Abstract

Mode conversion and radiation loss in integrated-optic tapers and Y-junctions are calculated by means of the beam propagation method combined with the effective refractive-index method. Simple design rules for the tapers and Y-junctions are derived from the obtained results.

© 1982 Optical Society of America

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References

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  1. J. A. Fleck, J. R. Morris, M. D. Feit, Appl. Phys. 10, 129 (1976).
    [CrossRef]
  2. M. D. Feit, J. A. Fleck, Appl. Opt. 18, 2843 (1979).
    [CrossRef] [PubMed]
  3. J. Van Roey, J. van der Donk, P. E. Lagasse, J. Opt. Soc. Am. 71, 803 (1981).
    [CrossRef]
  4. G. B. Hocker, W. K. Burns, Appl. Opt. 16, 113 (1977).
    [CrossRef] [PubMed]
  5. H. Kogelnik, Topics in Applied Physics, Vol. 7 (Springer, Berlin, 1979), Chap. 2.
  6. W. Streifer, E. Kapon, Appl. Opt. 18, 3724 (1979).
    [CrossRef] [PubMed]
  7. D. Marcuse, Bell Syst. Tech. J. 49, 273, 919 (1970).
  8. N. Tzoar, R. Pascone, J. Opt. Soc. Am. 71, 1107 (1981).
    [CrossRef]
  9. R. K. Winn, J. H. Harris, IEEE Trans. Microwave Theory Tech. MTT-23, 92 (1975).
    [CrossRef]
  10. A. F. Milton, W. K. Burns, IEEE J. Quantum Electron. QE-13, 828 (1977).
    [CrossRef]
  11. F. Sporleder, H. G. Unger, Waveguide Tapers, Transitions and Couplers (Peregrinus, Stevenage, 1979), Chap. 9.
  12. J. van der Donk, Ph.D. Thesis, U. Gent, Belgium (1981).

1981 (2)

1979 (2)

1977 (2)

A. F. Milton, W. K. Burns, IEEE J. Quantum Electron. QE-13, 828 (1977).
[CrossRef]

G. B. Hocker, W. K. Burns, Appl. Opt. 16, 113 (1977).
[CrossRef] [PubMed]

1976 (1)

J. A. Fleck, J. R. Morris, M. D. Feit, Appl. Phys. 10, 129 (1976).
[CrossRef]

1975 (1)

R. K. Winn, J. H. Harris, IEEE Trans. Microwave Theory Tech. MTT-23, 92 (1975).
[CrossRef]

1970 (1)

D. Marcuse, Bell Syst. Tech. J. 49, 273, 919 (1970).

Burns, W. K.

A. F. Milton, W. K. Burns, IEEE J. Quantum Electron. QE-13, 828 (1977).
[CrossRef]

G. B. Hocker, W. K. Burns, Appl. Opt. 16, 113 (1977).
[CrossRef] [PubMed]

Feit, M. D.

M. D. Feit, J. A. Fleck, Appl. Opt. 18, 2843 (1979).
[CrossRef] [PubMed]

J. A. Fleck, J. R. Morris, M. D. Feit, Appl. Phys. 10, 129 (1976).
[CrossRef]

Fleck, J. A.

M. D. Feit, J. A. Fleck, Appl. Opt. 18, 2843 (1979).
[CrossRef] [PubMed]

J. A. Fleck, J. R. Morris, M. D. Feit, Appl. Phys. 10, 129 (1976).
[CrossRef]

Harris, J. H.

R. K. Winn, J. H. Harris, IEEE Trans. Microwave Theory Tech. MTT-23, 92 (1975).
[CrossRef]

Hocker, G. B.

Kapon, E.

Kogelnik, H.

H. Kogelnik, Topics in Applied Physics, Vol. 7 (Springer, Berlin, 1979), Chap. 2.

Lagasse, P. E.

Marcuse, D.

D. Marcuse, Bell Syst. Tech. J. 49, 273, 919 (1970).

Milton, A. F.

A. F. Milton, W. K. Burns, IEEE J. Quantum Electron. QE-13, 828 (1977).
[CrossRef]

Morris, J. R.

J. A. Fleck, J. R. Morris, M. D. Feit, Appl. Phys. 10, 129 (1976).
[CrossRef]

Pascone, R.

Sporleder, F.

F. Sporleder, H. G. Unger, Waveguide Tapers, Transitions and Couplers (Peregrinus, Stevenage, 1979), Chap. 9.

Streifer, W.

Tzoar, N.

Unger, H. G.

F. Sporleder, H. G. Unger, Waveguide Tapers, Transitions and Couplers (Peregrinus, Stevenage, 1979), Chap. 9.

van der Donk, J.

Van Roey, J.

Winn, R. K.

R. K. Winn, J. H. Harris, IEEE Trans. Microwave Theory Tech. MTT-23, 92 (1975).
[CrossRef]

Appl. Opt. (3)

Appl. Phys. (1)

J. A. Fleck, J. R. Morris, M. D. Feit, Appl. Phys. 10, 129 (1976).
[CrossRef]

Bell Syst. Tech. J. (1)

D. Marcuse, Bell Syst. Tech. J. 49, 273, 919 (1970).

IEEE J. Quantum Electron. (1)

A. F. Milton, W. K. Burns, IEEE J. Quantum Electron. QE-13, 828 (1977).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

R. K. Winn, J. H. Harris, IEEE Trans. Microwave Theory Tech. MTT-23, 92 (1975).
[CrossRef]

J. Opt. Soc. Am. (2)

Other (3)

H. Kogelnik, Topics in Applied Physics, Vol. 7 (Springer, Berlin, 1979), Chap. 2.

F. Sporleder, H. G. Unger, Waveguide Tapers, Transitions and Couplers (Peregrinus, Stevenage, 1979), Chap. 9.

J. van der Donk, Ph.D. Thesis, U. Gent, Belgium (1981).

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Figures (13)

Fig. 1
Fig. 1

Sketch of the geometry of the strip waveguides.

Fig. 2
Fig. 2

Illustration of the effective-index method: (a) original 3-D profile; (b) slab waveguide used to calculate the effective refractive index for any value of x and z; and (c) resulting 2D effective profile.

Fig. 3
Fig. 3

Waveguide transition with ng being the effective index of the guide: (a) abrupt transition, (b) tapering transition.

Fig. 4
Fig. 4

Power transfer between fundamental modes in an abrupt transition for different reduction ratios: A, input guide multimode, output guide multimode; B, input guide multimode, output guide single mode; and C, input guide single mode, output guide single mode.

Fig. 5
Fig. 5

Normalized effective width of a slab waveguide as a function of the effective width V.

Fig. 6
Fig. 6

Radiation loss and mode conversion in tapers for different values of parameter sinθeff. The regions A, B, and C are defined as in Fig. 4. (a) Power transfer between fundamental modes for a reduction ratio of 2. (b) As (a) for a reduction ratio of 8. (c) Conversion from second-order input mode to fundamental output mode for a reduction ratio of 8.

Fig. 7
Fig. 7

Field amplitude in a taper with Vin = 10 and Vout = 1.25,θ = 1°,ng2ns2, =0.02, ns=1, λ = 1.3 μm. (a) Lowest-order mode at the input, (b) First-order mode at the input, (c) Second-order mode at the input, (d) Third-order mode at the input.

Fig. 8
Fig. 8

Y-junction configuration.

Fig. 9
Fig. 9

Representation of the Y-junction as a multiport.

Fig. 10
Fig. 10

Y-junction configurations: (a) straight input guides; (b) as (a), one input guide missing; (c) bent input guides; (d) non-symmetrical junction.

Fig. 11
Fig. 11

Effective refractive index ngns (ns = 1).

Fig. 12
Fig. 12

Radiation loss in Y-junctions: (a) straight guides; (b) bent guides; (c) nonsymmetrical guides.

Fig. 13
Fig. 13

Field amplitude in a Y-junction as in Fig. 10(c): α1 = 2°, α2 = 4°, λ = 1.3 μm.

Equations (12)

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2 E x + k 2 n 2 ( x , y ) E x = 0
p out = | ψ ( x ) ϕ in ( x ) dx | 2 ,
T 00 = | ϕ in ( x ) ϕ out ( x ) dx | 2 ,
V in = k d in ( n g 2 n s 2 ) 1 / 2 , V out = k d out ( n g 2 n s 2 ) 1 / 2 .
sin θ eff = sin θ N . A . ,
sin θ eff · V ( z ) = constant
[ b ¯ A b ¯ B ] = S ¯ ¯ · [ a ¯ A a ¯ B ] .
S ¯ ¯ = [ 0 S ¯ ¯ AB T S ¯ ¯ AB 0 ] .
ϕ e ( x ) = 1 2 ψ ( L 2 + x ) + 1 2 ψ ( L 2 x ) ,
ϕ o ( x ) = 1 2 ψ ( L 2 + x ) 1 2 ψ ( L 2 x ) ,
( ½ | S e + S o | 2 ) · ( ½ | S e S o | 2 ) = ¼ [ ( | S e | 2 + | S o | 2 ) 2 4 | S e | 2 | S o | 2 cos 2 ( θ e θ o ) ] ¼ [ 1 4 | S e | 2 | S o | 2 cos 2 ( θ e θ o ) ] 1 / 4.
½ ( 10 log ½ | S e + S o | 2 + 10 log ½ | S e + S o | 2 ) 3 dB

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