Abstract

A new quantitative method for optical imaging of inhomogeneous weak magnetic fields has been developed, using a thin paramagnetic liquid film on a surface in the region of the magnetic field. The deformation of the paramagnetic liquid film reveals the magnetic field distribution. The measurements were made interferometrically using a version of the Michelson interferometer through which an image could be observed. The expected theoretical behavior was developed, and the method was investigated experimentally using two different liquids in two temperature regions.

© 1996 Optical Society of America

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  1. H. Trauble, U. Essman, “Flux line arrangement in superconductors as revealed by direct observation,” J. Appl. Phys. 39, 4052–4059 (1968).
  2. P. L. Gammel, D. J. Bishop, G. J. Dolan, J. R. Kwo, C. A. Murray, L. F. Schneemeyer, J. V. Waszczak, “Observation of hexagonally correlated flux quanta in YBCO,” Phys. Rev. Lett. 59, 2592–2595 (1987).
  3. H. W. Weber, R. Riegler, “Measurements of the flux density distribution in type II superconductors with several micro-field probes,” Solid State Commun. 12, 121–124 (1973).
  4. D. A. Brawner, N. P. Ong, “Scanning Hall microprobe measurements of magnetization profiles in YBCO single crystals,” J. Appl. Phys. 73, 3890–3902 (1993).
  5. P. B. Alers, “Structure of intermediate state in superconducting lead,” Phys. Rev. 105, 104–108 (1957).
  6. H. Kirchner, “Improved Faraday technique for observing magnetic structures in superconductors,” Phys. Lett. A 30, 437–438 (1969).
  7. Th. Schuster, M. R. Koblischka, B. Ludescher, N. Moser, H. Kronmuller, “EuSe as magneto-optical active coating for use with the high resolution Faraday effect,” Cryogenics 31, 811–816 (1991).
  8. M. V. Indenbom, V. I. Nikitenko, A. A. Plyanskii, V. K. Vlasko-Vlasko, “The new method for direct study of magnetic flux distribution in superconductors,” Cryogenics 30, 747–749 (1990).
  9. A. Dorosinskii, M. V. Indenbom, V. I. Nikitenko, Yu. A. Ossip’yan, A. A. Polyanskii, V. K. Vlasko-Vlasko, “Studies of HTSC crystal magnetization features using indicator mag netooptic films with in plane anisotropy,” Physica C 203, 149–156 (1992).
  10. E. I. Sponable, “Eidophor system of theater television,” J. Soc. Motion Pict. Telev. Eng. 60, 337–343 (1953).
  11. J. R. Arni, U.S. patent2,276,339 (1953).
  12. L. D. Landau, E. M. Lifshitz, Fluid Mechanics, 2nd ed., Vol. 6 of Course of Theoretical Physics (Pergamon, Oxford, 1987).
  13. A. W. Adamson, Physical Chemistry of Surfaces, 3rd ed. (Wiley, New York, 1976).
  14. L. F. Bates, Modern Magnetism, 4th ed. (Cambridge U. Press, Cambridge, U.K., 1961).
  15. M. Takeda, H. Ina, S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–159 (1982).
  16. S. Kostianovski, S. G. Lipson, E. N. Ribak, “Interference microscopy and Fourier fringe analysis applied to measuring the spatial refractive-index distribution,” Appl. Opt. 32, 4744–4750 (1993).

1993 (2)

D. A. Brawner, N. P. Ong, “Scanning Hall microprobe measurements of magnetization profiles in YBCO single crystals,” J. Appl. Phys. 73, 3890–3902 (1993).

S. Kostianovski, S. G. Lipson, E. N. Ribak, “Interference microscopy and Fourier fringe analysis applied to measuring the spatial refractive-index distribution,” Appl. Opt. 32, 4744–4750 (1993).

1992 (1)

A. Dorosinskii, M. V. Indenbom, V. I. Nikitenko, Yu. A. Ossip’yan, A. A. Polyanskii, V. K. Vlasko-Vlasko, “Studies of HTSC crystal magnetization features using indicator mag netooptic films with in plane anisotropy,” Physica C 203, 149–156 (1992).

1991 (1)

Th. Schuster, M. R. Koblischka, B. Ludescher, N. Moser, H. Kronmuller, “EuSe as magneto-optical active coating for use with the high resolution Faraday effect,” Cryogenics 31, 811–816 (1991).

1990 (1)

M. V. Indenbom, V. I. Nikitenko, A. A. Plyanskii, V. K. Vlasko-Vlasko, “The new method for direct study of magnetic flux distribution in superconductors,” Cryogenics 30, 747–749 (1990).

1987 (1)

P. L. Gammel, D. J. Bishop, G. J. Dolan, J. R. Kwo, C. A. Murray, L. F. Schneemeyer, J. V. Waszczak, “Observation of hexagonally correlated flux quanta in YBCO,” Phys. Rev. Lett. 59, 2592–2595 (1987).

1982 (1)

M. Takeda, H. Ina, S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–159 (1982).

1973 (1)

H. W. Weber, R. Riegler, “Measurements of the flux density distribution in type II superconductors with several micro-field probes,” Solid State Commun. 12, 121–124 (1973).

1969 (1)

H. Kirchner, “Improved Faraday technique for observing magnetic structures in superconductors,” Phys. Lett. A 30, 437–438 (1969).

1968 (1)

H. Trauble, U. Essman, “Flux line arrangement in superconductors as revealed by direct observation,” J. Appl. Phys. 39, 4052–4059 (1968).

1957 (1)

P. B. Alers, “Structure of intermediate state in superconducting lead,” Phys. Rev. 105, 104–108 (1957).

1953 (1)

E. I. Sponable, “Eidophor system of theater television,” J. Soc. Motion Pict. Telev. Eng. 60, 337–343 (1953).

Adamson, A. W.

A. W. Adamson, Physical Chemistry of Surfaces, 3rd ed. (Wiley, New York, 1976).

Alers, P. B.

P. B. Alers, “Structure of intermediate state in superconducting lead,” Phys. Rev. 105, 104–108 (1957).

Arni, J. R.

J. R. Arni, U.S. patent2,276,339 (1953).

Bates, L. F.

L. F. Bates, Modern Magnetism, 4th ed. (Cambridge U. Press, Cambridge, U.K., 1961).

Bishop, D. J.

P. L. Gammel, D. J. Bishop, G. J. Dolan, J. R. Kwo, C. A. Murray, L. F. Schneemeyer, J. V. Waszczak, “Observation of hexagonally correlated flux quanta in YBCO,” Phys. Rev. Lett. 59, 2592–2595 (1987).

Brawner, D. A.

D. A. Brawner, N. P. Ong, “Scanning Hall microprobe measurements of magnetization profiles in YBCO single crystals,” J. Appl. Phys. 73, 3890–3902 (1993).

Dolan, G. J.

P. L. Gammel, D. J. Bishop, G. J. Dolan, J. R. Kwo, C. A. Murray, L. F. Schneemeyer, J. V. Waszczak, “Observation of hexagonally correlated flux quanta in YBCO,” Phys. Rev. Lett. 59, 2592–2595 (1987).

Dorosinskii, A.

A. Dorosinskii, M. V. Indenbom, V. I. Nikitenko, Yu. A. Ossip’yan, A. A. Polyanskii, V. K. Vlasko-Vlasko, “Studies of HTSC crystal magnetization features using indicator mag netooptic films with in plane anisotropy,” Physica C 203, 149–156 (1992).

Essman, U.

H. Trauble, U. Essman, “Flux line arrangement in superconductors as revealed by direct observation,” J. Appl. Phys. 39, 4052–4059 (1968).

Gammel, P. L.

P. L. Gammel, D. J. Bishop, G. J. Dolan, J. R. Kwo, C. A. Murray, L. F. Schneemeyer, J. V. Waszczak, “Observation of hexagonally correlated flux quanta in YBCO,” Phys. Rev. Lett. 59, 2592–2595 (1987).

Ina, H.

M. Takeda, H. Ina, S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–159 (1982).

Indenbom, M. V.

A. Dorosinskii, M. V. Indenbom, V. I. Nikitenko, Yu. A. Ossip’yan, A. A. Polyanskii, V. K. Vlasko-Vlasko, “Studies of HTSC crystal magnetization features using indicator mag netooptic films with in plane anisotropy,” Physica C 203, 149–156 (1992).

M. V. Indenbom, V. I. Nikitenko, A. A. Plyanskii, V. K. Vlasko-Vlasko, “The new method for direct study of magnetic flux distribution in superconductors,” Cryogenics 30, 747–749 (1990).

Kirchner, H.

H. Kirchner, “Improved Faraday technique for observing magnetic structures in superconductors,” Phys. Lett. A 30, 437–438 (1969).

Kobayashi, S.

M. Takeda, H. Ina, S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–159 (1982).

Koblischka, M. R.

Th. Schuster, M. R. Koblischka, B. Ludescher, N. Moser, H. Kronmuller, “EuSe as magneto-optical active coating for use with the high resolution Faraday effect,” Cryogenics 31, 811–816 (1991).

Kostianovski, S.

Kronmuller, H.

Th. Schuster, M. R. Koblischka, B. Ludescher, N. Moser, H. Kronmuller, “EuSe as magneto-optical active coating for use with the high resolution Faraday effect,” Cryogenics 31, 811–816 (1991).

Kwo, J. R.

P. L. Gammel, D. J. Bishop, G. J. Dolan, J. R. Kwo, C. A. Murray, L. F. Schneemeyer, J. V. Waszczak, “Observation of hexagonally correlated flux quanta in YBCO,” Phys. Rev. Lett. 59, 2592–2595 (1987).

Landau, L. D.

L. D. Landau, E. M. Lifshitz, Fluid Mechanics, 2nd ed., Vol. 6 of Course of Theoretical Physics (Pergamon, Oxford, 1987).

Lifshitz, E. M.

L. D. Landau, E. M. Lifshitz, Fluid Mechanics, 2nd ed., Vol. 6 of Course of Theoretical Physics (Pergamon, Oxford, 1987).

Lipson, S. G.

Ludescher, B.

Th. Schuster, M. R. Koblischka, B. Ludescher, N. Moser, H. Kronmuller, “EuSe as magneto-optical active coating for use with the high resolution Faraday effect,” Cryogenics 31, 811–816 (1991).

Moser, N.

Th. Schuster, M. R. Koblischka, B. Ludescher, N. Moser, H. Kronmuller, “EuSe as magneto-optical active coating for use with the high resolution Faraday effect,” Cryogenics 31, 811–816 (1991).

Murray, C. A.

P. L. Gammel, D. J. Bishop, G. J. Dolan, J. R. Kwo, C. A. Murray, L. F. Schneemeyer, J. V. Waszczak, “Observation of hexagonally correlated flux quanta in YBCO,” Phys. Rev. Lett. 59, 2592–2595 (1987).

Nikitenko, V. I.

A. Dorosinskii, M. V. Indenbom, V. I. Nikitenko, Yu. A. Ossip’yan, A. A. Polyanskii, V. K. Vlasko-Vlasko, “Studies of HTSC crystal magnetization features using indicator mag netooptic films with in plane anisotropy,” Physica C 203, 149–156 (1992).

M. V. Indenbom, V. I. Nikitenko, A. A. Plyanskii, V. K. Vlasko-Vlasko, “The new method for direct study of magnetic flux distribution in superconductors,” Cryogenics 30, 747–749 (1990).

Ong, N. P.

D. A. Brawner, N. P. Ong, “Scanning Hall microprobe measurements of magnetization profiles in YBCO single crystals,” J. Appl. Phys. 73, 3890–3902 (1993).

Ossip’yan, Yu. A.

A. Dorosinskii, M. V. Indenbom, V. I. Nikitenko, Yu. A. Ossip’yan, A. A. Polyanskii, V. K. Vlasko-Vlasko, “Studies of HTSC crystal magnetization features using indicator mag netooptic films with in plane anisotropy,” Physica C 203, 149–156 (1992).

Plyanskii, A. A.

M. V. Indenbom, V. I. Nikitenko, A. A. Plyanskii, V. K. Vlasko-Vlasko, “The new method for direct study of magnetic flux distribution in superconductors,” Cryogenics 30, 747–749 (1990).

Polyanskii, A. A.

A. Dorosinskii, M. V. Indenbom, V. I. Nikitenko, Yu. A. Ossip’yan, A. A. Polyanskii, V. K. Vlasko-Vlasko, “Studies of HTSC crystal magnetization features using indicator mag netooptic films with in plane anisotropy,” Physica C 203, 149–156 (1992).

Ribak, E. N.

Riegler, R.

H. W. Weber, R. Riegler, “Measurements of the flux density distribution in type II superconductors with several micro-field probes,” Solid State Commun. 12, 121–124 (1973).

Schneemeyer, L. F.

P. L. Gammel, D. J. Bishop, G. J. Dolan, J. R. Kwo, C. A. Murray, L. F. Schneemeyer, J. V. Waszczak, “Observation of hexagonally correlated flux quanta in YBCO,” Phys. Rev. Lett. 59, 2592–2595 (1987).

Schuster, Th.

Th. Schuster, M. R. Koblischka, B. Ludescher, N. Moser, H. Kronmuller, “EuSe as magneto-optical active coating for use with the high resolution Faraday effect,” Cryogenics 31, 811–816 (1991).

Sponable, E. I.

E. I. Sponable, “Eidophor system of theater television,” J. Soc. Motion Pict. Telev. Eng. 60, 337–343 (1953).

Takeda, M.

M. Takeda, H. Ina, S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–159 (1982).

Trauble, H.

H. Trauble, U. Essman, “Flux line arrangement in superconductors as revealed by direct observation,” J. Appl. Phys. 39, 4052–4059 (1968).

Vlasko-Vlasko, V. K.

A. Dorosinskii, M. V. Indenbom, V. I. Nikitenko, Yu. A. Ossip’yan, A. A. Polyanskii, V. K. Vlasko-Vlasko, “Studies of HTSC crystal magnetization features using indicator mag netooptic films with in plane anisotropy,” Physica C 203, 149–156 (1992).

M. V. Indenbom, V. I. Nikitenko, A. A. Plyanskii, V. K. Vlasko-Vlasko, “The new method for direct study of magnetic flux distribution in superconductors,” Cryogenics 30, 747–749 (1990).

Waszczak, J. V.

P. L. Gammel, D. J. Bishop, G. J. Dolan, J. R. Kwo, C. A. Murray, L. F. Schneemeyer, J. V. Waszczak, “Observation of hexagonally correlated flux quanta in YBCO,” Phys. Rev. Lett. 59, 2592–2595 (1987).

Weber, H. W.

H. W. Weber, R. Riegler, “Measurements of the flux density distribution in type II superconductors with several micro-field probes,” Solid State Commun. 12, 121–124 (1973).

Appl. Opt. (1)

Cryogenics (2)

Th. Schuster, M. R. Koblischka, B. Ludescher, N. Moser, H. Kronmuller, “EuSe as magneto-optical active coating for use with the high resolution Faraday effect,” Cryogenics 31, 811–816 (1991).

M. V. Indenbom, V. I. Nikitenko, A. A. Plyanskii, V. K. Vlasko-Vlasko, “The new method for direct study of magnetic flux distribution in superconductors,” Cryogenics 30, 747–749 (1990).

J. Appl. Phys. (2)

H. Trauble, U. Essman, “Flux line arrangement in superconductors as revealed by direct observation,” J. Appl. Phys. 39, 4052–4059 (1968).

D. A. Brawner, N. P. Ong, “Scanning Hall microprobe measurements of magnetization profiles in YBCO single crystals,” J. Appl. Phys. 73, 3890–3902 (1993).

J. Opt. Soc. Am (1)

M. Takeda, H. Ina, S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–159 (1982).

J. Soc. Motion Pict. Telev. Eng. (1)

E. I. Sponable, “Eidophor system of theater television,” J. Soc. Motion Pict. Telev. Eng. 60, 337–343 (1953).

Phys. Lett. A (1)

H. Kirchner, “Improved Faraday technique for observing magnetic structures in superconductors,” Phys. Lett. A 30, 437–438 (1969).

Phys. Rev. (1)

P. B. Alers, “Structure of intermediate state in superconducting lead,” Phys. Rev. 105, 104–108 (1957).

Phys. Rev. Lett. (1)

P. L. Gammel, D. J. Bishop, G. J. Dolan, J. R. Kwo, C. A. Murray, L. F. Schneemeyer, J. V. Waszczak, “Observation of hexagonally correlated flux quanta in YBCO,” Phys. Rev. Lett. 59, 2592–2595 (1987).

Physica C (1)

A. Dorosinskii, M. V. Indenbom, V. I. Nikitenko, Yu. A. Ossip’yan, A. A. Polyanskii, V. K. Vlasko-Vlasko, “Studies of HTSC crystal magnetization features using indicator mag netooptic films with in plane anisotropy,” Physica C 203, 149–156 (1992).

Solid State Commun. (1)

H. W. Weber, R. Riegler, “Measurements of the flux density distribution in type II superconductors with several micro-field probes,” Solid State Commun. 12, 121–124 (1973).

Other (4)

J. R. Arni, U.S. patent2,276,339 (1953).

L. D. Landau, E. M. Lifshitz, Fluid Mechanics, 2nd ed., Vol. 6 of Course of Theoretical Physics (Pergamon, Oxford, 1987).

A. W. Adamson, Physical Chemistry of Surfaces, 3rd ed. (Wiley, New York, 1976).

L. F. Bates, Modern Magnetism, 4th ed. (Cambridge U. Press, Cambridge, U.K., 1961).

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Figures (8)

Fig. 1
Fig. 1

Schematic diagram of the experimental system for the MnCl2 solution: 1, tilting table; 2, magnetic field stand; 3, magnetic field system; 4, sample mirror; 5, dish; 6, liquid film; 7, beam splitter; 8, image lens.

Fig. 2
Fig. 2

Schematic diagram of the experimental system for liquid oxygen: 1, cooling block; 2, sample; 3, heater; 4, sample cell; 5, reference mirror; 6, sample cell window; 7, electromagnetic coil; 8, cryostat window; 9, beam splitter; 10, mirror; 11, image lens.

Fig. 3
Fig. 3

Applied magnetic field for MnCl2 solution experiments.

Fig. 4
Fig. 4

Deformation of the MnCl2 solution film: (a) experimental measurements, (b) comparison with theory (solid curve, experimental results; dashed curve, theoretical results).

Fig. 5
Fig. 5

Spatial variations of the MnCl2 solution film surface as a function of the applied field (B = const × I 2).

Fig. 6
Fig. 6

Temporal response of the MnCl2 solution for various intensities of applied magnetic fields.

Fig. 7
Fig. 7

Deformation of the liquid oxygen film: (a) shape of the surface, (b) contour plot of the surface.

Fig. 8
Fig. 8

Cross section of the liquid oxygen film showing the experimental measurements (solid curve) and the simulation obtained from a complete Meissner effect under the experimental conditions (dashed curve).

Tables (1)

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Table 1 Properties of the Materials used in the Experiments

Equations (11)

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B = B ( x ) z ^ .
total + λ constraint = { 1 2 ( 1 μ 0 1 μ ) B ( x ) 2 z ( x , y ) + γ { 1 + 1 2 [ z ( x , y ) x ] 2 + 1 2 [ z ( x , y ) y ] 2 } + 1 2 ρ g z 2 ( x , y ) + λ z ( x , y ) } d x d y = minimum ,
2 z ( x , y ) x 2 + 2 z ( x , y ) y 2 ρ g γ z ( x , y ) = 1 2 ( 1 μ 0 1 μ ) B 2 ( x , y ) + λ .
z field ( x , y ) = l c 4 γ ( 1 μ 0 1 μ ) B ( u ) 2 × exp { 1 l c x u } d u ,
B ( x ) = B 0 cos ( k x ) z ^
z field ( x , y ) = B 0 2 4 γ ( 1 l c 2 + 4 k 2 ) ( 1 μ 0 1 μ ) cos ( 2 k x ) .
t = 1 k 2 E ¯ mech E ¯ ˙ mech ,
E ¯ mech = ρ v ( ϕ x i ) 2 d V , E ¯ ˙ mech = 2 η v ( 2 ϕ x k x i ) 2 d V ,
ϕ = ϕ 0 cos ( k x ω t ) cosh [ k ( h + z ) ] .
t = [ 2 η k 2 ρ sinh ( 2 k h ) 2 k h ] 1 .
B ( x ) = I 5 m = n n [ h h 2 + ( x m d ) 2 ( 1 ) m + 1 x ^ + x m d h 2 + ( x m d ) 2 ( 1 ) m z ^ ] ,

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