Abstract

We propose to use optical low coherence reflectometry to measure the reflectance of both faces of a plane substrate with one side coated in antireflective layers. We identify, through a detailed theoretical analysis, the optimum configuration and evaluate the expected sensitivity and accuracy of some realistic examples. Finally, we experimentally demonstrate the ability of this method to quantify reflection coefficients as low as 5×107. That way, an accurate characterization of the performances, at 1550  nm, of antireflective coatings deposited on various plane substrates is achieved.

© 2007 Optical Society of America

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References

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  1. T. Bosselman and R. Ulrich, "High-accuracy position sensing with fiber-coupled white-light interferometers," in Proceedings of the Second International Conference on Optical Fiber Sensors, M. Nijhoff, ed. (Springer Verlag, 1984), pp. 361-364.
  2. H. C. Lefèvre, "White-light interferometry in optical fibre sensors," in Proceedings of the 7th Optical Fiber Sensors Conference (Institution of Radio and Electronics Engineering, Sydney, Australia, 1990), pp. 345-352.
  3. M. Lequime, C. Lecot, H. Giovannini, and S. J. Huard, "Dual-wavelength passive homodyne detection unit for fiber-coupled white-light interferometers," in Fiber Optic Sensors IV, R. T. Kersten, ed., Proc. SPIE 1267, 288-298 (1990).
  4. P. Sansonetti, M. Lequime, D. Engrand, J. J. Guerin, R. Davidson, S. S. Roberts, B. Fomari, M. Martinelli, P. Escobar Rojo, V. Gusmeroli, P. Ferdinand, J. Plantey, M. F. Crowther, B. Culshaw, and W. C. Michie, "Intelligent composites containing measuring fiber-optic networks for continuous self-diagnosis," in Fiber Optic Smart Structures and Skins IV, R. O. Claus and E. Udd, eds., Proc. SPIE 1588, 198-209 (1991).
    [CrossRef]
  5. K. Takada, A. Himeno, and K. Yukimatsu, "Phase-noise and shot-noise limited operations of low coherence optical time domain reflectometry," Appl. Phys. Lett. 59, 2483-2485 (1991).
    [CrossRef]
  6. K. Kasaya, K. Yoshikuni, and H. Ishii, "Measurements of a semiconductor waveguide using a low-coherence interferometric reflectometer," IEEE Photon. Technol. Lett. 8, 251-253 (1996).
    [CrossRef]
  7. E. A. Swanson, J. A. Izatt, M. R. Hee, D. Huang, C. Lin, J. S. Schuman, C. A. Puliafito, and J. G. Fujimoto, "In vivo retinal imaging by optical coherence tomography," Opt. Lett. 18, 1864-1866 (1993).
    [CrossRef] [PubMed]
  8. G. J. Tearney, B. E. Bouma, S. A. Boppart, B. Golubovic, E. A. Swanson, and J. G. Fujimoto, "Rapid acquisition of in vivo biological images by use of optical coherence tomography," Opt. Lett. 21, 1408-1410 (1996).
    [CrossRef] [PubMed]
  9. U. Morgner, W. Drexler, F. X. Kärtner, X. D. Li, C. Pitris, E. P. Ippen, and J. G. Fujimoto, "Spectroscopic optical coherence tomography," Opt. Lett. 25, 111-113 (2000).
    [CrossRef]
  10. W. V. Sorin and D. F. Gray, "Simultaneous thickness and group index measurement using optical low-coherence reflectometry," IEEE Photon. Technol. Lett. 4, 105-107 (1992).
    [CrossRef]
  11. M. Haruna, M. Ohmi, T. Mitsuyama, H. Tajiri, H. Maruyama, and M. Hashimoto, "Simultaneous measurement of the phase and group indices and the thickness of transparent plates by low-coherence interferometry," Opt. Lett. 23, 966-968 (1998).
    [CrossRef]
  12. M. Duncan, J. Reintjes, and M. Bashkansky, "Subsurface defect detection in materials using optical coherence tomography," Opt. Express 2, 540-545 (1998).
    [CrossRef] [PubMed]
  13. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley-Interscience, 1991).
    [CrossRef]
  14. H. Kogelnik, "Coupling and conversion coefficients for optical modes," in Microwave Research Institute Symposia Series, J. Fox, ed. (Polytechnic Press, 1964), Vol. 14, p. 333.
  15. M. Saruwatari and K. Nawata, "Semiconductor laser to single-mode fiber coupler," Appl. Opt. 18, 1847-1856 (1979).
    [CrossRef] [PubMed]
  16. H. Giovannini, S. Huard, and M. Lequime, "Influence of chromatic dispersion on a dual-wavelength passive-homodyne detection method for fiber-coupled interferometers," Appl. Opt. 33, 2721-2733 (1994).
    [CrossRef] [PubMed]
  17. M. J. Weber, Handbook of Optical Materials (CRC Press, 2003).
  18. P. Martin, E. M. Skouri, L. Chusseau, C. Alibert and H. Bissessur, "Accurate refractive index measurements of doped and undoped InP by a grating coupling technique," Appl. Phys. Lett. 67, 881-883 (1995).
    [CrossRef]
  19. H. A. Macleod, Thin-Film Optical Filters, 3rd ed. (Institute of Physics, 2001).
  20. http://www.exfo.com/en/products/ProductsFamily.asp?Family=201.
  21. http://www.femto.de/datasheet/DE-DLPCA-200_15.pdf.

2000 (1)

1998 (2)

1996 (2)

G. J. Tearney, B. E. Bouma, S. A. Boppart, B. Golubovic, E. A. Swanson, and J. G. Fujimoto, "Rapid acquisition of in vivo biological images by use of optical coherence tomography," Opt. Lett. 21, 1408-1410 (1996).
[CrossRef] [PubMed]

K. Kasaya, K. Yoshikuni, and H. Ishii, "Measurements of a semiconductor waveguide using a low-coherence interferometric reflectometer," IEEE Photon. Technol. Lett. 8, 251-253 (1996).
[CrossRef]

1995 (1)

P. Martin, E. M. Skouri, L. Chusseau, C. Alibert and H. Bissessur, "Accurate refractive index measurements of doped and undoped InP by a grating coupling technique," Appl. Phys. Lett. 67, 881-883 (1995).
[CrossRef]

1994 (1)

1993 (1)

1992 (1)

W. V. Sorin and D. F. Gray, "Simultaneous thickness and group index measurement using optical low-coherence reflectometry," IEEE Photon. Technol. Lett. 4, 105-107 (1992).
[CrossRef]

1991 (2)

P. Sansonetti, M. Lequime, D. Engrand, J. J. Guerin, R. Davidson, S. S. Roberts, B. Fomari, M. Martinelli, P. Escobar Rojo, V. Gusmeroli, P. Ferdinand, J. Plantey, M. F. Crowther, B. Culshaw, and W. C. Michie, "Intelligent composites containing measuring fiber-optic networks for continuous self-diagnosis," in Fiber Optic Smart Structures and Skins IV, R. O. Claus and E. Udd, eds., Proc. SPIE 1588, 198-209 (1991).
[CrossRef]

K. Takada, A. Himeno, and K. Yukimatsu, "Phase-noise and shot-noise limited operations of low coherence optical time domain reflectometry," Appl. Phys. Lett. 59, 2483-2485 (1991).
[CrossRef]

1990 (1)

M. Lequime, C. Lecot, H. Giovannini, and S. J. Huard, "Dual-wavelength passive homodyne detection unit for fiber-coupled white-light interferometers," in Fiber Optic Sensors IV, R. T. Kersten, ed., Proc. SPIE 1267, 288-298 (1990).

1979 (1)

Appl. Opt. (2)

Appl. Phys. Lett. (2)

P. Martin, E. M. Skouri, L. Chusseau, C. Alibert and H. Bissessur, "Accurate refractive index measurements of doped and undoped InP by a grating coupling technique," Appl. Phys. Lett. 67, 881-883 (1995).
[CrossRef]

K. Takada, A. Himeno, and K. Yukimatsu, "Phase-noise and shot-noise limited operations of low coherence optical time domain reflectometry," Appl. Phys. Lett. 59, 2483-2485 (1991).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

K. Kasaya, K. Yoshikuni, and H. Ishii, "Measurements of a semiconductor waveguide using a low-coherence interferometric reflectometer," IEEE Photon. Technol. Lett. 8, 251-253 (1996).
[CrossRef]

W. V. Sorin and D. F. Gray, "Simultaneous thickness and group index measurement using optical low-coherence reflectometry," IEEE Photon. Technol. Lett. 4, 105-107 (1992).
[CrossRef]

Opt. Express (1)

Opt. Lett. (4)

Proc. SPIE (1)

P. Sansonetti, M. Lequime, D. Engrand, J. J. Guerin, R. Davidson, S. S. Roberts, B. Fomari, M. Martinelli, P. Escobar Rojo, V. Gusmeroli, P. Ferdinand, J. Plantey, M. F. Crowther, B. Culshaw, and W. C. Michie, "Intelligent composites containing measuring fiber-optic networks for continuous self-diagnosis," in Fiber Optic Smart Structures and Skins IV, R. O. Claus and E. Udd, eds., Proc. SPIE 1588, 198-209 (1991).
[CrossRef]

Other (9)

T. Bosselman and R. Ulrich, "High-accuracy position sensing with fiber-coupled white-light interferometers," in Proceedings of the Second International Conference on Optical Fiber Sensors, M. Nijhoff, ed. (Springer Verlag, 1984), pp. 361-364.

H. C. Lefèvre, "White-light interferometry in optical fibre sensors," in Proceedings of the 7th Optical Fiber Sensors Conference (Institution of Radio and Electronics Engineering, Sydney, Australia, 1990), pp. 345-352.

M. Lequime, C. Lecot, H. Giovannini, and S. J. Huard, "Dual-wavelength passive homodyne detection unit for fiber-coupled white-light interferometers," in Fiber Optic Sensors IV, R. T. Kersten, ed., Proc. SPIE 1267, 288-298 (1990).

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley-Interscience, 1991).
[CrossRef]

H. Kogelnik, "Coupling and conversion coefficients for optical modes," in Microwave Research Institute Symposia Series, J. Fox, ed. (Polytechnic Press, 1964), Vol. 14, p. 333.

M. J. Weber, Handbook of Optical Materials (CRC Press, 2003).

H. A. Macleod, Thin-Film Optical Filters, 3rd ed. (Institute of Physics, 2001).

http://www.exfo.com/en/products/ProductsFamily.asp?Family=201.

http://www.femto.de/datasheet/DE-DLPCA-200_15.pdf.

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Figures (13)

Fig. 1
Fig. 1

Schematic description of an OLCR.

Fig. 2
Fig. 2

Filtered signal recorded with an uncoated 1 mm thick silica window.

Fig. 3
Fig. 3

OLCR, alternative focused configuration.

Fig. 4
Fig. 4

Spectral properties of the AR2 stack.

Fig. 5
Fig. 5

Spectral properties of the AR4 stack.

Fig. 6
Fig. 6

Spectral profile of an EDFA-ASE source.

Fig. 7
Fig. 7

Influence of the spectral variation of the reflectance on the echo shape.

Fig. 8
Fig. 8

Bare silica window, experimental LCOR recording.

Fig. 9
Fig. 9

Bare silica window, zoomed view of the OLCR recording.

Fig. 10
Fig. 10

AR-coated silica window, raw signal.

Fig. 11
Fig. 11

AR-coated silica window, filtered signal.

Fig. 12
Fig. 12

AR-coated InP wafer, raw signal.

Fig. 13
Fig. 13

AR-coated InP wafer, filtered signal.

Tables (4)

Tables Icon

Table 1 Window Dispersion Phenomena—Main Parameters

Tables Icon

Table 2 Spectral Averaging Effects—Influence of the Source Profile

Tables Icon

Table 3 Bare Silica Window and Collimated Configuration; Comparison of Theoretical and Experimental Data

Tables Icon

Table 4 Bare Silica Window and Focused Configuration; Comparison of Theoretical and Experimental Data

Equations (35)

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

A M ( σ ) = A ( σ ) L 2 Y ( 1 Y ) R M η M ( z ) × e 4 i π σ ( z + f ) e i φ M ,
A S ( σ ) = A ( σ ) L 2 Y ( 1 Y ) k = 1 R k η k × e 4 i π σ ( z k + f ) e i φ k ,
P D ( σ ) = | A M ( σ ) + A S ( σ ) | 2 = P ( σ ) L 2 Y ( 1 Y ) × [ C S + C M ( z ) + C 0 ( z ) ] ,
C S = 2 k = 1 R k η k × l = k + 1 R l η l cos [ 4 π σ ( z k z l ) + ( φ k φ l ) ] ,
C M ( z ) = 2 R M η M ( z ) × k = 1 R k η k cos [ 4 π σ ( z z k ) + ( φ M φ k ) ] ,
C 0 ( z ) = R M η M ( z ) + k = 1 R k η k .
I ( z ) = σ S ( σ ) P D ( σ ) d σ ,
P ( σ ) = P 0 δ σ π e [ σ σ 0 δ σ ] 2 ,
n t π δ σ = n t π Δ λ λ 0 2 1 .
I ( z ) = S P 0 Y ( 1 Y ) L 2 { C 0 ( z ) + 2 R M η M ( z ) × k = 1 R k η k e [ 2 π δ σ ( z z k ) ] 2 cos [ 4 π σ 0 ( z z k ) + ( φ M φ k ) ] } .
I F ( z ) = 2 S P 0 Y ( 1 Y ) L 2 R M η M ( z ) × k = 1 R k η k e [ 2 π δ σ ( z z k ) ] 2 .
M k = S k S 1 = R k R 1 × η k η M ( z k ) η 1 η M ( z 1 ) ,
R 2 = ( n 1 n + 1 ) 2 η 1 η M ( z 1 ) η 2 η M ( z 2 ) × [ S 2 S 1 ] 2 .
η = 4 w 1 2 w 0 2 ( w 1 2 + w 0 2 ) 2 + ( λ 0 g / π ) 2 .
η M ( z ) = 4 W 1 2 W 0 2 ( W 1 2 + W 0 2 ) 2 + [ 2 λ 0 ( z z 1 ) π ] 2 ,
W 1 = W 0 = λ 0 f π w 0 ,
η M ( z k ) = 1 1 + [ π w 0 2 ( z k z 1 ) λ 0 f 2 ] 2 = 1 1 + [ π w 0 2 ( k 1 ) n t λ 0 f 2 ] 2 .
η k = 1 1 + [ π w 0 2 ( k 1 ) t n λ 0 f 2 ] 2 .
η ( α ) = η ( 0 ) e [ 2 f α w 0 ] 2 ,
η k = 1 1 + [ ( k 1 ) t λ f 2 n π w 0 2 ( z E f ) 2 ] 2 ,
z E = z 1 + f 2 [ 1 + 1 4 f z 1 + f ] .
η ( α ) = η ( 0 ) e [ 2 π w 0 α λ · z E f f ] 2 ,
I F ( z ) = 2 S P 0 Y ( 1 Y ) A 2 R M η M ( z ) k = 1 R k η k G k ( z ) ,
G k ( z ) = 1 + θ k 2 4 e [ 2 π δ σ 1 + θ k 2 ( z z k δ z k ) ] 2 ,
θ k = 2 π ( k 1 ) t λ 0 × ( δ λ λ 0 ) 2 × ( 2 n λ 2 ) λ 0 ,
δ z k = ( k 1 ) t λ 0 × ( n λ ) λ 0 ,
n 2 ( λ ) = 1 + λ 2 [ 0.6961663 λ 2 ( 0.0684043 ) 2 + 0.4079426 λ 2 ( 0.1162414 ) 2 + 0.8974794 λ 2 ( 9.896161 ) 2 ] ,
n 2 ( λ ) = 7.283 + 2.337 λ 2 λ 2 0.387.10 6 ,
SiO 2 n SiO 2 ( λ ) = 1.48144 + 0.007369 λ 2 ,
T a 2 O 5 n T a 2 O 5 ( λ ) = 2.08527 + 0.016975 λ 2 + 0.001625 λ 4 ,
I ( z ) = 1 δ λ π λ e ( λ λ 0 δ λ ) 2 cos [ φ AR ( λ ) + 4 π λ z ] d λ ,
I ( z ) = λ R ( λ ) P ( λ ) cos [ 4 π λ z ] d λ λ P ( λ ) d λ ,
R 2 = R AR ( 1 R ) 2 = R η 1 η M ( z 1 ) η 2 η M ( z 2 ) × [ S 2 S 1 ] 2 ,
R 1 × e ( t Δ z [ n 0 λ 0 ( n / λ ) λ 0 ] ) 2 10 2 × R 2 ,
δ λ λ 0 2 × 4 ln ( 10 ) + ln ( R 1 / R 2 ) 2 π 2 t [ n 0 λ 0 ( n / λ ) λ 0 ] .

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