Abstract

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

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References

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2012 (1)

2010 (4)

2008 (1)

2006 (1)

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

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).
[CrossRef]

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).
[CrossRef]

Southern, J. F.

Tajiri, H.

Tearney, G. J.

Yamaguchi, I.

Youngquist, R. C.

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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)

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Table 1. Variation of Phase Retardation with Rotation Angle

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Table 2. Number Solution of Unknown Numbers

Equations (3)

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δ=(lBClAD+lFGlEH)×90°,
δ=2πd(ne2sin2θno2sin2θ)λ2πN,
δ1=2πd(ne2sin2θ1no2sin2θ1)λ2πNδ2=2πd(ne2sin2θ2no2sin2θ2)λ2πNδ3=2πd(ne2sin2θ3no2sin2θ3)λ2πNδ4=2πd(ne2sin2θ4no2sin2θ4)λ2πN}d,ne,no,N.

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