Abstract

Narrow-band planar waveguide filters are sensitive to fabrication errors that make it difficult to realize multistage filters successfully and maintain tight center wavelength tolerances unless a tuning technique is available. An analysis algorithm combined with waveguide heaters has been successfully used to demonstrate that fabrication errors can be compensated in an autoregressive (AR) lattice architecture that makes it possible to concatenate conveniently multiple stages and to achieve higher-order filter functions. Compensation of fabrication errors on filter functions for a second- and third-order AR lattice filter is presented, and issues related to the application of the analysis algorithm are discussed. In combination with postfabrication tuning of the coupling ratios, the analysis algorithm will allow complete control of the filter function after fabrication.

© 1997 Optical Society of America

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References

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  1. B. H. Verbeek, C. H. Henry, N. A. Olsson, K. J. Orlowsky, R. F. Kazarinov, B. H. Johnson, “Integrated four-channel Mach-Zehnder multi/demultiplexer fabricated with phosphorous doped SiO2 waveguides on Si,” J. Lightwave Technol. 6(6), 1011–1015 (1988).
    [CrossRef]
  2. K. Sasayama, M. Okuno, K. Habara, “Coherent optical transversal filter using silica-based waveguides for high-speed signal processing,” J. Lightwave Technol. 9(10), 1225–1230 (1991).
  3. K. Sasayama, M. Okuno, K. Habara, “Photonic FDM multichannel selector using coherent optical transversal filter,” J. Lightwave Technol. 12, 664–669 (1994).
    [CrossRef]
  4. M. Kuznetsov, “Cascaded coupler Mach-Zehnder channel dropping filters for wavelength-division-multiplexed optical systems,” J. Lightwave Technol. 12, 226–230 (1994).
    [CrossRef]
  5. K. Takiguchi, K. Okamoto, S. Suzuki, Y. Ohmori, “Planar lightwave circuit optical dispersion equalizer,” IEEE Photon. Technol. Lett. 6, 86–88 (1994).
    [CrossRef]
  6. R. Adar, C. H. Henry, M. A. Milbrodt, R. C. Kistler, “Phase coherence of optical waveguides,” J. Lightwave Technol. 12, 603–606 (1994).
    [CrossRef]
  7. C. H. Henry, H. H. Yaffe, “Characterization of silicon optical bench waveguides,” (1994), pp. 105–108.
  8. K. Imoto, H. Sano, M. Miyazaki, H. Uethuka, M. Maeda, “Compensation for fabrication-induced center wavelength shift in a coupled waveguide type multi/demultiplexer,” Appl. Opt. 28(10), 1904–1909 (1989).
    [CrossRef]
  9. N. Takato, T. Kominato, A. Sugita, K. Jinguji, H. Toba, M. Kawachi, “Silica-based integrated optic Mach-Zehnder mult/demultiplexer family with channel spacing of 0.01–250 nm,” IEEE J. Selected Areas Commun. 8, 1120–1127 (1990).
    [CrossRef]
  10. S. J. Orfanidis, Optimum Signal Processing: an Introduction, 2nd ed. (McGraw-Hill, New York, 1988), pp. 264–286.
  11. E. M. Dowling, D. L. MacFarlane, “Lightwave lattice filters for optically multiplexed communication systems,” J. Lightwave Technol. 12, 471–486 (1994).
    [CrossRef]
  12. J. L. Frolik, A. E. Yagle, “An asymmetric discrete-time approach for the design and analysis of periodic waveguide gratings,” J. Lightwave Technol. 13, 175–185 (1995).
    [CrossRef]
  13. C. K. Madsen, J. H. Zhao, “A general planar waveguide autoregressive optical filter,” J. Lightwave Technol. 14, 437–447 (1996).
    [CrossRef]

1996 (1)

C. K. Madsen, J. H. Zhao, “A general planar waveguide autoregressive optical filter,” J. Lightwave Technol. 14, 437–447 (1996).
[CrossRef]

1995 (1)

J. L. Frolik, A. E. Yagle, “An asymmetric discrete-time approach for the design and analysis of periodic waveguide gratings,” J. Lightwave Technol. 13, 175–185 (1995).
[CrossRef]

1994 (5)

K. Sasayama, M. Okuno, K. Habara, “Photonic FDM multichannel selector using coherent optical transversal filter,” J. Lightwave Technol. 12, 664–669 (1994).
[CrossRef]

M. Kuznetsov, “Cascaded coupler Mach-Zehnder channel dropping filters for wavelength-division-multiplexed optical systems,” J. Lightwave Technol. 12, 226–230 (1994).
[CrossRef]

K. Takiguchi, K. Okamoto, S. Suzuki, Y. Ohmori, “Planar lightwave circuit optical dispersion equalizer,” IEEE Photon. Technol. Lett. 6, 86–88 (1994).
[CrossRef]

R. Adar, C. H. Henry, M. A. Milbrodt, R. C. Kistler, “Phase coherence of optical waveguides,” J. Lightwave Technol. 12, 603–606 (1994).
[CrossRef]

E. M. Dowling, D. L. MacFarlane, “Lightwave lattice filters for optically multiplexed communication systems,” J. Lightwave Technol. 12, 471–486 (1994).
[CrossRef]

1991 (1)

K. Sasayama, M. Okuno, K. Habara, “Coherent optical transversal filter using silica-based waveguides for high-speed signal processing,” J. Lightwave Technol. 9(10), 1225–1230 (1991).

1990 (1)

N. Takato, T. Kominato, A. Sugita, K. Jinguji, H. Toba, M. Kawachi, “Silica-based integrated optic Mach-Zehnder mult/demultiplexer family with channel spacing of 0.01–250 nm,” IEEE J. Selected Areas Commun. 8, 1120–1127 (1990).
[CrossRef]

1989 (1)

1988 (1)

B. H. Verbeek, C. H. Henry, N. A. Olsson, K. J. Orlowsky, R. F. Kazarinov, B. H. Johnson, “Integrated four-channel Mach-Zehnder multi/demultiplexer fabricated with phosphorous doped SiO2 waveguides on Si,” J. Lightwave Technol. 6(6), 1011–1015 (1988).
[CrossRef]

Adar, R.

R. Adar, C. H. Henry, M. A. Milbrodt, R. C. Kistler, “Phase coherence of optical waveguides,” J. Lightwave Technol. 12, 603–606 (1994).
[CrossRef]

Dowling, E. M.

E. M. Dowling, D. L. MacFarlane, “Lightwave lattice filters for optically multiplexed communication systems,” J. Lightwave Technol. 12, 471–486 (1994).
[CrossRef]

Frolik, J. L.

J. L. Frolik, A. E. Yagle, “An asymmetric discrete-time approach for the design and analysis of periodic waveguide gratings,” J. Lightwave Technol. 13, 175–185 (1995).
[CrossRef]

Habara, K.

K. Sasayama, M. Okuno, K. Habara, “Photonic FDM multichannel selector using coherent optical transversal filter,” J. Lightwave Technol. 12, 664–669 (1994).
[CrossRef]

K. Sasayama, M. Okuno, K. Habara, “Coherent optical transversal filter using silica-based waveguides for high-speed signal processing,” J. Lightwave Technol. 9(10), 1225–1230 (1991).

Henry, C. H.

R. Adar, C. H. Henry, M. A. Milbrodt, R. C. Kistler, “Phase coherence of optical waveguides,” J. Lightwave Technol. 12, 603–606 (1994).
[CrossRef]

B. H. Verbeek, C. H. Henry, N. A. Olsson, K. J. Orlowsky, R. F. Kazarinov, B. H. Johnson, “Integrated four-channel Mach-Zehnder multi/demultiplexer fabricated with phosphorous doped SiO2 waveguides on Si,” J. Lightwave Technol. 6(6), 1011–1015 (1988).
[CrossRef]

C. H. Henry, H. H. Yaffe, “Characterization of silicon optical bench waveguides,” (1994), pp. 105–108.

Imoto, K.

Jinguji, K.

N. Takato, T. Kominato, A. Sugita, K. Jinguji, H. Toba, M. Kawachi, “Silica-based integrated optic Mach-Zehnder mult/demultiplexer family with channel spacing of 0.01–250 nm,” IEEE J. Selected Areas Commun. 8, 1120–1127 (1990).
[CrossRef]

Johnson, B. H.

B. H. Verbeek, C. H. Henry, N. A. Olsson, K. J. Orlowsky, R. F. Kazarinov, B. H. Johnson, “Integrated four-channel Mach-Zehnder multi/demultiplexer fabricated with phosphorous doped SiO2 waveguides on Si,” J. Lightwave Technol. 6(6), 1011–1015 (1988).
[CrossRef]

Kawachi, M.

N. Takato, T. Kominato, A. Sugita, K. Jinguji, H. Toba, M. Kawachi, “Silica-based integrated optic Mach-Zehnder mult/demultiplexer family with channel spacing of 0.01–250 nm,” IEEE J. Selected Areas Commun. 8, 1120–1127 (1990).
[CrossRef]

Kazarinov, R. F.

B. H. Verbeek, C. H. Henry, N. A. Olsson, K. J. Orlowsky, R. F. Kazarinov, B. H. Johnson, “Integrated four-channel Mach-Zehnder multi/demultiplexer fabricated with phosphorous doped SiO2 waveguides on Si,” J. Lightwave Technol. 6(6), 1011–1015 (1988).
[CrossRef]

Kistler, R. C.

R. Adar, C. H. Henry, M. A. Milbrodt, R. C. Kistler, “Phase coherence of optical waveguides,” J. Lightwave Technol. 12, 603–606 (1994).
[CrossRef]

Kominato, T.

N. Takato, T. Kominato, A. Sugita, K. Jinguji, H. Toba, M. Kawachi, “Silica-based integrated optic Mach-Zehnder mult/demultiplexer family with channel spacing of 0.01–250 nm,” IEEE J. Selected Areas Commun. 8, 1120–1127 (1990).
[CrossRef]

Kuznetsov, M.

M. Kuznetsov, “Cascaded coupler Mach-Zehnder channel dropping filters for wavelength-division-multiplexed optical systems,” J. Lightwave Technol. 12, 226–230 (1994).
[CrossRef]

MacFarlane, D. L.

E. M. Dowling, D. L. MacFarlane, “Lightwave lattice filters for optically multiplexed communication systems,” J. Lightwave Technol. 12, 471–486 (1994).
[CrossRef]

Madsen, C. K.

C. K. Madsen, J. H. Zhao, “A general planar waveguide autoregressive optical filter,” J. Lightwave Technol. 14, 437–447 (1996).
[CrossRef]

Maeda, M.

Milbrodt, M. A.

R. Adar, C. H. Henry, M. A. Milbrodt, R. C. Kistler, “Phase coherence of optical waveguides,” J. Lightwave Technol. 12, 603–606 (1994).
[CrossRef]

Miyazaki, M.

Ohmori, Y.

K. Takiguchi, K. Okamoto, S. Suzuki, Y. Ohmori, “Planar lightwave circuit optical dispersion equalizer,” IEEE Photon. Technol. Lett. 6, 86–88 (1994).
[CrossRef]

Okamoto, K.

K. Takiguchi, K. Okamoto, S. Suzuki, Y. Ohmori, “Planar lightwave circuit optical dispersion equalizer,” IEEE Photon. Technol. Lett. 6, 86–88 (1994).
[CrossRef]

Okuno, M.

K. Sasayama, M. Okuno, K. Habara, “Photonic FDM multichannel selector using coherent optical transversal filter,” J. Lightwave Technol. 12, 664–669 (1994).
[CrossRef]

K. Sasayama, M. Okuno, K. Habara, “Coherent optical transversal filter using silica-based waveguides for high-speed signal processing,” J. Lightwave Technol. 9(10), 1225–1230 (1991).

Olsson, N. A.

B. H. Verbeek, C. H. Henry, N. A. Olsson, K. J. Orlowsky, R. F. Kazarinov, B. H. Johnson, “Integrated four-channel Mach-Zehnder multi/demultiplexer fabricated with phosphorous doped SiO2 waveguides on Si,” J. Lightwave Technol. 6(6), 1011–1015 (1988).
[CrossRef]

Orfanidis, S. J.

S. J. Orfanidis, Optimum Signal Processing: an Introduction, 2nd ed. (McGraw-Hill, New York, 1988), pp. 264–286.

Orlowsky, K. J.

B. H. Verbeek, C. H. Henry, N. A. Olsson, K. J. Orlowsky, R. F. Kazarinov, B. H. Johnson, “Integrated four-channel Mach-Zehnder multi/demultiplexer fabricated with phosphorous doped SiO2 waveguides on Si,” J. Lightwave Technol. 6(6), 1011–1015 (1988).
[CrossRef]

Sano, H.

Sasayama, K.

K. Sasayama, M. Okuno, K. Habara, “Photonic FDM multichannel selector using coherent optical transversal filter,” J. Lightwave Technol. 12, 664–669 (1994).
[CrossRef]

K. Sasayama, M. Okuno, K. Habara, “Coherent optical transversal filter using silica-based waveguides for high-speed signal processing,” J. Lightwave Technol. 9(10), 1225–1230 (1991).

Sugita, A.

N. Takato, T. Kominato, A. Sugita, K. Jinguji, H. Toba, M. Kawachi, “Silica-based integrated optic Mach-Zehnder mult/demultiplexer family with channel spacing of 0.01–250 nm,” IEEE J. Selected Areas Commun. 8, 1120–1127 (1990).
[CrossRef]

Suzuki, S.

K. Takiguchi, K. Okamoto, S. Suzuki, Y. Ohmori, “Planar lightwave circuit optical dispersion equalizer,” IEEE Photon. Technol. Lett. 6, 86–88 (1994).
[CrossRef]

Takato, N.

N. Takato, T. Kominato, A. Sugita, K. Jinguji, H. Toba, M. Kawachi, “Silica-based integrated optic Mach-Zehnder mult/demultiplexer family with channel spacing of 0.01–250 nm,” IEEE J. Selected Areas Commun. 8, 1120–1127 (1990).
[CrossRef]

Takiguchi, K.

K. Takiguchi, K. Okamoto, S. Suzuki, Y. Ohmori, “Planar lightwave circuit optical dispersion equalizer,” IEEE Photon. Technol. Lett. 6, 86–88 (1994).
[CrossRef]

Toba, H.

N. Takato, T. Kominato, A. Sugita, K. Jinguji, H. Toba, M. Kawachi, “Silica-based integrated optic Mach-Zehnder mult/demultiplexer family with channel spacing of 0.01–250 nm,” IEEE J. Selected Areas Commun. 8, 1120–1127 (1990).
[CrossRef]

Uethuka, H.

Verbeek, B. H.

B. H. Verbeek, C. H. Henry, N. A. Olsson, K. J. Orlowsky, R. F. Kazarinov, B. H. Johnson, “Integrated four-channel Mach-Zehnder multi/demultiplexer fabricated with phosphorous doped SiO2 waveguides on Si,” J. Lightwave Technol. 6(6), 1011–1015 (1988).
[CrossRef]

Yaffe, H. H.

C. H. Henry, H. H. Yaffe, “Characterization of silicon optical bench waveguides,” (1994), pp. 105–108.

Yagle, A. E.

J. L. Frolik, A. E. Yagle, “An asymmetric discrete-time approach for the design and analysis of periodic waveguide gratings,” J. Lightwave Technol. 13, 175–185 (1995).
[CrossRef]

Zhao, J. H.

C. K. Madsen, J. H. Zhao, “A general planar waveguide autoregressive optical filter,” J. Lightwave Technol. 14, 437–447 (1996).
[CrossRef]

Appl. Opt. (1)

IEEE J. Selected Areas Commun. (1)

N. Takato, T. Kominato, A. Sugita, K. Jinguji, H. Toba, M. Kawachi, “Silica-based integrated optic Mach-Zehnder mult/demultiplexer family with channel spacing of 0.01–250 nm,” IEEE J. Selected Areas Commun. 8, 1120–1127 (1990).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

K. Takiguchi, K. Okamoto, S. Suzuki, Y. Ohmori, “Planar lightwave circuit optical dispersion equalizer,” IEEE Photon. Technol. Lett. 6, 86–88 (1994).
[CrossRef]

J. Lightwave Technol. (8)

R. Adar, C. H. Henry, M. A. Milbrodt, R. C. Kistler, “Phase coherence of optical waveguides,” J. Lightwave Technol. 12, 603–606 (1994).
[CrossRef]

B. H. Verbeek, C. H. Henry, N. A. Olsson, K. J. Orlowsky, R. F. Kazarinov, B. H. Johnson, “Integrated four-channel Mach-Zehnder multi/demultiplexer fabricated with phosphorous doped SiO2 waveguides on Si,” J. Lightwave Technol. 6(6), 1011–1015 (1988).
[CrossRef]

K. Sasayama, M. Okuno, K. Habara, “Coherent optical transversal filter using silica-based waveguides for high-speed signal processing,” J. Lightwave Technol. 9(10), 1225–1230 (1991).

K. Sasayama, M. Okuno, K. Habara, “Photonic FDM multichannel selector using coherent optical transversal filter,” J. Lightwave Technol. 12, 664–669 (1994).
[CrossRef]

M. Kuznetsov, “Cascaded coupler Mach-Zehnder channel dropping filters for wavelength-division-multiplexed optical systems,” J. Lightwave Technol. 12, 226–230 (1994).
[CrossRef]

E. M. Dowling, D. L. MacFarlane, “Lightwave lattice filters for optically multiplexed communication systems,” J. Lightwave Technol. 12, 471–486 (1994).
[CrossRef]

J. L. Frolik, A. E. Yagle, “An asymmetric discrete-time approach for the design and analysis of periodic waveguide gratings,” J. Lightwave Technol. 13, 175–185 (1995).
[CrossRef]

C. K. Madsen, J. H. Zhao, “A general planar waveguide autoregressive optical filter,” J. Lightwave Technol. 14, 437–447 (1996).
[CrossRef]

Other (2)

C. H. Henry, H. H. Yaffe, “Characterization of silicon optical bench waveguides,” (1994), pp. 105–108.

S. J. Orfanidis, Optimum Signal Processing: an Introduction, 2nd ed. (McGraw-Hill, New York, 1988), pp. 264–286.

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Figures (7)

Fig. 1
Fig. 1

IIR lattice planar waveguide filter: a) schematic, b) top view of chip layout, and c) side view of chip showing substrate, cladding, and core areas.

Fig. 2
Fig. 2

Analysis algorithm for AR lattice filter realized with planar waveguides.

Fig. 3
Fig. 3

Measured AR response for the (top) N = 2 lattice filter and (bottom) N = 3 lattice filter without the waveguide heaters showing the impact of fabrication errors.

Fig. 4
Fig. 4

N = 3 pole–zero simulation for the ARMA #1 response as ϕ1 is varied from 0 to 0.4π, whereas ϕ2 = ϕ3 = 0.

Fig. 5
Fig. 5

Calculated phase for each stage of the N = 2 and N = 3 lattice filters with the analysis algorithm as the applied power to the heater on stage #1 is varied.

Fig. 6
Fig. 6

Measured AR response for the (top) N = 2 lattice filter and (bottom) N = 3 lattice filter optimized with the waveguide heaters.

Fig. 7
Fig. 7

ARMA responses for both polarizations normalized to unity peak transmission for the N = 3 lattice filter optimized with the waveguide heaters.

Tables (2)

Tables Icon

Table 1 Analysis Results for As-Fabricated N = 2 Lattice Filter

Tables Icon

Table 2 Analysis Results for As-Fabricated N = 3 Lattice Filter

Equations (10)

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

H11z=Eo1Ei1=iN+1z-N/2 expiϕtot/2σNANz,
H21z=Eo2Ei1=BNzANz,
ΦN0=ANzBNRzz-1BNzz-1ANRz=1-tNtN expiϕN+lz-1-expiϕN+lz-1 1-t0t0 expiϕlz-1-expiϕlz-1,
ANRz=-1N-1z-N expiϕtotAN*1z*,
BNRz=-1N-1z-N expiϕtotBN*1z*.
Tpeak=σN exp-aRLNANmin2.
BNzBNRz=ANzANRz+-1N expiϕtotσNz-N
aN0aNN=bN0 bNN.
AN-1z=1κNANz-tNBNz,
BN-1z=zκN expiϕNtNANz-BNz.

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