Abstract

Experimental and theoretical improvements to the propagation-mode near-field technique for refractive-index profiling have been made. The measured near-field profile is deconvoluted with the transfer function of the optical imaging system in order to recover the actual near-field profile. A new equation is also derived in order to use these data to reconstruct the refractive-index profile of the waveguide under consideration. The improved method, which is valid for all relevant wavelength ranges, is demonstrated in the determination of the refractive-index profiles of two single-mode planar waveguides.

© 1996 Optical Society of America

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References

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  1. R. V. Ramaswamy, R. Srivastava, “Ion-exchange glass waveguides: a review,” J. Lightwave Technol. 6, 984–1002 (1988).
    [CrossRef]
  2. L. McCaughan, E. Bergmann, “Index distribution of optical waveguides from their mode profile,” J. Lightwave Technol. 1, 241–244 (1983).
    [CrossRef]
  3. J. Helms, J. Schmidtchen, B. Schüppert, K. Petermann, “Error analysis for refractive-index profile determination from near-field measurements,” J. Lightwave Technol. 8, 625–633 (1990).
    [CrossRef]
  4. K. Morishita, “Refractive-index-profile determination of single-mode optical fibers by a propagation-mode near-field scanning technique,” J. Lightwave Technol. 1, 445–449 (1983).
    [CrossRef]
  5. K. Morishita, “Index profiling of three-dimensional optical waveguides by the propagation-mode near-field method,” J. Lightwave Technol. 4, 1120–1124 (1986).
    [CrossRef]
  6. M. Halfmann, A. Kunz, W. Heinlein, “Comparison of measured and simulated mode fields in InP waveguides,” in Integrated Photonics Research, Vol. 3 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 121–123.
  7. J. R. Meyer-Arendt, Introduction to Classical and Modern Optics, 2nd ed. (Prentice-Hall, Englewood Cliffs, N.J., 1984).
  8. L. Chen, T. H. Pham, S. Haumont, P. C. Moutsios, G. L. Yip, “Refractive index profile determination of graded-index (GRIN) waveguides from near-field measurements,” in Gradient Index Optical Systems, Vol. 12 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 45–48.
  9. P. B. Crilly, “A quantitative evaluation of various iterative deconvolution algorithms,” IEEE Trans. Instrum. Meas. 40, 558–562 (1988).
    [CrossRef]
  10. J. C. Sprott, Numerical Recipes: the Art of Scientific Computing (Cambridge U. Press, Cambridge, 1991).
  11. KP-M1 Black and White CCD Camera Operation Manual (Hitachi Denshi Ltd., Woodbury, N.Y., 1991).
  12. W. B. Wetherell, “The calculation of image quality,” in Applied Optics and Optical Engineering, R. R. Shannon, J. C. Wyant, eds. (Academic, New York, 1980), Vol. 8, pp. 171–315.
  13. P. Mishra, A. Sharma, “Analysis of single mode inhomogeneous planar waveguides,” J. Lightwave Technol. 4, 204–211 (1986).
    [CrossRef]
  14. G. L. Yip, J. Albert, “Characterization of planar optical waveguides by K+-ion exchange in glass,” Opt. Lett. 10, 151–153 (1985).
    [CrossRef] [PubMed]
  15. P. C. Noutsios, G. L. Yip, “Shallow buried waveguides made by purely thermal migration of K+ ions in glass,” Opt. Lett. 15, 212–214 (1990).
    [CrossRef] [PubMed]
  16. J. Albert, G. L. Yip, “Refractive-index profiles of planar optical waveguides made by ion-exchange in glass,” Appl. Opt. 24, 3692–3693 (1985).
    [CrossRef] [PubMed]

1990 (2)

J. Helms, J. Schmidtchen, B. Schüppert, K. Petermann, “Error analysis for refractive-index profile determination from near-field measurements,” J. Lightwave Technol. 8, 625–633 (1990).
[CrossRef]

P. C. Noutsios, G. L. Yip, “Shallow buried waveguides made by purely thermal migration of K+ ions in glass,” Opt. Lett. 15, 212–214 (1990).
[CrossRef] [PubMed]

1988 (2)

P. B. Crilly, “A quantitative evaluation of various iterative deconvolution algorithms,” IEEE Trans. Instrum. Meas. 40, 558–562 (1988).
[CrossRef]

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

1986 (2)

P. Mishra, A. Sharma, “Analysis of single mode inhomogeneous planar waveguides,” J. Lightwave Technol. 4, 204–211 (1986).
[CrossRef]

K. Morishita, “Index profiling of three-dimensional optical waveguides by the propagation-mode near-field method,” J. Lightwave Technol. 4, 1120–1124 (1986).
[CrossRef]

1985 (2)

1983 (2)

L. McCaughan, E. Bergmann, “Index distribution of optical waveguides from their mode profile,” J. Lightwave Technol. 1, 241–244 (1983).
[CrossRef]

K. Morishita, “Refractive-index-profile determination of single-mode optical fibers by a propagation-mode near-field scanning technique,” J. Lightwave Technol. 1, 445–449 (1983).
[CrossRef]

Albert, J.

Bergmann, E.

L. McCaughan, E. Bergmann, “Index distribution of optical waveguides from their mode profile,” J. Lightwave Technol. 1, 241–244 (1983).
[CrossRef]

Chen, L.

L. Chen, T. H. Pham, S. Haumont, P. C. Moutsios, G. L. Yip, “Refractive index profile determination of graded-index (GRIN) waveguides from near-field measurements,” in Gradient Index Optical Systems, Vol. 12 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 45–48.

Crilly, P. B.

P. B. Crilly, “A quantitative evaluation of various iterative deconvolution algorithms,” IEEE Trans. Instrum. Meas. 40, 558–562 (1988).
[CrossRef]

Halfmann, M.

M. Halfmann, A. Kunz, W. Heinlein, “Comparison of measured and simulated mode fields in InP waveguides,” in Integrated Photonics Research, Vol. 3 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 121–123.

Haumont, S.

L. Chen, T. H. Pham, S. Haumont, P. C. Moutsios, G. L. Yip, “Refractive index profile determination of graded-index (GRIN) waveguides from near-field measurements,” in Gradient Index Optical Systems, Vol. 12 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 45–48.

Heinlein, W.

M. Halfmann, A. Kunz, W. Heinlein, “Comparison of measured and simulated mode fields in InP waveguides,” in Integrated Photonics Research, Vol. 3 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 121–123.

Helms, J.

J. Helms, J. Schmidtchen, B. Schüppert, K. Petermann, “Error analysis for refractive-index profile determination from near-field measurements,” J. Lightwave Technol. 8, 625–633 (1990).
[CrossRef]

Kunz, A.

M. Halfmann, A. Kunz, W. Heinlein, “Comparison of measured and simulated mode fields in InP waveguides,” in Integrated Photonics Research, Vol. 3 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 121–123.

McCaughan, L.

L. McCaughan, E. Bergmann, “Index distribution of optical waveguides from their mode profile,” J. Lightwave Technol. 1, 241–244 (1983).
[CrossRef]

Meyer-Arendt, J. R.

J. R. Meyer-Arendt, Introduction to Classical and Modern Optics, 2nd ed. (Prentice-Hall, Englewood Cliffs, N.J., 1984).

Mishra, P.

P. Mishra, A. Sharma, “Analysis of single mode inhomogeneous planar waveguides,” J. Lightwave Technol. 4, 204–211 (1986).
[CrossRef]

Morishita, K.

K. Morishita, “Index profiling of three-dimensional optical waveguides by the propagation-mode near-field method,” J. Lightwave Technol. 4, 1120–1124 (1986).
[CrossRef]

K. Morishita, “Refractive-index-profile determination of single-mode optical fibers by a propagation-mode near-field scanning technique,” J. Lightwave Technol. 1, 445–449 (1983).
[CrossRef]

Moutsios, P. C.

L. Chen, T. H. Pham, S. Haumont, P. C. Moutsios, G. L. Yip, “Refractive index profile determination of graded-index (GRIN) waveguides from near-field measurements,” in Gradient Index Optical Systems, Vol. 12 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 45–48.

Noutsios, P. C.

Petermann, K.

J. Helms, J. Schmidtchen, B. Schüppert, K. Petermann, “Error analysis for refractive-index profile determination from near-field measurements,” J. Lightwave Technol. 8, 625–633 (1990).
[CrossRef]

Pham, T. H.

L. Chen, T. H. Pham, S. Haumont, P. C. Moutsios, G. L. Yip, “Refractive index profile determination of graded-index (GRIN) waveguides from near-field measurements,” in Gradient Index Optical Systems, Vol. 12 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 45–48.

Ramaswamy, R. V.

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

Schmidtchen, J.

J. Helms, J. Schmidtchen, B. Schüppert, K. Petermann, “Error analysis for refractive-index profile determination from near-field measurements,” J. Lightwave Technol. 8, 625–633 (1990).
[CrossRef]

Schüppert, B.

J. Helms, J. Schmidtchen, B. Schüppert, K. Petermann, “Error analysis for refractive-index profile determination from near-field measurements,” J. Lightwave Technol. 8, 625–633 (1990).
[CrossRef]

Sharma, A.

P. Mishra, A. Sharma, “Analysis of single mode inhomogeneous planar waveguides,” J. Lightwave Technol. 4, 204–211 (1986).
[CrossRef]

Sprott, J. C.

J. C. Sprott, Numerical Recipes: the Art of Scientific Computing (Cambridge U. Press, Cambridge, 1991).

Srivastava, R.

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

Wetherell, W. B.

W. B. Wetherell, “The calculation of image quality,” in Applied Optics and Optical Engineering, R. R. Shannon, J. C. Wyant, eds. (Academic, New York, 1980), Vol. 8, pp. 171–315.

Yip, G. L.

Appl. Opt. (1)

IEEE Trans. Instrum. Meas. (1)

P. B. Crilly, “A quantitative evaluation of various iterative deconvolution algorithms,” IEEE Trans. Instrum. Meas. 40, 558–562 (1988).
[CrossRef]

J. Lightwave Technol. (6)

P. Mishra, A. Sharma, “Analysis of single mode inhomogeneous planar waveguides,” J. Lightwave Technol. 4, 204–211 (1986).
[CrossRef]

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

L. McCaughan, E. Bergmann, “Index distribution of optical waveguides from their mode profile,” J. Lightwave Technol. 1, 241–244 (1983).
[CrossRef]

J. Helms, J. Schmidtchen, B. Schüppert, K. Petermann, “Error analysis for refractive-index profile determination from near-field measurements,” J. Lightwave Technol. 8, 625–633 (1990).
[CrossRef]

K. Morishita, “Refractive-index-profile determination of single-mode optical fibers by a propagation-mode near-field scanning technique,” J. Lightwave Technol. 1, 445–449 (1983).
[CrossRef]

K. Morishita, “Index profiling of three-dimensional optical waveguides by the propagation-mode near-field method,” J. Lightwave Technol. 4, 1120–1124 (1986).
[CrossRef]

Opt. Lett. (2)

Other (6)

J. C. Sprott, Numerical Recipes: the Art of Scientific Computing (Cambridge U. Press, Cambridge, 1991).

KP-M1 Black and White CCD Camera Operation Manual (Hitachi Denshi Ltd., Woodbury, N.Y., 1991).

W. B. Wetherell, “The calculation of image quality,” in Applied Optics and Optical Engineering, R. R. Shannon, J. C. Wyant, eds. (Academic, New York, 1980), Vol. 8, pp. 171–315.

M. Halfmann, A. Kunz, W. Heinlein, “Comparison of measured and simulated mode fields in InP waveguides,” in Integrated Photonics Research, Vol. 3 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 121–123.

J. R. Meyer-Arendt, Introduction to Classical and Modern Optics, 2nd ed. (Prentice-Hall, Englewood Cliffs, N.J., 1984).

L. Chen, T. H. Pham, S. Haumont, P. C. Moutsios, G. L. Yip, “Refractive index profile determination of graded-index (GRIN) waveguides from near-field measurements,” in Gradient Index Optical Systems, Vol. 12 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 45–48.

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Figures (7)

Fig. 1
Fig. 1

Experimental setup for near-field measurements.

Fig. 2
Fig. 2

Optical imaging system.

Fig. 3
Fig. 3

Determining the effective transfer function (ETF): (—) theoretical steplike intensity levels of inverted photomask, (*) measured intensity levels, (––) convolution of theoretical steplike intensity levels with ETF S(x) = A[J 1r)/γx]2.

Fig. 4
Fig. 4

Near-field power profile comparison between measured data after deconvolution and numerically stimulated intensity for (a) surface waveguide and (b) buried waveguide: (––) deconvoluted measured data, (—) simulated intensity.

Fig. 5
Fig. 5

Reconstructed RIP for surface waveguide using Eq. (12) with (a) exponential guess, (b) and (c) Gaussian guesses: (––) reconstructed profile, (—) actual profile.

Fig. 6
Fig. 6

Reconstructed RIP for buried waveguide using Eq. (12) with shifted Rayleigh guesses: (––) reconstructed profile, (—) actual profile.

Fig. 7
Fig. 7

Flowchart of iterative procedure to determine the optimal initial guess.

Equations (14)

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t 2 ϕ ( x , y ) + [ k 0 2 n 2 ( x , y ) - β 2 ] ϕ ( x , y ) = 0 ,
n 2 ( x , y ) = N eff 2 - 1 2 k 0 2 P ( x , y ) × { t 2 P ( x , y ) - 1 2 P ( x , y ) [ t P ( x , y ) ] 2 } .
I ( x , y ) = S 3 ( x , y ) S 2 ( x , y ) S 1 ( x , y ) P ( x , y ) ,
I ( x , y ) = S ( x , y ) P ( x , y ) .
S ( x ) = A [ J 1 ( γ x ) γ x ] 2 ,
n 2 + δ n 2 = N eff 2 - P 2 k 0 2 ( P + δ P ) + ( P ) 2 4 k 0 2 ( P + δ P ) 2 - δ P 2 k 0 2 ( P + δ P ) + 2 P δ P + ( δ P ) 2 4 k 0 2 ( P + δ P ) 2 .
1 P + δ P = 1 P ( 1 + δ P P ) = 1 P [ 1 - δ P P + ( δ P P ) 2 ] .
δ n 2 = P δ P 2 k 0 2 P 2 - ( P ) 2 δ P 2 k 0 2 P 3 - δ P 2 k 0 2 P ( 1 - δ P P ) + 2 P δ P + ( δ P ) 2 4 k 0 2 P 2 ( 1 - 2 δ P P ) .
δ n 2 = P δ P 2 k 0 2 P 2 - ( P ) 2 δ P 2 k 0 2 P 3 - δ P 2 k 0 2 P + 2 P δ P + ( δ P ) 2 4 k 0 2 P 2 .
t 2 ϕ r ( x , y ) + [ k 0 2 n r 2 ( x , y ) - β r 2 ] ϕ r ( x , y ) = 0.
t 2 ( ϕ r + δ ϕ ) + [ k 0 2 ( n r 2 + δ n 2 ) - ( β r 2 + δ β 2 ) ] ( ϕ r + δ ϕ ) = 0.
δ n 2 = δ β 2 k 0 2 - [ t 2 ( δ ϕ ) + ( k 0 2 n 2 - β 2 ) δ ϕ ] 1 k 0 2 ϕ r ,
n r 2 = n 2 + [ t 2 ( δ ϕ ) + ( k 0 2 n 2 - β 2 ) δ ϕ ] 1 k 0 2 ϕ r - δ β 2 k 0 2 ,
[ t 2 ( δ ϕ ) + ( k 0 2 n 2 - β 2 ) δ ϕ ] 1 k 0 2 ϕ r - δ β 2 k 0 2

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