We introduce a technique for simultaneous measurement of thickness and refractive index of birefringent materials. The principle is based on the laser feedback effect that laser polarization states flip between two orthogonal directions when a birefringent material is placed into the external cavity. The position of polarization flipping is determined by the phase-retardation magnitude of the birefringent material. Some feature points in the laser intensity curve can be used to calculate phase retardation. We derive an expression for phase retardation and rotation angle of a birefringent material to calculate thickness and refractive index. This technique is noncontact and compatible with in situ thickness and refractive-index measurement. The measurement precision of thickness is 59 nm and of refractive index is 0.0006.

© 2013 Optical Society of America

Full Article  |  PDF Article


  • View by:
  • |
  • |
  • |

  1. R. C. Youngquist, S. Carr, and D. E. N. Davies, Opt. Lett. 12, 158 (1987).
  2. G. J. Tearney, M. E. Brezinski, J. F. Southern, B. E. Bouma, M. R. Hee, and J. G. Fujimoto, Opt. Lett. 20, 2258 (1995).
  3. H. J. Choi, H. Lim, H. S. Moon, T. B. Eom, J. J. Ju, and M. Cha, Opt. Express 18, 9429 (2010).
  4. Y. Sik and S. W. Kim, Opt. Express 14, 11185 (2006).
  5. S. H. Kim, S. H. Lee, J. I. Lim, and K. H. Kim, Appl. Opt. 49, 910 (2010).
  6. G. Coppola, P. Ferratro, M. Iodice, and S. D. Nicola, Appl. Opt. 42, 3882 (2003).
  7. T. Fukano and I. Yamaguchi, Opt. Lett. 21, 1942 (1996).
  8. M. Haruna, M. Ohmi, T. Mitsuyama, H. Tajiri, H. Maruyama, and M. Hashimoto, Opt. Lett. 23, 966 (1998).
  9. S. Kim, J. Na, M. J. Kim, and B. H. Lee, Opt. Express 16, 5516 (2008).
  10. Y. P. Kumar and S. Chatterjee, Appl. Opt. 51, 3533 (2012).
  11. H. C. Cheng and Y. C. Liu, Appl. Opt. 49, 790 (2010).
  12. K. Hibino, B. F. Oreb, P. S. Fairman, and J. Burke, Appl. Opt. 43, 1241 (2004).
  13. M. T. Fathi and S. Donati, Opt. Lett. 35, 1844 (2010).

2012 (1)

2010 (4)

2008 (1)

2006 (1)

Y. Sik and S. W. Kim, Opt. Express 14, 11185 (2006).

2004 (1)

2003 (1)

1998 (1)

1996 (1)

1995 (1)

1987 (1)

Bouma, B. E.

Brezinski, M. E.

Burke, J.

Carr, S.

Cha, M.

Chatterjee, S.

Cheng, H. C.

Choi, H. J.

Coppola, G.

Davies, D. E. N.

Donati, S.

Eom, T. B.

Fairman, P. S.

Fathi, M. T.

Ferratro, P.

Fujimoto, J. G.

Fukano, T.

Haruna, M.

Hashimoto, M.

Hee, M. R.

Hibino, K.

Iodice, M.

Ju, J. J.

Kim, K. H.

Kim, M. J.

Kim, S.

Kim, S. H.

Kim, S. W.

Y. Sik and S. W. Kim, Opt. Express 14, 11185 (2006).

Kumar, Y. P.

Lee, B. H.

Lee, S. H.

Lim, H.

Lim, J. I.

Liu, Y. C.

Maruyama, H.

Mitsuyama, T.

Moon, H. S.

Na, J.

Nicola, S. D.

Ohmi, M.

Oreb, B. F.

Sik, Y.

Y. Sik and S. W. Kim, Opt. Express 14, 11185 (2006).

Southern, J. F.

Tajiri, H.

Tearney, G. J.

Yamaguchi, I.

Youngquist, R. C.

Cited By

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

Alert me when this article is cited.

Figures (4)

Fig. 1.
Fig. 1.

Setup for thickness and refractive-index measurement by laser feedback method. D1 and D2, photo detectors; M1 and M2, high reflectors; S, birefringence sample; θ, angle; ME, feedback mirror; PZT, piezoelectric transducer; P, polarizer; DA, digital-to-analog signal conversion; AD, analog-to-digital signal conversion; and AMP, voltage amplification.

Fig. 2.
Fig. 2.

Fast axis is (a) far away from x axis and (b) consistent with x axis.

Fig. 3.
Fig. 3.

Slow axis is (a) far away from x axis and (b) consistent with x axis.

Fig. 4.
Fig. 4.

Curve of laser intensity output.

Tables (2)

Tables Icon

Table 1. Variation of Phase Retardation with Rotation Angle

Tables Icon

Table 2. Number Solution of Unknown Numbers

Equations (3)

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