Abstract

We describe a method for differential phase measurement of Faraday rotation from multiple depth locations simultaneously. A polarization-maintaining fiber-based spectral-domain interferometer that utilizes a low-coherent light source and a single camera is developed. Light decorrelated by the orthogonal channels of the fiber is launched on a sample as two oppositely polarized circular states. These states reflect from sample surfaces and interfere with the corresponding states of the reference arm. A custom spectrometer, which is designed to simplify camera alignment, separates the orthogonal channels and records the interference-related oscillations on both spectra. Inverse Fourier transform of the spectral oscillations in k-space yields complex depth profiles, whose amplitudes and phase difference are related to reflectivity and Faraday rotation within the sample, respectively. Information along a full depth profile is produced at the camera speed without performing an axial scan for a multisurface sample. System sensitivity for the Faraday rotation measurement is 0.86 min of arc. Verdet constants of clear liquids and turbid media are measured at 687 nm.

© 2013 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  11. M. K. Al-Qaisi, H. Wang, and T. Akkin, “Measurement of Faraday rotation using phase-sensitive low-coherence interferometry,” Appl. Opt. 48, 5829–5833 (2009).
    [CrossRef]
  12. B. Cense, N. A. Nassif, T. C. Chen, M. C. Pierce, S.-H. Yun, B. H. Park, B. E. Bouma, G. J. Tearney, and J. F. de Boer, “Ultrahigh-resolution high-speed retinal imaging using spectral-domain optical coherence tomography,” Opt. Express 12, 2435–2447 (2004).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2012

M. Koralewski, J. W. Kłos, M. Baranowski, Z. Mitroova, P. Kopcansky, L. Melnikova, M. Okuda, and W. Schwarzacher, “The Faraday effect of natural and artificial ferritins,” Nanotechnology 23, 355704 (2012).
[CrossRef]

2011

S. C. Bera and S. Chakraborty, “Study of magneto-optic element as a displacement sensor,” Measurement 44, 1747–1752 (2011).
[CrossRef]

2009

P. K. Jain, Y. Xiao, R. Walsworth, and A. E. Cohen, “Surface plasmon resonance enhanced magneto-optics (SuPREMO): Faraday rotation enhancement in gold-coated iron oxide nanocrystals,” Nano Lett. 9, 1644–1650 (2009).

M. K. Al-Qaisi, H. Wang, and T. Akkin, “Measurement of Faraday rotation using phase-sensitive low-coherence interferometry,” Appl. Opt. 48, 5829–5833 (2009).
[CrossRef]

2008

H. Takeda and S. John, “Compact optical one-way waveguide isolators for photonic-band-gap microchips,” Phys. Rev. A 78, 023804 (2008).
[CrossRef]

2007

D. Pereda-Cubián, M. Todorović, J. L. Arce-Diego, and L. V. Wang, “Evaluation of the magneto-optical effect in biological tissue models using optical coherence tomography,” J. Biomed. Opt. 12, 060502 (2007).
[CrossRef]

2004

M. Yokota, Y. Sato, I. Yamaguchi, T. Kenmochi, and T. Yoshino, “A compact polarimetric glucose sensor using a high-performance fibre-optic Faraday rotator,” Meas. Sci. Technol. 15, 143–147 (2004).
[CrossRef]

B. Cense, N. A. Nassif, T. C. Chen, M. C. Pierce, S.-H. Yun, B. H. Park, B. E. Bouma, G. J. Tearney, and J. F. de Boer, “Ultrahigh-resolution high-speed retinal imaging using spectral-domain optical coherence tomography,” Opt. Express 12, 2435–2447 (2004).
[CrossRef]

2002

P. Jorge, P. Caldas, L. Ferreira, A. Ribeiro, J. Santos, and F. Farahi, “Electrical current metering with a dual interferometric configuration and serrodyne signal processing,” Meas. Sci. Technol. 13, 533–538 (2002).

2000

D. Budker, D. F. Kimball, S. M. Rochester, V. V. Yashchuk, and M. Zolotorev, “Sensitive magnetometry based on nonlinear magneto-optical rotation,” Phys. Rev. A 62, 043403 (2000).
[CrossRef]

1999

G. P. Clarke, H. W. McKenzie, and P. Stanley, “The magnetophotoelastic analysis of residual stresses in thermally toughened glass,” Proc. R. Soc. A 455, 1149–1173 (1999).

1996

1994

1993

K. Turkey, “Determine of Verdet constant from combined ac and dc measurements,” Rev. Sci. Instrum. 64, 1561–1568 (1993).
[CrossRef]

1985

1979

A. B. Villaverde and D. A. Donetti, “Verdet constant of liquids; measurements with a pulsed magnetic field,” J. Chem. Phys. 71, 4021–4024 (1979).
[CrossRef]

1969

W. J. Tabor and F. S. Chen, “Electromagnetic propagation through materials possessing both Faraday rotation and birefringence: experiments with ytterbium orthoferrite,” J. Appl. Phys. 40, 2760–2765 (1969).
[CrossRef]

Akkin, T.

Al-Qaisi, M. K.

Andres, M. V.

Arce-Diego, J. L.

D. Pereda-Cubián, M. Todorović, J. L. Arce-Diego, and L. V. Wang, “Evaluation of the magneto-optical effect in biological tissue models using optical coherence tomography,” J. Biomed. Opt. 12, 060502 (2007).
[CrossRef]

Baranowski, M.

M. Koralewski, J. W. Kłos, M. Baranowski, Z. Mitroova, P. Kopcansky, L. Melnikova, M. Okuda, and W. Schwarzacher, “The Faraday effect of natural and artificial ferritins,” Nanotechnology 23, 355704 (2012).
[CrossRef]

Bera, S. C.

S. C. Bera and S. Chakraborty, “Study of magneto-optic element as a displacement sensor,” Measurement 44, 1747–1752 (2011).
[CrossRef]

Bouma, B. E.

Budker, D.

D. Budker, D. F. Kimball, S. M. Rochester, V. V. Yashchuk, and M. Zolotorev, “Sensitive magnetometry based on nonlinear magneto-optical rotation,” Phys. Rev. A 62, 043403 (2000).
[CrossRef]

Caldas, P.

P. Jorge, P. Caldas, L. Ferreira, A. Ribeiro, J. Santos, and F. Farahi, “Electrical current metering with a dual interferometric configuration and serrodyne signal processing,” Meas. Sci. Technol. 13, 533–538 (2002).

Cense, B.

Chakraborty, S.

S. C. Bera and S. Chakraborty, “Study of magneto-optic element as a displacement sensor,” Measurement 44, 1747–1752 (2011).
[CrossRef]

Chen, F. S.

W. J. Tabor and F. S. Chen, “Electromagnetic propagation through materials possessing both Faraday rotation and birefringence: experiments with ytterbium orthoferrite,” J. Appl. Phys. 40, 2760–2765 (1969).
[CrossRef]

Chen, T. C.

Clarke, G. P.

G. P. Clarke, H. W. McKenzie, and P. Stanley, “The magnetophotoelastic analysis of residual stresses in thermally toughened glass,” Proc. R. Soc. A 455, 1149–1173 (1999).

Cohen, A. E.

P. K. Jain, Y. Xiao, R. Walsworth, and A. E. Cohen, “Surface plasmon resonance enhanced magneto-optics (SuPREMO): Faraday rotation enhancement in gold-coated iron oxide nanocrystals,” Nano Lett. 9, 1644–1650 (2009).

Cruz, J. L.

Dändliker, R.

de Boer, J. F.

Donetti, D. A.

A. B. Villaverde and D. A. Donetti, “Verdet constant of liquids; measurements with a pulsed magnetic field,” J. Chem. Phys. 71, 4021–4024 (1979).
[CrossRef]

Farahi, F.

P. Jorge, P. Caldas, L. Ferreira, A. Ribeiro, J. Santos, and F. Farahi, “Electrical current metering with a dual interferometric configuration and serrodyne signal processing,” Meas. Sci. Technol. 13, 533–538 (2002).

Ferreira, L.

P. Jorge, P. Caldas, L. Ferreira, A. Ribeiro, J. Santos, and F. Farahi, “Electrical current metering with a dual interferometric configuration and serrodyne signal processing,” Meas. Sci. Technol. 13, 533–538 (2002).

Frosio, G.

Hernandez, M. A.

Jain, P. K.

P. K. Jain, Y. Xiao, R. Walsworth, and A. E. Cohen, “Surface plasmon resonance enhanced magneto-optics (SuPREMO): Faraday rotation enhancement in gold-coated iron oxide nanocrystals,” Nano Lett. 9, 1644–1650 (2009).

John, S.

H. Takeda and S. John, “Compact optical one-way waveguide isolators for photonic-band-gap microchips,” Phys. Rev. A 78, 023804 (2008).
[CrossRef]

Jorge, P.

P. Jorge, P. Caldas, L. Ferreira, A. Ribeiro, J. Santos, and F. Farahi, “Electrical current metering with a dual interferometric configuration and serrodyne signal processing,” Meas. Sci. Technol. 13, 533–538 (2002).

Kawase, M.

Kenmochi, T.

M. Yokota, Y. Sato, I. Yamaguchi, T. Kenmochi, and T. Yoshino, “A compact polarimetric glucose sensor using a high-performance fibre-optic Faraday rotator,” Meas. Sci. Technol. 15, 143–147 (2004).
[CrossRef]

Kimball, D. F.

D. Budker, D. F. Kimball, S. M. Rochester, V. V. Yashchuk, and M. Zolotorev, “Sensitive magnetometry based on nonlinear magneto-optical rotation,” Phys. Rev. A 62, 043403 (2000).
[CrossRef]

Klos, J. W.

M. Koralewski, J. W. Kłos, M. Baranowski, Z. Mitroova, P. Kopcansky, L. Melnikova, M. Okuda, and W. Schwarzacher, “The Faraday effect of natural and artificial ferritins,” Nanotechnology 23, 355704 (2012).
[CrossRef]

Kopcansky, P.

M. Koralewski, J. W. Kłos, M. Baranowski, Z. Mitroova, P. Kopcansky, L. Melnikova, M. Okuda, and W. Schwarzacher, “The Faraday effect of natural and artificial ferritins,” Nanotechnology 23, 355704 (2012).
[CrossRef]

Koralewski, M.

M. Koralewski, J. W. Kłos, M. Baranowski, Z. Mitroova, P. Kopcansky, L. Melnikova, M. Okuda, and W. Schwarzacher, “The Faraday effect of natural and artificial ferritins,” Nanotechnology 23, 355704 (2012).
[CrossRef]

McKenzie, H. W.

G. P. Clarke, H. W. McKenzie, and P. Stanley, “The magnetophotoelastic analysis of residual stresses in thermally toughened glass,” Proc. R. Soc. A 455, 1149–1173 (1999).

Melnikova, L.

M. Koralewski, J. W. Kłos, M. Baranowski, Z. Mitroova, P. Kopcansky, L. Melnikova, M. Okuda, and W. Schwarzacher, “The Faraday effect of natural and artificial ferritins,” Nanotechnology 23, 355704 (2012).
[CrossRef]

Mitroova, Z.

M. Koralewski, J. W. Kłos, M. Baranowski, Z. Mitroova, P. Kopcansky, L. Melnikova, M. Okuda, and W. Schwarzacher, “The Faraday effect of natural and artificial ferritins,” Nanotechnology 23, 355704 (2012).
[CrossRef]

Nassif, N. A.

Okuda, M.

M. Koralewski, J. W. Kłos, M. Baranowski, Z. Mitroova, P. Kopcansky, L. Melnikova, M. Okuda, and W. Schwarzacher, “The Faraday effect of natural and artificial ferritins,” Nanotechnology 23, 355704 (2012).
[CrossRef]

Park, B. H.

Pereda-Cubián, D.

D. Pereda-Cubián, M. Todorović, J. L. Arce-Diego, and L. V. Wang, “Evaluation of the magneto-optical effect in biological tissue models using optical coherence tomography,” J. Biomed. Opt. 12, 060502 (2007).
[CrossRef]

Pierce, M. C.

Ribeiro, A.

P. Jorge, P. Caldas, L. Ferreira, A. Ribeiro, J. Santos, and F. Farahi, “Electrical current metering with a dual interferometric configuration and serrodyne signal processing,” Meas. Sci. Technol. 13, 533–538 (2002).

Rochester, S. M.

D. Budker, D. F. Kimball, S. M. Rochester, V. V. Yashchuk, and M. Zolotorev, “Sensitive magnetometry based on nonlinear magneto-optical rotation,” Phys. Rev. A 62, 043403 (2000).
[CrossRef]

Saito, M.

Santos, J.

P. Jorge, P. Caldas, L. Ferreira, A. Ribeiro, J. Santos, and F. Farahi, “Electrical current metering with a dual interferometric configuration and serrodyne signal processing,” Meas. Sci. Technol. 13, 533–538 (2002).

Sato, H.

Sato, Y.

M. Yokota, Y. Sato, I. Yamaguchi, T. Kenmochi, and T. Yoshino, “A compact polarimetric glucose sensor using a high-performance fibre-optic Faraday rotator,” Meas. Sci. Technol. 15, 143–147 (2004).
[CrossRef]

Schwarzacher, W.

M. Koralewski, J. W. Kłos, M. Baranowski, Z. Mitroova, P. Kopcansky, L. Melnikova, M. Okuda, and W. Schwarzacher, “The Faraday effect of natural and artificial ferritins,” Nanotechnology 23, 355704 (2012).
[CrossRef]

Stanley, P.

G. P. Clarke, H. W. McKenzie, and P. Stanley, “The magnetophotoelastic analysis of residual stresses in thermally toughened glass,” Proc. R. Soc. A 455, 1149–1173 (1999).

Tabor, W. J.

W. J. Tabor and F. S. Chen, “Electromagnetic propagation through materials possessing both Faraday rotation and birefringence: experiments with ytterbium orthoferrite,” J. Appl. Phys. 40, 2760–2765 (1969).
[CrossRef]

Takeda, H.

H. Takeda and S. John, “Compact optical one-way waveguide isolators for photonic-band-gap microchips,” Phys. Rev. A 78, 023804 (2008).
[CrossRef]

Tearney, G. J.

Todorovic, M.

D. Pereda-Cubián, M. Todorović, J. L. Arce-Diego, and L. V. Wang, “Evaluation of the magneto-optical effect in biological tissue models using optical coherence tomography,” J. Biomed. Opt. 12, 060502 (2007).
[CrossRef]

Turkey, K.

K. Turkey, “Determine of Verdet constant from combined ac and dc measurements,” Rev. Sci. Instrum. 64, 1561–1568 (1993).
[CrossRef]

Villaverde, A. B.

A. B. Villaverde and D. A. Donetti, “Verdet constant of liquids; measurements with a pulsed magnetic field,” J. Chem. Phys. 71, 4021–4024 (1979).
[CrossRef]

Walsworth, R.

P. K. Jain, Y. Xiao, R. Walsworth, and A. E. Cohen, “Surface plasmon resonance enhanced magneto-optics (SuPREMO): Faraday rotation enhancement in gold-coated iron oxide nanocrystals,” Nano Lett. 9, 1644–1650 (2009).

Wang, H.

Wang, L. V.

D. Pereda-Cubián, M. Todorović, J. L. Arce-Diego, and L. V. Wang, “Evaluation of the magneto-optical effect in biological tissue models using optical coherence tomography,” J. Biomed. Opt. 12, 060502 (2007).
[CrossRef]

Xiao, Y.

P. K. Jain, Y. Xiao, R. Walsworth, and A. E. Cohen, “Surface plasmon resonance enhanced magneto-optics (SuPREMO): Faraday rotation enhancement in gold-coated iron oxide nanocrystals,” Nano Lett. 9, 1644–1650 (2009).

Yamaguchi, I.

M. Yokota, Y. Sato, I. Yamaguchi, T. Kenmochi, and T. Yoshino, “A compact polarimetric glucose sensor using a high-performance fibre-optic Faraday rotator,” Meas. Sci. Technol. 15, 143–147 (2004).
[CrossRef]

Yashchuk, V. V.

D. Budker, D. F. Kimball, S. M. Rochester, V. V. Yashchuk, and M. Zolotorev, “Sensitive magnetometry based on nonlinear magneto-optical rotation,” Phys. Rev. A 62, 043403 (2000).
[CrossRef]

Yokota, M.

M. Yokota, Y. Sato, I. Yamaguchi, T. Kenmochi, and T. Yoshino, “A compact polarimetric glucose sensor using a high-performance fibre-optic Faraday rotator,” Meas. Sci. Technol. 15, 143–147 (2004).
[CrossRef]

Yoshino, T.

M. Yokota, Y. Sato, I. Yamaguchi, T. Kenmochi, and T. Yoshino, “A compact polarimetric glucose sensor using a high-performance fibre-optic Faraday rotator,” Meas. Sci. Technol. 15, 143–147 (2004).
[CrossRef]

Yun, S.-H.

Zolotorev, M.

D. Budker, D. F. Kimball, S. M. Rochester, V. V. Yashchuk, and M. Zolotorev, “Sensitive magnetometry based on nonlinear magneto-optical rotation,” Phys. Rev. A 62, 043403 (2000).
[CrossRef]

Appl. Opt.

J. Appl. Phys.

W. J. Tabor and F. S. Chen, “Electromagnetic propagation through materials possessing both Faraday rotation and birefringence: experiments with ytterbium orthoferrite,” J. Appl. Phys. 40, 2760–2765 (1969).
[CrossRef]

J. Biomed. Opt.

D. Pereda-Cubián, M. Todorović, J. L. Arce-Diego, and L. V. Wang, “Evaluation of the magneto-optical effect in biological tissue models using optical coherence tomography,” J. Biomed. Opt. 12, 060502 (2007).
[CrossRef]

J. Chem. Phys.

A. B. Villaverde and D. A. Donetti, “Verdet constant of liquids; measurements with a pulsed magnetic field,” J. Chem. Phys. 71, 4021–4024 (1979).
[CrossRef]

Meas. Sci. Technol.

P. Jorge, P. Caldas, L. Ferreira, A. Ribeiro, J. Santos, and F. Farahi, “Electrical current metering with a dual interferometric configuration and serrodyne signal processing,” Meas. Sci. Technol. 13, 533–538 (2002).

M. Yokota, Y. Sato, I. Yamaguchi, T. Kenmochi, and T. Yoshino, “A compact polarimetric glucose sensor using a high-performance fibre-optic Faraday rotator,” Meas. Sci. Technol. 15, 143–147 (2004).
[CrossRef]

Measurement

S. C. Bera and S. Chakraborty, “Study of magneto-optic element as a displacement sensor,” Measurement 44, 1747–1752 (2011).
[CrossRef]

Nano Lett.

P. K. Jain, Y. Xiao, R. Walsworth, and A. E. Cohen, “Surface plasmon resonance enhanced magneto-optics (SuPREMO): Faraday rotation enhancement in gold-coated iron oxide nanocrystals,” Nano Lett. 9, 1644–1650 (2009).

Nanotechnology

M. Koralewski, J. W. Kłos, M. Baranowski, Z. Mitroova, P. Kopcansky, L. Melnikova, M. Okuda, and W. Schwarzacher, “The Faraday effect of natural and artificial ferritins,” Nanotechnology 23, 355704 (2012).
[CrossRef]

Opt. Express

Phys. Rev. A

D. Budker, D. F. Kimball, S. M. Rochester, V. V. Yashchuk, and M. Zolotorev, “Sensitive magnetometry based on nonlinear magneto-optical rotation,” Phys. Rev. A 62, 043403 (2000).
[CrossRef]

H. Takeda and S. John, “Compact optical one-way waveguide isolators for photonic-band-gap microchips,” Phys. Rev. A 78, 023804 (2008).
[CrossRef]

Proc. R. Soc. A

G. P. Clarke, H. W. McKenzie, and P. Stanley, “The magnetophotoelastic analysis of residual stresses in thermally toughened glass,” Proc. R. Soc. A 455, 1149–1173 (1999).

Rev. Sci. Instrum.

K. Turkey, “Determine of Verdet constant from combined ac and dc measurements,” Rev. Sci. Instrum. 64, 1561–1568 (1993).
[CrossRef]

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Figures (7)

Fig. 1.
Fig. 1.

Schematic experimental setup: SLD, superluminescent diode; PC, polarization controller; C, collimator; FB, fiber bench; PM, polarization maintaining; QWP, quarter-wave plate; L, lens; R, reflector; M, mirror; G, transmission grating; WP, Wollaston prism; ASC, area scan camera; N, magnet’s north pole; S, magnet’s south pole.

Fig. 2.
Fig. 2.

Area scan camera is configured to select and output two spectral lines (white) with a vertical binning of 4 pixels.

Fig. 3.
Fig. 3.

(a) Time and (b) frequency domain representations of phase variations on individual channels (ϕ1 and ϕ2). The differential phase (Δϕ) signal in (c) time and (d) frequency domains indicate removal of common noise terms.

Fig. 4.
Fig. 4.

Glass cell and the depth profile showing its internal surfaces. Surface 1: glass-solution interface. Surface 2: solution-glass interface.

Fig. 5.
Fig. 5.

Faraday rotation measurement from the glass-water interface (red) and water-glass interface (blue) shows oscillations due to alternating magnetic field. (a) Time domain signals and their (b) Fourier transforms are plotted for a single trial.

Fig. 6.
Fig. 6.

Faraday rotation measurements in various liquids (B=2.05kG, d=780μm, λ=687nm).

Fig. 7.
Fig. 7.

Faraday rotations in de-ionized water containing various intralipid concentrations.

Tables (1)

Tables Icon

Table 1. Verdet Constants of Liquids at 687 nm Wavelength are Calculated from Measurements

Metrics