Abstract

An analysis of asymmetric directional couplers consisting of two parallel slab waveguides has been performed using the improved coupled-mode theory for multimode waveguides. The use of such couplers for multi-branch power dividers has been illustrated, and the expected performances have been discussed, both for a two-branch divider and a three-branch one. One notes in particular the high SNR and efficiency at the end of the coupling region.

© 1989 Optical Society of America

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References

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  1. M. E. Martin, “A New Waveguide Switch/Modulator for Integrated Optics,” Appl. Opt. 26, 562 (1975).
  2. H. A. Haus, N. A. Whitaker, “All Optical Logic Devices for Waveguide Optics,” Proc. Soc. Photo-Opt. Instrum. Eng. 517, 226 (1984).
  3. M. Kuznetsov, “Radiation Loss in Dielectric Waveguide y-Branch Structures,” IEEE/OSA J. Lightwave Technol LT-3, 674 (1985).
    [CrossRef]
  4. O. Hanaizumi, M. Miyagi, S. Kawakami, “Wide Y-Junction with Low Losses in Three-Dimensional Dielectric Optical Waveguides,” IEEE J. Quantum Electron. QE-21, 168 (1985).
    [CrossRef]
  5. M. Belanger, G. L. Yip, M. Haruna, “Passive Planar Multi-branch Optical Power Divider: Some Design Considerations,” Appl. Opt. 22, 2383 (1983).
    [CrossRef] [PubMed]
  6. R. A. Becker, L. M. Johnson, “Low Loss Multiple Branching in Ti-indiffused LiNbO. Channel Waveguides,” Opt. Lett. 9, 246 (1984).
    [CrossRef] [PubMed]
  7. R. A. Forber, E. Marom, “Symmetric Directional Coupler Switches,” IEEE J. Quantum Electron. QE-22, 911 (1986).
    [CrossRef]
  8. A. Hardy, M. Osinski, W. Streifer, “Application of Coupled-Mode Theory to Nearly Parallel Waveguide Systems,” Electron. Lett. 22, 1249 (1986).
    [CrossRef]
  9. R. M. Knox, P. P. Toulios, “Integrated Circuits for the Millimeter Through Optical Frequency Range,” in Proceedings, Symposium on Submillimeter Waves, Microwave Research In stitute Symposia Series, J. Fox, Ed. (Polytechnic Press, Brook-lyn, 1971), p. 497.
  10. G. B. Hocker, W. K. Burns, “Mode Dispersion in Diffused Channel Waveguides by Effective Index Method,” Appl. Opt. 16, 113 (1977), see references therein.
    [CrossRef] [PubMed]
  11. A. Hardy, W. Streifer, M. Osinski, “Coupled-Mode Equations for Multimode Systems in Isotropic or Anisotropic Media,” Opt. Lett. 11, 742 (1986).
    [CrossRef] [PubMed]
  12. E. A. J. Marcatili, L. L. Buhl, R. C. Alferness, “Experimental Verification of the Improved Coupled-Mode Equations,” Appl. Phys. Lett. 49, 1692 (1986).
    [CrossRef]
  13. Z. Weissman, E. Marom, A. Hardy, “Very Low-Loss Y-Function Power Divider,” Opt. Lett.14, in press (1989).
    [CrossRef] [PubMed]

1986 (4)

R. A. Forber, E. Marom, “Symmetric Directional Coupler Switches,” IEEE J. Quantum Electron. QE-22, 911 (1986).
[CrossRef]

A. Hardy, M. Osinski, W. Streifer, “Application of Coupled-Mode Theory to Nearly Parallel Waveguide Systems,” Electron. Lett. 22, 1249 (1986).
[CrossRef]

A. Hardy, W. Streifer, M. Osinski, “Coupled-Mode Equations for Multimode Systems in Isotropic or Anisotropic Media,” Opt. Lett. 11, 742 (1986).
[CrossRef] [PubMed]

E. A. J. Marcatili, L. L. Buhl, R. C. Alferness, “Experimental Verification of the Improved Coupled-Mode Equations,” Appl. Phys. Lett. 49, 1692 (1986).
[CrossRef]

1985 (2)

M. Kuznetsov, “Radiation Loss in Dielectric Waveguide y-Branch Structures,” IEEE/OSA J. Lightwave Technol LT-3, 674 (1985).
[CrossRef]

O. Hanaizumi, M. Miyagi, S. Kawakami, “Wide Y-Junction with Low Losses in Three-Dimensional Dielectric Optical Waveguides,” IEEE J. Quantum Electron. QE-21, 168 (1985).
[CrossRef]

1984 (2)

H. A. Haus, N. A. Whitaker, “All Optical Logic Devices for Waveguide Optics,” Proc. Soc. Photo-Opt. Instrum. Eng. 517, 226 (1984).

R. A. Becker, L. M. Johnson, “Low Loss Multiple Branching in Ti-indiffused LiNbO. Channel Waveguides,” Opt. Lett. 9, 246 (1984).
[CrossRef] [PubMed]

1983 (1)

1977 (1)

1975 (1)

M. E. Martin, “A New Waveguide Switch/Modulator for Integrated Optics,” Appl. Opt. 26, 562 (1975).

Alferness, R. C.

E. A. J. Marcatili, L. L. Buhl, R. C. Alferness, “Experimental Verification of the Improved Coupled-Mode Equations,” Appl. Phys. Lett. 49, 1692 (1986).
[CrossRef]

Becker, R. A.

Belanger, M.

Buhl, L. L.

E. A. J. Marcatili, L. L. Buhl, R. C. Alferness, “Experimental Verification of the Improved Coupled-Mode Equations,” Appl. Phys. Lett. 49, 1692 (1986).
[CrossRef]

Burns, W. K.

Forber, R. A.

R. A. Forber, E. Marom, “Symmetric Directional Coupler Switches,” IEEE J. Quantum Electron. QE-22, 911 (1986).
[CrossRef]

Hanaizumi, O.

O. Hanaizumi, M. Miyagi, S. Kawakami, “Wide Y-Junction with Low Losses in Three-Dimensional Dielectric Optical Waveguides,” IEEE J. Quantum Electron. QE-21, 168 (1985).
[CrossRef]

Hardy, A.

A. Hardy, M. Osinski, W. Streifer, “Application of Coupled-Mode Theory to Nearly Parallel Waveguide Systems,” Electron. Lett. 22, 1249 (1986).
[CrossRef]

A. Hardy, W. Streifer, M. Osinski, “Coupled-Mode Equations for Multimode Systems in Isotropic or Anisotropic Media,” Opt. Lett. 11, 742 (1986).
[CrossRef] [PubMed]

Z. Weissman, E. Marom, A. Hardy, “Very Low-Loss Y-Function Power Divider,” Opt. Lett.14, in press (1989).
[CrossRef] [PubMed]

Haruna, M.

Haus, H. A.

H. A. Haus, N. A. Whitaker, “All Optical Logic Devices for Waveguide Optics,” Proc. Soc. Photo-Opt. Instrum. Eng. 517, 226 (1984).

Hocker, G. B.

Johnson, L. M.

Kawakami, S.

O. Hanaizumi, M. Miyagi, S. Kawakami, “Wide Y-Junction with Low Losses in Three-Dimensional Dielectric Optical Waveguides,” IEEE J. Quantum Electron. QE-21, 168 (1985).
[CrossRef]

Knox, R. M.

R. M. Knox, P. P. Toulios, “Integrated Circuits for the Millimeter Through Optical Frequency Range,” in Proceedings, Symposium on Submillimeter Waves, Microwave Research In stitute Symposia Series, J. Fox, Ed. (Polytechnic Press, Brook-lyn, 1971), p. 497.

Kuznetsov, M.

M. Kuznetsov, “Radiation Loss in Dielectric Waveguide y-Branch Structures,” IEEE/OSA J. Lightwave Technol LT-3, 674 (1985).
[CrossRef]

Marcatili, E. A. J.

E. A. J. Marcatili, L. L. Buhl, R. C. Alferness, “Experimental Verification of the Improved Coupled-Mode Equations,” Appl. Phys. Lett. 49, 1692 (1986).
[CrossRef]

Marom, E.

R. A. Forber, E. Marom, “Symmetric Directional Coupler Switches,” IEEE J. Quantum Electron. QE-22, 911 (1986).
[CrossRef]

Z. Weissman, E. Marom, A. Hardy, “Very Low-Loss Y-Function Power Divider,” Opt. Lett.14, in press (1989).
[CrossRef] [PubMed]

Martin, M. E.

M. E. Martin, “A New Waveguide Switch/Modulator for Integrated Optics,” Appl. Opt. 26, 562 (1975).

Miyagi, M.

O. Hanaizumi, M. Miyagi, S. Kawakami, “Wide Y-Junction with Low Losses in Three-Dimensional Dielectric Optical Waveguides,” IEEE J. Quantum Electron. QE-21, 168 (1985).
[CrossRef]

Osinski, M.

A. Hardy, M. Osinski, W. Streifer, “Application of Coupled-Mode Theory to Nearly Parallel Waveguide Systems,” Electron. Lett. 22, 1249 (1986).
[CrossRef]

A. Hardy, W. Streifer, M. Osinski, “Coupled-Mode Equations for Multimode Systems in Isotropic or Anisotropic Media,” Opt. Lett. 11, 742 (1986).
[CrossRef] [PubMed]

Streifer, W.

A. Hardy, W. Streifer, M. Osinski, “Coupled-Mode Equations for Multimode Systems in Isotropic or Anisotropic Media,” Opt. Lett. 11, 742 (1986).
[CrossRef] [PubMed]

A. Hardy, M. Osinski, W. Streifer, “Application of Coupled-Mode Theory to Nearly Parallel Waveguide Systems,” Electron. Lett. 22, 1249 (1986).
[CrossRef]

Toulios, P. P.

R. M. Knox, P. P. Toulios, “Integrated Circuits for the Millimeter Through Optical Frequency Range,” in Proceedings, Symposium on Submillimeter Waves, Microwave Research In stitute Symposia Series, J. Fox, Ed. (Polytechnic Press, Brook-lyn, 1971), p. 497.

Weissman, Z.

Z. Weissman, E. Marom, A. Hardy, “Very Low-Loss Y-Function Power Divider,” Opt. Lett.14, in press (1989).
[CrossRef] [PubMed]

Whitaker, N. A.

H. A. Haus, N. A. Whitaker, “All Optical Logic Devices for Waveguide Optics,” Proc. Soc. Photo-Opt. Instrum. Eng. 517, 226 (1984).

Yip, G. L.

Appl. Opt. (3)

Appl. Phys. Lett. (1)

E. A. J. Marcatili, L. L. Buhl, R. C. Alferness, “Experimental Verification of the Improved Coupled-Mode Equations,” Appl. Phys. Lett. 49, 1692 (1986).
[CrossRef]

Electron. Lett. (1)

A. Hardy, M. Osinski, W. Streifer, “Application of Coupled-Mode Theory to Nearly Parallel Waveguide Systems,” Electron. Lett. 22, 1249 (1986).
[CrossRef]

IEEE J. Quantum Electron. (2)

O. Hanaizumi, M. Miyagi, S. Kawakami, “Wide Y-Junction with Low Losses in Three-Dimensional Dielectric Optical Waveguides,” IEEE J. Quantum Electron. QE-21, 168 (1985).
[CrossRef]

R. A. Forber, E. Marom, “Symmetric Directional Coupler Switches,” IEEE J. Quantum Electron. QE-22, 911 (1986).
[CrossRef]

IEEE/OSA J. Lightwave Technol (1)

M. Kuznetsov, “Radiation Loss in Dielectric Waveguide y-Branch Structures,” IEEE/OSA J. Lightwave Technol LT-3, 674 (1985).
[CrossRef]

Opt. Lett. (2)

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

H. A. Haus, N. A. Whitaker, “All Optical Logic Devices for Waveguide Optics,” Proc. Soc. Photo-Opt. Instrum. Eng. 517, 226 (1984).

Other (2)

R. M. Knox, P. P. Toulios, “Integrated Circuits for the Millimeter Through Optical Frequency Range,” in Proceedings, Symposium on Submillimeter Waves, Microwave Research In stitute Symposia Series, J. Fox, Ed. (Polytechnic Press, Brook-lyn, 1971), p. 497.

Z. Weissman, E. Marom, A. Hardy, “Very Low-Loss Y-Function Power Divider,” Opt. Lett.14, in press (1989).
[CrossRef] [PubMed]

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Figures (10)

Fig. 1
Fig. 1

Schematic illustration of two-branch equal distribution power divider, with a mode stripper (waveguide s) that eliminates undesired mode.

Fig. 2
Fig. 2

Illustration of the system geometry.

Fig. 3
Fig. 3

Variation of the field amplitudes | u 1 a | , | u 2 a | , | u 1 b | as a function of z.

Fig. 4
Fig. 4

Variation of the SNR ( P 2 a : P 1 a ) (left scale) and the efficiency ( P 2 a : P in ) (right scale) in a two-mode guide a, beyond the termination of guide b, as a function of the coupler length zo.

Fig. 5
Fig. 5

SNR ( P 2 a : P 1 a ) and efficiency ( P 2 a : P in ) versus the (a) refractive index n1 of waveguide a and (b) refractive index n2 of waveguide b.

Fig. 6
Fig. 6

Variation of SNR ( P 2 a : P 1 a ) and efficiency ( P 2 a : P in ) beyond the termination point of the mode stripper waveguide s, as a function of the length of guide s.

Fig. 7
Fig. 7

Field distribution in the two coupled guides a and b, at z = z0 =1mm (dash-dotline) and at z = z0 = 1.85mm (solid line). Power excitation at z = 0 is wholly contained in guide b. Dashed vertical lines delineate guide boundaries.

Fig. 8
Fig. 8

Variation of SNR [ P 3 a : ( P 2 a + P 1 a ) ] and efficiency ( P 3 a : P in ) in the case of a three-mode guide, as a function of the coupler length zo.

Fig. 9
Fig. 9

Variation of SNR [ P 3 a : ( P 2 a + P 1 a ) ] and efficiency ( P 3 a : P in ) in the case of a three-mode guide, as a function of the length of mode-stripper guide s.

Fig. 10
Fig. 10

Field distribution in the two coupled guides a and b, when a is a three-mode guide, at z = z0 = 1 mm (dash-dot line) and at z = z1 =3.6 mm (solid line). Guide boundaries delineated by dashed vertical lines.

Equations (4)

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E t ( y , z ) = m = 1 N u m ( a ) ( z ) E t m ( a ) ( y ) + u 1 ( b ) ( z ) E t 1 ( b ) ( y ) ,
dU d z = i ( B + P 1 K ) U .
P m ( a ) = 1 4 | u 1 ( b ) ( z 0 ) P m , N + 1 + u m ( a ) ( z 0 ) 2 ( m = 1 , , N ) , ( N = 2 , 3 ) ,
P m ( a ) = 1 4 | u 1 ( s ) ( z 1 ) P m , N + 1 + u m ( a ) ( z 1 ) 2 ( m = 1 ,…, N ) , ( N = 2 , 3 ) ,

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