Abstract

In this Letter we show that interferometers with unbalanced arm lengths can be balanced using optical elements with appropriate group delays. For matched group delays of the arms, the balanced interferometer becomes insensitive to the frequency noise of the source. For experimental illustration, a ring resonator is employed as a slow-light element to compensate the arm-length mismatch of a Mach–Zehnder interferometer. An arm-length mismatch of 9.4m is compensated by a ring resonator with a finesse of 70 and a perimeter of 42cm.

© 2011 Optical Society of America

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2009 (2)

K. McKenzie, R. E. Spero, and D. A. Shaddock, Phys. Rev. D 80, 102003 (2009).
[CrossRef]

M. Terrel, M. J. F. Digonnet, and S. Fan, Laser Photonics Rev. 3, 452 (2009).
[CrossRef]

2008 (1)

2007 (4)

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, Phys. Rev. Lett. 99, 133601 (2007).
[CrossRef] [PubMed]

Z. Shi and R. W. Boyd, Opt. Lett. 32, 915 (2007).
[CrossRef] [PubMed]

Z. Shi and R. W. Boyd, Phys. Rev. Lett. 99, 240801 (2007).
[CrossRef]

B. Liu and M. E. Brezinski, J Biomed. Opt. 12, 044007 (2007).
[CrossRef] [PubMed]

2005 (1)

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, Nature 438, 65 (2005).
[CrossRef] [PubMed]

2002 (1)

M. Tinto, F. B. Estabrook, and J. W. Armstrong, Phys. Rev. D 65, 082003 (2002).
[CrossRef]

1983 (1)

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

1965 (1)

Armstrong, J. W.

M. Tinto, F. B. Estabrook, and J. W. Armstrong, Phys. Rev. D 65, 082003 (2002).
[CrossRef]

Boyd, R. W.

Z. Shi and R. W. Boyd, Opt. Lett. 32, 915 (2007).
[CrossRef] [PubMed]

Z. Shi and R. W. Boyd, Phys. Rev. Lett. 99, 240801 (2007).
[CrossRef]

Brezinski, M. E.

B. Liu and M. E. Brezinski, J Biomed. Opt. 12, 044007 (2007).
[CrossRef] [PubMed]

Digonnet, M. J. F.

M. Terrel, M. J. F. Digonnet, and S. Fan, Laser Photonics Rev. 3, 452 (2009).
[CrossRef]

Drever, R. W. P.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Estabrook, F. B.

M. Tinto, F. B. Estabrook, and J. W. Armstrong, Phys. Rev. D 65, 082003 (2002).
[CrossRef]

Fan, S.

M. Terrel, M. J. F. Digonnet, and S. Fan, Laser Photonics Rev. 3, 452 (2009).
[CrossRef]

Ford, G. M.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Hall, J. L.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Hamann, H. F.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, Nature 438, 65 (2005).
[CrossRef] [PubMed]

Herriott, D. R.

Hough, J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Kowalski, F. V.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Liu, B.

B. Liu and M. E. Brezinski, J Biomed. Opt. 12, 044007 (2007).
[CrossRef] [PubMed]

Livas, J.

McKenzie, K.

K. McKenzie, R. E. Spero, and D. A. Shaddock, Phys. Rev. D 80, 102003 (2009).
[CrossRef]

McNab, S. J.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, Nature 438, 65 (2005).
[CrossRef] [PubMed]

Munley, A. J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Numata, K.

O’Boyle, M.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, Nature 438, 65 (2005).
[CrossRef] [PubMed]

Pati, G. S.

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, Phys. Rev. Lett. 99, 133601 (2007).
[CrossRef] [PubMed]

Salit, K.

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, Phys. Rev. Lett. 99, 133601 (2007).
[CrossRef] [PubMed]

Salit, M.

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, Phys. Rev. Lett. 99, 133601 (2007).
[CrossRef] [PubMed]

Schulte, J.

Shaddock, D. A.

K. McKenzie, R. E. Spero, and D. A. Shaddock, Phys. Rev. D 80, 102003 (2009).
[CrossRef]

Shahriar, M. S.

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, Phys. Rev. Lett. 99, 133601 (2007).
[CrossRef] [PubMed]

Shi, Z.

Z. Shi and R. W. Boyd, Opt. Lett. 32, 915 (2007).
[CrossRef] [PubMed]

Z. Shi and R. W. Boyd, Phys. Rev. Lett. 99, 240801 (2007).
[CrossRef]

Siegman, A. E.

A. E. Siegman, Lasers (University Science, 1986).

Spero, R. E.

K. McKenzie, R. E. Spero, and D. A. Shaddock, Phys. Rev. D 80, 102003 (2009).
[CrossRef]

Terrel, M.

M. Terrel, M. J. F. Digonnet, and S. Fan, Laser Photonics Rev. 3, 452 (2009).
[CrossRef]

Thorpe, J. I.

Tinto, M.

M. Tinto, F. B. Estabrook, and J. W. Armstrong, Phys. Rev. D 65, 082003 (2002).
[CrossRef]

Vlasov, Y. A.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, Nature 438, 65 (2005).
[CrossRef] [PubMed]

Ward, H.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (1)

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

J Biomed. Opt. (1)

B. Liu and M. E. Brezinski, J Biomed. Opt. 12, 044007 (2007).
[CrossRef] [PubMed]

Laser Photonics Rev. (1)

M. Terrel, M. J. F. Digonnet, and S. Fan, Laser Photonics Rev. 3, 452 (2009).
[CrossRef]

Nature (1)

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, Nature 438, 65 (2005).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. D (2)

M. Tinto, F. B. Estabrook, and J. W. Armstrong, Phys. Rev. D 65, 082003 (2002).
[CrossRef]

K. McKenzie, R. E. Spero, and D. A. Shaddock, Phys. Rev. D 80, 102003 (2009).
[CrossRef]

Phys. Rev. Lett. (2)

G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, Phys. Rev. Lett. 99, 133601 (2007).
[CrossRef] [PubMed]

Z. Shi and R. W. Boyd, Phys. Rev. Lett. 99, 240801 (2007).
[CrossRef]

Other (1)

A. E. Siegman, Lasers (University Science, 1986).

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Figures (4)

Fig. 1
Fig. 1

Schematic diagram of an MZI with a dispersive element in one arm. M1, M2, M3, interferometer mirrors; BS1, BS2, beam splitters; PD1, PD2, photodetectors.

Fig. 2
Fig. 2

Schematic diagram of an MZI with a resonator in one arm to compensate the arm-length mismatch. Laser frequency is locked to the cavity using a PDH scheme. HW, half-wave plate; PBS1, polarizing beam splitter; EOM, electro-optic modulator; LO, local oscillator; BS1, BS2, beam splitters, PD1, PD2, PD3, photodetectors; M1, M2, M3, inter ferometer mirrors; PZT, piezoelectric transducer.

Fig. 3
Fig. 3

Amplitude spectral density of the MZI output in different configurations while the laser frequency is modulated at 10 kHz : (a)  Δ L = 9.4 m without cavity, (b)  Δ L = 0 with cavity, (c)  Δ L = 0 without cavity, (d)  Δ L = 9.4 m with cavity.

Fig. 4
Fig. 4

Magnitude of MZI output at 10 kHz versus arm-length mismatch (solid curve is calculated for a simple MZI; y axis is in log scale).

Equations (11)

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

I out = I 0 cos ( k 0 Δ L k 3 L 3 + ϕ 0 ) ,
d I out d ω = I 0 ( Δ L c + L 3 d k 3 d ω ) sin ( k 0 Δ L k 3 L 3 + ϕ 0 ) .
Δ L c = L 3 d k 3 d ω v 3 gr d ω d k 3 = c L 3 Δ L ,
L 3 v 3 gr = Δ L c .
T r = T in T out exp ( j ω L in / out / c ) 1 R in R out R 3 exp ( j ω p m / c ) ,
T r = π ω L in / out c tan 1 ( g rt sin ( ω p m / c ) 1 g rt cos ( ω p m / c ) ) ,
t gr = d d ω T r | ω = ω q = L in / out c + p m c ( g rt 1 g rt ) .
g rt = Δ L p m + Δ L .
F π ( Δ L p m ) .
τ s = F p m π c , L eff = F p m π ,
σ ϕ = ω c Δ L p m σ pm ,

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