Abstract

We describe an interferometric method that uses an interference microscope that permits the determination of the complete two-dimensional refractive-index profile of integrated optical waveguides, provided that the form of the one-dimensional depth profile is known. Results are reported for potassium–sodium ion-exchanged channel waveguides and are shown to be in good agreement with theory.

© 1991 Optical Society of America

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References

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  1. R. A. Betts, F. Lui, S. Dagias, “Wavelength and polarisation insensitive optical splitters fabricated in K+/Na+ ion-exchanged glass,” IEEE Photon. Technol. Lett. 2, 481–483 (1990).
    [CrossRef]
  2. R. A. Betts, F. Lui, “Tunable couplers fabricated in K+/Na+ ion-exchanged glass,” Electron. Lett. 26, 786–788 (1990).
    [CrossRef]
  3. F. Lui, R. A. Betts, “An optical wavelength multiplexer/ demultiplexer fabricated in ion-exchanged glass,” in Proceedings of IREECON International (IREE, Sydney, 1989), pp. 547–550.
  4. R. C. Alferness, “Guided-wave devices for optical communication,” IEEE J. Quantum Electron. QE-17, 946–959 (1981).
    [CrossRef]
  5. R. A. Betts, F. Lui, “Broadband polarisation splitting couplers in ion-exchanged glass,” Electron. Lett. 26, 450–452 (1990).
    [CrossRef]
  6. R. G. Hunsperger, Integrated Optics: Theory and Technology (Springer-Verlag, Berlin, 1984).
  7. J. M. White, P. F. Heidrich, “Optical waveguide refractive index profiles determined from measurement of mode indices: a simple analysis,” Appl. Opt. 15, 151–155 (1976).
    [CrossRef] [PubMed]
  8. R. A. Betts, C. W. Pitt, K. R. Riddle, L. M. Walpita, “A comparative study of the dopant profiles in diffused planar optical waveguides by SIMS and guided wave probe,” Appl. Phys. A 31, 29–35 (1983).
  9. K. Morishita, “Index profiling of three dimensional waveguides by the propagation-mode near-field method,” IEEE J. Lightwave Technol. LT-4, 1120–1127 (1986).
    [CrossRef]
  10. R. V. Ramaswamy, R. Srivastava, “Ion-exchanged glass waveguides: a review,” IEEE J. Lightwave Technol. 6, 984–1002 (1988).
    [CrossRef]
  11. Technical Stereomicroscope Instruction Manual (Carl Zeiss, Jena).
  12. P. L. Chu, T. W. Whitbread, “Nondestructive determination of the refractive index profile of an optical fibre: fast Fourier transform method,” Appl. Opt. 18, 1117–1122 (1979).
    [CrossRef] [PubMed]
  13. M. E. Marhic, P. S. Ho, M. Epstein, “Nondestructive refractive index profile measurements of clad optical fibres,” Appl. Phys. Lett. 26, 574–575 (1975).
    [CrossRef]
  14. G. Stewart, C. A. Miller, P. J. R. Layborn, C. D. W. Wilkinson, R. M. DeLaRue, “Planar optical waveguides formed by silver ion migration in glass,” IEEE J. Quantum Electron. QE-13, 192–200 (1977).
    [CrossRef]
  15. J. Albert, G. L. Yip, “Refractive index profiles of planar waveguides made by ion-exchange in glass,” Appl. Opt. 24, 3692–3693 (1985).
    [CrossRef] [PubMed]
  16. A. Miliou, H. Zhenguang, H. C. Cheng, R. Srivastava, R. V. Ramaswamy, “Fibre compatible K+−Na+ ion exchanged channel waveguides: fabrication and characterisation,” IEEE J. Quantum Electron. 25, 1889–1897 (1989).
    [CrossRef]
  17. M. Fukama, J. Noda, H. Iwasaki, “Optical properties of titanium diffused LiNbO3 strip waveguides,” J. Appl. Phys. 49, 3693–3698 (1978).
    [CrossRef]
  18. G. B. Hocker, W. K. Burns, “Mode dispersion in different channel waveguides by the effective index method”Appl. Opt. 16, 113–118 (1977).
    [CrossRef] [PubMed]
  19. J. Crank, The Mathematics of Diffusion (Oxford U. Press, New York, 1967).
  20. J. Albert, G. L. Yip, “Stress induced index change for K+−Na+ ion exchange in glass,” Electron. Lett. 23, 737–738 (1987).
    [CrossRef]
  21. T. Findakly, “Glass waveguides by ion-exchange: a review,” Opt. Eng. 24, 244–250 (1985).
    [CrossRef]
  22. M. J. Adams, An Introduction to Optical Waveguides (Wiley, New York, 1981).

1990

R. A. Betts, F. Lui, S. Dagias, “Wavelength and polarisation insensitive optical splitters fabricated in K+/Na+ ion-exchanged glass,” IEEE Photon. Technol. Lett. 2, 481–483 (1990).
[CrossRef]

R. A. Betts, F. Lui, “Tunable couplers fabricated in K+/Na+ ion-exchanged glass,” Electron. Lett. 26, 786–788 (1990).
[CrossRef]

R. A. Betts, F. Lui, “Broadband polarisation splitting couplers in ion-exchanged glass,” Electron. Lett. 26, 450–452 (1990).
[CrossRef]

1989

A. Miliou, H. Zhenguang, H. C. Cheng, R. Srivastava, R. V. Ramaswamy, “Fibre compatible K+−Na+ ion exchanged channel waveguides: fabrication and characterisation,” IEEE J. Quantum Electron. 25, 1889–1897 (1989).
[CrossRef]

1988

R. V. Ramaswamy, R. Srivastava, “Ion-exchanged glass waveguides: a review,” IEEE J. Lightwave Technol. 6, 984–1002 (1988).
[CrossRef]

1987

J. Albert, G. L. Yip, “Stress induced index change for K+−Na+ ion exchange in glass,” Electron. Lett. 23, 737–738 (1987).
[CrossRef]

1986

K. Morishita, “Index profiling of three dimensional waveguides by the propagation-mode near-field method,” IEEE J. Lightwave Technol. LT-4, 1120–1127 (1986).
[CrossRef]

1985

1983

R. A. Betts, C. W. Pitt, K. R. Riddle, L. M. Walpita, “A comparative study of the dopant profiles in diffused planar optical waveguides by SIMS and guided wave probe,” Appl. Phys. A 31, 29–35 (1983).

1981

R. C. Alferness, “Guided-wave devices for optical communication,” IEEE J. Quantum Electron. QE-17, 946–959 (1981).
[CrossRef]

1979

1978

M. Fukama, J. Noda, H. Iwasaki, “Optical properties of titanium diffused LiNbO3 strip waveguides,” J. Appl. Phys. 49, 3693–3698 (1978).
[CrossRef]

1977

G. B. Hocker, W. K. Burns, “Mode dispersion in different channel waveguides by the effective index method”Appl. Opt. 16, 113–118 (1977).
[CrossRef] [PubMed]

G. Stewart, C. A. Miller, P. J. R. Layborn, C. D. W. Wilkinson, R. M. DeLaRue, “Planar optical waveguides formed by silver ion migration in glass,” IEEE J. Quantum Electron. QE-13, 192–200 (1977).
[CrossRef]

1976

1975

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

Adams, M. J.

M. J. Adams, An Introduction to Optical Waveguides (Wiley, New York, 1981).

Albert, J.

J. Albert, G. L. Yip, “Stress induced index change for K+−Na+ ion exchange in glass,” Electron. Lett. 23, 737–738 (1987).
[CrossRef]

J. Albert, G. L. Yip, “Refractive index profiles of planar waveguides made by ion-exchange in glass,” Appl. Opt. 24, 3692–3693 (1985).
[CrossRef] [PubMed]

Alferness, R. C.

R. C. Alferness, “Guided-wave devices for optical communication,” IEEE J. Quantum Electron. QE-17, 946–959 (1981).
[CrossRef]

Betts, R. A.

R. A. Betts, F. Lui, “Broadband polarisation splitting couplers in ion-exchanged glass,” Electron. Lett. 26, 450–452 (1990).
[CrossRef]

R. A. Betts, F. Lui, S. Dagias, “Wavelength and polarisation insensitive optical splitters fabricated in K+/Na+ ion-exchanged glass,” IEEE Photon. Technol. Lett. 2, 481–483 (1990).
[CrossRef]

R. A. Betts, F. Lui, “Tunable couplers fabricated in K+/Na+ ion-exchanged glass,” Electron. Lett. 26, 786–788 (1990).
[CrossRef]

R. A. Betts, C. W. Pitt, K. R. Riddle, L. M. Walpita, “A comparative study of the dopant profiles in diffused planar optical waveguides by SIMS and guided wave probe,” Appl. Phys. A 31, 29–35 (1983).

F. Lui, R. A. Betts, “An optical wavelength multiplexer/ demultiplexer fabricated in ion-exchanged glass,” in Proceedings of IREECON International (IREE, Sydney, 1989), pp. 547–550.

Burns, W. K.

Cheng, H. C.

A. Miliou, H. Zhenguang, H. C. Cheng, R. Srivastava, R. V. Ramaswamy, “Fibre compatible K+−Na+ ion exchanged channel waveguides: fabrication and characterisation,” IEEE J. Quantum Electron. 25, 1889–1897 (1989).
[CrossRef]

Chu, P. L.

Crank, J.

J. Crank, The Mathematics of Diffusion (Oxford U. Press, New York, 1967).

Dagias, S.

R. A. Betts, F. Lui, S. Dagias, “Wavelength and polarisation insensitive optical splitters fabricated in K+/Na+ ion-exchanged glass,” IEEE Photon. Technol. Lett. 2, 481–483 (1990).
[CrossRef]

DeLaRue, R. M.

G. Stewart, C. A. Miller, P. J. R. Layborn, C. D. W. Wilkinson, R. M. DeLaRue, “Planar optical waveguides formed by silver ion migration in glass,” IEEE J. Quantum Electron. QE-13, 192–200 (1977).
[CrossRef]

Epstein, M.

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

Findakly, T.

T. Findakly, “Glass waveguides by ion-exchange: a review,” Opt. Eng. 24, 244–250 (1985).
[CrossRef]

Fukama, M.

M. Fukama, J. Noda, H. Iwasaki, “Optical properties of titanium diffused LiNbO3 strip waveguides,” J. Appl. Phys. 49, 3693–3698 (1978).
[CrossRef]

Heidrich, P. F.

Ho, P. S.

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

Hocker, G. B.

Hunsperger, R. G.

R. G. Hunsperger, Integrated Optics: Theory and Technology (Springer-Verlag, Berlin, 1984).

Iwasaki, H.

M. Fukama, J. Noda, H. Iwasaki, “Optical properties of titanium diffused LiNbO3 strip waveguides,” J. Appl. Phys. 49, 3693–3698 (1978).
[CrossRef]

Layborn, P. J. R.

G. Stewart, C. A. Miller, P. J. R. Layborn, C. D. W. Wilkinson, R. M. DeLaRue, “Planar optical waveguides formed by silver ion migration in glass,” IEEE J. Quantum Electron. QE-13, 192–200 (1977).
[CrossRef]

Lui, F.

R. A. Betts, F. Lui, “Broadband polarisation splitting couplers in ion-exchanged glass,” Electron. Lett. 26, 450–452 (1990).
[CrossRef]

R. A. Betts, F. Lui, “Tunable couplers fabricated in K+/Na+ ion-exchanged glass,” Electron. Lett. 26, 786–788 (1990).
[CrossRef]

R. A. Betts, F. Lui, S. Dagias, “Wavelength and polarisation insensitive optical splitters fabricated in K+/Na+ ion-exchanged glass,” IEEE Photon. Technol. Lett. 2, 481–483 (1990).
[CrossRef]

F. Lui, R. A. Betts, “An optical wavelength multiplexer/ demultiplexer fabricated in ion-exchanged glass,” in Proceedings of IREECON International (IREE, Sydney, 1989), pp. 547–550.

Marhic, M. E.

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

Miliou, A.

A. Miliou, H. Zhenguang, H. C. Cheng, R. Srivastava, R. V. Ramaswamy, “Fibre compatible K+−Na+ ion exchanged channel waveguides: fabrication and characterisation,” IEEE J. Quantum Electron. 25, 1889–1897 (1989).
[CrossRef]

Miller, C. A.

G. Stewart, C. A. Miller, P. J. R. Layborn, C. D. W. Wilkinson, R. M. DeLaRue, “Planar optical waveguides formed by silver ion migration in glass,” IEEE J. Quantum Electron. QE-13, 192–200 (1977).
[CrossRef]

Morishita, K.

K. Morishita, “Index profiling of three dimensional waveguides by the propagation-mode near-field method,” IEEE J. Lightwave Technol. LT-4, 1120–1127 (1986).
[CrossRef]

Noda, J.

M. Fukama, J. Noda, H. Iwasaki, “Optical properties of titanium diffused LiNbO3 strip waveguides,” J. Appl. Phys. 49, 3693–3698 (1978).
[CrossRef]

Pitt, C. W.

R. A. Betts, C. W. Pitt, K. R. Riddle, L. M. Walpita, “A comparative study of the dopant profiles in diffused planar optical waveguides by SIMS and guided wave probe,” Appl. Phys. A 31, 29–35 (1983).

Ramaswamy, R. V.

A. Miliou, H. Zhenguang, H. C. Cheng, R. Srivastava, R. V. Ramaswamy, “Fibre compatible K+−Na+ ion exchanged channel waveguides: fabrication and characterisation,” IEEE J. Quantum Electron. 25, 1889–1897 (1989).
[CrossRef]

R. V. Ramaswamy, R. Srivastava, “Ion-exchanged glass waveguides: a review,” IEEE J. Lightwave Technol. 6, 984–1002 (1988).
[CrossRef]

Riddle, K. R.

R. A. Betts, C. W. Pitt, K. R. Riddle, L. M. Walpita, “A comparative study of the dopant profiles in diffused planar optical waveguides by SIMS and guided wave probe,” Appl. Phys. A 31, 29–35 (1983).

Srivastava, R.

A. Miliou, H. Zhenguang, H. C. Cheng, R. Srivastava, R. V. Ramaswamy, “Fibre compatible K+−Na+ ion exchanged channel waveguides: fabrication and characterisation,” IEEE J. Quantum Electron. 25, 1889–1897 (1989).
[CrossRef]

R. V. Ramaswamy, R. Srivastava, “Ion-exchanged glass waveguides: a review,” IEEE J. Lightwave Technol. 6, 984–1002 (1988).
[CrossRef]

Stewart, G.

G. Stewart, C. A. Miller, P. J. R. Layborn, C. D. W. Wilkinson, R. M. DeLaRue, “Planar optical waveguides formed by silver ion migration in glass,” IEEE J. Quantum Electron. QE-13, 192–200 (1977).
[CrossRef]

Walpita, L. M.

R. A. Betts, C. W. Pitt, K. R. Riddle, L. M. Walpita, “A comparative study of the dopant profiles in diffused planar optical waveguides by SIMS and guided wave probe,” Appl. Phys. A 31, 29–35 (1983).

Whitbread, T. W.

White, J. M.

Wilkinson, C. D. W.

G. Stewart, C. A. Miller, P. J. R. Layborn, C. D. W. Wilkinson, R. M. DeLaRue, “Planar optical waveguides formed by silver ion migration in glass,” IEEE J. Quantum Electron. QE-13, 192–200 (1977).
[CrossRef]

Yip, G. L.

J. Albert, G. L. Yip, “Stress induced index change for K+−Na+ ion exchange in glass,” Electron. Lett. 23, 737–738 (1987).
[CrossRef]

J. Albert, G. L. Yip, “Refractive index profiles of planar waveguides made by ion-exchange in glass,” Appl. Opt. 24, 3692–3693 (1985).
[CrossRef] [PubMed]

Zhenguang, H.

A. Miliou, H. Zhenguang, H. C. Cheng, R. Srivastava, R. V. Ramaswamy, “Fibre compatible K+−Na+ ion exchanged channel waveguides: fabrication and characterisation,” IEEE J. Quantum Electron. 25, 1889–1897 (1989).
[CrossRef]

Appl. Opt.

Appl. Phys.

R. A. Betts, C. W. Pitt, K. R. Riddle, L. M. Walpita, “A comparative study of the dopant profiles in diffused planar optical waveguides by SIMS and guided wave probe,” Appl. Phys. A 31, 29–35 (1983).

Appl. Phys. Lett.

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

Electron. Lett.

R. A. Betts, F. Lui, “Broadband polarisation splitting couplers in ion-exchanged glass,” Electron. Lett. 26, 450–452 (1990).
[CrossRef]

R. A. Betts, F. Lui, “Tunable couplers fabricated in K+/Na+ ion-exchanged glass,” Electron. Lett. 26, 786–788 (1990).
[CrossRef]

J. Albert, G. L. Yip, “Stress induced index change for K+−Na+ ion exchange in glass,” Electron. Lett. 23, 737–738 (1987).
[CrossRef]

IEEE J. Lightwave Technol.

K. Morishita, “Index profiling of three dimensional waveguides by the propagation-mode near-field method,” IEEE J. Lightwave Technol. LT-4, 1120–1127 (1986).
[CrossRef]

R. V. Ramaswamy, R. Srivastava, “Ion-exchanged glass waveguides: a review,” IEEE J. Lightwave Technol. 6, 984–1002 (1988).
[CrossRef]

IEEE J. Quantum Electron.

R. C. Alferness, “Guided-wave devices for optical communication,” IEEE J. Quantum Electron. QE-17, 946–959 (1981).
[CrossRef]

G. Stewart, C. A. Miller, P. J. R. Layborn, C. D. W. Wilkinson, R. M. DeLaRue, “Planar optical waveguides formed by silver ion migration in glass,” IEEE J. Quantum Electron. QE-13, 192–200 (1977).
[CrossRef]

A. Miliou, H. Zhenguang, H. C. Cheng, R. Srivastava, R. V. Ramaswamy, “Fibre compatible K+−Na+ ion exchanged channel waveguides: fabrication and characterisation,” IEEE J. Quantum Electron. 25, 1889–1897 (1989).
[CrossRef]

IEEE Photon. Technol. Lett.

R. A. Betts, F. Lui, S. Dagias, “Wavelength and polarisation insensitive optical splitters fabricated in K+/Na+ ion-exchanged glass,” IEEE Photon. Technol. Lett. 2, 481–483 (1990).
[CrossRef]

J. Appl. Phys.

M. Fukama, J. Noda, H. Iwasaki, “Optical properties of titanium diffused LiNbO3 strip waveguides,” J. Appl. Phys. 49, 3693–3698 (1978).
[CrossRef]

Opt. Eng.

T. Findakly, “Glass waveguides by ion-exchange: a review,” Opt. Eng. 24, 244–250 (1985).
[CrossRef]

Other

M. J. Adams, An Introduction to Optical Waveguides (Wiley, New York, 1981).

J. Crank, The Mathematics of Diffusion (Oxford U. Press, New York, 1967).

R. G. Hunsperger, Integrated Optics: Theory and Technology (Springer-Verlag, Berlin, 1984).

F. Lui, R. A. Betts, “An optical wavelength multiplexer/ demultiplexer fabricated in ion-exchanged glass,” in Proceedings of IREECON International (IREE, Sydney, 1989), pp. 547–550.

Technical Stereomicroscope Instruction Manual (Carl Zeiss, Jena).

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Figures (9)

Fig. 1
Fig. 1

Schematic diagram of the interference-microscope setup; CRO, cathode-ray oscilloscope.

Fig. 2
Fig. 2

Diffused channel waveguide produced by K+−Na+ ion exchange.

Fig. 3
Fig. 3

(a) Interference micrograph of a K+−Na+ ion-exchanged channel waveguide, (b) the corresponding phase difference Δϕ(x) versus x, and (c) the phase difference Δϕ(x) versus x for a wide K+−Na+ ion-exchanged channel waveguide.

Fig. 4
Fig. 4

Experimentally determined refractive index profile of a planar K+−Na+ ion-exchanged waveguide (○) and fitted semi-Gaussian profile (dotted curve). d = 8.0 μm.

Fig. 5
Fig. 5

Theoretical surface-index difference, Δnx(x), for an ideal, instantaneous source, stripe diffusion. Waveguide depth, d = 8.5 μm.

Fig. 6
Fig. 6

Measured surface-index difference, Δnx(x), for a K+−Na+ ion-exchanged channel waveguide (○) and a theoretical Δnx(x) from Eq. (9) (solid curve).

Fig. 7
Fig. 7

Representation of the two-dimensional refractive-index profile, Δn(x, y), for the waveguide of Fig. 6 [the fitted Δnx(x) has been used].

Fig. 8
Fig. 8

Measured surface-index difference Δnx(x) of a three-waveguide-coupler structure in K+−Na+ ion-exchanged glass.

Fig. 9
Fig. 9

Measured waveguide depth, d, of K+−Na+ ion-exchanged waveguides obtained by using prism coupling (○) and the interference-microscope method (+) versus the square root of the diffusion time.

Equations (10)

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

n ( x , y ) = n s + Δ n ( x , y ) = n s + Δ n x ( x ) Δ n y ( y ) ,
ϕ ( x ) = h 0 k 0 n ( x , y ) d y ,
Δ ϕ ( x ) = h 0 k 0 Δ n ( x , y ) d y = k 0 Δ n x ( x ) h 0 Δ n y ( y ) d y .
Δ ϕ ( x ) = Δ n x ( x ) k 0 0 exp [ ( y / d ) 2 ] d y = Δ n x ( x ) k 0 d π 2 Δ n x ( x ) = 2 Δ ϕ ( x ) k 0 d π .
ϕ ( x ) = tan 1 [ 0 2 n π I ( x , z ) sin ( ω z ) d z 0 2 n π I ( x , z ) cos ( ω z ) d z ]
C t = D 2 C ,
C ( x , y , z ) = C ( 0 , 0 , 0 ) exp [ ( y / d ) 2 ] , h y 0
C ( x , y , z ) = C ( 0 , 0 , 0 ) erfc ( y / d ) , h y 0
C ( x , y , z ) = C ( 0 , 0 , 0 ) exp [ ( y d ) 2 ] [ erf ( a + x d ) + erf ( a x d ) 2 erf ( a / d ) ] = C ( 0 , 0 , 0 ) f ( x ) g ( y ) .
Δ n ( x , y ) = Δ n ( 0 , 0 ) f ( x ) g ( y ) = Δ n x ( x ) Δ n y ( y ) .

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