limited differential-phase decoder is demonstrated and analyzed. The minimum-detectable differential phase is on the order of 107radHz when a 2.5mW He–Ne laser is used. Verified experimentally, the DPD is immune to the common-phase noise induced by an electro-optic phase modulator or by thermal disturbance within the interferometer. This signifies that the minimum-detectable differential phase can become 108radHz if a 300mW continuous wave laser is employed instead.

© 2008 Optical Society of America

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References

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2006 (2)

2004 (1)

2003 (2)

2002 (1)

2001 (1)

2000 (1)

J. Lawall and E. Kessler, “Michelson interferometry with 10 pm accuracy,” Rev. Sci. Instrum. 71, 2669-2676 (2000).
[CrossRef]

1999 (1)

1997 (2)

1996 (1)

K. X. Sun, M. M. Fejer, E. Gustafson, and R. L. Byer, “Sagnac interferometer for gravitational-wave detection,” Phys. Rev. Lett. 76, 3053-3056 (1996).
[CrossRef] [PubMed]

1993 (1)

1989 (1)

H. A. Bachor and P. T. H. Fisk, “Quantum noise--a limit in photodetection,” Appl. Phys. B: Photophys. Laser Chem. 49, 291-300 (1989).
[CrossRef]

1987 (2)

S. B. Alexander, “Design of wide-band optical heterodyne balanced mixer receivers,” J. Lightwave Technol. 5, 523-537 (1987).
[CrossRef]

J. W. Wagner and J. B. Spicer, “Theoretical noise-limited sensitivity of classical interferometry,” J. Opt. Soc. Am. B 4, 1316-1329 (1987).
[CrossRef]

1986 (1)

R. Stierlin, R. Battig, P. D. Henchoz, and H. P. Weber, “Excess-noise suppression in a fiber-optic balanced heterodyne detection system,” Opt. Quantum Electron. 18, 445-454 (1986).
[CrossRef]

1985 (1)

G. L. Abbas, V. W. S. Chan, and T. G. Yee, “A dual-detector optical heterodyne receiver for local oscillator noise suppression,” J. Lightwave Technol. 3, 1110-1122 (1985).
[CrossRef]

1975 (1)

Abbas, G. L.

G. L. Abbas, V. W. S. Chan, and T. G. Yee, “A dual-detector optical heterodyne receiver for local oscillator noise suppression,” J. Lightwave Technol. 3, 1110-1122 (1985).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, “Multichannel lightwave systems,” in Fiber-Optic Communication Systems (Wiley, 1992), pp. 284-394.

Alexander, S. B.

S. B. Alexander, “Design of wide-band optical heterodyne balanced mixer receivers,” J. Lightwave Technol. 5, 523-537 (1987).
[CrossRef]

Arain, M. A.

Bachor, H. A.

H. A. Bachor and P. T. H. Fisk, “Quantum noise--a limit in photodetection,” Appl. Phys. B: Photophys. Laser Chem. 49, 291-300 (1989).
[CrossRef]

Bachor, H.-A.

Battig, R.

R. Stierlin, R. Battig, P. D. Henchoz, and H. P. Weber, “Excess-noise suppression in a fiber-optic balanced heterodyne detection system,” Opt. Quantum Electron. 18, 445-454 (1986).
[CrossRef]

Beyersdorf, P. T.

Byer, R. L.

Chan, V. W. S.

G. L. Abbas, V. W. S. Chan, and T. G. Yee, “A dual-detector optical heterodyne receiver for local oscillator noise suppression,” J. Lightwave Technol. 3, 1110-1122 (1985).
[CrossRef]

Chou, C.

Cohen, S. C.

Daw, E.

Fejer, M. M.

Fisk, P. T. H.

H. A. Bachor and P. T. H. Fisk, “Quantum noise--a limit in photodetection,” Appl. Phys. B: Photophys. Laser Chem. 49, 291-300 (1989).
[CrossRef]

Fritschel, P.

Gonzalez, G.

Gray, M. B.

Gustafson, E.

K. X. Sun, M. M. Fejer, E. Gustafson, and R. L. Byer, “Sagnac interferometer for gravitational-wave detection,” Phys. Rev. Lett. 76, 3053-3056 (1996).
[CrossRef] [PubMed]

Gustafson, E. K.

Henchoz, P. D.

R. Stierlin, R. Battig, P. D. Henchoz, and H. P. Weber, “Excess-noise suppression in a fiber-optic balanced heterodyne detection system,” Opt. Quantum Electron. 18, 445-454 (1986).
[CrossRef]

Hobbs, P. C. D.

Kessler, E.

J. Lawall and E. Kessler, “Michelson interferometry with 10 pm accuracy,” Rev. Sci. Instrum. 71, 2669-2676 (2000).
[CrossRef]

Lantz, B.

Lawall, J.

J. Lawall and E. Kessler, “Michelson interferometry with 10 pm accuracy,” Rev. Sci. Instrum. 71, 2669-2676 (2000).
[CrossRef]

Lyu, C. W.

McClelland, D. E.

Mitrofanov, O.

Mlejnek, M.

Peng, L. C.

Podoleanu, A. G.

Riza, N. A.

Rong, H.

Rosa, C. C.

Spicer, J. B.

Stierlin, R.

R. Stierlin, R. Battig, P. D. Henchoz, and H. P. Weber, “Excess-noise suppression in a fiber-optic balanced heterodyne detection system,” Opt. Quantum Electron. 18, 445-454 (1986).
[CrossRef]

Stvenson, A. J.

Sun, K. X.

K. X. Sun, M. M. Fejer, E. K. Gustafson, and R. L. Byer, “Balanced heterodyne signal extraction in a postmodulated Sagnac interferometer at low frequency,” Opt. Lett. 22, 1485-1487 (1997).
[CrossRef]

K. X. Sun, M. M. Fejer, E. Gustafson, and R. L. Byer, “Sagnac interferometer for gravitational-wave detection,” Phys. Rev. Lett. 76, 3053-3056 (1996).
[CrossRef] [PubMed]

Teng, H. K.

Tsai, C. C.

Wagner, J. W.

Weber, H. P.

R. Stierlin, R. Battig, P. D. Henchoz, and H. P. Weber, “Excess-noise suppression in a fiber-optic balanced heterodyne detection system,” Opt. Quantum Electron. 18, 445-454 (1986).
[CrossRef]

Yee, T. G.

G. L. Abbas, V. W. S. Chan, and T. G. Yee, “A dual-detector optical heterodyne receiver for local oscillator noise suppression,” J. Lightwave Technol. 3, 1110-1122 (1985).
[CrossRef]

Yu, L. P.

Appl. Opt. (7)

Appl. Phys. B: Photophys. Laser Chem. (1)

H. A. Bachor and P. T. H. Fisk, “Quantum noise--a limit in photodetection,” Appl. Phys. B: Photophys. Laser Chem. 49, 291-300 (1989).
[CrossRef]

J. Lightwave Technol. (2)

G. L. Abbas, V. W. S. Chan, and T. G. Yee, “A dual-detector optical heterodyne receiver for local oscillator noise suppression,” J. Lightwave Technol. 3, 1110-1122 (1985).
[CrossRef]

S. B. Alexander, “Design of wide-band optical heterodyne balanced mixer receivers,” J. Lightwave Technol. 5, 523-537 (1987).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Opt. Soc. Am. B (2)

Opt. Lett. (2)

Opt. Quantum Electron. (1)

R. Stierlin, R. Battig, P. D. Henchoz, and H. P. Weber, “Excess-noise suppression in a fiber-optic balanced heterodyne detection system,” Opt. Quantum Electron. 18, 445-454 (1986).
[CrossRef]

Phys. Rev. Lett. (1)

K. X. Sun, M. M. Fejer, E. Gustafson, and R. L. Byer, “Sagnac interferometer for gravitational-wave detection,” Phys. Rev. Lett. 76, 3053-3056 (1996).
[CrossRef] [PubMed]

Rev. Sci. Instrum. (1)

J. Lawall and E. Kessler, “Michelson interferometry with 10 pm accuracy,” Rev. Sci. Instrum. 71, 2669-2676 (2000).
[CrossRef]

Other (1)

G. P. Agrawal, “Multichannel lightwave systems,” in Fiber-Optic Communication Systems (Wiley, 1992), pp. 284-394.

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Figures (5)

Fig. 1
Fig. 1

Optical setup of the DPD in the polarized common-path interferometer. ISO, isolator; HWP, half-wave plate; BS1, BS2, beam splitters; EOM, electro-optic modulator; AOM1, AOM2, acoustic-optic modulators; GTP, Glan–Thompson polarizer; M1–M4, plane mirrors; PBS1, PBS2, polarized beam splitters; SBC, Soleil Babinet compensator; Dp, Ds, photodetectors; DA, differential amplifier; SA, spectrum analyzer; DVM, digital voltmeter; PC, personal computer.

Fig. 2
Fig. 2

(a) Calculated minimum-detectable phase, (b) minimum-detectable distance of the DPD versus visibilities V S of the S wave while the visibility V P of the P wave is fixed. The output power of laser is 2.5 mW ; the inset shows the result of laser power at 300 mW .

Fig. 3
Fig. 3

Power spectral distributions of differential output signals over a bandwidth of 10 MHz with a halogen lamp under arrangement (1) at Δ Φ = 180 ° (green online). Spectral distribution at minimum-detectable phase Δ Φ Δ Φ min (2) with thermal noise (purple online) and (3) without thermal noise (blue online). (4) DA output spectrum without thermal noise and with the laser beam blocked (red online). (5) Single-detector output (cyan online) where one of the photodetectors was blocked.

Fig. 4
Fig. 4

Power spectrum of the DA output signal with phase noise generated by the EOM under the arrangement of (1) Δ Φ = 180 ° , (2) Δ Φ Δ Φ min , (3) the noise floor when the laser beam was blocked, and (4) single-detector output where one of the photodetectors was blocked.

Fig. 5
Fig. 5

Theoretical calculation of δ ( Δ Φ ) D P D versus Δ Φ induced by unequal amplitude at different amplitude ratios ε.

Equations (21)

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E P 1 = E 1 exp { i [ ( ω 0 + ω 1 ) t + ϕ 1 + Φ P 1 ] } ,
E S 1 = E 1 exp { i [ ( ω 0 + ω 1 ) t + ϕ 1 + Φ S 1 ] } ,
E P 2 = E 2 exp { i [ ( ω 0 + ω 2 ) t + ϕ 2 + Φ P 2 ] } ,
E S 2 = E 2 exp { i [ ( ω 0 + ω 2 ) t + ϕ 2 + Φ S 2 ] } ,
i P 1 + P 2 = G P P o ( q η P 2 h ν ) cos 2 ( θ ) [ 1 + V P cos ( Δ ω t + Δ ϕ + Δ Φ P ) ] ,
i S 1 + S 2 = G S P o ( q η S 2 h ν ) sin 2 ( θ ) [ 1 + V S cos ( Δ ω t + Δ ϕ + Δ Φ S ) ] ,
Δ Φ P = Φ P 1 Φ P 2 ,
Δ Φ S = Φ S 1 Φ S 2 ,
Δ i D A = C [ ( 1 V P 1 V S ) 2 sin ( Δ Φ 2 ) sin ( Δ ω t ) ] ,
P S = 2 R C 2 sin 2 ( Δ Φ 2 ) ,
i q n rms = ( 2 q B i dc ) 1 2 .
P q n P 1 + P 2 = R ( i q n , P 1 + P 2 rms ) 2 = 2 q B R C V P ,
P q n S 1 + S 2 = R ( i q n , S 1 + S 2 rms ) 2 = 2 q B R C V S .
P ex P 1 + P 2 = 2 γ q ( i P 1 + P 2 ) 2 R = 2 γ q R C 2 ( 1 2 + 1 V P 2 ) .
P ex S 1 + S 2 = 2 γ q R C 2 ( 1 2 + 1 V S 2 ) ,
P ex = P ex P 1 + P 2 P ex S 1 + S 2 = 2 γ q R C 2 ( 1 V P 2 1 V S 2 ) .
SNR = ( P S P N ) 1 2 = ( C q ) 1 2 sin ( Δ Φ 2 ) [ B ( 1 V P + 1 V S ) + γ C 1 V P 2 1 V S 2 ] 1 2 .
Δ Φ min = 2 sin 1 { q [ B C ( 1 V P + 1 V S ) + γ ( 1 V P 2 1 V S 2 ) ] 1 2 } .
V DA = V P 1 + P 2 V S 1 + S 2 = 2 A sin ( Δ Φ 2 ) [ ( 1 + ε 2 ) 2 + ( ε 2 ) 2 cot 2 ( Δ Φ 2 ) ] 1 2 sin ( Δ ω t + ρ ) = 2 A err sin ( Δ Φ 2 ) sin ( Δ ω t + ρ ) ,
V DA = 2 A err π sin [ Δ Φ 2 + δ ( Δ Φ ) DA 2 ] ,
δ ( Δ Φ ) DA = 2 tan ( Δ Φ 2 ) [ ( 1 + ε 2 ) 2 + ( ε 2 ) 2 cot 2 ( Δ Φ 2 ) 1 + ( ε 2 ) 1 ] .

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