Abstract

We propose a modification of the Rayleigh scattering method, which allows for measurement of polarization and intermodal beat length in single-mode and few-mode channel waveguides and optical fibers. A significant sensitivity increase is achieved by taking two high-resolution photographs in oblique scattered light of π-shifted intensity distributions produced by interference of polarization or spatial modes and applying Fourier analysis to the differential image. In the case of polarization beat length measurements, the π-phase shift is obtained by switching the polarization state at the fiber input, while in intermodal measurements, the π-phase shifting is realized by changing the excitation conditions. The usefulness of the method for characterization of channel waveguides and optical fibers is demonstrated in several examples. Moreover, we show that the combination of the spectral interferometry method with the proposed method allows for broadband measurements of differential phase and group effective indices.

© 2011 Optical Society of America

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References

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  1. C. D. Poole, N. S. Bergano, R. E. Wagner, and H. J. Schulte, “Polarization dispersion and principal states in a 147 kmundersea lightwave cable,” J. Lightwave Technol. 6, 1185–1190 (1988).
    [CrossRef]
  2. T. R. Wolinski, “Polarimetric optical fibers and sensors,” in Progress in Optics, E.Wolf, ed. (North Holland, 2000), Vol.  40, 1–75.
    [CrossRef]
  3. W. Eickhoff and O. Krumpholz, “Determination of the ellipticity of monomode glass fibres from measurements of scattered light intensity,” Electron. Lett. 12, 405–406 (1976).
    [CrossRef]
  4. K. Takada, J. Noda, and R. Ulrich, “Precision measurement of modal birefringence of highly birefringent fibers by periodic lateral force,” Appl. Opt. 24, 4387–4397 (1985).
    [CrossRef] [PubMed]
  5. W. J. Bock and W. Urbanczyk, “Measurement of polarization mode dispersion and modal birefringence in highly birefringent fibers by means of electronically scanned shearing-type interferometry,” Appl. Opt. 32, 5841–5848(1993).
    [CrossRef] [PubMed]
  6. P. Hlubina and D. Ciprian, “Spectral-domain measurement of phase modal birefringence in polarization-maintaining fiber,” Opt. Express 15, 17019–17024 (2007).
    [CrossRef] [PubMed]
  7. P. Zhang and D. Irvine-Halliday, “Measurement of the beat length in high-birefringent optical fiber by way of magneto-optic modulation,” J. Lightwave Technol. 12, 597–602 (1994).
    [CrossRef]
  8. A. Rodríguez, A. V. Khomenko, R. Cortés, and A. García-Weidner, “Ultralow-birefringence measurement in optical fibers by the twist method,” Opt. Lett. 22, 877–879 (1997).
    [CrossRef] [PubMed]
  9. B. Ibarra-Escamilla, E. A. Kuzin, F. Gutierrez-Zainos, R. Tellez-Garcia, J. W. Haus, R. Rojas-Laguna, J. M. Estudillo-Ayala, “Measurement of beat length in short low-birefringence fibers using the fiber optical loop mirror,” Opt. Commun. 217, 211–219 (2003).
    [CrossRef]
  10. F. P. Kapron, N. F. Borrelli, and D. B. Keck, “Birefringence in dielectric optical waveguide,” IEEE J. Quantum Electron. 8, 222–225 (1972).
    [CrossRef]
  11. A. J. Rogers, “Polarization optical time-domain reflectometry,” Electron. Lett. 16, 489–490 (1980).
    [CrossRef]
  12. M. Nakazawa, T. Horiguchi, M. Tokuda, and N. Uchida, “Polarisation beat length measurement in a single-mode optical fibre by backward Rayleigh scattering,” Electron. Lett. 17, 513–515 (1981).
    [CrossRef]
  13. D. A. Flavin, R. McBride, and J. D. C. Jones, “Dispersion of birefringence and differential group delay in polarization-maintaining fiber,” Opt. Lett. 27, 1010–1012 (2002).
    [CrossRef]
  14. P. Hlubina, T. Martynkien, and W. Urbańczyk, “Dispersion of group and phase modal birefringence in elliptical-core fiber measured by white-light spectral interferometry,” Opt. Express 11, 2793–2798 (2003).
    [CrossRef] [PubMed]
  15. M. G. Shlyagin, A. V. Khomenko, and D. Tentori, “Birefringence dispersion measurement in optical fibers by wavelength scanning,” Opt. Lett. 20, 869–871 (1995).
    [CrossRef] [PubMed]
  16. R. Calvani, R. Caponi, and F. Cisterno, “Polarization measurements on single-mode fibers,” J. Lightwave Technol. 7, 1187–1196 (1989).
    [CrossRef]
  17. U. Hollenbach, H.-J. Boehm, J. Mohr, D. Ross, and D. Samiec, “UV light induced single mode waveguides in polymer for visible range application,” Proceedings of the European Conference on Integrated Optics (ECIO), paper THD3, Copenhagen, Denmark, 25–27 April 2007.
  18. U. Hollenbach, H.-J. Boehm, J. Mohr, H. Sieber, J. Leuthold, and N. Lindenmann, “POLINA—Polymer Light Waveguides for Nanophotonics,” Proceedings of the European Conference on Integrated Optics (ECIO), poster WeP35, Cambridge, Great Britain, 07–09 April 2010.

2007

2003

P. Hlubina, T. Martynkien, and W. Urbańczyk, “Dispersion of group and phase modal birefringence in elliptical-core fiber measured by white-light spectral interferometry,” Opt. Express 11, 2793–2798 (2003).
[CrossRef] [PubMed]

B. Ibarra-Escamilla, E. A. Kuzin, F. Gutierrez-Zainos, R. Tellez-Garcia, J. W. Haus, R. Rojas-Laguna, J. M. Estudillo-Ayala, “Measurement of beat length in short low-birefringence fibers using the fiber optical loop mirror,” Opt. Commun. 217, 211–219 (2003).
[CrossRef]

2002

1997

1995

1994

P. Zhang and D. Irvine-Halliday, “Measurement of the beat length in high-birefringent optical fiber by way of magneto-optic modulation,” J. Lightwave Technol. 12, 597–602 (1994).
[CrossRef]

1993

1989

R. Calvani, R. Caponi, and F. Cisterno, “Polarization measurements on single-mode fibers,” J. Lightwave Technol. 7, 1187–1196 (1989).
[CrossRef]

1988

C. D. Poole, N. S. Bergano, R. E. Wagner, and H. J. Schulte, “Polarization dispersion and principal states in a 147 kmundersea lightwave cable,” J. Lightwave Technol. 6, 1185–1190 (1988).
[CrossRef]

1985

1981

M. Nakazawa, T. Horiguchi, M. Tokuda, and N. Uchida, “Polarisation beat length measurement in a single-mode optical fibre by backward Rayleigh scattering,” Electron. Lett. 17, 513–515 (1981).
[CrossRef]

1980

A. J. Rogers, “Polarization optical time-domain reflectometry,” Electron. Lett. 16, 489–490 (1980).
[CrossRef]

1976

W. Eickhoff and O. Krumpholz, “Determination of the ellipticity of monomode glass fibres from measurements of scattered light intensity,” Electron. Lett. 12, 405–406 (1976).
[CrossRef]

1972

F. P. Kapron, N. F. Borrelli, and D. B. Keck, “Birefringence in dielectric optical waveguide,” IEEE J. Quantum Electron. 8, 222–225 (1972).
[CrossRef]

Bergano, N. S.

C. D. Poole, N. S. Bergano, R. E. Wagner, and H. J. Schulte, “Polarization dispersion and principal states in a 147 kmundersea lightwave cable,” J. Lightwave Technol. 6, 1185–1190 (1988).
[CrossRef]

Bock, W. J.

Boehm, H.-J.

U. Hollenbach, H.-J. Boehm, J. Mohr, D. Ross, and D. Samiec, “UV light induced single mode waveguides in polymer for visible range application,” Proceedings of the European Conference on Integrated Optics (ECIO), paper THD3, Copenhagen, Denmark, 25–27 April 2007.

U. Hollenbach, H.-J. Boehm, J. Mohr, H. Sieber, J. Leuthold, and N. Lindenmann, “POLINA—Polymer Light Waveguides for Nanophotonics,” Proceedings of the European Conference on Integrated Optics (ECIO), poster WeP35, Cambridge, Great Britain, 07–09 April 2010.

Borrelli, N. F.

F. P. Kapron, N. F. Borrelli, and D. B. Keck, “Birefringence in dielectric optical waveguide,” IEEE J. Quantum Electron. 8, 222–225 (1972).
[CrossRef]

Calvani, R.

R. Calvani, R. Caponi, and F. Cisterno, “Polarization measurements on single-mode fibers,” J. Lightwave Technol. 7, 1187–1196 (1989).
[CrossRef]

Caponi, R.

R. Calvani, R. Caponi, and F. Cisterno, “Polarization measurements on single-mode fibers,” J. Lightwave Technol. 7, 1187–1196 (1989).
[CrossRef]

Ciprian, D.

Cisterno, F.

R. Calvani, R. Caponi, and F. Cisterno, “Polarization measurements on single-mode fibers,” J. Lightwave Technol. 7, 1187–1196 (1989).
[CrossRef]

Cortés, R.

Eickhoff, W.

W. Eickhoff and O. Krumpholz, “Determination of the ellipticity of monomode glass fibres from measurements of scattered light intensity,” Electron. Lett. 12, 405–406 (1976).
[CrossRef]

Estudillo-Ayala, J. M.

B. Ibarra-Escamilla, E. A. Kuzin, F. Gutierrez-Zainos, R. Tellez-Garcia, J. W. Haus, R. Rojas-Laguna, J. M. Estudillo-Ayala, “Measurement of beat length in short low-birefringence fibers using the fiber optical loop mirror,” Opt. Commun. 217, 211–219 (2003).
[CrossRef]

Flavin, D. A.

García-Weidner, A.

Gutierrez-Zainos, F.

B. Ibarra-Escamilla, E. A. Kuzin, F. Gutierrez-Zainos, R. Tellez-Garcia, J. W. Haus, R. Rojas-Laguna, J. M. Estudillo-Ayala, “Measurement of beat length in short low-birefringence fibers using the fiber optical loop mirror,” Opt. Commun. 217, 211–219 (2003).
[CrossRef]

Haus, J. W.

B. Ibarra-Escamilla, E. A. Kuzin, F. Gutierrez-Zainos, R. Tellez-Garcia, J. W. Haus, R. Rojas-Laguna, J. M. Estudillo-Ayala, “Measurement of beat length in short low-birefringence fibers using the fiber optical loop mirror,” Opt. Commun. 217, 211–219 (2003).
[CrossRef]

Hlubina, P.

Hollenbach, U.

U. Hollenbach, H.-J. Boehm, J. Mohr, H. Sieber, J. Leuthold, and N. Lindenmann, “POLINA—Polymer Light Waveguides for Nanophotonics,” Proceedings of the European Conference on Integrated Optics (ECIO), poster WeP35, Cambridge, Great Britain, 07–09 April 2010.

U. Hollenbach, H.-J. Boehm, J. Mohr, D. Ross, and D. Samiec, “UV light induced single mode waveguides in polymer for visible range application,” Proceedings of the European Conference on Integrated Optics (ECIO), paper THD3, Copenhagen, Denmark, 25–27 April 2007.

Horiguchi, T.

M. Nakazawa, T. Horiguchi, M. Tokuda, and N. Uchida, “Polarisation beat length measurement in a single-mode optical fibre by backward Rayleigh scattering,” Electron. Lett. 17, 513–515 (1981).
[CrossRef]

Ibarra-Escamilla, B.

B. Ibarra-Escamilla, E. A. Kuzin, F. Gutierrez-Zainos, R. Tellez-Garcia, J. W. Haus, R. Rojas-Laguna, J. M. Estudillo-Ayala, “Measurement of beat length in short low-birefringence fibers using the fiber optical loop mirror,” Opt. Commun. 217, 211–219 (2003).
[CrossRef]

Irvine-Halliday, D.

P. Zhang and D. Irvine-Halliday, “Measurement of the beat length in high-birefringent optical fiber by way of magneto-optic modulation,” J. Lightwave Technol. 12, 597–602 (1994).
[CrossRef]

Jones, J. D. C.

Kapron, F. P.

F. P. Kapron, N. F. Borrelli, and D. B. Keck, “Birefringence in dielectric optical waveguide,” IEEE J. Quantum Electron. 8, 222–225 (1972).
[CrossRef]

Keck, D. B.

F. P. Kapron, N. F. Borrelli, and D. B. Keck, “Birefringence in dielectric optical waveguide,” IEEE J. Quantum Electron. 8, 222–225 (1972).
[CrossRef]

Khomenko, A. V.

Krumpholz, O.

W. Eickhoff and O. Krumpholz, “Determination of the ellipticity of monomode glass fibres from measurements of scattered light intensity,” Electron. Lett. 12, 405–406 (1976).
[CrossRef]

Kuzin, E. A.

B. Ibarra-Escamilla, E. A. Kuzin, F. Gutierrez-Zainos, R. Tellez-Garcia, J. W. Haus, R. Rojas-Laguna, J. M. Estudillo-Ayala, “Measurement of beat length in short low-birefringence fibers using the fiber optical loop mirror,” Opt. Commun. 217, 211–219 (2003).
[CrossRef]

Leuthold, J.

U. Hollenbach, H.-J. Boehm, J. Mohr, H. Sieber, J. Leuthold, and N. Lindenmann, “POLINA—Polymer Light Waveguides for Nanophotonics,” Proceedings of the European Conference on Integrated Optics (ECIO), poster WeP35, Cambridge, Great Britain, 07–09 April 2010.

Lindenmann, N.

U. Hollenbach, H.-J. Boehm, J. Mohr, H. Sieber, J. Leuthold, and N. Lindenmann, “POLINA—Polymer Light Waveguides for Nanophotonics,” Proceedings of the European Conference on Integrated Optics (ECIO), poster WeP35, Cambridge, Great Britain, 07–09 April 2010.

Martynkien, T.

McBride, R.

Mohr, J.

U. Hollenbach, H.-J. Boehm, J. Mohr, H. Sieber, J. Leuthold, and N. Lindenmann, “POLINA—Polymer Light Waveguides for Nanophotonics,” Proceedings of the European Conference on Integrated Optics (ECIO), poster WeP35, Cambridge, Great Britain, 07–09 April 2010.

U. Hollenbach, H.-J. Boehm, J. Mohr, D. Ross, and D. Samiec, “UV light induced single mode waveguides in polymer for visible range application,” Proceedings of the European Conference on Integrated Optics (ECIO), paper THD3, Copenhagen, Denmark, 25–27 April 2007.

Nakazawa, M.

M. Nakazawa, T. Horiguchi, M. Tokuda, and N. Uchida, “Polarisation beat length measurement in a single-mode optical fibre by backward Rayleigh scattering,” Electron. Lett. 17, 513–515 (1981).
[CrossRef]

Noda, J.

Poole, C. D.

C. D. Poole, N. S. Bergano, R. E. Wagner, and H. J. Schulte, “Polarization dispersion and principal states in a 147 kmundersea lightwave cable,” J. Lightwave Technol. 6, 1185–1190 (1988).
[CrossRef]

Rodríguez, A.

Rogers, A. J.

A. J. Rogers, “Polarization optical time-domain reflectometry,” Electron. Lett. 16, 489–490 (1980).
[CrossRef]

Rojas-Laguna, R.

B. Ibarra-Escamilla, E. A. Kuzin, F. Gutierrez-Zainos, R. Tellez-Garcia, J. W. Haus, R. Rojas-Laguna, J. M. Estudillo-Ayala, “Measurement of beat length in short low-birefringence fibers using the fiber optical loop mirror,” Opt. Commun. 217, 211–219 (2003).
[CrossRef]

Ross, D.

U. Hollenbach, H.-J. Boehm, J. Mohr, D. Ross, and D. Samiec, “UV light induced single mode waveguides in polymer for visible range application,” Proceedings of the European Conference on Integrated Optics (ECIO), paper THD3, Copenhagen, Denmark, 25–27 April 2007.

Samiec, D.

U. Hollenbach, H.-J. Boehm, J. Mohr, D. Ross, and D. Samiec, “UV light induced single mode waveguides in polymer for visible range application,” Proceedings of the European Conference on Integrated Optics (ECIO), paper THD3, Copenhagen, Denmark, 25–27 April 2007.

Schulte, H. J.

C. D. Poole, N. S. Bergano, R. E. Wagner, and H. J. Schulte, “Polarization dispersion and principal states in a 147 kmundersea lightwave cable,” J. Lightwave Technol. 6, 1185–1190 (1988).
[CrossRef]

Shlyagin, M. G.

Sieber, H.

U. Hollenbach, H.-J. Boehm, J. Mohr, H. Sieber, J. Leuthold, and N. Lindenmann, “POLINA—Polymer Light Waveguides for Nanophotonics,” Proceedings of the European Conference on Integrated Optics (ECIO), poster WeP35, Cambridge, Great Britain, 07–09 April 2010.

Takada, K.

Tellez-Garcia, R.

B. Ibarra-Escamilla, E. A. Kuzin, F. Gutierrez-Zainos, R. Tellez-Garcia, J. W. Haus, R. Rojas-Laguna, J. M. Estudillo-Ayala, “Measurement of beat length in short low-birefringence fibers using the fiber optical loop mirror,” Opt. Commun. 217, 211–219 (2003).
[CrossRef]

Tentori, D.

Tokuda, M.

M. Nakazawa, T. Horiguchi, M. Tokuda, and N. Uchida, “Polarisation beat length measurement in a single-mode optical fibre by backward Rayleigh scattering,” Electron. Lett. 17, 513–515 (1981).
[CrossRef]

Uchida, N.

M. Nakazawa, T. Horiguchi, M. Tokuda, and N. Uchida, “Polarisation beat length measurement in a single-mode optical fibre by backward Rayleigh scattering,” Electron. Lett. 17, 513–515 (1981).
[CrossRef]

Ulrich, R.

Urbanczyk, W.

Wagner, R. E.

C. D. Poole, N. S. Bergano, R. E. Wagner, and H. J. Schulte, “Polarization dispersion and principal states in a 147 kmundersea lightwave cable,” J. Lightwave Technol. 6, 1185–1190 (1988).
[CrossRef]

Wolinski, T. R.

T. R. Wolinski, “Polarimetric optical fibers and sensors,” in Progress in Optics, E.Wolf, ed. (North Holland, 2000), Vol.  40, 1–75.
[CrossRef]

Zhang, P.

P. Zhang and D. Irvine-Halliday, “Measurement of the beat length in high-birefringent optical fiber by way of magneto-optic modulation,” J. Lightwave Technol. 12, 597–602 (1994).
[CrossRef]

Appl. Opt.

Electron. Lett.

W. Eickhoff and O. Krumpholz, “Determination of the ellipticity of monomode glass fibres from measurements of scattered light intensity,” Electron. Lett. 12, 405–406 (1976).
[CrossRef]

A. J. Rogers, “Polarization optical time-domain reflectometry,” Electron. Lett. 16, 489–490 (1980).
[CrossRef]

M. Nakazawa, T. Horiguchi, M. Tokuda, and N. Uchida, “Polarisation beat length measurement in a single-mode optical fibre by backward Rayleigh scattering,” Electron. Lett. 17, 513–515 (1981).
[CrossRef]

IEEE J. Quantum Electron.

F. P. Kapron, N. F. Borrelli, and D. B. Keck, “Birefringence in dielectric optical waveguide,” IEEE J. Quantum Electron. 8, 222–225 (1972).
[CrossRef]

J. Lightwave Technol.

P. Zhang and D. Irvine-Halliday, “Measurement of the beat length in high-birefringent optical fiber by way of magneto-optic modulation,” J. Lightwave Technol. 12, 597–602 (1994).
[CrossRef]

R. Calvani, R. Caponi, and F. Cisterno, “Polarization measurements on single-mode fibers,” J. Lightwave Technol. 7, 1187–1196 (1989).
[CrossRef]

C. D. Poole, N. S. Bergano, R. E. Wagner, and H. J. Schulte, “Polarization dispersion and principal states in a 147 kmundersea lightwave cable,” J. Lightwave Technol. 6, 1185–1190 (1988).
[CrossRef]

Opt. Commun.

B. Ibarra-Escamilla, E. A. Kuzin, F. Gutierrez-Zainos, R. Tellez-Garcia, J. W. Haus, R. Rojas-Laguna, J. M. Estudillo-Ayala, “Measurement of beat length in short low-birefringence fibers using the fiber optical loop mirror,” Opt. Commun. 217, 211–219 (2003).
[CrossRef]

Opt. Express

Opt. Lett.

Other

T. R. Wolinski, “Polarimetric optical fibers and sensors,” in Progress in Optics, E.Wolf, ed. (North Holland, 2000), Vol.  40, 1–75.
[CrossRef]

U. Hollenbach, H.-J. Boehm, J. Mohr, D. Ross, and D. Samiec, “UV light induced single mode waveguides in polymer for visible range application,” Proceedings of the European Conference on Integrated Optics (ECIO), paper THD3, Copenhagen, Denmark, 25–27 April 2007.

U. Hollenbach, H.-J. Boehm, J. Mohr, H. Sieber, J. Leuthold, and N. Lindenmann, “POLINA—Polymer Light Waveguides for Nanophotonics,” Proceedings of the European Conference on Integrated Optics (ECIO), poster WeP35, Cambridge, Great Britain, 07–09 April 2010.

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Figures (5)

Fig. 1
Fig. 1

(a) Evolution of the polarization azimuth in a birefringent waveguide excited with linearly polarized light at α = 45 ° with respect to x-polarization axis and orientation of the camera collecting scattered light. (b) Spatial intensity distribution in a core of a two-mode waveguide.

Fig. 2
Fig. 2

Original photograph of the Corning PMF 38 fiber captured in scattered light, differential images, and their Fourier spectra showing polarization beating for (a) fundamental mode, (b) two spatial modes, and (c) three spatial modes excited simultaneously. Exposition conditions: ISO 200, exp. 20 s , aperture f / 5.6 for (a) and (b), 10 s exposure for (c).

Fig. 3
Fig. 3

Examples of scattered intensity distributions, differential images, and their Fourier spectra showing polarization beating in (a) birefringent PMMA channel waveguide and (b) epoxy waveguide. Exposition conditions: ISO 200, exp. 1 s , aperture f / 5.6 for (a), 20 s exposure for (b).

Fig. 4
Fig. 4

Differential image obtained in scattered light with beating arising due to the interference of L P 01 y and L P 11 y modes in the (a) Corning PMF 38 fiber (electric vector parallel to shorter axis of the elliptical core) and (b) its Fourier spectrum. Exposition conditions: ISO 200, exp. 30 s , × 4 microscope objective.

Fig. 5
Fig. 5

(a) Spectrogram registered at the output of a channel epoxy waveguide of length L = 36 mm , (b) reconstructed spectral dependence of group modal birefringence, (c) and phase modal birefringence with the indicated red point obtained by the scattering method.

Equations (13)

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

Δ N = Δ n λ d Δ n d λ
L B = 2 π β x β y = Δ n λ ,
I S ( z ) = ρ S I 0 | sin α cos θ exp ( j β y z ) cos α sin θ exp ( j β x z ) | 2
I S ( z ) = ρ S I 0 [ sin 2 α cos 2 θ + cos 2 α sin 2 θ + 0.5 sin 2 α sin 2 θ cos ( Δ β z ) ] ,
I S α ( z ) I S α 90 ( z ) = ρ S I 0 [ cos 2 α cos 2 θ + sin 2 α sin 2 θ cos ( Δ β z ) ] .
I S 45 ( z ) I S 45 ( z ) = ρ S I 0 [ sin 2 θ cos ( Δ β z ) ] .
I S int ( z , Δ x ) = I 0 [ 1 + γ ( Δ x ) cos ( z Δ β ) ] ,
I S 1 ( z ) I S 2 ( z ) = 2 ρ s I 0 γ ( Δ x ) sin ( θ ) cos ( z Δ β ) ,
Δ φ ( λ ) = Δ β ( λ ) L φ ( λ 0 ) ,
Δ N = λ 2 2 π L d Δ ϕ d λ .
φ ( λ 0 ) = 2 π L L B ( λ 0 ) .
L B ( λ ) = 2 π L Δ φ ( λ ) + φ ( λ 0 )
Δ n ( λ ) = λ Δ φ ( λ ) 2 π L + Δ n ( λ 0 ) .

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