Abstract

Normalized analytical expressions are derived for the maximum value of the modal field width, of the squared field amplitude at the superstrate boundary, and of the total power propagating in the superstrate in the case of the TE modes of a step-index slab waveguide.

© 1994 Optical Society of America

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Corrections

O. Parriaux and P. Dierauer, "Normalized expressions for the optical sensitivity of evanescent wave sensors: erratum," Opt. Lett. 19, 1665-1665 (1994)
https://www.osapublishing.org/ol/abstract.cfm?uri=ol-19-20-1665

References

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  1. Ch. Fattinger, M. T. Gale, B. J. Curtis, H. Schütz, H. Heming, J. Otto, presented at European Conference on Integrated Optics, Neuchâtel, Switzerland, April 18–22, 1993.
  2. K. Tiefenthaler, W. Lukosz, J. Opt. Soc. Am. B 6, 209 (1989).
    [CrossRef]
  3. G. Albrand, C. Amra, F. Cléva, F. Flory, X. Liu, R. Mollenhauer, E. Pelletier, M. Ranier, presented at European Conference on Integrated Optics, Neuchâtel, Switzerland, April 18–22, 1993.
  4. M. Heming, B. Danielzik, J. Otto, V. Paquet, Ch. Fattinger, in Proceedings of Materials Research Society Symposia, Spring Meeting (Materials Research Society, Pittsburgh, Pa., 1992), p. 117.
    [CrossRef]
  5. O. Parriaux, in Fiber Optic Chemical Sensors and Biosensors, O. Wolfbeis, ed. (CRC, Boca Raton, Fla., 1991), Vol. 1, pp. 111–192.
  6. S. Löfas, M. Malmqvist, I. Rönnberg, E. Stenberg, B. Liedberg, I. Lundström, Sensors Actuators B 5, 79 (1991).
    [CrossRef]
  7. P. K. Tien, Appl. Opt. 16, 2395 (1971).
    [CrossRef]

1991 (1)

S. Löfas, M. Malmqvist, I. Rönnberg, E. Stenberg, B. Liedberg, I. Lundström, Sensors Actuators B 5, 79 (1991).
[CrossRef]

1989 (1)

1971 (1)

Albrand, G.

G. Albrand, C. Amra, F. Cléva, F. Flory, X. Liu, R. Mollenhauer, E. Pelletier, M. Ranier, presented at European Conference on Integrated Optics, Neuchâtel, Switzerland, April 18–22, 1993.

Amra, C.

G. Albrand, C. Amra, F. Cléva, F. Flory, X. Liu, R. Mollenhauer, E. Pelletier, M. Ranier, presented at European Conference on Integrated Optics, Neuchâtel, Switzerland, April 18–22, 1993.

Cléva, F.

G. Albrand, C. Amra, F. Cléva, F. Flory, X. Liu, R. Mollenhauer, E. Pelletier, M. Ranier, presented at European Conference on Integrated Optics, Neuchâtel, Switzerland, April 18–22, 1993.

Curtis, B. J.

Ch. Fattinger, M. T. Gale, B. J. Curtis, H. Schütz, H. Heming, J. Otto, presented at European Conference on Integrated Optics, Neuchâtel, Switzerland, April 18–22, 1993.

Danielzik, B.

M. Heming, B. Danielzik, J. Otto, V. Paquet, Ch. Fattinger, in Proceedings of Materials Research Society Symposia, Spring Meeting (Materials Research Society, Pittsburgh, Pa., 1992), p. 117.
[CrossRef]

Fattinger, Ch.

M. Heming, B. Danielzik, J. Otto, V. Paquet, Ch. Fattinger, in Proceedings of Materials Research Society Symposia, Spring Meeting (Materials Research Society, Pittsburgh, Pa., 1992), p. 117.
[CrossRef]

Ch. Fattinger, M. T. Gale, B. J. Curtis, H. Schütz, H. Heming, J. Otto, presented at European Conference on Integrated Optics, Neuchâtel, Switzerland, April 18–22, 1993.

Flory, F.

G. Albrand, C. Amra, F. Cléva, F. Flory, X. Liu, R. Mollenhauer, E. Pelletier, M. Ranier, presented at European Conference on Integrated Optics, Neuchâtel, Switzerland, April 18–22, 1993.

Gale, M. T.

Ch. Fattinger, M. T. Gale, B. J. Curtis, H. Schütz, H. Heming, J. Otto, presented at European Conference on Integrated Optics, Neuchâtel, Switzerland, April 18–22, 1993.

Heming, H.

Ch. Fattinger, M. T. Gale, B. J. Curtis, H. Schütz, H. Heming, J. Otto, presented at European Conference on Integrated Optics, Neuchâtel, Switzerland, April 18–22, 1993.

Heming, M.

M. Heming, B. Danielzik, J. Otto, V. Paquet, Ch. Fattinger, in Proceedings of Materials Research Society Symposia, Spring Meeting (Materials Research Society, Pittsburgh, Pa., 1992), p. 117.
[CrossRef]

Liedberg, B.

S. Löfas, M. Malmqvist, I. Rönnberg, E. Stenberg, B. Liedberg, I. Lundström, Sensors Actuators B 5, 79 (1991).
[CrossRef]

Liu, X.

G. Albrand, C. Amra, F. Cléva, F. Flory, X. Liu, R. Mollenhauer, E. Pelletier, M. Ranier, presented at European Conference on Integrated Optics, Neuchâtel, Switzerland, April 18–22, 1993.

Löfas, S.

S. Löfas, M. Malmqvist, I. Rönnberg, E. Stenberg, B. Liedberg, I. Lundström, Sensors Actuators B 5, 79 (1991).
[CrossRef]

Lukosz, W.

Lundström, I.

S. Löfas, M. Malmqvist, I. Rönnberg, E. Stenberg, B. Liedberg, I. Lundström, Sensors Actuators B 5, 79 (1991).
[CrossRef]

Malmqvist, M.

S. Löfas, M. Malmqvist, I. Rönnberg, E. Stenberg, B. Liedberg, I. Lundström, Sensors Actuators B 5, 79 (1991).
[CrossRef]

Mollenhauer, R.

G. Albrand, C. Amra, F. Cléva, F. Flory, X. Liu, R. Mollenhauer, E. Pelletier, M. Ranier, presented at European Conference on Integrated Optics, Neuchâtel, Switzerland, April 18–22, 1993.

Otto, J.

Ch. Fattinger, M. T. Gale, B. J. Curtis, H. Schütz, H. Heming, J. Otto, presented at European Conference on Integrated Optics, Neuchâtel, Switzerland, April 18–22, 1993.

M. Heming, B. Danielzik, J. Otto, V. Paquet, Ch. Fattinger, in Proceedings of Materials Research Society Symposia, Spring Meeting (Materials Research Society, Pittsburgh, Pa., 1992), p. 117.
[CrossRef]

Paquet, V.

M. Heming, B. Danielzik, J. Otto, V. Paquet, Ch. Fattinger, in Proceedings of Materials Research Society Symposia, Spring Meeting (Materials Research Society, Pittsburgh, Pa., 1992), p. 117.
[CrossRef]

Parriaux, O.

O. Parriaux, in Fiber Optic Chemical Sensors and Biosensors, O. Wolfbeis, ed. (CRC, Boca Raton, Fla., 1991), Vol. 1, pp. 111–192.

Pelletier, E.

G. Albrand, C. Amra, F. Cléva, F. Flory, X. Liu, R. Mollenhauer, E. Pelletier, M. Ranier, presented at European Conference on Integrated Optics, Neuchâtel, Switzerland, April 18–22, 1993.

Ranier, M.

G. Albrand, C. Amra, F. Cléva, F. Flory, X. Liu, R. Mollenhauer, E. Pelletier, M. Ranier, presented at European Conference on Integrated Optics, Neuchâtel, Switzerland, April 18–22, 1993.

Rönnberg, I.

S. Löfas, M. Malmqvist, I. Rönnberg, E. Stenberg, B. Liedberg, I. Lundström, Sensors Actuators B 5, 79 (1991).
[CrossRef]

Schütz, H.

Ch. Fattinger, M. T. Gale, B. J. Curtis, H. Schütz, H. Heming, J. Otto, presented at European Conference on Integrated Optics, Neuchâtel, Switzerland, April 18–22, 1993.

Stenberg, E.

S. Löfas, M. Malmqvist, I. Rönnberg, E. Stenberg, B. Liedberg, I. Lundström, Sensors Actuators B 5, 79 (1991).
[CrossRef]

Tiefenthaler, K.

Tien, P. K.

Appl. Opt. (1)

J. Opt. Soc. Am. B (1)

Sensors Actuators B (1)

S. Löfas, M. Malmqvist, I. Rönnberg, E. Stenberg, B. Liedberg, I. Lundström, Sensors Actuators B 5, 79 (1991).
[CrossRef]

Other (4)

Ch. Fattinger, M. T. Gale, B. J. Curtis, H. Schütz, H. Heming, J. Otto, presented at European Conference on Integrated Optics, Neuchâtel, Switzerland, April 18–22, 1993.

G. Albrand, C. Amra, F. Cléva, F. Flory, X. Liu, R. Mollenhauer, E. Pelletier, M. Ranier, presented at European Conference on Integrated Optics, Neuchâtel, Switzerland, April 18–22, 1993.

M. Heming, B. Danielzik, J. Otto, V. Paquet, Ch. Fattinger, in Proceedings of Materials Research Society Symposia, Spring Meeting (Materials Research Society, Pittsburgh, Pa., 1992), p. 117.
[CrossRef]

O. Parriaux, in Fiber Optic Chemical Sensors and Biosensors, O. Wolfbeis, ed. (CRC, Boca Raton, Fla., 1991), Vol. 1, pp. 111–192.

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Figures (4)

Fig. 1
Fig. 1

Step-index slab waveguide of width w and substrate, guide, and cover refractive indices ns, ng, and nc. The asymmetry parameter is a = (ng2nc2)/(ng2ns2).

Fig. 2
Fig. 2

Normalized curve expressing the condition for maximum TE0 field confinement in an arbitrary step-index slab waveguide. The abscissa is the asymmetry parameter a; the ordinate is the normalized variable xs = [(ɛeɛs)/(ɛgɛe)]1/2. For each value of a the curve gives the value xs0 of xs at the maximum TE0 field confinement from which the configuration of maximum field confinement can be retrieved for any particular set of refractive-index values with Eqs. (15)(17).

Fig. 3
Fig. 3

Normalized curve expressing the condition for maximum TE0 mode power in the cover of an arbitrary step-index slab waveguide. The coordinates are the same as in Fig. 2. Similarly, the condition for maximum relative power in the cover of any particular waveguide index distribution can be retrieved from the value xs0 for a given asymmetry parameter and from Eqs. (15)(17).

Fig. 4
Fig. 4

Same as in Fig. 3, except that here the normalized curve represents the condition for maximum value of the squared electric field of the TE0 mode in an arbitrary step-index slab waveguide.

Equations (20)

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k 0 w ( ɛ g - ɛ e ) 1 / 2 - arctan x s - arctan x c - m π = 0 ,
x s = [ ( ɛ e - ɛ s ) / ( ɛ g - ɛ e ) ] 1 / 2 , x c = [ ( ɛ e - ɛ c ) / ( ɛ g - ɛ e ) ] 1 / 2 .
x c 2 = a ( x s 2 + 1 ) - 1 ,
a = ɛ g - ɛ c ɛ g - ɛ s .
k 0 w e = k 0 w + ( ɛ e - ɛ s ) - 1 / 2 + ( ɛ e - ɛ c ) - 1 / 2 .
( k 0 w e ) / ( k 0 w ) = 0.
arctan x s + arctan x c + x s - 1 + x c - 1 - x s - 3 - x c - 3 + m π = 0.
( k 0 w e ) 0 = ( ɛ g - ɛ s ) 1 / 2 ( x s 0 - 3 + x c 0 - 3 ) ( 1 + x s 0 2 ) 1 / 2 ,
P c = P ɛ g - ɛ c ɛ g - ɛ e k 0 w e ( ɛ e - ɛ c ) 1 / 2 ,
( arctan x s + arctan x c + m π + x s - 1 + x c - 1 ) × ( 3 + x c - 2 ) - x s - 3 - x c - 3 = 0.
s m = ( 1 + x c 0 2 ) - 1 × [ 1 + x c 0 ( arctan x s 0 + arctan x c 0 + m π + x s 0 - 1 ) ] - 1 .
A c 2 = 4 ω μ 0 P n e ( ɛ g - ɛ c ) ɛ g - ɛ e k 0 w e .
arctan x c + arctan x s + m π - 1 x s 3 - 1 x c 3 + 1 3 x c + 1 3 x s = 0.
A c m 2 = 4 ω μ 0 P ( 1 - ɛ s / ɛ g x s 0 2 + ɛ s / ɛ g ) 1 / 2 × [ ( 1 + x c 0 2 ) ( arctan x s 0 + arctan x c 0 + m π + x c 0 - 1 + x s 0 - 1 ) ] - 1 .
x c 0 = [ a ( x s 0 2 + 1 ) - 1 ] 1 / 2 ,
ɛ e 0 = ɛ s + ɛ g x s 0 2 1 + x s 0 2 ,
( k 0 w ) 0 = ( 1 + x c 0 2 ɛ g - ɛ s ) 1 / 2 ( arctan x c 0 + arctan x s 0 + m π ) .
arctan x s + 1 x s - 1 x s 3 + m π 2 = 0.
( k 0 w e ) 0 = 4.92966 ( ɛ g - ɛ s ) - 1 / 2
( w e ) 0 = 0.78458 λ ( ɛ g - ɛ s ) - 1 / 2 .

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