Abstract

In this paper, the layer aggregation method is applied to coupled resonator optical waveguides. Starting from the frequency transfer function, the method yields the coupling constants between the resonators. The convergence of the algorithm developed is examined and the related parameters discussed.

© 2010 Optical Society of America

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  1. J. Capmany and M. Muriel, "A new transfer matrix formalism for the analysis of fiber ring resonators: compound coupled structures for FDMA demultiplexing," J. Lightwave Technol. 8, 1904-1919 (1990).
    [CrossRef]
  2. B. Little, S. Chu, H. Haus, J. Foresi, and J.-P. Laine, "Microring resonator channel dropping filters," J. Lightwave Technol. 15, 998-1005 (1997).
    [CrossRef]
  3. C. Madsen and J. Zhao, "A general planar waveguide autoregressive optical filter," J. Lightwave Technol. 14, 437-447 (1996).
    [CrossRef]
  4. V. Van, T. Ibrahim, P. Absil, F. Johnson, R. Grover, and P.-T. Ho, "Optical signal processing using nonlinear semiconductor microring resonators," IEEE J. Sel. Top. Quantum Electron. 8, 705-713 (2002).
    [CrossRef]
  5. F. Xia, L. Sekaric, and Y. Vlasov, "Ultra compact optical buffers on a silicon chip," Nat. Photonics 1, 65-71 (2007).
    [CrossRef]
  6. H. Tazawa and W. Steier, "Analysis of ring resonator-based traveling-wave modulators," IEEE Photon. Technol. Lett. 18, 211-213 (2006).
    [CrossRef]
  7. C. Madsen, G. Lenz, A. Bruce, M. Cappuzzo, L. Gomez, and R. Scotti, "Integrated all-pass filters for tunable dispersion and dispersion slope compensation," IEEE Photon. Technol. Lett. 11, 1623-1625 (1999).
    [CrossRef]
  8. B. Little, S. Chu, W. Pan, and Y. Kokubun, "Microring resonator arrays for VLSI photonics," IEEE Photon. Technol. Lett. 12, 323-325 (2000).
    [CrossRef]
  9. H.-C. Ren, F. Vollmer, S. Arnold, and A. Libchaber, "High-Q microsphere biosensor - analysis for adsorption of rod like bacteria," Opt. Express 15, 17410-17423 (2007).
    [CrossRef] [PubMed]
  10. K. Vahala, "Optical microcavities," Nature (London) 424, 839-846 (2003).
    [CrossRef]
  11. E. Peral, J. Capmany, and J. Marti, "Iterative solution to the Gel’fand-Levitan-Marchenko coupled equations and application to synthesis of fiber gratings," IEEE J. Quantum Electron. 32, 2078-2084 (1996).
    [CrossRef]
  12. R. Feced, M. Zervas, and M. Muriel, "An efficient inverse scattering algorithm for the design of nonuniform fiber Bragg gratings," IEEE J. Quantum Electron. 35, 1105-1115 (1999).
    [CrossRef]
  13. L. Poladian, "Simple grating synthesis algorithm," Opt. Lett. 25, 787-789 (2000).
    [CrossRef]
  14. J. Skaar, L. Wang, and T. Erdogan, "On the synthesis of fiber Bragg gratings by layer peeling," IEEE J. Quantum Electron. 37, 165-173 (2001).
    [CrossRef]
  15. J. Skaar, L. Wang, and T. Erdogan, "Synthesis of thick optical thin-film filters with a layer-peeling inverse scattering algorithm," Appl. Opt. 40, 2183-2189 (2001).
    [CrossRef]
  16. A. Rosenthal and M. Horowitz, "Inverse scattering algorithm for reconstructing strongly reflecting fiber bragg gratings," IEEE J. Quantum Electron. 39, 1018-1026 (2003).
    [CrossRef]
  17. J. Capmany, M. Muriel, and S. Sales, "Highly accurate synthesis of fiber and waveguide bragg gratings by an impedance reconstruction layer-aggregation method," IEEE J. Quantum Electron. 43, 889-898 (2007).
    [CrossRef]
  18. J. E. Heebner, P. Chak, S. Pereira, J. E. Sipe, and R. W. Boyd, "Distributed and localized feedback in microresonator sequences for linear and nonlinear optics," J. Opt. Soc. Am. B 21, 1818-1832 (2004).
    [CrossRef]
  19. J. Poon, J. Scheuer, S. Mookherjea, G. Paloczi, Y. Huang, and A. Yariv, "Matrix analysis of microring coupled resonator optical waveguides," Opt. Express 12, 90-103 (2004).
    [CrossRef] [PubMed]
  20. Y. Landobasa, S. Darmawan, and M.-K. Chin, "Matrix analysis of 2-D microresonator lattice optical filters," IEEE J. Quantum Electron. 41, 1410-1418 (2005).
    [CrossRef]
  21. D. L. MacFarlane and E. M. Dowling, "Z-domain techniques in the analysis of Fabry-Perot ´etalons and multilayer structures," J. Opt. Soc. Am. A 11, 236-245 (1994).
    [CrossRef]
  22. A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, "Coupled-resonator optical waveguide: a proposal and analysis," Opt. Lett. 24, 711-713 (1999).
    [CrossRef]
  23. A. Melloni and M. Martinelli, "Synthesis of direct-coupled-resonators bandpass filters for WDM systems," J. Lightwave Technol. 20, 296-303 (2002).
    [CrossRef]
  24. R. Orta, P. Savi, R. Tascone, and D. Trinchero, "Synthesis of multiple-ring-resonator filters for optical systems," IEEE Photon. Technol. Lett. 7, 1447-1449 (1995).
    [CrossRef]
  25. J. Capmany, P. Muñoz, J. D. Domenech, and M. A. Muriel, "Apodized coupled resonator waveguides," Opt. Express 15, 10196-10206 (2007).
    [CrossRef] [PubMed]
  26. A. Yariv, "Universal relations for coupling of optical power between microresonators and dielectric waveguides," Electron. Lett. 36, 321-322 (2000).
    [CrossRef]
  27. A. V. Oppenheim, R. W. Schafer, and J. R. Buck, Discrete-time signal processing, Signal Processing Series, 2nd ed. (Prentice-Hall International, 1999).

2007 (4)

F. Xia, L. Sekaric, and Y. Vlasov, "Ultra compact optical buffers on a silicon chip," Nat. Photonics 1, 65-71 (2007).
[CrossRef]

J. Capmany, M. Muriel, and S. Sales, "Highly accurate synthesis of fiber and waveguide bragg gratings by an impedance reconstruction layer-aggregation method," IEEE J. Quantum Electron. 43, 889-898 (2007).
[CrossRef]

J. Capmany, P. Muñoz, J. D. Domenech, and M. A. Muriel, "Apodized coupled resonator waveguides," Opt. Express 15, 10196-10206 (2007).
[CrossRef] [PubMed]

H.-C. Ren, F. Vollmer, S. Arnold, and A. Libchaber, "High-Q microsphere biosensor - analysis for adsorption of rod like bacteria," Opt. Express 15, 17410-17423 (2007).
[CrossRef] [PubMed]

2006 (1)

H. Tazawa and W. Steier, "Analysis of ring resonator-based traveling-wave modulators," IEEE Photon. Technol. Lett. 18, 211-213 (2006).
[CrossRef]

2005 (1)

Y. Landobasa, S. Darmawan, and M.-K. Chin, "Matrix analysis of 2-D microresonator lattice optical filters," IEEE J. Quantum Electron. 41, 1410-1418 (2005).
[CrossRef]

2004 (2)

2003 (2)

A. Rosenthal and M. Horowitz, "Inverse scattering algorithm for reconstructing strongly reflecting fiber bragg gratings," IEEE J. Quantum Electron. 39, 1018-1026 (2003).
[CrossRef]

K. Vahala, "Optical microcavities," Nature (London) 424, 839-846 (2003).
[CrossRef]

2002 (2)

V. Van, T. Ibrahim, P. Absil, F. Johnson, R. Grover, and P.-T. Ho, "Optical signal processing using nonlinear semiconductor microring resonators," IEEE J. Sel. Top. Quantum Electron. 8, 705-713 (2002).
[CrossRef]

A. Melloni and M. Martinelli, "Synthesis of direct-coupled-resonators bandpass filters for WDM systems," J. Lightwave Technol. 20, 296-303 (2002).
[CrossRef]

2001 (2)

J. Skaar, L. Wang, and T. Erdogan, "Synthesis of thick optical thin-film filters with a layer-peeling inverse scattering algorithm," Appl. Opt. 40, 2183-2189 (2001).
[CrossRef]

J. Skaar, L. Wang, and T. Erdogan, "On the synthesis of fiber Bragg gratings by layer peeling," IEEE J. Quantum Electron. 37, 165-173 (2001).
[CrossRef]

2000 (3)

B. Little, S. Chu, W. Pan, and Y. Kokubun, "Microring resonator arrays for VLSI photonics," IEEE Photon. Technol. Lett. 12, 323-325 (2000).
[CrossRef]

A. Yariv, "Universal relations for coupling of optical power between microresonators and dielectric waveguides," Electron. Lett. 36, 321-322 (2000).
[CrossRef]

L. Poladian, "Simple grating synthesis algorithm," Opt. Lett. 25, 787-789 (2000).
[CrossRef]

1999 (3)

R. Feced, M. Zervas, and M. Muriel, "An efficient inverse scattering algorithm for the design of nonuniform fiber Bragg gratings," IEEE J. Quantum Electron. 35, 1105-1115 (1999).
[CrossRef]

C. Madsen, G. Lenz, A. Bruce, M. Cappuzzo, L. Gomez, and R. Scotti, "Integrated all-pass filters for tunable dispersion and dispersion slope compensation," IEEE Photon. Technol. Lett. 11, 1623-1625 (1999).
[CrossRef]

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, "Coupled-resonator optical waveguide: a proposal and analysis," Opt. Lett. 24, 711-713 (1999).
[CrossRef]

1997 (1)

B. Little, S. Chu, H. Haus, J. Foresi, and J.-P. Laine, "Microring resonator channel dropping filters," J. Lightwave Technol. 15, 998-1005 (1997).
[CrossRef]

1996 (2)

C. Madsen and J. Zhao, "A general planar waveguide autoregressive optical filter," J. Lightwave Technol. 14, 437-447 (1996).
[CrossRef]

E. Peral, J. Capmany, and J. Marti, "Iterative solution to the Gel’fand-Levitan-Marchenko coupled equations and application to synthesis of fiber gratings," IEEE J. Quantum Electron. 32, 2078-2084 (1996).
[CrossRef]

1995 (1)

R. Orta, P. Savi, R. Tascone, and D. Trinchero, "Synthesis of multiple-ring-resonator filters for optical systems," IEEE Photon. Technol. Lett. 7, 1447-1449 (1995).
[CrossRef]

1994 (1)

1990 (1)

J. Capmany and M. Muriel, "A new transfer matrix formalism for the analysis of fiber ring resonators: compound coupled structures for FDMA demultiplexing," J. Lightwave Technol. 8, 1904-1919 (1990).
[CrossRef]

Absil, P.

V. Van, T. Ibrahim, P. Absil, F. Johnson, R. Grover, and P.-T. Ho, "Optical signal processing using nonlinear semiconductor microring resonators," IEEE J. Sel. Top. Quantum Electron. 8, 705-713 (2002).
[CrossRef]

Arnold, S.

Boyd, R. W.

Bruce, A.

C. Madsen, G. Lenz, A. Bruce, M. Cappuzzo, L. Gomez, and R. Scotti, "Integrated all-pass filters for tunable dispersion and dispersion slope compensation," IEEE Photon. Technol. Lett. 11, 1623-1625 (1999).
[CrossRef]

Capmany, J.

J. Capmany, P. Muñoz, J. D. Domenech, and M. A. Muriel, "Apodized coupled resonator waveguides," Opt. Express 15, 10196-10206 (2007).
[CrossRef] [PubMed]

J. Capmany, M. Muriel, and S. Sales, "Highly accurate synthesis of fiber and waveguide bragg gratings by an impedance reconstruction layer-aggregation method," IEEE J. Quantum Electron. 43, 889-898 (2007).
[CrossRef]

E. Peral, J. Capmany, and J. Marti, "Iterative solution to the Gel’fand-Levitan-Marchenko coupled equations and application to synthesis of fiber gratings," IEEE J. Quantum Electron. 32, 2078-2084 (1996).
[CrossRef]

J. Capmany and M. Muriel, "A new transfer matrix formalism for the analysis of fiber ring resonators: compound coupled structures for FDMA demultiplexing," J. Lightwave Technol. 8, 1904-1919 (1990).
[CrossRef]

Cappuzzo, M.

C. Madsen, G. Lenz, A. Bruce, M. Cappuzzo, L. Gomez, and R. Scotti, "Integrated all-pass filters for tunable dispersion and dispersion slope compensation," IEEE Photon. Technol. Lett. 11, 1623-1625 (1999).
[CrossRef]

Chak, P.

Chin, M.-K.

Y. Landobasa, S. Darmawan, and M.-K. Chin, "Matrix analysis of 2-D microresonator lattice optical filters," IEEE J. Quantum Electron. 41, 1410-1418 (2005).
[CrossRef]

Chu, S.

B. Little, S. Chu, W. Pan, and Y. Kokubun, "Microring resonator arrays for VLSI photonics," IEEE Photon. Technol. Lett. 12, 323-325 (2000).
[CrossRef]

B. Little, S. Chu, H. Haus, J. Foresi, and J.-P. Laine, "Microring resonator channel dropping filters," J. Lightwave Technol. 15, 998-1005 (1997).
[CrossRef]

Darmawan, S.

Y. Landobasa, S. Darmawan, and M.-K. Chin, "Matrix analysis of 2-D microresonator lattice optical filters," IEEE J. Quantum Electron. 41, 1410-1418 (2005).
[CrossRef]

Domenech, J. D.

Dowling, E. M.

Erdogan, T.

J. Skaar, L. Wang, and T. Erdogan, "Synthesis of thick optical thin-film filters with a layer-peeling inverse scattering algorithm," Appl. Opt. 40, 2183-2189 (2001).
[CrossRef]

J. Skaar, L. Wang, and T. Erdogan, "On the synthesis of fiber Bragg gratings by layer peeling," IEEE J. Quantum Electron. 37, 165-173 (2001).
[CrossRef]

Feced, R.

R. Feced, M. Zervas, and M. Muriel, "An efficient inverse scattering algorithm for the design of nonuniform fiber Bragg gratings," IEEE J. Quantum Electron. 35, 1105-1115 (1999).
[CrossRef]

Foresi, J.

B. Little, S. Chu, H. Haus, J. Foresi, and J.-P. Laine, "Microring resonator channel dropping filters," J. Lightwave Technol. 15, 998-1005 (1997).
[CrossRef]

Gomez, L.

C. Madsen, G. Lenz, A. Bruce, M. Cappuzzo, L. Gomez, and R. Scotti, "Integrated all-pass filters for tunable dispersion and dispersion slope compensation," IEEE Photon. Technol. Lett. 11, 1623-1625 (1999).
[CrossRef]

Grover, R.

V. Van, T. Ibrahim, P. Absil, F. Johnson, R. Grover, and P.-T. Ho, "Optical signal processing using nonlinear semiconductor microring resonators," IEEE J. Sel. Top. Quantum Electron. 8, 705-713 (2002).
[CrossRef]

Haus, H.

B. Little, S. Chu, H. Haus, J. Foresi, and J.-P. Laine, "Microring resonator channel dropping filters," J. Lightwave Technol. 15, 998-1005 (1997).
[CrossRef]

Heebner, J. E.

Ho, P.-T.

V. Van, T. Ibrahim, P. Absil, F. Johnson, R. Grover, and P.-T. Ho, "Optical signal processing using nonlinear semiconductor microring resonators," IEEE J. Sel. Top. Quantum Electron. 8, 705-713 (2002).
[CrossRef]

Horowitz, M.

A. Rosenthal and M. Horowitz, "Inverse scattering algorithm for reconstructing strongly reflecting fiber bragg gratings," IEEE J. Quantum Electron. 39, 1018-1026 (2003).
[CrossRef]

Huang, Y.

Ibrahim, T.

V. Van, T. Ibrahim, P. Absil, F. Johnson, R. Grover, and P.-T. Ho, "Optical signal processing using nonlinear semiconductor microring resonators," IEEE J. Sel. Top. Quantum Electron. 8, 705-713 (2002).
[CrossRef]

Johnson, F.

V. Van, T. Ibrahim, P. Absil, F. Johnson, R. Grover, and P.-T. Ho, "Optical signal processing using nonlinear semiconductor microring resonators," IEEE J. Sel. Top. Quantum Electron. 8, 705-713 (2002).
[CrossRef]

Kokubun, Y.

B. Little, S. Chu, W. Pan, and Y. Kokubun, "Microring resonator arrays for VLSI photonics," IEEE Photon. Technol. Lett. 12, 323-325 (2000).
[CrossRef]

Laine, J.-P.

B. Little, S. Chu, H. Haus, J. Foresi, and J.-P. Laine, "Microring resonator channel dropping filters," J. Lightwave Technol. 15, 998-1005 (1997).
[CrossRef]

Landobasa, Y.

Y. Landobasa, S. Darmawan, and M.-K. Chin, "Matrix analysis of 2-D microresonator lattice optical filters," IEEE J. Quantum Electron. 41, 1410-1418 (2005).
[CrossRef]

Lee, R. K.

Lenz, G.

C. Madsen, G. Lenz, A. Bruce, M. Cappuzzo, L. Gomez, and R. Scotti, "Integrated all-pass filters for tunable dispersion and dispersion slope compensation," IEEE Photon. Technol. Lett. 11, 1623-1625 (1999).
[CrossRef]

Libchaber, A.

Little, B.

B. Little, S. Chu, W. Pan, and Y. Kokubun, "Microring resonator arrays for VLSI photonics," IEEE Photon. Technol. Lett. 12, 323-325 (2000).
[CrossRef]

B. Little, S. Chu, H. Haus, J. Foresi, and J.-P. Laine, "Microring resonator channel dropping filters," J. Lightwave Technol. 15, 998-1005 (1997).
[CrossRef]

MacFarlane, D. L.

Madsen, C.

C. Madsen, G. Lenz, A. Bruce, M. Cappuzzo, L. Gomez, and R. Scotti, "Integrated all-pass filters for tunable dispersion and dispersion slope compensation," IEEE Photon. Technol. Lett. 11, 1623-1625 (1999).
[CrossRef]

C. Madsen and J. Zhao, "A general planar waveguide autoregressive optical filter," J. Lightwave Technol. 14, 437-447 (1996).
[CrossRef]

Marti, J.

E. Peral, J. Capmany, and J. Marti, "Iterative solution to the Gel’fand-Levitan-Marchenko coupled equations and application to synthesis of fiber gratings," IEEE J. Quantum Electron. 32, 2078-2084 (1996).
[CrossRef]

Martinelli, M.

Melloni, A.

Mookherjea, S.

Muñoz, P.

Muriel, M.

J. Capmany, M. Muriel, and S. Sales, "Highly accurate synthesis of fiber and waveguide bragg gratings by an impedance reconstruction layer-aggregation method," IEEE J. Quantum Electron. 43, 889-898 (2007).
[CrossRef]

R. Feced, M. Zervas, and M. Muriel, "An efficient inverse scattering algorithm for the design of nonuniform fiber Bragg gratings," IEEE J. Quantum Electron. 35, 1105-1115 (1999).
[CrossRef]

J. Capmany and M. Muriel, "A new transfer matrix formalism for the analysis of fiber ring resonators: compound coupled structures for FDMA demultiplexing," J. Lightwave Technol. 8, 1904-1919 (1990).
[CrossRef]

Muriel, M. A.

Orta, R.

R. Orta, P. Savi, R. Tascone, and D. Trinchero, "Synthesis of multiple-ring-resonator filters for optical systems," IEEE Photon. Technol. Lett. 7, 1447-1449 (1995).
[CrossRef]

Paloczi, G.

Pan, W.

B. Little, S. Chu, W. Pan, and Y. Kokubun, "Microring resonator arrays for VLSI photonics," IEEE Photon. Technol. Lett. 12, 323-325 (2000).
[CrossRef]

Peral, E.

E. Peral, J. Capmany, and J. Marti, "Iterative solution to the Gel’fand-Levitan-Marchenko coupled equations and application to synthesis of fiber gratings," IEEE J. Quantum Electron. 32, 2078-2084 (1996).
[CrossRef]

Pereira, S.

Poladian, L.

Poon, J.

Ren, H.-C.

Rosenthal, A.

A. Rosenthal and M. Horowitz, "Inverse scattering algorithm for reconstructing strongly reflecting fiber bragg gratings," IEEE J. Quantum Electron. 39, 1018-1026 (2003).
[CrossRef]

Sales, S.

J. Capmany, M. Muriel, and S. Sales, "Highly accurate synthesis of fiber and waveguide bragg gratings by an impedance reconstruction layer-aggregation method," IEEE J. Quantum Electron. 43, 889-898 (2007).
[CrossRef]

Savi, P.

R. Orta, P. Savi, R. Tascone, and D. Trinchero, "Synthesis of multiple-ring-resonator filters for optical systems," IEEE Photon. Technol. Lett. 7, 1447-1449 (1995).
[CrossRef]

Scherer, A.

Scheuer, J.

Scotti, R.

C. Madsen, G. Lenz, A. Bruce, M. Cappuzzo, L. Gomez, and R. Scotti, "Integrated all-pass filters for tunable dispersion and dispersion slope compensation," IEEE Photon. Technol. Lett. 11, 1623-1625 (1999).
[CrossRef]

Sekaric, L.

F. Xia, L. Sekaric, and Y. Vlasov, "Ultra compact optical buffers on a silicon chip," Nat. Photonics 1, 65-71 (2007).
[CrossRef]

Sipe, J. E.

Skaar, J.

J. Skaar, L. Wang, and T. Erdogan, "Synthesis of thick optical thin-film filters with a layer-peeling inverse scattering algorithm," Appl. Opt. 40, 2183-2189 (2001).
[CrossRef]

J. Skaar, L. Wang, and T. Erdogan, "On the synthesis of fiber Bragg gratings by layer peeling," IEEE J. Quantum Electron. 37, 165-173 (2001).
[CrossRef]

Steier, W.

H. Tazawa and W. Steier, "Analysis of ring resonator-based traveling-wave modulators," IEEE Photon. Technol. Lett. 18, 211-213 (2006).
[CrossRef]

Tascone, R.

R. Orta, P. Savi, R. Tascone, and D. Trinchero, "Synthesis of multiple-ring-resonator filters for optical systems," IEEE Photon. Technol. Lett. 7, 1447-1449 (1995).
[CrossRef]

Tazawa, H.

H. Tazawa and W. Steier, "Analysis of ring resonator-based traveling-wave modulators," IEEE Photon. Technol. Lett. 18, 211-213 (2006).
[CrossRef]

Trinchero, D.

R. Orta, P. Savi, R. Tascone, and D. Trinchero, "Synthesis of multiple-ring-resonator filters for optical systems," IEEE Photon. Technol. Lett. 7, 1447-1449 (1995).
[CrossRef]

Vahala, K.

K. Vahala, "Optical microcavities," Nature (London) 424, 839-846 (2003).
[CrossRef]

Van, V.

V. Van, T. Ibrahim, P. Absil, F. Johnson, R. Grover, and P.-T. Ho, "Optical signal processing using nonlinear semiconductor microring resonators," IEEE J. Sel. Top. Quantum Electron. 8, 705-713 (2002).
[CrossRef]

Vlasov, Y.

F. Xia, L. Sekaric, and Y. Vlasov, "Ultra compact optical buffers on a silicon chip," Nat. Photonics 1, 65-71 (2007).
[CrossRef]

Vollmer, F.

Wang, L.

J. Skaar, L. Wang, and T. Erdogan, "On the synthesis of fiber Bragg gratings by layer peeling," IEEE J. Quantum Electron. 37, 165-173 (2001).
[CrossRef]

J. Skaar, L. Wang, and T. Erdogan, "Synthesis of thick optical thin-film filters with a layer-peeling inverse scattering algorithm," Appl. Opt. 40, 2183-2189 (2001).
[CrossRef]

Xia, F.

F. Xia, L. Sekaric, and Y. Vlasov, "Ultra compact optical buffers on a silicon chip," Nat. Photonics 1, 65-71 (2007).
[CrossRef]

Xu, Y.

Yariv, A.

Zervas, M.

R. Feced, M. Zervas, and M. Muriel, "An efficient inverse scattering algorithm for the design of nonuniform fiber Bragg gratings," IEEE J. Quantum Electron. 35, 1105-1115 (1999).
[CrossRef]

Zhao, J.

C. Madsen and J. Zhao, "A general planar waveguide autoregressive optical filter," J. Lightwave Technol. 14, 437-447 (1996).
[CrossRef]

Appl. Opt. (1)

Electron. Lett. (1)

A. Yariv, "Universal relations for coupling of optical power between microresonators and dielectric waveguides," Electron. Lett. 36, 321-322 (2000).
[CrossRef]

IEEE J. Quantum Electron. (6)

Y. Landobasa, S. Darmawan, and M.-K. Chin, "Matrix analysis of 2-D microresonator lattice optical filters," IEEE J. Quantum Electron. 41, 1410-1418 (2005).
[CrossRef]

A. Rosenthal and M. Horowitz, "Inverse scattering algorithm for reconstructing strongly reflecting fiber bragg gratings," IEEE J. Quantum Electron. 39, 1018-1026 (2003).
[CrossRef]

J. Capmany, M. Muriel, and S. Sales, "Highly accurate synthesis of fiber and waveguide bragg gratings by an impedance reconstruction layer-aggregation method," IEEE J. Quantum Electron. 43, 889-898 (2007).
[CrossRef]

E. Peral, J. Capmany, and J. Marti, "Iterative solution to the Gel’fand-Levitan-Marchenko coupled equations and application to synthesis of fiber gratings," IEEE J. Quantum Electron. 32, 2078-2084 (1996).
[CrossRef]

R. Feced, M. Zervas, and M. Muriel, "An efficient inverse scattering algorithm for the design of nonuniform fiber Bragg gratings," IEEE J. Quantum Electron. 35, 1105-1115 (1999).
[CrossRef]

J. Skaar, L. Wang, and T. Erdogan, "On the synthesis of fiber Bragg gratings by layer peeling," IEEE J. Quantum Electron. 37, 165-173 (2001).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

V. Van, T. Ibrahim, P. Absil, F. Johnson, R. Grover, and P.-T. Ho, "Optical signal processing using nonlinear semiconductor microring resonators," IEEE J. Sel. Top. Quantum Electron. 8, 705-713 (2002).
[CrossRef]

IEEE Photon. Technol. Lett. (4)

H. Tazawa and W. Steier, "Analysis of ring resonator-based traveling-wave modulators," IEEE Photon. Technol. Lett. 18, 211-213 (2006).
[CrossRef]

C. Madsen, G. Lenz, A. Bruce, M. Cappuzzo, L. Gomez, and R. Scotti, "Integrated all-pass filters for tunable dispersion and dispersion slope compensation," IEEE Photon. Technol. Lett. 11, 1623-1625 (1999).
[CrossRef]

B. Little, S. Chu, W. Pan, and Y. Kokubun, "Microring resonator arrays for VLSI photonics," IEEE Photon. Technol. Lett. 12, 323-325 (2000).
[CrossRef]

R. Orta, P. Savi, R. Tascone, and D. Trinchero, "Synthesis of multiple-ring-resonator filters for optical systems," IEEE Photon. Technol. Lett. 7, 1447-1449 (1995).
[CrossRef]

J. Lightwave Technol. (4)

A. Melloni and M. Martinelli, "Synthesis of direct-coupled-resonators bandpass filters for WDM systems," J. Lightwave Technol. 20, 296-303 (2002).
[CrossRef]

J. Capmany and M. Muriel, "A new transfer matrix formalism for the analysis of fiber ring resonators: compound coupled structures for FDMA demultiplexing," J. Lightwave Technol. 8, 1904-1919 (1990).
[CrossRef]

B. Little, S. Chu, H. Haus, J. Foresi, and J.-P. Laine, "Microring resonator channel dropping filters," J. Lightwave Technol. 15, 998-1005 (1997).
[CrossRef]

C. Madsen and J. Zhao, "A general planar waveguide autoregressive optical filter," J. Lightwave Technol. 14, 437-447 (1996).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

Nat. Photonics (1)

F. Xia, L. Sekaric, and Y. Vlasov, "Ultra compact optical buffers on a silicon chip," Nat. Photonics 1, 65-71 (2007).
[CrossRef]

Nature (London) (1)

K. Vahala, "Optical microcavities," Nature (London) 424, 839-846 (2003).
[CrossRef]

Opt. Express (3)

Opt. Lett. (2)

Other (1)

A. V. Oppenheim, R. W. Schafer, and J. R. Buck, Discrete-time signal processing, Signal Processing Series, 2nd ed. (Prentice-Hall International, 1999).

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Figures (4)

Fig. 1.
Fig. 1.

CROW (a) naming convention, and layer aggregation for h[n] (b) n = 0, (c) n = 1 and (d) n ≥ 2

Fig. 2.
Fig. 2.

CROW (a) target TMM calculated response for m = 9 and m = 14 and (b) synthesized and target responses (inset transmission response).

Fig. 3.
Fig. 3.

Reconstructed Ki values for (a) N = 5 and (b) N = 10 rings for a uniform CROW with K = 0.1, and KN for uniform CROWs with K =0.1, 0.2 and 0.3, all vs. IDFT number of points M used.

Fig. 4.
Fig. 4.

Hamming (H=0.2) apodized CROW with nominal K = 0.1 (a) target TMM calculated response for m = 9 and m = 14, (b) synthesized and target responses (inset transmission response) and reconstructed Ki values for (c) N = 5 and (d) N = 10 rings, all vs. IDFT number of points M used.

Equations (5)

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[ b i b i + 1 ] = [ t i κ i κ i * t i * ] [ a i a i + 1 ]
h [ 0 ] = t 0 h [ 1 ] = - t 1 [ κ 0 ] 2
h [ n ] = h r [ n ] + h nr [ n ]
h nr [ n ] = ( 1 ) n t n i = 0 n 1 κ i 2
t i = 1 K 1 + H cos ( 2 π i 0.5 ( N 1 ) N ) 1 + H i = 0 , , N

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