Abstract

A major artifact of realistic photonic filters is the waveguide power loss. Its detrimental effect on the allpass structure is particularly alarming because the phase response is highly sensitive to perturbations. While the loss can be simply captured into a variation on the unit delay in signal processing analysis, its non-linearity makes it mathematically difficult to address. We present an allpass filter design algorithm that is able to provide filter coefficients that compensate for the waveguide power loss. By absorbing the loss parameter into the design cost function, the optimization problem becomes non-convex and NP hard. Our approach solves this problem by utilizing an iterative algorithm in conjunction with the branch and bound global optimization technique. The proposed algorithm is expected to improve the performance and increase the utilization of allpass filters for optical signal phase based applications such as distortion compensation and group delay equalization.

© 2013 Optical Society of America

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References

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  1. M. Lang, “Allpass filter design and applications,” IEEE Trans. Signal Process.46, 2505–2514 (1998).
    [CrossRef]
  2. P. A. Regalia, S. K. Mitra, and P. P. Vaidyanathan, “The digital all-pass filter: a versatile signal processing building block,” Proc. IEEE76, 19–37 (1988).
    [CrossRef]
  3. C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis (Wiley-Interscience, 1999).
    [CrossRef]
  4. C.-H. Cheng, “Signal processing for optical communication,” IEEE Signal Process. Mag.23, 88–96 (2006).
    [CrossRef]
  5. C. K. Madsen, “General iir optical filter design for wdm applications using all-pass filters,” J. Lightw. Technol.18, 860–868 (2000).
    [CrossRef]
  6. Y. Wang, A. Grieco, B. Slutsky, B. Rao, Y. Fainman, and T. Nguyen, “Design and analysis of a narrowband filter for optical platform,” in “IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP),” (IEEE, 2011), pp. 1633–1636.
  7. J. Azana and L. R. Chen, “Multiwavelength optical signal processing using multistage ring resonators,” IEEE Photon. Technol. Lett.14, 654–656 (2002).
    [CrossRef]
  8. M. Soltani, S. Yegnanarayanan, and A. Adibi, “Ultra-high q planar silicon microdisk resonators for chip-scale silicon photonics,” Opt. Express15, 4694–4704 (2007).
    [CrossRef] [PubMed]
  9. H. C. Kim, K. Ikeda, and Y. Fainman, “Resonant waveguide device with vertical gratings,” Opt. Lett.32, 539 (2007).
    [CrossRef] [PubMed]
  10. G. P. Agrawal, Nonlinear Fiber Optics (Springer, 2000).
  11. A. Grieco, B. Slutsky, and Y. Fainman, “Characterization of waveguide loss using distributed bragg reflectors,” Appl. Phys. B (to be published).
  12. D. T. H. Tan, K. Ikeda, P. C. Sun, and Y. Fainman, “Group velocity dispersion and self phase modulation in silicon nitride waveguides,” Appl. Phys. Lett.96, 061101 (2010).
    [CrossRef]
  13. X. Sun, M. Alam, J. Aitchison, and M. Mojahedi, “Comparison of confinement and loss of plasmonic waveguides,” in “IEEE Photonics Conference (IPC),” (IEEE, 2012), pp. 618–619.
  14. M. Heiblum and J. H. Harris, “Analysis of curved optical waveguides by conformal transformation,” IEEE J. Quantum Electron.QE-11, 75–83 (1975).
    [CrossRef]
  15. G. Lenz, B. Eggleton, C. Madsen, C. Giles, and G. Nykolak, “Optimal dispersion of optical filters for wdm systems,” IEEE Photon. Technol. Lett.10, 567–569 (1998).
    [CrossRef]
  16. G. Lenz, B. Eggleton, and C. Madsen, “Optical filter dispersion in wdm systems: A review,” in “Wavelength Division Multiplexing Components,” (Optical Society of America, 1999).
  17. P. A. Regalia and S. K. Mitra, “Phase sensitivity properties of cascaded digital lattice allpass filters,” Signal processing15, 1–21 (1988).
    [CrossRef]
  18. Y. Wang, A. Grieco, B. Slutsky, B. Rao, Y. Fainman, and T. Nguyen, “Stochastic model on the post-fabrication error for a bragg reflectors based photonic allpass filter,” in “IEEE Global Telecommunications Conference (GLOBECOM),” (IEEE, 2011), pp. 1–5.
  19. F. Payne and J. Lacey, “A theoretical analysis of scattering loss from planar optical waveguides,” Opt. Quantum. Electron.26, 977–986 (1994).
    [CrossRef]
  20. D. M. Shyroki, “Exact equivalent straight waveguide model for bent and twisted waveguides,” IEEE Trans. Microw. Theory Tech.56, 414–419 (2008).
    [CrossRef]
  21. W. R. McKinnon, D. X. Xu, C. Storey, E. Post, A. Densmore, A. Delâge, P. Waldron, J. H. Schmid, and S. Janz, “Extracting coupling and loss coefficientsfrom a ring resonator,” Opt. Express17, 18971–18982 (2009).
    [CrossRef]
  22. K. K. Lee, D. R. Lim, L. C. Kimerling, J. Shin, and F. Cerrina, “Fabrication of ultralow-loss si/sio2 waveguides by roughness reduction,” Opt. Lett.26, 1888–1890 (2001).
    [CrossRef]
  23. F. Y. Gardes, G. T. Reed, A. P. Knights, G. Mashanovich, P. E. Jessop, L. Rowe, S. McFaul, D. Bruce, and N. G. Tarr, “Sub-micron optical waveguides for silicon photonics formed via the local oxidation of silicon (locos),” Silicon Photonics III6898, 68980R (2008).
    [CrossRef]
  24. E. L. Lawler and D. E. Wood, “Branch-and-bound methods: A survey,” Oper. Res.14, 699–719 (1966).
    [CrossRef]
  25. K. Ikeda, R. E. Saperstein, N. Alic, Y. Fainman, and , “Thermal and kerr nonlinear properties of plasma-deposited silicon nitride/silicon dioxide waveguides,” Opt. Express16, 12987–12994 (2008).
    [CrossRef] [PubMed]
  26. J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “Cmos-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nature Photonics4, 37–40 (2009).
    [CrossRef]
  27. J. Löfberg, “Yalmip: A toolbox for modeling and optimization in MATLAB,” in Proceedings of the CACSD Conference, (Taipei, Taiwan, 2004).
  28. M. Renfors and T. Saramaki, “A class of approximately linear phase digital filters composed of allpass subfilters,” in “IEEE International Symposium on Circuits and Systems,” (IEEE, San Jose, CA, 1986), pp. 678–681.

2010

D. T. H. Tan, K. Ikeda, P. C. Sun, and Y. Fainman, “Group velocity dispersion and self phase modulation in silicon nitride waveguides,” Appl. Phys. Lett.96, 061101 (2010).
[CrossRef]

2009

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “Cmos-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nature Photonics4, 37–40 (2009).
[CrossRef]

W. R. McKinnon, D. X. Xu, C. Storey, E. Post, A. Densmore, A. Delâge, P. Waldron, J. H. Schmid, and S. Janz, “Extracting coupling and loss coefficientsfrom a ring resonator,” Opt. Express17, 18971–18982 (2009).
[CrossRef]

2008

K. Ikeda, R. E. Saperstein, N. Alic, Y. Fainman, and , “Thermal and kerr nonlinear properties of plasma-deposited silicon nitride/silicon dioxide waveguides,” Opt. Express16, 12987–12994 (2008).
[CrossRef] [PubMed]

D. M. Shyroki, “Exact equivalent straight waveguide model for bent and twisted waveguides,” IEEE Trans. Microw. Theory Tech.56, 414–419 (2008).
[CrossRef]

F. Y. Gardes, G. T. Reed, A. P. Knights, G. Mashanovich, P. E. Jessop, L. Rowe, S. McFaul, D. Bruce, and N. G. Tarr, “Sub-micron optical waveguides for silicon photonics formed via the local oxidation of silicon (locos),” Silicon Photonics III6898, 68980R (2008).
[CrossRef]

2007

2006

C.-H. Cheng, “Signal processing for optical communication,” IEEE Signal Process. Mag.23, 88–96 (2006).
[CrossRef]

2002

J. Azana and L. R. Chen, “Multiwavelength optical signal processing using multistage ring resonators,” IEEE Photon. Technol. Lett.14, 654–656 (2002).
[CrossRef]

2001

2000

C. K. Madsen, “General iir optical filter design for wdm applications using all-pass filters,” J. Lightw. Technol.18, 860–868 (2000).
[CrossRef]

1998

M. Lang, “Allpass filter design and applications,” IEEE Trans. Signal Process.46, 2505–2514 (1998).
[CrossRef]

G. Lenz, B. Eggleton, C. Madsen, C. Giles, and G. Nykolak, “Optimal dispersion of optical filters for wdm systems,” IEEE Photon. Technol. Lett.10, 567–569 (1998).
[CrossRef]

1994

F. Payne and J. Lacey, “A theoretical analysis of scattering loss from planar optical waveguides,” Opt. Quantum. Electron.26, 977–986 (1994).
[CrossRef]

1988

P. A. Regalia and S. K. Mitra, “Phase sensitivity properties of cascaded digital lattice allpass filters,” Signal processing15, 1–21 (1988).
[CrossRef]

P. A. Regalia, S. K. Mitra, and P. P. Vaidyanathan, “The digital all-pass filter: a versatile signal processing building block,” Proc. IEEE76, 19–37 (1988).
[CrossRef]

1975

M. Heiblum and J. H. Harris, “Analysis of curved optical waveguides by conformal transformation,” IEEE J. Quantum Electron.QE-11, 75–83 (1975).
[CrossRef]

1966

E. L. Lawler and D. E. Wood, “Branch-and-bound methods: A survey,” Oper. Res.14, 699–719 (1966).
[CrossRef]

Adibi, A.

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Springer, 2000).

Aitchison, J.

X. Sun, M. Alam, J. Aitchison, and M. Mojahedi, “Comparison of confinement and loss of plasmonic waveguides,” in “IEEE Photonics Conference (IPC),” (IEEE, 2012), pp. 618–619.

Alam, M.

X. Sun, M. Alam, J. Aitchison, and M. Mojahedi, “Comparison of confinement and loss of plasmonic waveguides,” in “IEEE Photonics Conference (IPC),” (IEEE, 2012), pp. 618–619.

Alic, N.

Azana, J.

J. Azana and L. R. Chen, “Multiwavelength optical signal processing using multistage ring resonators,” IEEE Photon. Technol. Lett.14, 654–656 (2002).
[CrossRef]

Bruce, D.

F. Y. Gardes, G. T. Reed, A. P. Knights, G. Mashanovich, P. E. Jessop, L. Rowe, S. McFaul, D. Bruce, and N. G. Tarr, “Sub-micron optical waveguides for silicon photonics formed via the local oxidation of silicon (locos),” Silicon Photonics III6898, 68980R (2008).
[CrossRef]

Cerrina, F.

Chen, L. R.

J. Azana and L. R. Chen, “Multiwavelength optical signal processing using multistage ring resonators,” IEEE Photon. Technol. Lett.14, 654–656 (2002).
[CrossRef]

Cheng, C.-H.

C.-H. Cheng, “Signal processing for optical communication,” IEEE Signal Process. Mag.23, 88–96 (2006).
[CrossRef]

Delâge, A.

Densmore, A.

Eggleton, B.

G. Lenz, B. Eggleton, C. Madsen, C. Giles, and G. Nykolak, “Optimal dispersion of optical filters for wdm systems,” IEEE Photon. Technol. Lett.10, 567–569 (1998).
[CrossRef]

G. Lenz, B. Eggleton, and C. Madsen, “Optical filter dispersion in wdm systems: A review,” in “Wavelength Division Multiplexing Components,” (Optical Society of America, 1999).

Fainman, Y.

D. T. H. Tan, K. Ikeda, P. C. Sun, and Y. Fainman, “Group velocity dispersion and self phase modulation in silicon nitride waveguides,” Appl. Phys. Lett.96, 061101 (2010).
[CrossRef]

K. Ikeda, R. E. Saperstein, N. Alic, Y. Fainman, and , “Thermal and kerr nonlinear properties of plasma-deposited silicon nitride/silicon dioxide waveguides,” Opt. Express16, 12987–12994 (2008).
[CrossRef] [PubMed]

H. C. Kim, K. Ikeda, and Y. Fainman, “Resonant waveguide device with vertical gratings,” Opt. Lett.32, 539 (2007).
[CrossRef] [PubMed]

A. Grieco, B. Slutsky, and Y. Fainman, “Characterization of waveguide loss using distributed bragg reflectors,” Appl. Phys. B (to be published).

Y. Wang, A. Grieco, B. Slutsky, B. Rao, Y. Fainman, and T. Nguyen, “Design and analysis of a narrowband filter for optical platform,” in “IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP),” (IEEE, 2011), pp. 1633–1636.

Y. Wang, A. Grieco, B. Slutsky, B. Rao, Y. Fainman, and T. Nguyen, “Stochastic model on the post-fabrication error for a bragg reflectors based photonic allpass filter,” in “IEEE Global Telecommunications Conference (GLOBECOM),” (IEEE, 2011), pp. 1–5.

Foster, M. A.

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “Cmos-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nature Photonics4, 37–40 (2009).
[CrossRef]

Gaeta, A. L.

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “Cmos-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nature Photonics4, 37–40 (2009).
[CrossRef]

Gardes, F. Y.

F. Y. Gardes, G. T. Reed, A. P. Knights, G. Mashanovich, P. E. Jessop, L. Rowe, S. McFaul, D. Bruce, and N. G. Tarr, “Sub-micron optical waveguides for silicon photonics formed via the local oxidation of silicon (locos),” Silicon Photonics III6898, 68980R (2008).
[CrossRef]

Giles, C.

G. Lenz, B. Eggleton, C. Madsen, C. Giles, and G. Nykolak, “Optimal dispersion of optical filters for wdm systems,” IEEE Photon. Technol. Lett.10, 567–569 (1998).
[CrossRef]

Gondarenko, A.

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “Cmos-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nature Photonics4, 37–40 (2009).
[CrossRef]

Grieco, A.

A. Grieco, B. Slutsky, and Y. Fainman, “Characterization of waveguide loss using distributed bragg reflectors,” Appl. Phys. B (to be published).

Y. Wang, A. Grieco, B. Slutsky, B. Rao, Y. Fainman, and T. Nguyen, “Stochastic model on the post-fabrication error for a bragg reflectors based photonic allpass filter,” in “IEEE Global Telecommunications Conference (GLOBECOM),” (IEEE, 2011), pp. 1–5.

Y. Wang, A. Grieco, B. Slutsky, B. Rao, Y. Fainman, and T. Nguyen, “Design and analysis of a narrowband filter for optical platform,” in “IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP),” (IEEE, 2011), pp. 1633–1636.

Harris, J. H.

M. Heiblum and J. H. Harris, “Analysis of curved optical waveguides by conformal transformation,” IEEE J. Quantum Electron.QE-11, 75–83 (1975).
[CrossRef]

Heiblum, M.

M. Heiblum and J. H. Harris, “Analysis of curved optical waveguides by conformal transformation,” IEEE J. Quantum Electron.QE-11, 75–83 (1975).
[CrossRef]

Ikeda, K.

Janz, S.

Jessop, P. E.

F. Y. Gardes, G. T. Reed, A. P. Knights, G. Mashanovich, P. E. Jessop, L. Rowe, S. McFaul, D. Bruce, and N. G. Tarr, “Sub-micron optical waveguides for silicon photonics formed via the local oxidation of silicon (locos),” Silicon Photonics III6898, 68980R (2008).
[CrossRef]

Kim, H. C.

Kimerling, L. C.

Knights, A. P.

F. Y. Gardes, G. T. Reed, A. P. Knights, G. Mashanovich, P. E. Jessop, L. Rowe, S. McFaul, D. Bruce, and N. G. Tarr, “Sub-micron optical waveguides for silicon photonics formed via the local oxidation of silicon (locos),” Silicon Photonics III6898, 68980R (2008).
[CrossRef]

Lacey, J.

F. Payne and J. Lacey, “A theoretical analysis of scattering loss from planar optical waveguides,” Opt. Quantum. Electron.26, 977–986 (1994).
[CrossRef]

Lang, M.

M. Lang, “Allpass filter design and applications,” IEEE Trans. Signal Process.46, 2505–2514 (1998).
[CrossRef]

Lawler, E. L.

E. L. Lawler and D. E. Wood, “Branch-and-bound methods: A survey,” Oper. Res.14, 699–719 (1966).
[CrossRef]

Lee, K. K.

Lenz, G.

G. Lenz, B. Eggleton, C. Madsen, C. Giles, and G. Nykolak, “Optimal dispersion of optical filters for wdm systems,” IEEE Photon. Technol. Lett.10, 567–569 (1998).
[CrossRef]

G. Lenz, B. Eggleton, and C. Madsen, “Optical filter dispersion in wdm systems: A review,” in “Wavelength Division Multiplexing Components,” (Optical Society of America, 1999).

Levy, J. S.

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “Cmos-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nature Photonics4, 37–40 (2009).
[CrossRef]

Lim, D. R.

Lipson, M.

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “Cmos-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nature Photonics4, 37–40 (2009).
[CrossRef]

Löfberg, J.

J. Löfberg, “Yalmip: A toolbox for modeling and optimization in MATLAB,” in Proceedings of the CACSD Conference, (Taipei, Taiwan, 2004).

Madsen, C.

G. Lenz, B. Eggleton, C. Madsen, C. Giles, and G. Nykolak, “Optimal dispersion of optical filters for wdm systems,” IEEE Photon. Technol. Lett.10, 567–569 (1998).
[CrossRef]

G. Lenz, B. Eggleton, and C. Madsen, “Optical filter dispersion in wdm systems: A review,” in “Wavelength Division Multiplexing Components,” (Optical Society of America, 1999).

Madsen, C. K.

C. K. Madsen, “General iir optical filter design for wdm applications using all-pass filters,” J. Lightw. Technol.18, 860–868 (2000).
[CrossRef]

C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis (Wiley-Interscience, 1999).
[CrossRef]

Mashanovich, G.

F. Y. Gardes, G. T. Reed, A. P. Knights, G. Mashanovich, P. E. Jessop, L. Rowe, S. McFaul, D. Bruce, and N. G. Tarr, “Sub-micron optical waveguides for silicon photonics formed via the local oxidation of silicon (locos),” Silicon Photonics III6898, 68980R (2008).
[CrossRef]

McFaul, S.

F. Y. Gardes, G. T. Reed, A. P. Knights, G. Mashanovich, P. E. Jessop, L. Rowe, S. McFaul, D. Bruce, and N. G. Tarr, “Sub-micron optical waveguides for silicon photonics formed via the local oxidation of silicon (locos),” Silicon Photonics III6898, 68980R (2008).
[CrossRef]

McKinnon, W. R.

Mitra, S. K.

P. A. Regalia and S. K. Mitra, “Phase sensitivity properties of cascaded digital lattice allpass filters,” Signal processing15, 1–21 (1988).
[CrossRef]

P. A. Regalia, S. K. Mitra, and P. P. Vaidyanathan, “The digital all-pass filter: a versatile signal processing building block,” Proc. IEEE76, 19–37 (1988).
[CrossRef]

Mojahedi, M.

X. Sun, M. Alam, J. Aitchison, and M. Mojahedi, “Comparison of confinement and loss of plasmonic waveguides,” in “IEEE Photonics Conference (IPC),” (IEEE, 2012), pp. 618–619.

Nguyen, T.

Y. Wang, A. Grieco, B. Slutsky, B. Rao, Y. Fainman, and T. Nguyen, “Stochastic model on the post-fabrication error for a bragg reflectors based photonic allpass filter,” in “IEEE Global Telecommunications Conference (GLOBECOM),” (IEEE, 2011), pp. 1–5.

Y. Wang, A. Grieco, B. Slutsky, B. Rao, Y. Fainman, and T. Nguyen, “Design and analysis of a narrowband filter for optical platform,” in “IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP),” (IEEE, 2011), pp. 1633–1636.

Nykolak, G.

G. Lenz, B. Eggleton, C. Madsen, C. Giles, and G. Nykolak, “Optimal dispersion of optical filters for wdm systems,” IEEE Photon. Technol. Lett.10, 567–569 (1998).
[CrossRef]

Payne, F.

F. Payne and J. Lacey, “A theoretical analysis of scattering loss from planar optical waveguides,” Opt. Quantum. Electron.26, 977–986 (1994).
[CrossRef]

Post, E.

Rao, B.

Y. Wang, A. Grieco, B. Slutsky, B. Rao, Y. Fainman, and T. Nguyen, “Stochastic model on the post-fabrication error for a bragg reflectors based photonic allpass filter,” in “IEEE Global Telecommunications Conference (GLOBECOM),” (IEEE, 2011), pp. 1–5.

Y. Wang, A. Grieco, B. Slutsky, B. Rao, Y. Fainman, and T. Nguyen, “Design and analysis of a narrowband filter for optical platform,” in “IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP),” (IEEE, 2011), pp. 1633–1636.

Reed, G. T.

F. Y. Gardes, G. T. Reed, A. P. Knights, G. Mashanovich, P. E. Jessop, L. Rowe, S. McFaul, D. Bruce, and N. G. Tarr, “Sub-micron optical waveguides for silicon photonics formed via the local oxidation of silicon (locos),” Silicon Photonics III6898, 68980R (2008).
[CrossRef]

Regalia, P. A.

P. A. Regalia, S. K. Mitra, and P. P. Vaidyanathan, “The digital all-pass filter: a versatile signal processing building block,” Proc. IEEE76, 19–37 (1988).
[CrossRef]

P. A. Regalia and S. K. Mitra, “Phase sensitivity properties of cascaded digital lattice allpass filters,” Signal processing15, 1–21 (1988).
[CrossRef]

Renfors, M.

M. Renfors and T. Saramaki, “A class of approximately linear phase digital filters composed of allpass subfilters,” in “IEEE International Symposium on Circuits and Systems,” (IEEE, San Jose, CA, 1986), pp. 678–681.

Rowe, L.

F. Y. Gardes, G. T. Reed, A. P. Knights, G. Mashanovich, P. E. Jessop, L. Rowe, S. McFaul, D. Bruce, and N. G. Tarr, “Sub-micron optical waveguides for silicon photonics formed via the local oxidation of silicon (locos),” Silicon Photonics III6898, 68980R (2008).
[CrossRef]

Saperstein, R. E.

Saramaki, T.

M. Renfors and T. Saramaki, “A class of approximately linear phase digital filters composed of allpass subfilters,” in “IEEE International Symposium on Circuits and Systems,” (IEEE, San Jose, CA, 1986), pp. 678–681.

Schmid, J. H.

Shin, J.

Shyroki, D. M.

D. M. Shyroki, “Exact equivalent straight waveguide model for bent and twisted waveguides,” IEEE Trans. Microw. Theory Tech.56, 414–419 (2008).
[CrossRef]

Slutsky, B.

A. Grieco, B. Slutsky, and Y. Fainman, “Characterization of waveguide loss using distributed bragg reflectors,” Appl. Phys. B (to be published).

Y. Wang, A. Grieco, B. Slutsky, B. Rao, Y. Fainman, and T. Nguyen, “Stochastic model on the post-fabrication error for a bragg reflectors based photonic allpass filter,” in “IEEE Global Telecommunications Conference (GLOBECOM),” (IEEE, 2011), pp. 1–5.

Y. Wang, A. Grieco, B. Slutsky, B. Rao, Y. Fainman, and T. Nguyen, “Design and analysis of a narrowband filter for optical platform,” in “IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP),” (IEEE, 2011), pp. 1633–1636.

Soltani, M.

Storey, C.

Sun, P. C.

D. T. H. Tan, K. Ikeda, P. C. Sun, and Y. Fainman, “Group velocity dispersion and self phase modulation in silicon nitride waveguides,” Appl. Phys. Lett.96, 061101 (2010).
[CrossRef]

Sun, X.

X. Sun, M. Alam, J. Aitchison, and M. Mojahedi, “Comparison of confinement and loss of plasmonic waveguides,” in “IEEE Photonics Conference (IPC),” (IEEE, 2012), pp. 618–619.

Tan, D. T. H.

D. T. H. Tan, K. Ikeda, P. C. Sun, and Y. Fainman, “Group velocity dispersion and self phase modulation in silicon nitride waveguides,” Appl. Phys. Lett.96, 061101 (2010).
[CrossRef]

Tarr, N. G.

F. Y. Gardes, G. T. Reed, A. P. Knights, G. Mashanovich, P. E. Jessop, L. Rowe, S. McFaul, D. Bruce, and N. G. Tarr, “Sub-micron optical waveguides for silicon photonics formed via the local oxidation of silicon (locos),” Silicon Photonics III6898, 68980R (2008).
[CrossRef]

Turner-Foster, A. C.

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “Cmos-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nature Photonics4, 37–40 (2009).
[CrossRef]

Vaidyanathan, P. P.

P. A. Regalia, S. K. Mitra, and P. P. Vaidyanathan, “The digital all-pass filter: a versatile signal processing building block,” Proc. IEEE76, 19–37 (1988).
[CrossRef]

Waldron, P.

Wang, Y.

Y. Wang, A. Grieco, B. Slutsky, B. Rao, Y. Fainman, and T. Nguyen, “Stochastic model on the post-fabrication error for a bragg reflectors based photonic allpass filter,” in “IEEE Global Telecommunications Conference (GLOBECOM),” (IEEE, 2011), pp. 1–5.

Y. Wang, A. Grieco, B. Slutsky, B. Rao, Y. Fainman, and T. Nguyen, “Design and analysis of a narrowband filter for optical platform,” in “IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP),” (IEEE, 2011), pp. 1633–1636.

Wood, D. E.

E. L. Lawler and D. E. Wood, “Branch-and-bound methods: A survey,” Oper. Res.14, 699–719 (1966).
[CrossRef]

Xu, D. X.

Yegnanarayanan, S.

Zhao, J. H.

C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis (Wiley-Interscience, 1999).
[CrossRef]

Appl. Phys. Lett.

D. T. H. Tan, K. Ikeda, P. C. Sun, and Y. Fainman, “Group velocity dispersion and self phase modulation in silicon nitride waveguides,” Appl. Phys. Lett.96, 061101 (2010).
[CrossRef]

IEEE J. Quantum Electron.

M. Heiblum and J. H. Harris, “Analysis of curved optical waveguides by conformal transformation,” IEEE J. Quantum Electron.QE-11, 75–83 (1975).
[CrossRef]

IEEE Photon. Technol. Lett.

G. Lenz, B. Eggleton, C. Madsen, C. Giles, and G. Nykolak, “Optimal dispersion of optical filters for wdm systems,” IEEE Photon. Technol. Lett.10, 567–569 (1998).
[CrossRef]

J. Azana and L. R. Chen, “Multiwavelength optical signal processing using multistage ring resonators,” IEEE Photon. Technol. Lett.14, 654–656 (2002).
[CrossRef]

IEEE Signal Process. Mag.

C.-H. Cheng, “Signal processing for optical communication,” IEEE Signal Process. Mag.23, 88–96 (2006).
[CrossRef]

IEEE Trans. Microw. Theory Tech.

D. M. Shyroki, “Exact equivalent straight waveguide model for bent and twisted waveguides,” IEEE Trans. Microw. Theory Tech.56, 414–419 (2008).
[CrossRef]

IEEE Trans. Signal Process.

M. Lang, “Allpass filter design and applications,” IEEE Trans. Signal Process.46, 2505–2514 (1998).
[CrossRef]

J. Lightw. Technol.

C. K. Madsen, “General iir optical filter design for wdm applications using all-pass filters,” J. Lightw. Technol.18, 860–868 (2000).
[CrossRef]

Nature Photonics

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “Cmos-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nature Photonics4, 37–40 (2009).
[CrossRef]

Oper. Res.

E. L. Lawler and D. E. Wood, “Branch-and-bound methods: A survey,” Oper. Res.14, 699–719 (1966).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Quantum. Electron.

F. Payne and J. Lacey, “A theoretical analysis of scattering loss from planar optical waveguides,” Opt. Quantum. Electron.26, 977–986 (1994).
[CrossRef]

Proc. IEEE

P. A. Regalia, S. K. Mitra, and P. P. Vaidyanathan, “The digital all-pass filter: a versatile signal processing building block,” Proc. IEEE76, 19–37 (1988).
[CrossRef]

Signal processing

P. A. Regalia and S. K. Mitra, “Phase sensitivity properties of cascaded digital lattice allpass filters,” Signal processing15, 1–21 (1988).
[CrossRef]

Silicon Photonics III

F. Y. Gardes, G. T. Reed, A. P. Knights, G. Mashanovich, P. E. Jessop, L. Rowe, S. McFaul, D. Bruce, and N. G. Tarr, “Sub-micron optical waveguides for silicon photonics formed via the local oxidation of silicon (locos),” Silicon Photonics III6898, 68980R (2008).
[CrossRef]

Other

Y. Wang, A. Grieco, B. Slutsky, B. Rao, Y. Fainman, and T. Nguyen, “Stochastic model on the post-fabrication error for a bragg reflectors based photonic allpass filter,” in “IEEE Global Telecommunications Conference (GLOBECOM),” (IEEE, 2011), pp. 1–5.

G. Lenz, B. Eggleton, and C. Madsen, “Optical filter dispersion in wdm systems: A review,” in “Wavelength Division Multiplexing Components,” (Optical Society of America, 1999).

C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis (Wiley-Interscience, 1999).
[CrossRef]

Y. Wang, A. Grieco, B. Slutsky, B. Rao, Y. Fainman, and T. Nguyen, “Design and analysis of a narrowband filter for optical platform,” in “IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP),” (IEEE, 2011), pp. 1633–1636.

G. P. Agrawal, Nonlinear Fiber Optics (Springer, 2000).

A. Grieco, B. Slutsky, and Y. Fainman, “Characterization of waveguide loss using distributed bragg reflectors,” Appl. Phys. B (to be published).

X. Sun, M. Alam, J. Aitchison, and M. Mojahedi, “Comparison of confinement and loss of plasmonic waveguides,” in “IEEE Photonics Conference (IPC),” (IEEE, 2012), pp. 618–619.

J. Löfberg, “Yalmip: A toolbox for modeling and optimization in MATLAB,” in Proceedings of the CACSD Conference, (Taipei, Taiwan, 2004).

M. Renfors and T. Saramaki, “A class of approximately linear phase digital filters composed of allpass subfilters,” in “IEEE International Symposium on Circuits and Systems,” (IEEE, San Jose, CA, 1986), pp. 678–681.

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Figures (6)

Fig. 1
Fig. 1

First order allpass realization using a Bragg mirror topology. The optical path length is represented by L, s is the phase delay of the unit, and ρ is the reflection coefficient.

Fig. 2
Fig. 2

Effect of γ = 0.9 on the magnitude and phase responses of a 6th order allpass. Note that minor changes in the phase response can result in significant distortion. The solid lines are the ideal allpass magnitude and phase responses.

Fig. 3
Fig. 3

Actual and desired phase responses for a bandpass structure with nonlinear chromatic dispersion near the pass band edges. The solid portions represent the frequency range of interest. The profile of the magnitude response is also shown for reference.

Fig. 4
Fig. 4

Phase responses of 4th-order allpass filters that are designed using the traditional minimax approach and the proposed algorithm for γ = 0.95. Note that the region of interest are confined to within the passband of the example bandpass filter (0.15π to 0.6π).

Fig. 5
Fig. 5

Phase errors for the traditional minimax allpass and that of the proposed design. The ideal response of the minimax is also plotted for reference.

Fig. 6
Fig. 6

Linear magnitude responses of lowpass filters generated using waveguide loss corrupted minimax and the proposed compensating design. The ideal magnitude response from a minimax design is also shown for reference.

Tables (2)

Tables Icon

Table 1 Normalized maximum phase differences for N = 7 allpass filters under various waveguide loss. Note that γ = 0.8 would correspond to a photonic allpass filter whose individual sections are composed of Bragg reflectors and 1μm × 0.5μm SiNx strip waveguides cladded in SiO2 that are 485 μm long.

Tables Icon

Table 2 Variance measurements across the frequencies for N = 7 allpass filters under various waveguide loss. Units are in 1 × 10−4

Equations (26)

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

A ( z ) = d N * + d N 1 * z 1 + + d 1 * z ( N 1 ) + 1 z N 1 + d 1 z 1 + d N 1 z ( N 1 ) + d N z N = z N D * ( 1 z * ) D ( z )
A ( 1 ) ( z ) = e j s ρ e j s + z 1 1 ρ e j s z 1
A err ( z ) = d N + γ d N 1 z 1 + + γ N z N 1 + γ d 1 z 1 + + γ N d N z N = A ( γ 1 z )
A err ( z ) = γ N z N D ( γ z 1 ) D ( γ 1 z )
Δ Θ ( ω ) d T A 1 P ( ω ) Ad d T A 1 Q ( ω ) Ad
d = [ 1 d 1 d N ] T A = diag { 1 γ γ N } P n , m ( ω ) = sin ( β ( ω ) n ω m ω ) Q n , m ( ω ) = cos ( β ( ω ) n ω m ω )
minimize d max ω W ( ω ) | d T A 1 P ( ω ) Ad d T A 1 Q ( ω ) Ad |
W k ( ω ) = 1 | d k 1 T A 1 Q ( ω ) Ad k 1 |
minimize d i , δ , γ δ + λ subject to δ W k ( ω ) d i T A 1 P ( ω ) Ad k δ λ d k T A 1 Q ( ω ) Ad k d k 1 T A 1 Q ( ω ) Ad k 1 λ
Θ pre ( ω ) = { ( N 1 ) ω 0 ω ω p ( N 1 ) ω π ω s ω π
H ( z ) = 1 2 ( z ( N 1 ) + A err ( z ) )
Θ err ( ω ) = N ω + arctan k = 0 N d k γ k sin k ω k = 0 N d k γ k cos k ω + arctan k = 0 N d k γ k sin k ω k = 0 N d k γ k cos k ω
Θ err ( ω ) = N ω + arctan d T A 1 s ( ω ) d T A 1 c ( ω ) + arctan d T As ( ω ) d T Ac ( ω )
d = [ 1 d 1 d N ] T s ( ω ) = [ 0 sin ω sin N ω ] T c ( ω ) = [ 1 cos ω cos N ω ] T A = diag { 1 γ γ N }
Δ Θ ( ω ) = Θ pre ( ω ) Θ err ( ω )
Δ Θ ( ω ) = β ( ω ) arctan d T A 1 s ( ω ) d T A 1 c ( ω ) arctan d T As ( ω ) d T Ac ( ω )
Δ Θ ( ω ) = arctan d T A 1 P ( ω ) Ad d T A 1 Q ( ω ) Ad
P n , m ( ω ) = sin ( β ( ω ) n ω m ω )
Q n , m ( ω ) = cos ( β ( ω ) n ω m ω )
arctan x = x x 3 3 + x 5 5 x 7 7 +
Δ Θ ( ω ) d T A 1 P ( ω ) Ad d T A 1 Q ( ω ) Ad
minimize d max ω W ( ω ) | d T A 1 P ( ω ) Ad | subject to d T A 1 Q ( ω ) Ad = 1
minimize δ , d δ subject to δ < W ( ω ) d T A 1 P ( ω ) Ad < δ
minimize d , δ , ε δ + ε subject to δ W ( ω ) d T A 1 P ( ω ) Ad δ ε d T A 1 Q ( ω ) Ad 1 ε
minimize d max ω W ( ω ) | d k T A 1 P ( ω ) Ad k d k 1 T A 1 Q ( ω ) Ad k 1 |
| d k T A 1 Q ( ω ) Ad k d k 1 T A 1 Q ( ω ) Ad k 1 | < λ

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