Abstract

A surface plasmon resonance (SPR) is excited between a metal film and a graded-index planar waveguide. After the propagation constant of the SPR is measured, the refractive index near the surface of the waveguides, which is difficult to obtain by conventional techniques, is determined experimentally. With this nondestructive technique, combined with the inverse analytical transfer matrix method, the planar waveguide can be profiled to a high degree of accuracy.

© 2005 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. C. T. Law, X. Zhang, G. A. Swartzlander, “Waveguiding properties of optical vortex solitons,” Opt. Lett. 25, 55–57 (2000).
    [CrossRef]
  2. R. Yin, X. Q. Jiang, J. Y. Yang, M. H. Wang, “Structure with improved self-imaging in its graded-index multimode interference region,” J. Opt. Soc. Am. B 19, 1301–1303 (2002).
    [CrossRef]
  3. C. R. Lavers, K. Itoh, S. C. Wu, M. Murabayashi, I. Mauchline, G. Stewart, T. Stout, “Planar optical waveguides for sensing applications,” Sens. Actuators B 69, 85–95 (2000).
    [CrossRef]
  4. A. Kaplan, S. Ruschin, “Optical switching and power control in LiNbO3coupled waveguide arrays,” IEEE J. Quantum Electron. 37, 1562–1573 (2001).
    [CrossRef]
  5. S. Blaize, L. Bastard, C. Cassagnetes, J. E. Broquin, “Multiwavelengths DFB waveguide laser arrays in Yb–Er codoped phosphate glass substrate,” IEEE. Photon. Technol. Lett. 15, 516–518 (2003).
    [CrossRef]
  6. D. V. Petrov, “Second-harmonic generation by off-axis propagation in an anisotropic optical waveguide,” J. Opt. Soc. Am. B 14, 331–338 (1997).
    [CrossRef]
  7. J. M. White, P. F. Heidrich, “Optical waveguide refractive index profiles determined from the measurement of mode indexes,” Appl. Opt. 15, 151–155 (1976).
    [CrossRef] [PubMed]
  8. K. S. Chiang, “Construction of refractive-index profiles of planar dielectric waveguides from the distribution of effective indexes,” J. Lightwave Technol. 3, 385–391 (1985).
    [CrossRef]
  9. K. S. Chiang, C. L. Wong, H. P. Chan, Y. T. Chow, “Refractive-index profiling of graded-index planar waveguides from effective indexes measured for both mode types and at different wavelengths,” J. Lightwave Technol. 14, 827–832 (1996).
    [CrossRef]
  10. K. S. Chiang, C. L. Wong, S. Y. Cheng, H. P. Chan, “Refractive-index profiling of graded-index planar waveguides from effective indexes with different external refractive indexes,” J. Lightwave Technol. 18, 1412–1417 (2000).
    [CrossRef]
  11. P. Hertel, H. P. Menzler, “Improved inverse WKB procedure to reconstruct refractive index profiles of dielectric planar waveguides,” Appl. Phys. B 44, 75–80 (1987).
    [CrossRef]
  12. R. Oven, S. Batchelor, D. G. Ashworth, D. Gelder, J. M. Bradshaw, “Iterative refinement technique for reconstructing refractive index profiles from mode indices,” Electron. Lett. 31, 229–231 (1995).
    [CrossRef]
  13. R. Ulrich, R. Torge, “Measurement of thin film parameters with a prism couple,” Appl. Opt. 12, 2901–2908 (1973).
    [CrossRef] [PubMed]
  14. Y. Ding, Z. Q. Cao, Q. S. Shen, “Determination of optical waveguide refractive-index profiles with the inverse analytic transfer matrix method,” Opt. Quantum. Electron. 36, 489–497 (2004).
    [CrossRef]
  15. Z. Q. Cao, Y. Jiang, Q. S. Shen, Y. L. Chen, “Exact analytical method for planar waveguides with arbitrary index profile,” J. Opt. Soc. Am. A 16, 2209–2212 (1999).
    [CrossRef]
  16. Z. Q. Cao, Q. Liu, Y. Jiang, Q. S. Shen, X. M. Dou, “Phase shift at a turning point in a planar optical waveguide,” J. Opt. Soc. Am. A 18, 2161–2163 (2001).
    [CrossRef]
  17. E. Kretschmann, “The determination of the optical constants of metals by excitation of surface plasmons,” Z. Phys. 241, 313–324 (1971).
    [CrossRef]
  18. W. P. Chen, J. M. Chen, “Use of surface plasma waves for determination of the thickness and optical constants of thin metallic films,” J. Opt. Soc. Am. 71, 189–191 (1981).
    [CrossRef]

2004 (1)

Y. Ding, Z. Q. Cao, Q. S. Shen, “Determination of optical waveguide refractive-index profiles with the inverse analytic transfer matrix method,” Opt. Quantum. Electron. 36, 489–497 (2004).
[CrossRef]

2003 (1)

S. Blaize, L. Bastard, C. Cassagnetes, J. E. Broquin, “Multiwavelengths DFB waveguide laser arrays in Yb–Er codoped phosphate glass substrate,” IEEE. Photon. Technol. Lett. 15, 516–518 (2003).
[CrossRef]

2002 (1)

2001 (2)

A. Kaplan, S. Ruschin, “Optical switching and power control in LiNbO3coupled waveguide arrays,” IEEE J. Quantum Electron. 37, 1562–1573 (2001).
[CrossRef]

Z. Q. Cao, Q. Liu, Y. Jiang, Q. S. Shen, X. M. Dou, “Phase shift at a turning point in a planar optical waveguide,” J. Opt. Soc. Am. A 18, 2161–2163 (2001).
[CrossRef]

2000 (3)

1999 (1)

1997 (1)

1996 (1)

K. S. Chiang, C. L. Wong, H. P. Chan, Y. T. Chow, “Refractive-index profiling of graded-index planar waveguides from effective indexes measured for both mode types and at different wavelengths,” J. Lightwave Technol. 14, 827–832 (1996).
[CrossRef]

1995 (1)

R. Oven, S. Batchelor, D. G. Ashworth, D. Gelder, J. M. Bradshaw, “Iterative refinement technique for reconstructing refractive index profiles from mode indices,” Electron. Lett. 31, 229–231 (1995).
[CrossRef]

1987 (1)

P. Hertel, H. P. Menzler, “Improved inverse WKB procedure to reconstruct refractive index profiles of dielectric planar waveguides,” Appl. Phys. B 44, 75–80 (1987).
[CrossRef]

1985 (1)

K. S. Chiang, “Construction of refractive-index profiles of planar dielectric waveguides from the distribution of effective indexes,” J. Lightwave Technol. 3, 385–391 (1985).
[CrossRef]

1981 (1)

1976 (1)

1973 (1)

1971 (1)

E. Kretschmann, “The determination of the optical constants of metals by excitation of surface plasmons,” Z. Phys. 241, 313–324 (1971).
[CrossRef]

Ashworth, D. G.

R. Oven, S. Batchelor, D. G. Ashworth, D. Gelder, J. M. Bradshaw, “Iterative refinement technique for reconstructing refractive index profiles from mode indices,” Electron. Lett. 31, 229–231 (1995).
[CrossRef]

Bastard, L.

S. Blaize, L. Bastard, C. Cassagnetes, J. E. Broquin, “Multiwavelengths DFB waveguide laser arrays in Yb–Er codoped phosphate glass substrate,” IEEE. Photon. Technol. Lett. 15, 516–518 (2003).
[CrossRef]

Batchelor, S.

R. Oven, S. Batchelor, D. G. Ashworth, D. Gelder, J. M. Bradshaw, “Iterative refinement technique for reconstructing refractive index profiles from mode indices,” Electron. Lett. 31, 229–231 (1995).
[CrossRef]

Blaize, S.

S. Blaize, L. Bastard, C. Cassagnetes, J. E. Broquin, “Multiwavelengths DFB waveguide laser arrays in Yb–Er codoped phosphate glass substrate,” IEEE. Photon. Technol. Lett. 15, 516–518 (2003).
[CrossRef]

Bradshaw, J. M.

R. Oven, S. Batchelor, D. G. Ashworth, D. Gelder, J. M. Bradshaw, “Iterative refinement technique for reconstructing refractive index profiles from mode indices,” Electron. Lett. 31, 229–231 (1995).
[CrossRef]

Broquin, J. E.

S. Blaize, L. Bastard, C. Cassagnetes, J. E. Broquin, “Multiwavelengths DFB waveguide laser arrays in Yb–Er codoped phosphate glass substrate,” IEEE. Photon. Technol. Lett. 15, 516–518 (2003).
[CrossRef]

Cao, Z. Q.

Cassagnetes, C.

S. Blaize, L. Bastard, C. Cassagnetes, J. E. Broquin, “Multiwavelengths DFB waveguide laser arrays in Yb–Er codoped phosphate glass substrate,” IEEE. Photon. Technol. Lett. 15, 516–518 (2003).
[CrossRef]

Chan, H. P.

K. S. Chiang, C. L. Wong, S. Y. Cheng, H. P. Chan, “Refractive-index profiling of graded-index planar waveguides from effective indexes with different external refractive indexes,” J. Lightwave Technol. 18, 1412–1417 (2000).
[CrossRef]

K. S. Chiang, C. L. Wong, H. P. Chan, Y. T. Chow, “Refractive-index profiling of graded-index planar waveguides from effective indexes measured for both mode types and at different wavelengths,” J. Lightwave Technol. 14, 827–832 (1996).
[CrossRef]

Chen, J. M.

Chen, W. P.

Chen, Y. L.

Cheng, S. Y.

Chiang, K. S.

K. S. Chiang, C. L. Wong, S. Y. Cheng, H. P. Chan, “Refractive-index profiling of graded-index planar waveguides from effective indexes with different external refractive indexes,” J. Lightwave Technol. 18, 1412–1417 (2000).
[CrossRef]

K. S. Chiang, C. L. Wong, H. P. Chan, Y. T. Chow, “Refractive-index profiling of graded-index planar waveguides from effective indexes measured for both mode types and at different wavelengths,” J. Lightwave Technol. 14, 827–832 (1996).
[CrossRef]

K. S. Chiang, “Construction of refractive-index profiles of planar dielectric waveguides from the distribution of effective indexes,” J. Lightwave Technol. 3, 385–391 (1985).
[CrossRef]

Chow, Y. T.

K. S. Chiang, C. L. Wong, H. P. Chan, Y. T. Chow, “Refractive-index profiling of graded-index planar waveguides from effective indexes measured for both mode types and at different wavelengths,” J. Lightwave Technol. 14, 827–832 (1996).
[CrossRef]

Ding, Y.

Y. Ding, Z. Q. Cao, Q. S. Shen, “Determination of optical waveguide refractive-index profiles with the inverse analytic transfer matrix method,” Opt. Quantum. Electron. 36, 489–497 (2004).
[CrossRef]

Dou, X. M.

Gelder, D.

R. Oven, S. Batchelor, D. G. Ashworth, D. Gelder, J. M. Bradshaw, “Iterative refinement technique for reconstructing refractive index profiles from mode indices,” Electron. Lett. 31, 229–231 (1995).
[CrossRef]

Heidrich, P. F.

Hertel, P.

P. Hertel, H. P. Menzler, “Improved inverse WKB procedure to reconstruct refractive index profiles of dielectric planar waveguides,” Appl. Phys. B 44, 75–80 (1987).
[CrossRef]

Itoh, K.

C. R. Lavers, K. Itoh, S. C. Wu, M. Murabayashi, I. Mauchline, G. Stewart, T. Stout, “Planar optical waveguides for sensing applications,” Sens. Actuators B 69, 85–95 (2000).
[CrossRef]

Jiang, X. Q.

Jiang, Y.

Kaplan, A.

A. Kaplan, S. Ruschin, “Optical switching and power control in LiNbO3coupled waveguide arrays,” IEEE J. Quantum Electron. 37, 1562–1573 (2001).
[CrossRef]

Kretschmann, E.

E. Kretschmann, “The determination of the optical constants of metals by excitation of surface plasmons,” Z. Phys. 241, 313–324 (1971).
[CrossRef]

Lavers, C. R.

C. R. Lavers, K. Itoh, S. C. Wu, M. Murabayashi, I. Mauchline, G. Stewart, T. Stout, “Planar optical waveguides for sensing applications,” Sens. Actuators B 69, 85–95 (2000).
[CrossRef]

Law, C. T.

Liu, Q.

Mauchline, I.

C. R. Lavers, K. Itoh, S. C. Wu, M. Murabayashi, I. Mauchline, G. Stewart, T. Stout, “Planar optical waveguides for sensing applications,” Sens. Actuators B 69, 85–95 (2000).
[CrossRef]

Menzler, H. P.

P. Hertel, H. P. Menzler, “Improved inverse WKB procedure to reconstruct refractive index profiles of dielectric planar waveguides,” Appl. Phys. B 44, 75–80 (1987).
[CrossRef]

Murabayashi, M.

C. R. Lavers, K. Itoh, S. C. Wu, M. Murabayashi, I. Mauchline, G. Stewart, T. Stout, “Planar optical waveguides for sensing applications,” Sens. Actuators B 69, 85–95 (2000).
[CrossRef]

Oven, R.

R. Oven, S. Batchelor, D. G. Ashworth, D. Gelder, J. M. Bradshaw, “Iterative refinement technique for reconstructing refractive index profiles from mode indices,” Electron. Lett. 31, 229–231 (1995).
[CrossRef]

Petrov, D. V.

Ruschin, S.

A. Kaplan, S. Ruschin, “Optical switching and power control in LiNbO3coupled waveguide arrays,” IEEE J. Quantum Electron. 37, 1562–1573 (2001).
[CrossRef]

Shen, Q. S.

Stewart, G.

C. R. Lavers, K. Itoh, S. C. Wu, M. Murabayashi, I. Mauchline, G. Stewart, T. Stout, “Planar optical waveguides for sensing applications,” Sens. Actuators B 69, 85–95 (2000).
[CrossRef]

Stout, T.

C. R. Lavers, K. Itoh, S. C. Wu, M. Murabayashi, I. Mauchline, G. Stewart, T. Stout, “Planar optical waveguides for sensing applications,” Sens. Actuators B 69, 85–95 (2000).
[CrossRef]

Swartzlander, G. A.

Torge, R.

Ulrich, R.

Wang, M. H.

White, J. M.

Wong, C. L.

K. S. Chiang, C. L. Wong, S. Y. Cheng, H. P. Chan, “Refractive-index profiling of graded-index planar waveguides from effective indexes with different external refractive indexes,” J. Lightwave Technol. 18, 1412–1417 (2000).
[CrossRef]

K. S. Chiang, C. L. Wong, H. P. Chan, Y. T. Chow, “Refractive-index profiling of graded-index planar waveguides from effective indexes measured for both mode types and at different wavelengths,” J. Lightwave Technol. 14, 827–832 (1996).
[CrossRef]

Wu, S. C.

C. R. Lavers, K. Itoh, S. C. Wu, M. Murabayashi, I. Mauchline, G. Stewart, T. Stout, “Planar optical waveguides for sensing applications,” Sens. Actuators B 69, 85–95 (2000).
[CrossRef]

Yang, J. Y.

Yin, R.

Zhang, X.

Appl. Opt. (2)

Appl. Phys. B (1)

P. Hertel, H. P. Menzler, “Improved inverse WKB procedure to reconstruct refractive index profiles of dielectric planar waveguides,” Appl. Phys. B 44, 75–80 (1987).
[CrossRef]

Electron. Lett. (1)

R. Oven, S. Batchelor, D. G. Ashworth, D. Gelder, J. M. Bradshaw, “Iterative refinement technique for reconstructing refractive index profiles from mode indices,” Electron. Lett. 31, 229–231 (1995).
[CrossRef]

IEEE J. Quantum Electron. (1)

A. Kaplan, S. Ruschin, “Optical switching and power control in LiNbO3coupled waveguide arrays,” IEEE J. Quantum Electron. 37, 1562–1573 (2001).
[CrossRef]

IEEE. Photon. Technol. Lett. (1)

S. Blaize, L. Bastard, C. Cassagnetes, J. E. Broquin, “Multiwavelengths DFB waveguide laser arrays in Yb–Er codoped phosphate glass substrate,” IEEE. Photon. Technol. Lett. 15, 516–518 (2003).
[CrossRef]

J. Lightwave Technol. (3)

K. S. Chiang, “Construction of refractive-index profiles of planar dielectric waveguides from the distribution of effective indexes,” J. Lightwave Technol. 3, 385–391 (1985).
[CrossRef]

K. S. Chiang, C. L. Wong, H. P. Chan, Y. T. Chow, “Refractive-index profiling of graded-index planar waveguides from effective indexes measured for both mode types and at different wavelengths,” J. Lightwave Technol. 14, 827–832 (1996).
[CrossRef]

K. S. Chiang, C. L. Wong, S. Y. Cheng, H. P. Chan, “Refractive-index profiling of graded-index planar waveguides from effective indexes with different external refractive indexes,” J. Lightwave Technol. 18, 1412–1417 (2000).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

J. Opt. Soc. Am. B (2)

Opt. Lett. (1)

Opt. Quantum. Electron. (1)

Y. Ding, Z. Q. Cao, Q. S. Shen, “Determination of optical waveguide refractive-index profiles with the inverse analytic transfer matrix method,” Opt. Quantum. Electron. 36, 489–497 (2004).
[CrossRef]

Sens. Actuators B (1)

C. R. Lavers, K. Itoh, S. C. Wu, M. Murabayashi, I. Mauchline, G. Stewart, T. Stout, “Planar optical waveguides for sensing applications,” Sens. Actuators B 69, 85–95 (2000).
[CrossRef]

Z. Phys. (1)

E. Kretschmann, “The determination of the optical constants of metals by excitation of surface plasmons,” Z. Phys. 241, 313–324 (1971).
[CrossRef]

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 (6)

Fig. 1
Fig. 1

Plot of planar waveguide with graded-index profile.

Fig. 2
Fig. 2

Equivalent indices neq as functions of the truncation depth xc of the exponential, Gaussian, and fast Fermi profile.

Fig. 3
Fig. 3

Sample experimental configuration.

Fig. 4
Fig. 4

Measured results from the IATM method and the other existing techniques. (A) 180 min, (B) 240 min, (C) 360 min.

Fig. 5
Fig. 5

Numerical results of the profiles calculated from the IATM method and the other existing techniques. (a) Exponential profile, (b) Gaussian profile, (c) Fast Fermi profile.

Fig. 6
Fig. 6

Experimental and numerical comparisons of the profiles constructed with the IWKB method and the IATM method. (a) Ion-exchanged BK7 glass waveguides, sample A; (b) Fast Fermi profile.

Tables (1)

Tables Icon

Table 1 Measured Equivalent and Effective Indices for Three Ion-Exchanged BK7 Glass Waveguides

Equations (8)

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

n 2 ( x ) = { n s 2 + ( n f 2 n s 2 ) f ( x / d ) ( x > 0 ) n a 2 ( x < 0 ) ,
0 x t κ ( x ) d x + Φ ( s ) = ( m + 1 2 ) π + tan 1 ( n f 2 p a n a 2 κ f ) , m = 0 , 1 , 2 , ,
κ ( x ) = [ k 0 2 n 2 ( x ) β 2 ] 1 / 2 , κ f = ( k 0 2 n f 2 β 2 ) 1 / 2 , p a = ( β 2 k 0 2 n a 2 ) 1 / 2 ,
n ( x t ) = β / k 0 ,
β k 0 = ( n g 2 n eq 2 n g 2 + n eq 2 ) 1 / 2 ,
n ( x ) = 1.50779 + 0.04 exp ( x / 2.5 ) ,
n ( x ) = 1.50779 + 0.04 exp ( x 2 / 25 ) ,
n ( x ) = 1.50779 + 0.04 1 exp ( 10 ) + exp ( 2 x 10 ) .

Metrics