Abstract

We propose a simple nondestructive method to obtain refractive-index profiles of a graded-index (GRIN) light-focusing rod by means of a diffraction grating. In our proposed method, a laser beam is illuminated through a diffraction grating perpendicular to the axis of the GRIN lens and the separation between the zeroth and first-order diffraction peaks is measured and analyzed. The results demonstrate that the refractive-index profiles of commercially available GRIN lenses can be successfully reconstructed.

© 2009 Optical Society of Korea

PDF Article

References

  • View by:
  • |
  • |

  1. C. G. Reino, M. V. Perez, and C. Bao, Gradient-index Optics (Springer, Berlin, Germany, 2002).
  2. D. T. Moore, “Gradient-index optics: a review,” Appl. Opt. 19, 1035-1038 (1980).
    [CrossRef]
  3. Y. Koike, Y. Takezawa, and Y. Ohtsuka, “New interfacialgel copolymerization technique for steric GRIN polymer optical waveguides and lens arrays,” Appl. Opt. 27, 486-491 (1988).
    [CrossRef]
  4. C. Ye and R. R. McLeod, “GRIN lens and lens array fabrication with diffusion-driven photopolymer,” Opt. Lett. 33, 2575-2577 (2008).
    [CrossRef]
  5. H. Kobayashi and T. Horiuchi, “Novel projection exposure system using gradient-index lens array,” Jpn. J. Appl. Phys. 47, 5702-5707 (2008).
    [CrossRef]
  6. F. Okano, M. Kobayashi, J. Arai, and M. Okui, “Depth control GRIN lens array for integral photography,” Proc. SPIE 5243, 30-41 (2003).
    [CrossRef]
  7. S. Janz, B. Lamontagne, A. Delage, A. Bogdanov, D. X. Xu, and K. P. Yap, “Single layer a-Si GRIN waveguide coupler with lithographically defined facets,” in Proc. 2nd IEEE International Conference on Group IV Photonics (Antwerp, Belgium, Sep. 2005), pp. 129-131.
    [CrossRef]
  8. S. Rios, R. Srivastava, and C. G. Reino, “Coupling of single-mode fibers to single-mode GRIN waveguides by butt-joining,” Opt. Comm. 119, 517-522 (1995).
    [CrossRef]
  9. S. C. J. Lee, F. Breyer, S. Randel, B. Spinnler, I. L. L. Polo, D. van den Borne, J. Zeng, H. P. A. van den Boom, and A. M. J. Koonen, “Performance of maximum likelihood sequence estimation in 10 Gb/s transmission systems with polymer optical fiber,” in Proc. Symposium IEEE/LEOS Benelux Chapter (Eindhoven, Netherlands, Nov. 2006), pp. 17-19.
  10. I. T. Monroy, H. P. A. vd Boom, A. M. J. Koonen, G. D. Khoe, Y. Watanabe, Y. Koike, and T. Ishigure, “Data transmission over polymer optical fibers,” Optical Fiber Technology 9, 159-171 (2003).
    [CrossRef]
  11. D. G. Kim, S. Y. Woo, D. K. Kim, T. Y. Hwang, D. Y. Kim, and S.-H. Park, “Generation of 1.5 Gbps pseudo-random binary sequence optical signals by using a gain switched Fabry-Perot semiconductor laser,” J. Opt. Soc. Korea 9, 103-106 (2005).
    [CrossRef]
  12. W. C. Chen, Y. Chang, and J. P. Hsu, “Theoretical analysis on a multilayer coextrusion process for preparing gradient-index polymer optical fibers,” J. Phys. Chem. B 103, 7584-7590 (1999).
    [CrossRef]
  13. P. L. Chu, “Nondestructive measurement of index profile of an optical-fibre preform,” Electron. Lett. 13, 736-738 (1977).
    [CrossRef]
  14. L. S. Watkins, “Laser beam refraction transversely through a graded-index preform to determine refractive-index ratio and gradient profile,” Appl. Opt. 18, 2214-2222 (1979).
    [CrossRef]
  15. H. H. Lim, M. S. Kwon, H. J. Choi, B. J. Kim, and M. Cha, “Measurement of refractive index of solid medium by critical angle method when air gap is present,” J. Opt. Soc. Korea 12, 210-214 (2008).
    [CrossRef]
  16. W. E. Martin, “Refractive index profile measurements of diffused optical waveguides,” Appl. Opt. 13, 2112-2116 (1974).
    [CrossRef]
  17. J. Stone and R. M. Derosier, “Elimination of errors due to sample polishing in refractive index profile measurements by interferometry,” Rev. Sci. Instru. 47, 885-887 (1976).
    [CrossRef]
  18. M. E. Marhic, P. S. Ho, and M. Epstein, “Nondestructive refractive-index profile measurements of clad optical fibers,” Appl. Phys. Lett. 26, 574-575 (1975).
    [CrossRef]
  19. M. J. Saunders and W. B. Gardner, “Nondestructive interferometric measurement of the delta and alpha of clad optical fibers,” Appl. Opt. 16, 2368-2371 (1977).
    [CrossRef]
  20. Y. Ohtsuka and Y. Shimizu, “Radial distribution of the refractive index in light-focusing rods: determination using interphako interference microscopy,” Appl. Opt. 16, 1050-1053 (1979).
    [CrossRef]
  21. Y. Kokubun and K. Iga, “Refractive-index profile measurement of preform rods by a transverse differential interferograms,” Appl. Opt. 19, 846-851 (1980).
    [CrossRef]
  22. K. S. R. Krishna and A. Sharma, “Chromatic aberrations of radial gradient-index lenses. II. Selfoc lenses,” Appl. Opt. 35, 1037-1040 (1996).
    [CrossRef]
  23. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill Book Co., Singapore, 1996), Chapter 4.
  24. F. G. Smith, T. A. King, and D. Wilkins, Optics and Photonics (John Wiley & Sons, Ltd., West Sussex, UK, 2007), Chapter 2.
  25. S. P. Morgan, “General solution of the Luneberg lens problem,” J. Appl. Phys. 29, 1358-1368 (1958).
    [CrossRef]
  26. Gradient-index lenses, “Gradient-index lenses, antireflection coated, for $\lambda$ = 632.8nm,” (Product number, 06 LGD 111), http://www.mellesgriot.com/pdf/0015.16-15.20.pdf.

2008 (3)

C. Ye and R. R. McLeod, “GRIN lens and lens array fabrication with diffusion-driven photopolymer,” Opt. Lett. 33, 2575-2577 (2008).
[CrossRef]

H. Kobayashi and T. Horiuchi, “Novel projection exposure system using gradient-index lens array,” Jpn. J. Appl. Phys. 47, 5702-5707 (2008).
[CrossRef]

H. H. Lim, M. S. Kwon, H. J. Choi, B. J. Kim, and M. Cha, “Measurement of refractive index of solid medium by critical angle method when air gap is present,” J. Opt. Soc. Korea 12, 210-214 (2008).
[CrossRef]

2007 (1)

F. G. Smith, T. A. King, and D. Wilkins, Optics and Photonics (John Wiley & Sons, Ltd., West Sussex, UK, 2007), Chapter 2.

2006 (1)

S. C. J. Lee, F. Breyer, S. Randel, B. Spinnler, I. L. L. Polo, D. van den Borne, J. Zeng, H. P. A. van den Boom, and A. M. J. Koonen, “Performance of maximum likelihood sequence estimation in 10 Gb/s transmission systems with polymer optical fiber,” in Proc. Symposium IEEE/LEOS Benelux Chapter (Eindhoven, Netherlands, Nov. 2006), pp. 17-19.

2005 (2)

S. Janz, B. Lamontagne, A. Delage, A. Bogdanov, D. X. Xu, and K. P. Yap, “Single layer a-Si GRIN waveguide coupler with lithographically defined facets,” in Proc. 2nd IEEE International Conference on Group IV Photonics (Antwerp, Belgium, Sep. 2005), pp. 129-131.
[CrossRef]

D. G. Kim, S. Y. Woo, D. K. Kim, T. Y. Hwang, D. Y. Kim, and S.-H. Park, “Generation of 1.5 Gbps pseudo-random binary sequence optical signals by using a gain switched Fabry-Perot semiconductor laser,” J. Opt. Soc. Korea 9, 103-106 (2005).
[CrossRef]

2003 (2)

I. T. Monroy, H. P. A. vd Boom, A. M. J. Koonen, G. D. Khoe, Y. Watanabe, Y. Koike, and T. Ishigure, “Data transmission over polymer optical fibers,” Optical Fiber Technology 9, 159-171 (2003).
[CrossRef]

F. Okano, M. Kobayashi, J. Arai, and M. Okui, “Depth control GRIN lens array for integral photography,” Proc. SPIE 5243, 30-41 (2003).
[CrossRef]

2002 (1)

C. G. Reino, M. V. Perez, and C. Bao, Gradient-index Optics (Springer, Berlin, Germany, 2002).

1999 (1)

W. C. Chen, Y. Chang, and J. P. Hsu, “Theoretical analysis on a multilayer coextrusion process for preparing gradient-index polymer optical fibers,” J. Phys. Chem. B 103, 7584-7590 (1999).
[CrossRef]

1996 (2)

K. S. R. Krishna and A. Sharma, “Chromatic aberrations of radial gradient-index lenses. II. Selfoc lenses,” Appl. Opt. 35, 1037-1040 (1996).
[CrossRef]

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill Book Co., Singapore, 1996), Chapter 4.

1995 (1)

S. Rios, R. Srivastava, and C. G. Reino, “Coupling of single-mode fibers to single-mode GRIN waveguides by butt-joining,” Opt. Comm. 119, 517-522 (1995).
[CrossRef]

1988 (1)

Y. Koike, Y. Takezawa, and Y. Ohtsuka, “New interfacialgel copolymerization technique for steric GRIN polymer optical waveguides and lens arrays,” Appl. Opt. 27, 486-491 (1988).
[CrossRef]

1980 (2)

D. T. Moore, “Gradient-index optics: a review,” Appl. Opt. 19, 1035-1038 (1980).
[CrossRef]

Y. Kokubun and K. Iga, “Refractive-index profile measurement of preform rods by a transverse differential interferograms,” Appl. Opt. 19, 846-851 (1980).
[CrossRef]

1979 (2)

Y. Ohtsuka and Y. Shimizu, “Radial distribution of the refractive index in light-focusing rods: determination using interphako interference microscopy,” Appl. Opt. 16, 1050-1053 (1979).
[CrossRef]

L. S. Watkins, “Laser beam refraction transversely through a graded-index preform to determine refractive-index ratio and gradient profile,” Appl. Opt. 18, 2214-2222 (1979).
[CrossRef]

1977 (2)

P. L. Chu, “Nondestructive measurement of index profile of an optical-fibre preform,” Electron. Lett. 13, 736-738 (1977).
[CrossRef]

M. J. Saunders and W. B. Gardner, “Nondestructive interferometric measurement of the delta and alpha of clad optical fibers,” Appl. Opt. 16, 2368-2371 (1977).
[CrossRef]

1976 (1)

J. Stone and R. M. Derosier, “Elimination of errors due to sample polishing in refractive index profile measurements by interferometry,” Rev. Sci. Instru. 47, 885-887 (1976).
[CrossRef]

1975 (1)

M. E. Marhic, P. S. Ho, and M. Epstein, “Nondestructive refractive-index profile measurements of clad optical fibers,” Appl. Phys. Lett. 26, 574-575 (1975).
[CrossRef]

1974 (1)

W. E. Martin, “Refractive index profile measurements of diffused optical waveguides,” Appl. Opt. 13, 2112-2116 (1974).
[CrossRef]

1958 (1)

S. P. Morgan, “General solution of the Luneberg lens problem,” J. Appl. Phys. 29, 1358-1368 (1958).
[CrossRef]

Applied Optics (8)

D. T. Moore, “Gradient-index optics: a review,” Appl. Opt. 19, 1035-1038 (1980).
[CrossRef]

Y. Koike, Y. Takezawa, and Y. Ohtsuka, “New interfacialgel copolymerization technique for steric GRIN polymer optical waveguides and lens arrays,” Appl. Opt. 27, 486-491 (1988).
[CrossRef]

L. S. Watkins, “Laser beam refraction transversely through a graded-index preform to determine refractive-index ratio and gradient profile,” Appl. Opt. 18, 2214-2222 (1979).
[CrossRef]

W. E. Martin, “Refractive index profile measurements of diffused optical waveguides,” Appl. Opt. 13, 2112-2116 (1974).
[CrossRef]

M. J. Saunders and W. B. Gardner, “Nondestructive interferometric measurement of the delta and alpha of clad optical fibers,” Appl. Opt. 16, 2368-2371 (1977).
[CrossRef]

Y. Ohtsuka and Y. Shimizu, “Radial distribution of the refractive index in light-focusing rods: determination using interphako interference microscopy,” Appl. Opt. 16, 1050-1053 (1979).
[CrossRef]

Y. Kokubun and K. Iga, “Refractive-index profile measurement of preform rods by a transverse differential interferograms,” Appl. Opt. 19, 846-851 (1980).
[CrossRef]

K. S. R. Krishna and A. Sharma, “Chromatic aberrations of radial gradient-index lenses. II. Selfoc lenses,” Appl. Opt. 35, 1037-1040 (1996).
[CrossRef]

Applied Physics Letters (1)

M. E. Marhic, P. S. Ho, and M. Epstein, “Nondestructive refractive-index profile measurements of clad optical fibers,” Appl. Phys. Lett. 26, 574-575 (1975).
[CrossRef]

Electronics Letters (1)

P. L. Chu, “Nondestructive measurement of index profile of an optical-fibre preform,” Electron. Lett. 13, 736-738 (1977).
[CrossRef]

Group IV Photonics, 2005. 2nd IEEE International Conference on (1)

S. Janz, B. Lamontagne, A. Delage, A. Bogdanov, D. X. Xu, and K. P. Yap, “Single layer a-Si GRIN waveguide coupler with lithographically defined facets,” in Proc. 2nd IEEE International Conference on Group IV Photonics (Antwerp, Belgium, Sep. 2005), pp. 129-131.
[CrossRef]

Japanese Journal of Applied Physics (1)

H. Kobayashi and T. Horiuchi, “Novel projection exposure system using gradient-index lens array,” Jpn. J. Appl. Phys. 47, 5702-5707 (2008).
[CrossRef]

Journal of Applied Physics (1)

S. P. Morgan, “General solution of the Luneberg lens problem,” J. Appl. Phys. 29, 1358-1368 (1958).
[CrossRef]

Journal of the Optical Society of Korea (2)

H. H. Lim, M. S. Kwon, H. J. Choi, B. J. Kim, and M. Cha, “Measurement of refractive index of solid medium by critical angle method when air gap is present,” J. Opt. Soc. Korea 12, 210-214 (2008).
[CrossRef]

D. G. Kim, S. Y. Woo, D. K. Kim, T. Y. Hwang, D. Y. Kim, and S.-H. Park, “Generation of 1.5 Gbps pseudo-random binary sequence optical signals by using a gain switched Fabry-Perot semiconductor laser,” J. Opt. Soc. Korea 9, 103-106 (2005).
[CrossRef]

Optical Fiber Technology (1)

I. T. Monroy, H. P. A. vd Boom, A. M. J. Koonen, G. D. Khoe, Y. Watanabe, Y. Koike, and T. Ishigure, “Data transmission over polymer optical fibers,” Optical Fiber Technology 9, 159-171 (2003).
[CrossRef]

Optics Communications (1)

S. Rios, R. Srivastava, and C. G. Reino, “Coupling of single-mode fibers to single-mode GRIN waveguides by butt-joining,” Opt. Comm. 119, 517-522 (1995).
[CrossRef]

Optics Letters (1)

C. Ye and R. R. McLeod, “GRIN lens and lens array fabrication with diffusion-driven photopolymer,” Opt. Lett. 33, 2575-2577 (2008).
[CrossRef]

Proc. SPIE (1)

F. Okano, M. Kobayashi, J. Arai, and M. Okui, “Depth control GRIN lens array for integral photography,” Proc. SPIE 5243, 30-41 (2003).
[CrossRef]

Proc. Symposium IEEE/LEOS Benelux Chapter (1)

S. C. J. Lee, F. Breyer, S. Randel, B. Spinnler, I. L. L. Polo, D. van den Borne, J. Zeng, H. P. A. van den Boom, and A. M. J. Koonen, “Performance of maximum likelihood sequence estimation in 10 Gb/s transmission systems with polymer optical fiber,” in Proc. Symposium IEEE/LEOS Benelux Chapter (Eindhoven, Netherlands, Nov. 2006), pp. 17-19.

Review of Scientific Instruments (1)

J. Stone and R. M. Derosier, “Elimination of errors due to sample polishing in refractive index profile measurements by interferometry,” Rev. Sci. Instru. 47, 885-887 (1976).
[CrossRef]

The Journal of Physical Chemistry B (1)

W. C. Chen, Y. Chang, and J. P. Hsu, “Theoretical analysis on a multilayer coextrusion process for preparing gradient-index polymer optical fibers,” J. Phys. Chem. B 103, 7584-7590 (1999).
[CrossRef]

Other (4)

C. G. Reino, M. V. Perez, and C. Bao, Gradient-index Optics (Springer, Berlin, Germany, 2002).

Gradient-index lenses, “Gradient-index lenses, antireflection coated, for $\lambda$ = 632.8nm,” (Product number, 06 LGD 111), http://www.mellesgriot.com/pdf/0015.16-15.20.pdf.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill Book Co., Singapore, 1996), Chapter 4.

F. G. Smith, T. A. King, and D. Wilkins, Optics and Photonics (John Wiley & Sons, Ltd., West Sussex, UK, 2007), Chapter 2.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.