Abstract

Mode propagation and field distribution in a strip-loaded waveguide are analyzed for the case where the refractive index of the loading film is higher than that of the waveguide. It is found that the propagation constant is remarkably changed by loading the film with the thickness around the cutoff. As a result, the effect of the optical energy confinement below the strip film is large compared with the previously proposed case where the low-index film is loaded, and the use of the high refractive-index film as the loading strip is very attractive for constructing a three-dimensional waveguide structure.

© 1976 Optical Society of America

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References

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  1. P. K. Tien, Appl. Opt. 10, 2395 (1971).
    [Crossref] [PubMed]
  2. H. F. Taylor, A. Yariv, Proc. IEEE 62, 1044 (1974).
    [Crossref]
  3. H. Kogelnik, IEEE Trans. Microwave Theory Tech. MTT-23, 2 (1975).
    [Crossref]
  4. H. Furuta, H. Noda, A. Ihaya, Appl. Opt. 13, 322 (1974).
    [Crossref] [PubMed]
  5. V. Ramaswamy, Bell Syst. Tech. J. 53, 697 (1974).
  6. E. A. J. Marcatili, Bell Syst. Tech. J. 53, 645 (1974).
  7. Y. Suematsu, Y. Sasaki, H. Noda, E. Asai, M. Hakuta, J. Inst. Electr. Commun. Engineers Japan 55C, 98 (1972) (in Japanese).
  8. E. A. J. Marcatili, Bell Syst. Tech. J. 48, 2071 (1969).
  9. N. Uchida, O. Mikami, S. Uehara, J. Noda, Appl. Opt. 15, 000 (1976).
  10. E. A. J. Marcatili, Bell Syst. Tech. J. 48, 2103 (1969).

1976 (1)

N. Uchida, O. Mikami, S. Uehara, J. Noda, Appl. Opt. 15, 000 (1976).

1975 (1)

H. Kogelnik, IEEE Trans. Microwave Theory Tech. MTT-23, 2 (1975).
[Crossref]

1974 (4)

H. Furuta, H. Noda, A. Ihaya, Appl. Opt. 13, 322 (1974).
[Crossref] [PubMed]

V. Ramaswamy, Bell Syst. Tech. J. 53, 697 (1974).

E. A. J. Marcatili, Bell Syst. Tech. J. 53, 645 (1974).

H. F. Taylor, A. Yariv, Proc. IEEE 62, 1044 (1974).
[Crossref]

1972 (1)

Y. Suematsu, Y. Sasaki, H. Noda, E. Asai, M. Hakuta, J. Inst. Electr. Commun. Engineers Japan 55C, 98 (1972) (in Japanese).

1971 (1)

1969 (2)

E. A. J. Marcatili, Bell Syst. Tech. J. 48, 2103 (1969).

E. A. J. Marcatili, Bell Syst. Tech. J. 48, 2071 (1969).

Asai, E.

Y. Suematsu, Y. Sasaki, H. Noda, E. Asai, M. Hakuta, J. Inst. Electr. Commun. Engineers Japan 55C, 98 (1972) (in Japanese).

Furuta, H.

Hakuta, M.

Y. Suematsu, Y. Sasaki, H. Noda, E. Asai, M. Hakuta, J. Inst. Electr. Commun. Engineers Japan 55C, 98 (1972) (in Japanese).

Ihaya, A.

Kogelnik, H.

H. Kogelnik, IEEE Trans. Microwave Theory Tech. MTT-23, 2 (1975).
[Crossref]

Marcatili, E. A. J.

E. A. J. Marcatili, Bell Syst. Tech. J. 53, 645 (1974).

E. A. J. Marcatili, Bell Syst. Tech. J. 48, 2071 (1969).

E. A. J. Marcatili, Bell Syst. Tech. J. 48, 2103 (1969).

Mikami, O.

N. Uchida, O. Mikami, S. Uehara, J. Noda, Appl. Opt. 15, 000 (1976).

Noda, H.

H. Furuta, H. Noda, A. Ihaya, Appl. Opt. 13, 322 (1974).
[Crossref] [PubMed]

Y. Suematsu, Y. Sasaki, H. Noda, E. Asai, M. Hakuta, J. Inst. Electr. Commun. Engineers Japan 55C, 98 (1972) (in Japanese).

Noda, J.

N. Uchida, O. Mikami, S. Uehara, J. Noda, Appl. Opt. 15, 000 (1976).

Ramaswamy, V.

V. Ramaswamy, Bell Syst. Tech. J. 53, 697 (1974).

Sasaki, Y.

Y. Suematsu, Y. Sasaki, H. Noda, E. Asai, M. Hakuta, J. Inst. Electr. Commun. Engineers Japan 55C, 98 (1972) (in Japanese).

Suematsu, Y.

Y. Suematsu, Y. Sasaki, H. Noda, E. Asai, M. Hakuta, J. Inst. Electr. Commun. Engineers Japan 55C, 98 (1972) (in Japanese).

Taylor, H. F.

H. F. Taylor, A. Yariv, Proc. IEEE 62, 1044 (1974).
[Crossref]

Tien, P. K.

Uchida, N.

N. Uchida, O. Mikami, S. Uehara, J. Noda, Appl. Opt. 15, 000 (1976).

Uehara, S.

N. Uchida, O. Mikami, S. Uehara, J. Noda, Appl. Opt. 15, 000 (1976).

Yariv, A.

H. F. Taylor, A. Yariv, Proc. IEEE 62, 1044 (1974).
[Crossref]

Appl. Opt. (3)

Bell Syst. Tech. J. (4)

E. A. J. Marcatili, Bell Syst. Tech. J. 48, 2103 (1969).

E. A. J. Marcatili, Bell Syst. Tech. J. 48, 2071 (1969).

V. Ramaswamy, Bell Syst. Tech. J. 53, 697 (1974).

E. A. J. Marcatili, Bell Syst. Tech. J. 53, 645 (1974).

IEEE Trans. Microwave Theory Tech. (1)

H. Kogelnik, IEEE Trans. Microwave Theory Tech. MTT-23, 2 (1975).
[Crossref]

J. Inst. Electr. Commun. Engineers Japan (1)

Y. Suematsu, Y. Sasaki, H. Noda, E. Asai, M. Hakuta, J. Inst. Electr. Commun. Engineers Japan 55C, 98 (1972) (in Japanese).

Proc. IEEE (1)

H. F. Taylor, A. Yariv, Proc. IEEE 62, 1044 (1974).
[Crossref]

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Figures (6)

Fig. 1
Fig. 1

Geometry of the strip-loaded waveguide.

Fig. 2
Fig. 2

Relation between the propagation constant n and the waveguide thickness D for λ = 1.05 μm, nt = 1, ng = 2.142, and ns = 2.14. Solid (TE0) and broken (TE1) curves are for the case of loading the high-index film (nl = 2.2) with t as the parameter. Dotted curves represent the TE0 and TE1 modes for the case of low-index film loading (nl = 2.14 and t = ∞).

Fig. 3
Fig. 3

Relation between (ngneq) and D for λ = 1.05 μm, nt = 1, ng = 2.142, and ns = 2.14. Solid curves represent TE0 and TE1 modes for the case of loading the high-index film (nl = 2.2) with t as the parameter. Dotted and dot–dash curves are for nl = 2.14 and 2.141, respectively, with t = ∞ for the examples of the low-index film loading.

Fig. 4
Fig. 4

Configuration of equivalent three-dimensional waveguide. The actual strip-loaded waveguide structure shown in Fig. 1 is converted to this configuration using the equivalent refractive index neq

Fig. 5
Fig. 5

Relation between the propagation constant n and the strip width W for λ = 1.05 μm, nt = 1, ng = 2.142, ns = 2.14, and D = 5 μm. Solid and broken curves are for the case of loading the high-index film (nl = 2.2) with t as the parameter, and dotted curves are for the case of loading the low-index film (nl = 2.14 with t = ∞).

Fig. 6
Fig. 6

Field distribution of the E00x mode along the strip-width direction (x direction) for λ = 1.05 μm, nt = 1, nl = 2.2, ng = 2.142, ns = 2.14, and W = D = 5 μm with t as the parameter. The distribution for the case of loading the low-index film (nl = 2.14 and t = ∞) is also shown by dotted curve for comparison.

Equations (11)

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bD = tan 1 ( P s / b ) + tan 1 [ P l b P t cosh ( P l t ) + P l sinh ( P l t ) P l cosh ( P l t ) + P t sinh ( P l t ) ] + q π , ( q = 0 , 1 , 2 . . . ) ,
b = k ( n g 2 n 2 ) 1 / 2
P i = k ( n 2 n i 2 ) 1 / 2 ( i = t , l , and s ) .
bD = tan 1 ( P s / b ) + tan 1 [ P l b P t cos ( P l t ) P l sin ( P l t ) P l cos ( P l t ) + P t sin ( P l t ) ] + q π .
bD = tan 1 ( P s / b ) + tan 1 ( P t / b ) + q π .
n eq = ( n g 2 n I 2 + n II 2 ) 1 / 2 .
b y D = tan 1 ( P sy / b y ) + tan 1 [ P ly b y P ty cos ( P ly t ) P ly sin ( P ly t ) P ly cos ( P ly t ) + P ty sin ( P ly t ) ] + q π , ( P , q = 0 , 1 , 2 . . . ) ,
b x W = 2 tan 1 [ ( n g n eq ) 2 P sx b x ] + P π ,
b y = k ( n g 2 n 2 n x 2 ) 1 / 2 , b x = k ( n g 2 n 2 n y 2 ) 1 / 2 ,
P iy = k ( n 2 + n x 2 n i 2 ) 1 / 2 ( i = s , t ) , P ly = k ( n l 2 n 2 n x 2 ) 1 / 2 , and P sx = k ( n 2 + n y 2 n eq 2 ) 1 / 2 . }
n = ( n g 2 n x 2 n y 2 ) 1 / 2 .

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