Abstract

We introduce a new general class of hybrid optical filters, which reduce to either transversal or lattice filters in particular limits, and are suitable for implementation as planar lightwave circuits. They can be used to synthesize arbitrary periodic transfer functions with finite impulse responses. Design tradeoffs can be used to minimize insertion loss and optimize layout. Examples of filter synthesis are presented.

© 2002 Optical Society of America

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References

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  1. M. Oguma, T. Kitoh, K. Jinguji, T. Shibata, A. Himeno, and Y. Ibino, “Flat-top and low-loss WDM filter composed of lattice-form interleave filter and arrayed-waveguide gratings on one chip,” in OSA Trends in Optics and Photonics (TOPS) Vol. 54, Optical Fiber Communication Conference, Technical Digest, Postconference Edition (Optical Society of America, Washington, D.C., 2001), pp. WB3-1-WB3-3.
  2. T. Chiba, H. Arai, K. Ohira, H. Nonen, H. Okano, and H. Uetsuka, “Novel architecture of wavelength interleaving filter with Fourier transform-based MZIs,” in OSA Trends in Optics and Photonics (TOPS) Vol. 54, Optical Fiber Communication Conference, Technical Digest, Postconference Edition (Optical Society of America, Washington, D.C., 2001), pp. WB5-1-WB5-3.
  3. E. Pawlowski, K. Takiguchi, M. Okuno, K. Sasayama, A. Himeno, K. Okamoto, and Y. Ohmori, “Variable bandwidth and tunable center frequency filter using transversal-form programmable optical filter,” IEE Electron. Lett. 32, 113–114 (1996).
    [Crossref]
  4. M. E. Marhic, “Parallel optical filters,” in ICT98 - International Conference on Telecommunications, F. N. Pavlidou, ed. (Thessaloniki, Greece : Aristotle Univ. Thessaloniki, 1998), pp. 503–508.
  5. K. Jinguji and M. Kawachi, “Synthesis of coherent two-port lattice-form optical delay-line circuit,” J. Lightwave Technol. 13, 73–82 (1995).
    [Crossref]

1996 (1)

E. Pawlowski, K. Takiguchi, M. Okuno, K. Sasayama, A. Himeno, K. Okamoto, and Y. Ohmori, “Variable bandwidth and tunable center frequency filter using transversal-form programmable optical filter,” IEE Electron. Lett. 32, 113–114 (1996).
[Crossref]

1995 (1)

K. Jinguji and M. Kawachi, “Synthesis of coherent two-port lattice-form optical delay-line circuit,” J. Lightwave Technol. 13, 73–82 (1995).
[Crossref]

Arai, H.

T. Chiba, H. Arai, K. Ohira, H. Nonen, H. Okano, and H. Uetsuka, “Novel architecture of wavelength interleaving filter with Fourier transform-based MZIs,” in OSA Trends in Optics and Photonics (TOPS) Vol. 54, Optical Fiber Communication Conference, Technical Digest, Postconference Edition (Optical Society of America, Washington, D.C., 2001), pp. WB5-1-WB5-3.

Chiba, T.

T. Chiba, H. Arai, K. Ohira, H. Nonen, H. Okano, and H. Uetsuka, “Novel architecture of wavelength interleaving filter with Fourier transform-based MZIs,” in OSA Trends in Optics and Photonics (TOPS) Vol. 54, Optical Fiber Communication Conference, Technical Digest, Postconference Edition (Optical Society of America, Washington, D.C., 2001), pp. WB5-1-WB5-3.

Himeno, A.

E. Pawlowski, K. Takiguchi, M. Okuno, K. Sasayama, A. Himeno, K. Okamoto, and Y. Ohmori, “Variable bandwidth and tunable center frequency filter using transversal-form programmable optical filter,” IEE Electron. Lett. 32, 113–114 (1996).
[Crossref]

M. Oguma, T. Kitoh, K. Jinguji, T. Shibata, A. Himeno, and Y. Ibino, “Flat-top and low-loss WDM filter composed of lattice-form interleave filter and arrayed-waveguide gratings on one chip,” in OSA Trends in Optics and Photonics (TOPS) Vol. 54, Optical Fiber Communication Conference, Technical Digest, Postconference Edition (Optical Society of America, Washington, D.C., 2001), pp. WB3-1-WB3-3.

Ibino, Y.

M. Oguma, T. Kitoh, K. Jinguji, T. Shibata, A. Himeno, and Y. Ibino, “Flat-top and low-loss WDM filter composed of lattice-form interleave filter and arrayed-waveguide gratings on one chip,” in OSA Trends in Optics and Photonics (TOPS) Vol. 54, Optical Fiber Communication Conference, Technical Digest, Postconference Edition (Optical Society of America, Washington, D.C., 2001), pp. WB3-1-WB3-3.

Jinguji, K.

K. Jinguji and M. Kawachi, “Synthesis of coherent two-port lattice-form optical delay-line circuit,” J. Lightwave Technol. 13, 73–82 (1995).
[Crossref]

M. Oguma, T. Kitoh, K. Jinguji, T. Shibata, A. Himeno, and Y. Ibino, “Flat-top and low-loss WDM filter composed of lattice-form interleave filter and arrayed-waveguide gratings on one chip,” in OSA Trends in Optics and Photonics (TOPS) Vol. 54, Optical Fiber Communication Conference, Technical Digest, Postconference Edition (Optical Society of America, Washington, D.C., 2001), pp. WB3-1-WB3-3.

Kawachi, M.

K. Jinguji and M. Kawachi, “Synthesis of coherent two-port lattice-form optical delay-line circuit,” J. Lightwave Technol. 13, 73–82 (1995).
[Crossref]

Kitoh, T.

M. Oguma, T. Kitoh, K. Jinguji, T. Shibata, A. Himeno, and Y. Ibino, “Flat-top and low-loss WDM filter composed of lattice-form interleave filter and arrayed-waveguide gratings on one chip,” in OSA Trends in Optics and Photonics (TOPS) Vol. 54, Optical Fiber Communication Conference, Technical Digest, Postconference Edition (Optical Society of America, Washington, D.C., 2001), pp. WB3-1-WB3-3.

Marhic, M. E.

M. E. Marhic, “Parallel optical filters,” in ICT98 - International Conference on Telecommunications, F. N. Pavlidou, ed. (Thessaloniki, Greece : Aristotle Univ. Thessaloniki, 1998), pp. 503–508.

Nonen, H.

T. Chiba, H. Arai, K. Ohira, H. Nonen, H. Okano, and H. Uetsuka, “Novel architecture of wavelength interleaving filter with Fourier transform-based MZIs,” in OSA Trends in Optics and Photonics (TOPS) Vol. 54, Optical Fiber Communication Conference, Technical Digest, Postconference Edition (Optical Society of America, Washington, D.C., 2001), pp. WB5-1-WB5-3.

Oguma, M.

M. Oguma, T. Kitoh, K. Jinguji, T. Shibata, A. Himeno, and Y. Ibino, “Flat-top and low-loss WDM filter composed of lattice-form interleave filter and arrayed-waveguide gratings on one chip,” in OSA Trends in Optics and Photonics (TOPS) Vol. 54, Optical Fiber Communication Conference, Technical Digest, Postconference Edition (Optical Society of America, Washington, D.C., 2001), pp. WB3-1-WB3-3.

Ohira, K.

T. Chiba, H. Arai, K. Ohira, H. Nonen, H. Okano, and H. Uetsuka, “Novel architecture of wavelength interleaving filter with Fourier transform-based MZIs,” in OSA Trends in Optics and Photonics (TOPS) Vol. 54, Optical Fiber Communication Conference, Technical Digest, Postconference Edition (Optical Society of America, Washington, D.C., 2001), pp. WB5-1-WB5-3.

Ohmori, Y.

E. Pawlowski, K. Takiguchi, M. Okuno, K. Sasayama, A. Himeno, K. Okamoto, and Y. Ohmori, “Variable bandwidth and tunable center frequency filter using transversal-form programmable optical filter,” IEE Electron. Lett. 32, 113–114 (1996).
[Crossref]

Okamoto, K.

E. Pawlowski, K. Takiguchi, M. Okuno, K. Sasayama, A. Himeno, K. Okamoto, and Y. Ohmori, “Variable bandwidth and tunable center frequency filter using transversal-form programmable optical filter,” IEE Electron. Lett. 32, 113–114 (1996).
[Crossref]

Okano, H.

T. Chiba, H. Arai, K. Ohira, H. Nonen, H. Okano, and H. Uetsuka, “Novel architecture of wavelength interleaving filter with Fourier transform-based MZIs,” in OSA Trends in Optics and Photonics (TOPS) Vol. 54, Optical Fiber Communication Conference, Technical Digest, Postconference Edition (Optical Society of America, Washington, D.C., 2001), pp. WB5-1-WB5-3.

Okuno, M.

E. Pawlowski, K. Takiguchi, M. Okuno, K. Sasayama, A. Himeno, K. Okamoto, and Y. Ohmori, “Variable bandwidth and tunable center frequency filter using transversal-form programmable optical filter,” IEE Electron. Lett. 32, 113–114 (1996).
[Crossref]

Pawlowski, E.

E. Pawlowski, K. Takiguchi, M. Okuno, K. Sasayama, A. Himeno, K. Okamoto, and Y. Ohmori, “Variable bandwidth and tunable center frequency filter using transversal-form programmable optical filter,” IEE Electron. Lett. 32, 113–114 (1996).
[Crossref]

Sasayama, K.

E. Pawlowski, K. Takiguchi, M. Okuno, K. Sasayama, A. Himeno, K. Okamoto, and Y. Ohmori, “Variable bandwidth and tunable center frequency filter using transversal-form programmable optical filter,” IEE Electron. Lett. 32, 113–114 (1996).
[Crossref]

Shibata, T.

M. Oguma, T. Kitoh, K. Jinguji, T. Shibata, A. Himeno, and Y. Ibino, “Flat-top and low-loss WDM filter composed of lattice-form interleave filter and arrayed-waveguide gratings on one chip,” in OSA Trends in Optics and Photonics (TOPS) Vol. 54, Optical Fiber Communication Conference, Technical Digest, Postconference Edition (Optical Society of America, Washington, D.C., 2001), pp. WB3-1-WB3-3.

Takiguchi, K.

E. Pawlowski, K. Takiguchi, M. Okuno, K. Sasayama, A. Himeno, K. Okamoto, and Y. Ohmori, “Variable bandwidth and tunable center frequency filter using transversal-form programmable optical filter,” IEE Electron. Lett. 32, 113–114 (1996).
[Crossref]

Uetsuka, H.

T. Chiba, H. Arai, K. Ohira, H. Nonen, H. Okano, and H. Uetsuka, “Novel architecture of wavelength interleaving filter with Fourier transform-based MZIs,” in OSA Trends in Optics and Photonics (TOPS) Vol. 54, Optical Fiber Communication Conference, Technical Digest, Postconference Edition (Optical Society of America, Washington, D.C., 2001), pp. WB5-1-WB5-3.

IEE Electron. Lett. (1)

E. Pawlowski, K. Takiguchi, M. Okuno, K. Sasayama, A. Himeno, K. Okamoto, and Y. Ohmori, “Variable bandwidth and tunable center frequency filter using transversal-form programmable optical filter,” IEE Electron. Lett. 32, 113–114 (1996).
[Crossref]

J. Lightwave Technol. (1)

K. Jinguji and M. Kawachi, “Synthesis of coherent two-port lattice-form optical delay-line circuit,” J. Lightwave Technol. 13, 73–82 (1995).
[Crossref]

Other (3)

M. E. Marhic, “Parallel optical filters,” in ICT98 - International Conference on Telecommunications, F. N. Pavlidou, ed. (Thessaloniki, Greece : Aristotle Univ. Thessaloniki, 1998), pp. 503–508.

M. Oguma, T. Kitoh, K. Jinguji, T. Shibata, A. Himeno, and Y. Ibino, “Flat-top and low-loss WDM filter composed of lattice-form interleave filter and arrayed-waveguide gratings on one chip,” in OSA Trends in Optics and Photonics (TOPS) Vol. 54, Optical Fiber Communication Conference, Technical Digest, Postconference Edition (Optical Society of America, Washington, D.C., 2001), pp. WB3-1-WB3-3.

T. Chiba, H. Arai, K. Ohira, H. Nonen, H. Okano, and H. Uetsuka, “Novel architecture of wavelength interleaving filter with Fourier transform-based MZIs,” in OSA Trends in Optics and Photonics (TOPS) Vol. 54, Optical Fiber Communication Conference, Technical Digest, Postconference Edition (Optical Society of America, Washington, D.C., 2001), pp. WB5-1-WB5-3.

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Figures (1)

Fig. 1.
Fig. 1.

Hybrid transversal-lattice filter for synthesizing a polynomial F(z), with V = 4.

Tables (1)

Tables Icon

Table I. Losses of hybrid transversal-lattice Chebyshev filters for possible values of U.

Equations (5)

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

F ( z ) = n = 0 N b n z n = u = 1 U z ( u 1 ) ( V + 1 ) ( v = 0 V b v ( u ) z v ) = u = 1 U z ( u 1 ) ( V + 1 ) F u ( z ) ,
F ( z ) = D F a ( z ) = D u = 1 U ( w u ) 2 z ( u 1 ) ( V + 1 ) F u , a ( z )
= D u = 1 U ( w u ) 2 z ( u 1 ) ( V + 1 ) F u ( z ) D u = u = 1 U z ( u 1 ) ( V + 1 ) F u ( z ) .
D = u = 1 U D u = u = 1 U Max { F u ( z ) } .
Max { F a ( z ) } = Max { F ( z ) } / D = Max { F ( z ) } / u = 1 U Max { F u ( z ) } .

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