Abstract

A simplified method is presented for analyzing the optical characteristics of ridge MOS optical waveguides. Equations are derived for calculating the effective refractive indices and the absorption loss coefficients of the Epqx modes. The computations are performed for air–Au–air/SiO2/GaAs/AlGaAs ridge MOS waveguides. To achieve single-mode propagation with low absorption loss, appropriate selection of the structural parameters for this kind of waveguide is discussed.

© 1990 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. C. Shelton, F. K. Reinhart, R. A. Logan, “Single-Mode GaAs-AlxGa1−xAs Rib Waveguide Switches,” Appl. Opt. 17, 890–891 (1978).
    [CrossRef] [PubMed]
  2. J. C. Shelton, F. K. Reinhart, R. A. Logan, “Rib Waveguide Switches with MOS Electrooptic Control for Monolithic Integrated Optics in GaAs-AlxGa1−xAs,” Appl. Opt. 17, 2548–2555 (1978).
    [CrossRef] [PubMed]
  3. H. Kawaguchi, “GaAs Rib-Waveguide Directional-Coupler Switch with Schottky Barriers,” Electron. Lett. 14, 387–388 (1978).
    [CrossRef]
  4. Y. Suematsu, M. Hakuta, K. Furuya, K. Chiba, R. Hasumi, “Fundamental Transverse Electric Field (TE0) Mode Selection for Thin-Film Asymmetric Light Guides,” Appl. Phys. Lett. 21, 291–293 (1972).
    [CrossRef]
  5. V. Ramaswamy, “Strip-Loaded Film Waveguide,” Bell Syst. Tech. J. 53, 697–704 (1974).
  6. M. S. Sodha, A. K. Ghatak, Inhomogeneous Optical Waveguides (Plenum, New York, 1977), p. 20.
  7. H. C. Casey, M. B. Panish, Heterostructure Lasers (Academic, New York, 1978), pp. 43–44.
  8. W. G. Driscoll, W. Vaughan, Eds., Handbook of Optics (McGraw-Hill, New York, 1978), p. 7–150.

1978 (3)

1974 (1)

V. Ramaswamy, “Strip-Loaded Film Waveguide,” Bell Syst. Tech. J. 53, 697–704 (1974).

1972 (1)

Y. Suematsu, M. Hakuta, K. Furuya, K. Chiba, R. Hasumi, “Fundamental Transverse Electric Field (TE0) Mode Selection for Thin-Film Asymmetric Light Guides,” Appl. Phys. Lett. 21, 291–293 (1972).
[CrossRef]

Casey, H. C.

H. C. Casey, M. B. Panish, Heterostructure Lasers (Academic, New York, 1978), pp. 43–44.

Chiba, K.

Y. Suematsu, M. Hakuta, K. Furuya, K. Chiba, R. Hasumi, “Fundamental Transverse Electric Field (TE0) Mode Selection for Thin-Film Asymmetric Light Guides,” Appl. Phys. Lett. 21, 291–293 (1972).
[CrossRef]

Furuya, K.

Y. Suematsu, M. Hakuta, K. Furuya, K. Chiba, R. Hasumi, “Fundamental Transverse Electric Field (TE0) Mode Selection for Thin-Film Asymmetric Light Guides,” Appl. Phys. Lett. 21, 291–293 (1972).
[CrossRef]

Ghatak, A. K.

M. S. Sodha, A. K. Ghatak, Inhomogeneous Optical Waveguides (Plenum, New York, 1977), p. 20.

Hakuta, M.

Y. Suematsu, M. Hakuta, K. Furuya, K. Chiba, R. Hasumi, “Fundamental Transverse Electric Field (TE0) Mode Selection for Thin-Film Asymmetric Light Guides,” Appl. Phys. Lett. 21, 291–293 (1972).
[CrossRef]

Hasumi, R.

Y. Suematsu, M. Hakuta, K. Furuya, K. Chiba, R. Hasumi, “Fundamental Transverse Electric Field (TE0) Mode Selection for Thin-Film Asymmetric Light Guides,” Appl. Phys. Lett. 21, 291–293 (1972).
[CrossRef]

Kawaguchi, H.

H. Kawaguchi, “GaAs Rib-Waveguide Directional-Coupler Switch with Schottky Barriers,” Electron. Lett. 14, 387–388 (1978).
[CrossRef]

Logan, R. A.

Panish, M. B.

H. C. Casey, M. B. Panish, Heterostructure Lasers (Academic, New York, 1978), pp. 43–44.

Ramaswamy, V.

V. Ramaswamy, “Strip-Loaded Film Waveguide,” Bell Syst. Tech. J. 53, 697–704 (1974).

Reinhart, F. K.

Shelton, J. C.

Sodha, M. S.

M. S. Sodha, A. K. Ghatak, Inhomogeneous Optical Waveguides (Plenum, New York, 1977), p. 20.

Suematsu, Y.

Y. Suematsu, M. Hakuta, K. Furuya, K. Chiba, R. Hasumi, “Fundamental Transverse Electric Field (TE0) Mode Selection for Thin-Film Asymmetric Light Guides,” Appl. Phys. Lett. 21, 291–293 (1972).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

Y. Suematsu, M. Hakuta, K. Furuya, K. Chiba, R. Hasumi, “Fundamental Transverse Electric Field (TE0) Mode Selection for Thin-Film Asymmetric Light Guides,” Appl. Phys. Lett. 21, 291–293 (1972).
[CrossRef]

Bell Syst. Tech. J. (1)

V. Ramaswamy, “Strip-Loaded Film Waveguide,” Bell Syst. Tech. J. 53, 697–704 (1974).

Electron. Lett. (1)

H. Kawaguchi, “GaAs Rib-Waveguide Directional-Coupler Switch with Schottky Barriers,” Electron. Lett. 14, 387–388 (1978).
[CrossRef]

Other (3)

M. S. Sodha, A. K. Ghatak, Inhomogeneous Optical Waveguides (Plenum, New York, 1977), p. 20.

H. C. Casey, M. B. Panish, Heterostructure Lasers (Academic, New York, 1978), pp. 43–44.

W. G. Driscoll, W. Vaughan, Eds., Handbook of Optics (McGraw-Hill, New York, 1978), p. 7–150.

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 (4)

Fig. 1
Fig. 1

Ridge MOS waveguide and its equivalent slab waveguide.

Fig. 2
Fig. 2

The E 00 x mode effective index N and absorption loss coefficient α vs oxide buffer layer thickness l: h = 0.2b; —, a = b; – · –, a = 2b; - - - -, a = 3b; (a) Nl curves; (b) αl curves.

Fig. 3
Fig. 3

The E 00 x mode effective index N and absorption loss coefficient α vs normalized ridge height h/b: l = 0.17 μm; —, a = b; – · –, a = 2b; - - - -, a = 3b; (a) Nh/b curves; (b) αh/b curves.

Fig. 4
Fig. 4

The E 09 x mode effective index N and absorption loss coefficient α vs core thickness b: a = 2b; h = 0.2b; l = 0.17 μm; —, results of Eqs. (30) and (31); - - - -, numerical results of the effective index method5; (a) Nb curves; (b) αb curves.

Equations (51)

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

n ^ m = n m - j K m ,
ɛ i = n i 2             ( i = 0 , 1 , 2 , 3 ) ,
ɛ ^ m = n ^ m 2 = ( n m - j K m ) 2 = n m 2 - K m 2 - j 2 n m K m .
ɛ ^ m = - ɛ m - j K m             ( ɛ m , K m > 0 )
ɛ m = K m 2 - n m 2 ,             K m = 2 n m K m .
E ^ 1 = N ^ 1 2 , E 2 = N 2 2 ;
k 0 ( ɛ 1 - E ^ 1 ) 1 / 2 b = q π + arctan [ ( E ^ 1 - ɛ 2 ) 1 / 2 ( ɛ 1 - E ^ 1 ) 1 / 2 ] + arctan [ ( E ^ 1 - ɛ 3 ) 1 / 2 ( ɛ 1 - E ^ 1 ) 1 / 2 δ ^ 1 ] ,
k 0 ( ɛ 1 - E 2 ) 1 / 2 ( b - h ) = q π + arctan [ ( E 2 - ɛ 2 ) 1 / 2 ( ɛ 1 - E 2 ) 1 / 2 ] + arctan [ ( E 2 - ɛ 3 ) 1 / 2 ( ɛ 1 - E 2 ) 1 / 2 δ 2 ] ,
δ ^ 1 = ( E ^ 1 - ɛ ^ m ) 1 / 2 tanh [ k 0 ( E ^ 1 - ɛ 3 ) 1 / 2 l ] + ( E ^ 1 - ɛ 3 ) 1 / 2 ( E ^ 1 - ɛ ^ m ) 1 / 2 + ( E ^ 1 - ɛ 3 ) 1 / 2 tanh [ k 0 ( E ^ 1 - ɛ 3 ) 1 / 2 l ] ,
δ 2 = ( E 2 - ɛ 0 ) 1 / 2 tanh [ k 0 ( E 2 - ɛ 3 ) 1 / 2 l ] + ( E 2 - ɛ 3 ) 1 / 2 ( E 2 - ɛ 0 ) 1 / 2 + ( E 2 - ɛ 3 ) 1 / 2 tanh [ k 0 ( E 2 - ɛ 3 ) 1 / 2 l ] ,
V 1 = k 0 ( ɛ 1 - ɛ 2 ) 1 / 2 b ,
P ^ 1 = ( ɛ 1 - E ^ 1 ) 1 / 2 / ( ɛ 1 - ɛ 2 ) 1 / 2 ,
Q ^ 1 = ( ɛ 1 - ɛ 2 ) 1 / 2 / ( ɛ 1 - ɛ ^ m ) 1 / 2 ,
V 2 = k 0 ( ɛ 1 - ɛ 2 ) 1 / 2 ( b - h ) ,
P 2 = ( ɛ 1 - E 2 ) 1 / 2 / ( ɛ 1 - ɛ 2 ) 1 / 2 ,
Q 2 = ( ɛ 1 - ɛ 2 ) 1 / 2 / ( ɛ 1 - ɛ 0 ) 1 / 2 ,
V 3 = k 0 ( ɛ 1 - ɛ 2 ) 1 / 2 l ,
Q 3 = ( ɛ 1 - ɛ 2 ) 1 / 2 / ( ɛ 1 - ɛ 3 ) 1 / 2
E ^ 1 = E 1 - j L 1 ,
{ E 1 = ɛ 1 - ( q + 1 ) 2 π 2 ( ɛ 1 - ɛ 2 ) ( 1 + V 1 + Q 3 δ 11 ) 2 + ( Q 3 δ 12 ) 2 × cos [ 2 arctan ( Q 3 δ 12 1 + V 1 + Q 3 δ 11 ) ] , L 1 = ( q + 1 ) 2 π 2 ( ɛ 1 - ɛ 2 ) ( 1 + V 1 + Q 3 δ 11 ) 2 + ( Q 3 δ 12 ) 2 × sin [ 2 arctan ( Q 3 δ 12 1 + V 1 + Q 3 δ 11 ) ] ,
E 2 = ɛ 1 - ( q + 1 ) 2 π 2 ( ɛ 1 - ɛ 2 ) ( 1 + V 2 + Q 3 δ 2 ) 2 .
δ 11 = γ cos φ ,             δ 12 = γ sin φ ,
{ γ = { [ Q 3 tanh ( V 3 / Q 3 ) + Q 11 ] 2 + Q 12 2 [ Q 3 + Q 11 tanh ( V 3 / Q 3 ) ] 2 + [ Q 12 tanh ( V 3 / Q 3 ) ] 2 } 1 / 2 , φ = arctan [ Q 12 Q 3 tanh ( V 3 / Q 3 ) + Q 11 ] - arctan [ Q 12 tanh ( V 3 / Q 3 ) Q 3 + Q 11 tanh ( V 3 / Q 3 ) ] ,
{ Q 11 = ( ɛ 1 - ɛ 2 ) 1 / 2 [ ( ɛ 1 + ɛ m ) 2 + K m 2 ] 1 / 4 cos [ 1 2 arctan ( K m ɛ 1 + ɛ m ) ] , Q 12 = ( ɛ 1 - ɛ 2 ) 1 / 2 [ ( ɛ 1 + ɛ m ) 2 + K m 2 ] 1 / 4 sin [ 1 2 arctan ( K m ɛ 1 + ɛ m ) ] ,
δ 2 = Q 3 tanh ( V 3 / Q 3 ) + Q 2 Q 3 + Q 2 tanh ( V 3 / Q 3 ) .
F ( N ^ , E ^ 1 ) = p π + 2 arctan [ E ^ 1 ( N ^ 2 - E 2 ) 1 / 2 E 2 ( E ^ 1 - N ^ 2 ) 1 / 2 ] - k 0 ( E ^ 1 - N ^ 2 ) 1 / 2 a = 0 ,
Δ E ^ 1 = - j L 1 .
Δ N ^ = - j Δ N ,
N ^ = N - j Δ N .
α = - 2 k 0 Im ( N ^ ) = 2 k 0 Δ N = k 0 L 1 N { 1 - 2 E 2 ( E 1 - N 2 ) [ E 1 + 2 ( N 2 - E 2 ) ] 2 E 1 E 2 ( E 1 - E 2 ) + k 0 a ( N 2 - E 2 ) 1 / 2 [ E 2 2 ( E 1 - N 2 ) + E 1 2 ( N 2 - E 2 ) ] } ,
k 0 ( E 1 - N 2 ) 1 / 2 a = p π + 2 arctan [ E 1 ( N 2 - E 2 ) 1 / 2 E 2 ( E 1 - N 2 ) 1 / 2 ] .
B V = E max l ,
V 1 P ^ 1 = ( q + 1 ) π - arctan [ P ^ 1 ( 1 - P ^ 1 2 ) 1 / 2 ] - arctan [ δ ^ 1 Q 3 P ^ 1 ( 1 - Q 3 2 P ^ 1 2 ) 1 / 2 ] ,
V 2 P 2 = ( q + 1 ) π - arctan [ P 2 ( 1 - P 2 2 ) 1 / 2 ] - arctan [ δ 2 Q 3 P 2 ( 1 - Q 3 2 P 2 2 ) 1 / 2 ] ,
δ ^ 1 = ( 1 - Q ^ 1 2 P ^ 1 2 ) 1 / 2 Q 3 tanh [ ( 1 - Q 3 2 P ^ 1 2 ) 1 / 2 V 3 / Q 3 ] + ( 1 - Q 3 2 P ^ 1 2 ) 1 / 2 Q ^ 1 ( 1 - Q ^ 1 2 P ^ 1 2 ) 1 / 2 Q 3 + ( 1 - Q 3 2 P ^ 1 2 ) 1 / 2 Q ^ 1 tanh [ ( 1 - Q 3 2 P ^ 1 2 ) 1 / 2 V 3 / Q 3 ] ,
δ 2 = ( 1 - Q 2 2 P 2 2 ) 1 / 2 Q 3 tanh [ ( 1 - Q 3 2 P 2 2 ) 1 / 2 V 3 / Q 3 ] + ( 1 - Q 3 2 P 2 2 ) 1 / 2 Q 2 ( 1 - Q 2 2 P 2 2 ) 1 / 2 Q 3 + ( 1 - Q 3 2 P 2 2 ) 1 / 2 Q 2 tanh [ ( 1 - Q 3 2 P 2 2 ) 1 / 2 V 3 / Q 3 ] .
V 1 P ^ 1 = ( q + 1 ) π - arctan ( P ^ 1 ) - arctan ( δ ^ 1 Q 3 P ^ 1 ) ,
V 2 P 2 = ( q + 1 ) π - arctan ( P 2 ) - arctan ( δ 2 Q 3 P 2 ) ,
δ ^ 1 = Q 3 tanh ( V 3 / Q 3 ) + Q ^ 1 Q 3 + Q ^ 1 tanh ( V 3 / Q 3 ) ,
δ ^ 2 = Q 3 tanh ( V 3 / Q 3 ) + Q 2 Q 3 + Q 2 tanh ( V 3 / Q 3 ) ,
V 1 P ^ 1 = ( q + 1 ) π - P ^ 1 - δ ^ 1 Q 3 P ^ 1 ,
V 2 P 2 = ( q + 1 ) π - P 2 - δ 2 Q 3 P 2 .
P ^ 1 = ( q + 1 ) π 1 + V 1 + Q 3 δ ^ 1 ,
P 2 = ( q + 1 ) π 1 + V 2 + Q 3 δ 2 .
E ^ 1 = ɛ 1 - ( q + 1 ) 2 π 2 ( ɛ 1 - ɛ 2 ) ( 1 + V 1 + Q 3 δ ^ 1 ) 2
Q ^ 1 = Q 11 - j Q 12 ,
δ ^ 1 = δ 11 - j δ 12 ,
( δ F δ N ^ ) 0 Δ N ^ + ( F E ^ 1 ) 0 Δ E ^ 1 = 0 ,
Δ N = - L 1 ( F E ^ 1 ) 0 / ( F N ^ ) 0 .
{ ( F N ^ ) 0 = N ( E 1 - N 2 ) 1 / 2 { k 0 a + 2 E 1 E 2 ( E 1 - E 2 ) ( N 2 - E 2 ) 1 / 2 [ E 2 2 ( E 1 - N 2 ) + E 1 2 ( N 2 - E 2 ) ] } , ( F E ^ 1 ) 0 = 1 2 ( E 1 - N 2 ) 1 / 2 { k 0 a + 2 E 2 ( N 2 - E 2 ) 1 / 2 [ E 1 - 2 ( E 1 - N 2 ) ] E 2 2 ( E 1 - N 2 ) + E 1 2 ( N 2 - E 2 ) } .
Δ N = L 1 2 N { 1 - 2 E 2 ( E 1 - N 2 ) [ E 1 + 2 ( N 2 - E 2 ) ] 2 E 1 E 2 ( E 1 - E 2 ) + k 0 a ( N 2 - E 2 ) 1 / 2 [ E 2 2 ( E 1 - N 2 ) + E 1 2 ( N 2 - E 2 ) ] } .

Metrics