Abstract

A honeycomb waveguide network for parallel signal processing, consisting of single-mode symmetrical Y junctions, is proposed. In this waveguide network, input guided-wave amplitudes are divided and then combined with the amplitudes of the adjacent waveguides. It is shown that the operations of spatial filtering, such as smoothing, edge extraction, and edge enhancement, can be performed. An example of the honeycomb waveguide network is discussed.

© 1988 Optical Society of America

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References

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  1. F. T. S. Yu, Optical Information Processing (Wiley, New York, 1983).
  2. R. G. Hunsperger, Integrated Optics: Theory and Technology (Springer-Verlag, New York, 1984), Chap. 1.
  3. R. Shubert, J. H. Harris, “Optical Surface Waves on Thin Films and Their Application to Integrated Data Processors,” IEEE Trans. Microwave Theory Tech. MTT-16, 1048 (1968).
    [CrossRef]
  4. D. B. Anderson, R. L. Davis, J. T. Boyd, R. R. August, “Comparison of Optical-Waveguide Lens Technologies,” IEEE J. Quantum Electron. QE-13, 275 (1977).
    [CrossRef]
  5. D. B. Anderson, J. T. Boyd, M. C. Hamilton, R. R. August, “An Integrated-Optical Approach to the Fourier Transform,” IEEE J. Quantum Electron. QE-13, 268 (1977).
    [CrossRef]
  6. M. K. Barnoski, B.-U. Chen, T. R. Joseph, J. Y. Lee, O. G. Ramer, “Integrated-Optic Spectrum Analyzer,” IEEE Trans. Circuits Syst. CAS-26, 1113 (1979).
    [CrossRef]
  7. K. Tsutsumi, T. Sueta, “A Proposed Integrated-Optical Device for Hadamard Transformation,” Trans. IECE Jpn. J60-C, 500 (1977).
  8. K. Tsutsumi, T. Sueta, “A Synthesis of Optical Guided-Wave Signal Transformers,” Trans. IECE Jpn. J62-C, 381 (1979).
  9. K. Tsutsumi, “Studies on Synthesis of Guided-Wave Optical Signal Transformers,” Doctoral Thesis, Osaka U. (1980).
  10. M. E. Marhic, “Discrete Fourier Transforms by Single-Mode Star Networks,” Opt. Lett. 12, 63 (1987).
    [CrossRef] [PubMed]
  11. D. Marcuse, Light Transmission Optics (Van Nostrand-Reinhold, New York, 1982), Chap. 9.
  12. M. Izutsu, Y. Nakai, T. Sueta, “Operation Mechanism of the Single-Mode Optical-Waveguide Y Junction,” Opt. Lett. 7, 136 (1982).
    [CrossRef] [PubMed]
  13. K. Tsutsumi, Y. Imada, H. Hirai, Y. Yuba, “Analysis of Single-Mode Optical Y-Junctions by the Bounded Step and Bend Approximation,” IEEE/OSA J. Lightwave Technol. LT-6, 590 (1988).
    [CrossRef]

1988

K. Tsutsumi, Y. Imada, H. Hirai, Y. Yuba, “Analysis of Single-Mode Optical Y-Junctions by the Bounded Step and Bend Approximation,” IEEE/OSA J. Lightwave Technol. LT-6, 590 (1988).
[CrossRef]

1987

1982

1979

K. Tsutsumi, T. Sueta, “A Synthesis of Optical Guided-Wave Signal Transformers,” Trans. IECE Jpn. J62-C, 381 (1979).

M. K. Barnoski, B.-U. Chen, T. R. Joseph, J. Y. Lee, O. G. Ramer, “Integrated-Optic Spectrum Analyzer,” IEEE Trans. Circuits Syst. CAS-26, 1113 (1979).
[CrossRef]

1977

K. Tsutsumi, T. Sueta, “A Proposed Integrated-Optical Device for Hadamard Transformation,” Trans. IECE Jpn. J60-C, 500 (1977).

D. B. Anderson, R. L. Davis, J. T. Boyd, R. R. August, “Comparison of Optical-Waveguide Lens Technologies,” IEEE J. Quantum Electron. QE-13, 275 (1977).
[CrossRef]

D. B. Anderson, J. T. Boyd, M. C. Hamilton, R. R. August, “An Integrated-Optical Approach to the Fourier Transform,” IEEE J. Quantum Electron. QE-13, 268 (1977).
[CrossRef]

1968

R. Shubert, J. H. Harris, “Optical Surface Waves on Thin Films and Their Application to Integrated Data Processors,” IEEE Trans. Microwave Theory Tech. MTT-16, 1048 (1968).
[CrossRef]

Anderson, D. B.

D. B. Anderson, R. L. Davis, J. T. Boyd, R. R. August, “Comparison of Optical-Waveguide Lens Technologies,” IEEE J. Quantum Electron. QE-13, 275 (1977).
[CrossRef]

D. B. Anderson, J. T. Boyd, M. C. Hamilton, R. R. August, “An Integrated-Optical Approach to the Fourier Transform,” IEEE J. Quantum Electron. QE-13, 268 (1977).
[CrossRef]

August, R. R.

D. B. Anderson, J. T. Boyd, M. C. Hamilton, R. R. August, “An Integrated-Optical Approach to the Fourier Transform,” IEEE J. Quantum Electron. QE-13, 268 (1977).
[CrossRef]

D. B. Anderson, R. L. Davis, J. T. Boyd, R. R. August, “Comparison of Optical-Waveguide Lens Technologies,” IEEE J. Quantum Electron. QE-13, 275 (1977).
[CrossRef]

Barnoski, M. K.

M. K. Barnoski, B.-U. Chen, T. R. Joseph, J. Y. Lee, O. G. Ramer, “Integrated-Optic Spectrum Analyzer,” IEEE Trans. Circuits Syst. CAS-26, 1113 (1979).
[CrossRef]

Boyd, J. T.

D. B. Anderson, J. T. Boyd, M. C. Hamilton, R. R. August, “An Integrated-Optical Approach to the Fourier Transform,” IEEE J. Quantum Electron. QE-13, 268 (1977).
[CrossRef]

D. B. Anderson, R. L. Davis, J. T. Boyd, R. R. August, “Comparison of Optical-Waveguide Lens Technologies,” IEEE J. Quantum Electron. QE-13, 275 (1977).
[CrossRef]

Chen, B.-U.

M. K. Barnoski, B.-U. Chen, T. R. Joseph, J. Y. Lee, O. G. Ramer, “Integrated-Optic Spectrum Analyzer,” IEEE Trans. Circuits Syst. CAS-26, 1113 (1979).
[CrossRef]

Davis, R. L.

D. B. Anderson, R. L. Davis, J. T. Boyd, R. R. August, “Comparison of Optical-Waveguide Lens Technologies,” IEEE J. Quantum Electron. QE-13, 275 (1977).
[CrossRef]

Hamilton, M. C.

D. B. Anderson, J. T. Boyd, M. C. Hamilton, R. R. August, “An Integrated-Optical Approach to the Fourier Transform,” IEEE J. Quantum Electron. QE-13, 268 (1977).
[CrossRef]

Harris, J. H.

R. Shubert, J. H. Harris, “Optical Surface Waves on Thin Films and Their Application to Integrated Data Processors,” IEEE Trans. Microwave Theory Tech. MTT-16, 1048 (1968).
[CrossRef]

Hirai, H.

K. Tsutsumi, Y. Imada, H. Hirai, Y. Yuba, “Analysis of Single-Mode Optical Y-Junctions by the Bounded Step and Bend Approximation,” IEEE/OSA J. Lightwave Technol. LT-6, 590 (1988).
[CrossRef]

Hunsperger, R. G.

R. G. Hunsperger, Integrated Optics: Theory and Technology (Springer-Verlag, New York, 1984), Chap. 1.

Imada, Y.

K. Tsutsumi, Y. Imada, H. Hirai, Y. Yuba, “Analysis of Single-Mode Optical Y-Junctions by the Bounded Step and Bend Approximation,” IEEE/OSA J. Lightwave Technol. LT-6, 590 (1988).
[CrossRef]

Izutsu, M.

Joseph, T. R.

M. K. Barnoski, B.-U. Chen, T. R. Joseph, J. Y. Lee, O. G. Ramer, “Integrated-Optic Spectrum Analyzer,” IEEE Trans. Circuits Syst. CAS-26, 1113 (1979).
[CrossRef]

Lee, J. Y.

M. K. Barnoski, B.-U. Chen, T. R. Joseph, J. Y. Lee, O. G. Ramer, “Integrated-Optic Spectrum Analyzer,” IEEE Trans. Circuits Syst. CAS-26, 1113 (1979).
[CrossRef]

Marcuse, D.

D. Marcuse, Light Transmission Optics (Van Nostrand-Reinhold, New York, 1982), Chap. 9.

Marhic, M. E.

Nakai, Y.

Ramer, O. G.

M. K. Barnoski, B.-U. Chen, T. R. Joseph, J. Y. Lee, O. G. Ramer, “Integrated-Optic Spectrum Analyzer,” IEEE Trans. Circuits Syst. CAS-26, 1113 (1979).
[CrossRef]

Shubert, R.

R. Shubert, J. H. Harris, “Optical Surface Waves on Thin Films and Their Application to Integrated Data Processors,” IEEE Trans. Microwave Theory Tech. MTT-16, 1048 (1968).
[CrossRef]

Sueta, T.

M. Izutsu, Y. Nakai, T. Sueta, “Operation Mechanism of the Single-Mode Optical-Waveguide Y Junction,” Opt. Lett. 7, 136 (1982).
[CrossRef] [PubMed]

K. Tsutsumi, T. Sueta, “A Synthesis of Optical Guided-Wave Signal Transformers,” Trans. IECE Jpn. J62-C, 381 (1979).

K. Tsutsumi, T. Sueta, “A Proposed Integrated-Optical Device for Hadamard Transformation,” Trans. IECE Jpn. J60-C, 500 (1977).

Tsutsumi, K.

K. Tsutsumi, Y. Imada, H. Hirai, Y. Yuba, “Analysis of Single-Mode Optical Y-Junctions by the Bounded Step and Bend Approximation,” IEEE/OSA J. Lightwave Technol. LT-6, 590 (1988).
[CrossRef]

K. Tsutsumi, T. Sueta, “A Synthesis of Optical Guided-Wave Signal Transformers,” Trans. IECE Jpn. J62-C, 381 (1979).

K. Tsutsumi, T. Sueta, “A Proposed Integrated-Optical Device for Hadamard Transformation,” Trans. IECE Jpn. J60-C, 500 (1977).

K. Tsutsumi, “Studies on Synthesis of Guided-Wave Optical Signal Transformers,” Doctoral Thesis, Osaka U. (1980).

Yu, F. T. S.

F. T. S. Yu, Optical Information Processing (Wiley, New York, 1983).

Yuba, Y.

K. Tsutsumi, Y. Imada, H. Hirai, Y. Yuba, “Analysis of Single-Mode Optical Y-Junctions by the Bounded Step and Bend Approximation,” IEEE/OSA J. Lightwave Technol. LT-6, 590 (1988).
[CrossRef]

IEEE J. Quantum Electron.

D. B. Anderson, R. L. Davis, J. T. Boyd, R. R. August, “Comparison of Optical-Waveguide Lens Technologies,” IEEE J. Quantum Electron. QE-13, 275 (1977).
[CrossRef]

D. B. Anderson, J. T. Boyd, M. C. Hamilton, R. R. August, “An Integrated-Optical Approach to the Fourier Transform,” IEEE J. Quantum Electron. QE-13, 268 (1977).
[CrossRef]

IEEE Trans. Circuits Syst.

M. K. Barnoski, B.-U. Chen, T. R. Joseph, J. Y. Lee, O. G. Ramer, “Integrated-Optic Spectrum Analyzer,” IEEE Trans. Circuits Syst. CAS-26, 1113 (1979).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

R. Shubert, J. H. Harris, “Optical Surface Waves on Thin Films and Their Application to Integrated Data Processors,” IEEE Trans. Microwave Theory Tech. MTT-16, 1048 (1968).
[CrossRef]

IEEE/OSA J. Lightwave Technol.

K. Tsutsumi, Y. Imada, H. Hirai, Y. Yuba, “Analysis of Single-Mode Optical Y-Junctions by the Bounded Step and Bend Approximation,” IEEE/OSA J. Lightwave Technol. LT-6, 590 (1988).
[CrossRef]

Opt. Lett.

Trans. IECE Jpn.

K. Tsutsumi, T. Sueta, “A Proposed Integrated-Optical Device for Hadamard Transformation,” Trans. IECE Jpn. J60-C, 500 (1977).

K. Tsutsumi, T. Sueta, “A Synthesis of Optical Guided-Wave Signal Transformers,” Trans. IECE Jpn. J62-C, 381 (1979).

Other

K. Tsutsumi, “Studies on Synthesis of Guided-Wave Optical Signal Transformers,” Doctoral Thesis, Osaka U. (1980).

D. Marcuse, Light Transmission Optics (Van Nostrand-Reinhold, New York, 1982), Chap. 9.

F. T. S. Yu, Optical Information Processing (Wiley, New York, 1983).

R. G. Hunsperger, Integrated Optics: Theory and Technology (Springer-Verlag, New York, 1984), Chap. 1.

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Figures (9)

Fig. 1
Fig. 1

Addition and subtraction by a single-mode symmetrical Y junction. (a) Addition: two input waves of the same complex amplitude form an even (lowest-order) mode, and its power is transmitted through the output waveguide port c. (b) Subtraction: if the phase of the wave incident on the waveguide port b is shifted by π rad, the waves form an odd (first-order) mode, and its power is radiated from the tapered waveguide section.

Fig. 2
Fig. 2

Schematic of a honeycomb waveguide network: (a) honeycomb waveguide network; (b) unit structure. Operations of a unit structure are division and weighted addition of amplitudes.

Fig. 3
Fig. 3

Signal flow diagram of a honeycomb waveguide network. Here a i ( p ) and b i ( p ) are the coefficients of weighted addition at the pth stage.

Fig. 4
Fig. 4

Smoothing of Gaussian noise by four stages of addition units. The wave without noise, the input wave, and the output wave are shown. These waves are assumed to be sampled by 270 straight waveguides, i.e., the number of parallel signals N = 270 is assumed. The power profiles are normalized by the peak value of the input wave.

Fig. 5
Fig. 5

Edge extraction of a wave. A single stage of subtraction units and N = 270 are assumed. The power profile of the output wave is normalized by its peak value.

Fig. 6
Fig. 6

Edge extraction of a wave in Gaussian noise. A single stage of subtraction units, four stages of addition units, and N = 270 are assumed. The power profiles of the input and output waves are normalized by those peak values.

Fig. 7
Fig. 7

Coupling with the radiated wave. The radiated wave is coupled with the first-order mode of the next-stage Y junction.

Fig. 8
Fig. 8

Honeycomb waveguide on which optical absorbers are deposited.

Fig. 9
Fig. 9

Edge enhancement of a wave. Two stages of subtraction units [ a i ( 1 ) = 1 , b i ( 1 ) = - 1 ; a i ( 2 ) = - 1 , b i ( 2 ) = 1 ] and N = 270 are assumed. The coupled power is 10% of the radiated power. The power profile of the output wave is normalized by its peak value.

Equations (13)

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A a f a ( x , y ) + A b f b ( x , y ) = A 0 f 0 ( x , y ) + A 1 f 1 ( x , y ) .
f a ( x , y ) = [ f 0 ( x , y ) + f 1 ( x , y ) ] / 2 , f b ( x , y ) = [ f 0 ( x , y ) - f 1 ( x , y ) ] / 2 .
A 0 = ( A 0 + A b ) / 2 , A 1 = ( A a - A b ) / 2 .
A 0 = ± ( A a - A b ) / 2 , A 1 = ± ( A a + A b ) / 2 .
s i ( p ) = [ a i ( p ) s i - 1 ( p - 1 ) + b i ( p ) s i ( p - 1 ) ] / 2 for odd p , s i ( p ) = [ a i ( p ) s i ( p - 1 ) + b i ( p ) s i + 1 ( p - 1 ) ] / 2 for even p .
s m ( p ) = i = - N / 2 N / 2 s i ( p - 1 ) h m - i ,
H k = i = - N / 2 N / 2 h i exp ( - j 2 π k i / N ) .
H k = exp [ ( - 1 ) p + 1 j π k / N ] cos ( π k / N )
H k = j exp [ ( - 1 ) p + 1 j π k / N ] sin ( π k / N )
H k = cos 4 ( π k / N ) .
H k = cos 4 ( π k / N ) sin ( π k / N ) .
L = P [ ( S - W ) / 2 + W / cos θ ] / tan θ + P L S .
n ( x , y ) = { 1.520 + 0.01 exp [ - ( y / d ) 2 ] d = 1.413 μ m 1.520 for y 0 and inside the waveguide width 1.0 for y 0 and outside the waveguide width for y < 0 ,

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